jpg
imagewidth (px) 58
3.05k
| txt
stringlengths 22
3.93k
| __key__
stringlengths 21
29
| __url__
stringclasses 1
value |
|---|---|---|---|
\frac { x + 4 } { 3 } \geq \frac { \pi } { 2 } + 1
x = - \frac { b + 1 } { 4 }
\frac { A O } { A A ^ { \prime } } = \frac { O H } { A ^ { \prime } E }
( a - b ) ^ { 2 } - ( b - a ) ^ { 3 } = - ( b - a )
|
HME100K/composed/0404
|
/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
|
|
a = \frac { \sqrt { 2 } } { 2 } \rightarrow h ^ { \prime } ( a ) = 0
\sqrt [ 3 ] { 5 \frac { 5 } { 1 2 4 } } = 5 \sqrt [ 3 ] { \frac { 5 } { 1 2 4 } }
x _ { \min } = 4 0
B M = \frac { 1 } { 2 } C E = C M
|
HME100K/composed/0408
|
/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
|
|
A O / / B C
A B / / C D
4 \times 2 = 8 ( c m ^ { 2 } )
x = \frac { - b \pm \sqrt { b - 4 a c } } { 2 c }
|
HME100K/composed/0412
|
/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 < 1 - \frac { 2 x - 3 } { k }
\angle B A C + \angle C + \angle A B C = 1 8 0 ^ { \circ }
\frac { 7 } { 1 0 } < \frac { 5 } { 1 2 } < \frac { 8 } { 1 5 }
\frac { 1 } { 4 } \div 3 = \frac { 1 } { 4 } \times \frac { 1 } { 3 } = \frac { 1 } { 1 2 }
|
HME100K/composed/0416
|
/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 0 + ( x - 2 0 ) - 0 . 8 ( x - 2 0 0 ) > 3 0
\tan \angle D E M = \frac { D M } { E M } = \frac { M N } { B M } = \frac { x } { x + x } = \frac { 1 } { 3 }
\angle O C A = \angle O A C = 4 5 ^ { \circ }
5 7 0 + 2 1 0 = 7 8 0
|
HME100K/composed/0420
|
/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 { x ^ { 2 } - 2 x + 1 } { x + b } \div \frac { x - 1 } { x ^ { 2 } + x } + x
\sqrt { B C ^ { 2 } - C D ^ { 2 } } = B D
\cos \beta + \cos a \sin \beta = \frac { 5 } { 1 3 }
a _ { m } ^ { 2 } + b _ { n } ^ { 2 } - 2 a _ { n } b _ { m } > a _ { n } ^ { 2 } + b _ { m } ^ { 2 } - 2 a _ { m } b _ { n }
|
HME100K/composed/0424
|
/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 [ \frac { 4 } { 5 } x - \frac { 2 } { 3 } x + \frac { 1 } { 2 } ] = \frac { 3 } { 4 } x
\cdot \angle B E D = \angle D F C = 9 0 ^ { \circ }
\because B G = F G , C G \bot B E
b ^ { 2 } - 4 a c \geq 0
|
HME100K/composed/0428
|
/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 { 1 3 } { 4 } a b = 2 6 ^ { 2 } \times \frac { 4 } { 1 3 }
\angle 2 + \angle 3 = \angle A B F = 9 0 ^ { \circ }
4 x = k \pi \Rightarrow x = \frac { k \pi } { 4 }
\angle B = \angle A C D = 6 0 ^ { \circ }
|
HME100K/composed/0432
|
/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 { B F } { B D } + \frac { B F } { B E }
x = \frac { b + 2 a } { a - 1 } .
y _ { 1 } = \frac { \sqrt { 5 } } { 2 } , y _ { 2 } = - \frac { \sqrt { 5 } } { 2 }
[ 3 . 4 . 6 ] = 1 2
|
HME100K/composed/0436
|
/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
|
|
f ( x _ { 1 } ) - f ( x _ { 2 } ) < 0
\frac { 1 } { 6 } : \frac { 1 } { 4 } = x : \frac { 1 } { 1 2 }
\angle A = \angle C = 1 2 0
n C O _ { 2 } = \frac { m } { M } = \frac { 8 . 8 } { 4 4 g / m o l } = 0 . 2 m o l
|
HME100K/composed/0440
|
/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
|
|
7 + 5 \times 6 = 3 7 9 5 - 5 \times 9 = 5 0
5 u - v = \frac { 3 } { 4 }
\therefore \vert 5 0 \sqrt { 3 } \times 3 0 \approx
R _ { x } = \frac { 1 . 6 V } { 0 . 1 4 A } = 1 1 . 5 \Omega
|
HME100K/composed/0444
|
/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
|
|
A C = 1 6
\frac { 4 } { 5 } [ 3 ( \frac { 7 } { 2 0 0 } \times ) ] = 1 2 6 0
y = \frac { 7 } { 1 2 } \sqrt { 3 } \neq \frac { \sqrt { 3 } } { 2 }
1 ) m ( B a C l _ { 2 } ) \% = \frac { 2 0 . 8 g } { 1 0 4 g } \times 1 0 0 \% = 2 0 \% .
|
HME100K/composed/0448
|
/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
|
|
S O _ { 2 } + 2 H _ { 2 } S \rightarrow 3 S \downarrow + 2 H _ { 2 } O
a : \frac { 2 } { 3 } \times \frac { 1 } { 2 } + \frac { 1 } { 3 } = \frac { 2 } { 3 }
P _ { 2 } O _ { 5 } + 3 H _ { 2 } O = 2 H _ { 3 } P O y
\tan \angle O B C = \frac { O C } { O B } = \frac { 3 } { 6 } = \frac { 1 } { 2 }
|
HME100K/composed/0452
|
/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 O C D = 9 0 ^ { \circ }
\angle B = 9 0
\angle E B F = 9 0 ^ { \circ }
1 3 x - 1 = ( 1 3 - x ) + 2
|
HME100K/composed/0456
|
/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
|
|
( \cos - x ) = \pi - \arccos x
1 8 0 0 0 d m ^ { 3 } = 1 8 m ^ { 3 }
v = s \div t = d \div \frac { \pi - 4 } { w } = \frac { d \omega } { \pi - 4 }
4 x ^ { 2 } + 5 x = 8 1
|
HME100K/composed/0460
|
/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
|
|
\Delta A O B \cong \Delta B ^ { \prime } O A ^ { \prime } ( A S A )
y = \frac { 3 } { 4 } x - \frac { 5 } { 2 }
y - 2 = \frac { 2 \sin \varphi - 2 } { 4 \cos \varphi }
\frac { g } { w ^ { 2 } } = R + h
|
HME100K/composed/0464
|
/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 2 + \angle 3 = 9 0 ^ { \circ }
\angle F A C + \angle A C E + \angle E C F = 9 0 ^ { \circ }
f ( x ) = a x ^ { 3 } - 3 x ^ { 2 } + 1
v = \frac { s } { t }
|
HME100K/composed/0468
|
/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 2 = 8 5 ^ { \circ }
\frac { 8 0 } { 1 2 } = \frac { 2 0 } { 3 }
\frac { x + 1 } { 3 } - \frac { x - 1 } { 2 } \geq \frac { x - 1 } { 6 }
a + \frac { 1 } { a } - 5 = 0
|
HME100K/composed/0472
|
/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
|
|
f ( x ) + f ( \frac { 1 } { x } ) = \frac { 5 } { 2 }
\angle 1 + \angle 2 + \angle B A P + \angle P C D = 1 8 0 ^ { \circ }
y = \frac { 5 } { 6 } x ^ { 2 } + \frac { 1 3 } { 6 } x
1 1 . x ^ { 2 } + 2 ( k - 1 ) x + k ^ { 2 } - 1 < 0 .
|
HME100K/composed/0476
|
/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 { M E } { C E } = \frac { A M } { B C } = \frac { 1 } { 2 }
4 H ^ { + } + 4 e ^ { - } = 2 H _ { 2 } \uparrow
6 \times 1 0 ^ { 3 }
x ^ { 2 } + a x
|
HME100K/composed/0480
|
/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
|
|
= ( t + \frac { 1 } { 2 } ) ^ { 2 } + \frac { 1 1 } { 4 }
- \frac { \pi } { 2 } + 2 k \pi \leq x + \frac { \pi } { 2 } + 2 k \pi _ { 1 } k \in z
\frac { 4 } { 7 5 } \frac { c ^ { 2 } - a ^ { 2 } } { a ^ { 2 } } = \frac { 1 } { e ^ { 2 } + 5 e + \frac { 1 } { 4 } }
\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 2 } =
|
HME100K/composed/0484
|
/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 s \rightarrow 6 \downarrow \times 6 = 1 8 0 0 c m
\frac { 3 0 } { 1 0 0 } \times 3 6 0 ^ { \circ } = 1 0 8 ^ { \circ }
S = \frac { t } { T } \times 4 A = ( \frac { 1 } { 0 . 0 0 5 } \times 4 \times 0 . 0 2 ) _ { m } = 1
3 0 - 2 0 = 1 0
|
HME100K/composed/0488
|
/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
|
|
( - \infty , - 2 ) \cup ( 0 , + \infty ) x ^ { 2 } + 2 k x + k ^ { 2 } + y ^ { 2 } + 2 y + 1 = 1
y = \frac { 1 } { 2 } x + 1
\frac { a _ { n + 1 } } { a _ { n } } = \frac { n } { n + 1 }
N a _ { 2 } O O _ { 3 } + 2 H d = 2 N a d + H _ { 2 } O
|
HME100K/composed/0492
|
/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 2 \times 4 8 \approx 1 5 0 0
n C a C C _ { 3 } = \frac { 1 C } { 1 c c } = c . 1 m o l
B M = \sqrt { 3 }
\leq 1 + \frac { - 2 } { t + 2 } \leq \frac { 1 } { 3 }
|
HME100K/composed/0496
|
/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 A D B = 9 0 ^ { \circ }
\frac { V ^ { 2 } } { R } = \frac { G M } { R ^ { 2 } }
\frac { m \cdot 2 ^ { m + 1 } } { n \cdot 2 ^ { n + 1 } } = \frac { m [ \frac { m ( m + 3 ) } { 2 } + \lambda ] } { n [ \frac { n ( n + 3 ) } { 2 } + \lambda ] }
M N = \frac { 1 } { 2 } x + \frac { 1 } { 2 } y .
|
HME100K/composed/0500
|
/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
|
|
y = \frac { 1 } { 2 } x ^ { 2 } + \frac { 3 } { 2 } x - 2
a x ^ { 2 } - 2 x - 5 a + 6 \geq 0
\angle E D C = \angle E + \angle B
\angle 2 = \frac { 1 } { 2 } \angle A B C , \angle 4 = \frac { 1 } { 2 } \angle O C F
|
HME100K/composed/0504
|
/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 { 3 } { 4 }
A E + B E = A B = 3 0
a _ { 1 } = - 5 ; a _ { 2 } = 1
7 ^ { 2 } = 4 9
|
HME100K/composed/0508
|
/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 . \mu ^ { 3 } n - \mu n ^ { 3 }
\because \frac { P F } { B F } = \frac { C O } { B C }
R = \frac { U } { I }
y = \frac { b } { a } x
|
HME100K/composed/0512
|
/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
|
|
S _ { \Delta A O B } = \frac { 1 } { 2 } \vert O A \vert \cdot \vert O B \vert \cdot \sin \angle A O B = 4 + 2 \sqrt { 3 }
[ 2 k \pi + \frac { \pi } { 6 } , 2 k \pi + \frac { 5 } { 6 } \pi ] . k \in z
2 D E + 2 E C = 7 c m
\frac { 5 } { 9 } + x = \frac { 3 } { 5 }
|
HME100K/composed/0516
|
/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 x + 3 ) ^ { 2 }
x = \frac { 1 } { 5 } \Rightarrow f ( \frac { 1 } { 2 5 } ) = \frac { 1 } { 4 }
\frac { x } { y } + \frac { y } { x } = \frac { \sqrt { 2 } - 1 } { \sqrt { 2 } + 1 } + \frac { \sqrt { 2 } + 1 } { \sqrt { 2 } - 1 } = \frac { ( \sqrt { 2 } - 1 ) ^ { 2 } } { ( \sqrt { 2 } + 1 ) ( \sqrt { 2 } - 1 ) } + \frac { ( \sqrt { 2 } + 1 ) ^ { 2 } } { ( \sqrt { 2 } - 1 ) ( \sqrt { 2 } + 1 ) }
\angle b = 9 0 ^ { \circ }
|
HME100K/composed/0520
|
/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
|
|
p = \frac { w } { t } = \frac { 4 5 0 0 J } { 3 0 s } = 1 5 0 W
9 \div \frac { 3 } { 4 } x = \frac { 1 } { 3 }
\angle O A C = \angle B A O - \angle B
x ^ { 2 } - 2 x + 1 < 0
|
HME100K/composed/0524
|
/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
|
|
a _ { 1 } = \frac { 2 } { 3 } , q = \frac { 3 } { 4 }
( 1 6 0 - 1 3 0 ) x + ( 1 2 0 - 1 0 0 ) ( 1 0 0 - x ) \geq 2 5 8 0 \textcircled { 2 }
B C - \frac { 1 } { 3 } \times d \times \sqrt { 3 } = \frac { 1 \sqrt { 3 } } { 3 } d = \frac { 1 \sqrt { 2 } } { 3 }
1
|
HME100K/composed/0528
|
/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 ^ { 2 } + 4 x + 2 = x
\angle P _ { 1 } A P _ { 2 } = 6 0 ^ { \circ }
\frac { 3 } { 5 } [ \frac { 7 } { 3 } x - 4 ] = \frac { 7 } { 3 } x - 7
\angle B C D = 9 0 ^ { \circ }
|
HME100K/composed/0532
|
/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
|
|
C F + C E = B E + E C
f ^ { \prime } ( x ) = 2 x
\frac { 1 } { x } \times 2 = 3 - \sqrt [ 2 ] { 2 }
O P \bot B C
|
HME100K/composed/0536
|
/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
|
|
a _ { 1 } ^ { 2 } + a _ { 5 } ^ { 2 } = 8
x _ { 1 } = - 4
f ( x ) = a x ^ { 2 } + b x + c
- x ^ { 2 } \geq - 4
|
HME100K/composed/0540
|
/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
|
|
\sin ( \frac { \pi } { 2 } + \beta ) = \frac { 1 } { \sqrt { 3 } }
8 - n = \sqrt { n ^ { 2 } + 1 6 }
y _ { 1 } ^ { 2 } = x _ { 1 }
\angle M A B = 4 5 ^ { \circ }
|
HME100K/composed/0544
|
/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 D A C = \frac { 1 } { 2 } \angle B A C = 4 5 ^ { \circ } .
a = - \frac { 1 } { 3 }
\frac { 7 } { 8 } - x = \frac { 3 } { 4 }
x = - \frac { b } { 2 a } = 6 5
|
HME100K/composed/0548
|
/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 \times 1 . 5 = 4 . 5 ( c m ^ { 2 } )
A B : A C
\frac { 3 } { 1 0 } \times \frac { 3 } { 5 } = \frac { 3 \times 3 } { 1 0 \times 5 } = \frac { 9 } { 5 0 } ( d m
y = 5
|
HME100K/composed/0552
|
/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 B D F + \angle F D G = \angle G D E = \angle F D G
1 0 0 \times 1 0 0 \div 1 0 0 0 = 1 0 ( c m )
l = \frac { \alpha \pi R } { 1 8 0 } = \frac { \alpha \pi \cdot 4 } { 1 8 0 } = 2
2 3 9 - 1 2 1 = 1 1 8
|
HME100K/composed/0556
|
/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
|
|
A B = A C
f ( x ) = \frac { 1 } { t }
( 2 - 0 . 5 ) \times 8 0 + 2 x = 4 1 0 - 2 \times 8 0
2 0 0 \times - 2 0 0 1 2 0 x + 2 4 0 = 6 0
|
HME100K/composed/0560
|
/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
|
|
E F \bot A C
F e + 2 H C l = F e C l _ { 2 } + H _ { 2 } \uparrow
\angle A D C = 9 0 ^ { \circ }
r = \sqrt { 3 ^ { 2 } - 1 ( - 4 ) ^ { 2 } } = 5
|
HME100K/composed/0564
|
/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
|
|
p ( B ) = C ^ { 3 } _ { 4 } - ( \frac { 3 } { 4 } ) ^ { 3 } \cdot \frac { 1 } { 4 } = \frac { 2 7 } { 6 4 }
\angle B C Q = \angle B O A = 9 0 ^ { \circ }
\frac { x - 3 } { 7 } = \frac { y + 6 } { 3 }
a + b = 1 4
|
HME100K/composed/0568
|
/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
|
|
V = \frac { m } { \rho } .
\vert \tan A \vert = \frac { \sqrt { 3 } } { 3 } < \vert \tan B \vert = 1
x < \frac { \sqrt { 3 } - 1 } { \sqrt { 3 } - 2 . }
A B / / D E
|
HME100K/composed/0572
|
/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 { 3 5 . 2 8 N } { 9 . 8 N / k g } \approx 0 . 8 k g
A B / / C D
E B = G D
( 1 3 0 - 9 1 ) \div a \cdots 0
|
HME100K/composed/0576
|
/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
|
|
A B = \frac { 1 } { 2 } A C
\frac { 1 - \sqrt { 5 } } { 2 } < a < 0
C A = C B
\angle A = 5 0 ^ { \circ }
|
HME100K/composed/0580
|
/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
|
|
y = \frac { 2 } { x }
\angle 1 + \angle 2 = 9 0 ^ { \circ }
\alpha + \beta = 1 8 0 ^ { \circ }
C u O + C \xlongequal { \Delta } C u + C O _ { 2 } \uparrow
|
HME100K/composed/0584
|
/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 B C D = 9 0 ^ { \circ }
A C = 5 \sqrt { 3 } k m
2 0 1 5 \times \frac { 1 } { 2 } = 1 0 0 7 . 5
E O = \frac { - x ^ { 2 } + 4 } { 2 - x } \times 2
|
HME100K/composed/0588
|
/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
|
|
t ^ { 2 } + \sqrt { 1 0 } t - 2 0 = 0
x - \frac { 3 } { 8 } = \frac { 2 } { 5 } - x
\textcircled { 2 } - ( - 2 ) + ( \pi - 3 . 1 4 ) ^ { 6 } + \sqrt [ 3 ] { 2 7 } + ( - \frac { 1 } { 3 } ) ^ { - 2 }
\frac { T } { 4 } = \frac { 2 \pi } { 9 } - \frac { 3 } { 1 3 }
|
HME100K/composed/0592
|
/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
|
|
4 x + 2 [ x ] + 5 = 0
C _ { n } ^ { 3 } = C _ { n } ^ { 7 } \Rightarrow n = 1 0
e = \frac { c } { a } = \sqrt { 1 + \frac { b ^ { 2 } } { a ^ { 2 } } } = \frac { \sqrt { 2 2 } } { 3 }
\Delta A C P \cong \Delta B C Q
|
HME100K/composed/0596
|
/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 A O C = \frac { C H } { O C } = \frac { 2 } { 5 } \sqrt { 5 . }
\frac { 1 } { x } - \frac { 1 } { x + 2 } + \frac { 1 } { x + 1 } - \frac { 1 } { x + 3 } + \frac { 1 } { x + 2 } - \frac { 1 } { x + 4 } \dot { s } - \frac { 1 } { x + 9 } + \frac { 1 } { x + 8 } - \frac { 1 } { x + 1 0 } = 0
\frac { 1 8 } { 2 7 } + \frac { 8 } { 5 } + \frac { 1 8 } { 2 7 } \times \frac { 3 } { 8 }
) f ( x ) = \cos ^ { 2 } x = \frac { 1 + \cos 2 x } { 2 }
|
HME100K/composed/0600
|
/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 { 1 } { a + 2 } = u \frac { 1 } { b - 1 } = V
A A ^ { \prime } \bot O M . A ^ { \prime } K = A K .
\frac { 5 } { 6 } + \frac { 2 } { 7 } + \frac { 1 } { 6 }
x = \frac { - 2 \pm \sqrt { 4 - 3 a } } { 3 a }
|
HME100K/composed/0604
|
/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 O A D = 4 0 ^ { \circ }
\frac { 3 } { 5 } [ 2 \frac { 1 } { 3 } x - 4 ] = \frac { 7 } { 3 } x - 7
b _ { n + 1 } - b _ { n } = 2 ( s _ { n } - s _ { n - 1 } ) \Rightarrow b _ { n + 1 } = 3 b _ { n }
a n \alpha \geq 2 \tan 2 \beta = \frac { 2 \tan \beta } { 1 - \tan ^ { 2 } \beta } > 0
|
HME100K/composed/0608
|
/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
|
|
1 2 0 \div 8 = 1 5 ( m / \min )
a _ { n + 1 } = \frac { a _ { n } \cdot 3 ^ { n } - 2 } { 3 ^ { n + 1 } }
A = \{ x \vert 0 < x < 2 \}
7 k g 2 0 g = ( 7 . 2 0 ) k g
|
HME100K/composed/0612
|
/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 { 9 } { x }
L H S = \frac { 1 } { 2 } - \frac { 5 } { 2 } = - \frac { 4 } { 2 } = - 2
B ( 1 , + \infty )
x = \frac { a \pm \sqrt { a ^ { 2 } + 8 0 } } { 2 a }
|
HME100K/composed/0616
|
/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
|
|
R t \Delta A D E \sim R t \Delta A ^ { \prime } D ^ { \prime } E ^ { \prime }
\tan \angle C M N = \frac { C H } { M H } = \frac { \frac { 3 } { 2 } } { \frac { 3 } { 4 } } = 2
f ( x ) = \frac { 1 } { 2 } a \cos x ( \cos x + \sqrt { 3 } \sin x ) + 1
\sqrt [ 3 ] { 4 + \frac { 4 } { 6 3 } } = 4 \sqrt [ 3 ] { \frac { 4 } { 6 3 } }
|
HME100K/composed/0620
|
/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 x ^ { 2 } y - 8 x ^ { 3 } y ^ { 6 } + 8 x ^ { 3 } y ^ { 3 } + ( x ^ { 2 } y ^ { 4 }
\frac { F Q } { C Q } - \frac { D Q } { E Q } = 1
M N ^ { 2 } = A M ^ { 2 } +
O A = \frac { 1 } { 2 } A C = 3
|
HME100K/composed/0624
|
/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 D F = \angle B C G
l : - \frac { 3 } { 4 } \times - y = 0 \rightarrow 3 x + 4 y =
R t \Delta A B C
a + b > 0
|
HME100K/composed/0628
|
/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
|
|
N H _ { 4 } C l \xrightarrow { \Delta } N H _ { 3 } \uparrow + H C l \uparrow
\angle A B D = 3 0 ^ { \circ }
1 2 \div 4 = 3 ( d m )
\angle B D C = 4 5 ^ { \circ } .
|
HME100K/composed/0632
|
/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
|
|
y _ { 0 } \leq 2 - \sqrt { 2 }
( x - y ) ^ { 2 }
\sin 3 2 0 ^ { \circ } < 0 , \cos 3 8 5 ^ { \circ } > 0 \tan 1 5 5 ^ { \circ } > 0
A C = \frac { 1 0 0 \sin 3 3 ^ { \circ } } { \sin 6 7 ^ { \circ } } \approx 5 9 .
|
HME100K/composed/0636
|
/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
|
|
D F \cap B E = B
\angle C = 9 0 ^ { \circ }
\angle C A B =
( x + 1 ) ^ { 2 } + ( y - 2 ) ^ { 2 } + 2 \geq 2
|
HME100K/composed/0640
|
/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 { 1 } { 4 } + - \frac { 3 } { 8 } = \frac { 2 } { 8 } + \frac { 4 } { 8 } \neq \frac { 5 } { 8 }
C a C O _ { 3 } + 2 H C l = C a C l _ { 2 } + H _ { 2 } O + C O _ { 2 } A
\tan \angle G C D = \frac { B D } { C D } = \frac { 3 0 m } { 3 0 m } = 1
A \{ x \vert 3 \leq x \leq 6 \}
|
HME100K/composed/0644
|
/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 2 = 6 0 ^ { \circ }
\varphi ( x ) = \frac { 1 } { x } - \frac { 1 } { x ^ { 2 } } = \frac { x - 1 } { x ^ { 2 } }
\angle D O E = \angle O E B = 7 5 ^ { \circ }
3 6 . 0 7 0 = 3 6 . 0 7 1 0 8 . 8 0 0 = 1 0 8 . 8 1 0 . 0 = 1 0
|
HME100K/composed/0648
|
/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 \tan ^ { 2 } \alpha + 4 \tan \alpha = 4 ( \tan ^ { 2 } \alpha + 1 )
D ( \frac { 5 } { 2 } , - \frac { 9 } { 8 } )
A K = A D - K D = 4 - \sqrt { 2 } - x
\widehat { B D } = 2 \widehat { B C }
|
HME100K/composed/0652
|
/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
|
|
g ( 2 ) > g ( e ) > g ( 3 )
x - \frac { 5 } { 1 2 } = \frac { 1 } { 3 }
1 4 . 2 8 \div 3 . 5 \div 2
x _ { 1 } x _ { 2 } = - k ^ { 2 } + 2 > 0
|
HME100K/composed/0656
|
/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
|
|
6 4 \times 1 2 \div 2 = 3 8 4 ( c m ^ { 2 } )
( 5 \div 2 ) ^ { 2 } \times 3 . 1 4 = 1 9 . 6 2 5 ( m ^ { 2 } )
y = k x + b
A D / / B C , A B / / D C
|
HME100K/composed/0660
|
/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
|
|
g ( a ) = 1 n a + 1
x _ { 2 } \in [ 0 , 1 ]
( n - 4 ) ( n - 7 ) = 0
1 3 - 8 = 1 0 - 8 + \square = \square
|
HME100K/composed/0664
|
/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 ^ { 2 } - 1 0 x > 0
y = k x - \frac { 1 } { 3 }
x _ { 1 } = 0 , x _ { 2 } = - 2 , x _ { 3 } = 5
B O = \frac { 5 } { 4 } ( 2 - \frac { 1 } { 2 } t ) = \frac { 5 } { 2 } - \frac { 5 } { 8 } t
|
HME100K/composed/0668
|
/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
|
|
f ( x ) = a x ^ { 3 } - 3 x ^ { 2 } + 1
\angle D A C = \frac { 1 } { 2 } \angle B A C
f ( f ( x ) ) = x ^ { 4 } + 1 + 2 x ^ { 2 } + 1 = x ^ { 4 } + 2 x ^ { 2 } + 2
1 \frac { a + b } { a b } - \frac { b + c } { b c }
|
HME100K/composed/0672
|
/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
|
|
\sqrt { 3 } = a \times 3 \times 1
\frac { a + 1 } { a ^ { 2 } + 2 a + 1 } \div ( 1 + \frac { 2 } { a - 1 } )
D E + E C = D C = 3 . 5 c m
8 2 \div 5 \approx 2 0
|
HME100K/composed/0676
|
/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
|
|
f ( x ) = 4 x ^ { 3 } - 6 x ^ { 2 } + 2 x
\angle A O B = 1 8 0 ^ { \circ } - ( \angle A B O + \angle B A O ) = 1 8 0 ^ { \circ } - 3 0 ^ { \circ } = 1 5 0 ^ { \circ }
A E = B G = B F
a ^ { 2 } - 2 a - 1 5 = 0
|
HME100K/composed/0680
|
/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
|
|
8 . 6 2 \times 1 0 ^ { 4 } 8 . 6 1 6 4 0 9 \times 1 0 ^ { 4 }
C \frac { 1 2 1 } { 2 7 } < x \leq 3 6
a _ { 1 } q ^ { 4 } - a _ { 1 } q ^ { 7 } = 6
P _ { \max } = \frac { F _ { \max } + S _ { \max } } { \sin x } = \frac { ( 3 p v + n ) g } { s }
|
HME100K/composed/0684
|
/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
|
|
\vert X _ { 1 } - X _ { 2 } \vert = \frac { \sqrt { 9 + 4 0 } } { 2 } = \frac { 7 } { 2 }
2 7 + 9 b + 3 b - 3 = 0
( 1 + 4 k ^ { 2 } ) x ^ { 2 } + 8 k m x + 4 m ^ { 2 } - 4 = 0
E F / / C D
|
HME100K/composed/0688
|
/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
|
|
m = p v = 1 . 0 \times 1 0 ^ { 3 } k g / m ^ { 3 } \times 1 0 ^ { - 3 } m ^ { 3 } = 1 k g
x + 3 y = 1 - a
\times 0 . 1 4
= \frac { 1 } { 2 } \times 5 D K = 2 . 5 D K
|
HME100K/composed/0692
|
/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 F } { A C } = \frac { 2 } { 3 } \times \frac { A F } { A C }
H D = \frac { ( 3 - x ) \sqrt { 3 } } { 2 }
\frac { \cos a - \sin a } { \cos a + \sin a } = \frac { 1 - \tan a } { 1 + \tan a }
B \neq \phi
|
HME100K/composed/0696
|
/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
|
|
\because x ^ { 2 } + 4 y ^ { 2 } - 4 x + 4 y + 5 = 0
\angle A E B = 1 8 0 ^ { \circ } - 4 5 ^ { \circ } = 1 3 5 ^ { \circ }
m ^ { 2 } + 4 = 5
\frac { A D ^ { 2 } + C D ^ { 2 } - A C ^ { 2 } } { 2 A D \cdot C D } \approx 0 .
|
HME100K/composed/0700
|
/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 F C A = 4 5 ^ { \circ }
a = \frac { 1 } { 2 }
y = \sqrt { 3 } ( x - 1 ) - 5
P = \frac { w } { t }
|
HME100K/composed/0704
|
/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 - 1 ) - 1 \frac { 9 } { x - 1 } + 1 0 \geq 2 \times 3 + 1 0 = 1 6
\angle B = 9 0 ^ { \circ }
\angle B = \angle C = 6 0 ^ { \circ }
T ^ { 2 } = 4 \pi ^ { 2 } \frac { L } { 9 }
|
HME100K/composed/0708
|
/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 B F C = 9 0 ^ { \circ }
2 y - x = - 3
M N = \frac { 1 } { 2 } B C
\frac { C H } { A H } = \frac { 1 } { \sqrt { 3 } } . \tan 3 0 ^ { \circ } = \frac { 1 } { \sqrt { 3 } }
|
HME100K/composed/0712
|
/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 A G H = 1 8 0 ^ { \circ } - 9 0 ^ { \circ } - \frac { 1 } { 2 } \angle E A C
\angle A C B = 9 0 ^ { \circ } .
P _ { B } = P _ { 0 }
W ( H _ { 2 } S O 4 ) = \frac { 4 . 9 } { 2 5 } \times 1 0 0 \%
|
HME100K/composed/0716
|
/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 \leq n < \frac { 8 } { 3 }
\angle B O D = \frac { 1 } { 2 } \angle A O B = 7 0 ^ { \circ }
P F = \frac { 3 } { 5 } P M
= - 1 2 k ^ { 2 } + 4
|
HME100K/composed/0720
|
/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
|
|
\cdot \frac { 1 } { 2 } P H \cdot O C = \frac { 1 } { 2 } \cdot A P \cdot O P
x ^ { 2 } + 4 x + 2
R _ { 2 } = \frac { U _ { 2 } } { I _ { 2 } } = \frac { 3 V } { 0 . 6 a } = 5 \Omega
\frac { 4 a c - b ^ { 2 } } { 4 a } = \frac { - 1 2 - 4 } { 4 } = - 4
|
HME100K/composed/0724
|
/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 { x + 2 } { ( x - 2 ) ( x + 3 ) ^ { 2 } } - \frac { 5 ( x - 2 ) } { ( x + 3 ) ^ { 2 } ( x - 2 ) } = \frac { ( x + 2 ) - 5 x + 1 0 } { ( x - 2 ) ( x + 3 ) ^ { 2 } } = \frac { 1 2 - 4 x } { ( x - 2 ) ( x + 1 ) } = \frac { 4 ( 3 - x ) } { ( x - 2 ) ( x + 2 ) } = - \frac { 4 } { ( x - 2 ) ( x + 2 ) }
3 x - 3 + x + 3 + 2 \sqrt { 3 ( x - 1 ) ( x + 3 ) } = 2
\angle A O B = 3 6 0 ^ { \circ } - 1 2 0 ^ { \circ } - 1 0 8 ^ { \circ } = 1 3 2 ^ { \circ }
\angle E A D = 6 0 ^ { \circ }
|
HME100K/composed/0728
|
/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
|
|
y = \sqrt { x - 1 } + \frac { 1 } { x - 2 }
1 2 0 m L = 1 2 0 c m ^ { 3 }
a - b < c
\angle D = 1 8 0 ^ { \circ } - \angle 2 - \angle 5 - \angle 3
|
HME100K/composed/0732
|
/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 D = D C \cdot \tan 6 0 ^ { \circ } = 8 \times \sqrt { 3 } = 8 \sqrt { 3 }
3 4 0 \div 1 7 = 2 0
\frac { 7 } { 8 } - \frac { 3 } { 8 } = \frac { 4 } { 8 }
1 0 0 0 0 \times \frac { 1 } { 5 0 0 0 } = 2 ( c m )
|
HME100K/composed/0736
|
/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
|
|
\vert P Q \vert = 2 a \sqrt { k ^ { 2 } + 1 } \vert P G \vert = \frac { 2 a k \sqrt { k ^ { 2 } - 1 } } { 2 + k ^ { 2 } }
1 2 5 \times 4 8
\sin 3 0 ^ { \circ } = \frac { B C } { A B } = \frac { 1 } { 2 }
t ^ { 2 } = ( x - \frac { 1 } { x } ) ^ { 2 } = x ^ { 2 } + \frac { 1 } { x ^ { 2 } } - 2
|
HME100K/composed/0740
|
/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 = 1
\angle C O D = 6 0 ^ { \circ }
\Delta A B M \cong \Delta A D F ( S A S )
5 0 \times 5 0 = 2 5 0 0 ( m ^ { 2 } )
|
HME100K/composed/0744
|
/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
|
|
1 . 0 2 m ^ { 3 } = 1 0 2 0 d m ^ { 3 }
x ^ { 2 } - 1 \geq 0
N a _ { 3 } C O _ { 3 } + 2 H C l = 2 N a C O + H _ { 2 } O + C O _ { 2 }
N a _ { 2 } S O _ { 4 } + B a C l _ { 2 } = B a S O _ { 4 } \downarrow + 2 N a C l
|
HME100K/composed/0748
|
/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
|
|
4 \times \frac { 5 } { 7 }
P E / / A B
\angle A B D = \angle B C G
y = k x + b ( k \neq 0 )
|
HME100K/composed/0752
|
/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 { 8 \times 1 1 + 1 2 \times 1 2 } { 2 0 } = 1 1 . 6
\therefore A G = G C , \angle 3 = \angle 4
9 ( \frac { 1 } { 2 } ) = 2 \ln \frac { 1 } { 2 } + 2 - a = 2 - 2 \ln 2 -
1 0 5 6 + 3 2
|
HME100K/composed/0756
|
/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 { 4 } { 3 } + b =
4 8 \div 2 = 2 4 ( c m ^ { 2 } )
\vert m + m - 1 3 \vert = 1
3 . 1 4 \times 7 = 2 1 . 9 8 c m ^ { 3 }
|
HME100K/composed/0760
|
/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
|
|
5 0 \times 5 0 - 2 1 1 6 = 3 8 4 ( m ^ { 2 } )
\frac { \pi } { 6 } \leq \frac { x } { 2 } + \frac { \pi } { 6 } \leq \frac { 2 5 } { 6 } \pi
\frac { 1 } { 3 } : \frac { 1 } { 9 } = \frac { 1 } { 2 } : \frac { 1 } { 6 }
B E = 1 3 x - 1
|
HME100K/composed/0764
|
/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
|
|
( \sqrt { 3 } ) ^ { 2 } - \sqrt { 1 6 } - \sqrt [ 3 ] { - 8 }
1 4 \times 2 . 5 ^ { 2 } = 1 9 . 6 2 5 ( d m ^ { 2 } )
\Delta = 6 ^ { 2 } - 4 a c = 3 2 4 - 7 2 0 < 0
\angle B O C + \angle 2 + \angle 3 = 1 8 0 ^ { \circ }
|
HME100K/composed/0768
|
/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
|
|
E P = 2 t , E Q = 6
x + \frac { 3 } { 7 } = \frac { 3 } { 4 }
I _ { \min } = \frac { U } { R _ { \max } } = \frac { 1 5 V } { 1 0 \Omega + 5 0 \Omega } = 0 . 2 5 A
2 x - y = - 3
|
HME100K/composed/0772
|
/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 1 + \angle 2 = 1 8 0 ^ { \circ }
\frac { \tan a + \tan B } { 1 - \tan a + \tan \beta } = - 1
v = \frac { s } { t }
P = \frac { 3 } { 6 } = \frac { 1 } { 2 }
|
HME100K/composed/0776
|
/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
|
|
1 y = - 1
x \vert - \sqrt { x ^ { 2 } - 8 x + 1 6 }
6 2 . 8 \times 2 = 1 2 5 . 6 ( m ^ { 2 } )
\alpha + \beta \in ( \pi , \frac { 3 } { 2 } \pi )
|
HME100K/composed/0780
|
/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 、 2 \angle M A C _ { 1 } + 2 \angle B A C _ { 1 } = 1 8 0 ^ { \circ }
- \frac { b } { 2 a } = \frac { b - 1 } { 2 } \leq - 2
y = x ^ { 2 } + 2 a x + 1 = ( x + a ) ^ { 2 } + 1 - a ^ { 2 } .
T _ { 1 } + T _ { 2 } + F _ { 3 } = ( T _ { 4 } - 1 ) g ( 4 )
|
HME100K/composed/0784
|
/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
|
|
a = 2
\angle B A C = 6 0 ^ { \circ }
\angle D C B = 9 0 ^ { \circ }
2 7 k + 2 = 9 \times 3 = 2 7
|
HME100K/composed/0788
|
/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 { 1 } { 2 } + \frac { 1 } { y } + \frac { 1 } { x } + \frac { 1 } { z } - \frac { 1 } { y } - \frac { 1 } { z } = \frac { 1 } { 6 } + \frac { 2 } { 1 5 } - \frac { 1 } { 1 0 }
\frac { I _ { 2 } } { I } = \frac { I _ { 2 } } { I _ { p } + I _ { 2 } } = \frac { 0 . 4 A } { 3 A + 0 . 4 A } = \frac { 2 } { 1 7 }
\textcircled { 2 } \frac { 7 } { 3 } = 7 \div 3 = 2 \frac { 7 } { 3 }
C _ { 2 } : y = - x ^ { 2 } + 2 x + 3
|
HME100K/composed/0792
|
/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 { 4 } { 3 } x - 6 \geq \frac { 6 - 5 x } { 3 }
\angle A = \angle A ^ { \prime } \frac { A B } { A ^ { \prime } B ^ { \prime } } = \frac { A C } { A ^ { \prime } C ^ { \prime } }
A E = C E = \frac { 1 } { 2 } A C = 2 \sqrt { 5 }
\therefore S _ { \Delta } B C D = \frac { 1 } { 2 } \times B C \times B D = \frac { \sqrt { 3 } } { 2 }
|
HME100K/composed/0796
|
/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
|
|
C D \bot A B \angle A C B = 9 0 ^ { \circ } \angle C A B = \angle C A D
( a + 1 ) x - 3 x = - 4 - 2 b
P H = \frac { 1 } { 2 } \theta H = \frac { 8 } { 5 }
4 0 x + 5 \times 1 . 2 = 2 5
|
HME100K/composed/0800
|
/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
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.