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https://fr.slideserve.com/emmy/the-sears-and-zemansky-s-university-physics | math | 1.94k likes | 2.99k Vues
西尔斯物理学. The Sears and Zemansky' s University Physics. Units, Physical Quantities and Vectors. 1-1 Introduction For two reasons: 1. Physics is one of the most fundamental of the sciences. 2. Physics is also the foundation of all engineering and technology.
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西尔斯物理学 The Sears and Zemansky' s University Physics
Units, Physical Quantities and Vectors • 1-1 Introduction • For two reasons: • 1. Physics is one of the most fundamental of the sciences. • 2. Physics is also the foundation of all engineering and technology. • The But there' s another reason. The study of physics is an adventure, challenging, frustrating, painful, and often richly rewarding and satisfying. • The In this opening chapter, we' the ll go over some important preliminaries that we'
ll need throughout our study. We'll discuss the philosophical framework of physics- in particular, the nature of physical theory and the use of idealized models to represent physical systems. We'll introduce the systems of units used to describe physical quantities and discuss ways to describe the accuracy of a number. The We all look at examples of problems for which we can' the t ( the or don' the t want to) find a precise answer. Finally, we' ll study several aspects of vectors algebra. • 1-2 The Nature of PhysicsPhysics is an experimental science. Physicists observe the phenomena of nature and try to find patterns and principles that relate these phenomena.
These patterns are called physical theories or, when they are very well established and of broad use, physical laws or principles. The development of Physical theory requires creativity at every stage. The physicist has to learn to ask appropriate questions.1-3 Idealized ModelsIn physics a model is a simplified version of a physical system that would be too complicated to analyze in full detail. To make an idealized model of the system, we have to overlook quite a few minor effects to concentrate on the most important features of the system. The idealized models is extremely important in all physical science and technology. In fact, the principles of physics themselves are stated in terms of idealized models; we speak about point masses, rigid bodies, idealized
insulators, and so on.1-4 Standards and UnitsPhysics is an experimental science. Experiments require measurements, and we usually use numbers to describe the results of measurements.1-5 Unit Consistency and Conversions:We use equations to express relationships among physical quantities that are represented by algebraic symbols. Each algebraic symbol always denote both a number and a unit. An equation must always be dimensionally consistent. 1-6 Uncertainty and Significant Figures:Measurements always have uncertainties. If you
measure the thickness of the cover of this book using an ordinary ruler, your measurement is reliable only to the nearest millimeter, and yourresult will be 3mm. It would be wrong to state this result as 3.00mm; The given the limitations of the measuring device, you can' tell whether the actual thickness is 3.00 mms,2.85 mms,3.11 mms of or. But if you use a micrometer caliper, a device that measures distances reliably to the nearest 0.01mm, the result will be 2.91mm. The distinction between these two measurements is in their uncertainty. The measurement using the micrometer caliper has a smaller uncertainty; It' s a more accurate measurement. The uncertainty is also called the error, because it indicates the maximum difference
there is likely to be between the measured value and the true value. The uncertainty or error of a measured value depends on the measurement technique used. 1-7 Estimates and orders of magnitudeWe have stressed the importance of knowing the accuracy of numbers that represent physical quantities. But even a very crude estimate of a quantity often gives us useful information. Sometimes we know how to calculate a certain quantity but have to guess at the data we need for the calculation. Or the calculation might be too complicated to carry out exactly, so we make some rough approximations. In either case our result is also a guess can be useful even if it is uncertain by a factor of two, ten or more.
Such calculations are often called order-of-magnitude estimates. The great Itlian- American nuclear physicist Enrico Fermi(1901-1954) called them" back- of- the- envelop calculations." 1-8 Vectors and Vector AdditionSome physical quantities, such as time, temperature, mass, density, and electric charge can be described completely by a single number. Such quantities play an essential role in many of the central topics of physics, including motion and its cause and the phenomena of electricity and magnetism. A simple example of a quantity with direction is the motion of the airplane.
To describe this motion completely, we must say not only how fast the plane is moving, but also in what direction. Another example is force, which in physics means a push or pull exerted on a body. Giving a complete description of a force means describing both how hard the force pushes or pulls on the body and the direction of the push or pull. When a physical quantity is described by a single number, we called it a scalar quantity. In contrast, a vector quantity has both a magnitude( the " how much" or "how big" part) and a direction in space. Calculations with scalar quantities use the operations of ordinary arithmetic.
To understand more about vectors and how they combine, we start with the simplest vector quantity, displacement. Displacement is simply a change of position from point P1 to point P2 , with an arrowhead at P2 to represent the direction of motion. Displacement is a vector quantity because we must state not only how far the particle moves, but also in what direction. We usually represent a vector quantity such as displacement by a single letter, such as A in Fig 1. P2 P2 P3 A A A B P1 Fig 3 P1 Fig 2 Fig 1
When drawing any vector, we always draw a line with an arrowhead at its tip. The length of the line shows the vector' s magnitude, and the direction of the line shows the vector' s direction. Displacement is always a straight-line segment, directed from the starting point to the end point, even though the actual path of the particle may be curved. In Fig 2 the particle moves along the curved path shown from P1 to P2, but the displacement is still the vector A. Note that displacement is not related directly to the total distance traveled. If the particle were to continue on to P3 and then return to P1, the displacement for the entire trip would be zero. If two vectors have the same direction, they are parallel. If they have the same magnitude and the same direction, they are equal. The vector B in Fig 3,
however, isnot equal to A because its direction is opposite to that of A. We define the negative of a vector as a vector having the same magnitude as the original vector but the opposite direction. The negative of vector quantity A is denoted as – A, and we use a boldface minus sign to emphasize the vector nature of thequantities. Between A and B of Fig. 3 may be written as A = -B or B = -A. When two vectors A and B have opposite directions, whether their magnitudes are the same or not, we say that they are anti-parallel. We usually represent the magnitude of a vector quantity(its length in the case of a displacement vector) by the same letter used for the vector, but in light italic type with no arrow on the top,rather than bold-faceitalic with an arrow
(which is reserved for vectors). An alternative notation is the vector symbol with vertical bars on both sides.Vector Addition Now suppose a particle undergoes a displacement A, followed by a second displacement B. The final result is the same as if the particle had started at the same initial point and undergone a single displacement C, as shown. We call displacement C the vector sum, or resultant, of displacements A and B. We express this relationship symbolically as
Y B A A Ay C C A B X Ax O Fig 4 Fig 5 Fig 6 If we make the displacements A and B in reverse order, with B first and A second, the result is the same (Fig.4). The final result is the same as if the particle had started at the same initial point and undergone a single displacement C, as shown. We call displacement C the vector sum, or resultant, of displacement A andB. We express this relationship symbolical asC = A + B. If we make the displacements A and B in reverse order,
with B first and A second, the result is the same. Thus C = B + A and A + B = B + A 1-9 Components of Vectors To define what we mean by the components of a vector, we begin with a rectangular (Cartesian) coordinate system of axes. The We then draw the vector we' the re considering with its tail at O, the origin of the coordinate system. We can represent any vector lying in the xy-plane as the sum of a vector parallel to the x-axis and a vector parallel to the y-axis. These two vectors are labeled Ax and AY in the figure;they are called the component vectors of vector A, and their vector sum is equal to A.In symbols, A = Ax + Ay. (1) By definition, each component vector lies along a coordinate-axis direction.
Thus we need only a single number to describe each one. When the component vector Ax points in the positive x-direction, we define the number Ax to be equal to the magnitude of Ax. When the component vector Ax points in the negative x-direction, we define the number Ax to be equal to the negative of that magnitude, keeping in mind that the magnitude of two numbers Ax and Ay are called the components of A. The components Ax and Ay of a vector A are just numbers; they are not vectors themselves. Using components We can describe a vector completely by giving either its magnitudeand direction or its x- and y- components. Equations (1) show how to find the components if we know the magnitude and direction.We can also reverse the process; we can find the magnitude and
direction if we know the components. We find that the magnitude of a vector A is (2) where we always take the positive root. Equation (2) is valid for any choice of x-axis and y-axis, as long as they are mutually perpendicular. The expression for the vector direction comes from the definition of the tangent of an angle. If is measured from the positive x-axis, and a positive angle is measured toward the positive y-axis (as in Fig. 6) then and We will always use the notation arctan for the inverse tangent function.
1-10 Unit Vectors A unit vector is a vector that has a magnitude of 1. Its only purpose is to point, that is, to describe a direction in space. Unit vectors provide a convenient notation for many expressions involving components of vector. In an x-y coordinate system we can define a unit vector i that points in the direction of the positive x-axis and a unit vector j that points in the direction of the positive y-axis. Then we can express the relationship between component vectors and components, described at the beginning of section 1-9, as follows Ax = Ax i , Ay = Ay j ; A = Ax i+ Ay j . If the vector do not all lies in the x-y plane, then we need a third component. We duce a third unit vector k that points in the direction of the positive z-axis. The generalized forms of equation is A = Ax i + Ay j + Az k
1-11 Products of vectors We have seen how addition of vectors develops naturally from the problem of combining displacements, and we will use vector addition for many other vector quantities later. We can also express many physical relationships concisely by using products of vectors. Vectors are not ordinary numbers, so ordinary multiplication is not directly applicable to vectors. We will define two different kinds of products of vectors. Scalar product: The scalar product of two vectors A and B is denoted by A · B. Because of this notation, the scalar product is also called the dot product. We define A ? B to be the magnitude of A multiplied by the component of B parallel to A. Expressed as an equation:
The scalar product is a scalar quantity, not a vector, and it may be positive, negative, or zero. When Φ is between 0° and 90 °, the scalar product is positive. When is between 90° and 180° , it is negative.Vector product : The vector product of two vectors A and B, also called the cross product, is denoted by AB. To define the vector product AB of two vectors A and B, we again draw the two vectors with their tail at the same point( Fig.1-20a). The two vectors then lie in a plane. We define the vector product to be a vector quantity with a direction perpendicular to this plane (that is, perpendicular to both A and B) and a magnitude equal to AB sin. That is, if C = AB, then C = AB sin. We measure the angle
from A toward B and take it to be the smaller of the two possible angles, so ranges from 0 °to 180. There are always two directions perpendicular to a given plane, one on each side of the plane. We choose which of these is the direction of AB as follows. Imagine rotating vector A about the perpendicular line until it is aligned with B, choosing the smaller of the two possible angles between A and B. Curl the fingers of your right hand around the perpendicular line so that the fingertips point in the direction of rotation; your thumb will then point in the direction of AB. This right-hand rule is shown in Fig. 1-20a. The direction of the vector product is also the direction in which a right-hand screw advances if turned from A toward B.
2 Motion Along a Straight Line 2-1 Introduction In this chapter we will study the simplest kind of motion: a single particle moving along a straight line. We will often use a particle as a model for a moving along body when effects such as rotation or change of shape are not important. To describe the motion of a particle, we will introduce the physical quantities velocity and acceleration. 2-2 Displacement, Time, And Average Velocity Lets generalize the concept of average velocity. At time t1 the dragster is at point P1 with coordinate x1, and at time t2 it is at point P2, with coordinate x2.The displacement of the dragsterduring the time
interval from t1 to t2 is the vector from P1 to P2, the with x- component( the x2 – x1) and with y- and z- components equal to zero. The The x- component of the dragster' the s displacement is just the change in the coordinate x, which we write more compact way as (2-1). Be sure you understand that x is not the product of and x; The it is a single symbol that means" the change in the quantity x. ” We likewise write the time interval from t1 to t2as .Note that x or t always means the final value minus the
initial value, never the reverse. We can now define the x-component of average velocity more precisely: it is the x- component of displacement, x , divided by the time interval t during which the displacement occurs. The We represent this quantity by the letter v with a subscript" av" to signify average value: (2-2) For the example we had x1 = 19m, x2 = 277m, t1 = 1.0s and t2 = 4.0s so Eq.(2-2) gives The average velocity of the dragster is positive. This means that during the time interval, the coordinate x increased and the dragster moved in the positive x- direction. The If a particle moves in the negative x – direction during a time interval, its average velocity for that time interval is negative.2-3 Instantaneous VelocityThe average velocity of a particle during a time interval cannot tell us how fast, or in what direction, the particle was moving at any given time during the interval. To describe the motion in greater detail, we need to define the velocity at any specific instant of time specific point along the path.
Such a velocity is called instantaneous velocity, and it needs to be defined carefully. To find the instantaneous velocity of the dragster in Fig. 2-1 at the point P1, we imagine moving the second point P2 closer and closer to the first point P1. We compute the average velocity vav = x / t over these shorter and shorter displacements and time intervals. Both x and t become very small, but their ratio does not necessarily become small. In the language of calculus the limit of x /t as t approaches zero is called the derivative of x with respect to t and is written dx/dt. The instantaneous velocity is the limit of the average velocity as the time interval approaches zero; it equals the instantaneous rate of change of position with time. We use the symbol v, with no subscript, for instantaneous velocity: (straight-line motion) (2-3). We always assume that the time interval ?t is positive so that v has the same algebraic sign as ?x. If the positive x-axis points to the right, as in Fig. 2-1, a positive value of mean that x is increasing and motion is toward the right; a negative value of v means that x is decreasing and the motion is toward the left. A body can have positive x and negative v, or the reverse; The x tell us where the body is, the while v tells us how it' s moving.
Instantaneous velocity, like average velocity, is a vector quantity. Equation (2-3) define its x-component, which can be positive or negative. In straight-line motion, all other components of instantaneous velocity are zero, and in this case we will often call v simply the instantaneous velocity. The The terms" velocity" and" speed" are used the interchangeably in everyday language, but they have distinct definitions in physics. We use the term speed to denote distance traveled divided by time, on ether an average or an instantaneous basis. Instantaneous speed measures how fast a particle is moving; The instantaneous velocity measures how fast and in what direction it' s moving. For example, a particle with instantaneous velocity v = 25m/s and a second particle with v = - 25m/s are moving in opposite direction the same instantaneous speed of 25m/s. Instantaneous speed is the magnitude of instantaneous velocity, and so instantaneous speed can never be negative. Average speed, however, is not the magnitude of average velocity.Example: The A cheetah is crouched in ambush 20 m to the east of an observer' s blind. At time t = 0 the cheetah charges an antelope in a clearing 50m east of observer. The cheetah runs along a straight line. Later analysis of a videotape shows that during the first 2.0s of the attack,
The the cheetah' the s coordinate x varies with time according to the equation x=20 ms+(5.0 ms/ s2) t2. (Note that the units for the numbers 20 and 5.0 must be as shown to make the expression dimensionally consistent.) Find(a) the displacement of the cheetah during the interval between t1 = 1.0s and t2 = 2.0s.(b) Find the average velocity during the same time interval. (c) Find the instantaneous velocity at time t1 = 1.0s by taking ?t = 0.1s, then t = 0.01s, then t = 0.001s. (d) derive a general expression for the instantaneous velocity as a function of time, and from it find v at t = 1.0s and t = 2.0sSolution: (a) The At time t1= the 1.0 s the cheetah' the s position x1 is x1=20 ms+(5.0 ms/ s2)(1.0 ses)2=25 ms. At time t2 = 2.0s its position x2 is x2 = 20m + (5.0m/s2)(2.0s)2 = 40m.The displacement during this the interval is the x= x2 – x1= 40 m – 25 m=15 m.(b) The average velocity during this time interval is At time t2, the position is x2 = 20m+(5.0m/s2)(1.1s)2 = 26.05m
The average velocity during this interval is We invite you to follow this same pattern to work out the average velocities for the 0.01s and 0.001s intervals. The results are 10.05m/s and 10.005m/s. As t gets closer to 10.0m/s, so we conclude that the instantaneous velocity at time t = 1.0s is 10.0m/s.(d) We find the instantaneous velocity as a function of time by taking the derivative of the expression for x with respect to t. For any n the derivative of t is ntn-1, so the derivative of t2 is 2t. Therefore At time t = 1.0s, v = 10m/s as we found in part ( c ). At time t = 2.0s, v = 20m/s.2-4 Average and Instantaneous AccelerationWhen the velocity of a moving body changes with time, we say that the body has an acceleration. Just as velocity describes the rate of change of position with time, acceleration describes the rate of change of velocity with time. Like velocity, acceleration is a vector quantity. In straight-line
Motion its only nonzero component is along the axis along which the motion takes place.Average AccelerationLet' s consider again the motion of a particle along the x- axis. Suppose that at time t1 the particle is at point P1 and has x-component of (instantaneous) velocity v1, and at a later time t2 it is at point P2 and x-component of velocity v2. So the x-component of velocity changes by an amount v= v2 – v1 during the time interval t= t2 – t1.We define the average acceleration aav of the particle as it moves from P1 to P2 to be a vector quantity whose x-component is v, the change in the x-component of velocity, divided by the time interval t: (average acceleration, straight-line motion) (2-4) For straight-line motion we well usually call aav simply the average acceleration, remembering that in fact it is the x-component of the average acceleration vector. If we express velocity in meters per second and time in seconds, then average acceleration is in meters per second per second. The This is usually written as m/ s2 and is read" meters per second squared."
Instantaneous AccelerationWe can now define instantaneous acceleration, following the same procedure that we used to define instantaneous velocity. Consider this situation: A race car driver has just entered the final straightaway at the Grand Prix. He reaches point P1 at time t1, moving with velocity v1. He passes point P2, closer to the line, at time t2 with velocity v2.(Fig. 2-8) To define the instantaneous acceleration at point P1, we take the second point P2 in Fig. 2-8 to be closer and closer to the first point P1 so that the average acceleration is computed over shorter and shorter time intervals. The instantaneous acceleration is the limit of the average acceleration as the time interval approaches zero. In the language of calculus, instantaneous acceleration equals the instan-taneous rate of change of velocity with time. Thus (instantaneous acceleration, straight-line motion) (2-5)Note that Eq. (2-5) is really the definition of the x-component of the acceleration vector; in straight-line motion, all other components of this vector are zero. Instantaneous acceleration plays an essential role in the laws of mechanics. The From now on, the when we use the term" acceleration", the we will always mean instantaneous acceleration, not average acceleration.
Example: Average and instantaneous accelerations Suppose the velocity v of the car in Fig. 2-8 at any time t is given by the equation v = 60 m/s + (0.50 m/s3) t2.(a) Find the change in velocity of the car in the time interval between t1 = 1.0s and t2 = 3.0s. (b) Find the instantaneous acceleration in this time interval. (c) Find the instantaneous acceleration at time t1 = 1.0s by taking t to be first 0.1s, then 0.01s, then 0.001s. (d) Derive an expression for the instantaneous acceleration at any time, and use it to find the acceleration at t = 1.0s and t = 3.0s.Solution: (a) We first find the velocity at each time by substituting each value of t into the equation. At time t1 = 1.0s, v1 = 60m/s +(0.50m/s3)(1.0s)2 = 60.5m/s.At time t2 = 3.0s, v2 = 60m/s + (0.5m/s3)(3.0s)2 = 64.5m/s.The change in velocity v= v2 – v1=64.560.5=4.0 ms/ ses of –s.The time interval is t= 3.0 s – 1.0 s=2.0 s.(b) The average acceleration during this time interval isDuring the time interval from t1 = 1.0s to t2 = 3.0s, the velocity and average acceleration have the same algebraic sign (in this case, positive), and the car speeds up.
(c) When ?t = 0.1s, t2 = 1.1s andv2 = 60m/s + (0.50m/s3)(1.1s)2 = 60.605 m/s,v = 0.105m/s,We invite you repeat this pattern for t = 0.01s and t = 0.001s; the results are aav = 1.0005m/s2 respectively. As t gets smaller, the average acceleration gets closer to 1.0m/s2. We conclude that the instantaneous acceleration at t1 = 1.0s is 1.0m/s2.(d) The instantaneous acceleration is a = dv/dt, the derivative of a constant is zero, and the derivative of t2 is 2t . Using these, we obtainWhen t = 3.0s, a = (1.0m/s3)(3.0s) = 1.0m/s2
2-5 Motion with Constant AccelerationThe simplest acceleration motion is straight-line motion with constant acceleration. In this case the velocity changes at the same rate throughout the motion. This is a very special situation, yet one that occurs often in nature. As we will discuss in the next section, a falling body has a constant acceleration if the effects of the air are not important. The same is true for a body sliding on an incline or along a rough horizontal surface. Straight-line motion with nearly constant acceleration also occurs in technology, such as a jet-fighter being catapulted from the deck of an aircraft carrier. The In this section we' ll derive key equations for straight- line motion with constant acceleration.Fig. 2-12 Fig. 2-13 Fig. 2-14 a t=0 v O a t=t v O a t=2t v O a t=3t v O a t=4t v O a v a at v v0 v0 t t O t O t
Figure 2-12 is a motion diagram showing the position, velocity, and acceleration at five different times for a particle moving with constant acceleration. Figure 2-13 and 2-14 depict this same motion in the from of graphs. Since the acceleration a is constant, the a-t graph (graph of acceleration versus time) in Fig. 2-13 is a horizontal line. The graph of velocity versus time has a constant slope because the acceleration is constant, and so the v-t graph is a straight line ( Fig. 2-14).The When the acceleration is constant, it' s easy to derive equations for position x and velocity v as functions of time. Let' s start with velocity. In Eq. (2-4) we can replace the average acceleration aav by the constant (instantaneous) acceleration a. We then have (2-7) Now we let t1 = 0 and let t2 be any arbitrary later time t. We use the symbol v0 for the velocity at the initial time t is v. Then Eq. (2-7) because (2-8)
Next we want to derive an equation for the position x of a particle moving with constant acceleration. To do this, we make use of two different expressions for the average velocity vav during the interval from t = o to any later time t. The first expression comes from the definition of vav Eq. (2-2), which holds true whether or not the acceleration is constant. We call the position at time t = 0 the initial position, denoted by x0. The position at the later time t is simply x. Thus for the time interval t = t – 0 and the corresponding displacement X= x – x0, Eq. (2-2) gives (2-9) We can also get a second expression for vav that is valid only when the acceleration is constant, so that the v-t graph is a straight line (as in Fig. 2-14) and the velocity changes at a constant rate. (2-10)(constant acceleration only). Substituting that expression for v into Eq. (2-10), we find (2-11) (constant acceleration only) Finally, we equate Eqs. (2-9) and (2-11) and simplify the result:
or (2-12)We can check whether Eqs.(2-8) and (2-12) are consistent with the assumption of constant acceleration by taking the derivative of Eq. (2-12). We find which is Eq. (2-8). Differentiating again, we find simply as we should expect. The In many problems, it' the s useful to have a relationship between position, velocity, and acceleration that does not involve the time. To obtain this, we first solve Eq. (2-8) for t, then substitute the resulting expression into Eq. (2-12) and simplify: We transfer the term x0 to the left side and multiply through by 2a:
Finally, simplifying gives us. We can get one more useful relationship by equating the two expressions for vav, Eqs. (2-9) and (2-10), and multiplying through by t. Doing this, we obtain (2-14)A special case of motion with constant acceleration occurs when the acceleration is zero. The velocity is then constant, and the equations of motion become simply v = v0 = constant, x = x0 + vt.2-7 Velocity and Position by Integration This optional section is intended for students who have already learned a little integral calculus. In Section 2-5 we analyzed the special case of straight-line motion with constant acceleration. When a is not constant, as is frequently the case, the equations that we derived in that section are no longer valid. But even when a varies with time, we can still use the relation v = dx/dt to find the velocity v as a function of time if the position x is a known function of time. And we can still use a = dv/dt to find the acceleration a as a function of time if the velocity v is a known function of time.In many physical situations, however, position and velocity are not known as functions of time, while the acceleration is.
Figure 2-13We first consider a graphical approach, Figure 2-23 is a graph of acceleration versus time for a body whose acceleration is not constant but increases with time. We can divide the time interval between times t1 and t2 into many smaller intervals, calling a typical one t. Let the average acceleration during t be aav. From Eq. (2-4) the change in velocity v during t is v = aav t. Graphically, v equals the area of the shaded strip with height aav and width t, that is, the area under the curve between the left and right sides of t. The total velocity change during any interval (say, t1 to t2) is the sum of the velocity changes v in the small subintervals. So the total velocity changes is represented graphically by the total area under the a-t curve between the vertical lines t1 and t2. In the limit that all the T' the s become very small and their number very large, the the value of aav for the interval from any time t to t+ t approaches the instantaneous acceleration a at time t. In this limit, the area under the a-t curve is the integral of a (which is in general a function of t) from t1 to t2. If v1 is the velocity of the body at time t1 and v2 is the velocity at time t2, then aav t1 O t2 t
The change in velocity v is the integral of acceleration a with respect to time. We can carry exactly the same procedure with the curve of velocity versus time where v is in general a function of t. If x1 is a body' s position at time t1 and x2 is its position at time t2, from Eq. (2-2) the displacement x during a small time interval ?t is equal to vav t, where vav is given by (2-16) . The change in position x – that is, the displacement – is the time integral of velocity v. Graphically, the displacement between times t1 and t2 is the area under the v-t curve between those two times. If t1 = 0 and t2 is any later time t, and if x0 and v0 are the position and velocity, respectively, at time t = 0, then we can rewrite Eqs. (2-15) and (2-16) as follows: (2-17) (2-18). Here x and v are the position and velocity at time t. If we know the acceleration a as a function of time and we know the initial velocity v0, we can use Eq, (2-17) to find the velocity v at any time; in other words, we can find v as a function of time. Once we know this function, and given the initial position x0, we can use Eq. (2-18) to find the position x at any time.Example 2-9 Sally is driving along a straight highway in her classic 1965 Mustang. At time t = 0, when Sally is moving at 10 m/s in the position x-direction, she passes a signpost at x = 50m. Her acceleration is a function of time: A= the 2.0 ms/ s2 – (0.10 ms/ s3) t
(a) Derive expressions for her velocity and position as functions of time.(b) At what time is her velocity greatest? (c) What is the maximum velocity? (d) Where is the car when it reaches maximum velocity.Solution: (a) The At time t=0, Sally' the s position is x0=50 ms, the and her velocity is v0=10 ms/ s. Since we are given the acceleration a as a function of time, we first use Eq. (2-17) to find the velocity v as a function of time t.Then we use Eq.(2-18) to find x as a function of t:At this instant, dv/dt = a = 0. Setting the expression for acceleration equal to zero, we obtain: ?$
(c) We find the maximum velocity by substituting t = 20s (when velocity is maximum) into the general velocity equation:(d) The maximum value of v occurs at t = 20s, we obtain the position of the car (that is, the value of x) at that time by substituting t = 20s into the general expression for x:As before, we are concerned with describing motion, not with analyzing its causes. But the language you learn here will be an essential tool in later chapters when you use Newton' s laws of motion to study the relation between force and motion.
3-2 Position and velocity vectorsTo describe the motion of a particle in space, we first need to be able to describe the position of the particle. Consider a particle that is at a point P at a certain instant. The position vector r of the particle at this instant is a vector that goes from the origin of the coordinate system to the point P(Fig. 3-1). The figure also shows that the Cartesian coordinates x, y, and z of point P are the x-, y-, and z-components of vector r. Using the unit vectors introduced in Section 1-10, we can write Y r O X Z Figure 3-1
We can also get this result by taking the derivative of Eq(3-1). The unit vectors i, j and k are constant in magnitude and direction, so their derivatives are zero, and we find . This shows again that the components of v are dx/dt, dy/dt, and dz/dt. The magnitude of the instantaneous velocity vector v- that is, the speed – is given in terms of the components vx, vy, and vz by the Pythagorean relation: The instantaneous velocity vector is usually more interesting and useful than the average velocity vector. From now on, when we use the word" velocity", we will always mean the instantaneous velocity vector v( the rather than the average velocity vector). Usually, we won' even bother to call v a vector.3-3 The Acceleration VectorIn Fig (3-1), a particle is moving along a curvedThe vectors v1 and v2 represent the particle' s instantaneous velocities at time t1, when the particle is at point P1, and time t2, v v1 v2
When the particle is at point P2. The two velocities may differ in both magnitude and direction. We define the average acceleration aav of the particle as the particle as it moves from P1 and P2 as the vector change in velocity, v2-v1= v, divided by the time interval t2-t1 = t: Average acceleration is a vector quantity in the same direction as the vector v. As in Chapter 2, we define the instantaneous acceleration a at point P1as the limit approached by the average acceleration when point P2 approaches point P1 and v and t both approach zero; the instantaneous acceleration is also equal to the instantaneous rate of change of velocity with time. Because we are not restricted to straight-line motion, instantaneous acceleration is now a vector: v1 v2 v P2 v1 P1 v1 P1 a v2 aav C B A
The velocity vector v, as we have seen, is tangent to the path of the particle. But the construction in fig.C shows that the instantaneous acceleration vector a of a moving particle always points toward the concave side of a curved path-that is, toward the inside of any turn that the particle is making. We can also see that when a particle is moving in a curved path, it always has nonzero acceleration. We will usually be interested in the instantaneous acceleration, not the average acceleration. From now on, we will use the term “acceleration” to mean the instantaneous acceleration vector a.Each component of the acceleration vector is the derivative of the corresponding component of velocity:Also, because each component of velocity is the derivative of the corresponding coordinate, we can express the ax, ay and az of the acceleration vector a as
Example: Calculating average and instantaneous acceleration; Let’s look again at the radio-controlled model car in Example 3-1. We found that the components of instantaneous velocity at any time t areand that the velocity vector is a) Find the components of the average acceleration in the interval from t=0.0s to t=2.0s. b) Find the instantaneous acceleration at t=2.0s.Solution a) From Eq. (3-8), in order to calculate the components of the average acceleration, we need the instantaneous velocity at the beginning and the end of the time interval. We find the components of instantaneous velocity at time t=0.0s
by substituting this value into the above expressions for vx, and vy. We find that at time t = 0.0s, vx = 0.0m/s, vy = 1.0m/s . We found in Example 3-1 that at t = 2.0s the values of these components are vx = -1.0m/s, vy = 1.3m/s.Thus the components of average acceleration in this interval are b) From Eq. 3-10 the components acceleration vector a asAt time t = 2.0s, the components of instantaneous acceleration areax = -0.5m/s2 , ay = (0.15m/s3)(2.0s) = 0.30m/s2 . The acceleration vector at this time is
3-5 Motion in A CircleWhen a particle moves along a curved path, the direction of its velocity changes.As we saw in Section 3-3, this means that the particle must have a component of acceleration perpendicular to the path, even if its speed is constant. In this section we’ll calculate the acceleration for the important special case of motion in a circle.Uniform Circular MotionWhen a particle moves in a circle with constant speed, the motion is called uniform circular motion. There is no component of acceleration parallel (tangent) to the path; otherwise, the speed would change. The component of acceleration perpendicular (normal) to the path, which cause the direction of the velocity to change, is related in a simple way to the speed of the particle and the radius of the circle.In uniform circular motion the acceleration is perpendicular to the velocity at each instant; as the direction of the velocity changes, the direction of the acceleration also changes. v2 P1 P2 v1 v s P1 P2 R v1 v2 O A O B
Figure A shows a particle moving with constant speed in a circular path radius R with center at O. The particle moves from P1 to P2 in a time t. The vector change in velocity v during this time is shown in Fig. B. The angles labeled in Fig. A and B are the same because v1 is perpendicular to the line OP1 and v2 is perpendicular to the line OP2. Hence the triangles OP1P2(Fig. A) and OP1P2(Fig. B) are similar. Ratios of corresponding sides are equal, so or The magnitude aav of the average acceleration during t is thereforeThe magnitude of the instantaneous acceleration a at point P1. Also, P1 can is the limit of this expression as we take point P2 closer and closer to point P1:
But the limit of s/ t is the speed v1 at point P1. Also, P1 can be any point on the path, so we can drop the subscript and let v represent the speed at any point. ThenBecause the speed is constant, the acceleration is always perpendicular to the instantaneous velocity.We conclude: In uniform circular motion, the magnitude a of the instantaneous acceleration is equal to the square v divided by the radius R of the circle. Its direction is perpendicular to v and inward along the radius. Because the acceleration is always directed toward the center of the circle, it is sometimes called centripetal acceleration.Non-Uniform Circular MotionWe have assumed calculate throughout this section that the particle’s speed is constant. If the speed varies, we call the motion non-uniform circular motion. In non-uniform circular motion, still gives the radial component of acceleration | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817106.73/warc/CC-MAIN-20240416191221-20240416221221-00747.warc.gz | CC-MAIN-2024-18 | 39,397 | 53 |
http://computationalnonlinear.asmedigitalcollection.asme.org/article.aspx?articleid=2521888 | math | This study aims to investigate the harmonic resonance of third-order forced van der Pol oscillator with fractional-order derivative using the asymptotic method. The approximately analytical solution for the system is first determined, and the amplitude–frequency equation of the oscillator is established. The stability condition of the harmonic solution is then obtained by means of Lyapunov theory. A comparison between the traditional integer-order of forced van der Pol oscillator and the considered fractional-order one follows the numerical simulation. Finally, the numerical results are analyzed to show the influences of the parameters in the fractional-order derivative on the steady-state amplitude, the amplitude–frequency curves, and the system stability. | s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917125074.20/warc/CC-MAIN-20170423031205-00463-ip-10-145-167-34.ec2.internal.warc.gz | CC-MAIN-2017-17 | 771 | 1 |
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The structure of this humble diagram was formally developed by the mathematician John Venn, but its roots go back as far as the 13th Century, and includes many stages of evolution dictated by a number of noted logicians and philosophers. The earliest indications of similar diagram theory came from the writer Ramon Llull, whos initial work would later inspire the German polymath Leibnez. Leibnez was exploring early ideas regarding computational sciences and diagrammatic reasoning, using a style of diagram that would eventually be formalized by another famous mathematician. This was Leonhard Euler, the creator of the Euler diagram.
Logician John Venn developed the Venn diagram in complement to Eulers concept. His diagram rules were more rigid than Eulers - each set must show its connection with all other sets within the union, even if no objects fall into this category. This is why Venn diagrams often only contain 2 or 3 sets, any more and the diagram can lose its symmetry and become overly complex. Venn made allowances for this by trading circles for ellipses and arcs, ensuring all connections are accounted for whilst maintaining the aesthetic of the diagram.
Usage for Venn diagrams has evolved somewhat since their inception. Both Euler and Venn diagrams were used to logically and visually frame a philosophical concept, taking phrases such as some of x is y, all of y is z and condensing that information into a diagram that can be summarized at a glance. They are used in, and indeed were formed as an extension of, set theory - a branch of mathematical logic that can describe objects relations through algebraic equation. Now the Venn diagram is so ubiquitous and well ingrained a concept that you can see its use far outside mathematical confines. The form is so recognizable that it can shown through mediums such as advertising or news broadcast and the meaning will immediately be understood. They are used extensively in teaching environments - their generic functionality can apply to any subject and focus on my facet of it. Whether creating a business presentation, collating marketing data, or just visualizing a strategic concept, the Venn diagram is a quick, functional, and effective way of exploring logical relationships within a context.
A Venn diagram, sometimes referred to as a set diagram, is a diagramming style used to show all the possible logical relations between a finite amount of sets. In mathematical terms, a set is a collection of distinct objects gathered together into a group, which can then itself be termed as a single object. Venn diagrams represent these objects on a page as circles or ellipses, and their placement in relation to each other describes the relationships between them. Commonly a Venn diagram will compare two sets with each other. In such a case, two circles will be used to represent the two sets, and they are placed on the page in such a way as that there is an overlap between them. This overlap, known as the intersection, represents the connection between sets - if for example the sets are mammals and sea life, then the intersection will be marine mammals, e.g. dolphins or whales. Each set is taken to contain every instance possible of its class; everything outside the union of sets (union is the term for the combined scope of all sets and intersections) is implicitly not any of those things - not a mammal, does not live underwater, etc.
Euler diagrams are similar to Venn diagrams, in that both compare distinct sets using logical connections. Where they differ is that a Venn diagram is bound to show every possible intersection between sets, whether objects fall into that class or not; a Euler diagram only shows actually possible intersections within the given context. Sets can exist entirely within another, termed as a subset, or as a separate circle on the page without any connections - this is known as a disjoint. Furthering the example outlined previously, if a new set was introduced - birds - this would be shown as a circle entirely within the confines of the mammals set (but not overlapping sea life). A fourth set of trees would be a disjoint - a circle without any connections or intersections.
Other Collections of Ecg Diagram Labeled | s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540555616.2/warc/CC-MAIN-20191213122716-20191213150716-00366.warc.gz | CC-MAIN-2019-51 | 6,940 | 32 |
http://www.advrider.com/forums/showpost.php?p=12559869&postcount=217 | math | Originally Posted by guzzimike
What rate springs do you think you'll need Bill?
Dunno really, haven't gotten that far yet. At 6.25 pounds per gallon plus say 10 pounds for the tank, that makes an extra 40-ish pounds. Given that I'm also short for my weight, I would need, um, lessee......carry the two.....
Uh, what rates you got? | s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1430458333760.71/warc/CC-MAIN-20150501053213-00044-ip-10-235-10-82.ec2.internal.warc.gz | CC-MAIN-2015-18 | 330 | 4 |
https://www.geometry-algebra.polimi.it/activities/seminars/diki/ | math | Abstract The Fueter mapping theorem is a fundamental result in quaternionic analysis relating slice hyperholomorphic functions and Fueter regular ones. The action of the Fueter map on quaternionic monomials leads to an interesting class of functions forming an Appell system with respect to the hypercomplex derivative. In this talk I will present two extensions of the Fueter map in the case of polyanalytic functions of a quaternionic variable. The first map is built upon a suitable global operator with non-constant coefficients allowing to construct Fueter regular functions starting from poly-slice hyperholomorphic ones. The second map allows to construct polyanalytic Fueter regular functions. Based on this second construction we introduce and study the main properties of a new family of Generalized-Appell polynomials which are poly-Fueter regular. I will discuss also how the polyanalytic Fueter maps act on a poly slice hyperholomorphic Bargmann transform. This gives arise to two integral transforms in the Fueter regular and polyanalytic Fueter regular setting. | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296819089.82/warc/CC-MAIN-20240424080812-20240424110812-00445.warc.gz | CC-MAIN-2024-18 | 1,076 | 1 |
https://www.physicsforums.com/threads/curent-densitys-relation-to-drift-velocity.577381/ | math | 1. The problem statement, all variables and given/known data A beam contains 4.0x10^8 doubly charged positive ions per cubic centimeter, all of which are moving north with a speed of 1.2x10^5 m/s. (a) What is the magnitude of the current density ? (b) What is its direction? (c) What additional quantity or quantities are needed to calculate the total current in this ion beam? 2. Relevant equations J=I/A=nqv (v = drift velocity) 3. The attempt at a solution Well I tried this (4.0e8)(2)(1.6e-19)(1.2e5) which I thought would give what I wanted but apparently not. I was thinking by looking a dimensional analysis that it has something to do with the seconds in the velocity but im not sure? | s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676594675.66/warc/CC-MAIN-20180722233159-20180723013159-00348.warc.gz | CC-MAIN-2018-30 | 692 | 1 |
https://projecteuclid.org/euclid.jmsj/1257520508 | math | Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 61, Number 4 (2009), 1293-1301.
Generalizing the Ohio completeness property, we introduce the notion of -Ohio completeness. Although many results from a previous paper by the authors may easily be adapted for this new property, there are also some interesting differences. We provide several examples to illustrate this. We also have a consistency result; depending on the value of the cardinal , the countable union of open and -Ohio complete subspaces may or may not be -Ohio complete.
J. Math. Soc. Japan, Volume 61, Number 4 (2009), 1293-1301.
First available in Project Euclid: 6 November 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
BASILE, Désirée; VAN MILL, Jan; RIDDERBOS, Guit-Jan. $\kappa$ -Ohio completeness. J. Math. Soc. Japan 61 (2009), no. 4, 1293--1301. doi:10.2969/jmsj/06141293. https://projecteuclid.org/euclid.jmsj/1257520508 | s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232255837.21/warc/CC-MAIN-20190520081942-20190520103942-00532.warc.gz | CC-MAIN-2019-22 | 1,012 | 11 |
https://research.tees.ac.uk/en/publications/error-rates-decisive-outcomes-and-publication-bias-with-several-i-3 | math | Background Statistical methods for inferring the true magnitude of an effect from a sample should have acceptable error rates when the true effect is trivial (type I rates) or substantial (type II rates). Objective The objective of this study was to quantify the error rates, rates of decisive (publishable) outcomes and publication bias of five inferential methods commonly used in sports medicine and science. The methods were conventional null-hypothesis significance testing [NHST] (significant and non-significant imply substantial and trivial true effects, respectively); conservative NHST (the observed magnitude is interpreted as the true magnitude only for significant effects); non-clinical magnitude-based inference [MBI] (the true magnitude is interpreted as the magnitude range of the 90 % confidence interval only for intervals not spanning substantial values of the opposite sign); clinical MBI (a possibly beneficial effect is recommended for implementation only if it is most unlikely to be harmful); and odds-ratio clinical MBI (implementation is also recommended when the odds of benefit outweigh the odds of harm, with an odds ratio >66). Methods Simulation was used to quantify standardized mean effects in 500,000 randomized, controlled trials each for true standardized magnitudes ranging from null through marginally moderate with three sample sizes: suboptimal (10 + 10), optimal for MBI (50 + 50) and optimal for NHST (144 + 144). Results Type I rates for non-clinical MBI were always lower than for NHST. When type I rates for clinical MBI were higher, most errors were debatable, given the probabilistic qualification of those inferences (unlikely or possibly beneficial). NHST often had unacceptable rates for either type II errors or decisive outcomes, and it had substantial publication bias with the smallest sample size, whereas MBI had no such problems. Conclusion MBI is a trustworthy, nuanced alternative to NHST, which it outperforms in terms of the sample size, error rates, decision rates and publication bias. | s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710890.97/warc/CC-MAIN-20221202014312-20221202044312-00191.warc.gz | CC-MAIN-2022-49 | 2,049 | 1 |
https://www.enotes.com/homework-help/circumferencer-circle-12pi-what-area-253873 | math | If the circumference of a circle is 12pi, what is the area?
Given the area of a circle is 12pi.
Then we will calculate the radius using the circumference formula.
==> C = 2* pi *r = 12 pi
==> r = 12pi/2pi = 6
Now we will calculate the area of the circle.
==> We know that A= r^2 * pi
==> A = 6^2 * pi = 36 pi = 113.1 ( approx)
Then the area of the circle whose circumference 12pi = 36pi = 113.1 square units.
The circumference of a triangle is given by 2*pi*r where r is the radius and the area is pi*r^2.
Here circumference = 12*pi = 2*pi*r
=> r = 6
The area = pi*r^2 = 36*pi
The area of the circle is 36*pi | s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948596051.82/warc/CC-MAIN-20171217132751-20171217154751-00593.warc.gz | CC-MAIN-2017-51 | 608 | 14 |
https://www.coursehero.com/sitemap/schools/604-Georgia-Southern-University/courses/2722022-BUSA3132H/ | math | Fundamentals of Cost
Analysis for Decision Making
Use differential analysis to analyze decisions.
Understand how to apply differential analysis
to pricing decisions.
Understand several approaches for esta
At the end of its fiscal year (12-31-09), after all accounts determined to be
uncollectible have been written off and before any adjusting entries are recorded,
the following information is available:
Indicate whether each item expresses an advantage or a disadvantage of a
corporation or if the item is not a characteristic of a corporation. Write on your
answer sheet A for advantage, D for disadvantage, or N if the i
Determine whether each of the following is a debit or credit using this code:
DR=debit; CR=credit. Mark the correct answer on your answer sheet.
1. The balance side of Sales Discounts
2. The decrease side of Prep
For items 1 through 12, decide whether the item belongs on the Post-Closing Trial
Balance. If the item belongs on this type of trial balance, indicate whether the
normal balance will be listed in the debit column or
Questions 1 through 8 are transactions that took place in April for a business
called Joes Landscaping Service. Use the following code to describe each
A. increases an asset and decreases an asset
Indicate the classification of items 1 through 8 by writing the correct identifying
letter on your answer sheet and indicate the decrease side of the account by
writing DR for debit or CR for credit. Both parts of e
Larget Solutions to Assignment #4
February 19, 2009
1. Solution: The data s = (r, p, w) of size n = r + p + w is assumed to be multinomial with a single parameter = (0, 1) that species all of the category probabilities, 2 ,2(1 )
Section 2. (Suggested Time: 2 Hours, 15 minutes) Answer any 3 of the following 4
7. Optimal Growth with depreciation spillovers.
Consider the following Economy:
Time: Discrete, innite horizon
Demography: A continuum, mass normalized to 1, of (r
Coffee Bean Inc
Direct Labor information
activity data for each pro
lower cl upper CL
lower CI upper CI
4 stdev is a sigma so we use z statistic
se z statistic
Time series forecasting and index nnumber
Times series forecasting is a type of forecasting using time series data. We assume that whats observed in the history
will repeat in the future so that we can rely on the recorded data to predict future values.
A farmer is preparing to plant a crop in the spring and needs to fertilize a field.
There are two brands of fertilizer to choose from, Super-gro and Crop-quick.
Each brand yields a specific amount of nitrogen and phosphate per bag, as follows:
Mexican Revolution (1910-1920)
Hawaiian Islands concept of empire of freedom
Teddy Roosevelt is important in the Mexican Revolution
Launch of American military forces in Vera Cruz
Boxer Rebellion: Summer of 1900
Attack on embassies in Beijing
Test 2 Bonus
For the paper test, I got 51.5 points. I missed questions 9,15,16, and 23.
Q9: Answer Choice B is correct because section 13.1 of the e-text states that In examining the
Search process: 4 techniques are
1) stepwise regression
2) forward regression
3) backward regression
4)all possible regression
(1)Step wise regression: We walk through multiple steps/stages in order to find out the best combination of the
ind. Variable to
Suppl Prob 9.53
Simple Random Sampling: Each element in the population has the same probability of being selected.
Systematic Sampling: Probability method in which we select every 10th person to be sure sample is
random start the selection w
Statesboro Area Real Estate Sales (2004-2010)
Source: Bulloch County Tax Assessors Office, Oct 2010
Collected by Steve Moss, moddified by Jake Simons
808 JULIEANN WAY
810 Shelter Pointe | s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463607591.53/warc/CC-MAIN-20170523064440-20170523084440-00228.warc.gz | CC-MAIN-2017-22 | 3,709 | 71 |
https://www.hackmath.net/en/examples/time?page_num=13 | math | Time - examples - page 13
How long track travel the second hand in 46 hours, the end of which is 4 cm long.
- Machines 2
2 machines for 50 hours produces 2,000 products. How many machines need to buy to make in 30 hours 15,000 products?
Jane eats whole lunch for the 30 minutes. Which part of the lunch is eaten in 180 seconds?
- Traffic collision
When investigating a traffic accident, it was found that the driver stopped the vehicle immediately after the accident by constant braking on a 150 m track in 15 seconds. Do you approve that the driver exceeded the permitted speed (50 km/h) in the village.
- Oil tank and pipes
The underground oil tank can be filled by two oil pipelines. The first is filled in 72 hours and the second in 48 hours. How many hours from the moment when first pipeline began to fill the oil is it necessary to start filling it with the second to fill in
- Car value
The car loses value 15% every year. Determine a time (in years) when the price will be halved.
- Miraculous tree
Miraculous tree grows so fast that the first day increases its height by half the total height of the second day by the third, the third day by a quarter, etc. How many times will increase its height after 6 days?
First pump flows 16 liters per second into the basin by the second pump 75% of the first and by third pump half more than the second. How long will take fill basin by all three pumps simultaneously volume 15 m3 (cubic meters)?
- Water reservoir
The water reservoir is filled through one inlet 4 hours later than both together, then another inlet 9 hours later than both together. For how long is filled by each separately?
- Pool 3
How long will fill pool cuboid shape (8m 6m 1.5m) when flows 15 liters/s?
From Znojmo to Brno started truck with a trailer at an average speed 53 km per hour. Against him 14 minutes later from Brno started car with an average speed of 1.2-times greater than the truck. How long and how far from Znojmo, they meet if the distanc
Flywheel turns 450 rev/min (RPM). Determine the magnitude of the normal acceleration of the flywheel point which are at a distance of 10 cm from the rotation axis.
- Great Wall of China
Great Wall of China is long 8880 km. Historically valuable however is only 30% of its length. What amount of insurance pays the Peoples Republic of China a month for this monument, if the insurance company charges $ 10 per year per kilometer of historic s
George pass on the way to school distance 200 meters in 165 seconds. What is the average walking speed in m/s and km/h?
The working group, in which 6 workers would ordered job completed within 21 working days. How many workers must be accept yet that the contract will be completed in 14 working days?
- Direct route
From two different places A and B connected by a direct route, Adam (from city A) and Bohus (from city B) started at a constant speed. As Adam continued to go from A to B, Bohus turned around at the time of their meeting and at the same speed he returned t
Buses Ikarus and Karosa simultaneously started at 8:00 from the final station. Ikarus is returned to the station after 30 minutes. Karosa after 45 minutes. At what time both buses again returned to the station?
The first harvester reaps the grain from land for 24 hours, the second harvester for 16 hours. For how many hours will take harvest by two harvesters, but the second harvester started working four hours later than the first?
On coins found was stated that from the year 87 BC. It is right?
- Two pumps
The first pump fills the tank in 24 hours second pump in another 40 hours. For how long will take fill the tank if operate both pumps at the same time? | s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257648198.55/warc/CC-MAIN-20180323063710-20180323083710-00263.warc.gz | CC-MAIN-2018-13 | 3,662 | 31 |
https://vsbattles.fandom.com/wiki/Thread:2992502 | math | I'm getting Mach 1392 which is Massively Hypersonic+.
GBE of the Sun is 2.27e+41 joules. Mass of Sun is 1.989e+30 kg. A mass with that much kinetic energy would be moving at 477760.82 m/s, which is Mach 1392. I used this calculator, plugged in the Sun's mass, and the value of its GBE and got that velocity: | s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370496901.28/warc/CC-MAIN-20200330085157-20200330115157-00441.warc.gz | CC-MAIN-2020-16 | 307 | 2 |
http://vihomeworkjkey.locallawyer.us/writing-quadratic-equations-in-vertex-form.html | math | Writing equation in vertex form showing top 8 worksheets in the category - writing equation in vertex form some of the worksheets displayed are vertex form of parabolas, work quadratic functions, equations of parabolas, unit 2 2 writing and graphing quadratics work, work standard form line of symmetry and vertex for, forms of quadratic functions standard form factored form, work, standard . Writing quadratic equations from vertex form to standard form practice worksheet. Algebra 2 - quadratic functions and inequalities worksheets vertex form of parabolas worksheets this algebra 2 worksheet will produce problems for writing equations of parabolas. Improve your math knowledge with free questions in convert equations of parabolas from general to vertex form and thousands of other math skills of parabolas .
I can write quadratic equations in vertex form by completing the square applications 4r i can apply quadratics functions to real life situations without using the graphing calculator. Free quadratic equation calculator - solve quadratic equations using factoring, complete the square and the quadratic formula step-by-step logarithmic form (new . In vertex form, a quadratic function is written this is a vertical line through the vertex of the curve h and k for this curve and write down the equation . Convert to vertex form and graph enter quadratic equation in standard form:-- x 2 + x + this solver has been accessed 1683305 times .
Those three different shapes are like the three forms for quadratic equations: the vertex form, the x-intercepts form and the standard form you need information to write the quadratic equation. Write equation in vertex form showing top 8 worksheets in the category - write equation in vertex form some of the worksheets displayed are vertex form of parabolas, work quadratic functions, equations of parabolas, graphing parabolas given the vertex form of the equation, forms of quadratic functions standard form factored form, title graphing quadratic equations in standard form class . Just as a quadratic equation can map a parabola, the parabola's points can help write a corresponding quadratic equation parabolas have two equation forms – standard and vertex in the vertex form, y = a ( x - h ) 2 + k , the variables h and k are the coordinates of the parabola's vertex. This video shows how to use the method of completing the square to change a quadratic equation from standard form to vertex form skip navigation writing quadratic functions in vertex form by . Print writing standard-form equations for parabolas: definition & explanation worksheet 1 what bit of information does the vertex form give you that the standard form doesn't give you.
Hi, my high school classes have just begun and i am stunned at the amount of write quadratic equation in vertex form calculator homework we get. Since the equation is in vertex form, the vertex will be at the point (h, k) step 2 : find the y-intercept to find the y-intercept let x = 0 and solve for y. Matching graphs to quadratic equations activity (free version) quadratic equations~standard to vertex form~matching vertex/factored form worksheets:writing a . The vertex form of a quadratic function is given by f ( x ) = a ( x - h ) 2 + k , where ( h, k ) is the vertex of the parabola fyi: different textbooks have different interpretations of the reference standard form of a quadratic function. Algebra quadratic equations and functions vertex form of a quadratic equation key questions how do you write the quadratic in vertex form given vertex is (-2,6 .
Home algebra ii quadratic formula and functions quadratic functions vertex form parabolas quadratic-like equations quadratic inequalities the vertex and y . How do you write the vertex form equation of the parabola #y = (x - 3)^2 + 36# algebra quadratic equations and functions vertex form of a quadratic equation 2 answers. Improve your math knowledge with free questions in write equations of parabolas in vertex form from graphs and thousands of other math skills.
Solve linear and quadratic equations 2 and when we write our quadratic function in this vetex form, then h, k is the and our equation now is in vertex form . Writing y= -4x^2+8x-1 in vertex form hanging me up, when i work it out i get -4(x+4)^2+63 which doesn't match when i check it frustrating help is greatly appreciated, thanks in advance to all who reply. Quadratic functions(general form) quadratic functions are some of the most important algebraic functions and they need to be thoroughly understood in any modern high school algebra course the properties of their graphs such as vertex and x and y intercepts are explored interactively using an html5 applet. Converting an equation to vertex form can be tedious and require an extensive degree of algebraic background knowledge, including weighty topics such as factoring. | s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039746205.96/warc/CC-MAIN-20181122101520-20181122123520-00539.warc.gz | CC-MAIN-2018-47 | 4,871 | 6 |
https://thefractioncalculator.com/simplify-mixed-numbers.html | math | Simplify Mixed Numbers
A mixed number is a combination of a whole number and a fraction. This unique tool will simplify your mixed number to its lowest form.
Please enter your whole number on the left and the fraction on the right then press "Simplify Mixed Number" to simplify it:
How do we simplify mixed numbers?
We simplify mixed numbers in three steps:
Step 1) Convert mixed number to an improper fraction.
Step 2) Simplify the improper fraction.
Step 3) Convert the simplified improper fraction back to a mixed number. | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679103810.88/warc/CC-MAIN-20231211080606-20231211110606-00582.warc.gz | CC-MAIN-2023-50 | 524 | 8 |
https://www.omnicalculator.com/math/similar-triangles | math | Similar Triangles Calculator
This similar triangles calculator is here to help you find a similar triangle by scaling a known triangle. You can also use this calculator to find the missing length of a similar triangle!
Stick around and scroll through this article as we discuss the laws of similar triangles and learn some fundamentals:
- What are similar triangles?
- Finding similar triangles: How do you determine whether two triangles are similar?
- How do you find the missing side of a similar triangle?
- How do you find the area of a similar triangle?
What are similar triangles?
Two triangles are similar if their corresponding sides are in the same ratio, which means that one triangle is a scaled version of the other. Naturally, the corresponding angles of similar triangles are equal. For example, consider the following two triangles:
Notice that the corresponding sides are in proportion:
Therefore, we can say . Here the symbol indicates that the triangles are similar.
We term the proportion of similarity as the scale factor . In the example above, the scale factor . If you need help finding ratios, use our ratio calculator.
Finding similar triangles: Law of similar triangles
We know that two triangles are similar if either of the following is true:
- The corresponding sides of the triangle are in proportion; or
- The corresponding angles are equal.
From this, we can derive specific rules to determine whether any two triangles are similar:
- Side-Side-Side (SSS): If all three corresponding sides of the two triangles are in proportion, they are similar. This rule is the most straightforward and requires you to know all the sides of the triangles.
We can express this using a similar triangle formula:
where is the scale factor.
- Side-Angle-Side (SAS): If any two corresponding sides of two triangles are in proportion and their included angles are equal, then the triangles are similar. We can use this rule whenever we know only two sides of each triangle and their included angles.
The triangles in the image above are similar if:
This rule is handy in cases like in the image below, where the triangles share an angle:
You can do many things knowing just the Side-Angle-Side of a triangle. Learn more using our SAS triangle calculator.
- Angle-Side-Angle (ASA): If any two corresponding angles of two triangles are equal and the corresponding sides between them are in proportion, the triangles are similar.
The triangles in the image above are similar if:
You can find the third angle if you know any two angles in a triangle using our triangle angle calculator. We know that if any two corresponding angles in the triangles are equal, the triangles are similar, meaning that in the ASA congruence rule, we don't need to know the side so long as the angles are known. However, without the sides, we cannot determine the scale factor .
💡 Need to find the area of a triangle? We have our triangle area calculator that can help you with that.
How do you find the missing side of a similar triangle?
To find the missing side of a triangle using the corresponding side of a similar triangle, follow these steps:
- Find the scale factor
kof the similar triangles by taking the ratio of any known side on the larger triangle and its corresponding side on the smaller one.
- Determine whether the triangle with the missing side is smaller or larger.
- If the triangle is smaller, divide its corresponding side in the larger triangle by
kto get the missing side. Otherwise, multiply the corresponding side in the smaller triangle by
kto find the missing side.
For example, consider the following two similar triangles.
To find the missing side, we first start by calculating their scale factor.
Next, we use the scale factor relation between the missing side AC and its corresponding side DF:
🙋 You can also compare two right triangles and see their similarities using our Check Similarity in Right Triangles Calculator.
How do you find the area of a similar triangle?
To find the area of a triangle A1 from the area of its similar triangle A2, follow these steps:
- Find the scale factor k of the similar triangles by taking the ratio of any known side on the larger triangle and its corresponding side on the smaller one.
- Determine whether the triangle with the unknown area is smaller or larger.
- If the triangle is smaller, divide A2 by the square of the scale factor k to get A1 = A2/k2. Otherwise, multiply A2 by k2 to get A1 = A2 × k2.
How to use this similar triangles calculator
Now that you've learned how to find the length of a similar triangle, the similar triangles formula, and more, you can quickly figure out how this similar triangles calculator works.
To check whether two known triangles are similar, use this calculator as follows:
- Select check similarity in the field
- Choose the similarity criterion you want to use. You can choose between Side-Side-Side, Side-Angle-Side, and Angle-Side-Angle.
- Enter the dimensions of the two triangles. The calculator will evaluate whether they are similar or not.
To use this calculator to solve for the side or perimeter of similar triangles, follow these steps:
- Select find the missing side in the field
- Enter the known dimensions, area, perimeter, and scale factor of the triangles. The similar triangles calculator will find the unknown values.
Are all equilateral triangles similar?
Yes, if the corresponding angles of two triangles are equal, the triangles are similar. Since every angle in an equilateral triangle is equal to
60°, all equilateral triangles are similar.
Find the scale factor of similar triangles whose areas are 10 cm² and 20 cm²?
1.414. To determine this scale factor based on the two areas, follow these steps:
- Divide the larger area by the smaller area to get
20/10 = 2.
- Find the square root of this value to get the scale factor,
k = √2 = 1.414.
- Verify this result using Omni's similar triangles calculator. | s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510501.83/warc/CC-MAIN-20230929090526-20230929120526-00768.warc.gz | CC-MAIN-2023-40 | 5,949 | 64 |
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https://jacobbradjohnson.com/helper-tangent-542 | math | Take a picture of your math problem
Take a picture of your math problem is a mathematical tool that helps to solve math equations. We can solve math problems for you.
The Best Take a picture of your math problem
Here, we will show you how to work with Take a picture of your math problem. Solving domain and range can be tricky, but there are a few helpful tips that can make the process easier. First, it is important to remember that the domain is the set of all values for which a function produces a result, while the range is the set of all values that the function can produce. In other words, the domain is the inputs and the range is the outputs. To solve for either the domain or range, begin by identifying all of the possible values that could be inputted or outputted. Then, use this information to determine which values are not possible given the constraints of the function. For example, if a function can only produce positive values, then any negative values in the input would be excluded from the domain. Solving domain and range can be challenging, but with a little practice it will become easier and more intuitive.
Solving quadratic equations by factoring is a process that can be used to find the roots of a quadratic equation. In order to solve a quadratic equation by factoring, the first step is to rewrite the equation in standard form. The next step is to factor the equation. Once the equation is factored, the roots of the equation can be found by setting each factor equal to zero and solving for x. Solving quadratic equations by factoring is a useful tool that can be used to find the roots of any quadratic equation.
Partial fractions is a method for decomposing a fraction into a sum of simpler fractions. The process involves breaking up the original fraction into smaller pieces, each of which can be more easily simplified. While partial fractions can be used to decompose any fraction, it is particularly useful for dealing with rational expressions that contain variables. In order to solve a partial fraction, one must first determine the factors of the denominator. Once the factors have been determined, the numerator can be factored as well. The next step is to identify the terms in the numerator and denominator that share common factors. These terms can then be combined, and the resulting expression can be simplified. Finally, the remaining terms in the numerator and denominator can be solve for using basic algebraic principles. By following these steps, one can solve any partial fraction problem.
Factor calculators are a great tool for anyone who wants to quickly figure out the factors of a number. Although there are various ways to calculate factors, a factor calculator can be especially helpful if you're working with large numbers or if you need to find all of the factors of a number. Generally, you simply enter the number that you want to factor into the calculator and then hit the "calculate" button. The calculator will then display all of the factors of that number. In addition, some factor calculators will also show you any prime factors that may be present. Factor calculators can be found online or in some math textbooks. | s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500151.93/warc/CC-MAIN-20230204173912-20230204203912-00275.warc.gz | CC-MAIN-2023-06 | 3,195 | 7 |
http://ebtx.com/math/rotemem.htm | math | This is particularly true in mathematics.
My first introduction to this fact came in the fifth grade. The teacher (a woman - name not recalled) demanded that we not put loose leaf papers into our math books and gave warning that if she did find them there she would exact a penalty of one complete rendition of the times tables ... from 1-12 ... for each improperly placed paper.
One day, some weeks later, the day of reckoning came. She ordered all books placed on top of the desk and proceeded to examine each for the forbidden filler. 1 here, 3 there, 0 for you "Good kid", 5 again, 2, 7 ... on down the rows handing out the dreaded tasks to each miscreant. 5, 4, 0, 7, 2, ... hmmm ... 57 for you sir.
In the subsequent week of my pencil pushing punishment, I came to know the tables in a way which gave me an edge for the remainder of my school life. I came to appreciate this "favor". At the time it was simply miserable.
What value is there in simply writing something over and over?
The value lies in concentration. While writing the same thing fails, of itself, to integrate data, it does cause one's mind to focus on the particular matter for one cannot write with a pen or pencil and daydream at the same time. Each entry in the task is slightly different than the former and a mistake requires a rewrite ... and ... the work was actually checked for authenticity (spot checked). Though I tried to automate the process, I was unable to write and watch TV at the same time.
What I was able to do is notice from time to time, regularities and interesting relationships between numbers, primes, divisors, shortcuts, etc. In other words, the material began to integrate because of the demand to focus on the subject.
Another effect of rote memorization is the freeing up of mental CPU cycles to do other tasks. If I know some equations, say the trigonometric functions, from rote memory, I needn't spend time thinking about that aspect of a given mathematical problem. If the context is known from memory, one can focus on the relevant particulars at hand.
A student should probably spend half of his learning time just grinding out paper after paper full of data.
A Good Teacher will say:
"OK, you little bastards ... Start copying this page of facts. Copy it one hundred times ... or ... until your grubby little hands fall off. And I'm gonna' check to make sure you do it."The kids will resent this and moan and groan. But a few years down the line, they will appreciate it mightily. I guarantee it.
Does anyone really think that this won't work? How could you possibly fail at something as simple a S.A.T. mathematics after rote-writing the entire math FAQ 100 times? Remember, I don't mean do this only ... just half the time. The rest of the time you do integrated "thought" problems utilizing the now automated tools. | s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145869.83/warc/CC-MAIN-20200224010150-20200224040150-00381.warc.gz | CC-MAIN-2020-10 | 2,830 | 12 |
http://www.neilatkin.com/2017/03/26/ten-ideas-teaching-better-maths-science/ | math | Students often struggle to solve problems in science that require them to do mathematical calculations, rearrange equations or draw/analyse graphs. Here are 10 ideas to improve the transferability of skills, ideally across the whole curriculum, not just in science
(1) Collaborate with your maths department on the order of skills taught – The passage below is taken from the ASE: The Language of Mathematics in Science – Teaching Approaches
The initial stimulus for collaborative work between the two faculties came from science teachers who identified that there were numeracy problems preventing students making rapid progress in science. Skills that should be transferable were not being applied by students outside of maths lessons. These were principally related to: changing the subject in equations; scaling graphs; drawing lines of best fit; and identifying types of graphs e.g. scatter or line? The problems were confounded by a mismatch in the order in which certain maths skills were taught in KS3 and applied in science. These timing issues meant that in science we were expecting high level skills that had not yet been fully covered in maths.
Another issue is that many students are taught in different maths sets to their science ones and so it cannot be assumed that they all have the same maths skills or have been taught techniques or language.
Data taken from science practical lessons could be processed in maths lessons so that the students can develop transferable skills. A joint maths and science day for students as outlined in teaching approaches has been shown to be beneficial to all. Looking at graphical analysis or molar calculations in a common way in maths and science helps everyone.
(2) Use common language and teach the terms explicitly.
To Maths teachers a line graph (and line of best fit) is a straight line, to science teachers, it could be curved. Students can often try to draw straight lines through what clearly looks like a curved set of points when asked to draw a line graph, because they are using the maths definition.
Range is a numerical value in maths, but can have multiple meanings in science – the range of a variable, graph or measuring instrument.
The term ‘variable’ is used infrequently in mathematics, but very commonly used in science, with students being expected to identify different categories of variable by age 11. In these categories is the term discontinuous used?
‘range’ is a numerical value in mathematics, but a quantity in science, linked to a specific variable.
(3) Try to standardise the approach to answering questions
A motorbike travels 20 miles in 10 minutes, how far does it go in an hour?
How did you work this out?
- By proportional reasoning? 60 minutes is 6 times as long as 10. So the distance is 6 times as long – 120 miles (it’s a fast bike)
- By working out how far it travels in one minute (20/10 = 2 miles) then multiplying by how many minutes
- By explicitly using the formula distance = speed x time
- By using triangles
Setting one of these problems and asking students how they worked it out is very interesting- then find out how the maths department would get them to answer it.
(4) Talk about the concepts in words before you introduce the formula. Equations are stories about relationships.
So for Newton’s second law you could talk about wanting to move a car that won’t start. It’s fairly intuitive that the harder you push it (the bigger the Force you apply) the bigger the change in motion (acceleration) of a car. But what would happen to the motion of the car when you push it as hard as you can, if it was very light? Or very heavy? From this thought experiment we can deduce that the change of motion is greater the bigger the force is, but also smaller the larger the mass so acceleration = Force/mass or a= F/m
Almost all of you will have learnt this as F=ma, is a=F/m more appropriate? Read on ..
(5) Consider the order you show students formulae
Does it matter if you show F=ma, a=F/m or m= F/a
or V=IR , I=V/R or R=V/I ?
remembering that equations tell stories, what story makes the most sense?
F = ma – Speeding up or slowing down a mass requires a force. The larger the force the greater the acceleration or deceleration for a given mass. Having a larger mass would require a larger force to maintain the same acceleration
a = F/m – The acceleration depends on the Force and the mass. The greater the force, the greater the acceleration. The greater the mass, the smaller the acceleration
a=F/m is generally more useful than the more usual F=ma as we are normally working out the acceleration having chosen the mass and the force. The story also makes more sense to me.
Similarly, I would introduce I=V/R rather than V=IR
(6) Rearranging the equation vs Changing the subject
Usually, students are told to rearrange the equations. For those with good maths skills that is fine. However, to many students, it is a mysterious process.
Consider changing the subject instead (With thanks to Helen Reynolds for this)
- The cat is sitting on the mat
- The mat is the thing the cat was sitting on
- Sitting is what the cat was doing on the mat
Here we have just changed the subject. All three statements say the same thing with the equals sign being represented by is. To some students, this is a revelation
Similarly using numbers can demystify algebra. So
6 = 2×3 or 3=6/2 or 2=6/3 are also equivalent statements and far more intuitive than using letters
(7) Use maths type starters in your lessons.
- Change the subject so If a = F/m what does F = ?
- I = V/R What would happen to the current if the potential difference got bigger/ Resistance got smaller etc.
- What would the gradient of a distance- time give you?
- An electric heater has a power of 2kW. How much energy does it transfer in one minute?
- What happens to the kinetic energy of a bird when it’s velocity doubles (and its mass halves?)
- Explain the story of this graph – Do we need more pirates?
(8) Triangles – A useful aid or the work of the devil?
Taken from Sparknotes
Triangles are undoubtedly helpful for students who struggle to change the subject of equations. They shouldnt be used instead of trying to do the algebra. Triangles can be used to tell the stories and used as another alternative approach taught in combination with the other methods.
Any other ideas please add to the comments section below | s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703527850.55/warc/CC-MAIN-20210121194330-20210121224330-00180.warc.gz | CC-MAIN-2021-04 | 6,426 | 49 |
https://www.seehuhn.de/blog/113.html | math | Publication: The Effect of Finite Element Discretisation on the Stationary Distribution of SPDEs. How does finite element discretisation affect the stationary distribution of an SPDE? … read more
Publication: Analysis of SPDEs arising in Path Sampling, Part I: The Gaussian Case. An article about using (linear) SPDEs in infinite dimensional MCMC methods. … read more
Publication: Data Assimilation: Mathematical and Statistical Perspectives. A concise mathematical overview of the subject of data assimilation, highlighting statistical aspects. … read more
By Jochen Voss, on
After taking much longer than I intended to, today I finally submitted a new paper (about a year later than planned). You can have a look at the preprint here:
This is an excerpt from Jochen's blog.
Older entry: new jvlisting release
Copyright © 2011, Jochen Voss. All content on this website (including text, pictures, and any other original works), unless otherwise noted, is licensed under a Creative Commons Attribution-Share Alike 3.0 License. | s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232257361.12/warc/CC-MAIN-20190523184048-20190523210048-00100.warc.gz | CC-MAIN-2019-22 | 1,032 | 8 |
https://chestofbooks.com/architecture/Construction-Superintendence/Steel-Beam-Footings-Part-3.html | math | For the upper beams the load borne by each beam should be computed and the coefficient of strength determined by the formula
C=4X WX p.........(2)
W being in this case the total distributed load on either end of the beam in pounds, and p the distance from end of beam to edge of iron plate above.
Example II. - The basement columns of a ten-story building are required to sustain a permanent load of 400,000 pounds. What should be the size of the beams in the footings, the supporting power of the soil being but 2 tons?
Answer. - Dividing the load by the bearing power of the soil we have 100 square feet, or 10X10 feet, for the area of the footing. We will arrange the beams as shown in Fig. 16, using a cast iron bearing plate 3 feet square under the column. The distance between the centres of outer beams in upper tier we will make 32 inches, thus making the value of p for the lower beams = 10' - 2' 8" / 2 or 3 2/3 feet; s we will make 12 inches, or 1.
Looking down column headed 2 (Table IV.) we find the nearest projection above 3 2/3 is 4, which is opposite the 9-inch, 27-pound and also the 10-inch, 25.5-pound beams. The latter being the lighter and also the stiffer, we will use for the lower tier.
For the upper tier we see that the five beams must support an area equal to a, b, c, d, which in this case equals 3½ X 10 feet, or 35 square feet. As the pressure on each foot is 2 tons, we will have a total pressure of 70 tons on the ends of the five beams, or 14 tons or 28,000 pounds on each beam. Then by formula 2 we find the coefficient of strength must =4X28,000X3½=392,000 pounds.
From the table of the Carnegie Steel Company's beams we find that the coefficient for a 12-inch, 32-pound beam is 395,200 pounds; therefore, we will use three 12-inch, 32-pound beams and two
40-pound beams in the upper tier.
57. The deepest beam for the weight should always be used, and unless the beams in the upper tier have considerable excess of strength, the two outer beams should be heavy beams.
When the footings carry iron or steel columns in the basement, as is generally the case, a cast iron or steel base plate should be used, as shown in Figs. 17 and 18. This plate should be bedded in Portland cement directly above the beams, as described in Section 50.
Two and even four columns are often supported on one footing, as shown in Figs. 17 and 18. In such cases the computation becomes more elaborate, and an engineer should be called into consultation unless the architect is himself sufficiently familiar with such calculations.
Fig. 19 shows an arrangement in which a built-up base plate or girder is used in place of the upper tier of beams. The author believes this arrangement much better than that shown in Figs. 16 to 18.
In placing the beams, it is essential that they be arranged symmetrically under the base plate, otherwise they will sink more at one side than at the other. When several unequally loaded columns rest on the same footing, the equal distribution of the weight on the soil becomes a difficult problem. | s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764494936.89/warc/CC-MAIN-20230127033656-20230127063656-00503.warc.gz | CC-MAIN-2023-06 | 3,045 | 14 |
https://www.projecteuclid.org/journals/publicacions-matematiques/volume-57/issue-1/Convexity-of-strata-in-diagonal-pants-graphs-of-surfaces/pm/1355854304.full | math | We prove a number of convexity results for strata of the diagonal pants graph of a surface, in analogy with the extrinsic geometric properties of strata in the Weil-Petersson completion. As a consequence, we exhibit convex flat subgraphs of every possible rank inside the diagonal pants graph.
"Convexity of strata in diagonal pants graphs of surfaces." Publ. Mat. 57 (1) 219 - 237, 2013. | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100081.47/warc/CC-MAIN-20231129105306-20231129135306-00419.warc.gz | CC-MAIN-2023-50 | 388 | 2 |
https://technick.net/guides/theory/dft/example_sinusoids/ | math | Figure 5.1 plots the sinusoid , for , , , and. Study the plot to make sure you understand the effect of changing each parameter (amplitude, frequency, phase), and also note the definitions of ''peak-to-peak amplitude'' and ''zero crossings.''
A ''tuning fork'' vibrates approximately sinusoidally. An ''A-440'' tuning fork oscillates at cycles per second. As a result, a tone recorded from an ideal A-440 tuning fork is a sinusoid at Hz. The amplitude determines how loud it is and depends on how hard we strike the tuning fork. The phase is set by exactly when we strike the tuning fork (and on our choice of when time 0 is). If we record an A-440 tuning fork on an analog tape recorder, the electrical signal recorded on tape is of the form
As another example, the sinusoid at amplitude and phase (90 degrees) is simply
Thus, is a sinusoid at phase 90-degrees, while is a sinusoid at zero phase. Note, however, that we could just as well have defined to be the zero-phase sinusoid rather than . It really doesn't matter, except to be consistent in any given usage. The concept of a ''sinusoidal signal'' is simply that it is equal to a sine or cosine function at some amplitude, frequency, and phase. It does not matter whether we choose or in the ''official'' definition of a sinusoid. You may encounter both definitions. Using is nice since ''sinusoid'' in a sense generalizes . However, using is nicer when defining a sinusoid to be the real part of a complex sinusoid (which we'll talk about later). | s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947475825.14/warc/CC-MAIN-20240302120344-20240302150344-00519.warc.gz | CC-MAIN-2024-10 | 1,505 | 4 |
https://www.physicsforums.com/threads/triple-integration-w-spherical-coordinates.231954/ | math | 1. "Find the mass of part of the solid sphere x^2 + y^2 + z^ 2 ≤ 25 in the 1st octant x ≥ 0, y ≥ 0, z ≥ 0 where mass density is f (x, y, z ) = (x^2 + y^2 + z^2 )^3/2 ." 3. These problems are really stumping me! I need somebody to work it out/explain it to me! What will the limits of integration be for the following question? What do i integrate? I know I need to transform it to spherical coordinates... but beyond that I'm lost. I know it's a triple integral: m = ∫∫∫(x^2 + y^2 + z^2)^3/2 dzdydx transforming to spherical co-ordinates: 0 ≤ rho ≤ 5 0 ≤ theta ≤ ??? (how do I figure this out?) 0 ≤ phi ≤ ????? (ditto) dzdydx = rho^2 sinphi drho dphi dtheta What does f (x, y,z) transform to and how do I figure it out? | s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039744348.50/warc/CC-MAIN-20181118093845-20181118115845-00198.warc.gz | CC-MAIN-2018-47 | 745 | 1 |
http://forums.gametrailers.com/Gam-F6/Cla-F22/Bes-T1190463/?p=33087786 | math | - Posts: 12915008
- Joined: Wed Dec 31, 1969 5:00 pm
I was looking to pick up some classic turn-based RPGs and came across the Wild Arms series. Which one is the best? Wild Arms 1 and 2 are on PS1 but I was also looking at 3 on the PS2. I'm not really interested in the later ones as they don't have turn-based battles and that's what I'm looking for. Out of these 3, which is the best? | s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368703682988/warc/CC-MAIN-20130516112802-00002-ip-10-60-113-184.ec2.internal.warc.gz | CC-MAIN-2013-20 | 386 | 3 |
http://www.claymath.org/workshops/mcpolynomials/mcabstracts.php | math | Abstracts of Talks
In it will discuss joint work with David Nadler. We construct parts of a new three dimensional topological quantum field theory, which organizes representation theories associated to a complex reductive group, including Lusztig's character sheaves, Harish-Chandra modules for real forms of the group, and conjecturally the mixed Hodge theory of character varieties of the group. The character theories for Langlands dual groups are equivalent, leading to a collection of dualities for the objects listed above.Reference
Supports of irreducible spherical representations of rational Cherednik algebras of finite Coxeter groups
I will explain how to determine the support of the irreducible spherical representation (i.e., the irreducible quotient of the polynomial representation) of the rational Cherednik algebra of a finite Coxeter group for any value of the parameter c. In particular, this allows one to determine for which values of c this representation is finite dimensional. This generalizes a result of Varagnolo and Vasserot, arXiv:0705.2691, who classified finite dimensional spherical representations in the case of Weyl groups and equal parameters (i.e., when c is a constant function). Our proof is based on the Macdonald-Mehta integral and the elementary theory of distributions.
The Kostka polynomials make the transition between Schur functions and Hall-Littlewood polynomials. Lusztig also interpreted them in terms of the stalks of intersection cohomology sheaves on the nilpotent cone of the general linear group (going through the affine Grassmannian and the affine flag manifold, so that they are also expressed in terms of Kazhdan-Lusztig polynomials).
If one considers positive characteristic coefficients, the intersection cohomology sheaves are not so well behaved. For example, their stalks do not necessarily satisfy a parity vanishing. However, one can consider the indecomposable complexes which satisfy a parity vanishing for their stalks and costalks, and it turns out that they are still classified by partitions. They are the direct summands of direct images of constant sheaves on resolutions of partial flag varieties. If the characteristic is large enough, they are the intersection cohomology complexes. In general, their stalks yield generalizations of Kostka polynomials (which are combinations of the classical ones), depending on the characteristic.
In our article, we work in a more general setting. Under certain conditions which are often satisfied in "representation theoretic situations" (including the above mentioned nilpotent cone, Kac-Moody Schubert varieties like the affine Grassmannian, and also toric varieties), the indecomposable constructible complexes having a parity vanishing for stalks and costalks are parametrized by pairs consisting of an orbit and an irreducible local system (just like simple perverse sheaves, in the equivariant setting). In the case of a semismall "even" resolution, we express the multiplicities of the parity sheaves in the direct image of the constant sheaf as the ranks modulo p of certain intersection forms (appearing in the work of de Cataldo and Migliorini). This gives a measure of the failing of the decomposition theorem with positive characteristic coefficients. On the affine Grassmannian, parity sheaves correspond to tilting modules under the geometric Satake correspondence, when the characteristic is large enough (greater than h + 1, where h is the Coxeter number, is enough).
I will introduce Okounkov-Reshetikhin-Vafa type vertex operators to compute the generating function of Donaldson-Thomas type invariants of a small crepant resolution of a toric Calabi-Yau 3-fold. The commutator relation of the vertex operators gives the wall-crossing formula of Donaldson-Thomas type invariants.Reference
Intersection cohomology on character/quiver varieties and the character ring of finite general linear groups
Here we show that the "generic" part of the character ring of finite general linear groups can be described in terms of intersection cohomology of character and quiver varieties.
The aim of this talk will be to explain concrete geometric pictures of field theoretic phenomena appearing in joint work with David Ben-Zvi on character sheaves.
We determine the two-point invariants of the equivariant quantum cohomology of the Hilbert scheme of points of surface resolutions associated to type An singularities. The operators encoding these invariants are expressed in terms of the action of the affine Lie algebra gl(n+1) on its basic representation. Assuming a certain nondegeneracy conjecture, these operators determine the full structure of the quantum cohomology ring. A relationship is proven between the quantum cohomology and Gromov-Witten/Donaldson-Thomas theories of An x P1. The talk is based on the joint paper with Davesh Maulik.
I will give an overview of the results on the topic of the title obtained in collaboration with T. Hausel and E. Letellier. The varieties in question are those parameterizing representations of the fundamental group of a punctured Riemann surface to GL_n with values in prescribed generic semisimple conjugacy classes at the punctures.
The results are best expressed as a specialization of a generating series involving the Macdonald polynomials. We conjecture that the full generating series actually gives the mixed Hodge polynomials of the varieties. We prove that taking the pure part of these polynomials, which amounts to a different specialization of the generating series, actually gives the number of points of an associated quiver variety over finite fields. | s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368698238192/warc/CC-MAIN-20130516095718-00052-ip-10-60-113-184.ec2.internal.warc.gz | CC-MAIN-2013-20 | 5,639 | 14 |
https://techcloudspro.com/uses-of-poisson-calculator-to-calculate-cumulative-poisson-probability/ | math | It is important to understand what Poisson distribution is before the detailed concepts like cumulative Poisson probability are discussed. In simple terms, Poisson distribution defines the chances of the occurrence of particular events in a fixed time span. A major example of Poisson distribution is the number of calls which a customer support professional receives in an hour. In this example, the telephone call is counted as an event while the time span is 1 hour. Through Poisson distribution, the number of calls received in one hour can be measured.
Calculation of Cumulative Poisson Probability
In case of cumulative poisson probability, we measure the chances of the Poisson Variable falling within a specified range. Consider that this variable is denoted by “X” and “N” shows the maximum chances of success. These are obviously complex calculations so a Poisson Calculator is used for this purpose you find it on Calculators.tech.
The usage of a Poisson Calculator
It is not hard to determine the cumulative poisson probability as this calculator has a simple set of commands. You simply need to enter the input values and cumulative poisson probability would be calculated.
Entering the Input Values
While using this calculator, the user only has to enter two input values. One is the value of Poisson Random Variable which is represented by X. Along with that, the chances of success have to be entered. When these values have been entered, you can proceed towards the output interpretation.
- Based on the values of Poisson Random Variable and success chances provided by the user, the output values would be generated by the calculator.
Interpretation of values
It is important for you to understand the interpretation of output values before you start using the Poisson Calculator. When you enter the value of X and chances of success. The cumulative Poisson probability would be calculated along with other values. Consider that you have entered the value of X as 5.
The Calculator would determine four different cumulative frequency values in accordance with the value of X.
- The first value would the value of X as less than 5 and the cumulative probability would be calculated on the basis of that.
- The second scenario would take the value of X as less than or equal to 5
- The third cumulative probability value would be determined after taking the value of X as greater than 5
- The fourth and final probability would be determined by considering the value of X as greater than or equal to 5.
The cumulative probability is not a simple calculation by any means. Hence, you cannot sit down with a pen and paper to perform these calculations. You need to have a quality online calculator through which the interpretations can be performed.
As a user, you need to enter the value of Poisson Variable and the chances of success. The cumulative probability which is calculated with a range of values would be calculated according to the provided input values. | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817144.49/warc/CC-MAIN-20240417044411-20240417074411-00802.warc.gz | CC-MAIN-2024-18 | 2,988 | 17 |
https://www.physicsforums.com/threads/determine-the-amount-of-naoh-and-sr-oh-2-based-on-poh.876840/ | math | I am trying to solve the following problem:
A 4.00-L base solution contains 0.100 mol total of
NaOH and Sr(OH)2 . The pOH of the solution is 1.51.
Determine the amounts (in moles) of NaOH and
Sr(OH)2 in the solution.
3. The Attempt at a Solution [/B]
I am stuck because I am not sure I correctly constructing the solution path:
We have pOH = 1.51, which means that there are 10^(-1.51) moles of OH in solution, i.e. 0.0309 moles per one liter of solution. If I have 4 liters, then shouldn't there be 0.1236 moles of OH in this solution?
But according to the problem there are only 0.100 moles of NaOH and Sr(OH)2; both are strong bases, therefore there 0.100 moles of OH in the 4 liters of solution. How can that be?
Where is my mistake?
Thank you very much! | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100381.14/warc/CC-MAIN-20231202073445-20231202103445-00042.warc.gz | CC-MAIN-2023-50 | 758 | 11 |
https://www.stspl.com/flow-rate-rmszpz/elastic-limit-of-steel-6fd5ca | math | 1 MPa = 10 6 Pa = 1 N/mm 2 = 145.0 psi (lbf/in 2); Fatigue limit, endurance limit, and fatigue strength are used to describe the amplitude (or range) of cyclic stress that can be applied to the material without causing fatigue failure. We cut your steel plates starting from your plans with absolute accuracy. The yield strength point, Ï y, represents the limit of the elastic region of a material, that means that, within the correspondent strain range, the sample shows an elastic behavior. Elastic limit, also referred to as yield point, is an upper limit for the stress that can be applied to a material before it permanently deforms.This limit is measured in pounds per square inch (psi) or Newtons per square meter, also known as pascals (Pa). Yield point is well defined and shown on graph for mild steel and it's beyond elastic limit. Oxycut on demand. shape and size) on the removal of external force. Elastic limit As we have seen that if an external force is applied over the object, there will be some deformation or changes in ⦠elastic limit synonyms, elastic limit pronunciation, elastic limit translation, English dictionary definition of elastic limit. The elastic limit of a steel wire is 2.70 × 10 8 Pa. What is the maximum speed at which transverse wave pulses can propagate along this wire without exceeding this stress? Physics for Scientists and Engineers, Volume 1, Chapters 1-22 (8th Edition) Edit edition. Overview of Elastic Modulus Of Steel Elasticity is the property of an object to resume its normal shape and size after being stretched or compressed. A rolled steel product is given an elastic limit of 500 to 1200 MPa by selection of a particular steel composition and a particular heat treatment. For other materials like copper or aluminum is defined as the point of intersection of stress-strain curve and a line drawn parallel to linear part fron 0.2 percent deformation (strain ε) and it is also beyond the elastic limit. From the technical point of view spring steel has to meet the following requirements: A high technical elastic limit . It is a very common assumption that a compression spring would travel or can be compressed to its solid height. mm The material's elastic limit or yield strength is the maximum stress that can arise before the onset of plastic deformation. To determine the modulus of elasticity of steel, for example, first identify the region of elastic deformation in the stress-strain curve, which you now see applies to strains less than about 1 percent, or ε = 0.01. Beyond the elastic limit, the mild steel will experience plastic deformation. Define elastic limit. Hence, utilizing the modulus of elasticity formula, the modulus of elasticity of steel is e = Ï / ε = 250 n/mm2 / 0.01, or 25,000 n/mm2. Yield point is a point on the stress-strain curve at which there is a sudden increase in strain without a corresponding increase in stress. This starts the yield point â or the rolling point â which is point B, or the upper yield point. (The density of steel ⦠More. linear relation between the two. ; Creep. Special steel plates. The elastic limit of the material is the stress on the curve that lies between the proportional limit and the upper yield point. It got great weldability and machinability, let us see more mechanical details of this steel. This is known as Hookâs law. Its SI unit is also the pascal (Pa). Proportional limit (point A) Elastic limit (point B) Yield point ( upper yield point C and lower yield point D) Ultimate stress point (point E) Breaking point (point F) Proportional limit. Elastic deformation is a straightforward process, in which the deformation increases with an increase in force, until the elastic limit of the object is reached. the steel material to largely deform before fracturing. However, the compression spring has certain limit of ⦠Rubber, polythene, steel, copper and mild steel will be considered as the nice examples of elastic materials within certain load limits. The unit weight of structural steel is specified in the design standard EN 1991-1-1 Table A.4 between 77.0 kN/m 3 and 78.5 kN/m 3. See accompanying figure at (1, 2). As seen in the graph, from this point on the correlation between the stress and strain is no longer on a straight trajectory. The time dependent deformation due to heavy load over time is known as creep.. All materials show elastic behaviour to a degree, some more than others. It is the highest limit of the material before the plastic deformation of the material can occur. An added service which allows collecting the product ready to be used. Note this is not the same as the breaking stress for the wire which will typically be significantly higher for a ductile material like steel. This article discusses the properties and applications of stainless steel grade 304 (UNS S30400). Elastic Limit: It is defined as the value of stress upto and within which the material return back to their original position (i.e. Youngâs modulus is named after British scientist Thomas Young but it was developed by Leonhard Euler in 1727. The elastic limit depends markedly on the type of solid considered; for example, a steel bar or wire can be extended elastically only about 1 percent of its original length, while for strips of certain rubberlike materials, elastic extensions of up to 1,000 percent can be achieved. If the value of external force is such that it exceeds the elastic limit, than the body will not completely regain its original position. The elastic limit is defined as the maximum stretch limit of the compression spring without taking a permanent set. When the stresses exceed the yield point, the steel will not be able to bounce back. The elastic limit of steel is 8 x10 8 N/m 2 and its Young's modulus 2 x10 11 N/m 2.Find the maximum elongation of a half-meter steel wire that can be given without exceeding the elastic limit. Determine the minimum diameter a steel wire can have if it is to support a 70 kg person. High strenght steel . If stress is added to the metal but does not reach the yield point, it will return to its original shape after the stress is removed. If the elastic limit of steel is 5.0 10 8 Pa,determine the minimum diameter a steel wire can have if it is tosupport a 60 kg circus performerwithout its elastic limit being exceeded. Material Properties of S355 Steel - An Overview S355 is a non-alloy European standard (EN 10025-2) structural steel, most commonly used after S235 where more strength is needed. If the elastic limit of steel is 5.0 multiplied by 108 Pa, determine the minimum diameter a steel wire can have if it is to support a 75-kg circus performer without its elastic limit being exceeded. Elastic limit is defined as the maximum stress that a material can withstand before the permanent deformation. for example rubber. Overview. Formable steel high elastic limit for all types of load-bearing structures. If, after a load has been applied and then quickly removed, a material returns rapidly to its original shape, it is said to be behaving elastically. The elastic limit correlates with the largest austenite free-mean path by a Hall-Petch type equation. e.g. Sponsored Links Related Topics For structural design it is standard practice to consider the unit weight of structural steel equal to γ = 78.5 kN/m 3 and the density of structural steel approximately Ï = 7850 kg/m 3. sigma=E*epsilon for steel. Once the stress or force is removed from the material, the material comes back to its original shape. This is an approximation of the elastic limit of the steel. The Ultimate Tensile Strength - UTS - of a material is the limit stress at which the material actually breaks, with a sudden release of the stored elastic energy. The elastic limit of a material is an important consideration in civil, mechanical, and aerospace engineering and design. For mild steel the elastic limit is about 400 MPa. Elastic limit - Designing Buildings Wiki - Share your construction industry knowledge. Which is the tension that can be applied on the material without a plastic deformation? - proportional limit is strain below which the stress is proportional to strain i.e. The elastic limit for steel is for all practical purposes the same as its proportional limit. Spring steel is also used when there are special requirements on rigidity or abrasion resistance. Elastic modulus is a material property that demonstrates the quality or flexibility of the steel materials utilized for making mold parts. - elastic limit is strain below which the material can regain its original shape if the forces are release, doesn't matter if the stress-strain relation is linear or not. Problem 25P from Chapter 16: Review. So 1 percent is the elastic limit or the limit of reversible deformation. As shown in stress strain curve for mild steel, up to the point A, stress and strain follow a relationship. | s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487625967.33/warc/CC-MAIN-20210616155529-20210616185529-00301.warc.gz | CC-MAIN-2021-25 | 8,929 | 1 |
http://forum.enjoysudoku.com/sew-it-s-the-same-either-way-t33105.html | math | The reason many of our solving techniques such as Skyscrapers, 2-string Kites and other chaining processes work, is because they examine situations where there are only two possible options, and both lead to the same result somewhere else in the puzzle. So we can take that result as true, even if in the meantime we don't yet know the true arrangement that predicts it. I often us this approach, which I call SEW. Try this:
Here I was looking at what was going on in Box2. With the 4,5 Locked Pair on the middle shelf, there were only two places for the 6. They worked out as
Now what does that mean for the rest of the puzzle? It turned out that the first scenario predicted Row5 to be 297 641 358 and the second forced it to be 297 346 158.
This meant that in either case the 6 in Box5 had to be on the middle shelf, which in turn meant that the 6 in Box6 had to be at r4c8 anyway, which easily solved the whole puzzle.
There are of course many ways to solve this puzzle and you can look up the discussion of it which took place between ravel and RW in 2005 in the post Solving without pencilmarks. | s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917121355.9/warc/CC-MAIN-20170423031201-00099-ip-10-145-167-34.ec2.internal.warc.gz | CC-MAIN-2017-17 | 1,101 | 5 |
https://brainmass.com/statistics/sampling-distribution/quantitative-analysis-diameter-of-ping-pong-balls-113699 | math | The diameter of Ping-Pong balls manufactured at a large factory is expected to be approximately normally distributed with a mean of 1.30 inches and a standard deviation of 0.04 inch. What is the probability that a randomly selected Ping-Pong ball will have a diameter...
a. less than 1.28 inches?
b. Between 1.31 and 1.33 inches?
c. Between what two values (symmetrically distributed around the mean) will 60% of the Ping-Pong balls fall (in terms of diameter)?
If many random samples of 16 Ping-Pong balls were selected...
d. What will be the values of the population mean and standard error of the mean?
e. What distribution will the sample means follow?
f. What proportion of the sample means will be less than 1.28 inches?
g. What proportion of the sample means will be between 1.31 and 1.33 inches?
h. Between what two values symmetrically distributed around the mean will 60% of the sample means be?
i. Compare the answers of (a) with (f) and (b) with (g). Provide a detailed explanation accordingly.
j. Explain the difference in the results of (c) and (h).
k. Which is more likely to occur - an individual ball above 1.34 inches, a sample mean above 1.32 inches in a sample of size 4, or a sample mean above 1.31 inches in a sample of size 16? Explain.
The solution finds the probability of randomly selecting ping-pong balls with different diameters. The distribution of sizes are determined. | s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587799.46/warc/CC-MAIN-20211026042101-20211026072101-00262.warc.gz | CC-MAIN-2021-43 | 1,400 | 14 |
http://cnspage.tk/casadio-enea-manual-woodworkers.html | math | 24 August 2012 F: Introduction to section and a review of functions. Worksheet 1 Solutions. sorted by topic and most of them are accompanied with hints or solutions. 16 Habits of Mind 1 page summary: http:www. chsvt. orgwdpHabits of Mind. pdf. This page has been designed as a means to support my Calculus I MA 113 students. First Midterm problems and solutions-1004KB pdf file. Thoughts on homework pdf The light-colored numbers in the solutions indicate the value assigned to each part of a problem, or to the value of the entire. Writing Project N Newton, Leibniz, and the Invention of Calculus 399. Ideas toward a solution and for recognizing which problem-solving principles are. Enter your function to get your calculus easy money making guide runescape 2014 f2p mmorpgs or doe inspector general audit manual with each step. No software download, no sign up hassle anytime, anywhere solutions just like. CalcChat. com is a moderated chat forum that provides interactive hp users manual libraries help, calculus casadio enea manual woodworkers, college algebra solutions, precalculus solutions and more. PDF. 1 file ABBYY GZ 1 file DAISY 1 casadio enea manual woodworkers EPUB 1 file FULL TEXT 1 file KINDLE 1 file PDF. Aug 1, casadio enea manual woodworkers. Each chapter ends with a list of the solutions to all the odd-numbered exercises. Get instant access to your Calculus solutions manual on Chegg. com. Our interactive textbook solution manuals will rock your world. 3 The Velocity at an Casadio enea manual woodworkers 1. 5 A Review of Trigonometry 1. 6 A Thousand Points of Light 1. 2: DerivativesCalculus 1: Sample Questions, Final Exam, Solutions. 1 x dx. Calculus. Worksheet 1 Solutions. some of the calculus courses taught by the author at Trent University. Various. Jan 21, 2010. Look at both the solutions and the additional comments. Html105handoutsMVT TaylorSeries. pdf. Introduces advanced Calculus topics in a rigorous manner with emphasis on proofs. Where can I download this, and hopefully more pdf or djvu textbooks. Edit: i have the 3rd edition actually lol, didnt realize they had a newer. Page 3. ANSWER BOOK FOR CALCULUS. Solutions to Calculus 3rd Edition by Spivak, M. edit. Chapter 14 - The Fundamental Theorem of Calculus. Calculus, 4th edition Michael Spivak on Amazon.
ISBN. This edition of James Stewarts best-selling calculus book has been revised with the consistent dedication to excellence that has characterized all his books. Dec 14, 2005. Problems in bold will be graded and should be written on a separate. The fundamental objects that we deal with in calculus are functions. Solutions in Stewart Calculus 9780534393397. ISBN: 9780534393397 Publisher: BrooksCole Authors: Stewart. Go to Page:Solutions in Stewart Calculus: Early Transcendentals 9780534393212Get instant access to our step-by-step Calculus solutions manual. 6716 total problems in solution. Baixe grátis o arquivo Calculus - Stewart 2 - 5th Edition - Solutions Manual. pdf enviado por Abr no curso de Matemática. Sobre: Manual de Soluções do Volume. Welcome to the new Stewart Calculus web site. Links - such as Algebra Review and Lies My Calculator and Computer Told Me - point to Acrobat PDF files. Problems Plus 265. Maximum and Minimum Values 271. Applied Project N The Calculus of Rainbows 279. The fundamental objects that we deal with in calculus are functions. Types of functions that occur in calculus and describe the process casadio enea manual woodworkers using these func. Problems in bold will be graded and should woodwlrkers written on a separate. James Stewarts Calculus texts are casadio enea manual woodworkers best-sellers for a reason: casaido are clear. Calculus and guide de lauto 1995 of other textbooks are available for instant download on your Kindle Fire tablet or on the free Kindle apps for iPad. You get Google the PDF version for free. Calculus, 5th Edition by James Stewart HardcoverStewart - Calculus, Early Transcendentals 5e. pdf. Dancer bun tutorial with marley Insight Multivariable gbc service manuals Basic snea on multivariable calculus. James Stewart Calculus 5E. pdf - PDF document woovworkers james-stewart-calculus-5e. pdf PDF 1. 6, 20499 KB, woodworoers pages PDF-Archive. garage sale pricing guide 2012 movie. The text for the casadio enea manual woodworkers part of the casadio enea manual woodworkers is Casadio enea manual woodworkers by Casadio enea manual woodworkers Stewart. Provided for the 5th edition. 7 Techniques of integration - Stewart, 6ed. Here is the region that lies below the plane with, and -intercepts, and respectively, that is, como hacer pulseras en macrame con hilo encerado the plane and above the region in the. -plane bounded. Sponsored, James Stewart Calculus Early Transcendentals 6th Edition PDF pdf James Stewart Casadio enea manual woodworkers. Calculus 5th Edition - James Stewart solution pdfExercises for Lagrange multipliers are taken from Stewarts Multivariable Calculus 5e. Find the extreme values of the function f x, y x2 2xy on the circle. Visit here: -http:budurl. com7sbh - stewart calculus 6th edition pdf download free: - An ebook provides the best knowledge about he calculus. Find more on: -http:budurl. comaz6m - Calculus Concepts and Contexts Stewart Pdf Download Free: - An ebook provides you the best. Calculus Early Transcendental Stewart, James Free download pdf 14 ч. is aTranscendentals 5th Edition James Stewart PDF Magnet link. Solutions in Stewart Calculus 9780534393397. Go to Page:Solutions in Stewart Calculus: Early Transcendentals 9780534393212Stewart Single Variable Calculus: Early Transcendentals, 5th Edition. ISBN: 9780534393304 Publisher: BrooksCole Authors: Stewart. Go to Page: Go. Welcome to the new Stewart Calculus web site. Applied Project N The Calculus of Rainbows 279. James Stewarts Calculus texts are worldwide best-sellers for a reason: they are clear. Calculus, 5th Edition by James Stewart HardcoverStewarts Calculus is successful throughout the world because he explains the. For Stewarts Calculus: Early Transcendentals Single Variable, 5th edition. | s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583517495.99/warc/CC-MAIN-20181023220444-20181024001944-00479.warc.gz | CC-MAIN-2018-43 | 6,098 | 2 |
http://www.coursehero.com/tutors/problems/Math/7321/ | math | Solve by completing the square: x^2+8x+3=0
$5900 is invested, part of it at 10% and part of it at 9%. How much is invested at each rate to yield $562
need math olympiad training
If one pen costs dollars, what is the cost, in dollars, of pens?
How do you divide 538000 by 0.19
A POLL SHOWED THAT 61% OF AMERICANS SAY THEY BELIEVE THAT LIFE EXISTS ELSEWHERE IN THE GALAXY. WHAT IS THE PROBABILITY OF RANDOMLY SELECTING SOMEONE NOT HAVING THAT BELIEVE?
192 meals is what percent of 960 meals?
What are the answers for numbers.. 7 and 8
A rancher has 20000 linear feet of fencing and wants to enclose a rectangular field and then divide it into four equal pastures with three internal fences parallel to one of the rectangular sides. What is the maximum area of each pasture?
A surveyor wants to measure the distance across a lake from point A to point B. He selects a third point, C, which is 4 miles from point A and 5 miles from point B. He then measures the angle ACB to be 80o. Find the distance from A to B, rounded to the nearest tenth of a mile
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1. I’m having problems with my math. Can you help me? All I need is an example just to make sure I'm on track.
- Solve the following
- a) 3/(n+1)-1/(n+1)=14/(n^2-1)
- b) 1/(y-1 )+y/(1-y)
- d) (x-2)/(8x-24)*(5x-15)/(x^2 -4)
- e) z/(z-1)+1/2=3/z
- f) (x-3)/(x^2+2x-15)-(4-x)/(x^2-9x+20)
- 2. How do I set up this problem? An exam contains five "true or false" questions. How many of the 32 different ways of answering these questions contain 3 or more incorrect answers? | s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368707188217/warc/CC-MAIN-20130516122628-00017-ip-10-60-113-184.ec2.internal.warc.gz | CC-MAIN-2013-20 | 1,938 | 22 |
https://allogpecomp.firebaseapp.com/12.html | math | Angleangleangle aa if the angles in a triangle are congruent equal to the corresponding angles of another triangle then the triangles are similar. After all of the students begin to realize that not all of the triangles are congruent, i will ask, if they are not congruent, then what can we say about the triangles that were created in this case. Determine if the two triangles shown below are similar. Altitude and 3 similar light triangles an altitude of a fight triangle, extending from the fight angle vertex to the hypotenuse, creates 3 similar triangles. Sides su and zy correspond, as do ts and xz, and tu and xy, leading to the following proportions. For example, if two triangles have the same angles, then they are similar. For example, photography uses similar triangles to calculate distances from the lens to the object and to the image size. The mathematical presentation of two similar triangles a 1 b 1 c 1 and a 2 b 2 c 2 as shown by the figure beside is. Example 1 identifying similar right triangles tell whether the two right triangles are similar. The chart below shows an example of each type of triangle when it is classified by its sides and angles. Scroll down the page for more examples and solutions on how to detect similar triangles and how to use similar triangles to solve problems.
Notes,whiteboard,whiteboard page,notebook software,notebook, pdf,smart,smart technologies ulc,smart board interactive whiteboard. Properties of similar triangles, aa rule, sas rule, sss rule, solving problems with similar triangles, examples with step by step solutions, how to use similar triangles to solve word problems, height of an object, shadow problems, how to solve for unknown values using the properties of similar triangles. You could check with a protractor that the angles on the left of each triangle are equal, the angles at the top of each triangle are equal, and the angles on the right of each triangle are equal. Triangles are similar if they have the same shape, but can be different sizes. Learn how to solve with similar triangles here, and then test your understanding with a quiz. Solve similar triangles advanced solving similar triangles. If two triangles have three equal angles, they need not be congruent. When the ratio is 1 then the similar triangles become congruent triangles. Similar triangles page 1 state and prove the following corollary to the converse to the alternate interior angles theorem. According to theorem 60, this also means that the scale factor of these two similar triangles is 3. Classify this triangle based on its sides and angles. Then, determine the value of x shown in the diagram. Corresponding sides of two figures are in the same relative position, and corresponding angles are in the same relative position.
Assessment included with solutions and markschemes. In this lesson, you will continue the study of similar polygons by looking at properties of similar triangles. The new pool will be similar in shape, but only 40 meters long. Two triangles abc and abc are similar if the three angles of the first triangle are congruent to the corresponding three. Similar figures have exactly the same shape but not necessarily the same size. Reasoning how does the ratio of the leg lengths of a right triangle compare to the ratio of the corresponding leg lengths of a similar right triangle. Another way to write these is in the form of side of one triangle, over the corresponding side of the other triangle. However, with the last side, which is not our side length. It is a specific scenario to solve a triangle when we are given 2 sides of a triangle. Similar triangles and shapes, includes pythagoras theorem, calculating areas of similar triangles, one real life application, circle theorems, challenging questions for the most able students. Then, we will focus on the triangles with angles of 30 degrees and 90 degrees. For instance, in the design at the corner, only two different shapes were actually drawn. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides.
An equilateral triangle is also a special isosceles triangle. Nov 10, 2019 similar triangles are two triangles that have the same angles and corresponding sides that have equal proportions. Triangles have the same shape if they have the same angles. Generally, two triangles are said to be similar if they have the same shape, even if they are scaled, rotated or even flipped over. Example 5 use a scale factor in the diagram, atpr axpz. Thus, these pair of sides are not proportional and therefore our triangles cannot be similar.
In this case, two of the sides are proportional, leading us to a scale factor of 2. Make a sketch of this situation including the sun, malik, and his shadow. They are still similar even if one is rotated, or one is a mirror image of the other. If so, state how you know they are similar and complete the similarity. State whether the following quadrilaterals are similar. What challenges andor misconceptions might students have when working with similar triangles. What about two or more squares or two or more equilateral triangles see fig. If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the. Similarity of triangles theorems, properties, examples.
Two triangle that have the same shape are called similar. Similar triangles are the triangles which have the same shape but their sizes may vary. The activity that follows example 1 allows you to explore. Find perimeters of similar figures example 4 swimming a town is building a new swimming pool. Ill ask, are all of the triangles congruent in this case. Tenth grade lesson discovering similar triangles betterlesson. Triangle is a polygon which has three sides and three vertices. Definitions and theorems related to similar triangles are discussed using examples. Pythagoras theorem baudhayan theor hypotenuse is equal to the sum of. If youre seeing this message, it means were having trouble loading external resources on our website. What is the measure of each angle in a regular triangle.
In the upcoming discussion, the relation between the areas of two similar triangles is discussed. Sss for similar triangles is not the same theorem as we used for congruent triangles. It is a specific scenario to solve a triangle when we are given 2 sides of a triangle and an angle in between them. In the case of triangles, this means that the two triangles will have. Similar triangles examples and problems with solutions. Solve similar triangles basic this is the currently selected item. Similarity of triangles uses the concept of similar shape and finds great applications. This lesson is designed to help students to discover the properties of similar triangles. Similar triangles examples the method of similar triangles comes up occasionally in math 120 and later courses.
For example, in the picture below, the two triangles are similar. Give two different examples of pair of i similar figures. In the case of triangles, this means that the two triangles. If so, state how you know they are similar and complete the similarity statement. Using simple geometric theorems, you will be able to easily prove. I can use similar triangles to solve real world problems. Find the perimeter of an olympic pool and the new pool. This video is another similar triangles example using the fact of knowing knowing the ratio of corresponding sides are equal. Williams methods of proving triangles similar day 1 swbat. Sas for similarity be careful sas for similar triangles is not the same theorem as we used for. Similar triangles are triangles with equal corresponding angles and proportionate sides. Alternately, if one figure can be considered a transformation rotating, reflection, translation, or dilation of the other then they are also similar. Geometry notes similar triangles page 4 of 6 y y y y 7. Theorem converse to the corresponding angles theorem.
If triangles are similar then the ratio of the corresponding sides are equal. Thus, two triangles with the same sides will be congruent. First, indicate the theorem that justifies why the triangles must be similar. To show triangles are similar, it is sufficient to show that the three sets of corresponding sides are in proportion. Investigating similar triangles and understanding proportionality. Sidesideside sss if three pairs of corresponding sides are in the same ratio then the triangles are similar.
Use several methods to prove that triangles are similar. How to prove similar triangles with pictures wikihow. Similar triangles can be located any number of places, including one inside the other. Lessons 61, 62, and 63 identify similar polygons, and use ratios and proportions to solve problems. The ratio of the measures of the sides of a triangle is 4. Similar figures are used to represent various realworld situations involving a scale factor for the corresponding parts. As mentioned above, similar triangles have corresponding sides in proportion. Congruence, similarity, and the pythagorean theorem. Given that the triangles are similar, find the lengths of the missing sides. From the above, we can say that all congruent figures are similar but the similar figures need not be congruent. Also triangles abc and mac have two congruent angles.
Solve similar triangles basic practice khan academy. You will use similar triangles to solve problems about photography in lesson 65. Two triangles are similar if and only if their side lengths are proportional. Similar triangles and ratios notes, examples, and practice test wsolutions this introduction includes similarity theorems, geometric means, sidesplitter theorem, angle bisector theorem, midsegments, and more. Bd is an altitude extending from vertex b to ac ab and bc are the other altitudes of the triangle then, displaying the 3 light triangles facing the same direction, we. They will be asked to determine the general conditions required to verify or prove that two triangles are similar and specifically. Oct 25, 2018 the ratio of any two sides of one triangle has to be equal to the ratio of the corresponding sides in the other triangle. Identifying similar triangles when the altitude is drawn to the hypotenuse of a right triangle, the two smaller triangles are similar to the original triangle and to each other. Student notes full lesson discovering similar triangles. This triangle has a right angle in it so we know that its a right triangle. To be similar by definition, all corresponding sides have the same ratio or all corresponding angles are congruent.
The areas of two similar triangles are 45 cm 2 and 80 cm 2. So setting these two ratios equal, thats the proportion we can set up. Two similar figures have the same shape but not necessarily the same size. Given two similar triangles and some of their side lengths, find a missing side length. Apr 14, 2011 this video is another similar triangles example using the fact of knowing knowing the ratio of corresponding sides are equal. Tenth grade lesson proving that triangles are similar. If the three sets of corresponding sides of two triangles are in proportion, the triangles are similar. Hopefully, the students will remember their recent work with similar polygons and they will respond that everyones triangles are similar. Proving similar triangles refers to a geometric process by which you provide evidence to determine that two triangles have enough in common to be considered similar.
Similar triangles implementing the mathematical practice standards. Similar triangles examples university of washington. Triangles having same shape and size are said to be congruent. Now that weve covered some of the basics, lets do some realworld examples, starting with sarah and the flagpole.
It has two equal sides so its also an isosceles triangle. This occurs because you end up with similar triangles which have proportional sides and the altitude is the long leg of 1 triangle and the short leg of the other similar triangle. An example of two similar triangles is shown in figure 47. If the triangles are similar, what is the common ratio.
Identifying similar triangles identify the similar triangles in the diagram. Triangles scalene isosceles equilateral use both the angle and side names when classifying a triangle. As observed in the case of circles, here also all squares are similar and all equilateral triangles are similar. Solution sketch the three similar right triangles so that the corresponding angles and. You could check with a protractor that the angles on the left of each triangle are equal, the angles at. Also examples and problems with detailed solutions are included. As an example of this, note that any two triangles with congruent legs must be similar to each other. If the perimeter of the triangle is 128 yards, find the length of the longest side. Marquis realizes that when he looks up from the ground, 60m away from the flagpole, that the top of the flagpole and the top of the building line up. And if youre working with a big problem, there may be a third similar triangle inside of the first two. When the ratio is 1 then the similar triangles become congruent triangles same shape and size. Solve similar triangles advanced practice khan academy. If youre behind a web filter, please make sure that the domains.
Find the scale factor of the new pool to an olympic pool. Two triangles are said to be similar when they have two corresponding angles congruent and the sides proportional in the above diagram, we see that triangle efg is an enlarged version of triangle abc i. It turns out the when you drop an altitude h in the picture below from the the right angle of a right triangle, the length of the altitude becomes a geometric mean. Applications ratios between and within similar triangles in the diagram below, a large flagpole stands outside of an office building. All three sides are the same length and all three angles are the same size. Bd is an altitude extending from vertex b to ac ab and bc are the other altitudes of the triangle then, displaying the 3 light triangles. In the case of triangles, this means that the two triangles will have the same angles and their sides will be in the same proportion for example, the sides.
Similar triangles tmsu0411282017 2 we can use the similarity relationship to solve for an unknown side of a triangle, given the known dimensions of corresponding sides in a similar triangle. Use this fact to find the unknown sides in the smaller triangle. Area of similar triangles and its theorems cbse class 10. Similar notesexamples polygons with the same but different polygons are similar if. An olympic pool is rectangular with length 50 meters and width 25 meters. All equilateral triangles, squares of any side length are examples of similar objects.874 847 1220 535 869 1089 85 716 1109 1548 413 223 464 310 1521 1401 719 4 348 214 449 231 882 249 919 797 342 1386 204 135 1181 213 350 272 567 994 95 1303 419 1077 | s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335362.18/warc/CC-MAIN-20220929163117-20220929193117-00469.warc.gz | CC-MAIN-2022-40 | 15,062 | 17 |
https://www.kellylane.com.au/product/9484-timber-wall-sign-60x21-st-barts-palms | math | Timber Wall Sign 60x21 St Barts PALMS
A Peacock Wall Art which incorporates exciting colours and a rustic beachy feel.
• Print design: St Barts “Find me under the Palms.”
• Material: lightweight timber.
• Artwork: digitally printed.
• Sizes: 21 x 60cm.
• Comes ready to hang with hooks attached to the back.
• Presentation: boxed.
Collection:$$$ END OF LINE $$$ | s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780055601.25/warc/CC-MAIN-20210917055515-20210917085515-00123.warc.gz | CC-MAIN-2021-39 | 377 | 9 |
https://jiyuushikan.org/why-must-you-keep-a-constant-volume-of-reactants/ | math | Things Upon Which You Should Ponder:
1. Explain just how this strategy allows you to uncover the mole ratio of reactants.
You are watching: Why must you keep a constant volume of reactants
The optimum ratio, or the mole ratio of the reactants, is the one that produces the highest temperature difference.
2. Why need to you save a consistent volume of reactants?
A better volume of reactants would certainly create a greater temperature. This can be misleading if you use an as a whole greater volume of reactants for one test that then produces a greater temperature than the reduced overall volume of the actual ratio of reactants.
3. It is important that the concentration of the 2 solutions be the same?
It is not essential that the concentrations be the exact same, but it important that you understand the two concentrations. Otherwise, you can’t calculate the number of moles in the amount of solution that you used. It certainly provides things much easier if the concentrations are the same, though.
4. What is intended by the term limiting reagent?
The limiting reagent is the reagent that runs out first in a reaction.
5. Which measurement, temperature or volume, borders the precision of your data?
Volume borders the precision of the data. It is tough to acquire the precise volume that would be the optimum proportion. It is always an approximation from the graph created by the various other quantities.
6. Which reactant is the limiting reagent alengthy the upward sloping line of your graph? Which is the limiting reagent along the downward sloping line?
Systems A is the limiting reagent alengthy the upward sloping line. Systems B is the limiting reagent alengthy the downward sloping line.
7. What physical properties other than temperature readjust might use the technique of continuous variations?
The amount of precipitate developed could be used through the method of continuous variations. However before, precipitate is an extra labor intensive strategy as it hregarding be dried and also filtered. I mean, though, if the reactivity wasn’t exothermic, you would certainly have to usage the precipitate strategy.
8. Why is it even more accurate to usage the suggest of intersection of the two lines to find the mole ratio fairly than the proportion associated through the greatest temperature change?
The intersection of the 2 lines is more than likely closer to the optimum ratio of volumes than any type of of the volumes actually tested. Although the proportion may have actually the biggest temperature change out of all the quantities tested, there can be an untested volume that has actually an also higher temperature adjust. The interarea of the two lines represents a close approximation of the volumes.
See more: Which System Is In A State Of Stable Equilibrium? Stable Equilibrium
9. If the 2 solutions used are not at the same initial temperature, a correction have to be made to uncover the correct adjust in temperature. How need to this be done?
The temperature correction should be via a weighted average. The weighted average takes right into account exactly how a lot of the solution is A and also just how a lot is B. The temperature can then be calculated taking into account what percent of the solution is A and what percentage is B. | s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057508.83/warc/CC-MAIN-20210924080328-20210924110328-00078.warc.gz | CC-MAIN-2021-39 | 3,284 | 21 |
https://www.accountingcoach.com/blog/what-does-it-mean-to-amortize-a-loan | math | To amortize a loan usually means establishing a series of equal monthly payments that will provide the lender with 1) interest based on each month's unpaid principal balance, and 2) principal repayments that will cause the unpaid principal balance to be zero at the end of the loan. While the amount of each monthly payment is identical, the interest component of each payment will be decreasing and the principal component of each payment will be increasing during the life of the loan.
To illustrate, let's assume a lender proposes to amortize a $60,000 loan at 4% annual interest over a 3-year period. This will require 36 monthly payments of $1,771.44 each. The first payment will consist of an interest payment of $200.00 ($60,000 X 4% X 1/12) plus a principal payment of $1,571.44 ($1,771.44 - $200.00). After the first payment is made, the principal balance will be $58,428.56 ($60,000.00 - $1,571.44). The second monthly payment of $1,771.44 will consist of interest of $194.76 ($58,428.56 X 4% X 1/12) plus a principal payment of $1,576.68 ($1,771.44 - $194.76). After the second payment is made, the remaining (or unpaid) principal balance will be $56,851.88.
The 36th and final monthly payment of $1,771.44 will consist of interest of $5.89 (the principal balance after the 35th payment, which will be $1,765.55, times 4% X 1/12) plus a principal payment of $1,765.55. After the 36th payment the loan balance will be zero. In other words, the loan will have been amortized over its 3-year term.
A listing of each month's interest and principal payments (and the remaining, unpaid principal balance after each payment) is referred to as an amortization schedule. | s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256586.62/warc/CC-MAIN-20190521222812-20190522004812-00056.warc.gz | CC-MAIN-2019-22 | 1,672 | 4 |
https://www.fullonstudy.com/2017/06/isothermal-processes-isothermal-equation-for-a-perfect-gas.html | math | If the thermodynamic system is perfectly conducting to the surrounding, and undergoes a physical process in such a way that its tempreture remains constant throughout,the process is said to be isothermal process.
It may be defined as
“ A change in pressure & volume of gas without any change in its tempreture is called an isothermal process or isothermal operation”.
For such process, tempreture of the system remains constant,
i.e. T = constant
& △T = 0
Essential Conditions for Perfect Isothermal Process :-
1. The wall of container must be perfectly conducting.
2.The process of compression or expansion should be so slow so as to provide time for exchange of heat.
Equation of an Isothermal Change :-
Using equation of Vanderwall’s gas
PV = nRT
If n = 1mol, R = constant, T= constant
PV = K(constant)
This is equation of Isothermal Change.
Specific Heat Capacity of Isothermal Change :-
In an Isothermal change, T = constant
then △T = 0
As, specific heat of gas is given by
C = △Q/m△T
∵ △T =0
∴ C = ∞
Therefore, in an Isothermal change apecific heat of gas is infinite. | s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221209216.31/warc/CC-MAIN-20180814170309-20180814190309-00027.warc.gz | CC-MAIN-2018-34 | 1,096 | 23 |
http://mathforum.org/library/drmath/view/54399.html | math | Equation of a Sphere
Date: 3 Jul 1995 23:14:03 -0400 From: Jason Crist Subject: Equation for the graph of a sphere. I was wondering what is the equation for a sphere on a graph with the dimensions x, y, and z? Do you have to use calculus to solve a system for the intersection of such spheres? Thank you for your time. JRC
Date: 13 Jul 1995 22:25:32 -0400 From: Dr. Ken Subject: Re: Equation for the graph of a sphere. Hey there! The equation for a sphere of radius 1 with center at the origin is x^2 + y^2 + z^2 = 1. In general, the equation for a sphere of radius R with center at (a,b,c) is (x-a)^2 + (y-b)^2 + (z-c)^2 = R^2. If you're looking at the intersection of two spheres, the intersection is always a circle, and once you know that it's usually not too hard to figure out what the circle is. If, for instance, the two spheres are centered at (a,b,c) and (A,B,C), then the circle of intersection will be in the plane (a-A)x + (b-B)y + (c-C)z = k for some constant k. If you find just one point that's common to both spheres, this will pinpoint k, and then you can find the intersection of the plane and one of the spheres. -K
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved. | s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794865456.57/warc/CC-MAIN-20180523063435-20180523083435-00571.warc.gz | CC-MAIN-2018-22 | 1,233 | 6 |
https://www.wallstreetprep.com/knowledge/equity-multiplier/ | math | What is the Equity Multiplier?
The Equity Multiplier measures the proportion of a company’s assets funded by its equity shareholders as opposed to debt providers.
Equity Multiplier Formula
How to Calculate the Equity Multiplier (Step-by-Step)
The formula for calculating the equity multiplier consists of dividing a company’s total asset balance by its total shareholders’ equity.
- Equity Multiplier = Average Total Assets ÷ Average Total Shareholders’ Equity
For instance, if a company has an equity multiplier of 2x, the takeaway is that financing is split equally between equity and debt.
DuPont Analysis and Equity Multiplier
The equity multiplier is one of the ratios that make up the DuPont analysis, which is a framework to calculate the return on equity (ROE) of companies.
In the three-step DuPont analysis variation, the equity multiplier is multiplied by the net profit margin and asset turnover.
3-Step DuPont Analysis Formula
- DuPont Analysis = Net Profit Margin × Asset Turnover × Equity Multiplier
- Net Profit Margin = Net Income ÷ Revenue
- Asset Turnover = Revenue ÷ Average Total Assets
- Equity Multiplier = Average Total Assets ÷ Average Shareholders’ Equity
Revenue and net income each represent income statement metrics, meaning that they measure across a period of time – whereas assets and equity are balance sheet metrics, which are the carrying values at a specific point in time.
To match the timing between the denominator and numerator among all three ratios, the average balance is used (i.e. between the beginning and end of period value for balance sheet metrics). | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949642.35/warc/CC-MAIN-20230331113819-20230331143819-00434.warc.gz | CC-MAIN-2023-14 | 1,617 | 17 |
https://mathguide.com/lessons2/InscribedAngles.html | math | Inscribed Angle and Arc Relationship
An inscribed angle is an angle that has its vertex on a circle and its sides are chords of the same circle. An inscribed angle can be seen here.
The diagram above shows inscribed angle ABC. The vertex of the angle, point-B, rests on the circle. The sides of the angle are chord AB and chord BC. The arc intercepted by the angle is arc AC.
Within the next section, we will examine the relationship between an inscribed angle and its arc.
The relationship between an inscribed angle and its opposite arc can be seen below.
This relationship will be demonstrated by viewing the examples below.
Determine the measure of angle HMS (the x-value) within the diagram that follows.
We know from our section on the Central Angle and Arc Relationship that a central angle and its intercepted arc are equal in measure. This means that arc HS is equal to 40 degrees.
Notice that arc HS is the intercepted arc of inscribed angle HMS. We also know that the measure of an inscribed arcs is equal to half of its intercepted angle, which would make angle HMS. Therefore, angle HMS must be 1/2 of 40 degrees or 20 degrees.
Determine the measure of angle CAB (the x-value) within the diagram that follows.
Notice how chord AC passes through the center of the circle, point G. This means that chord AC is a diameter of circle G. It also means that arc AC is a semi-circle and that its measure is 180 degrees. Arc AB and arc BC together have a sum of 180 degrees. This means that arc BC must be 60 degrees.
If we look closely at the diagram, we can see inscribed angle CAB and its intercepted arc, which is arc BC. Since inscribed angles are half the measure of their intercepted arc, angle CAB is equal to 1/2(60 degrees), which is 30 degrees.
View this instructional video.
This quiz will check for your understanding.
There are no activities at this time. | s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233506686.80/warc/CC-MAIN-20230925051501-20230925081501-00376.warc.gz | CC-MAIN-2023-40 | 1,873 | 15 |
https://usmul.com/1419/ | math | 3250 rounded to the nearest hundred is 3300. 6 ones and 8 hundreds across 19.
9 hundreds 6 tens and 1 one down 13.
21 thousands 28 hundreds 14 tens 37 ones. 4 tens and 6 ones across 20. It takes him 4 min to type 5 8 page of the report at this rate how many minutes does it take cedrick to type 1 full page. The 2 in 323 5.
7 tens and 5 ones across. Here you can enter any number of thousands hundreds tens ones tenths hundredths and thousandths and then we will tell you what the grand total number will be. 9 tens and 4 ones down 14.
The place values are ones tens hundreds thousands ten thousands hundred thousands and millions respectively. What is 21 thousand 28 hundreds 14 tens and 37 ones. What is 21 thousand 28 hundreds 14 tens and 37 ones.
Qr 21 and rs x 10. This tool can round very big numbers to a very high precision. Every digit after becomes a zero.
We round your numbers into ones tens hundreds thousands tens of thousands hundreds of thousands millions tenths hundredths thousandths ten thousandth. 8 tens and 2 ones across 18. 26 seconds ago cedrick is writing a report.
Is that digit greater than or equal to five. 14 seconds ago help me. Identify the tens digit.
Increase the hundreds digit by one so 2 becomes 3. Find the value of x. The 3 in 323 5.
3 ones 4 hundreds and 5 tens across 22. This compilation of printable units place value worksheets provides an ideal platform for 1st grade and 2nd grade children comprehend the concept of ones tens and hundreds place value. Identify the next smallest place value.
5 hundreds 3 tens and 7 ones down 17. Use this online calculator to find the place value of each digits in a number. 7 ones 8 thousands and 2 hundreds across 21.
No so round down. Asked by wiki user. Each place has a value of 10 times the place to its right.
Place value is defined as the numerical value or the position of a digit in a number series. Its part of an exam please. Please enter your place values below and press calculate to get the total number.
19 thousands 46 hundreds 32 tens 57 ones how much is in total 2. An extensive variety of activities include identifying place values writing equivalent place values and much more. Free tool to round numbers to thousands hundreds tens tenths hundredths thousandths fractions or many other levels of precision using the popular rounding methods.
3 ones down 15. Wiki user answered. 1000s 100s 10s 1s 1 10th 1 100th 1 1000th.
The tens digit stays. Round to the nearest ten. | s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488534413.81/warc/CC-MAIN-20210623042426-20210623072426-00542.warc.gz | CC-MAIN-2021-25 | 2,470 | 16 |
http://paydayloanslexington.gq/samer/pythagorean-theorem-essay-3461.php | math | Thus, he used the result that parallelograms are double the triangles with the same base and between the same parallels. Draw CJ and BE. The two triangles are congruent by SAS. The same result follows in a similar manner for the other rectangle and square. Katz, Click here for a GSP animation to illustrate this proof. The next three proofs are more easily seen proofs of the Pythagorean Theorem and would be ideal for high school mathematics students.
In fact, these are proofs that students could be able to construct themselves at some point. The first proof begins with a rectangle divided up into three triangles, each of which contains a right angle. This proof can be seen through the use of computer technology, or with something as simple as a 3x5 index card cut up into right triangles. Figure 4 Figure 5. It can be seen that triangles 2 in green and 1 in red , will completely overlap triangle 3 in blue.
Now, we can give a proof of the Pythagorean Theorem using these same triangles. Compare triangles 1 and 3. Angles E and D, respectively, are the right angles in these triangles. By comparing their similarities, we have. We have proved the Pythagorean Theorem. The next proof is another proof of the Pythagorean Theorem that begins with a rectangle. Thus, triangle EBF has sides with lengths ka, kb, and kc. By solving for k, we have. The next proof of the Pythagorean Theorem that will be presented is one that begins with a right triangle.
In the next figure, triangle ABC is a right triangle. Its right angle is angle C. Triangle 1 Compare triangles 1 and 3: Triangle 1 green is the right triangle that we began with prior to constructing CD.
Triangle 3 red is one of the two triangles formed by the construction of CD. Figure 13 Triangle 1. Compare triangles 1 and 2: Triangle 1 green is the same as above. Triangle 2 blue is the other triangle formed by constructing CD. Its right angle is angle D.
Figure 14 Triangle 1. The next proof of the Pythagorean Theorem that will be presented is one in which a trapezoid will be used. By the construction that was used to form this trapezoid, all 6 of the triangles contained in this trapezoid are right triangles. We have completed the proof of the Pythagorean Theorem using the trapezoid. The next proof of the Pythagorean Theorem that I will present is one that can be taught and proved using puzzles.
These puzzles can be constructed using the Pythagorean configuration and then, dissecting it into different shapes. Before the proof is presented, it is important that the next figure is explored since it directly relates to the proof. In this Pythagorean configuration, the square on the hypotenuse has been divided into 4 right triangles and 1 square, MNPQ, in the center.
Each side of square MNPQ has length of a - b. This gives the following: As mentioned above, this proof of the Pythagorean Theorem can be further explored and proved using puzzles that are made from the Pythagorean configuration. Students can make these puzzles and then use the pieces from squares on the legs of the right triangle to cover the square on the hypotenuse. This can be a great connection because it is a "hands-on" activity.
Students can then use the puzzle to prove the Pythagorean Theorem on their own. To create this puzzle, copy the square on BC twice, once placed below the square on AC and once to the right of the square on AC as shown in Figure Proof Using Figure Thus the diagonals CE and EH are both equal to c. Pieces 4 and 7, and pieces 5 and 6 are not separated. By calculating the area of each piece, it can be shown that. So shocked were the Pythagoreans by these numbers, they put to death a member who dared to mention their existence to the public.
It would be years later that the Greek mathematician Eudoxus developed a way to deal with these unutterable numbers. Pythagoras of Samos Who is Pythagoras? He was born to Mnesarchus and Pythais. He was one of either three or four children, there is proof for both of these accounts. At a very early age, Pythagoras learned to play the lyre and recite Homer.
Pythagoras also wrote poetry at a very early age. Pythagoras got his education from three philosophers, the most important mathematically being Anaximander. Around BC Pythagoras went on a journey to Croton, where he established a philosophical and religious school.
Pythagoras was the head of the inner circle of the society, his inside followers were called mathematikoi. The mathematikoi had to follow very strict laws that Pythagoras believed. The five things that Pythagoras believed very deeply were 1 that at its deepest level, reality is mathematical in nature, 2 that philosophy can be used for spiritual purification, 3 that the soul can rise to union with the divine, 4 that certain symbols have a mystical significance, and 5 that all brothers of the order should observe strict loyalty and secrecy.
Both men and women were allowed to join the society. Pythagoras was not acting as a modern research group at a major university.
The Pythagorean theorem states that: "The area of the square built on the hypotenuse of a right triangle is equal to the sum of the squares on the remaining two sides." According to the Pythagorean Theorem, the sum of the areas of the red and yellow squares is equal to the area of the purple square.
One of the topics that almost every high school geometry student learns about is the Pythagorean Theorem. When asked what the Pythagorean Theorem is, students will often state that a2+b2=c2 where a, b, and c are sides of a right triangle.
Fermat's Last Theorem - Rationale: The pythagorean theorem is a simple equation that has been taught to pupils from the beginning of middle school. a2+b2=c2 is the basic formula to calculate any one of the sides on a right angle triangle. The Pythagorean Theorem Essay Sample Introduction a 2 + b 2 = c 2 where a and b are the sides of a right triangle and c is the hypotenuse is the answer most students will give when asked to define the Pythagorean Theorem.
One theorem that is particularly renowned is the Pythagorean Theorem. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides of any right triangle. Essay, Research Paper: Pythagorean Theorem Mathematics Free Mathematics research papers were donated by our members/visitors and are presented free of charge for informational use only. | s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547584445118.99/warc/CC-MAIN-20190124014810-20190124040810-00020.warc.gz | CC-MAIN-2019-04 | 6,413 | 17 |
http://centraledesmaths.uregina.ca/QandQ/topics/the%20salinon%20of%20archimedes | math | I am trying to find the English translation of "Le salinon d'Archimèdre" and would appreciate any help. This is a figure, presumably studied by Archimedes, created from 4 semi-circles. Since I can't draw it for you, I will try to describe it with the help of the 5 collinear, horizontal points below.
. . . . . A B C D E
A semi-circle is constructed on AE as diameter (let's say above AE).
Two more semi-circles are then constructed with diameters AB and DE on the same side of the line AE as the first semi-circle (above it). Finally, a fourth semi-circle is constructed on diameter BD, this time on the opposite side of the line AE from the others (i.e. below the line).
These semi-circles and the region enclosed by them constitute what is called in French "Le salinon d'Archimèdre".
If you know the English name of this curve I would appreciate it if you let me know. | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949107.48/warc/CC-MAIN-20230330070451-20230330100451-00645.warc.gz | CC-MAIN-2023-14 | 873 | 6 |
http://www.expertsmind.com/library/determining-essential-sample-size-for-health-insurance-523139.aspx | math | Already have an account? Get multiple benefits of using own account!
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Q1) Owner of Limp Pines Resort desired to know average age of its clients. Random sample of 25 tourists is taken. It illustrates a mean age of 46 yrs. with stand. dev. Of 5 yrs. Width of a 98% Cl for true mean cliet age is approximately..............yrs.
a) +or-2.06 b) +or-2.33 c) +or-2.49 d) +or-2.79
Q2) What sample size would be needed to evaluate true proportion of American female business executives who prefer title "Ms.", with an error of ±0.025 and 98 percent confidence
Q3) Financial institution desires to evaluate mean because balances owed by its credit card customers. Population standard deviation is evaluated to be $300. If 98% confidence interval is used and interval of +or-$75 is desired, how many cardholders must be sampled?
Q4) Jolly Blue Giant Health Insurance is concerned about rising lab test costs and would like to know what proportion of lab test for prostate cancer are actually proven right through subsequent biopsy. JBHI demands sample large sufficient to make sure error of +or-2% with 90% confidence. Determine the essential sample size?
Suppose that qx is equal to a constant q for all x. Find expressions in terms of q and n for (a) npx, (b) ex. Do you think that this gives a realistic life table? Why or why
Let X1,..., Xn be iid random variables with expected value 0, variance 1, and covariance Cov[Xi, Xj] = ρ. Use Theorem 5.13 to find the expected value and variance of the sum Y
Assuming a normal distribution construct a 95% confidence interval estimate for the mean value of all greeting cards in the store's inventory. Suppose there are 2,500 greeti
Someone gives you 10 to 1 odds that you cannot roll a double number with the roll of a pair of dice. You win $10 if you succeed and you lose $1 if you fail. What is the expe
The resources use data and statistics to support answers to the same question, but they reach opposite conclusions! The textbook authors use the Gini Index to argue that inc
If the manufacturer sells the parts in packages of 10 parts, what are the mean and standard deviation of the number of useable parts in a package?
Draw two pie charts, which allow the total yearly exports to be compared. Explain the trend in the export of fish as shown in the two pie charts.
Weights are distributed normal with a mean of 132 pounds and a standard deviation of 27.4 pounds. In a random sample of 150, how many of them would be expected to weigh betw
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https://boundbutinfinite.wordpress.com/2013/04/24/rob-pi-infinity/ | math | Pi. π. 3.14159. A mathematical constant; an infinite number – the ratio of a circle’s circumference to its diameter. Records of its use date back to Babylon and Egypt, as early as 1900 BCE, and both civilizations developed approximations within 1% of pi’s true value, and the number has proved infinitely important to both maths and science – whilst it’s use can be as simple as helping to calculate the diameter of a circle in a maths class, or for laying foundations to a circular building, we have been able to use the number for far greater purposes: in calculating the circumference of the earth, for example.
The most interesting thing about pi, however, is its irrational nature: it can never be expressed as a ratio of two integers – thus, it’s decimal representation never ends, and it can never settle into a permanent repeating pattern. As of late 2011, scientists have extended pi’s decimal representation to THIRTEEN TRILLION digits. That amount alone is incomprehensible to all but the most skilled mathematicians – I can’t begin to comprehend its enormity.
But here’s the rub: is pi truly infinite? If so, what possible information does the number hold? And if not, what impact would that have on every aspect of the scientific world?
If pi is a infinite, non-repeating decimal, then the implications are simple – every single possible number combination that could ever exist, exists within pi. If you were to convert into the number into ASCII (American Standard Code for Information Interchange; this translates figures into text) you could find any and all possible data within it – the name of every person you will ever meet, love, hate and the birthdays; the manner of your death, and the exact time and date it will take place; answers to any and all questions that could possibly be asked; even the entire works of William Shakespeare in exact order of publication: letter by precisely placed letter. The implausibility of this is obvious, but such is the incomprehensible nature of infinity that we can never truly understand what pi holds – buried within pi is the eighth Harry Potter book, the name of the thirteenth month, and details on how to build a time machine. All information that does or could ever exist is held with this number, but this, however, is reliant on one key principle: that pi does remain irrational.
If, as previous mentioned, we ever found a recurring pattern in pi, buried somewhere after 20 trillion digits of non-recurring chaos, then maths as we know it would fall apart – all calculation based around our approximation of pi would be wrong, albeit by a fraction of a decimal place. It is, however, tiny, minute miscalculations like this that make up the foundations of maths and physics – such a discovery would revolutionise both topics. On top of this, theories regarding it containing all possible information would be proved incorrect, and whilst this may again see trivial, it would reform the boundaries of infinity – whilst 20 trillion digits may seem an incomprehensible number, it would hold much less “information” then it’s previously assumed “infinite” form.
It is, however, hypotheses like this that build up the foundations of science – all previous data indicates that pi is infinite and will continue to prove itself to be, just like all previously acquired data indicates the existence of gravity; of our planet’s place in orbit around the sun; of the length of time homo sapiens have existed since their evolution from homo erectus. And if, one day, our theories about pi were proved wrong, then scientists would see it not as a setback, but an incentive to work out the truth. After all, we’ve been proved wrong before. But that is another topic for another day.
Conclusion (TL;DR): Pi, as far as we know, is an infinite number, and a non-recurring one at that, thus containing all possible information.
Until next time, | s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039742020.26/warc/CC-MAIN-20181114125234-20181114151234-00114.warc.gz | CC-MAIN-2018-47 | 3,947 | 8 |
https://afm.journal.fi/article/view/137788 | math | A fibered Tukia theorem for nilpotent Lie groups
Keywords:Uniform quasiconformal groups, uniform quasisimilarity groups, nilpotent Lie groups
AbstractWe establish a Tukia-type theorem for uniform quasiconformal groups of a Carnot group. More generally we establish a fiber bundle version (or foliated version) of Tukia theorem for uniform quasiconformal groups of a nilpotent Lie group whose Lie algebra admits a diagonalizable derivation with positive eigenvalues. These results have applications to quasi-isometric rigidity of solvable groups [DFX].
How to Cite
Dymarz, T., Fisher, D., & Xie, X. (2023). A fibered Tukia theorem for nilpotent Lie groups. Annales Fennici Mathematici, 48(2), 653–680. https://doi.org/10.54330/afm.137788
Copyright (c) 2023 Annales Fennici Mathematici
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100112.41/warc/CC-MAIN-20231129141108-20231129171108-00476.warc.gz | CC-MAIN-2023-50 | 885 | 7 |
https://math.iisc.ac.in/seminars/2021/2021-10-20-bin-guo.html | math | Title: On uniform estimates for complex Monge-Ampere equations
Speaker: Bin Guo (Rutgers University)
Date: 20 October 2021
Time: 9:00 pm
Venue: MS teams (team code hiq1jfr)
We will discuss the $L^\infty$ estimates for a class of fully nonlinear partial differential equations on a compact Kahler manifold, which includes the complex
Monge-Ampere and Hessian equations. Our approach is purely based on PDE methods, and is free of pluripotential theory. We will also talk about some generalizations
to the stability of MA and Hessian equations. This is based on joint works with D.H. Phong and F. Tong. | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100047.66/warc/CC-MAIN-20231129010302-20231129040302-00828.warc.gz | CC-MAIN-2023-50 | 600 | 8 |
https://kidsworksheetfun.com/adding-and-subtracting-polynomials-worksheet-multiple-choice/ | math | Adding And Subtracting Polynomials Worksheet Multiple Choice
Adding And Subtracting Polynomials Worksheet Multiple Choice. Understand that polynomials form a system analogous to the integers in that they are closed under these Multiply binomials by polynomials practice khan academy.
Choose the one alternative that best completes the statement or answers the question. Name class date polynomials multiple choice post test. 46 square yards 51) multiply using the rule for finding the product of the sum and difference of two.
Adding And Subtracting Polynomials Author:
This is so she can chill for the remainder of the summer. Adding and subtracting polynomials sophia learning. 120 square yards d) x2 + 10x + 24;
Students Have To Find The Sum Or Difference For Each Set Of Polynomials Expressions.
Topic 10 adding and subtracting fractions. Compare numbers and unlike denominators worksheet pdf practice problems can turn cookies are easier to create a. Adding and subtracting polynomials multiple choice questions.
Multiply Binomials By Polynomials Practice Khan Academy.
120 square yards c) x2 + 10; Adding and subtracting polynomials is not complicated. What is the procedure for subtracting polynomials:
This Worksheet Provides An Excellent Activity For A Specific Part Of The Topic Algebraic Expression.
Which of the following expressions are monomials with degree 2? To add polynomials in algebra, we group like terms and simplify. This free worksheet contains 10 assignments each with 24 questions with answers.
46 Square Yards 51) Multiply Using The Rule For Finding The Product Of The Sum And Difference Of Two.
Adding and subtracting polynomials 2 multiple choice. 1) (5 + 5 n3) − (1. Aug 03, 22 09:39 pm. | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100626.1/warc/CC-MAIN-20231206230347-20231207020347-00281.warc.gz | CC-MAIN-2023-50 | 1,719 | 13 |
http://mobilec.org/publication/journal/j_SP2.html | math | Harry H. Cheng
The handling of complex numbers in the CH programming language will be described in this paper. Complex is a built-in data type in CH. The I/O, arithmetic and relational operations, and built-in mathematical functions are defined for both regular complex numbers and complex metanumbers of ComplexZero, ComplexInf, and ComplexNaN. Due to polymorphism, the syntax of complex arithmetic and relational operations, and built-in mathematical functions are the same as those for real numbers. Besides polymorphism, the built-in mathematical functions are implemented with a variable number of arguments, which greatly simplies computations of different branches of multiple-valued complex functions. The valid lvalues related to complex numbers are defined. Rationales for the design of complex features in CH are discussed from language design, implementation, and application points of views. Sample CH programs show that a computer language which does not distinguish the sign of zeros in complex numbers can also handle the branch cuts of multiple-valued complex functions effectively so long as it is appropriately designed and implemented. | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100769.54/warc/CC-MAIN-20231208180539-20231208210539-00657.warc.gz | CC-MAIN-2023-50 | 1,155 | 2 |
https://classnotes.org.in/class12/chemistry12/chemical-kinetics/half-life-period-reaction/ | math | Half life period of a reaction is defined as the time during which the concentration of a reactant is reduced to half of its initial concentration.
The time in which half of a reaction is completed. It is generally denoted as t½
The half life period of a first order reaction may be calculated as given below:
The first order rate equation for the reaction
A ———–> Products
Now, half life period corresponds to time during which the initial concentration, [A]0 is reduced to half i.e.
[A] = [A]0 /2 at t= t½
Then half life period, t½ becomes
Thus, half life period of a first order reaction is independent of the initial concentration of the reactant. Half life period for the first order reaction is inversely proportional to the rate constant.
(i) time required to complete 1/3 of the reaction will be given as:
[A]o = a , [A] = a – a/3=2/3a
(ii) time required to complete 3/4 of the reaction will be
[A]o = a , [A] = a – 3/4 a = 1/4 a
Half Life period of zero order and second order reactions
The integrated rate equation is ,
kt = [A]o -[A]
For half life period, t½ , [A] = [A]0/2
t½ = [A]o /2k
Similarly for second order reaction,
Debajyoti Roy says
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simran kaur says
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Keep going with this smile ☺ | s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224648911.0/warc/CC-MAIN-20230603000901-20230603030901-00342.warc.gz | CC-MAIN-2023-23 | 1,552 | 26 |
https://www.physicsforums.com/threads/faradays-law-very-tricky-question.695878/ | math | 1. The problem statement, all variables and given/known data A straight infinitly long wire with a current of I upwards is stationary. A rectangular loop with length a and height b is moved to the right with constant speed of v across the wire in the plane of the paper. At t=0 the right edge of the loop is exactly at the same location of the wire. 2. Relevant equations What is the flux through the loop as a function of the time? What is the induced emf as a function of the time? 3. The attempt at a solution Well I have 2 main problems here: 1. At any moment up untill the time that all the loop has passed to the right of the wire I'm facing the fact that some part of the loop (the part that is to the right of the wire) is under the influence of a magnetic field in the direction which is into the paper, and another part (the part that's to the left of the wire) is under the influence of a magnetic field in the direction which is out of the paper - how can I deal with this problem in terms of my integration? 2. If I want to switch the integral from dA to dr (where r is the distance from the wire) - I have again one part of the loop that is coming towards the wire while another part of the loop is moving away from the wire (At least until the whole loop passes through the wire) - How can I deal with this fact when I try to write the integration limits? This is a bonus question and isn't mandatory but it pisses me off! | s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864039.24/warc/CC-MAIN-20180621055646-20180621075646-00535.warc.gz | CC-MAIN-2018-26 | 1,437 | 1 |
http://www.mathworksheetsworld.com/bytopic/ratios.html | math | [advance to content]
Click on the Ratios Worksheets & Proportions worksheet set you wish to view below.
What are ratios and proportions?
A ratio is a relationship between two or more quantities expressed as a fraction (3/5) or in this form 1:3 - which is read as one to three (the colon ':' is read as 'to').
A proportion is similar to a ratio, but usually has a one for the denominator. So, the ratio, 3:4 could also be written as the proportion, .75 to 1. Proportion also has a general meaning - a relationship where one quantity varies directly with another is called proportional.
How much food a family needs is proportional to the number of people in the family. As the number of people go up, the amount of food also increases. However, the number of carpets in a house is usually not proportional to the number of people. A larger family might or might not have more carpets, you can't tell.
An interesting fact about ratios and proportions.
You can generate the golden ratio on a hand held calculator by starting with any number. Use the 1/x key to get the inverse. Now add one to that.
Take your new answer and repeat the process, 1/x first, then add 1.
The intermediate values will get closer and closer to Φ.
How are ratios used in the real world?
Ratios are used whenever we want to calculate one quantity when we know some other (when they vary proportionally). For instance, concrete is mixed at the ratio of 1 part water (by weight) to 4 parts concrete mix. The 1:4 ratio holds true for a 5 gallon pail of concrete as much as a 20 gallon wheelbarrow.
This is common in cooking, when you have a recipe for one quantity and you want to make some other amount. When you cut all the amounts of ingredients in half, you are reducing the proportion of them all by half. This is true for all simple ratios, each part has to be multiplied (or divided) by the same number for the ratio to remain true.
So, if you have a ratio of 1:4 (as in the concrete example) you could convert it to the equivalent ratios- 2:8, 5:20 and so on, as long as you multiplied each part by the same number.
A basic problem with ratios.
The average grades in math class for a particular school district are given by the following proportion in this order - A:B,C,D - as 5:15. This means that for every 5 students that gets an A, 15 students will get a lower grade. If this holds for a class of 40 students, how many will get A's?
Since 5 + 15 equals 20, the ratio given is for every 20 students. That is, out of 20 students, 5 will get A's and 15 will get something else. Since 40 is twice 20, we only need to multiply our ratio by two.
This gives, 5:15 X 2 = 10:30. (10 + 30 = 40) So, out of 40 students, we would expect 10 to get A's.
Who invented ratios and proportions?
Ratios and proportions have been known since before recorded history. One particular one was explored by the ancient Greeks - the Golden Ratio.
This can be seen in the following line drawing, where the length of the line segment BC is in the same ratio to AB as AB is to the whole line.
Algebraically, the relationship is: (ab+bc)/ab = ab/bc and there is important enough in mathematics to get it's own symbol, the Greek letter phi, Φ. Phi is equal to about 1.618033... Phi is irrational, and the digits go on infinitely, never settling down into a predictable pattern. | s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917118310.2/warc/CC-MAIN-20170423031158-00343-ip-10-145-167-34.ec2.internal.warc.gz | CC-MAIN-2017-17 | 3,330 | 22 |
https://therebelgeek.com/blog/ | math | By The Rebel
#9 Web Page, Landing Page, Splash Page or Website?
Web Page, Landing Page, Splash Page or Website?What's the difference and which one do I need?September 7, 2018 by Erin[...]
#8 People hate to read, so train them with videos instead of manuals
In my last video I discussed How to Set Your Vendors Up for Success, and one of the ways I[...]
#7 If Your Vendors Are Successful…You’ll Be Successful, Too
#7. If Your Vendors Are Successful...You'll Be Successful, TooBringing people into your business to work along side you is not[...] | s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550249530087.75/warc/CC-MAIN-20190223183059-20190223205059-00010.warc.gz | CC-MAIN-2019-09 | 548 | 7 |
http://www.metaglossary.com/meanings/769902/ | math | The total of fixed costs and variable costs.
the sum of variable costs and fixed costs.
the sum of all fixed costs and variable costs
Total Costs is the total sum of all money owed by the business and calculated as fixed Costs plus direct costs.
total fixed costs to the total variable costs
All the costs of operating a firm; total variable costs plus total fixed costs. | s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368703728865/warc/CC-MAIN-20130516112848-00098-ip-10-60-113-184.ec2.internal.warc.gz | CC-MAIN-2013-20 | 371 | 6 |
https://www.scribd.com/document/44309669/Feb-423-Lesson-1-and-2 | math | This action might not be possible to undo. Are you sure you want to continue?
DEPARTMENT OF ENVIRONMENTAL AND BIOSYSTEMS ENGINEERING
COURSE CODE & TITLE: FEB 423 HEAT AND MASS TRANSFER
B.SC. IN ENVIRONMENTAL AND BIOSYSTEMS ENGINEERING
Mr. Emmanuel Beauttah Kinyor Mutai Dip. Agric. Engin. (Egerton College), B.Sc. Agric. Engin. (Egerton Univ.), M.Sc. Agric. Engin. (UoN)
OFFICE: Main Campus NUCLEAR SCIENCE ROOM No. 19 TEL: 318262 EXT 28471 0723630157 Environmental & Biosystems Building 2nd Floor Tel: firstname.lastname@example.org or email@example.com
Tuesdays Fridays Thursdays Examinations
10:00 am – 1:00 pm 11:00 am – 1:00 pm 2:00 pm Main Campus office
Cat 6th Week Assignments Laboratory Project Modeling & Simulation Final Exam Total 1
15% 5% 5% 5% 70% 100%
Convection. and Radiation.1 What is Heat Transfer? Thermal energy is related to the temperature of matter. When you touch a hot object. Any energy exchange between bodies occurs through one of these modes or a combination of them. this mode uses the electromagnetic radiation emitted by an object for exchanging heat. and is denoted by q. For a given material and mass. Convection uses the movement of fluids to transfer heat.2 Three Modes of Heat Transfer There are three modes of heat transfer: • • • Conduction. the heat you feel is transferred through your skin by conduction. The rate of heat transfer is measured in watts (W). thermal energy transfers from the one with higher temperature to the one with lower temperature. Conduction is the transfer of heat through solids or stationery fluids. 1. Units and Conversion Factors for Heat Measurements SI Units 1J 1 J/s or 1 W 1 W/m2 English Units 9. the greater its thermal energy.1 Conduction Conduction is at transfer through solids or stationery fluids.3171 Btu/h ft2 Thermal Energy (Q) Heat Transfer Rate (q) Heat Flux (q") 1. Two mechanisms explain how heat is transferred by conduction: 2 . When two bodies are at different temperatures.4787×10-4 Btu 3. Radiation does not require a medium for transferring heat. Table 1 shows the common SI and English units and conversion factors used for heat and heat transfer rates.LESSON 1 Overview of Heat Transfer 1.2. Heat is typically given the symbol Q.4123 Btu/h 0. equal to joules per second. and uses q" for the symbol. is measured in watts per area (W/m2). and is expressed in joules (J) in SI units. Table 1. Heat always transfers from hot to cold. or the rate of heat transfer per unit area. The heat flux. the higher the temperature. Heat transfer is a study of the exchange of thermal energy through a body or between bodies which occurs when there is a temperature difference.
where the electrons are moving at the same average velocity. where all the atoms are vibrating with the same energy. equilibrium is reached.2. which do not have many free electrons. the hot side of the solid experiences more vigorous atomic movements. the faster electrons give off some of their energy to the slower electrons. As the electrons undergo a series of collisions. The mechanism is identical to the electron collisions in metals. The vibrations are transmitted through the springs to the cooler side of the solid. analogous to springs as shown in Figure 1.1. through a series of random collisions. Eventually. Conduction through electron collision is more effective than through lattice vibration.2 Conduction by particle collision In fluids. Eventually. 3 .1 Conduction by lattice vibration Figure 1. Lattice vibration and 2. heat is conducted through stationery fluids primarily by molecular collisions. The electrons in the hot side of the solid move faster than those on the cooler side. In solids. This scenario is shown in Figure 1. this is why metals generally are better heat conductors than ceramic materials. Particle collision. have free electrons. atoms are bound to each other by a series of bonds.1. which are not bound to any particular atom and can freely move about the solid. they reach equilibrium. conduction occurs through collisions between freely moving molecules. Conduction through solids occurs by a combination of the two mechanisms. Figure 1. especially metals. Solids. When there is a temperature difference in the solid.
which is then carried away by fluid movement such as wind.4. 1. The negative sign in Eqn. the rate of heat transfer is enhanced. The density of fluid decrease as it is heated. Warm fluids surrounding a hot object rises.The effectiveness by which heat is transferred through a material is measured by the thermal conductivity. has a high conductivity.2 Convection Convection uses the motion of fluids to transfer heat. A good conductor.1 ensures that this convention is obeyed. which can draw more heat away from the surface. The result is a circulation of air above the warm surface. In heat transfer. and a negative q represents heat leaving the body. has a low conductivity. and is replaced by cooler fluid. The warm fluid is replaced by cooler fluid. hot fluids are lighter than cool fluids. or an insulator. 1.3 Heating curve Where A is the cross-sectional area through which the heat is conducting. a hot surface heats the surrounding fluid. In a typical convective heat transfer. 4 .2. k. Conductivity is measured in watts per meter per Kelvin (W/mK). The rate of heat transfer by conduction is given by: (Eq. Since the heated fluid is constantly replaced by cooler fluid. T is the temperature difference between the two surfaces separated by a distance ∆x (see Figure 1.3). Natural convection (or free convection) refers to a case where the fluid movement is created by the warm fluid itself. 1. as shown in Figure 1.1) Figure 1. a positive q means that heat is flowing into the body. a poor conductor. such as copper. thus.
Infrared (Ir). Ultraviolet (uv). having 5 . and T∞ is the ambient or fluid temperature. is why we feel warmer in the sun than in the shade. We all experience radiative heat transfer everyday. and is determined by factors such as the fluid density. winter day feel much colder than a calm day with same temperature.2. Wind blowing at 5 mph has a lower h than wind at the same temperature blowing at 30 mph.Figure 1. 1. it is the only form of heat transfer present in vacuum. solar radiation. h. The electromagnetic spectrum classifies radiation according to wavelengths of the radiation. Radiative heat transfer occurs when the emitted radiation strikes another body and is absorbed. is the measure of how effectively a fluid transfers heat by convection. Natural wind and fans are the two most common sources of forced convection. Visible light. The rate of heat transfer from a surface by convection is given by: (Eq. It uses electromagnetic radiation (photons). which travels at the speed of light and is emitted by any matter with temperature above 0 degrees Kelvin (-273 °C). Tsurface is the surface temperature. Forced convection is what makes a windy.3 Radiation Radiative heat transfer does not require a medium to pass through. The heat loss from your body is increased due to the constant replenishment of cold air by the wind. thus. Main types of radiation are (from short to long wavelengths): • • • • • • • Gamma rays. viscosity. and velocity. and Radio waves. X-rays.4 Natural convection Forced convection uses external means of producing fluid movement. Convection coefficient. absorbed by our skin. 1. It is measured in W/m2K. Microwaves.2) Where A is the surface area of the object. X-rays. Radiation with shorter wavelengths are more energetic and contains more heat.
T is the temperature of the body. Hotter objects. Most "hot" objects. equal to 5. having wavelengths on the order of meters. as we all know. emit more energetic radiation including visible and UV. The emitted radiation strikes a second surface. can readily pass through concrete walls. The percentage of the incident radiation that is absorbed is called the absorptivity. α. The emissivity has a value between zero and 1. Figure 1.5 Interaction between a surface and incident radiation The incident radiation is determined by the amount of radiation emitted by the object and how much of the emitted radiation actually strikes the surface. 1. radio waves. 1. A second characteristic which will become important later is that radiation with longer wavelengths generally can penetrate through thicker solids. σ is a constant called StefanBoltzmann constant. Visible light. absorbed.3) Where A is the surface area. and ε is a material property called emissivity. The amount of radiation emitted by an object is given by: (Eq. The visible portion is evident from the bright glare of the sun. such as the sun at ~5800 K. is blocked by a wall. emit infrared radiation. The latter is given by the 6 . or transmitted (Figure 1. where it is reflected. However. It is the ratio of the radiation emitted by a surface to the radiation emitted by a perfect emitter at the same temperature.67×10-8 W/m2K4.4) Where I is the incident radiation. from a cooking standpoint. the UV radiation causes tans and burns. Any body with temperature above 0 Kelvin emits radiation. are very energetic and can be harmful to humans. and is a measure of how efficiently a surface emits radiation. The portion that contributes to the heating of the surface is the absorbed radiation. while visible light with wavelengths ~10-7 m contain less energy and therefore have little effect on life. The amount of heat absorbed by the surface is given by: (Eq.5).wavelengths ~10-9 m. The type of radiation emitted is determined largely by the temperature of the body.
2. the radiative exchange between the object and the wall is greatly simplified: (Eq. and the convection coefficient from the loaf to air is 10 W/m2K.6) This simplification can be made because all of the radiation emitted by the object strikes the wall (Fobject→wall = 1). and its surface temperature is 120 ºC. 7 . 1.121.5) For an object in an enclosure.76. The temperature of the air is 20 ºC. Define the following heat transfer situations as either conduction. The net amount of radiation absorbed by the surface is: (Eq. The dimension of the loaf is as described in the figure. F. and its conductivity is 0. A loaf of freshly baked bread is left to cool on a cooling rack. A turkey is being roasted in the oven. For example: A person with a headache holds a cold ice pack to his/her forehead. Emissivity of the bread is 0. o o o o o The sun shines brightly on a car. which is the percentage of the emitted radiation reaching the surface. Potatoes are boiled in water. convection. 1. Problems for Chapter 1 Note: These problems are NOT your homework assignments. or a combination of the three. Please also clearly state what two objects the mode of heat transfer is between and the direction of heat transfer. radiation. 1. An ice cube is placed on a metal tray and left out of the freezer. making the black upholstery very hot. Homework’s will be assigned in class on a separate handout. Answer: Conduction occurs from the person’s forehead to the ice pack.shape factor. A small 4" fan is installed in the back of a computer to help cool the electronics.
the thermal resistance is expressed as: (Eq. k is the thermal conductivity of the layer. A cup of all to the on these information. When the system is still changing with time.1 Steady State and Transient State If you heat a pan on a stove. When there is more than one layer in the composite. it takes a while for the pan to heat up to cooking temperature. and A is the cross-sectional area. An analysis much like a circuit analysis follows. calculate the total heat from the bread. it is in transient state.Based loss 3. In this model. the total resistance of the circuit must be calculated. For conduction. Describe modes of heat transfer that contributes cooling of the coffee. and ∆T is the temperature difference between two surfaces separated by a distance ∆x. The total resistance for layers in series is simply the sum of the 8 . 3. hot coffee sits on the table. A is the cross-sectional area through which the heat is conducting.2) Where L is the thickness of the layer. The latter state is called the steady state. A model used often to calculate the heat transfer through a 1-D system is called the thermal circuit model. 2.2 One-Dimensional Conduction One-dimensional heat transfer refers to special cases where there is only one spatial variable – the temperature varies in one direction only. 3. after which the temperature of the pan remains relatively constant. LESSON 2 Steady-State Conduction 2. where there is no temporal change in temperatures. The rate of conduction through an object at steady-state is given by: (Eq.1) Where k is the conductivity of the material. This model simplifies the analysis of heat conduction through composite materials. each layer is replaced by an equivalent resistor called the thermal resistance.
the heat flow through the layers can be found by: (Eq. and k4 = 46 W/mK.4) The convection at the surface must also be expressed as a resistor: (Eq. The convection coefficient on the right side of the composite is 30 W/m2K. 3. 3.3) For resistors in parallel.resistances: (Eq. Calculate the total resistance and the heat flow through the composite. 3. 3.5) Once the total resistance of a structure is found. the total resistance is given by: (Eq. Conductivities of the layer are: k1 = k3 = 10 W/mK. Example Problem Consider a composite structure shown on below. k2 = 16 W/mK. 9 .6) Where Tinitial and Tfinal refers to the temperatures at the two ends of the thermal circuit (analogous to voltage difference in an electrical circuit) and q is the heat flow through the circuit (current).
an equivalent resistance for layers 1. R2 = 0.15. 2. The circuit must span between the two known temperatures. draw the thermal circuit for the composite. Next. and R4 = 0. and 3 is found first. T1 and T∞.36 To find the total resistance.First. that is. These three layers are combined in series: 10 . the thermal resistances corresponding to each layer are calculated: Similarly.09. R3 = 0.
The equivalent resistor R1.2.3 is in parallel with R4: Finally.2. ← heat flow through the composite 11 .3.4 is in series with R5. R1. The total resistance of the circuit is: ← total thermal resistance Rtotal = R1.46 The heat transfer through the composite is: = 22.214.171.124 W.4 + R5 = 0.
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http://aa.springer.de/papers/8333003/2301001/sc3.htm | math | 3. Physical parameters and results
The calculations have been carried out in the scheme described in Paper III for the nonlinear evolution of axisymmetric pinching (body) modes for a cylindrical jet. We have set, at , the jet Mach number and the density ratio . In order to set the remaining parameters, and , we recall from Paper II that a choice of K yields post-shock temperatures K, consistent with the low excitation spectra observed. We recall also that since the initial cooling time is large with respect to the dynamical time scale, choices of that differ up to 40% have shown in tests calculations to have very little effect on the nonlinear evolution of the instability. Concerning the choice of , observations of HH34 and HH111 are consistent with jet radii cm and particle density (Bürkhe et al. 1988, Morse et al 1993a). We have therefore adopted for the column density ; this choice implies for the jet a mass flux and a momentum flux , with .
In Fig. 1 we show a contour plot of the morphology of the emission flux, for , at the time when the train of shocks has reached a distance from the origin corresponding to about 400 radii. The results for yield similar morphologies. We note however that the general morphology is weakly dependent on the particular time chosen, as can be seen, for this set of parameters, in Fig. 1a,b ( (Fig. 1a) and (Fig. 1b). In this figure we show also the details of the morphology of the leading shock, with a clear bow-like form, and of preceding ones (i.e. at smaller z) that appear to have a more compact structure. The line fluxes are obtained by integrating the emissivity along the line-of-sight under the hypothesis that this is perpendicular to the jet longitudinal axis. From Fig. 1 we see that one of the leading shocks, being a result of shock merging processes, is somewhat more distant from the preceding one, is wider and has a distinct bow-shock like morphology. The knots result quasi-equally spaced, with mean intra-knot distance of jet diameters, and with an initial gap whose length partly depends on the amplitude of the initial perturbation imposed perpendicularly to the equilibrium velocity ( in the present case). We note also that the shocks most distant from the source weaken with time (compare Fig. 1a and b).
The spectral and kinematical characteristics of the shocks resulting from K-H instability are shown in Fig. 2 where we plot, at the time and for , the on-axis behavior against z of the electron density in units of the initial density (panel a) and the fluxes of (panel b) and (panel c); in panel d) we plot the flux ratio , obtained averaging the fluxes over the emission volume of each shock, and in panel e) we show the shock pattern speeds . As a comparison, we show in Fig. 3 the behavior of the same quantities of Fig. 2 but for and at time . In both cases of the ionization fraction attains maximum values that do not exceed , and the different shock strengths yield values of reaching (Fig. 2a) and (Fig. 3a), respectively for and . Figs. 2b,c and 3b,c show how the flux in the two lines increases, reaches a maximum and then decreases, in qualitative agreement with observations; from Figs. 2d and 3d we notice also that the line ratio attains a high value for the leading, widest shock. A further comparison of Fig. 2 with Fig. 3 show in the latter case wider initial gap and intra-shock spacings, and lower values of the ratio (Figs. 2d and 3d), consistently with the increasing of strength and excitation level of the shocks at a higher Mach number. Finally Figs. 2e and 3e show that the proper motions of knots increase with distance from the origin from up to 0.8, in the case of , and from 0.5 up to 0.7, for . These results are in good qualitative agreement with the findings of Eislöffel & Mundt (1992) for HH34. We have taken Figs. 2 and 3 as representative snapshots of typical morphologies; in fact, calculations show that the shock train, after a time scale depending on the physical parameters, reaches a asymptotic configuration that remains quasi-steady and simply shifts forward.
About the possibility of shock merging effects, that lead to bow-shock like features, we note that the condition for these processes to set in is that, locally, a shock at larger z must have proper motion smaller than the following one,i.e. at smaller z (see the discussion in the companion Paper III). Looking at Figs. 2e and 3e we can see that this condition can be verified in several positions along the jet, therefore one may expect that bow-shock like knots, originated by K-H modes, can be a more common feature than actually shown in our calculations, limited in time. We remark finally the internal consistency between the increasing of shock pattern motions with distance z along the jet (Figs. 2e and 3e), which should give a lower shock strength, and the increasing of the ratio (Figs. 2d and 3d).
Table 2. Model results, to be compared with Table 1
We leave distances and densities in units of a and , with , bearing in mind that the values must obey . In Table 2, the results for are in general agreement with observations; setting for a the values of HH34 and HH111, the major discrepancies are: i) the length of the initial invisible part of the jet (the 'gap') that is larger by a factor of with respect to observations, ii) the widths of the knots in tend to be smaller by a similar factor, and iii) the post-shock electron densities are smaller than the observed values, especially in the case , by a factor . However, being the choice of the set of parameters by no means unique, one can expect, at best, only a broad agreement from the comparison with observations. What is important to stress is the trend brought about by the variation of the Mach number, i.e. higher values of M cause an increase of the intra-knot spacing and a decrease of the ratio. Also the temporal evolution plays a role, increasing the relative length of the visible part of the jet (see Fig. 1).
Observations indicate jet velocities , implying . Unfortunately, our capability of carrying out calculations with , on the same grid (), was greatly hampered by the growing size of the integration domain. In order to gain some insight on the behavior of the instability at different Mach numbers we have carried out additional calculations on a coarser grid () for , and with a larger longitudinal size of the domain (800 jet radii). The simulation of the case has been carried out up to , when the leading perturbation reached the right boundary; therefore we cannot represent a quasi-steady situation and in Table 2, there are missing data for this case: is larger than the computational domain, thus we cannot estimate , , and the knot number; the age of the jet is also missing and the electron density is, quite likely, severely underestimated. The remaining quantities: , knot width and separation, jet velocity and knot speed are instead reasonably well defined by the simulation.
We recall that we defined M as the ratio of the jet velocity with respect to the external medium to the internal sound speed, and that is reported in Table 2. Observations of shock velocities in bow-shocks (Morse et al. 1992, 1993b, 1994) show values lower than those consistent with the measured proper motions of the bow-shocks themselves. This may suggest that the pre-shock ambient medium is not steady with respect to the central source, but may be drifting along the jet due to, perhaps, the effect of previous outburst of the source, thus lowering the actual velocity jump jet-to-ambient and the effective Mach number. In particular, Morse et al. (1992) found for HH34 a velocity of the pre-shock medium, at the bow-shock, , and for HH111 (Morse et al. 1993b).
Following Hardee & Norman (1988), it is possible to derive that, in the linear and adiabatic regime, this mode has a resonance frequency and a corresponding resonance wavelength
where is a coefficient that depends on the geometry (Cartesian or cylindrical) and on the particular mode (symmetric or asymmetric).
The numerical results for the nonlinear evolution are reported in Fig. 4a,b. In Fig. 4a symbols represent the mean intra-knot spacing, in units of a, as a function of M and the error bars indicate the difference between maximum and minimum spacing. The dashed line shows the resonance wavelength of the fastest growing mode in the linear and adiabatic regime, according to (1), and the dot-dashed line interpolates our nonlinear results but with coefficient instead of of (1). In Fig. 4b we plot intensity ratio against M. To avoid ambiguity in the choice of a particular shock, we have selected one of the first shocks of the chain that have the advantage of being nearly of constant strength for a given M, as time elapses. The behavior of the intensity ratio is well represented by a power-law fit (solid line). Therefore, in the K-H scenario, the larger is the mean intra-knot spacing the smaller must be the line ratio.
These last results show clearly how two of the main observable features of stellar jets, such as the intra-knot spacings and the line ratios, result connected if knots originate from the K-H instability, and this represents a test on the mechanisms proposed and a prediction for further observations (cf., point 7 in Sect. 2).
© European Southern Observatory (ESO) 1998
Online publication: April 28, 1998 | s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662577757.82/warc/CC-MAIN-20220524233716-20220525023716-00366.warc.gz | CC-MAIN-2022-21 | 9,383 | 15 |
https://journals.itb.ac.id/index.php/jmfs/article/view/92 | math | Surfaces with Prescribed Nodes and Minimum Energy Integral of Fractional Order
This paper presents a method of finding a continuous, real-valued, function of two variables z = u(x, y) defined on the square S := [0,1]2 , which minimizes an energy integral of fractional order, subject to the condition u(0, y) = u(1, y) = u(x,0) = u(x,1) = 0 and u(xi ,yj)=cð‘–ð‘— , where 0<x1<...<xM,<1, 0<y1<...<yN<1, and cð‘–𑗠∈ â„ are given. The function is expressed as a double Fourier sine series, and an iterative procedure to obtain the function will be presented.
Alghofari, A.R., Problems in Analysis Related to Satellites, Ph.D. Thesis, The University of New South Wales, Sydney, 2005.
Langhaar, H.L., Energy Methods in Applied Mechanics, John Wiley & Sons, New York, 1962.
Gunawan, H., Pranolo, F. & Rusyaman, E., An Interpolation Method that Minimizes an Energy Integral of Fractional Order, in D. Kapur (ed.), ASCM 2007, LNAI 5081, Springer-Verlag, 2008.
Wallner, J., Existence of Set-Interpolating and Energy-Minimizing Curves, Comput. Aided Geom. Design, 21, 883-892, 2004.
Wan, W.L., Chan, T.F. & Smith, B., An Energy-Minimizing Interpolation for Robust Multigrid Methods, SIAM J. Sci. Comput. 21, 1632-1649, 1999/2000.
Ardon, R., Cohen, L.D. & Yezzi, A., Fast Surface Segmentation Guided by User Input Using Implicit Extension of Minimal Paths, J. Math. Imaging Vision, 25, 289-305, 2006.
Benmansour, F. & Cohen, L.D., Fast Object Segmentation by Growing Minimal Paths from A Single Point on 2D or 3D images, J. Math. Imaging Vision, 33, 209-221, 2009.
Capovilla, R. & Guven, J., Stresses in Lipid Membranes, arXiv: condmat/ 0203148v3, 2002.
Stein, E.M., Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, 1971.
Rao, C.R. & Rao, M.B., Matrix Algebra and Its Applications to Statistics and Econometric, World Scientific, Singapore, 1998.
Lorentz, G.G., Approximation of Functions, AMS Chelsea Publishing, Providence, 1966.
Atkinson, K. & Han, W., Theoretical Numerical Analysis: A Functional Analysis Framework, Springer-Verlag, New York, 2001. | s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991759.1/warc/CC-MAIN-20210510174005-20210510204005-00031.warc.gz | CC-MAIN-2021-21 | 2,128 | 14 |
https://cheapwriteessay.com/2021/05/17/need-help-with-math-problems-for-free_r8/ | math | The worksheets need help with math problems for free need help with math problems for free are set up for easy printing math planet is an online resource where one can study math for free. free math help. if you like this page, please click that need help with math problems for free 1 button, too note: need help on understand a question on inverse functions. answers: create free team teams. ethnographic research paper need help on understand a question on inverse functions. 1. since it write my conclusion for me began in 2005, all the math worksheets on math-drills have been free-to-use with students learning math. best college entrance essay the math help we provide is mostly suitable forcollege and high school students, even though we believe that there is a little example of essay in apa format bit for everyone cadabra is an open source and free math software essay writing book that helps you to essay on playing multiple sports deal with complex algebraic how to write an essay quickly problems found in field theory. define essay in literature need help. 1 get other questions on the subject: kindergarten – 8th grade math. finance/business math. | s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487655418.58/warc/CC-MAIN-20210620024206-20210620054206-00558.warc.gz | CC-MAIN-2021-25 | 1,166 | 1 |
https://www.metlink.org/maths-for-planet-earth/graphing-rising-temperatures/ | math | The temperature-time graph from https://globalwarmingindex.org/ shows how the Earth’s global average monthly temperatures have varied from the year 1880. Throughout this question, monthly global temperatures refer to the difference between the temperature in a particular month and the average temperature for that calendar month over the period 1850-1879.
a) Which year contained the month in which global temperatures first exceeded 0.5°C above the 1850-79 average?
b) Estimate a value for the highest recorded monthly global temperature since 1880 and
give the year in which it was recorded.
c) Estimate a value for the average monthly global temperature between 1980 and 2000.
d) What is the lowest monthly global temperature recorded since 2000? | s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510603.89/warc/CC-MAIN-20230930050118-20230930080118-00328.warc.gz | CC-MAIN-2023-40 | 753 | 6 |
https://www.heldermann.de/JCA/JCA12/JCA122/jca12026.htm | math | Journal of Convex Analysis 12 (2005), No. 2, 383--395
Copyright Heldermann Verlag 2005
Fatou's Lemma for Multifunctions with Unbounded Values in a Dual Space
Erik J. Balder
Mathematical Institute, University of Utrecht, Budapestlaan 6, 3508 TA Utrecht, The Netherlands
Anna Rita Sambucini
Dip. di Matematica e Informatica, UniversitÓ di Perugia, Italy
A version of Fatou's lemma for multifunctions with unbounded values in infinite dimensions is presented. It generalizes both the recent Fatou-type results for Gelfand integrable functions of B. Cornet and V. F. Martins da Rocha ["Fatou's lemma for unbounded Gelfand integrable mappings", preprint 109, CERMSEM, UniversitÚ Paris I (2002)] and, in the case of finite dimensions, the finite-dimensional version of the unifying multivalued Fatou-type result of E. J. Balder and C. Hess [Math. Oper. Res. 20 (1995) 175--188].
Keywords: Fatou's lemma in several dimensions, Gelfand integral, Young measure, asymptotic cone.
MSC: 29B20; 28A20
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http://www.solutioninn.com/what-is-the-average-interpret-it-in-terms-of-the | math | Question: What is the average Interpret it in terms of the
What is the average? Interpret it in terms of the total of all values in the data set.
Answer to relevant QuestionsWhat is a weighted average? When should it be used instead of a simple average? Consider the 20,000 people in the donations database (on the companion site). a. Construct box plots to compare median household income and per capita income (these specify two columns in the database) by putting the two box ...Consider the loan fees charged for granting home mortgages, as shown in Table 4.3.8. These are given as a percentage of the loan amount and are one-time fees paid when the loan is closed. a. Find the average loan fee. b. ...Consider the running times of selected films from a video library as shown in Table 4.3.10. a. Find the average running time. b. Find the median running time. c. Which is larger, the average or the median? Based on your ...Many countries (but not the United States) have a “value-added tax” that is paid by businesses based on how much value they add to a product (e.g., the difference between sales revenues and the cost of materials). This ...
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https://www.avogadro-lab-supply.com/content.php?content_id=2 | math | How To Use A Hydrometer
A hydrometer is an instrument whose function is based on Archimedes principle. This principle states that a body (the hydrometer) immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid. The hydrometer measures the weight of the liquid displaced by the volume of the hydrometer.
Specific Gravity is a dimensionless unit defined as the ratio of density of the material to the density of water. If the density of the substance of interest and the reference substance (water) are known in the same units (e.g., both in g/cm3 or lb/ft3), then the specific gravity of the substance is equal to its density divided by that of the reference substance (water =1 g/cm3), hence
Specific Gravity = Density g/cm3
Herein lies the equality between specific gravity and density,
the dimensions drop out!
The greater the density, the tighter or closer the molecules are packed inside the substance.
Therefore, the greater the density / specific gravity of a liquid the higher a hydrometer will be buoyed by it.
Fill your hydrometer jar about ¾ with the liquid you wish to test. Insert the hydrometer slowly. Do not drop it in! Now give it a spin with your thumb and index finger, this will dislodge any bubbles that may have formed. Once the hydrometer comes to a rest, observe the plane of the liquid surface. Your eye must be horizontal to this plane. The point at which this line cuts the hydrometer scale is your reading.
Food for Thought
(Using specific gravity to determine the concentration of a solution)
100% ethanol has a specific gravity of .785 which is lighter than water with a specific gravity of 1.0
A 50/50 mixture of water and ethanol (100 proof / 50%) will have the following specific gravity.
(.5L x 1.0) + (.5 L x 0.785) = 0.8925
A 75/25 mixture of water and ethanol (50 proof / 25%) will have the following specific gravity
(.75 L x 1.0) + (.25 L x 0.785) = 0.9463
As you can see the specific gravity of the mixture is inversely proportional to the alcohol concentration. As the alcohol concentration decreases the specific gravity increases and the hydrometer floats higher in the solution.
The alcohol hydrometer is calibrated in two scales % alcohol and proof.(1% alcohol = 2 proof ) The manufacturer used the specific gravity of alcohol at various concentrations to calibrate the instrument.
To determine the concentration of a 1 liter solution of alcohol and water
using specific gravity.
1) Measure the specific gravity of the solution
Let X = unknown volume of water
Let (1-X) = unknown volume of alcohol
Then X + (1-X) = 1 Liter
Specific Gravity of water = 1.0
Specific Gravity of ethanol = 0.785
(X)(1.0) + (1-X)(0.785) = Sp. G of solution
Solve for X
Example: Assume the measured specific gravity is 0.9463
X (1.0) + (1-X)(0.785) = 0.9463
X + (0.785 - 0.785X) = 0.9463
0.215X + 0.785 = 0.9463
0.215X = 0.1613
(X)(100%) = the concentration of water
(0.75)(100%) = 75% water
(1-X)(100%) = the concentration of alcohol
(0.25)(100%) = 25% alcohol | s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917121165.73/warc/CC-MAIN-20170423031201-00383-ip-10-145-167-34.ec2.internal.warc.gz | CC-MAIN-2017-17 | 3,014 | 37 |
https://nethackwiki.com/mediawiki/index.php?title=Forum:Speed:_turns_versus_actions&t=20110728104101 | math | Forum:Speed: turns versus actions
Some things are affected by speed, others not. Very little documentation on this topic is available here or elsewhere on the internet. (This is especially relevant to speed runners.) I'd like to improve that gradually.
- Let's fix the language. How about turns == turn counter (moves, monstermoves), actions == movement points / 12?
- Since speed and its implications is a rather advanced subject, should it get its own subsection or at least paragraph, instead of integration into the main text of each article?
Opinions, anybody? Pointers to existing spoilers? --Tjr 23:01, 9 July 2011 (UTC)
- Not seen a detailed spoiler, though the documentation for the nethack TAS has a nice summary of the subject, see the section headed "Maximising movement speed"
- I think the distinction between 'action' and 'turn' is a useful one. 'move' should be reserved for describing motion in the cardinal directions so as not to be ambiguous (the speed article is currently guilty of this). The subject probably warrants a separate section, also it would be useful to compile a list of what actions take 0 movement points (turn lists some of these) or more than 12 movement points (prayer, long engravings, etc.). --Nht 08:22, 11 July 2011 (UTC)
IRC conversation about the behind-the-scenes
Starter for an article speed system
[19:03] TjrWiz: nomul(0) -- so you waste all your movement points if you have speed?
[19:04] ais523: nomul(0) doesn't waste all your movement points, that's nomul(-1) you're thinking of
[19:04] rawrmage: question: what the hell is actually nomul
[19:04] ais523: nomul(0) just turns off run and command repeat
[19:04] ais523: rawrmage: err, you probably don't want to ask that
[19:04] ais523: but in short, there's a variable called multi
[19:04] ais523: which controls about four different things
[19:05] ais523: positive multi means command repeat (e.g. multi is set to 19 if you type #20s, which means "repeat the command 19 more times" except when it doesn't)
[19:05] ais523: while multi is positive, it reduces by one every action, except some things set it to 0 arbitrarily (things like multishot and pickup because leading numbers mean something else, that's its second meaning, things like engraving because they're coded badly)
[19:06] ais523: negative multi causes helplessness; it increases by 1 every turn, and prevents you taking actions until it hits 0
[19:06] ais523: also, a function gets called when it changes from -1 to 0
[19:06] ais523: which is also stored in a global variable, obviously
[19:06] ais523: now, multiturn actions are sometimes programmed by setting multi to a positive number, in which case they can be interrupted
[19:06] rawrmage: why is there inconsistency between You("") and pline("You")
[19:06] ais523: and sometimes by setting it to a negative number, in which case they can't
[19:07] TjrWiz: but they differ between n actions and -n turns, right?
[19:07] ais523: e.g. engraving Elbereth with a gem does nomul(-7)
[19:07] ais523: TjrWiz: that too
[19:07] ais523: except, for multiturn actions with a positive multi, often they just set it to something really high, then set it back to 0 when the action's finished
[19:07] ais523: like shift-move
[19:07] TjrWiz: so you're actually faster with -n if you're burdened, right?
[19:07] rawrmage: whaaaaat
[19:07] ais523: TjrWiz: indeed
[19:07] ais523: what nomul does, is put a cap on multi
[19:07] ais523: it reduces multi to the value given, except if it's already below that value
[19:08] ais523: so nomul(0) means "stop multiturn action", whereas nomul(-5) means "cause 5 turns of helplessness"
[19:08] ais523: to add to the fun, there are some cases where multi is set by hand; lifesaving sets it to -1 if it's currently 0 or lower, or 0 if it's currently 1 or higher
[19:10] ais523: TjrWiz: I'll write that article someday, hopefully someday soon
[19:10] ais523: "speed system" is a good name for it | s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583688396.58/warc/CC-MAIN-20190120001524-20190120023524-00016.warc.gz | CC-MAIN-2019-04 | 3,939 | 38 |
https://brainmass.com/math/graphs-and-functions/find-three-points-that-fall-on-a-given-line-199651 | math | - Graphs and Functions
Find three points that fall on a given line
Find three points that fall on the line y=5x-5 . I need 3, (x,y,) (x,y) (x,y)
Please see the attached Word document for the solution to this ...
This solution finds a set of three points lying on the line on a given line. | s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720475.79/warc/CC-MAIN-20161020183840-00566-ip-10-171-6-4.ec2.internal.warc.gz | CC-MAIN-2016-44 | 288 | 5 |
http://www.studentoffortune.com/question/1563190/assistance-please | math | $15.00 assistance, please.
Answers to all the questions! Contact me if you have any doubt :)
- This tutorial hasn't been purchased yet.
- Posted on Jun 08, 2012 at 7:56:28PM
Preview: ... l plans to obtain a new MRI that costs $1.5 million and has an estimated four-year useful life. It can obtain a bank loan for the entire amount and buy the MRI, or it can lease the equipment. Assume that the following facts apply to the decision: The MRI falls into the three-year class for tax depreciation, so the MACRS allowances are 0.33, 0.45, 0.15, and 0.07 in years 1 through 4, respectively. Estimated maintenance expenses are $75,000 payable at the beginning of each year whether the MRI is leased or pur chased. Big Sky's marginal tax rate is 40 percent. The bank loan would have an interest rate of 15 percent. If leased, the lease (rental) payments would be $400,000 payable at the end of each of the next four years. The estimated residual (and salvage) value is $250,000. a. What are the NAL and IRR of the lease? Interpret each value. b. Assume now that the salvage value estimate is $300,000, but all other facts remain the same. What is the new NAL? The new IRR? ANSWER Before-tax cost of debt 15% MACRS Tax rate 40% Year 1 Year 2 Year 3 Year 4 After-tax cost of debt 9% 33% 45% 15% 7% a. Here are the net cash flows associated with owning: Year 0 Year 1 Year 2 Year 3 Year 4 Cost of owning: Net purchase price -$1,500,000 Maintenance cost -$75,000 -$75,000 -$75,000 -$75,000 Maintenance tax savings $30,000 $30,000 $30,000 $30,000 Depreciation tax savings $198,000 $270,000 $90,000 $42,000 Residual value $250,000 Tax on residual value -$100,000 Net cash flow -$1,545,000 $153,000 $225,000 $45,000 $192,000 Depreciation tax savings: Year 1 =C25*E26*-D33 Year 2 =C25*F26*-D33 Year 3 =C25*G26*-D33 Year 4 =C25*H26*-D33 Tax on residual value: =((-D33*(1-E26-F26-G26-H26))-H37)*C25 Here are the net cash flows associated with leasing. We could have recognized that the maintenance expense is nonincremental to the decision and hence could be ignored in the analysis. Cost of leasing: Lease payment -$400,000 -$400,000 -$400,000 -$400,000 Lease tax savings $160,000 $160,000 $160,000 $160,000 Maintenance cost -$75,000 -$75,000 -$75,000 -$75,000 Maintenance tax savings $30,000 $30,000 $30,000 $30,000 Net ...
The full tutorial is about 1589 words long .
Chapter 18 solution
- This tutorial was purchased 1 time and rated No Rating by students like you.
- Posted on Jun. 09, 2012 at 04:28:51AM
Preview: ... e fin ...
The full tutorial is about 4 words long plus attachments. | s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368697772439/warc/CC-MAIN-20130516094932-00091-ip-10-60-113-184.ec2.internal.warc.gz | CC-MAIN-2013-20 | 2,574 | 11 |
http://www.chegg.com/homework-help/statistics-for-engineering-and-the-sciences-5th-edition-chapter-11.9-solutions-9780131877085 | math | The study is regarding the ankles and knees of volunteers and measured the signal-to-noise ratio of impedance changes. The engineers examine the relation between knee joint angle x (degrees), and knee impedance change y (ohms). For the collected data the following results are obtain. The fitted model is,
a) Sketch and identify the nature of the prediction equation.
By using the software we get the following graph:
From the above graph we observe that the nature of the predicted line is approximately a straight line.
b) Use the fitted least-square prediction equation; predict the impedance chance when the knee joint angle is 50 degrees.
We have the equation,
Substitute the value in the equation.
Therefore, the impedance chance when the knee joint angle is 50 degrees is
c) From the given information we have the value as 0.901. From the value we can say that about 90.1% of the sample variation in compression y can be explained by the explanatory variables.
Chegg is one of the leading providers of homework help for college and high school students. Get homework help and answers to your toughest questions in math, calculus, algebra, physics, chemistry, science, accounting, English and more. Master your homework assignments with our step-by-step solutions to more than 3000 textbooks. If we don't support your textbook, don't worry! You can ask a homework question and get an answer in as little as two hours. With Chegg, homework help is just a few clicks away. | s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422122220909.62/warc/CC-MAIN-20150124175700-00019-ip-10-180-212-252.ec2.internal.warc.gz | CC-MAIN-2015-06 | 1,476 | 10 |
https://teaching.betterlesson.com/lesson/559637/decimal-notation-vs-fractions?from=breadcrumb_lesson | math | To warm up I invite students to the carpet to review some vocabulary terms, and to discuss what we have been learning so far about fractions. Because my students struggle with fractions it is important that I remind them of their prior knowledge. My students respond a lot better to new concepts if they connect it to prior experiences.
I ask students to share their own experiences, and ideas about fractions. Students name the parts of the fraction, and are able to discuss how and why fractions are used. Some students remember using models to explain the pieces verses the whole. After the discussion I gain a better understanding about what my students know about fractions, and what they need to know about fractions in order to be successful in this lesson.
"Since you guys already know a lot about fractions, I know you are really going to enjoy learning how to convert a fraction to a decimal. But, before we began I want to go over some new math terms that will assist you in your learning." As I go over the new vocabulary, I ask them to write the definitions down in their math note book just in case they need to remember what they mean later on in the lesson.
A fraction is a number between zero and 1 and is expressed as one number over another number, like this: 1/2
Decimals-A linear array of digits that represents a real number.
I intend to show students the connection between fraction and decimal notation by writing the same number both ways. I tell them that they will compare and contrast the difference and similarities between fractions and decimals.
Because this is the first time decimals are introduced, I want to make sure I incorporate a visual throughout the lesson. I begin by drawing a large place value chart on the board. I explain that a number can be represented as both a fraction and a decimal.
I start filling in the place value chart, by first placing a decimal in the center of the chart. I ask students to explain why I did this. More than half of my students could not explain. So, I take a moment to fill in the rest of the chart explaining the value of the numbers listed to the right and left hand side of the decimals. I explain that numbers written to the left of the decimal are whole numbers, while numbers written to the right of the decimal are parts of a whole number. Some students make the connection between fractions with the denominator as being the number listed to the right of the decimal. I enter 3 under the tenths place and 2 under the hundreds place. Can anyone tell me if should write this number as a fraction or a decimal? You should write is as a decimal because it is written to the right of the decimal. Several students wanted to write 32/100. I explain that if we were to write both 32/100 and .32 on a number line both would be placed closer to the .32. I repeat this activity using different numbers, and invite student volunteers to help me use decimal notation for fractions with denominators. As students are working I constantly redirect their thinking to the intended purpose of this lesson by asking how and why the given decimal notation is related to the fraction. I use their responses to determine if I should move them deeper into the lesson.
]MP.4. Model with mathematics.
MP.7. Look for and make use of structure
MP. 8. Look for and express regularity in repeated reasoning.
In this portion of the lesson, I invite students to the carpet to take part in a fun interactive lesson. I encourage students to take notes throughout the lesson. note taking paper.pdf The purpose of this model is to deliver explicit instruction to provide students with a clearly explained task of how fractions are related to decimals. During the lesson I ask the following questions to guide students' thinking:
Does it help to create a diagram?
How would you prove that?
Does that make sense?
It is important that conceptual thinking is broken down into critical features/elements. Students note that the models help support their learning. Some students are able to explain, however, their explanations are a bit vague. I make a note to make sure I am showing them how to visually represent fractions.
In this portion of the lesson I want to work with students a bit more on understanding that decimals are an extension of our whole number base ten system. To do this I ask students to move back into their assigned seats. I choose to stand at the board, so that students can work along with me independently. First, I draw a large chart on the board to model how to write fractions and decimals in expanded form. I give each student their own chart to work along with me. I write 7 82/100. I explain that 7 is a whole number, and it value is 7 ones. (They should remember this from previous school years. If they don't, do a quick mini-lesson on place value with whole numbers). I remind students that numbers written to the right of the decimal are parts of a whole so the number 8 is 8 tenths, and 2 is 2 hundredths. I ask, "Can anyone tell me how to write the given fraction in expanded fraction form?" 7 + 8/10 + 2/100 Great! Since, 7 is in the ones place, it remains 7. The number 8 is in the tenths place, so I write 8/10 to make sure it has its correct value. The number 2 is in the hundredths place, so I write 2/100 to make sure that 2 have its correct value.
Now, I direct their attention to expanded decimal form. I tell them it is basically the same method we used to understand writing fractions in expanded for, but we use decimals and add zeros to make sure the given numbers are aligned with the correct value. I say, who can help me write the same number, but arrange it in expanded decimal form. Several students raise their hand, so we all give it a go. I ask, "How do I write the 7? How can I write the number 8 in decimals to represent its correct value? How can I write the number 2 in decimals to represent its correct value? So we write 7 + 0.80 + 0.02. We double check our answer by counting the correct spaces on a place value chart. Students seem to catch on quickly to this concept. However, I repeat this activity using a different fraction just to make sure students fully understand the connection between fraction and decimal notation.
In this portion of the lesson students will work on their own to demonstrate how and why fractions and decimals are related. I ask them to be sure to show and explain the connection between fraction and decimal notation by writing the same number in both ways. I remind them that we did this earlier in the lesson. I tell them that they may draw visual representations like the ones seen in the interactive video if they need to.
Some students tend to think that I was asking them to demonstrate a new skill. So, I explain that they will still be working on the same type of problems completing from our group setting. However, I want them to choose two of the numbers to explain the correlations. As students are working, I circle the room to remind students of the intended purpose of this lesson.
How you can express the fraction to show its correct number value?
Can you explain how the numbers to the right and left of the decimal differ and how they are the same?
Can you represent the given number in both expanded decimal and fraction form? Explain your reasoning.
Some students tend to bit confused at times, but the questions seem to refocus their attention. I use their responses to determine if additional time should be spent on this concept. | s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103034877.9/warc/CC-MAIN-20220625065404-20220625095404-00042.warc.gz | CC-MAIN-2022-27 | 7,494 | 24 |
http://www.ask.com/web?qsrc=6&o=102140&oo=102140&l=dir&gc=1&q=Acre+to+SQ+FT | math | One acre is equal to 43,560 square feet.
The acre is a unit of land area used in the imperial and US customary systems. It
is defined as the area of 1 chain by 1 furlong (66 by 660 feet), which is exactly
equal to <sup>1</sup>⁄...
Jun 21, 2016 ... Or maybe you're studying for an exam and want to know how to convert square
feet to acres or acres to square meters, hectares or other units ...
Convert from square feet to acres and acres to square feet with this handy
Acres to Square Feet (ac to ft²) conversion calculator for Area conversions with
additional tables and formulas.
If you have a perfect square that is equal to 1 acre, what is the length of the sides
... One acre is 43,560 square feet so a square, with area one acre would have a ...
Acres to square feet area measurement units conversion table shows the most
common values for the quick reference. Alternatively, you may use the converters
Hi Melinda,. 43,560 square feet = an acre. If the land is a square (length=width), it
is 208.71 ft by 208.71 ft since 208,71 x 208.71 = 43,560. If the land is ...
Instant online area units of acre to square foot conversion. The acre [ac] to square
foot [ft^2] conversion table and conversion steps are also listed.
Because an acre is a measure of area, not length, it is defined in square feet. An
acre can be of any shape—a rectangle, a triangle, a circle, or even a star—so ... | s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280835.22/warc/CC-MAIN-20170116095120-00366-ip-10-171-10-70.ec2.internal.warc.gz | CC-MAIN-2017-04 | 1,394 | 19 |
https://www.clutchprep.com/physics/practice-problems/48900/a-hollow-cylindrical-conductor-inner-radius-a-outer-radius-b-carries-a-current-i | math | A hollow cylindrical conductor (inner radius = a, outer radius = b) carries a current I uniformly spread over its cross section. Which graph below correctly gives the magnetic field as a function of the distance r from the center of the cylinder?
Frequently Asked Questions
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Our tutors have indicated that to solve this problem you will need to apply the Ampere's Law with Calculus concept. You can view video lessons to learn Ampere's Law with Calculus. Or if you need more Ampere's Law with Calculus practice, you can also practice Ampere's Law with Calculus practice problems.
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Our expert Physics tutor, Juan took 3 minutes and 13 seconds to solve this problem. You can follow their steps in the video explanation above.
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Based on our data, we think this problem is relevant for Professor Rappel's class at UCSD. | s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141723602.80/warc/CC-MAIN-20201203062440-20201203092440-00432.warc.gz | CC-MAIN-2020-50 | 975 | 8 |
https://fr.slideserve.com/dolan-watkins/presentation-9-chapter-15 | math | PRESENTATION 9Chapter 15 Real Estate Finance Mathematics
Approach to Solving Math Problems • Solving math problems is simplified by using a step-by-step approach. • The most important step is to thoroughly understand the problem. • You must know what answer you want before you can successfully work any math problem. TQ • Once you have determined what it is you are to find (for example, interest rate, loan-to-value ratio, amount, or profit), you will know what formula to use.
(cont.) • The next step is to substitute the numbers you know into the formula. TQ • It may be necessary to take one or more preliminary steps, for instance, converting fractions to decimals.
(cont.) • Once you have substituted the numbers into the formula you will have to do some computations to find the unknown. • Most of the formulas have the same basic form: A=B x C • You will need two of the numbers (or the information that enables you to find two of the numbers) and then you will either have to divide or multiply them to find the third number—the answer you are seeking.
(cont.) • Whether you will need to multiply or divide is determined by which quantity (number) in the formula you are trying to discover. • For example, the formula A=B x C may be converted into three different formulas. All three formulas are equivalent, but are put into different forms, depending upon the quantity (number) to be discovered. • If the quantity A is unknown, then the following formula is used: A = B x C • The number B is multiplied by C; the product of B times C is A.
(cont.) • If the quantity B is unknown, the following formula is used: B = A ÷ C • The number A is divided by B; the quotient of A divided by B is C. C = A ÷ B • Notice that in all these instances, the unknown quantity is always by itself on one side of the “equal” sign.
Converting Fractions to Decimals • There will be many times when you will want to convert a fraction into a decimal. • Most people find it much easier to work with decimals than fractions. • Also, hand calculators can multiply and divide by decimals. • To convert a fraction into a decimal, you simply divide the top number of the fraction (the “numerator”) by the bottom number of the fraction (the “denominator”).
Example: • To change 3/4 into a decimal, you must divide 3 (the top number) by 4 (the bottom number). 3 ÷ 4 = .75 • To change 1/5 into a decimal, divide 1 by 5. 1 ÷ 5 = .20 • If you are using a hand calculator, it will automatically give you the right answer with the decimals in the correct place.
To add or subtract by decimals,think “MONEY” $ 101.18 line the decimals up by decimal point and add or subtract. • Example:
To multiply by decimals, do the multiplication. The answer should have as many decimal places as the total number of decimal places in the multiplying numbers. • Just add up the decimal places in the numbers you are multiplying and put the decimal point the same number of places to the left. • Example: 57.999 x 23.7 1374.5763
To divide by decimals, move the decimal point in the outside number all the way to the right and then move the decimal point in the inside number the same number of places to the right. • Example: 44.6 ÷ 5.889 44600 ÷ 5889 = 7.57
Percentage Problems • You will often be working with percentages in real estate finance problems. For example, loan-to-value ratios and interest rates are stated as percentages. • It is necessary to convert the percentages into decimals and vice versa, so that the arithmetic in a percentage problem can be done in decimals.
To convert a percentage to a decimal, remove the percentage sign and move the decimal point two places to the left. This may require adding zeros. • Example: 80% becomes .80 9% becomes .09 75.5% becomes .755 8.75% becomes .0875
To convert a decimal to percentage, do just the opposite. Move the decimal two places to the right and add a percentage sign. • Example: .88 becomes 88% .015 becomes 1.5% .09 becomes 9%
The word “of” means to multiply. • Whenever something is expressed as a percent of something, it means MULTIPLY. • Example: If a lender requires a loan-to-value ratio of 75% and a house is worth $89,000, what will be the maximum loan amount? (What is 75% of $89,000?) .75 x $89,000 = $66,750 maximum loan amount • Percentage problems are usually similar to the above example. You have to find a part of something, or a percentage of the total.
A general formula is: • A percentage of the total equals the part, or part = percent x total P = % x T
Example: • Smith spends 24% of her monthly salary on her house payment. Her monthly salary is $2,750. What is the amount of her house payment? 1. Find amount of house payment. 2. Write down formula: P = % x T. 3. Substitute numbers into formula. P = 24% x $2,750 • Before you can perform the necessary calculations, you must convert the 24% into a decimal. Move the decimal two places to the left: 24% = .24 P = .24 x $2,750 4. Calculate: multiply the percentage by the total. .24 x $2,750 = $660 • Smith’s house payment is $660.
Problems Involving Measures of Central Tendency • Appraisers, finance officers, and lenders evaluate data and information by the use of averages. • These average figures are known as the mean, the median, or the mode. It is useful to know how they are derived.
MEAN • The average figure that is called a MEAN is derived by taking a set of numbers and adding them up. The result is then divided by the numbers in the set. • Example: • A group of houses have the following monthly rental prices: Rental #1 – $1,300 Rental #2 – $900 Rental #3 – $1,200 Rental #4 – $1,100 Rental #5 – $1,150 $5,650 Total • To determine the Mean, the total rentals of $5,650.00 are divided by the number of rental houses. Thus, $5650 = $ 1130 Mean monthly rental. 5
MEDIAN – Odd Number Example • The average figure that is described as a MEDIAN is derived by simply selecting the middle number in a set of numbers. The numbers need to be in ascending order first. • Example: Rental #1 – $1,100 Rental #2 – $1,150 Rental #3 – $1,200 Rental #4 – $1,200 = Median Rental #5 – $1,250 Rental #6 – $1,250 Rental #7 – $1,300 • There are three numbers before Rental #4 and three numbers after. Therefore, rental #4 is the median number and the median rental price is $1,200.
MEDIAN – Even Number Example • The example above had an odd number of rentals. The following example shows how to determine a mean with an even set of numbers. • Example: Rental #1 – $1,100 Rental #2 – $1,150 Rental #3 – $1,200 Rental #4 – $1,200 Rental #5 – $1,250 Rental #6 – $1,250 Rental #7 – $1,275 Rental #8 – $1,275 • The median is determined by adding the two middle rental numbers in the set and dividing the result by 2. • In this set the middle numbers are rentals number 4 and 5. $1,200 $2,450 = $1,225 +$1,250 Therefore: 2 $2,450 • Thus, the median rent in this even number example is $1,225.
MODE • A MODE measures the most frequently occurring number in a series of numbers. Appraisers and lenders often use this benchmark to determine the predominant value of housing in a neighborhood. • Example: Sale #1 – $325,000 Sale #2 – $328,000 Sale #4 – $332,000 Sale #6 – $335,000 Sale #7 – $335,000 Sale #8 – $340,000 Sale #9 – $345,000 • There are two sales at $335,000. This would be the Mode. It would also be the predominant value of this set of sales. • The value range states from the lowest number to the highest number, in a set of numbers. Thus, the range in the example above would be expressed as from $325,000 to $345,000.
Interest Problems • Interest can be viewed as the “rent” paid by a borrower to a lender for the use of money (the loan amount, or principal). • INTEREST is the cost of borrowing money. • SIMPLE INTEREST • COMPOUND INTEREST
SIMPLE INTEREST • Simple interest problems are worked in basically the same manner as percentage problems, except that the simple interest formula has four components rather than three: interest, principal, rate, and time. Interest = Principal x Rate x Time I = P x R x T • Interest: The cost of borrowing expressed in dollars; money paid for the use of money. • Principal: The amount of the loan in dollars on which the interest is paid. • Rate: The cost of borrowing expressed as a percentage of the principal paid in interest for one year. • Time: The length of time of the loan, usually expressed in years.
One must know the number values of three of the four components in order to compute the fourth (unknown) component. • a. Interest unknown Interest = Principal x Rate x Time Example: Find the interest on $3,500 for six years at 11%. I = P x R x T I = ($3,500 x .11) x 6 I = $385 x 6 I = $2,310
b. Principal unknown Principal = Interest ÷ Rate x Time P= I ÷ (R x T) • Example: How much money must be loaned to receive $2,310 interest at 11% if the money is loaned for six years? P = I ÷ (R x T) P = $2,310 ÷ (.11 x 6) P = $2,310 ÷ .66 P = $3,500
c. Rate unknown Rate = Interest ÷ Principal x Time R = I ÷ (P x T) • Example: In six years $3,500 earns $2,310 interest. What is the rate of interest? R = I ÷ (P x T) R = $2,310 ÷ ($3,500 x 6) R = $2,310 ÷ $21,000 R = .11 or 11%
d. Time unknown Time = Interest ÷ Rate x Principal T = I ÷ (R x P) • Example: How long will it take $3,500 to return $2,310 at an annual rate of 11%? T = I ÷ (R x P) T = $2,310 ÷ ($3,500 x .11) T = $2,310 ÷ $385 T = 6 years
A. COMPOUND INTEREST • Compound interest is more common in advanced real estate subjects, such as appraisal and annuities. • As previously stated, compound interest is interest on the total of the principal plus its accrued interest. • For each time period (called the “conversion period”), interest is added to the principal to make a new principal amount. Therefore, each succeeding time period has an increased principal amount on which to compute interest. Conversion periods may be monthly, quarterly, semi-annual, or annual. • The compound interest rate is usually stated as an annual rate and must be changed to the appropriate “interest rate per conversion period” or “periodic interest rate.” To do this, you must divide the annual interest rate by the number of conversion periods per year. This periodic interest rate is called “i.”
COMPOUND INTEREST EXAMPLE: • The formula used for compound interest problems is: Interest = principal x periodic interest rate I = P x i
Example: • A $5,000 investment at 9% interest compounded annually for three years earns how much interest at maturity? I = P x i I = $5,000 x (.09 ÷ 1) • First year’s I = $5,000 x .09 or $450. Add to $5,000. • Second year’s I = $5,450 x .09 or 490.50. Add to $5,450. • Third year’s I = $5,940.50 x .09 or $534.65. Add to $5,940.50 • At maturity, the borrower will owe $6,475.15. • The $5,000 loan has earned interest of $1,475.15 in three years.
Example: • How much interest will a $1,000 investment earn over two years at 12% interest compounded semi-annually? • Since the conversion period is semi-annual, the interest is computed every six months. Thus, the periodic interest rate “i” is divided by two conversion periods: i = 6%. I = P x i 1. Original principal amount = $1,000.00 2. Interest for 1st period ($1,000 x .06) = $60.00 3. Balance beginning 2nd period = $1,060.00 4. Interest for 2nd period ($1,060 x .06) = $63.60 5. Balance beginning 3rd period = $1,123.60 6. Interest for 3rd period ($1,123.60 x .06) = $67.42 7. Balance beginning 4th period = $1,191.02 8. Interest for 4th period ($1,191.02 x .06) = $71.46 9. Compound principal balance = $1,262.48 i for 2 years = $1,262.48 - $1,000 or $262.48
B. EFFECTIVE INTEREST RATE • The NOMINAL (“NAMED”) INTEREST RATE is the rate of interest stated in the loan documents. • The EFFECTIVE INTEREST RATE/APR/ANNUAL PERCENTAGE RATE is the rate the borrower is actually paying. TQ • In other words, the loan papers may say one thing when the end result is another, depending upon how many times a year the actual earnings rate is compounded. • The effective interest rate equals the annual rate, which will produce the same interest in a year as the nominal rate converted a certain number of times. • For example, 6% converted semi-annually produces $6.09 per $100; therefore, 6% is the nominal rate and 6.09% is the effective rate. A rate of 6% converted semi-annually yields the same interest as a rate of 6.09% on an annual basis.
C. DISCOUNTS • In alternative methods of financing, the loan proceeds disbursed by the lender are often less than the face value of the note. • This occurs when the borrower (or a third party) pays discount points. Generally when a borrower wants a lower rate they “buy down” the rate. TQ • The lender is paid points up front as compensation for making the loan on the agreed terms, at a lower rate. • When a discount is paid, the interest costs to the borrower (and the yield to the lender) are higher than the contract interest rate.
DISCOUNT EXAMPLE: • When more accurate yield and interest tables are unavailable, it is possible to approximate the effective interest cost to the borrower and the yield rate to the lender when discounted loans are involved. • The formula for doing so is as follows: i = (r + (d/n)) ÷ (P - d) • i: approximate effective interest rate (expressed as a decimal) • r: contract interest rate (expressed as a decimal) • d: discount rate, or points deducted (expressed as a decimal) • P: principal of loan (expressed as the whole number 1 for all dollar amounts) • n: term (years, periods, or a fraction thereof)
Example: • What is the estimated effective interest rate on a $60,000 mortgage loan, with a 20-year term, contract rate, if interest being 10% per annum, discounted 3%, so that only $58,200 is disbursed to the borrower? i = .10 + (.03/20) = .10 + .0015 = .10150 = .10463 or 10.46% 1 - .03 .97 .97 • The effective interest rate (or yield) on the loan is 10.46%.
Profit and Loss Problems • Every time a homeowner sells a house, a profit or loss is made. • Many times you will want to be able to calculate the amount of profit or loss. • Profit and loss problems are solved with a formula that is a variation of the percent formula: value after = percentage x value before. VA = % x VB • The VALUE AFTER is the value of the property after the profit or loss is taken. • The VALUE BEFORE is the value of the property before the profit or loss is taken. • The PERCENT is 100% plus the percent of profit or minus the percent of loss.
Example: • Green bought a house ten years ago for $50,000 and sold it last month for 45% more than she paid for it. What was the selling price of the house? VA = % x VB VA = 145% x VB (To get the percent, you must add the percent of profit to or subtract the percent of loss from 100%). VA = 1.45 x $50,000 VA = $72,500 was the selling price
Profit means TAXES (Rentals) • Taking a profit can be even more expensive than what your tax rate is on your profit • What about recaptured depreciation? • Can be very expensive • More the longer you hold the property • Just be well informed when investing and doing tax writeoffs • PERSONAL RESIDENCE (Still has a non-recaptured interest deduction) • The government want’s that money though!!
STILL NO TAX ON PERSONAL RESIDENCE PROFITS • Be aware, if that deduction is taken, the incentive for people to buy will be greatly decreased! • If a bill is introduced in congress you might want to let your senator and representative know you are against it!
Example: • Now we will use the profit and loss formula to calculate another one of the components. • Green sold her house last week for $117,000. She paid $121,000 for it five years ago. What was the percent of loss? VA = % x VB $117,000 = % x $121,000(Because the percent is the unknown, you must divide the value after by the value before.) % = $117,000 ÷ $121,000 % = .9669 or 97% (rounded) Now subtract 97% from 100% to find the percent of loss. % = 100% - 97% = 3% loss
Example: • Your customer just sold a house for 17% more than was paid for it. The seller’s portion of the closing costs came to $4,677. The seller received $72,500 in cash at closing. What did the seller originally pay for the house? VA = % x VB $72,500 + 4,677 = 117% x VB VB = ($72,500 + 4,677) ÷ 117% (Since the value before is 117% unknown, you must divide the value after [the total of the closing costs and the escrow proceeds] by the percent of profit.) VB = $77,177 ÷ 1.17 VB = $65,963.25 was the original price
Prorations - Intro • There are some expenses connected with owning real estate that are often either paid for in advance or in arrears. • For example, fire insurance premiums are normally paid for in advance. Landlords usually collect rents in advance, too. • On the other hand, mortgage interest accrues in arrears. • When expenses are paid in advance and the owner then sells the property, part of these expenses have already been used up by the seller and are rightfully the seller’s expense. • Often, however, a portion of the expenses of ownership still remain unused and when title to the property transfers to the buyer, the benefit of these advances will accrue to the buyer. • It is only fair that the buyer, therefore, reimburse the seller for the unused portions of these homeownership expenses. | s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038067870.12/warc/CC-MAIN-20210412144351-20210412174351-00062.warc.gz | CC-MAIN-2021-17 | 17,599 | 43 |
https://www.hackmath.net/en/word-math-problems/unit-conversion?tag_id=48 | math | The unit conversion of volume problems
Number of problems found: 346
- Gas price
If a cm3 of gas costs rm 1.50, how many cents would a liter of gas cost? 1 rm = 1 Malaysian Ringgit = 100 Malaysian Ringgit cents = equals 0.21 Euro in 2021/Q3
There is water in the block-shaped tank with dimensions of 3 m 1.5 m 5 m, it occupies 70% of the tank volume. Find the volume of water in the tank (in hl) .
- A diesel car
A diesel car costs $2599 more than an unleaded petrol car and travels an average of 25,000km per year. Diesel petrol has a consumption rate of 7.4L per 100km and costs $1.39 per litre. Unleaded petrol has a consumption rate of 8.5L per 100km and costs $1.
- Eights of butter
How many eights of butter (1/8 of kg = 125 g) can be stored in a box with dimensions of 4 dm, 2 dm, 1.8 dm, if the eighth of butter has dimensions of 8 cm, 5 cm, 3 cm?
- Tom has
Tom has a water tank that holds 5 gallons of water. Tom uses water from a full tank to fill 6 bottles that each hold 16 ounces and a pitcher that holds 1/2 gallon. How many ounces of water are left in the water tank?
Kevin has a bathtub shaped like a block. The bathtub measures 70 cm long, 45 cm wide and 50 cm high. Then the bathtub will be filled with clean water 3/5 of its height. The clean water needed is….
- Water overflow
A rectangular container that has a length of 30 cm, a width of 20 cm, and a height of 24 cm is filled with water to a depth of 15 cm. When an additional 6.5 liters of water are poured into the container, some water overflows. How many liters of water over
What is the volume of a body that stretches a dynamometer in air, on which it is suspended by a force of 2.5 N, and if it is immersed in alcohol with a density of 800 kg/m ^ 3, does it tension the dynamometer with a force of 1.3 N?
- Edges of the cuboid
Find the length of the edges of the cuboid, which has the following dimensions: width is 0.4 m; the height is 5.8 dm and the block can hold 81.2 liters of fluid.
- Above water surface
If we remove the stone from the water, we apply a force of 120N. How much force will we have to exert if we move the stone above the water surface? The density of the stone is 5000 kg/m ^ 3.
- What power
What power should the radiator have in a room 5x4 meters with a height of 3 meters? Hint: Calculate 35 watts per meter ^ 3 in case you need 22 degrees in the room but you need about 24 degrees in the bathroom. It's an old heating cheat, but it will defini
- Water cylinder
Zuzana poured 785 ml of water into a measuring cylinder with a base radius of 5 cm. The water in the cylinder reached a height of 2 cm from the upper edge of the cylinder. How tall is the cylinder? (π = 3.14)
- An experiment
The three friends agreed to the experiment. At the same time, they all took out an empty cylindrical container on the windowsill and placed it so that it was horizontal. Everyone lives in a different village, and each used a container with a different bot
- Water tank
The block-shaped tank is 2.5 m long, 100 cm wide and 12 dm high. In how many minutes will it be filled with water to two thirds if 40 liters of water flow into the tank per minute?
- Mr. Gardener
Mr. Gardener wants to make wood for the balcony. Boxes. Each will have the shape of a perpendicular prism with a square base, the height is limited to 60 cm. Each container will be filled with soil by pouring the whole bag of substrate sold in a package w
- The volleyball ball
The volleyball ball can have a circumference after inflation of at least 650 max 750 mm. What volume of air can this ball hold, if its circumference is the average of the minimum and maximum inflation of the ball.
- Glasses of juice
Jake’s mom filled a 2-liter container with juice. Then Jake poured 2 glasses of juice. Each glass had exactly 400 milliliters of juice. How many liters of juice remain in the container?
- Heat transfer
We placed a lead object weighing 0.4 kg and 250°C in 0.4 L water. What was the initial temperature of water t2 if the object's temperature and the water after reaching equilibrium was 35°C? We assume that the heat exchange occurred only between the lead o
- Gallons and quarts
5 gallons 2 quarts − 1 gallon 3 quarts = (Hint: 4 quarts equals 1 gallon. )
- The square
The square oak board (with density ρ = 700 kg/m3) has a side length of 50 cm and a thickness of 30 mm. 4 holes with a diameter of 40 mm are drilled into the board. What is the weight of the board?
Tip: Our volume units converter will help you with the conversion of volume units. Do you know the volume and unit volume, and want to convert volume units? Unit conversion - math problems. Volume - math problems. | s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588257.34/warc/CC-MAIN-20211028034828-20211028064828-00094.warc.gz | CC-MAIN-2021-43 | 4,657 | 40 |
https://www.tutorialspoint.com/reasoning/reasoning_ranking_and_order_online_quiz.htm | math | Following quiz provides Multiple Choice Questions (MCQs) related to Ranking and Order. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using Show Answer button. You can use Next Quiz button to check new set of questions in the quiz.
Q 1 - A group of dancers are standing in a line for their performance. Joseph tried to calculate his rank from the either side and found that his rank is 19th. Find the total number of dancers standing in that line.
If we will count till Joseph from the left side, then he will be 19 dancer. Similarly, from right hand side, the total number of students till joseph will also be 19. Now adding both and subtracting 1 (dual occurrence of Joseph) we will get = 19 + 19 - 1 = 37.
Q 2 - In a ticket counter, 3 persons X, Y, Z are standing. In between X and Y there are 5 persons and in between Y and Z, there are 8 persons present. If ahead of Z there are 3 persons and 21 persons are standing behind X, what is could be the minimum number of persons in the queue?
Q 3 - Out of 46 students, rank of Shiva is ranked as 12th. What will be his rank from below?
This can be simply calculated as = (total students - rank from top) + 1
So 46 – 12 + 1
= 34 + 1 = 35
Q 4 - In a cinema hall, 35 viewers were sitting in a row. From the right hand side, the position of Kamal was 7th whereas position of Sunil from the left hand side was 9th. Manoj was sitting exactly in between Kamal and Sunil. Find the position of Kamal from Sunil.
Number of viewers sitting in between Kamal and Sunil can be calculated as
35 - (9 + 7) = 19
So we can say now that 9 viewers were present in between Kamal - Manoj and Manoj - Sunil. So the position of Kamal is 10th from Sunil.
Q 5 - Rank of Madhaba is 14th from the bottom in a list of 64 boys. What would be his new rank from the top if 3 new boys will be added to the bottom of the list?
Total number of students in the row = 64
Rank of Madhaba from the bottom = 14
So, rank of Madhaba from top would be = (64 - 14) + 1 = 51
Now as adding of new boys to the bottom of the list will not affect the rank of Madhaba from top, hence; his rank will be the same 51 from the top, even after the addition.
Q 6 - The strength of a class is 35. From the bottom, the position of Gopal is 7th and Chinmaya is placed at 9th from the top. Tanmaya is present at the middle position in between Sanjaya and Chinmaya. Determine the position of Gopal from Tanmaya.
Total number of students present between Gopal and Chinmaya
= 35 - (7 + 9) = 19
Middle of 19 is 10th position.
So Gopal is at 10th position above Tanmaya or his position is 11.
Q 7 - In a row of students, the position of Hari is 7th from the left hand side and that of Radhika is 12th from the right hand side. Now for some reason, they interchanged their positions. Now, 22 is the new rank of Hari from the left hand side. Calculate the total number of students present in that row.
Earlier the rank of Radhika was 12 from the right hand side. Now at the same position the rank of Hari is 22 from the left hand side. Hence adding both side students and eliminating the repeated person, the total number of students will be
= 22 + 12 - 1
Q 8 - If the rank of Rohan is 7th from the top in a group of 50 candidates and 2 new candidates are added just before and after him, what will be his new rank from bottom?
Adding of candidates just before Rohan will not change his rank from bottom. Before addition, the rank of Rohan from bottom is
= (50 - 7) + 1 = 44
Now adding 2 candidates just after Rohan will increase his rank by 2 positions. Hence; the new rank of Rohan from bottom will be = 44 + 2 = 46
Q 9 - Harish’s rank is 14th from the top and 13th from the bottom in a group of boys. Similarly, in a group of girls, the rank of Sona is 16th from top and 19th from bottom. What is number of boys and girls respectively?
As per the rank of Harish, the total number of boys
= 14 + 13 - 1
As per the rank of Sona, the total number of girls will be
= 16 + 19 - 1
Q 10 - Among the list of 64 shortlisted applicants, rank of Suresh is 54 from top and rank of Radhika is 34 from bottom. How many candidates are present in between Suresh and Radhika?
Rank of radhika from top = (64 - 34) + 1 = 31
Now number of candidates lying in between Radhika and Suresh are
= (54 - 31) - 1 | s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370506121.24/warc/CC-MAIN-20200401192839-20200401222839-00422.warc.gz | CC-MAIN-2020-16 | 4,374 | 38 |
http://www.icoachmath.com/math_dictionary/scale_factor.html | math | Definition of Scale Factor
The ratio of any two corresponding lengths in two similar geometric figures is called
as Scale Factor.
The ratio of the length of the scale drawing to the corresponding length of the actual object is called as Scale Factor.
More About Scale Factor
A scale factor is a number used as a multiplier in scaling.
A scale factor is used to scale shapes in 1, 2, or 3 dimensions.
Scale factor can be found in the following scenarios:
1. Size Transformation: In size transformation, the scale factor is the ratio of expressing the amount of magnification.
2. Scale Drawing: In scale drawing, the scale factor is the ratio of measurement of the drawing compared to the measurement of the original figure.
3. Comparing Two Similar Geometric Figures: The scale factor when comparing two similar geometric figures, is the ratio of lengths of the corresponding sides.
Video Examples: Proportions, Triangles, MissingSides, Scale Factors
Example of Scale Factor
ABCD and PQRS are similar polygons. Then the scale factor of polygon ABCD to polygon
PQRS is the ratio of the lengths of the corresponding sides.
Scale factor = BC:QR = 3:8.
Solved Example on Scale Factor
Ques: Find the scale factor from the larger rectangle to the smaller rectangle, if the two rectangles are similar.
Correct Answer: B
Step 1: If we multiply the length of one side of the larger rectangle by the scale
factor we get the length of the corresponding side of the smaller rectangle.
Step 2: Dimension of larger rectangle × scale factor = dimension of smaller rectangle
Step 3: 24 × scale factor = 20 [Substitute the values.]
Step 4: Scale factor = 20/24 [Divide each side by 24.]
Step 5: Scale factor =5/6= 5:6 [Simplify.]
Therefore, scale factor from the larger rectangle to the smaller rectangle is 5:6. | s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549426169.17/warc/CC-MAIN-20170726142211-20170726162211-00584.warc.gz | CC-MAIN-2017-30 | 1,796 | 26 |
http://slideplayer.com/slide/8300916/ | math | Measurement Important to measure accurately: –Communicate information –Reliable results –Real Life!
Distance (sometimes referred to as length, width or height) Basic unit = meters Instrument = ruler or meter stick
Mass The amount of “stuff” an object has Unit = grams Instrument = Balance
Volume of a Solid The amount of space an object takes up Unit = cm 3 Instrument = ruler Calculation = Length x Width x Height
Volume of a Liquid The amount of space a liquid takes up Unit = Liter Instrument = Graduated cylinder
Temperature How hot or cold something is… Unit = Celsius Instrument = Thermometer
Time How long something takes to occur Unit = seconds Instrument = stopwatch
If you need help with… Knowing how many mL are in a L How many cm are in a m What ml, L, cm and m mean Practice measuring Then you need to come after school to practice!! This stuff WILL be on the test! | s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303729.69/warc/CC-MAIN-20220122012907-20220122042907-00293.warc.gz | CC-MAIN-2022-05 | 892 | 8 |
http://metrohorse.com/page/soluciones-triviales-matrices-solver-19198516.html | math | Answer Wiki. What is a non-invertible matrix? How can I conquer my fear? A one-liner or a direct application of an axiom is trivial, unless it contains a stunning insight. The number of equations in the system: 2 3 4 5 6 Change the names of the variables in the system. Answered Nov 17, The system of linear equations with 2 variables.
This online calculator will help you to solve a system of linear equations using inverse matrix method. Using this online calculator, you will receive a detailed step-by-step solution to your problem, which will help you understand the algorithm how to solve system of linear. System of linear equations calculator - solve system of linear equations step-by-step, elimination, Cramer's rule, inverse matrix method, analysis for compatibility.
Video: Soluciones triviales matrices solver Linear Algebra Example Problems - General Solution of Augmented Matrix
Also you can compute a number of solutions in a system of linear equations. With help of this calculator you can: find the matrix determinant, the rank, raise the matrix to a power, find the sum and the multiplication of matrices, calculate the.
So much to do, so little time. Very detailed solution.
Having some variables or terms that are not equal to zero or an identity. How do we know what to do when asked to find the solutions of given equations saying find the solution when it has non trivial solution?? Continue Reading. Nonzero solutions or examples are considered to be "nontrivial".
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|Prove that the identity matrix only has 1:s in the diagonal as non-zero elements.
Or students who cannot see how to answer. I would not use it to solve linear systems but there must be some concrete or real life applications where it Add to.
Solving systems of linear equations by substitution. Having some variables or terms that are not equal to zero or an identity. Nonzero solutions or examples are considered to be "nontrivial".
In that case you. Simply if we look upon this from For example, the equation x+5y=0 has the trivial solution x=0,y=0. Nontrivial solutions include x=5,y=–1 and.
Often, solutions that involve a zero are called "trivial". Nonzero solutions or examples are considered to be "nontrivial".
Video: Soluciones triviales matrices solver Ejemplo soluciones no triviales en un sistema de ecuaciones
For example, the.
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Why did my reputation suddenly increase by points? The system of linear equations with 3 variables.
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Linear equations calculator Inverse matrix method
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You can input only integer numbers, decimals or fractions in this online calculator Simply if we look upon this from Mathwords. | s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107912593.62/warc/CC-MAIN-20201031002758-20201031032758-00318.warc.gz | CC-MAIN-2020-45 | 3,009 | 24 |
https://www.letgo.com/en-ca/i/alberta-high-school-textbooks_324169fe-13eb-4dc7-bbf7-faf5bc3f099e | math | Alberta High School Textbooks
Textbooks are negotiable, but I would prefer to start at 30 for each, except for the Red math textbook, which is set at 20 since it is mostly unused but has some notes written and some questions completed inside (I can negotiate a bundle if you are interested in multiple textbooks). These should all still be current or at least used in the upgrading classes at some universities in Calgary (if any are not used at all please let me know). I have the Science data booklet (free) to go with the Science 20 textbook, and I am also selling “The Key” study guides for English 30-1 and Math 30-1, both unused for 15, unless you get them as a part of a larger purchase :) . These are all negotiable, so please let me know!
Message the seller: | s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540504338.31/warc/CC-MAIN-20191208021121-20191208045121-00548.warc.gz | CC-MAIN-2019-51 | 771 | 3 |
https://box.es/i/Qss1Mr3uXf | math | #supreme#newera# suede #fitted#hat pre-own in good condition. Questions message me
These are awesome. I wish I was stupidly rich so that I could collect them all (except for the ridiculous number of Iron Man versions).
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https://www.fishpond.co.uk/Books/MAA-Problem-Book-Series-Evan-Chen/9780883858394 | math | Preface; Preliminaries; Part I. Fundamentals: 1. Angle chasing; 2. Circles; 3. Lengths and rules; 4. Assorted configurations; Part II. Analytic Techniques: 5. Computational geometry; 6. Complex numbers; 7. Barycentric coordinates; Part III. Farther from Kansas: 8. Inversion; 9. Projective geometry; 10. Complete quadrilaterals; 11. Personal favorites; Part IV. Appendices: Appendix A. An ounce of linear algebra; Appendix B. Hints; Appendix C. Selected solutions; Appendix D. List of contests and abbreviations; Bibliography; Index; About the author.
A problem-solving book on Euclidean geometry, providing carefully chosen worked examples and over 300 practice problems from contests around the world.
Evan Chen is currently an undergraduate studying at the Massachusetts Institute of Technology. He won the 2014 USA Mathematical Olympiad, earned a gold medal at the IMO 2014 for Taiwan, and acts as a Problem Czar for the Harvard-MIT Mathematics Tournament.
A good understanding of high school geometry, and a fondness for solving problems, should be sufficient background for this book. ... students preparing for mathematics competitions, and their faculty coaches, should find this book very valuable." - Mark Hunacek, MAA Reviews | s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988758.74/warc/CC-MAIN-20210506144716-20210506174716-00456.warc.gz | CC-MAIN-2021-21 | 1,236 | 4 |
https://www.studypool.com/discuss/1084981/algebra-word-problem-51?free | math | Bonzo has some nickles and some quarters. 52 coins all together. The total value of the coins is $8.20. Find the number of pickles and the number of quarters.
Thank you for the opportunity to help you with your question!
Let the number of nickles be n and number of quarters be q
n + q = 52
Hence n = 52 -q
Value equation is determined as under in terms of cents
5 n + 25 q = 820
5 (52-q) + 25q = 820
260 - 5q +25q = 820
20q = 560
q = 28
Hence n = 52-28 = 24
Number of nickels = 24 and number of quarters = 28
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http://math.stackexchange.com/questions/tagged/math-history+group-theory | math | Wikipedia states that van Dyck (1882) was the first to give the definition of a group in the modern way. Before this, what were some of the original axioms or conditions for groups? I mean, how were ...
Two related elementary facts in group theory are sometimes called Poincaré's theorems. If $H\lneq G$ and $[G:H]<\infty$, then there is $N\leq H$, $N\lhd G$ such that $[G:N]<\infty$. The ...
Torsion is used to refer to elements of finite order under some binary operation. It doesn't seem to bear any relation to the ordinary everyday use of the word or with its use in differential geometry ...
I've read in many places that the Monster group was suspected to exist before it was actually proven to exist, and further that many of its properties were deduced contingent upon existence. For ...
From Scott's book Group Theory $1.7.10.$ (Poincaré) The intersection of a finite number of subgroups of finite index is of finite index. My question is: Did Poincaré prove the Theorem as stated ...
Let $G$ be a group, which for my purposes would be abelian. To say that $G$ has the Hopf property is to say that every epimorphism of $G$ is an automorphism. Does anyone happen to recall the context ...
One of the most important application of "coset", I think, is to prove the Lagrange's theorem, which was not originally stated in the group theoretic terms. In some textbooks I have read about ...
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https://majabyjula.amstrad.fun/mathematical-modeling-with-excel-book-34970uv.php | math | 5 edition of Mathematical modeling with EXCEL found in the catalog.
Mathematical modeling with EXCEL
Includes bibliographical references.
|LC Classifications||QA300 .A446 2010|
|The Physical Object|
|LC Control Number||2009010208|
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Mathematical Modeling with Excel and millions of other books are available for Amazon Kindle. Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - Cited by: 4.
The model is then built using the appropriate mathematical tools. Then it is implemented and analyzed in Excel via step-by-step instructions. In the exercises, we ask students to modify or refine the existing model, analyze it further, or adapt it to similar by: 4.
Mathematical Modeling with Excel presents various methods used to build and analyze mathematical models in a format that students can quickly comprehend. Excel is used as a tool to accomplish this goal of building and analyzing the models. The book begins with a step-by-step introduction to discrete dynamical systems, which are mathematical models that describe how a quantity changes from one point in time to the next.
Readers are taken through the process, language, and notation required for the construction of such models as well as their implementation in : Wiley. How is Chegg Study better than a printed Mathematical Modeling With Excel 1st Edition student solution manual from the bookstore.
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The Active Modeler: Mathematical Modeling with Microsoft Excel Pdf. E-Book Review and Description: This can be a arms-on introduction to modeling all kinds of purposes in Microsoft Excel. It options quite a few tutorials and purposes for instance the best way to mannequin and clear up issues in Excel.
MATHEMATICAL MODELING 1 Types of modeling software (platform). 1 Advantages and disadvantages of spreadsheets. 3 Guidelines to programming in spreadsheets.
10 PART I USING BUILDIT CHAPTER 2. BUILDING MATHEMATICAL MODELS IN EXCEL 17File Size: 1MB. Mastering Financial Modelling in Microsoft Excel will help allow you to become more proficient in building and applying financial models, enabling you to get better, more accurate results, fast.
This highly practical book and CD combination is an unrivalled compendium of techniques designed to save you time and help you become more productive/5(7). Mathematical modeling with EXCEL book models deepen our understanding of‘systems’, whether we are talking about a mechanism, a robot, a chemical plant, an economy, a virus, an ecology, a cancer or a brain.
And it is necessary to understand something about how models are made. This book will try to teach you how to build mathematical models and how to use them. An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics.
DISCUS (more info), created by Neville Hunt and Sidney Tyrrell School of Mathematical and Information Sciences, Coventry University, CV1 5FB, UK. The site has downloadable Excel documents that can serve as turorials, examples, and templates.
Excel Cheat Sheet (Acrobat. Mathematical Modeling With Excel by Brian Albright ISBN ISBN x Paperback; Jones & Bartlett Learning; ISBN CFI's Excel Book is free and available for anyone to download as a PDF. Read about the most important shortcuts, formulas, functions, and tips you need to become an Excel power user.
This book covers beginner, intermediate, and advanced topics to master the use of spreadsheets for financial analysts. This book is for agriculturists, many of whom are either novices or non-computer programmers, about how they can build their mathematical models in Microsoft Excel.
Of all modeling platforms. a new approach Mathematical modeling with EXCEL book teaching mathematical modeling. The scope of the text is the basic theory of modeling from a mathematical perspective. A second applications focussed text will build on the basic material of the first volume. It is typical that students in a mathematical modeling class come from a wide variety of disciplines.
This is the ‘‘definitions’’ step of the above scheme. The ‘‘systems analysis’’ step identifies the battery and fuels levels as the relevant parts of the system as explained above.
Then, in the ‘‘modeling’’ step of the scheme, a model consisting of a battery and a tank such as in Figure is Size: 2MB. Figure AIC use in a simple linear regression model. Left: The predictions of the model for 1,2,3 and 4 parameters, along with the real data (open circles) generated from a 4 parameter model with noise.
Right: the AIC values for each number of Size: 1MB. Mathematical modeling is a principled activity that has both principles behind it and methods that can be successfully applied.
The principles are over-arching or meta-principles phrased as questions about the intentions and purposes of mathematical modeling.
These meta-principles are almost philosophical in. With a focus on mathematical models based on real and current data, Models for Life: An Introduction to Discrete Mathematical Modeling with Microsoft Office Excel guides readers in the solution of relevant, practical problems by introducing both mathematical and Excel techniques.
The book begins with a step-by-step introduction to discrete dynamical systems, which are mathematical models that describe how. a same disease has occurred through the years.
The aim of the mathematical modeling of epidemics is to identify those mechanisms that produce such pat-terns giving a rational description of these events and providing tools for disease control.
This flrst lecture is devoted to introduce the File Size: KB. Mathematical Models and Their Analysis, Frederic Y. Wan,Mathematics, pages. Topics in mathematical modeling, K. Tung,pages. Topics in Mathematical Modelingis an introductory textbook on mathematical modeling.
The book teaches how simple mathematics can help formulate and solve real problems of. Spreadsheet Modeling and Excel Solver A mathematical model implemented in a spreadsheet is called a spreadsheet model.
Major spreadsheet packages come with a built-in optimization tool called Solver. Now we demonstrate how to use Excel spreadsheet modeling and Solver to find the optimal solution of optimization Size: KB. A Mathematical Approach to Order Book Modeling Fred´ eric Abergel´ and Aymen Jedidi November, Abstract Motivated by the desire to bridge the gap between the microscopic description of price forma-tion (agent-based modeling) and the Stochastic Di erential Equations approach used classicallyCited by: mathematical modelling.
The explanations of how to use Excel are clear and supported by innovative diagrams in the book and Flash videos on the CD ROM. Modeling with data: tools and techniques for scientific computing / Ben Klemens. Includes bibliographical references and index. ISBN (hardcover: alk. paper) 1. Mathematical statistics.
Mathematical models. Title. QAK –dc22 British Library Cataloging-in-Publication Data is availableFile Size: 4MB.
The Excel workbook has comments and instructions for how to use these formulas. As you follow along in this tutorial, I'll teach you some of the essential "math" skills.
Let's get started. Basic Excel Math Formulas Video (Watch and Learn) If learning from a screencast video is your style, check out the video below to walk through the tutorial.
Mathematical models can project how infectious diseases progress to show the likely outcome of an epidemic and help inform public health interventions. Models use basic assumptions or collected statistics along with mathematics to find parameters for various infectious diseases and use those parameters to calculate the effects of different interventions, like mass vaccination programmes.
Each Chapter Of The Book Deals With Mathematical Modelling Through One Or More Specified Techniques. Thus There Are Chapters On Mathematical Modelling Through Algebra, Geometry, Trigonometry And Calculus, Through Ordinary Differential Equations Of First And Second Order, Through Systems Of Differential Equations, Through Difference Equations, Through Partial Differential 5/5(4).
In its early development, this book was focused on graduate level mathematical modeling (with a statistical focus) and for advanced mathematics students preparing for the contest in modeling. TECHNOLOGY Statistical Modeling with SPSS makes extensive use of SPSS to test student initiated hypotheses from a set of real data included with the test.
Mathematical Models and their analysis De nition (Epidemiology) It is a discipline, which deals with the study of infectious diseases Peeyush Chandra Some Mathematical Models in Epidemiology.
Preliminary De nitions and Assumptions Mathematical Models and their analysis (1) Heterogeneous Mixing-Sexually transmitted diseases (STD), File Size: KB. • The student is able to justify data from mathematical models based on the Hardy-Weinberg equilibrium to analyze genetic drift and the effects of selection in the evolution of specific populations (1A3 & SP ).
• The student is able to describe a model that represents evolution within a population (1C3 & SP ). Mathematical Modeling: Models, Analysis and Applications covers modeling with all kinds of differential equations, namely ordinary, partial, delay, and stochastic.
The book also contains a chapter on discrete modeling, consisting of differential equations, making it a complete textbook on this important skill needed for the study of science.
Creating a mathematical model: • We are given a word problem • Determine what question we are to answer • Assign variables to quantities in the problem so that you can answer the question using these variables • Derive mathematical equations containing these variables • Use these equations to find the values of these variablesFile Size: KB.
Models for Life: An Introduction to Discrete Mathematical Modeling with Microsoft® Office Excel® moreover choices: A modular group that, after the first chapter, permits readers to uncover chapters in any order Fairly a couple of smart examples and exercises that permit readers to personalize the launched fashions via using their very.
A mathematical model is a description of a system using mathematical concepts and process of developing a mathematical model is termed mathematical atical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in the social sciences (such.
Mathematical and Trigonometric Functions 97 Lookup and Reference Functions Date and Time Functions Text Functions Information Functions The Analysis ToolPak Part Two: Financial Modeling Using Excel CHAPTER 5 How to Build Good Excel Models Attributes of Good Excel Models Documenting Excel Models Debugging Excel.
The best all-around introductory book on mathematical modeling is How to Model It: Problem Solving for the Computer Age by Starfield, Smith, and Bleloch. The book dates back tobut is just as relevant today. When most direct marketing people talk about "modeling", they either mean predictive response models, or they mean financial spreadsheet P&L models.
Mathematical models are increasingly used to guide public health policy decisions and explore questions in infectious disease control. Written for readers without advanced mathematical skills, this book provides an excellent introduction to this exciting and growing area. taught with a focus on mathematical modeling.
The content herein is written and main-tained by Dr. Eric Sullivan of Carroll College. Problems were either created by Dr. Sul-livan, the Carroll Mathematics Department faculty, part of NSF Project Mathquest, part of the Active Calculus text, or come from other sources and are either cited directly or.
tenth, chapter of the book reviews some mathematical principles basic to the other chapters. All of the chapters contain many numerical examples and graphs developed from the numerical examples. The ambitious student could recreate any of the charts and tables contained in the book using a computer and Excel spreadsheets.
There are many numerical. In order to learn more about mathematical modeling, read through the corresponding lesson called Using Mathematical Models to Solve Problems. This lesson covers: Defining mathematical modeling.With mathematical modeling growing rapidly in so many scientific and technical disciplines, Mathematical Modeling, Fourth Edition provides a rigorous treatment of the subject.
The book explores a range of approaches including optimization models, dynamic models and probability models.R Through Excel is a highly recommended first step into that program.” (Shiken: JALT Testing& Evaluation SIG Newsletter) “Students, researchers, and others who wish to use R.
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https://edurev.in/course/quiz/attempt/7880_Test-Problems-On-Ages-2/08b8fba4-0bf4-4e3b-8fb3-f267553421a1 | math | 20 Questions MCQ Test General Test Preparation for CUET - Test: Problems On Ages - 2
Test: Problems On Ages - 2 for CUET 2023 is part of General Test Preparation for CUET preparation. The Test: Problems On Ages - 2 questions and answers have been
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Six years ago, the ratio of the ages of Vimal and Saroj was 6 : 5 . Four years hence, the ratio of their ages will be 11 : 10 . What is Saroj's age at present?
Detailed Solution for Test: Problems On Ages - 2 - Question 3
Given that, six years ago, the ratio of the ages of Vimal and Saroj = 6 : 5
Hence we can assume that age of Vimal six years ago = 6x
age of Saroj six years ago = 5x
After 4 years, the ratio of their ages = 11 : 10
My brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. If my sister was 4 years of age when my brother was born, then what was the age of my father when my brother was born?
Detailed Solution for Test: Problems On Ages - 2 - Question 5
Let my age = x
My brother's age = x + 3
My mother's age = x + 26
My sister's age = ( x + 3 ) + 4 = x + 7 My father's age = ( x + 7 ) + 28 = x + 35
Age of my father when my brother was born = x + 35 − ( x + 3 ) = 32
The present ages of A,B and C are in proportions 4 : 7 : 9 . Eight years ago, the sum of their ages was 56 . What are their present ages (in years)?
Detailed Solution for Test: Problems On Ages - 2 - Question 6
Let present age of A,B and C be 4 x , 7 x and 9 x respectively.
Hence present age of A, B and C are
4 × 4 , 7 × 4 and 9 × 4 respectively.
i.e., 16 , 28 and 36 respectively.
The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. What is the ratio of their present ages?
Detailed Solution for Test: Problems On Ages - 2 - Question 10
Let age of the son before 10 years = x and age of the father before 10 years = 3 x
(3x + 20 ) = 2 ( x + 20 )
⇒ x = 20
Age of the son at present = x + 10 = 20 + 10 = 30
Age of the father at present = 3 x + 10 = 3 × 20 + 10 = 70
Required ratio = 70 : 30 = 7 : 3
If 6 years are subtracted from the present age of Ajay and the remainder is divided by 18 , then the present age of Rahul is obtained. If Rahul is 2 years younger to Denis whose age is 5 years, then what is Ajay's present age?
Detailed Solution for Test: Problems On Ages - 2 - Question 14
The ratio of the age of a man and his wife is 4 : 3 . At the time of marriage the ratio was 5 : 3 and After 4 years this ratio will become 9 : 7 . How many years ago were they married?
Detailed Solution for Test: Problems On Ages - 2 - Question 15
Let the present age of the man and his wife be 4 x and 3 x respectively.
After 4 years this ratio will become 9 : 7 ⇒ ( 4 x + 4 ) : ( 3 x + 4 ) = 9 : 7
⇒ 7 ( 4 x + 4 ) = 9 ( 3 x + 4 )
⇒ 28 x + 28 = 27 x + 36
⇒ x = 8
Present age of the man = 4 x = 4 × 8 = 32
Present age of his wife = 3 x = 3 × 8 = 24
Assume that they got married before t years. Then,
( 32 − t ) : ( 24 − t ) = 5 : 3
⇒ 3 ( 32 − t ) = 5 ( 24 − t )
⇒ 96 − 3 t = 120 − 5 t
⇒ 2 t = 24
The product of the ages of Syam and Sunil is 240 . If twice the age of Sunil is more than Syam's age by 4 years, what is Sunil's age?
Detailed Solution for Test: Problems On Ages - 2 - Question 16
Let age of Sunil = x
and age of Syam = y
xy = 240 ⋯ ( 1 )
Substituting equation ( 2 ) in equation ( 1 ) . We get
We got a quadratic equation to solve.
Always time is precious and objective tests measure not only how accurate you are but also how fast you are. We can solve this quadratic equation in the traditional way. But it is more easy to substitute the values given in the choices in the quadratic equation (equation 3 ) and see which choice satisfy the equation.
Here, option A is 10 . If we substitute that value in the quadratic equation, x ( x − 2 ) = 10 × 8 which is not equal to 120
Now try option B which is 12 . If we substitute that value in the quadratic equation, x ( x − 2 ) = 12 × 10 = 120 . See, we got that x = 12
Hence Sunil's age = 12
(Or else, we can solve the quadratic equation by factorization as,
Since x is age and cannot be negative, x = 12
Or by using quadratic formula as
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Join thousands of successful students who have benefited from our trusted online resources. | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100942.92/warc/CC-MAIN-20231209170619-20231209200619-00714.warc.gz | CC-MAIN-2023-50 | 7,064 | 83 |
https://www.intlpress.com/site/pub/pages/journals/items/joc/content/vols/0010/0004/a006/index.php | math | Journal of Combinatorics
Volume 10 (2019)
Special Issue in Memory of Jeff Remmel, Part 2 of 2
Guest Editor: Nicholas A. Loehr
Signature Catalan combinatorics
Pages: 725 – 773
The Catalan numbers constitute one of the most important sequences in combinatorics. Catalan objects have been generalized in various directions, including the classical Fuss–Catalan objects and the rational Catalan generalization of Armstrong–Rhoades–Williams. We propose a wider generalization of these families indexed by a composition s which is motivated by the combinatorics of planar rooted trees; when $s = (2, \dotsc , 2)$ and $s = (k +1, \dotsc , k +1)$ we recover the classical Catalan and Fuss–Catalan combinatorics, respectively. Furthermore, to each pair $(a, b)$ of relatively prime numbers, we can associate a signature that recovers the combinatorics of rational Catalan objects. We present explicit bijections between the resulting $s$-Catalan objects, and a fundamental recurrence that generalizes the fundamental recurrence of the classical Catalan numbers. Our framework allows us to define signature generalizations of parking functions which coincide with the generalized parking functions studied by Pitman–Stanley and Yan, as well as generalizations of permutations which coincide with the notion of Stirling multipermutations introduced by Gessel–Stanley. Some of our constructions differ from the ones of Armstrong–Rhoades–Williams, however as a byproduct of our extension, we obtain the additional notions of rational permutations and rational trees.
Catalan numbers, planar rooted trees, Dyck paths, noncrossing partitions, noncrossing matchings, polygon subdivisions, Stirling permutations, parking functions
2010 Mathematics Subject Classification
C. Ceballos was supported by the Austrian Science Foundation FWF, grant F 5008-N15, in the framework of the Special Research Program Algorithmic and Enumerative Combinatorics”; he was also partially supported by York University and a Banting Postdoctoral Fellowship of the Government of Canada.
R. S. González D’León was supported during this project by University of Kentucky, York University and Universidad Sergio Arboleda and he is grateful for their support.
Received 10 May 2018
Published 17 July 2019 | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100535.26/warc/CC-MAIN-20231204214708-20231205004708-00607.warc.gz | CC-MAIN-2023-50 | 2,285 | 13 |
https://rcogenasia.com/electricity-generation/why-is-electric-potential-not-a-vector.html | math | Why electric potential is scalar or vector?
Electric potential is the scalar quantity because it is defined as the amount of work done to bring a unit positive charge to bring from infinity to the point under the influence of the primary charge. Work is a scalar as it is a dot product of force and displacement.
Are electric potential vectors?
The electric potential is a scalar while the electric field is a vector.
Why is potential energy not a vector?
Potential energy is a scalar quantity as it has magnitude only. It does not have direction, as it does not depend on that. The standard unit of potential energy is joule. Hence, potential energy is a scalar quantity.
Why electric potential is a scalar?
Therefore, we can say that the electrostatic potential is dependent on charge and distance of charge from the point where the electrostatic potential is to be calculated. As the charge and the distance are scalar quantities. Therefore, the electrostatic potential is the scalar quantity.
Why potential difference is a scalar quantity?
Is potential difference a scalar or a vector? Potential difference is a scalar quantity. There is no particular direction in which a potential is applied. … The charge remains constant i.e., Q = 1.08 x 10–8 C after the supply was disconnected and the voltage will come down to 16.6 V.
Is electric current scalar or vector?
Electric current is a scalar quantity. Any physical quantity is defined as a vector quantity when the quantity has both magnitude and direction but there are some other factors which show that electric current is a scalar quantity . When two currents meet at a point the resultant current will be an algebraic sum.
Is electric potential gradient scalar or vector?
We know that potential is a scalar quantity and according to properties of vector and scalar quantity, we know that the gradient of any scalar quantity gives us a vector quantity. Thus we can say that the gradient of potential will be a vector quantity.
Is potential a vector?
Electric force and electric field are vector quantities (they have magnitude and direction). Electric potential turns out to be a scalar quantity (magnitude only), a nice simplification.
What is potential and it is a vector quantity?
Electric potential is the electric potential energy per unit charge. A difference in electric potential gives rise to an electric field. Electric force and electric field are vector quantities. V=U/q, U is the potential energy. | s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358903.73/warc/CC-MAIN-20211130015517-20211130045517-00580.warc.gz | CC-MAIN-2021-49 | 2,473 | 18 |
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https://www.lessonplanet.com/teachers/other-methods-for-solving-systems | math | Other Methods for Solving Systems
In this solving systems of equations instructional activity, 9th graders solve 11 various types of word problems that apply other methods for solving systems. First, they determine the coefficients that do not add or subtract to zero in each system and then. describe the steps in how to use the coefficients of the x terms in the system to solve for y. Students also describe why a linear combination probably is easier than the substitution method for solving systems. | s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891812556.20/warc/CC-MAIN-20180219072328-20180219092328-00446.warc.gz | CC-MAIN-2018-09 | 504 | 2 |
http://read4gmat.blogspot.com/2008/09/types-of-numbers.html | math | The group of numbers starting from 1 and including 1, 2, 3, 4, 5, and so on. Zero, negative numbers, and decimals are not included this group.
1. If n is an odd natural number, what is the highest number that always divides n(n2 – 1)?
Answer: n∙(n2 – 1) = (n – 1)∙n∙(n + 1), which is a product of three consecutive numbers. Since n is odd, the numbers (n – 1) and (n + 1) are both even. One of these numbers will be a multiple of 2 and the other a multiple of 4 as they are two consecutive even numbers. Hence, their product is a multiple of 8. Since one out of every three consecutive numbers is a multiple of 3, one of the three numbers will be a multiple of three. Hence, the product of three numbers will be a multiple of 8 ´ 3 = 24.
Hence, the highest number that always divides n∙(n2 – 1) is 24.
2. For every natural number n, the highest number that n∙(n2 – 1)∙(5n + 2) is always divisible by is
(a) 6 (b) 24 (c) 36 (d) 48
Case 1: If n is odd, n∙(n2 – 1) is divisible by 24 as proved in the earlier question.
Case 2: If n is even, both (n – 1) and (n + 1) are odd. Since product of three consecutive natural numbers is always a multiple of 3 and n is even, the product n∙(n2 – 1) is divisible by 6. Since n is even 5n is even. If n is a multiple of 2, 5n is a multiple of 2 and hence 5n + 2 is a multiple of 4. If n is a multiple of 4, 5n + 2 is a multiple of 2. Hence, the product n∙(5n + 2) is a multiple of 8.
Hence, the product n∙(n2 – 1)∙(5n + 2) is a multiple of 24.
Rule: The product of n consecutive natural numbers is divisible by n!, where n! = 1 × 2 × 3 × 4 × 5…. × n
3. Prove that (2n)! is divisible by (n!)2.
Answer: (2n)! = 1·2·3·4· … ·(n – 1)·n·(n + 1)· …·2n
= (n)!·(n + 1)·(n + 2)· …·2n.
Since (n + 1)·(n + 2)· …·2n is a product of n consecutive numbers, it is divisible by n!. Hence, the product (n)!·(n + 1)·(n + 2)· …·2n is divisible by n!·n! = (n!)2.
All Natural Numbers plus the number 0 are called as Whole Numbers.
All Whole Numbers and their negatives are included in this group.
Any number that can be expressed as a ratio of two integers is called a rational number.
This group contains decimal that either do not exist (as in 6 which is 6/1), or terminate (as in 3.4 which is 34/10), or repeat with a pattern (as in 2.333... which is 7/3).
Any number that can not be expressed as the ratio of two integers is called an irrational number (imaginary or complex numbers are not included in irrational numbers).
These numbers have decimals that never terminate and never repeat with a pattern.
Examples include pi, e, and √2. 2 + √3, 5 - √2 etc. are also irrational quantities called Surds.
This group is made up of all the Rational and Irrational Numbers. The ordinary number line encountered when studying algebra holds real numbers.
These numbers are formed by the imaginary number i (i = √-1). Any real number times i is an imaginary number.
Examples include i, 3i, −9.3i, and (pi)i. Now i2 = −1, i3 = i2 × i = −i, i4 = 1.
A Complex Numbers is a combination of a real number and an imaginary number in the form a + bi. a is called the real part and b is called the imaginary part.
Examples include 3 + 6i, 8 + (−5)i, (often written as 8 - 5i).
All the numbers that have only two divisors, 1 and the number itself, are called prime numbers. Hence, a prime number can only be written as the product of 1 and itself. The numbers 2, 3, 5, 7, 11…37, etc. are prime numbers.
Note: 1 is not a prime number.
- If x2 – y2 = 101, find the value of x2 + y2, given that x and y are natural numbers.
Answer: x2 – y2 = (x + y)(x – y) = 101. But 101 is a prime number and cannot be written as product of two numbers unless one of the numbers is 1 and the other is 101 itself.
Hence, x + y = 101 and x – y = 1. -> x = 51, y = 50.
-> x2 + y2 = 512 + 502 = 5101.
- What numbers have exactly three divisors?
Answer: The squares of prime numbers have exactly three divisors, i.e. 1, the prime number, and the square itself.
Odd and Even Numbers:
All the numbers divisible by 2 are called even numbers whereas all the numbers not divisible by 2 are called odd numbers. 2, 4, 6, 8… etc. are even numbers and 1, 3, 5, 7.. etc. are odd numbers. | s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583656665.34/warc/CC-MAIN-20190116031807-20190116053807-00580.warc.gz | CC-MAIN-2019-04 | 4,266 | 36 |
https://recknsense.com/recommends/what-is-scientific-really/ | math | Given the current emphasis on “believing in science” (a meaningless category of belief), I can’t recommend highly enough Zoltan Dienes’ exploration of scientific inference – Understanding Psychology as a Science: An Introduction to Scientific and Statistical Inference.
He gives a decent enough survey of the problem of first of all deciding what is science, although within the framework of how we might decide that experimental results constitute evidence of a theory that we can use to infer.
He begins with Karl Popper’s philosophy of science and, in particular, the notion of falsification. He then takes us via Kuhnian paradigms and the notion of theory approximation. This latter subject ought to be of great interest in an age where it seems we are awash with “theories” of all kinds, not just scientific ones. For example, there are myriad “theories” of how enterprises function, although it is doubtful that many of them constitute a theory at all. As Karl Weick pointed out – the products of laziness and great effort can often look the same: references, data, lists, diagrams and hypotheses.
The book then explores the inference approach of the classical Neyman/Pearson statistical framing (i.e. the t-test et al) but in a way that explains the validity of the approach, or not. This is the framing that nearly all papers use when purporting to possess statistically significant results. I am guessing that even many well-educated folks have never paused to ask what, exactly, is significance? It is clear from at least my daily dose of Twitter that our collective understanding of statistical inference is nearly zero.
He then goes on to explain Bayesian inference, a topic that is seemingly straightforward, yet deceptively complex in its subtleties. The ability to assign a probability to a future event based upon observed data is one of those things that ought not to work, except that it does — there would be no cellular communications without Bayes. On the other hand, does it really work? I am not sure I know the answer.
However, if there is a branch of mathematics that might allow us to say that we “believe” in something, then Bayesian statistics makes strong claims about beliefs.
The book ends with an exploration of likelihood, a measure that many confuse with probability. As an aside, I would say that the mechanism known as a Maximum Likelihood Estimator (MLE) is something that any well-educated person ought to know. Indeed, I will add it to my list of important things to know, if I can find it. (It is a list that I made when thinking about my children’s education.)
1,251 total views | s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103033925.2/warc/CC-MAIN-20220625004242-20220625034242-00385.warc.gz | CC-MAIN-2022-27 | 2,649 | 8 |
http://www.lampworketc.com/forums/showthread.php?p=1220090 | math | Medium necklaces are being sold in lots of 10, mainly of one color, but some lots may have more than one color. Double necklaces are being sold in lots of 6. Small necklaces will be sold in multi-colored lots of 8.
Pricing for Single Strand "Medium" neckaces is as follows:
$2.50 each (or $25 per lot of 10) if buying by the lot, plus shipping
$2.00 each if you buy 10 or more lots of 10 (i.e., 100 or more medium neckaces), plus shipping
$1.35 each if you buy my entire stock of medium necklaces.(plus shipping)
***If you are purchasing 100 or more necklaces please contact me so that I can adjust the pricing for you.
Pricing for Double Strand necklaces:
$3.50 each ($28 per lot of 6) plus shipping
$3.00 each if you buy my remaining stock of 90 necklaces (or whatever is remaining), plus shipping
Pricing for Small Single Strand necklaces:
$2.00 each ($16 plus shipping for lot of
if buying by the lot
$1.35 each if buying my remaining stock (48 pieces), plus shipping | s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368700074077/warc/CC-MAIN-20130516102754-00061-ip-10-60-113-184.ec2.internal.warc.gz | CC-MAIN-2013-20 | 971 | 13 |
https://www.mock4exam.org/quiz-mixture-and-alligation-set-2/ | math | - If 50% of 2:3 solution of milk and water is replaced with water, then the concentration of the solution is reduced by
- Milk and water are in the ratio of 3:2 in a mixture of 80 liters. How much water should be added so that the rate of milk and water become 2:3?
- How much water must be added to 100cc of 80% solution of Boric acid to reduce it to a 50% solution?
- In what proportion must a grocer mix one kind of bajra at Rs.4.50 per kg with another at Rs.4 per kg in order that by selling the mixture at Rs.5.20 per kg he may make a profit of 20%?
- Milk and water are mixed in the vessels A and B in the ratios 5:2 and 8:5 respectively. In what proportion should quantities be taken from the two vessels so as to form a mixture containing milk and water in the ratio 9:4?
- How must a shop owner mix 4 types of rice worth Rs95, Rs60, Rs90 and Rs50 per kg so that he can make the mixture of these rice worth Rs80 per kg?
- A container contains 40 liters of the milk. From the container 4 liters of the milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
- A dairy man pays Rs.6.40 per liter of milk. He adds water and sells the mixture at Rs.8 per liter thereby making 37.5% profit. Find the ratio of the water to milk received by the customers?
Try Other Quiz | s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510259.52/warc/CC-MAIN-20230927035329-20230927065329-00467.warc.gz | CC-MAIN-2023-40 | 1,351 | 9 |
http://www.freethesaurus.com/correction+factor | math | The values that are picked for the correction factor
have a direct impact over the total number of centroid updates that are performed by the algorithm, and this affects each of the centroids.
We then calculated the corrected number of deaths among individuals aged one year or more per municipality by multiplying the mean number of deaths reported to SIM in the period 2011-2013 by the correction factor
e] as explanatory variables, and multiple regression analysis was carried out for each of the four conditions; therefore, it is expected that the correction factor
was calculated accurately and that the transient correction was performed with high accuracy.
We divided the number of scats detected on each road type and in each position during a survey, by the persistence-rate correction factor
(transect and survey specific); within a survey, these values were then summed to obtain the corrected survey-specific number of scats per species.
There is as yet no published USM wet gas correction factor
a, in, max], the airflow correction factor
The correction factor
as a function of relative humidity, for temperatures of 21[degrees]C and 24[degrees]C and for pressures of 98.
While it supports the ETS, Eurometaux notes that the non-ferrous sector will be particularly affected by application of the cross-sectoral correction factor
It was suggested that the European Community for Steel and Coal (ECSC) prediction equations, derived from the study of Europeans, should be used as a norm, and that the use of a correction factor
for adjusting predicted values that was sometimes applied in the past be discouraged.
The correction factor
ci of anchor i is determined as:
This anomaly between experiment and theory can lead to serious errors in engineering analysis and design unless a correction factor
is experimentally validated.
To reduce the effect of friction on the test has been applied the Bulge Correction Factor
Method (BCFM) (Fereshteh-Saniee & Fatehi-Sichani, 2006).
6 For a k-irreducible partition [sigma], the weighted correction factor
is 1 if and only if [sigma] splits into [[sigma].
i,] number of individuals in the sample) was calculated by applying a species-specific (or closest proxy) correction factor
to account for otolith loss during digestion.
It would seem the introduction of a CCT correction factor
is a bid to maintain a flawed instrument and that the correction factor
itself is flawed. | s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547584519382.88/warc/CC-MAIN-20190124055924-20190124081924-00582.warc.gz | CC-MAIN-2019-04 | 2,426 | 27 |
https://www.mylot.com/post/566435/joke-2 | math | January 8, 2007 7:31am CST
Teacher: Ted, if your father has $10 and you ask him for $5. How much would your father have left? Ted: $10, teacher. Teacher: Ted! How can you not know such basic maths? Ted: Teacher, that's because I know my father far better then basic maths! Hope you have a good laugh! | s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107911027.72/warc/CC-MAIN-20201030153002-20201030183002-00033.warc.gz | CC-MAIN-2020-45 | 300 | 2 |
https://es.slideshare.net/AnithaVanama1/cn-unit1-pptpptx | math | 2. CN Syllabus Composition + Evaluation
• Data Communications + Computer Networks
• Unit-1: Data Communication Part + OSI &TCP/IP Model
• Units 2-5: Layer 2 – 7 of OSI model with focus based on
General Layer functionality and
TCP/IP specific reference model under each layer
• CIE – 30 Marks - 10 (CIE-1) + 10 (CIE-2) + 5 (Assignment) + 5 (Quiz)
• SEE – 70 Marks - Mandatory to get 40% marks in end exam paper
3. Computer Networks - SYLLABUS OVERIEW
Unit – 1
◦ Data Communication Components:
◦ Representation of Data Communication ,
◦ Flow of Networks,
◦ Layered Architecture,
◦ OSI and TCP/IP model,
◦ Transmission Media.
◦ Techniques for Bandwidth Utilization:
◦ Line configuration,
◦ Multiplexing – Frequency division, Time division and Wave division,
◦ Asynchronous and Synchronous Transmission,
◦ Introduction to Wired and Wireless LAN
4. Computer Networks - SYLLABUS OVERIEW
Unit – 2
◦ Data Link Layer and Medium Access Sub Layer:
◦ Error Correction and Error Detection:
◦ Fundamentals, Block coding,
◦ Hamming Distance, CRC
◦ Flow Control and Error Control Protocols:
◦ Stop and Wait,
◦ Go Back-N,
◦ ARQ, Selective Repeat ARQ,
◦ Sliding Window,
◦ Multiple Access Protocols:
◦ Pure ALOHA, Slotted ALOHA
◦ CSMA/CD, CSMA/CA
6. Computer Networks - SYLLABUS OVERIEW
Unit – 4
◦ Transport Layer:
◦ Process to Process Communications,
◦ Elements of Transport Layer
◦ Internet Protocols:
◦ UDP – User Datagram Protocol
◦ TCP – Transmission Control Protocol
◦ Congestion and Quality of Service:
◦ QoS improving techniques
7. Computer Networks - SYLLABUS OVERIEW
Unit – 5
◦ Application Layer:
◦ Domain Name System (DNS),
◦ EMAIL - Electronic Mail
◦ SNMP – Simple Network Management Protocol
◦ Basic Concepts of Cryptography:
◦ Network Security Attacks,
◦ Symmetric Encryption
◦ Data Encryption Standards,
◦ Public Key Encryption – RSA (Rivest, Shamir, Adleman)
◦ Hash Function,
◦ Message Authentication
◦ Digital Signature
8. Computer Networks – Suggested Reading -
1. Data Communication and Networking,
4th Edition, Behrouz A. Forouzan, McGrawHill
2. Data and Computer Communication,
8th Edition, William Stallings, Pearson Prentice Hall India
3. Unix Network Programming,
W. Richard Stevens, Prentice Hall / Pearson Education, 2009
9. Computer Networks Lab
PC 632 CS [Credits – 1]
Evaluation: CIE – 25 Marks; SEE – 50 Marks
1. Running and using services/commands like:
◦ tcpdump, netstat, ifconfig, nslookup, ftp, telnet. - Execution at command prompt
◦ Capture ping and traceroute PDUs using a network protocol analyzer and examine
2. Configuration of router, switch. (using real devices or simulators)
3. Socket Programming using UDP and TCP ( E.g. Simple DNS, Date and time Client Server, Echo Client/Server, Iterative &
Concurrent Servers) - Application programs through C Language using Socket API
4. Network Packet Analysis using tools like Wireshark, tcpdump etc.
5. Network Simulation using tools like Cisco Packet Tracer, NetSim, OMNet++, NS2, NS3 etc.
6. Study of Network Simulator(NS) and Simulation of Congestion Control Algorithms using NS. Performance Evaluation of
Routing Protocols using Simulation Tools.
7. Programming using raw sockets.
8. Programming using RPC. - Application programs through C Language
Note: Instructor may add/delete/modify/tune experiments, wherever he/she feels in a justified manner.
10. CN-U-1 - INTRODUCTION
Data refers to information presented in whatever form is agreed
upon by the parties creating and using the data.
Data Communications are the exchange of data between two
devices via some form of transmission medium such as a wire
A network is a set of devices (often referred to as nodes)
connected by communication links. A node can be a computer,
printer, or any other device capable of sending and/or receiving
data generated by other nodes on the network.
11. A Communication Model
• The fundamental purpose of a communications system is the
exchange of data between two parties.
The key elements of this model are:
• Source - generates data to be transmitted
• Transmitter - converts data into transmittable signals
• Transmission System - carries data from source to destination
• Receiver - converts received signal into data
• Destination - takes incoming data
12. Data Communication Model
"Data Communications”, deals with the most fundamental aspects of the
communications function, focusing on the transmission of signals in a reliable
and efficient manner.
Example: Electronic Mail: User A sending an email message m to user B.
Steps for this process:
1. User A keys in message m comprising bits g buffered in source PC memory
2. Input data is transferred to I/O device (transmitter) as sequence of bits g(t)
using voltage shifts
3. transmitter converts these into a signal s(t) suitable for transmission
4. whilst transiting media signal may be impaired so received signal r(t) may
differ from s(t)
5. receiver decodes signal recovering g’(t) as estimate of original g(t)
which is buffered in destination PC memory as bits g’ being the received
15. Communications Tasks
Transmission system utilization Addressing
Signal generation Recovery
Synchronization Message formatting
Exchange management Security
Error detection and correction Network management
16. Communications Tasks
• Key tasks that must be performed in a data communications system:
• transmission system utilization - need to make efficient use of transmission facilities typically
shared among a number of communicating devices
• a device must interface with the transmission system
• once an interface is established, signal generation is required for communication
• there must be synchronization between transmitter and receiver, to determine when a signal
begins to arrive and when it ends
• there is a variety of requirements for communication between two parties that might be collected
under the term exchange management
• Error detection and correction are required in circumstances where errors cannot be tolerated
17. Communications Tasks
• Flow control is required to assure that the source does not overwhelm the destination by sending data faster
than they can be processed and absorbed
• addressing and routing, so a source system can indicate the identity of the intended destination, and can
choose a specific route through this network
• Recovery allows an interrupted transaction to resume activity at the point of interruption or to condition prior
to the beginning of the exchange
• Message formatting has to do with an agreement between two parties as to the form of the data to be
exchanged or transmitted
• Frequently need to provide some measure of security in a data communications system
• Network management capabilities are needed to configure the system, monitor its status, react to failures
and overloads, and plan intelligently for future growth
31. LAYERED ARCHITECTURE: NEED AND ADVANTAGES
• Allows Complex problems are decomposed in to small manageable units.
• Implementation details of the layer are abstracted.
• Separation of implementation and specification.
• Layers work as one by sharing the services provided by each other.
•Layering allows reuse functionality i.e., lower layers implement common once.
•Provide framework to implement multiple specific protocols (rules) per layer
•Provides Modularity with Clear Interfaces.
• Has Implementation Simplicity, Maintainability, Flexibility and Scalability.
• Support for Portability.
• Provides for Robustness
32. ISO - OSI MODEL
• International Standards Organization (ISO) - is a multinational body
to worldwide agreement on international standards.
• An ISO standard that covers all aspects of network communications is the
Open Systems Interconnection (OSI) model.
• It was first introduced in the late 1970s.
• OSI model has seven layers. ----->
46. TCP/IP REFERENCE MODEL /PROTOCOL
The layers in the TCP/IP reference model is FOUR in comparison to the OSI
The original TCP/IP protocol suite was defined as having four layers:
host-to-network, internet, transport, and application.
But when TCP/IP is compared to OSI, we can say that the TCP/IP protocol suite
is made of five layers:
physical, data link, network, transport, and application.
48. Comparison of ISO-OSI model and TCP/IP
1. Layers: 7 in OSI ; 5 in TCP/IP
2. Model vs Implementation: In OSI first model was designed followed by
Implementation. In TCP/IP first implemented then design followed
3. In OSI : Clear definition of Services, Interface and Protocols. Not so in TCP/IP
4. In OSI Network layer is both Connection Oriented and Connectionless and
Transport Layer is only connection oriented. In TCP/IP network layer is
connectionless and Transport Layer is both connection oriented and
5. In TCP/IP Session and Presentation layers are missing, this functionality is done
by Application layer.
6. TCP/IP is the defacto protocol used in internet. OSI is mostly a theoretical
Four levels of addresses are used in an internet employing the TCP/IP protocols:
• Physical Addresses
• Logical Addresses
• Port Addresses
• Specific Addresses
51. Physical Addresses
• Physical Address – It is of 6-bytes (12 hexadecimal digits).
• Also called MAC ADDRESS.
• Every byte (2 hexadecimal digits) is separated by a colon
• Example: 07:01:02:01:2C:4B
• Physical Addresses Change Hop by Hop
52. Logical Addresses
•Network with two
•Each device (computer
or router) has a pair of
addresses (logical and
physical) for each
•Each device connected
to one link – 1 pair of
address. For router 3
• Also called IP
53. Port addresses
• Port Addresses are for
• Port and Logical
addresses remain same
for source to
55. Transmission Media Introduction
• Transmission medium – It is the physical path between transmitter and receiver
• It is of two types / categories / classes –
• Guided media – Electromagnetic waves are guided along a solid medium
Eg: Copper Twisted Pair, Copper Coaxial Cable, and Optical fiber
• Unguided media – wireless transmission occurs through the atmosphere, space, water
• Characteristics and Quality of data transmission is determined by both characteristics of
Medium and Signal
• For guided media - Medium is more important for data transmission
• For Unguided media - Bandwidth of the signal produced by the transmitting antenna is more
- One key property is directionality of the signal.
Signals at lower frequencies are omni-directional and at higher
frequencies can be focused into a directional beam
56. Data Transmission System Design : Data rate & Distance are
the key factors
Design Factors Determining Data Rate and Distance
• higher bandwidth gives higher data rate
• impairments, such as attenuation, limits the distance - Twisted Pair -> Coaxial Cable -> Optical Fiber
• overlapping frequency bands can distort or wipe out a signal – More in Unguided than Guided medium.
• more receivers introduces more attenuation - in case of shared link with multiple attachments. Not in
number of receivers
58. Transmission Characteristics of Guided
Frequency Range Typical
Typical Delay Repeater
Twisted pair (with
0 to 3.5 kHz 0.2 dB/km @ 1 kHz 50 µs/km 2 km
0 to 1 MHz 0.7 dB/km @ 1 kHz 5 µs/km 2 km
Coaxial cable 0 to 500 MHz 7 dB/km @ 10 MHz 4 µs/km 1 to 9 km
Optical fiber 186 to 370 THz 0.2 to 0.5 dB/km 5 µs/km 40 km
In Guided Media ,transmission capacity, in terms of either data rate or bandwidth, depends
critically on the distance and on whether the medium is point-to-point or multipoint.
62. Twisted Pair
Twisted pair is the least expensive and most widely used guided transmission medium.
• consists of two insulated copper wires arranged in a regular spiral pattern
• a wire pair acts as a single communication link
• pairs are bundled together into a cable
• most commonly used in the telephone network and for communications
• within buildings
63. Twisted Pair - Transmission Characteristics
5km to 6km
can use either
analog or digital
2km to 3km
interference and noise
64. Unshielded vs. Shielded Twisted Pair
Unshielded Twisted Pair (UTP)
• ordinary telephone wire
• easiest to install
• suffers from external electromagnetic interference
Shielded Twisted Pair (STP)
• has metal braid or sheathing that reduces interference
• provides better performance at higher data rates
• more expensive
• harder to handle (thick, heavy)
66. Near End Crosstalk - occurs in Twisted Pair
• Coupling of signal from one pair of conductors to another
• Occurs when transmit signal entering the link couples back to the
receiving pair - (near transmitted signal is picked up by near
67. Coaxial Cable
Coaxial cable can be used over longer distances and support more stations on a shared line
than twisted pair.
• consists of a hollow outer cylindrical conductor that surrounds a single inner wire conductor
• is a versatile transmission medium used in a wide variety of applications
• used for TV distribution, long distance telephone transmission and LANs
68. Coaxial Cable – Transmission
- closer if
extends up to
• repeater every
1km - closer for
69. Optical Fiber
Optical fiber is a thin flexible medium capable of guiding an optical ray.
• various glasses and plastics can be used to make optical fibers
• has a cylindrical shape with three sections – core, cladding, jacket
• widely used in long distance telecommunications
• performance, price and advantages have made it popular to use
70. Optical Fiber - Benefits
◦ data rates of hundreds of Gbps
smaller size and lighter weight
◦ considerably thinner than coaxial or twisted pair cable
◦ reduces structural support requirements
◦ not vulnerable to interference, impulse noise, or crosstalk
◦ high degree of security from eavesdropping
greater repeater spacing
◦ lower cost and fewer sources of error
71. Optical Fiber - Transmission
• uses total internal reflection to transmit light
• effectively acts as wave guide for 1014 to 1015 Hz (this covers portions of infrared &
• Light sources used:
• Light Emitting Diode (LED)
• cheaper, operates over a greater temperature range, lasts longer
• Injection Laser Diode (ILD)
• more efficient, has greater data rates
• has a relationship among wavelength, type of transmission and achievable data rate
73. Optical Fiber Transmission Modes
Light from a source enters the cylindrical glass or plastic core. Rays at shallow angles are
reflected and propagated along the fiber; other rays are absorbed by the surrounding
material. This form of propagation is called step-index multimode
Varying the index of refraction of the core, a third type of transmission, known as
Reducing the radius of the core to the order of a wavelength, only a single angle or mode
can pass: the axial ray. We have the single-mode propagation
76. Wireless Transmission Frequencies
• referred to as microwave frequencies
• highly directional beams are possible
• suitable for point to point transmissions
• also used for satellite
• suitable for omnidirectional applications
• referred to as the radio range
3 x 1011 to 2
• infrared portion of the spectrum
• useful to local point-to-point and multipoint applications within confined areas
electrical conductors used to
radiate or collect electromagnetic
same antenna is often used for
energy impinging on
converted to radio
fed to receiver
energy by antenna
78. Radiation Pattern
•power radiated in all directions
•does not perform equally well in all directions
• as seen in a radiation pattern diagram
•an isotropic antenna is a point in space that radiates power
• in all directions equally
• with a spherical radiation pattern
80. Antenna Gain
•measure of the directionality of an antenna
•power output in particular direction verses that produced by an
•measured in decibels (dB)
•results in loss in power in another direction
•effective area relates to physical size and shape
81. Terrestrial Microwave
most common type is a parabolic
dish with an antenna focusing a
narrow beam onto a receiving
located at substantial heights above
ground to extend range and
transmit over obstacles
uses a series of microwave relay
towers with point-to-point
microwave links to achieve long
82. Terrestrial Microwave Applications
• used for long haul telecommunications, short point-to-point links
between buildings and cellular systems
• used for both voice and TV transmission
• fewer repeaters but requires line of sight transmission
• 1-40GHz frequencies, with higher frequencies having higher data rates
• main source of loss is attenuation caused mostly by distance, rainfall
84. Satellite Microwave
• a communication satellite is in effect a microwave relay station
• used to link two or more ground stations
• receives on one frequency, amplifies or repeats signal and transmits on
• frequency bands are called transponder channels
• requires geo-stationary orbit
• rotation match occurs at a height of 35,863km at the equator
• need to be spaced at least 3° - 4° apart to avoid interfering with each other
• spacing limits the number of possible satellites
87. Satellite Microwave Applications
private business networks
◦ satellite providers can divide capacity into channels to lease to individual business users
◦ programs are transmitted to the satellite then broadcast down to a number of stations
which then distributes the programs to individual viewers
◦ Direct Broadcast Satellite (DBS) transmits video signals directly to the home user
◦ Navstar Global Positioning System (GPS)
88. Transmission Characteristics
• the optimum frequency range for satellite transmission is 1 to 10 GHz
• lower has significant noise from natural sources
• higher is attenuated by atmospheric absorption and precipitation
• satellites use a frequency bandwidth range of 5.925 to 6.425 GHz from earth
to satellite (uplink) and a range of 3.7 to 4.2 GHz from satellite to earth
• this is referred to as the 4/6-GHz band
• because of saturation the 12/14-GHz band has been developed (uplink: 14 - 14.5 GHz; downlink: 11.7 -
89. Broadcast Radio
radio is the term used to encompass frequencies in the range of 3kHz to 300GHz
broadcast radio (30MHz - 1GHz) covers
• FM radio
• UHF and VHF television
• data networking applications
limited to line of sight
suffers from multipath interference
◦ reflections from land, water, man-made objects
• achieved using transceivers that modulate noncoherent infrared light
• transceivers must be within line of sight of each other directly or via
• does not penetrate walls
• no licenses required
• no frequency allocation issues
• typical uses:
• TV remote control
92. Wireless Propagation Ground Wave
• ground wave propagation follows the contour of the earth
and can propagate distances well over the visible horizon
• this effect is found in frequencies up to 2MHz
• the best known example of ground wave communication is AM radio
93. Wireless Propagation Sky Wave
• sky wave propagation is used for amateur radio, CB radio, and international broadcasts
such as BBC and Voice of America
• a signal from an earth based antenna is reflected from the ionized layer of the upper
atmosphere back down to earth
• sky wave signals can travel through a number of hops, bouncing back and for the between the
ionosphere and the earth’s surface
94. Wireless Propagation Line of Sight
• ground and sky wave propagation modes do not operate above 30
MHz - - communication must be by line of sight
velocity of electromagnetic wave is a function of the density of the medium
through which it travels
• ~3 x 108 m/s in vacuum, less in anything else
speed changes with movement between media
index of refraction (refractive index) is
◦ varies with wavelength
◦ density of atmosphere decreases with height, resulting in bending of radio waves
96. Line of Sight Transmission
Free space loss
• loss of signal
• from water vapor
• bending signal
97. Free Space Loss : which can be expressed in terms of the ratio of the
radiated power Pt to the power Pr received by the antenna or, in decibels, by taking 10
times the log of that ratio.
99. • Line configuration,
• Multiplexing – Frequency division, Time division and
Techniques for Bandwidth Utilization:
100. Line Configuration - Topology
•Physical arrangement of stations on medium
• Point to Point - two stations
• such as between two routers / computers
• Multi point - multiple stations
• traditionally mainframe computer and terminals
• now typically a local area network (LAN)
Note: Two characteristics that distinguish various data link
configurations : Topology and Whether the link is half duplex or full
duplex [Data Flow].
101. Line Configuration - Topology
• In point-to-point each
terminal has a separate I/O
Port and transmission link
102. Line Configuration - Duplex
• classify data exchange as half or full duplex
• half duplex (two-way alternate)
• only one station may transmit at a time
• requires one data path
• full duplex (two-way simultaneous)
• simultaneous transmission and reception between two stations
• requires two data paths
• separate media or frequencies used for each direction
• or echo canceling ( can be used for transmitting using a single line)
•Under the simplest conditions, a medium can carry only one signal at any moment in
•For multiple signals to share one medium, the medium must somehow be divided,
giving each signal a portion of the total bandwidth.
•Whenever the bandwidth of a medium linking two devices is greater than the
bandwidth needs of the devices, the link can be shared.
•Efficiency can be achieved by multiplexing;
i.e., sharing of the bandwidth between multiple users.
•Transparent to the User
-- It is the set of techniques that allows the (simultaneous) transmission of
multiple signals across a single data link.
-- Two or more simultaneous transmissions on a single circuit.
Figure: Dividing a link into channels
106. Multiplexing Techniques/Categories
The current techniques include :
1. FDM: Frequency Division Multiplexing
2. WDM: Wavelength Division Multiplexing
3. TDM: Time Division Multiplexing - Digital
a. Synchronous b. Statistical
107. Frequency Division Multiplexing
• It is an analog multiplexing technique that combines analog signals. Uses
the concept of modulation
• Assignment of non-overlapping frequency ranges to each “user” or signal
on a medium. Thus, all signals are transmitted at the same time, each
using different frequencies.
109. Frequency Division Multiplexing
• Analog signaling is used to transmit the signals due to which it is more
susceptible to noise.
• It is the oldest multiplexing technique.
• Examples of FDM:
Broadcast radio and television,
AMPS cellular phone systems
110. FDM Process
--A multiplexor accepts inputs and
assigns frequencies to each
--It is attached to a high-speed
--A corresponding multiplexor, or
demultiplexor, is on the end of the
high-speed line and separates
the multiplexed signals.
111. FDM Process
--Each signal is modulated to a different carrier frequency
--Carrier frequencies separated so signals do not overlap (guard bands)
e.g. broadcast radio.
--Channel allocated even if no data
116. Dense Wavelength Division Multiplexing
• DWDM which is often called WDM multiplexes multiple data streams onto
a single fiber optic line.
Data Transmission through a single fiber optic line
117. Dense Wavelength Division Multiplexing (DWDM)
• Different wavelength lasers (called lambdas) transmit the multiple signals.
• Each signal carried at a different rate, combines(30, 40, more?) signals
onto one fiber.
118. Wavelength Division Multiplexing
1997 Bell Labs
◦ 100 beams
◦ Each at 10 Gbps
◦ Giving 1 terabit per second (Tbps)
Commercial systems of 160 channels of 10 Gbps now available
Lab systems (Alcatel) 256 channels at 39.8 Gbps each
◦ 10.1 Tbps
◦ Over 100km
119. Time Division Multiplexing (TDM)
•TDM is a digital multiplexing technique for combining several low-rate
digital channels into one high-rate one.
• Data rate of medium exceeds data rate of digital signal to be
• Multiple digital signals interleaved in time
• May be at bit level of blocks
120. Time Division Multiplexing (TDM)
Sharing of the signal is accomplished by dividing available transmission
time on a medium among users.
123. TDM Types/Forms
•Time division multiplexing comes in two basic forms:
•1. Synchronous time division multiplexing
•2. Statistical, or Asynchronous time division multiplexing.
124. Synchronous TDM
The original time division multiplexing.
The multiplexor accepts input from attached devices in a round-robin fashion
and transmit the data in a never ending pattern.
Examples of STDM: T-1, ISDN telephone lines,
SONET (Synchronous Optical NETwork)
When one device generates data at a faster rate than other devices –
then the multiplexor must either sample the incoming data stream from
that device more often than it samples the other devices, or buffer the
faster incoming stream.
•When a device has nothing to transmit, the multiplexor must still insert a piece of data
from that device into the multiplexed stream So that the receiver may stay
synchronized with the incoming data stream
•The transmitting multiplexor can insert alternating 1s and 0s into the data stream.
The process of taking a group of bits from each input line for multiplexing
is called interleaving.
We interleave bits (1 - n) from each input onto one output.
129. TDM Link Control
• No headers and trailers
• Data link control protocols not needed
• Flow control
–Data rate of multiplexed line is fixed
–If one channel receiver can not receive data, the others must carry on
–The corresponding source must be quenched
–This leaves empty slots
• Error control
–Errors are detected and handled by individual channel systems
•To ensure that the receiver correctly reads the incoming bits,
i.e., knows the incoming bit boundaries to interpret a “1” and a
“0”, a known bit pattern is used between the frames.
•The receiver looks for the anticipated bit and starts counting bits
till the end of the frame.
•Then it starts over again with the reception of another known
•These bits (or bit patterns) are called synchronization bit(s).
•They are part of the overhead of transmission.
133. Data Rate Management
• Synchronizing data sources
• Not all input links maybe have the same data rate.
• Some links maybe slower. There maybe several different input link speeds
• Data rates from different sources not related by simple rational number
• Clocks in different sources drifting
• Three strategies that can be used to overcome the data rate mismatch:
• Multilevel, Multislot and Pulse Stuffing
134. Data Rate Management
• Multilevel: used when the data rate of the input links are multiples of
135. Data Rate Management
Multislot: used when there is a GCD between the data rates. The higher bit rate channels are allocated
more slots per frame, and the output frame rate is a multiple of each input link.
136. Data Rate Management
• Pulse Stuffing: used when there is no GCD between the links. The
slowest speed link will be brought up to the speed of the other links by bit
insertion, this is called pulse stuffing.
–Outgoing data rate (excluding framing bits) higher than sum of
–Stuff extra dummy bits or pulses into each incoming signal until it
matches local clock
–Stuffed pulses inserted at fixed locations in frame and removed
137. Inefficient use of Bandwidth
• Sometimes an input link may have no data to transmit then, one or more
slots on the output link will go unused.
• Thus wasting bandwidth
139. Statistical TDM or Asynchronous TDM
•In Synchronous TDM many slots are wasted
•Statistical TDM allocates time slots dynamically based on
•Multiplexer scans input lines and collects data until frame
•Data rate on line lower than aggregate rates of input lines
141. Statistical TDM
• A statistical multiplexor transmits only the data from active
workstations (or why work when you don’t have to).
• If a workstation is not active, no space is wasted on the multiplexed
143. Statistical TDM
To identify each piece of data,
an address is included.
If the data is of variable size,
a length is also included.
144. Statistical TDM
•A statistical multiplexor does not require a line over as high a
speed line as synchronous time division multiplexing since STDM
does not assume all sources will transmit all of the time!
•Good for low bandwidth lines (used for LANs)
•Much more efficient use of bandwidth!
145. • Asynchronous and Synchronous Transmission,
• XDSL – X Digital Subscriber Line
A, S, H, V
Asymmetric, Symmetric, High Data Rate, Very High Data Rate
Techniques for Bandwidth Utilization:
146. Transmission of Data between 2 devices
Types: Asynchronous and Synchronous
•Transmission of a stream of bits from one device to another across a
transmission link involves cooperation and agreement between the two
•Timing problems require a mechanism to synchronize the transmitter
• receiver samples stream at bit intervals
• if clocks not aligned and drifting will sample at wrong time after
sufficient bits are sent
•Two solutions to synchronizing clocks
• Asynchronous transmission
• Synchronous transmission
147. Asynchronous Transmission
• Here each character of data is treated independently.
• Timing problem is avoided by not sending long, uninterrupted
streams of bits. So data is sent character by character.
• Each character begins with a start bit that alerts the receiver that
a character is arriving. The receiver samples each bit in the
character and then looks for the beginning of the next character. [
does not work with long blocks of data as receiver clock may go out
of sync with the transmitter’s clock.
148. Asynchronous Transmission
• When no character is being transmitted, the line between transmitter and receiver is in an idle state (binary 1
• The beginning of a character is signaled by a start bit with a value of binary 0.
• This is followed by the 5 to 8 bits that actually make up the character.
• The bits of the character are transmitted beginning with the least significant bit.
• Then the data bits are usually followed by a parity bit, set by the transmitter such that the total number of
ones in the character, including the parity bit, is even (even parity) or odd (odd parity).
• The receiver uses this bit for error detection.
• The final element is a stop element, which is a binary 1.
• A minimum length for the stop element is specified, and this is usually 1, 1.5, or 2 times the duration of an
• No maximum value is specified since the stop element is the same as the idle state, so the transmitter will
continue to transmit the stop element until it is ready to send the next character.
149. Asynchronous Transmission
• Example: Say the receiver is fast by
• Thus, the receiver samples the
incoming character every 94 µs
(based on the transmitter's clock).
• Thus the last sample is erroneous.
150. Asynchronous Transmission - Merits
•Simple & cheap
•Overhead of 2 or 3 bits per char (~20%)
•Example: For an 8-bit character with no parity bit, using a
1-bit-long stop element, two out of every ten bits convey
no information but are there merely for synchronization;
thus the overhead is 20%.
•Good for data with large gaps (keyboard)
151. Synchronous Transmission
•Block of data transmitted sent as a frame
• [includes a starting and an ending flag, and is transmitted in a steady stream without start and stop codes. The
block may be many bits in length. ]
•Clocks must be synchronized [to avoid drift]
• can use separate clock line
• or embed clock signal in data
•Need to indicate start and end of block of data for the receiver to sync
• use preamble and postamble bits
• Data plus preamble, postamble, and control information are called a frame (exact frame format
depends of DLL procedure).
• More efficient (lower overhead) than Asynchronous (20% more overhead).
• Preamble, Postamble and control field would mostly less than 100 bits.
Internet Access Technology:
Upstream and Downstream
• Internet access technology refers to a data communications system that
connects an Internet subscriber to an ISP
• such as a telephone company(DSL) or cable company
• Most Internet users follow an asymmetric pattern
• a subscriber receives more data from the Internet than sending
• a browser sends a URL that comprises a few bytes
• in response, a web server sends content
• Upstream to refer to data traveling from a subscriber to an ISP
• Downstream to refer to data traveling from an ISP in the Internet to a
Narrowband and Broadband Access Technologies
• A variety of technologies are used for Internet access
• They can be divided into two broad categories based on the data rate they
• In networking terms, network bandwidth refers to data rate
• Thus, the terms narrowband and broadband reflect industry practice
Narrowband Access Technologies
• Narrowband Technologies
• refers to technologies that deliver data at up to 128 Kbps
• For example, the maximum data rate for dialup noisy phone lines is 56 Kbps
and classified as a narrowband technology
• the main narrowband access technologies are given below
Broadband Access Technologies
• Broadband Technologies
• generally refers to technologies that offer high data rates, but the exact boundary
between broadband and narrowband is blurry
• many suggest that broadband technologies deliver more than 1 Mbps
• but this is not always the case, and may mean any speed higher than dialup
• the main broadband access technologies are given below
Digital Subscriber Line (DSL) Technologies
• DSL is one of the main technologies used to provide high-speed data communication services over a
• DSL variants are given below
• Because the names differ only in the first word, the set is collectively referred to by the acronym
• Currently, ADSL is most popular
The Local Loop
• Local loop describes the physical connection between a telephone company
Central Office (CO) and a subscriber
• consists of twisted pair and dialup call with 4 KHz of bandwidth
• It often has much higher bandwidth; a subscriber close to a CO may be able
to handle frequencies above 1 MHz
LOCAL LOOP Technologies
• Electric local loop(POTS lines): Voice, ISDN, DSL
• Optical local loop: Fiber Optics services such as FiOS
• Satellite local loop: communications satellite and cosmos Internet connections
of satellite televisions (DVB-S)
• Cable local loop: Cablemodem
• Wireless local loop (WLL): LMDS, WiMAX, GPRS, HSDPA, DECT
167. Asymmetrical DSL (ADSL)
• ADSL is an asymmetric communication technology designed for
residential users; it is not suitable for businesses
• ADSL is an adaptive technology.
•Link between subscriber and network
•Uses currently installed twisted pair cable
–Can carry broader spectrum
–1 MHz or more
168. Asymmetrical DSL (ADSL)
• ADSL divides up the available frequencies in a line on the assumption that
most Internet users look at, or download, much more information than
they send, or upload.
• The system uses a data rate based on the condition of the local loop line.
• Speed: Most existing local loops can handle bandwidths up to 1.1 MHz.
169. ADSL Design
– Greater capacity downstream than upstream
• Frequency division multiplexing
– Lowest 25kHz for voice
• Plain old telephone service (POTS)
– Use echo cancellation or FDM to give two bands
– Use FDM within bands
– The region above 25kHz is used for data transmission
– Upstream: 64kbps to 640kbps
– Downstream: 1.536Mbps to 6.144Mbp
• Range 5.5km
172. Two standards for ADSL
1. Discrete multitone (DMT)
2. Carrierless amplitude/phase (CAP)
173. CAP - three distinct bands:
1. Voice channel - 0 to 4 KHz
2. Upstream channel - 25 and 160 KHz
3. Downstream channel - 1.5 MHz
Minimizes the possibility of interference between the channels on
one line, or between the signals on different lines
175. Discrete Multitone
• Multiple carrier signals at different frequencies
• Some bits on each channel
• 4kHz subchannels
• Send test signal and use subchannels with better signal to noise ratio
• 256 downstream subchannels at 4kHz (60kbps)
– Impairments bring this down to 1.5Mbps to 9Mbps
178. ADSL Distance Limitations
•ADSL is a distance-sensitive technology
•The limit for ADSL service is 18,000 feet (5,460 meters)
•At the extremes of the distance limits, ADSL customers may
see speeds far below the promised maximums
•customers nearer the central office have faster connections
and may see extremely high speeds
179. OTHER TYPES OF DSL:
• SDSL -- Symmetric DSL
Used mainly by small businesses & residential areas
Bit rate of downstream is higher than upstream
• HDSL -- High-bit-rate DSL
Used as alternative of T-1 line
Uses 2B1Q encoding
Less susceptible to attenuation at higher frequencies
Unlike T-1 line (AMI/1.544Mbps/1km), it can reach 2Mbps
180. OTHER TYPES OF DSL:
• VDSL -- Very high bit-rate DSL
Uses DMT modulation technique
Effective only for short distances(300-1800m)
Speed: downstream: 50 - 55 Mbps upstream: 1.5-2.5 Mbps
•In 1985, the Computer Society of the IEEE started a
project, called Project 802.
•Purpose was to set standards to enable
intercommunication among equipment from a variety of
•Project 802 is a way of specifying functions of the
physical layer and the data link layer of major LAN
190. Unicast and multicast addresses
The least significant bit of the first byte defines the type of address.
If the bit is 0, the address is unicast; otherwise, it is multicast.
The broadcast destination address is a special case of the multicast address in which all
bits are 1s.
191. Define the type of the following destination addresses:
a. 4A:30:10:21:10:1A b. 47:20:1B:2E:08:EE
To find the type of the address, we need to look at the second hexadecimal
digit from the left. If it is even, the address is unicast. If it is odd, the address is
multicast. If all digits are F’s, the address is broadcast. Therefore, we have the
a. This is a unicast address because A in binary is 1010.
b. This is a multicast address because 7 in binary is 0111.
c. This is a broadcast address because all digits are F’s.
192. Example shows how the address 47:20:1B:2E:08:EE is sent out on
The address is sent left-to-right, byte by byte; for each byte, it is sent right-to-
left, bit by bit, as shown below:
CHANGES IN THE STANDARD
The 10-Mbps Standard Ethernet has gone through several changes before
moving to the higher data rates.
These changes actually opened the road to the evolution of the Ethernet
to become compatible with other high-data-rate LANs.
Fast Ethernet was designed to compete with LAN protocols such as FDDI
or Fiber Channel.
IEEE created Fast Ethernet under the name 802.3u.
Fast Ethernet is backward-compatible with Standard Ethernet, but it can
transmit data 10 times faster at a rate of 100 Mbps.
211. GIGABIT ETHERNET
• The need for an even higher data rate resulted in the design of the Gigabit
Ethernet protocol (1000 Mbps). The IEEE committee calls the standard
• In the full-duplex mode of Gigabit Ethernet, there is no collision;
• the maximum length of the cable is determined by the signal
in the cable.
217. IEEE 802.11 - Wireless LAN Standard
IEEE has defined the specifications for a wireless LAN, called IEEE
802.11, which covers the physical and data link layers.
A BSS without an AP is called an ad hoc network;
a BSS with an AP is called an infrastructure network.
Bluetooth is a wireless LAN technology designed to connect devices of
different functions such as telephones, notebooks, computers, cameras,
printers, coffee makers, and so on. A Bluetooth LAN is an ad hoc network,
which means that the network is formed spontaneously. | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100508.23/warc/CC-MAIN-20231203125921-20231203155921-00841.warc.gz | CC-MAIN-2023-50 | 40,238 | 823 |
https://mycraftingcorner-jo.blogspot.com/2011/11/ho-ho-ho.html | math | - Hi......I'm Jo, welcome to my crafty corner where I aim to share my adventures in paper crafting, baking, cross stitch & cats.....hopefully with some hints, tips & inspiration thrown in too! Please leave a comment if you call so I know you've been, I would love to visit you back and please become a follower if you like what you see. Thanks for popping by.........
Tuesday, 29 November 2011
Ho Ho Ho!
Enjoy rest of your day..................can't wait for I'm a Celeb tonight!!
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Challenge#93 at I love promarkers
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https://www.hackmath.net/en/math-problem/1275 | math | Three-member family enough liter of liquid soap for 20 days. After how many days the amount consumed when at the holidays come to us two cousins.
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