formula stringlengths 5 635 | image stringlengths 80 86 |
|---|---|
s \in [ c , d ] , f \in G _ { L } ( a , b ) | 4365dfef-f33d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_8.jpg |
6 x ^ { 2 } - 1 5 y - 8 z ^ { 3 } - [ 4 x ^ { 2 } - 5 y - ( 3 x ^ { 2 } - 1 2 y ) - ( 9 x ^ { 2 } | 43d27156-2259-11ea-8d84-001b63bd97ba__mathematical-expression-and-equation_10.jpg |
3 \prime \prime - 4 \prime \prime - 8 \prime \prime | 43d2e864-0d7f-11e3-3085-001143e3f55c__mathematical-expression-and-equation_1.jpg |
t _ { 0 } \in \mathbb { R } ^ { 1 } , x _ { 0 } \in \bar { C } ^ { n } | 4419c6d9-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_9.jpg |
\delta _ { v } \approx \frac { d _ { v - 1 } d _ { v } } { d _ { v - 1 } - d _ { v } } | 44282a85-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_0.jpg |
p = \max ( p _ { 1 } , p _ { 2 } ) | 44282a92-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_8.jpg |
= R _ { \xi } ( o ) - \int _ { - \infty } ^ { \infty } \int _ { - \infty } ^ { \infty } \int _ { - \infty } ^ { \infty } \int _ { - \infty } ^ { \infty } \tilde { h } ( r _ { 1 } ) \tilde { h } ( r _ { 2 } ) R _ { v } ( r _ { 2 } - r _ { 1 } ) d r _ { 2 1 } d r _ { 2 2 } d r _ { 1 1 } d r _ { 1 2 } + | 443c0847-46a6-451c-849e-103d0d5699db__mathematical-expression-and-equation_7.jpg |
\sum _ { j = 1 } ^ { p } a _ { 2 q + 1 , j } \epsilon _ { 2 q + 1 , j } = \sum _ { r = 1 } ^ { m } ( 2 q p + r ) - \sum _ { r = m + 1 } ^ { 3 m - 2 } ( 2 q p + r ) + | 44e14029-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg |
T = \sum _ { n = 1 } ^ { \infty } \mu _ { n } e _ { n } \otimes e _ { n + 1 } , | 463fda98-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_1.jpg |
V ( \sigma ( \gamma ) , \gamma ) \le V ( \sigma ( \alpha ) , \alpha ) - \int _ { \alpha } ^ { \gamma } c ( g ( s ( \theta ) , \theta ) ) d \theta < b ( \Omega ) - c ( \psi ( \zeta ) ) . T ( \zeta ) = 0 , | 46490e9d-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg |
\int _ { 0 } ^ { T } V _ { 1 } \prime \prime V _ { 2 } \prime d t = \int _ { 0 } ^ { T } [ B _ { 1 } x _ { 1 } e ^ { x _ { 1 } t } + B _ { 2 } x _ { 2 } e ^ { x _ { 2 } t } + B _ { 3 } x _ { 3 } e ^ { x _ { 3 } t } + B _ { 4 } x _ { 4 } e ^ { x _ { 4 } t } ] | 46c92b15-d87a-4019-a4c6-6eff9f86d2a5__mathematical-expression-and-equation_9.jpg |
3 : 1 , 4 , 9 | 46fe53bd-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_7.jpg |
\int _ { X } a \cdot \theta _ { i } d \mu \le \int _ { X } f \theta _ { i } d \mu \le \int _ { X } b \theta _ { i } d \mu | 4702b5bd-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_1.jpg |
v = 2 . 4 2 5 \sqrt { R } \cdot \sqrt { J } | 4755dd20-7822-11e7-ad78-001b63bd97ba__mathematical-expression-and-equation_3.jpg |
E ^ { 3 } = \frac { F ^ { 2 } . v ^ { 2 } } { g . b ^ { 2 } } = \frac { b ^ { 2 } . a ^ { 2 } . k ^ { 2 } . R . J } { g . b ^ { 2 } } \doteq \frac { a ^ { 3 } . k ^ { 2 } . J } { g } | 47573cf6-7822-11e7-ad78-001b63bd97ba__mathematical-expression-and-equation_3.jpg |
\kappa _ { 1 } ^ { 4 } = 0 | 47ac1fe2-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_13.jpg |
\omega _ { 2 } ^ { 3 } = \omega ^ { 1 } | 47ac200e-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_6.jpg |
Q ( t , s ) = \{ \begin{array} { c } P ( t , s + ) \\ P ( t , 1 - ) \end{array} | 47babb91-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_0.jpg |
\bar { \alpha } _ { i } = \alpha _ { i } - \alpha _ { i } \prime o n \bar { \Omega } | 485928c7-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_7.jpg |
\ge ( ( p ^ { * } - p ) \sigma - \epsilon ) \zeta ^ { n } - \alpha C _ { \epsilon } \parallel h \parallel _ { Q } ^ { \frac { p } { ( p - q ) } } ) | 4877a2ca-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_4.jpg |
p = \frac { 1 } { 2 } ( p _ { 1 } + p _ { 2 } ) , | 48b5c7f0-7a07-11e4-964c-5ef3fc9bb22f__mathematical-expression-and-equation_7.jpg |
^ { i } \tilde { \tilde { F } } ( ^ { i } \mathbf { H } _ { k } ^ { 2 } \mathbf { m } ) - ^ { i } \tilde { \tilde { F } } ( ^ { i } \mathbf { H } _ { k } ^ { 1 } \mathbf { m } ) = ^ { i } D _ { F } ( ^ { i } \mathbf { H } _ { k } ( ^ { 2 } \mathbf { m } - ^ { 1 } \mathbf { m } ) ) + ^ { i } \mathbf { H } _ { k + 1 } ^ ... | 48c39b56-ec17-4d6a-99de-183f33ccf745__mathematical-expression-and-equation_7.jpg |
[ a b ] + [ b b ] + [ b c ] + [ b l ] + [ b s ] = 0 | 49658cc0-63b1-11e3-bc9f-5ef3fc9bb22f__mathematical-expression-and-equation_24.jpg |
N ^ { – } : N \prime = \emptyset ; I = \emptyset : \emptyset \prime | 49740763-518b-11e1-1431-001143e3f55c__mathematical-expression-and-equation_9.jpg |
| u ^ { ( k - i ) } ( t ) | \ge | u ^ { ( k - i ) } ( 2 ^ { - m + k + 1 } t ) | \ge | 49b13f1b-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_7.jpg |
B _ { 1 } ( t , s ) = U ( t ) S _ { 1 } V ( s ) | 49b14011-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_12.jpg |
\frac { \Delta h } { h } 1 5 - 2 0 \% . | 4ad810bc-8368-47e5-8924-fe1f293d04c5__mathematical-expression-and-equation_2.jpg |
\dot { V } = - \lambda z ^ { T } Q Q ^ { T } z | 4b40f63b-3552-4c56-88b1-f34be64f7b66__mathematical-expression-and-equation_1.jpg |
\mathbf { v } _ { r } = \frac { d \mathbf { r } } { d t } = \{ \frac { \partial H } { \partial n } \} _ { n } = \{ \frac { \partial H } { \partial n _ { L } } i _ { L } + \frac { \partial H } { \partial n _ { T } } i _ { T } \} _ { n } | 4be82dec-10ac-4828-800d-8657e12177e6__mathematical-expression-and-equation_0.jpg |
p = - 2 , q = 3 , a = \sqrt { 1 6 } = 4 . | 4cd27b34-2dac-11ec-b355-001b63bd97ba__mathematical-expression-and-equation_5.jpg |
3 : 1 , 5 , 6 | 4d29621d-b740-4bbd-acba-2c2483f2fb13__mathematical-expression-and-equation_8.jpg |
\frac { a } { b } = \frac { a : m } { b : m } | 4df205e5-22be-11ec-b1c8-001b63bd97ba__mathematical-expression-and-equation_9.jpg |
\frac { a } { e } : \frac { b } { f } = \frac { c } { g } : \frac { d } { h } | 4df49d17-22be-11ec-b1c8-001b63bd97ba__mathematical-expression-and-equation_6.jpg |
\psi ( \mathbf { p } ) = \sum _ { i = 0 } ^ { 2 } \tilde { F } _ { 1 } ( 7 0 + i . 2 , 5 , \mathbf { p } ) | 4e597959-3220-4964-8fb3-21145812301b__mathematical-expression-and-equation_0.jpg |
P = 2 \pi r v + \pi ( \rho _ { 1 } ^ { 2 } + \rho _ { 2 } ^ { 2 } ) | 4e8045a4-c073-11e6-ae7e-001b63bd97ba__mathematical-expression-and-equation_9.jpg |
+ 2 . 5 8 ( c \times 0 . 7 0 4 9 P _ { 1 } + 0 . 0 2 7 8 t ) | 51a2c05c-dbdb-11e6-95e2-001b63bd97ba__mathematical-expression-and-equation_15.jpg |
\frac { d y } { d x } = \frac { \frac { d y } { d t } } { \frac { d x } { d t } } | 51cc8c9c-0920-455c-b379-9e9d3bf33562__mathematical-expression-and-equation_0.jpg |
A E _ { i ( r - 1 ) } = \frac { \partial \psi } { \partial x _ { i ( r - 1 ) } } = \sum _ { j = 1 } ^ { q } \frac { \partial \psi } { \partial x _ { j } } \frac { \partial x _ { j } } { \partial x _ { i ( r - 1 ) } } = - \sum _ { j = 1 } ^ { q } ( t _ { j } - x _ { j } ) ( 1 - x _ { j } ) x _ { j } w _ { i j r } | 51fccaaf-0894-43a1-84a0-d6f73fdbcbb8__mathematical-expression-and-equation_1.jpg |
+ A g C l + C _ { 2 } H _ { 5 } O H | 52b3b470-029d-11e8-816d-5ef3fc9bb22f__mathematical-expression-and-equation_3.jpg |
B D = \frac { n \cdot p \cdot \alpha } { n \cdot \alpha } = p | 52b4c371-59b9-11e8-b45f-001999480be2__mathematical-expression-and-equation_0.jpg |
0 . 3 9 - 0 . 3 6 = 0 . 0 3 | 52b4c382-59b9-11e8-b45f-001999480be2__mathematical-expression-and-equation_4.jpg |
x _ { m } - x _ { 1 } = m ( x _ { 2 } - x _ { 1 } ) | 5306a860-5d9e-11e6-95c7-005056825209__mathematical-expression-and-equation_12.jpg |
V _ { 3 } = \frac { M v _ { 3 } } { 1 0 0 } | 537cb2e1-0d86-11e8-8ee8-001b63bd97ba__mathematical-expression-and-equation_2.jpg |
\rho _ { 2 } = \frac { 1 } { R _ { 2 } } | 5519c6eb-4495-46f4-899a-194987f37dfd__mathematical-expression-and-equation_5.jpg |
\Gamma ( E ^ { * } ) = \frac { \overline { E } ^ { 2 } e ^ { - ( \nu - a ) t ^ { * } } } { \nu - a } + \frac { E ^ { * 2 } e ^ { - ( \nu + a ) t ^ { * } } } { \nu + a } - \frac { 2 E ^ { * } \overline { E } e ^ { - \nu t ^ { * } } } { \nu } | 557698ed-951e-418a-88b9-b68ac53e4f75__mathematical-expression-and-equation_1.jpg |
X _ { 1 } - X _ { 3 } + X _ { 4 } - X _ { 5 } = 0 | 5645f11c-0550-dc24-6ddf-d737caee0a95__mathematical-expression-and-equation_14.jpg |
\log \mathrm { n a t } p = - \frac { l } { R T } + \mathrm { k o n s t } . | 57ad34e0-d035-11e3-93a3-005056825209__mathematical-expression-and-equation_0.jpg |
C _ { 6 } H _ { 5 } . J O = C _ { 6 } H _ { 5 } . J O _ { 2 } + A g . O H = A g J O _ { 3 } + ( C _ { 6 } H _ { 5 } ) _ { 2 } . J . | 580b3d9f-7eca-4017-8426-acfca32fa4d7__mathematical-expression-and-equation_5.jpg |
\omega _ { i } ^ { n + 1 } \equiv a _ { i j } \omega ^ { j } ( a _ { i j } = a _ { j i } ) | 589e53df-5882-4ff6-a404-3a8a047f3ea6__mathematical-expression-and-equation_8.jpg |
N = 6 6 4 \cdot 4 9 7 | 591f1179-3fb9-463b-9fff-bc9bc41a56ae__mathematical-expression-and-equation_2.jpg |
p O = p \frac { m } { \rho } = R T | 59286dc0-d036-11e3-93a3-005056825209__mathematical-expression-and-equation_2.jpg |
c = V _ { K } ^ { - 1 } | 5951c8aa-7cbf-4cd9-a6c5-55b264331208__mathematical-expression-and-equation_3.jpg |
2 w - 2 k - \delta - ( n - 2 k - k _ { 1 } + 4 ) \le n + k _ { 1 } - \delta - 4 | 59f0c3e9-4299-41ac-9a8b-229c7f13898d__mathematical-expression-and-equation_2.jpg |
\beta \prime = \frac { s \prime } { E \prime U \prime \prime } , \beta \prime \prime = \frac { s \prime \prime } { E \prime \prime U \prime \prime } , \beta \prime \prime \prime = \frac { s \prime \prime \prime } { E \prime \prime \prime U \prime \prime \prime } | 59f189b2-c1f2-11eb-a5d1-001b63bd97ba__mathematical-expression-and-equation_3.jpg |
u ^ { \prime 2 } + ( \frac { u ^ { 4 } + a ^ { 4 } } { 2 u ^ { 3 } } ) u \prime + \frac { a ^ { 4 } } { u ^ { 2 } } = 0 , | 5a790a90-c04f-11e6-86b1-001b63bd97ba__mathematical-expression-and-equation_1.jpg |
| \begin{array} { c c c } u _ { n } & ( \frac { 1 + \sqrt { 5 } } { 2 } ) ^ { n } & ( \frac { 1 - \sqrt { 5 } } { 2 } ) ^ { n } \\ 1 & \frac { 1 + \sqrt { 5 } } { 2 } & \frac { 1 - \sqrt { 5 } } { 2 } \\ 2 & \frac { 3 + \sqrt { 5 } } { 2 } & \frac { 3 - \sqrt { 5 } } { 2 } \end{array} | = 0 | 5b15b3f5-ae40-49f0-91d1-5202d28fe8b6__mathematical-expression-and-equation_1.jpg |
\frac { \partial i ( x , t ) } { \partial x } = \frac { \partial u ( x , t ) } { \partial t } \cdot c ( x ) | 5b5abc12-4d9e-11e1-1431-001143e3f55c__mathematical-expression-and-equation_1.jpg |
x = 2 ^ { 2 } . x _ { 1 } = 1 6 , | 5ba79b28-082e-9ae9-fb73-664362ed3bd7__mathematical-expression-and-equation_6.jpg |
m _ { C } = m C E F Q _ { m } | 5db57c64-ba20-11e1-1211-001143e3f55c__mathematical-expression-and-equation_9.jpg |
\cos ^ { 2 } \beta = \frac { \overline { N _ { 1 } N ^ { 2 } } } { R _ { 1 } ^ { 2 } } = \frac { d ^ { 2 } \sin ^ { 2 } \omega } { a ^ { 2 } - d ^ { 2 } } | 5de55ec5-435f-11dd-b505-00145e5790ea__mathematical-expression-and-equation_3.jpg |
\Sigma \mathbf { y } = \mathbf { n } \cdot \mathbf { a } + \mathbf { b } \Sigma \mathbf { x } | 5e56035c-8817-11e7-b67d-005056a54372__mathematical-expression-and-equation_0.jpg |
\frac { 2 } { \alpha _ { 1 } + \alpha _ { 2 } } \lim p ^ { \alpha _ { 6 } + \alpha _ { 3 } } | 5e5696c8-435f-11dd-b505-00145e5790ea__mathematical-expression-and-equation_1.jpg |
x ^ { 2 } + y ^ { 2 } = \text { k o n s t . } | 5e7ae85c-435f-11dd-b505-00145e5790ea__mathematical-expression-and-equation_5.jpg |
H _ { r } = - \frac { M _ { r } } { h } = - \frac { p l ^ { 2 } } { 8 v } \cdot \frac { I } { \cos \tau } | 5ea2b4a1-dbba-11e6-8be1-001b63bd97ba__mathematical-expression-and-equation_2.jpg |
n = \frac { \sin i } { \sin r } | 5f50e720-695e-11e8-943b-5ef3fc9ae867__mathematical-expression-and-equation_0.jpg |
= \frac { 1 } { 2 } \int _ { V } E _ { i j k l } [ \epsilon _ { i j } \epsilon _ { k l } + ( \epsilon _ { k l } + \eta _ { k l } ) \eta _ { i j } + \epsilon _ { i j } \eta _ { k l } ] d V = | 5fbe9849-e504-4a7d-a78b-28e44a4421c0__mathematical-expression-and-equation_10.jpg |
\log ( - 1 0 ^ { 7 } \cdot \chi _ { a } ) = 2 . 2 6 + 0 . 0 0 5 6 4 a | 5fe36bff-ac13-4c0d-b036-fffdf152eef1__mathematical-expression-and-equation_1.jpg |
\mu _ { 2 } = 0 . 5 4 + 0 . 4 6 \frac { h _ { 2 } } { h _ { 1 } } | 613ea82d-5cf1-11e8-a84a-001999480be2__mathematical-expression-and-equation_2.jpg |
V = \frac { \Delta c _ { r } \cdot 1 0 0 } { \beta } | 6280ca52-a59a-446f-b6bc-e74eaea791fb__mathematical-expression-and-equation_0.jpg |
\tan \{ \frac { \pi } { 4 } - [ \gamma - \arcsin \frac { \tan \gamma } { \sqrt { \{ } 2 [ 2 ( 1 + \tan \gamma ) + \tan ^ { 2 } \gamma ] \} } ] \} = \frac { 1 - \epsilon _ { x } } { 1 + \epsilon _ { y } } | 63416285-cc76-4567-b4bd-66a8c278888a__mathematical-expression-and-equation_5.jpg |
E + \Sigma T = R J . | 63b29e8f-16b1-4d48-957a-67b4c19b2608__mathematical-expression-and-equation_2.jpg |
m _ { y } ^ { 2 } = \beta _ { 1 } ^ { 2 } m _ { 1 } ^ { 2 } + \beta _ { 2 } ^ { 2 } m _ { 2 } ^ { 2 } + \dots + \beta _ { n } ^ { 2 } m _ { n } ^ { 2 } = \frac { k ^ { 2 } } { p _ { n } } | 63fd35e3-10d0-471a-9b17-3ef14aa1b897__mathematical-expression-and-equation_11.jpg |
c o \frac { 4 8 } { 1 0 } : \frac { 1 2 } { 1 0 } = \frac { 4 8 } { 1 0 } \times \frac { 1 0 } { 1 2 } = \frac { 4 8 0 } { 1 2 0 } = \frac { 4 8 } { 1 2 } = 4 | 6506032d-533b-4cdd-8af3-7b767a7c72f6__mathematical-expression-and-equation_2.jpg |
7 2 \times 1 = 8 \times 9 | 6513b035-a016-402e-a653-a0d156cef32d__mathematical-expression-and-equation_19.jpg |
= 2 . 5 ^ { 5 } - 3 . 5 ^ { 4 } + 1 . 5 ^ { 3 } - 4 . 5 ^ { 2 } + 1 . 5 + 2 | 66ba385f-1abb-4e30-92c4-5f73e89ecdee__mathematical-expression-and-equation_14.jpg |
\overline { 1 1 1 } = 0 , \overline { 2 1 2 } = 0 | 67ab1b60-a42e-4cae-81b2-a37ff8c4b632__mathematical-expression-and-equation_7.jpg |
\frac { p + q ) - f ( p ) } { q } = f \prime p + \phi ( p , q ) \text { o d e r , w e n n } y = f ( x ) , p = x , q = d x : \frac { d y } { d x } = f \prime x + \phi ( x , d x ) | 6801c529-b426-49b5-9710-49fcc272eaa2__mathematical-expression-and-equation_0.jpg |
\frac { v } { u + v } u _ { i } R T \ln \frac { P } { p \prime } | 6a93a994-99b0-4d7f-990d-62bb2eac126d__mathematical-expression-and-equation_0.jpg |
\delta = \frac { 1 } { 2 } C \cdot E ^ { 2 } , | 6b2f08a4-8549-40e7-b5b1-b0eab3c7a209__mathematical-expression-and-equation_0.jpg |
y \prime = \cos 2 x | 6b5c7650-989e-11de-a593-0030487be43a__mathematical-expression-and-equation_18.jpg |
\binom { n } { 4 } = \frac { n ( n - 1 ) ( n - 2 ) ( n - 3 ) } { 1 \cdot 2 \cdot 3 \cdot 4 } = \frac { n ( n - 1 ) ( n - 2 ) ( n - 3 ) } { 4 ! } | 6b76dc20-989e-11de-b5dc-0030487be43a__mathematical-expression-and-equation_8.jpg |
\frac { \partial } { \partial t } \mathbf { u } = \nabla ; \mathbf { v } - \nabla ; ( \mathbf { v } \cdot \nabla ; \mathbf { u } ) | 6b9826e9-e341-418b-8b17-af1ca3166f33__mathematical-expression-and-equation_5.jpg |
\frac { 7 } { 1 6 } = \frac { 2 1 } { 4 8 } | 6d1cc91e-e3d9-11e6-9608-001b63bd97ba__mathematical-expression-and-equation_3.jpg |
( 0 , 7 - ) 1 , 5 - 5 , 6 ( - 6 , 1 ) | 6d746983-0d7f-11e3-4047-001143e3f55c__mathematical-expression-and-equation_5.jpg |
\% = \frac { 1 0 0 \times 5 0 0 } { 5 0 0 \times 2 5 } = 4 \% | 6e06c320-f959-11e4-9f08-005056825209__mathematical-expression-and-equation_0.jpg |
3 ( n + 2 ) ( 2 n + 3 ) - 5 n + 4 ( n + 1 ) ^ { 2 } - ( 2 n + 2 ) = 2 n ^ { 2 } - 2 n | 6f0b5454-7d9e-4d1a-af65-43bea1c455d5__mathematical-expression-and-equation_4.jpg |
p \wedge p , p \vee p , p \rightarrow p , | 70062f75-37c6-44a1-af23-a06604b9c7b1__mathematical-expression-and-equation_11.jpg |
m = - c \ln n + c \frac { n } { n _ { 2 } } + c \ln n _ { 2 } - c = c [ \frac { n } { n _ { 2 } } + \ln ( \frac { n _ { 2 } } { n } ) - 1 ] \dots | 7170c284-ed72-11e8-b65a-00155d012102__mathematical-expression-and-equation_3.jpg |
\lambda _ { 0 } = \frac { \pi \omega ^ { 2 } r ^ { 3 } l ^ { 2 } \sigma } { 2 . 1 0 ^ { 4 } d ^ { 2 } E _ { g } } [ ( \frac { \pi r } { h } - \frac { h } { \pi r } ) ( \alpha _ { 0 } - \frac { 2 ( 1 - \cos \alpha _ { 0 } ) } { \alpha _ { 0 } } ) ] | 717137f2-ed72-11e8-b65a-00155d012102__mathematical-expression-and-equation_4.jpg |
\bar { x } = \phi ( x ) | 7178d1e4-77df-4d3a-bb13-7f084808bbd6__mathematical-expression-and-equation_8.jpg |
C _ { 1 5 } H _ { 2 3 } . O . C _ { 1 0 } H _ { 1 9 } , | 71ace160-fa5c-11e7-9854-5ef3fc9ae867__mathematical-expression-and-equation_1.jpg |
a _ { 1 } ^ { 2 } \cos ^ { 2 } \alpha + b _ { 1 } ^ { 2 } \cos ^ { 2 } ( \omega - \alpha ) ] y ^ { 2 } = a _ { 1 } ^ { 2 } b _ { 1 } ^ { 2 } \sin ^ { 2 } \omega | 720c8ab8-224a-11ea-b704-001b63bd97ba__mathematical-expression-and-equation_9.jpg |
A = \lim \{ \log \frac { x } { 1 - e ^ { - 2 x \pi } } + \int _ { 2 x \pi } ^ { \infty } \frac { e ^ { z ( 1 - v ) } - 1 } { e ^ { z } - 1 } d z \} | 722d229d-9e77-492d-807a-b972a939c319__mathematical-expression-and-equation_3.jpg |
- \beta + \gamma + \alpha = \emptyset , | 72d2a0a0-f6b6-4fde-b4d2-365594daeade__mathematical-expression-and-equation_0.jpg |
\dot { \mathbf { q } } = \mathbf { F } ( \mathbf { q } ) \mathbf { u } , | 731de6e6-89f2-4b66-b504-350739ee29b5__mathematical-expression-and-equation_2.jpg |
y = { } _ { \beta } \{ \frac { x \prime \equiv d } { v } \} ^ { \beta \prime } | 731fb0f4-b934-11e1-1027-001143e3f55c__mathematical-expression-and-equation_3.jpg |
a ^ { 2 } \cdot \overline { M P } ^ { 2 } + ( a ^ { 2 } + e ^ { 2 } ) \overline { C P } ^ { 2 } = a ^ { 2 } ( a ^ { 2 } + e ) | 74508580-d210-11e2-b081-5ef3fc9ae867__mathematical-expression-and-equation_8.jpg |
\beta \cdot 1 \cdot \frac { w ^ { 2 } } { 2 g } = h _ { d } \cdot 1 = H _ { d } ( \gamma _ { H g } - 1 ) | 74a26c70-5a1a-11e6-b155-001018b5eb5c__mathematical-expression-and-equation_2.jpg |
T = \frac { \lambda } { \omega } | 74e6af90-e580-11e8-9984-005056825209__mathematical-expression-and-equation_9.jpg |
\frac { d x \sqrt { 3 } } { \sqrt { 1 + x ^ { 2 } + x ^ { 4 } } } = \frac { d y } { \sqrt { 1 - x ^ { 2 } + x ^ { 4 } } } | 75994c88-476d-4d8d-9463-8bda7082f078__mathematical-expression-and-equation_0.jpg |
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