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\angle E F A = 1 8 0 ^ { \circ } - 1 3 1 ^ { \circ } = 4 9 ^ { \circ }
\frac { 1 } { 2 } \div 3 = \frac { 1 } { 2 } \times \frac { 1 } { 3 } = \frac { 1 } { 6 }
G \frac { M n } { T 2 } = m a = m \frac { v ^ { 2 } } { r }
\sqrt { 1 8 - 6 x } = 3 \sqrt { x ^ { 2 } - 2 x + 2 }
| HME100K/composed/0804 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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2 x + 3 y - z + 4 x - 2 y + z + 3 x - y - z = 3 + \frac { 5 } { 2 }
\therefore R _ { 2 } = \frac { V _ { 2 } } { I _ { 2 } } = \frac { 6 V } { 1 5 A } = \frac { 6 0 V } { 1 5 A } = 4 \Omega
B D \bot C E
1 2 + b ^ { 2 } = 1 6
| HME100K/composed/0808 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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4 x ^ { 2 } + 4 x y + y ^ { 2 } - 4 x - 2 y - 3
A B : 2 4 \frac { 3 } { 4 } - ( - 1 0 \frac { 1 } { 4 } ) = 3 5
P N = \sqrt { ( - 1 - b ) ^ { 2 } + 1 }
\cos = \frac { a ^ { 2 } + b ^ { 2 } - c ^ { 2 } } { 2 a b }
| HME100K/composed/0812 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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f ( x ) = 2 x ^ { 3 } - x
x : 4 = \frac { 4 5 } { 2 6 } - \frac { 3 } { 4 }
= c + \frac { m } { c }
\Delta A E C \cong \Delta B F D ( S S S )
| HME100K/composed/0816 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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3 0 0 ( 1 2 0 a + 1 6 0 b ) = 2 0 0 0 \times 1 2 0
\frac { 8 0 7 } { 8 1 0 } \times \frac { 9 7 } { 1 0 0 } \approx 8 1 0 0 6
2 x + m x - x = - 5
\Delta C B Q \cong \Delta P D Q
| HME100K/composed/0820 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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3 x - \frac { 3 } { 2 } a x = 6
\therefore \frac { 1 0 } { 6 } = \frac { x } { 4 }
m \geq 4
1 8 0 0 0
| HME100K/composed/0824 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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C G = E C = F E = F G
x ^ { 2 } - 4 x + 4 - 4
y = \frac { 6 } { x }
= m x - \frac { 1 } { 3 } ,
| HME100K/composed/0828 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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C D = D E B D = 2 C D
\angle 3 = 6 0 ^ { \circ } ( 1 8 0 ^ { \circ } - 1 2 0 ^ { \circ }
C u O + H _ { 2 } S O _ { 4 } = C u S O _ { 4 } + H _ { 2 } O
\angle 2 + \angle 4 + \angle I = 1 8 0 ^ { \circ }
| HME100K/composed/0832 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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B E = 2 D E
\times 6 = 1 3 . 5 ( d m ) ^ { 2 } 1 3 . 5 \times 1 . 4 = 1 8 . 9 ( d m ^ { 2 } )
\textcircled { 2 } \frac { 5 } { 7 } - [ \frac { 3 } { 4 } - ( \frac { 2 } { 5 } - \frac { 1 } { 4 } ) ]
x + 1 = 5 ( y + 2 )
| HME100K/composed/0836 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\angle 1 = \angle 2
1 - 1 / 6 = \frac { 5 } { 6 } .
l W = P t : t = \frac { W } { P }
\angle A + \angle A D E = 5 5 ^ { \circ } + 1 2 5 ^ { \circ } = 1 8 0 ^ { \circ }
| HME100K/composed/0840 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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g ^ { + } + I ^ { - } \rightarrow A g I \downarrow
S _ { \Delta M P Q } = \frac { 1 } { 2 } P Q \cdot \vert X M - M Q \vert
3 2 - 2 = 3 0 ( m ) .
D E = O E - O D = \frac { \sqrt { 2 } } { 2 } ( x + 4 ) y
| HME100K/composed/0844 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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x _ { 1 } + x _ { 2 } = \frac { \pi } { 2 }
\angle C E D = - 7 0 ^ { \circ }
S _ { 2 } = 3 6 \div 2 = 1 8
S _ { \Delta A O B } = \frac { 1 } { 2 } \cdot A B \cdot O H
| HME100K/composed/0848 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\therefore \angle C D F = 9 0 ^ { \circ } - 3 0 ^ { \circ }
0 . 5 6 x + 0 . 2 8 y = 9 5 . 2 .
\alpha = \frac { h } { 3 5 } \tan \beta = \frac { h } { 8 0 \cdot }
\lambda \overrightarrow { A B } \cdot \overrightarrow { A C } + . ( 1 - \lambda ) \overrightarrow { A C } = 1 6 .
| HME100K/composed/0852 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\cot ( \frac { 3 \pi } { 2 } + \alpha ) = - \tan \alpha
b _ { 3 } = \frac { a _ { 3 } } { 2 } + 3 = \frac { a _ { 1 } q ^ { 2 } } { 2 } + 3 = b _ { 1 } + 2 d
2 N H _ { 3 } + H _ { 2 } S O _ { 4 } \rightarrow ( N H _ { 4 } ) _ { 2 } S O _ { 4 }
\frac { 1 } { m ^ { 2 } - m } + \frac { m - 5 } { 2 m ^ { 2 } - 2 }
| HME100K/composed/0856 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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0 . 8 \times m g \mu = m g 0 . 6 + F .
9 \times 4 0 = 3 6 0 ( k m )
2 x - y + 2 = 5 \textcircled { 2 }
N H _ { 3 } + H _ { 2 } O \rightleftharpoons N H _ { 3 } \cdot H _ { 2 } O
| HME100K/composed/0860 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\Delta A B E \cong \Delta D C F ( S A S )
2 N a O H + C u C a _ { 3 } = N a _ { 2 } C O _ { 3 } + C u O + H _ { 2 } \uparrow
\frac { A D } { \sin C } = \frac { C D } { \sin ( A - B ) } \Rightarrow \frac { \frac { 2 } { 3 } a } { \sin C } = \frac { \frac { 1 } { 3 } a } { \sin ( A - B ) }
\sqrt { 2 } + 6
| HME100K/composed/0864 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\angle A B O = \angle B A O = 1 5 ^ { \circ }
\angle B C D - \angle 3 = \angle E C G - \angle 3
O C = 2 \sqrt { 5 } , \sin \angle A C C = \frac { 2 } { 5 } \sqrt { 5 }
a ^ { 2 } = b ^ { 2 } + c ^ { 2 } - 2 b c - \cos A
| HME100K/composed/0868 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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( 1 ) . C a ( O H ) _ { 2 } + 2 H C l = C a C l _ { 2 } + 2 H _ { 2 } O
x ^ { 2 } - a x + 1
9 - 1 2 t + 4 t ^ { 2 }
5 x + 1 < 3 ( x - 1 )
| HME100K/composed/0872 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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I _ { 2 } = \frac { U _ { 2 } } { R _ { 2 } }
C = 8
1 1 - 2 ( 8 - 5 x ) = 3 ( 1 0 - x
\frac { T _ { 1 } } { T _ { 2 } } = \sqrt { \frac { R _ { 1 } ^ { 3 } } { R _ { 2 } ^ { 3 } } } = \sqrt { 1 8 } ^ { 3 } \approx 7 6
| HME100K/composed/0876 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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6 - 1 0 = C C B A C
B G = \frac { 4 } { 5 } x G D = \frac { 3 } { 5 } x
\frac { 4 } { 5 } \times \frac { 5 } { 6 } = \frac { 1 } { 3 }
a _ { 1 } = \frac { - b + \sqrt { \Delta } } { 2 a } = \frac { 6 + \sqrt { 4 0 } } { 2 } = \frac { 6 + 2 \sqrt { 1 0 } } { 2 } = 3 + \sqrt { 1 0 }
| HME100K/composed/0880 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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f ( x ) = a x ^ { 2 } + b x + c
x _ { 1 } = x _ { 2 } = 1
5 y ^ { 2 } - ( 1 - 2 y ) ^ { 2 } - y - 3 = 0
x ^ { 2 } - 3 x + 2 = 0
| HME100K/composed/0884 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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B P = \sqrt { 4 0 ^ { 2 } - 2 0 ^ { 2 } } = 2 0 \sqrt { 3 }
3 0 \times ( 2 0 - 5 ) = 4 5 0 ( m ^ { 2 } )
N a _ { 2 } C O _ { 3 } + 2 H C l = H _ { 2 } C O _ { 3 } + 2 N a C l
\angle A B C = 9 0 ^ { \circ } ( 2 )
| HME100K/composed/0888 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\textcircled { 1 } + \textcircled { 2 } \times 2
R _ { 2 } ^ { 2 } = 1 - \frac { 1 6 4 } { 6 0 5 0 }
\{ x \vert x = \frac { k \pi } { 2 } + \frac { 1 } { 2 } \arctan \frac { 3 } { 2 } k \in z \}
2 ( 2 - a ) = 2 a - 2
| HME100K/composed/0892 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\angle M C A + \angle E C F + \angle F C B = 1 8 0 ^ { \circ }
S _ { \Delta A B C } = S _ { \Delta A P C } - S _ { \Delta A P B }
\angle C A B = \angle C B A = 4 5 ^ { \circ }
H _ { 2 } S O _ { 4 } + C a ( O H ) _ { 2 } = C a S O _ { 4 } + 2 H _ { 2 } O
| HME100K/composed/0896 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\frac { T _ { m } } { T _ { n } } = \frac { m ( S _ { m } + \lambda ) } { n ( S _ { n } + \lambda ) . }
x = - \frac { b } { 2 a } = - \frac { - \frac { 2 } { 3 } } { \frac { 2 } { 3 } } = 1
( - 1 6 , - 1 1 ) D ^ { \prime } ( - 1 6 , - 9 )
C A B C D = 2 \times ( 4 \sqrt { 2 } + 4 ) = 8 \sqrt { 2 } + 8
| HME100K/composed/0900 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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b _ { n } = b _ { 1 } q ^ { n - 1 } = - \frac { 1 1 } { 2 } \cdot 2 ^ { n - 1 }
\angle E A C + \angle A E C = 9 0 ^ { \circ }
\frac { 2 ( x _ { 1 } - x _ { 2 } ) } { x _ { 1 } x _ { 2 } } < 0
( 2 ) x = \frac { 0 - V _ { 2 } } { - 2 a } = \frac { 0 - 2 0 ^ { 2 } } { - 2 \times 4 } m = 5 0 m
| HME100K/composed/0904 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\frac { 1 } { 2 } \leq a ^ { 2 }
D A = A F
R _ { \min } = \frac { V } { 2 \max } = \frac { 1 5 V } { 1 A } = 1 5 \Omega
\widehat { E } = \frac { E } { 2 } = \frac { 1 } { 2 } B V ^ { 2 } \cdot t \cdot \tan \theta
| HME100K/composed/0908 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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S _ { \Delta A C M } = \frac { 1 } { 3 } S _ { \Delta A B C }
\frac { 1 } { 3 } x > - \frac { 1 } { 2 } x + 2
2 8
\angle B A D = \angle C A E = \alpha
| HME100K/composed/0912 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\angle 1 = 5 5 ^ { \circ }
1 6 0 + 7 6 = 2 3 6 ( d m ^ { 3 } )
x \in ( \frac { z } { 4 } , \frac { n } { 2 } )
\angle P A ^ { \prime } = P B )
| HME100K/composed/0916 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\angle B D A = 1 8 0 ^ { \circ } - 6 6 ^ { \circ } - 3 0 ^ { \circ } = 8 4 ^ { \circ }
: \frac { C E } { C O } = \frac { E F } { O B }
\frac { - 4 a } { a ^ { 2 } + 4 } - \frac { - 2 } { 2 + a } = \frac { - 4 } { 2 + a } a ^ { 2 } + 6 a - 8 =
7 。 6 \div ( 5 \times 3 . 8 ) = 0 . 4 m
| HME100K/composed/0920 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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x - \frac { 3 } { 2 } = \pm \frac { 1 } { 2 }
3 N O _ { 2 } + H _ { 2 } O \rightarrow 2 H N O _ { 3 } + N O
B A C D B D D D B D
2 0 0 c m ^ { 3 } = ( 1 \frac { 2 0 0 } { 1 0 0 0 } ) d m ^ { 3 }
| HME100K/composed/0924 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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F _ { 1 } = \frac { F _ { 2 } L _ { 2 } } { L _ { 1 } } = \frac { 5 0 0 N \times 0 . 9 m } { 0 . 9 m + 0 . 6 m } = 3 0 0 N
a ( 1 0 a - 1 1 ) = 0
0 < t < \frac { 1 } { 2 }
2 8 . 2 6 - 1 2 . 5 6 = 1 5 . 7 ( c m ^ { 2 } )
| HME100K/composed/0928 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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2 a x - a - 3 x + 5 = 0
x ^ { 4 } - 8 x ^ { 3 } y + 2 4 x ^ { 2 } y ^ { 2 } + 1 6 y ^ { 4 } - 3 2 x y ^ { 3 } - 3 x + y = 5
\frac { 5 } { 6 } = \frac { O Q } { \sqrt { 2 6 } }
5 x + 3 y = 4 \textcircled { 2 }
| HME100K/composed/0932 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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R : 3 . 2 \times 4 = 1 2 . 8
: \angle A K C + \angle K A C + \angle K C A = 1 8 0
\frac { A D } { C E } = \frac { D F } { F C }
\angle B + \angle C = 1 8 0 ^ { \circ }
| HME100K/composed/0936 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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a ^ { 2 } - b ^ { 2 }
x _ { 1 } = \sqrt [ 3 ] { - \frac { 1 } { 3 } } \approx - 0 . 6 9
x + y - 2 = 4 \textcircled { 1 }
2 \sqrt { 5 } + 3 \sqrt { 7 } - 5 \sqrt { 5 } - 3 \sqrt { 7 }
| HME100K/composed/0940 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\frac { x } { 8 } = \frac { 4 } { 3 }
\angle D A N = \angle A D B = \frac { \pi } { 3 }
a _ { 1 } = \frac { G M } { r ^ { 2 } } .
\angle C = 2 0 ^ { \circ }
| HME100K/composed/0944 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\therefore ( 1 ) \because y = c a ^ { 2 } + b x + 4
\alpha - \frac { \pi } { 6 } \epsilon ( \frac { 2 } { 3 } \pi , \pi )
\angle A C B = 4 5 ^ { \circ }
x _ { 2 } = - 1
| HME100K/composed/0948 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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f ( x ) = a x ^ { 2 } + b x + c
( 1 + k ^ { 2 } ) x ^ { 2 } - 4 k ^ { 2 } x + 4 k ^ { 2 } - 1 = c
= 1 \times 7 0 ^ { - 3 } m
a = 1 6 0 ^ { \circ }
| HME100K/composed/0952 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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x > a
2 . 6 3 k m = ( ) m
\tan 3 0 ^ { \circ } = \frac { \sqrt { 3 } } { 3 }
8 3 \times 9 9
| HME100K/composed/0956 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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y = 1
1 . 3 \cdot \frac { a _ { 1 } } { 1 - q } = \frac { a _ { 1 } } { 1 - q ^ { 2 } }
S \ln P = \frac { 1 } { 3 } = \frac { O E } { P O } = \frac { O E } { 6 2 }
f ( A ) = \sin ( 2 A - \frac { \pi } { 6 } ) + 1 = 2
| HME100K/composed/0960 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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2 0 0 \div 4 = 5 0 ( k m )
5 . 8 8 \times 1 0 ^ { 5 } J
1 0 x = 7 2 0 0 - 2 5 0 0
\sqrt [ 3 ] { 2 + \frac { 2 } { 7 } } = 2
| HME100K/composed/0964 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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- 2 x + 1 < x + 4
a \neq \frac { 3 } { 2 }
\frac { 1 } { 2 } x \div \frac { 1 } { 2 } = \frac { 1 } { 1 2 } \div \frac { 1 } { 2 }
\frac { 1 } { 5 } = \frac { 1 } { 6 } + \frac { 1 } { 3 0 }
| HME100K/composed/0968 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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[ x ] \leq x < [ x ] + 1
x = \frac { - b \pm \sqrt { b ^ { 2 } - 4 a c } } { 2 a } = \frac { - 1 \pm \sqrt { ( - 6 ) ^ { 2 } - 4 \times 1 \times ( - 6 ) } } { 2 \times 1 } = \frac { - 1 \pm \sqrt { 2 5 } } { 2 } = \frac { - 1 \pm 5 } { 2 }
W = \frac { \theta } { t } = \frac { 3 } { 4 } \pi
R _ { 2 } = \frac { V _ { 2 } } { Z _ { 2 } } = \frac { 6 V } { 0 . 4 A } = 1 5 \Omega
| HME100K/composed/0972 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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g ( x ) = x - x ^ { 2 } = - ( x - \frac { 1 } { 2 } ) ^ { 2 } + \vert \frac { 1 } { 4 } \vert
\Delta A O B \cong \Delta C O D ( A S A )
N a _ { 2 } C O _ { 3 } + H _ { 2 } S O 4 = N a _ { 2 } S O 4 + H _ { 2 } O + C O _ { 2 } \uparrow
\angle B + \angle D = 2 4 0 ^ { \circ }
| HME100K/composed/0976 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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F A = F B = F C
( \frac { 8 } { 9 } \times \frac { 1 } { 4 } = \frac { 2 } { 9 } ) 。
\sin ( 2 A - 3 0 ^ { \circ } ) = 1
\angle D E B = \angle D E C = 9 0 ^ { \circ }
| HME100K/composed/0980 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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d = \frac { \vert 4 x - y - 5 \vert } { \sqrt { 1 6 + 1 } } = \frac { \vert 1 - 4 x ^ { 2 } + 4 x - 5 \vert } { \sqrt { 1 7 } }
2 \sqrt { 2 5 - ( 1 . 4 ) ^ { 2 } } = \frac { 2 8 } { 5 }
5 9 . 0 2 > 5 8 . 5 2 > 5 8 . 1 7 > 5 8 . 0 9
\because \angle A O C = 4 5 ^ { \circ } \therefore \angle A O D = \angle A O C + \angle C O D = 4 5 ^ { \circ } + 4 5 ^ { \circ } = 9 0
| HME100K/composed/0984 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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E _ { n } = E k + E P = - \frac { k e ^ { 2 } } { 2 Y _ { n } }
S _ { \Delta A B C } = O A
( 3 5 - 3 0 ) x + ( 2 6 - x ) \cdot ( 2 8 - 2 0 ) \geq 1 9 5
a x ^ { 2 } - 1 5 x + c > 0
| HME100K/composed/0988 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\angle B O D = \angle C O D = \frac { 1 } { 2 } \angle B O C = 6 0 ^ { \circ }
2 [ \frac { 4 } { 3 } x - \frac { 2 } { 3 } x + \frac { 1 } { 2 } ] = \frac { 3 } { 4 } x
R _ { 0 \max } = \frac { v _ { 0 } } { I _ { 0 } } = \frac { 6 . 0 v } { 0 . 2 A } = 3 0 \Omega
, f ( B ) = 2 \sin ( 2 B + \frac { \pi } { 6 } ) - 1 = 0
| HME100K/composed/0992 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\frac { C _ { \Delta A B C } } { C _ { \Delta A ^ { \prime } B ^ { \prime } C ^ { \prime } } } = k
\angle A = \angle B C D
2 a + \frac { 3 } { 6 } = \frac { 7 } { 6 }
( \lambda \overrightarrow { A D } - \overrightarrow { A B } ) = \lambda \overrightarrow { A D } ^ { 2 } + ( \frac { 1 } { 2 } \lambda - 1 ) \overrightarrow { A B }
| HME100K/composed/0996 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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3 x ^ { 2 } + 3 y ^ { 2 } - 1 0 a x + 3 a ^ { 2 } = 0
x > \frac { 1 } { 2 }
B 1 3 < x \leq 1 2 \frac { 4 } { 9 }
a = 1 , b = - 3 , c = - 1
| HME100K/composed/1000 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\angle G H M = \frac { 1 } { 2 }
2 - 3 a \leq 0 \Rightarrow a \geq \frac { 2 } { 3 } \Rightarrow \frac { 2 } { 3 } \leq a < 1
\therefore x = 2
\angle D B E = \frac { 1 } { 2 } \angle A B C
| HME100K/composed/10000 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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F _ { 1 } = \frac { 1 } { 2 } F _ { 2 } \div 2 0 N
x _ { 1 } = - 6 , x _ { 2 } = 4
4 ( y - z + 3 ) = ( 4 - z ) ( x + 2 )
f ^ { \prime } ( x ) = ( - s i
| HME100K/composed/10004 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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x \geq - \frac { 1 } { 2 }
2 4 0 0 0 0 0 0 c m = 2 4 k m
y _ { 2 } = - \frac { 1 0 } { 3 }
y _ { 4 } = \frac { 5 } { 2 }
| HME100K/composed/10008 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\angle A B P - \angle A B P = \angle A E P - \angle C F P = \angle P
\Delta A D E \sim \Delta A B C
P F = P F _ { 1 } + 4
\sqrt { ( a - \frac { 1 } { a } ) ^ { 2 } } = a - \frac { 1 } { a }
| HME100K/composed/10012 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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x _ { 1 } ^ { 2 } + x _ { 2 } ^ { 2 } - x _ { 1 } x _ { 2 } = 1 6
n = 3 6 0 ^ { \circ } \div 3 6
\angle B C N = 6 0 ^ { \circ } (
\frac { 5 } { 2 x - 3 + 2 x } - \frac { 6 } { 2 x + 3 - 2 x } = - 1
| HME100K/composed/10016 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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y = \frac { 7 } { 2 4 }
\angle B C A = \angle D F E B C = F E
x = 1 \times \frac { 8 } { 3 }
A D = 2 A F = \frac { 1 4 } { 5 }
| HME100K/composed/10020 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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P = \frac { F } { S } = \frac { 6 5 0 N } { 2 . 5 \times 1 0 ^ { - 3 } m ^ { 2 } } = 2 . 6 \times 1 0 ^ { 5 } P a
F = f = 0 . 2 G = 0 . 2 \times 1 . 4 6 \times 1 0 ^ { 4 } N = 5 . 9 2 \times 1 0 ^ { 3 } N
A D \bot B C
S ^ { 2 } = \frac { 1 } { b } [ ( x _ { 1 } - \overline { x } ) ^ { 2 } + ( x _ { 2 } - \overline { x } ) ^ { 2 } + \cdots + ( x _ { n } - \overline { x } ) ^ { 2 } ) ]
| HME100K/composed/10024 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\frac { 1 } { 1 + 2 t } + 2 + t = \frac { 1 } { 1 + 2 t } + \frac { 1 } { 2 } ( 1 + 2 t ) + \frac { 3 } { 2 } \geq 2 \sqrt { \frac { 1 } { 2 } } + \frac { 3 } { 2 } \geq \sqrt { 2 } +
5 1 2 \div 8 9 = 5 \cdots 6 7
y _ { 2 } = \frac { 1 } { 5 }
3 1 0 \div x = 4 5 + 5 5
| HME100K/composed/10028 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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- x _ { 1 } = 0
) 3 2 . 8 4 - 5 . 6 7 - 1 2 . 8 4 - 3 . 2 3
\angle A D C + \angle 1 = \angle A B C + \angle 2 = 1 8 0 ^ { \circ } (
3 a + \frac { 1 } { 5 } b > 2
| HME100K/composed/10032 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\sqrt { 2 } ( \cos \frac { \pi } { 4 } \cos n x + \sin \frac { \pi } { 4 } \cos x ) = a
A P = 8 - 4 . 3 = 3 . 7 > 3
1 3 = 1 3 . 0 0 0 5 8 . 4 = 5 8 . 4 0 0 0 . 8 0 = 0 . 8 0 0
y _ { 1 } = \sqrt { 2 }
| HME100K/composed/10036 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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s _ { \Delta A B C } = 7 0 c m ^ { 2 }
( a - b ) ^ { 2 } > 0
S _ { \Delta } A B C = \frac { 1 } { 2 } \times 6 \times \frac { 8 } { 3 } = 8
\angle D E A = \angle D F B = 9 0 ^ { \circ }
| HME100K/composed/1004 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\frac { 9 2 } { 1 0 0 } = \frac { 4 6 } { 5 0 } = \frac { 2 3 } { 2 5 }
5 6 8 \div 6 7 = 8 \cdots 3 2
P ( 2 + 2 \sqrt { 2 } , - 2 \sqrt { 2 } )
1 7 \div 1 3 = \frac { 1 7 } { 1 3 }
| HME100K/composed/10040 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\angle A O C = 1 4 5 ^ { \circ }
2 8 . 2 6 \times \frac { 1 } { 3 } = 9 . 4 2 ( c m ^ { 2 } )
x > - \frac { 7 } { 1 3 }
\angle B A C = 6 0 ^ { \circ }
| HME100K/composed/10044 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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x _ { 1 } = \frac { 5 } { 3 }
\frac { A P } { E A } = \frac { A B } { A C } = k
y = - \frac { 1 } { 4 } x ^ { 2 } + \frac { 1 } { 2 } x + 2
3 1 4 0 + 6 2 8 + 4 0 0 0 = 7 7 6 8 ( c m ^ { 2 } )
| HME100K/composed/10048 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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A C = 2 A O = 2 \times 3 \sqrt { 3 } = 6 \sqrt { 3 }
( 4 . 4 8 ) ( 4 . 4 9 ) ( 4 . 5 0 )
a = 0
1 . ( 1 ) \times ( 2 ) v ( 3 ) \times 2 . 9 0 ^ { \circ } 8 5 ^ { \circ } 9 5 ^ { \circ } 3 \angle 1 \times 2 )
| HME100K/composed/10052 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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5 \div \frac { 1 } { 9 0 0 0 0 0 } = 4 5 0 0 0 0 0 0 c m = 4 5 0 ( k m ) .
m ( x + y - 3 ) + n ( 2 x - y ) + 3 x - 3 = 0
3 d = 3
\frac { N B } { N C } = \frac { B M } { B C }
| HME100K/composed/10056 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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O A = O C , O B = O D
2 . 5 : \frac { 1 } { 5 } = 2 : \frac { 1 } { 4 }
C a C O _ { 3 } + 2 H C l _ { 2 } = C a C _ { 2 } + H _ { 2 } O + C O _ { 2 } \uparrow .
2 x = 2 3
| HME100K/composed/10060 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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x = \frac { 2 0 } { 7 }
\therefore x _ { 1 } = - 3 , x _ { 2 } = 2
\sin \alpha = \frac { 1 } { 2 }
\frac { A C } { C F } = \frac { A D } { C D }
| HME100K/composed/10064 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\cos \theta = \frac { B D } { B C }
- \frac { 6 } { 5 } x = \frac { 4 } { 2 } - \frac { 1 } { 2 }
4 7 \div 5 = 9 \frac { 2 } { 5 }
4 \frac { 1 } { 5 } : \frac { 1 } { 4 } = 3 0 : 2 4
| HME100K/composed/10068 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\frac { \sqrt { 2 } } { x + \sqrt { 3 } } = \frac { \sqrt { 3 } } { x }
3 b ^ { 2 } = 1 2 + 6 \sqrt { 3 }
x = \frac { 1 } { 2 0 } \times 2
\frac { 6 } { x } - \frac { 6 } { x + 1 } = \frac { 1 } { 2 }
| HME100K/composed/10072 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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x _ { 1 } + x _ { 2 } = - \frac { 8 \sqrt { 3 } k ^ { 2 } } { 1 + 4 k ^ { 2 } }
\frac { 1 } { 5 } + \frac { 2 } { 5 } - \frac { 3 } { 5 } = 0
a ^ { 2 } = \frac { 2 - \sqrt { 3 } } { 2 }
a - \sqrt { 2 } = b
| HME100K/composed/10076 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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l : x = m y - \sqrt { 3 }
\frac { 7 . 3 g } { 1 5 3 g - 8 0 g } \times 1 0 0 \% = 1 0 \%
f ( x ) _ { \max } = f ( - \frac { b } { 2 a } )
\frac { a } { \sin A } = \frac { b } { \sin B }
| HME100K/composed/1008 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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3 A D = A D + \sqrt { 1 0 }
P = P g h
\angle B D E = \angle B E D = \frac { 1 } { 2 } ( 1 8 0 ^ { \circ } - 3 0 ^ { \circ } ) = 7 5 ^ { \circ }
S _ { \Delta A B C } = \frac { a ^ { 2 } \sin B \sin C } { 2 \sin ( B + C ) }
| HME100K/composed/10080 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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C _ { E } = \sqrt { o c ^ { 2 } - o E ^ { 2 } } = \sqrt { ( 2 \sqrt { 5 } ) ^ { 2 } - 2 ^ { 2 } } = 4
\frac { 6 } { 3 0 } = \frac { 1 } { 5 }
\frac { 5 } { 6 } > \frac { 1 1 } { 1 8 }
x _ { 1 } = \sqrt { 3 } + 2
| HME100K/composed/10084 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\angle A C M + \angle D C M + \angle C A M = 9 0 ^ { \circ }
F e + 2 H C l = F e C l _ { 2 } + H _ { 2 } \uparrow
\frac { 1 } { m } + \frac { 4 } { n } = \frac { 1 } { 3 } ( m + n ) ( \frac { 1 } { m } + \frac { 4 } { n } ) = \frac { 1 } { 3 } [ 5 + \frac { n } { m } + \frac { 4 n } { n } ] \geq \frac { 1 } { 3 } ( 5 + 2 \sqrt { \frac { n } { m } \frac { 4 m } { n } } )
x = \frac { 1 0 } { 9 }
| HME100K/composed/10088 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
|
\angle E + \angle F + \angle 4 = 1 8 0 ^ { \circ } .
C E = \frac { 1 } { 2 } C D
k = \pm \frac { \sqrt { 6 } } { 3 }
y B C = \frac { 1 } { 2 } x + b
| HME100K/composed/10092 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
|
2 N H _ { 4 } C l + C a ( O H ) _ { 2 }
2 x ^ { 2 } + m ^ { 2 } - 2 m x - 8 = 0
\frac { s } { 3 } = \frac { 4 } { E C }
\angle A F B = \angle 2 = 9 0 ^ { \circ }
| HME100K/composed/10096 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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2 5 \times 1 0 0 0 = 2
V = \frac { s } { t } = \frac { 1 3 5 0 k m } { 4 . 5 h } = 3 0 0 k m / h .
3 6 - 2 4 y + 1 6 y ^ { 2 } - 1 2 y + 8 y ^ { 2 } + y ^ { 2 } - 1 = 0
\angle B A C = \angle 1 + \angle D A C
| HME100K/composed/10100 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\angle B A C = 3 0 ^ { \circ }
\frac { x + 1 } { 2 } - 1 < x - \frac { 2 x + 3 } { 3 }
I _ { R } = \frac { U } { R } = \frac { 1 0 V } { 1 0 \Omega } = 1 A
x = \frac { 2 b } { a - 3 }
| HME100K/composed/10104 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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a _ { 1 } = \frac { 1 } { 3 }
A H = 3 . B H = 4
O B = \sqrt { O E ^ { 2 } + B E ^ { 2 } } = 1 5 0 \sqrt { 2 }
1 0 0 0 ( 2 5 - x ) - 1 0 \times ( 2 5 - x ) - 1 3 5 0 x = 0
| HME100K/composed/10108 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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P = \frac { F } { S }
A B ^ { 2 } = 4 ( 5 - \frac { 3 ( m + 1 ) ^ { 2 } } { ( m + 2 n + 3 ) ^ { 2 } + ( m - n ) ^ { 2 } } )
x _ { 1 } = - \frac { 2 3 } { 4 }
\tan \angle D A B = \frac { D E } { A E } = \frac { 1 } { 2 }
| HME100K/composed/10112 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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d = \frac { \vert 4 x - y - 5 \vert } { \sqrt { 1 6 + 1 } } = \frac { \vert 1 - 4 x ^ { 2 } + 4 x - 5 \vert } { \sqrt { 1 7 } }
O C = A O = \frac { 1 } { 2 } A C = \frac { 1 } { 2 } \times 9 = 4 . 5 c m
A C = 2 A O = 2 \sqrt { 3 } \angle B D = 2 8 0 ^ { \circ } = 2 c m
\frac { 1 2 0 } { 2 7 + x } + \frac { 1 2 0 } { 2 7 - x } = 9
| HME100K/composed/10116 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\angle A E D - \angle E D A = 4 5 ^ { \circ }
8 0 \div 2 = \square
\frac { T } { 2 } = \frac { 4 \pi } { 9 } - \frac { \pi } { 9 } = \frac { \pi } { 3 }
g ( x ) _ { \min } = g ( \frac { 3 } { 4 } ) = \frac { 7 } { 1 6 }
| HME100K/composed/1012 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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k \pi + \frac { 5 \pi } { 8 } ]
\frac { 1 2 0 } { \frac { 6 } { 5 } y } + 6 0 = \frac { 1 2 0 } { y }
3 0 1 2 < 3 0 2 1 < 3 1 0 2 < 3 1 2 0 < 3 2 0 1 < 3 2 1 0 。
F _ { 2 } O _ { 2 } + 6 H C l = 2 F e C l _ { 3 } + 3 H _ { 2 } \uparrow , F e + 2 H C l = F e C l _ { 2 } + H _ { 2 }
| HME100K/composed/10120 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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A D = \sqrt { 3 } P D = \sqrt { 3 } \times k m
A E = \frac { 1 } { 2 } A B
\frac { 5 0 } { 1 3 } < O P < 1 0
\angle A F B = \angle C F E = 9 0 ^ { \circ } - 6 0 ^ { \circ } = 3 0 ^ { \circ }
| HME100K/composed/10124 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\angle C P O = \angle B = 9 0 ^ { \circ }
\frac { 5 } { 8 } > \frac { 1 } { 2 } > \frac { 3 } { 7 }
\angle B = \angle C = 3 0 ^ { \circ } = \angle B M D = \angle E N C
k _ { 1 } = \frac { C c o } { C c o _ { 2 } }
| HME100K/composed/10128 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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y _ { 1 } = - 0 . 1 x + 5 0 ( 0 < x \leq 5 0 0 )
H _ { 2 } S O _ { 4 } + F e = F e S O _ { 4 } + H _ { 2 } \uparrow
\times 4 , - \textcircled { 2 } \times 3 .
= \frac { ( x _ { 1 } + x _ { 2 } ) ^ { 2 } - 2 x _ { 1 } x _ { 2 } + ( x _ { 1 } + x _ { 2 } ) } { x _ { 1 } x _ { 2 } + ( x _ { 1 } + x _ { 2 } ) } + 1 = \frac { 1 0 1 } { 3 2 }
| HME100K/composed/10132 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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2 b _ { 1 } + 2 ^ { 2 } b _ { 2 } + 2 ^ { 3 } b _ { 3 } + \cdots + 2 ^ { n } b _ { n } = 2 ^ { a n } - 4
V = \frac { 1 } { 3 } \pi r ^ { 2 }
\angle A E D = 9 0 ^ { \circ }
x ^ { \prime } = \pm \sqrt { \frac { 2 } { a - 1 } }
| HME100K/composed/10136 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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\frac { x } { 1 5 } = \frac { 1 . 5 } { 0 . 5 }
\Delta A E F = ( x + 2 ) \cdot ( \frac { 2 } { \alpha } - 6 ) \div \frac { 1 } { 2 } - \frac { 1 } { 2 } \cdot ( \frac { 1 2 } { \alpha } - 6 ) \cdot 2
2 ^ { n + 1 } + \frac { n } { 2 } - 2
c = c
| HME100K/composed/10140 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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1 1 . 7 6 d m ^ { 3 } = 1 1 7 6 0 c m ^ { 3 } :
0 . 5 < 0 . 5 1 < 0 . 5 0 1 < 0 . 5 1 1
\frac { 5 } { 9 } x \div \frac { 5 } { 9 } = \frac { 7 } { 1 5 } \div \frac { 5 } { 9 }
x = \frac { 5 } { 3 }
| HME100K/composed/10144 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
|
\overrightarrow { C A } - \overrightarrow { O A } + \overrightarrow { O A } = \overrightarrow { C A }
C n H 2 n + 2 + \frac { 3 n + 1 } { 2 } 0
x = - \frac { 1 2 5 } { 2 3 }
x \geq \frac { 1 } { 2 } .
| HME100K/composed/10148 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
|
\frac { A E } { A B } : \frac { D E } { B C } = \frac { 1 } { 3 }
M < \frac { 1 } { 2 }
x _ { 3 } = - 2 + 2 \sqrt { 2 }
\angle F A O = \angle C A O - \angle C A F
| HME100K/composed/10152 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
|
Z n + H _ { 2 } S O _ { 4 } = Z n S O _ { 4 }
E B = F C
1 2 . 5 6 + 3 . 1 4 = 1 5 . 7 m ^ { 2 }
6 . 2 8 \div 3 . 1 4 \div 2 = 1 c m
| HME100K/composed/10156 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
|
3 0 0 + 5 0 0 =
8 \times 4 \times 3 = 9 6 ( d m ^ { 3 } ) 3 - 0 . 2 = 2 . 8 ( d m )
\angle C O D = 5 5 ^ { \circ }
4
| HME100K/composed/1016 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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A \cap B = A \cap C \neq 0
= \frac { \sqrt { 2 } - 1 } { \sqrt { 2 } } = \frac { 2 - \sqrt { 2 } . } { 2 }
b _ { n } = 2 ^ { n } ( n \in N ^ { \ast } )
\frac { 1 } { a } + \frac { 1 } { b }
| HME100K/composed/10160 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
|
b _ { 2 n - 1 } \cdot b _ { 2 n + 1 } = \frac { 1 } { 4 } ( \frac { 1 } { n } - \frac { 1 } { n + 1 } )
m ^ { 2 } - m - 6 = 0
( 3 ) ( - 8 ) - \frac { 2 } { 5 }
\because D - 1 = \sqrt { 3 } a
| HME100K/composed/10164 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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a \div b = \frac { 1 } { 1 0 0 }
7 2 \div 1 2 = 6 ( c m )
f ( x ) = \frac { \sin \pi + \pi } { \cos \pi + \pi ^ { 2 } } = \frac { 0 + \pi } { - 1 + \pi ^ { 2 } } > . 0
\angle O E B + \angle B A E = 9 0 ^ { \circ }
| HME100K/composed/10168 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
|
\frac { 2 } { 3 } x \div \frac { 2 } { 3 } = 1 0 0 \div \frac { 2 } { 3 }
1 L = 1 d m ^ { 3 }
\sin x \in [ - 1 , \frac { \sqrt { 2 } } { 2 } ]
1 4 . 3 - 5 . 5 1 + 4 . 4 9 = 1 4 . 3
| HME100K/composed/10172 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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a x ^ { 2 } + ( 2 b - 9 ) x + c = 0
\square \square \square \square ( a + b + c )
a - c > b - d
x _ { 1 } = - 1 , x _ { 2 } = 2
| HME100K/composed/10176 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
|
x = - \frac { 1 } { 5 }
6 2 . 8 \div 3 . 1 4 \div 2 = 1 0 c m
\frac { B E } { D E } = \frac { C E } { A E }
D E = \frac { 1 } { 2 } B C = \frac { 5 } { 2 }
| HME100K/composed/10180 | /tmp/hf-datasets-cache/medium/datasets/78915396673401-config-parquet-and-info-boydcheung-TAL_OCR_Compos-e25b3c38/hub/datasets--boydcheung--TAL_OCR_Composed_37K/snapshots/741622f82cd5acc1a5c9d7b9180040b6cce45582/TAL_OCR_Composed.tar.gz |
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