formula stringlengths 5 635 | image stringlengths 80 86 |
|---|---|
k _ 3 \cos \sqrt { k _ c + 1 } ( u + v ) + k _ 4 \sin \sqrt { k _ c + 1 } ( u + v ) + \frac { k _ c } { k - 1 } | ff097809-40e3-11e1-1418-001143e3f55c__mathematical-expression-and-equation_14.jpg |
m = \frac { M } { \frac { 4 } { 3 } \pi K ^ { 3 ^ \cdot } } | ff09791f-40e3-11e1-1418-001143e3f55c__mathematical-expression-and-equation_0.jpg |
w _ { A \vee B \vee C \vee \dots \vee K } = \bigoplus _ { i = 0 } ^ { n - k } ( ( - 1 ) ^ i \bigoplus _ { | d | = k + i , A \vee B \vee C \vee \dots \vee K \subset d } w _ d ^ 0 ) | ff49c307-ac0a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_7.jpg |
Z ( 0 , N ) [ \begin{array} { c } N \\ 0 \end{array} ] | ff49c4d9-ac0a-11e1-7963-001143e3f55c__mathematical-expression-and-equation_7.jpg |
2 ^ { q \prime - 1 } ( 1 + \frac { \lambda c _ 2 } { c _ 1 } ) ^ { q \prime } [ \int _ T ^ t k _ 2 ^ { p \prime } ( t - \sigma ) d \sigma ] ^ { q \prime / p \prime } \exp [ 2 ^ { q \prime - 1 } ( 1 + \frac { \lambda c _ 2 } { c _ 1 } ) ^ { q \prime } ] | ff505641-570a-11e1-7459-001143e3f55c__mathematical-expression-and-equation_1.jpg |
\parallel f \parallel _ { \hat { p } } = ( \int _ { R ^ n } ( 1 + | x | ^ 2 ) ^ p | f ( x ) | ^ 2 d x ) ^ { 1 / 2 } | ff5056d2-570a-11e1-7459-001143e3f55c__mathematical-expression-and-equation_1.jpg |
\le ( \int _ { R ^ n } | f ( y ) | ^ 2 . \sigma ( y ) ^ { 2 p } d y ) ^ { 1 / 2 } | ff5056d4-570a-11e1-7459-001143e3f55c__mathematical-expression-and-equation_1.jpg |
e _ 4 \prime = - 4 \lambda e _ 2 - 2 \mu e _ 3 | ff505761-570a-11e1-7459-001143e3f55c__mathematical-expression-and-equation_5.jpg |
( U V A _ 1 B _ 1 ) = \lambda , | ffa9618a-40e3-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg |
Q _ 1 + 3 0 = 4 S , | ffa962ec-40e3-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg |
\frac { c } { x } l + \frac { ( l - x ) ^ 2 } { 2 r } = ( s _ 1 + c ) | uuid:219ca550-0d35-11e5-b309-005056825209__mathematical-expression-and-equation_3.jpg |
r \prime ( 1 + \frac { d \alpha } { d \phi } ) = \lambda | uuid:69fb0fa2-55e1-4de4-b85e-8923626f0f1e__mathematical-expression-and-equation_3.jpg |
A M = u _ 1 , B M = u _ 2 , C M = u _ 3 | uuid:786f05e0-feae-4302-98f4-35e1dcabf058__mathematical-expression-and-equation_2.jpg |
\frac { 1 } { 2 } ( \Gamma _ 1 + \Gamma _ 2 ) \equiv x ^ 2 + y ^ 2 - ( u _ 1 + u _ 2 ) x + u _ 1 u _ 2 = 0 | uuid:ca108de7-34ab-4f97-903d-2cc8077df9f4__mathematical-expression-and-equation_1.jpg |
\frac { d x ^ 2 } { d x } = 2 x ^ { 2 - 1 } | uuid:f2d29e0b-e656-45b4-8b90-12130f54c4bc__mathematical-expression-and-equation_0.jpg |
d _ { 1 } = 2 d _ { 2 } + 2 \Re ( \frac { \cosh a w - 1 } { a \sinh a w } ) = 2 . 4 \cdot 1 0 ^ { - 3 } m | 249e4844-3c62-11e1-1211-001143e3f55c__mathematical-expression-and-equation_1.jpg |
b _ { r } = \frac { I } { n ( m - 2 r ) } ( \frac { \partial u } { \partial x } \frac { \partial \theta _ { r } } { \partial y } - \frac { \partial u } { \partial y } \frac { \partial \theta _ { r } } { \partial x } ) | 4efe45cc-7929-4043-800b-063b84fae1ee__mathematical-expression-and-equation_0.jpg |
( x + c ^ { 2 } ) ^ { 2 } + ( x - a + c ^ { 2 } ) ^ { 2 } - b ^ { 2 } = ( a + b ) ^ { 2 } | 32d5d8ed-45de-4bcb-8174-f0aa7bf01d70__mathematical-expression-and-equation_17.jpg |
+ \frac { 2 } { v } [ \frac { 1 } { ( 1 - P ^ { 2 } v ^ { 2 } ) ^ { 1 / 2 } } + \frac { 1 } { ( 1 - Q ^ { 2 } v ^ { 2 } ) ^ { 1 / 2 } } ] d D = 2 d t | 69898cbe-f2e9-44d8-9ee8-0de124073d57__mathematical-expression-and-equation_5.jpg |
L _ { t } = L _ { t 1 } + L _ { t } \prime + L _ { t } \prime \prime + L _ { t } \prime \prime \prime + L _ { t 2 } = 5 9 6 \text { m k g } | 9ff44460-32d4-11e6-a344-5ef3fc9ae867__mathematical-expression-and-equation_3.jpg |
u _ { 1 } = - \frac { a } { 2 } + \sqrt { ( \frac { a } { 2 } ) ^ { 2 } + b } | 3877d9a6-df28-11e1-6101-001143e3f55c__mathematical-expression-and-equation_1.jpg |
\alpha ( p ) = - ( p _ { 0 } - p _ { s } ) ^ { - 1 } ( p - p _ { s } ) | 1926dff3-c893-4670-8d74-2b212b7e0103__mathematical-expression-and-equation_0.jpg |
\Omega _ { 1 } = \frac { \alpha c } { 1 + \alpha c } \Omega | 9f21383a-4334-11e1-8339-001143e3f55c__mathematical-expression-and-equation_6.jpg |
u _ { t } - \sum _ { i , j = 1 } ^ { n } a _ { i , j } ( u _ { x _ { 1 } } , \dots , u _ { x _ { n } } ) u _ { x _ { i } x _ { j } } + c u _ { t } - b \Delta u _ { t } = g | 046d3d5b-570b-11e1-3052-001143e3f55c__mathematical-expression-and-equation_0.jpg |
\sphericalangle N C q = \sphericalangle M C A \prime | 027a842d-2bc6-4cfb-bf93-954d2e1dae36__mathematical-expression-and-equation_1.jpg |
: 1 2 = ( y - 1 5 0 ) : y | 5aa33ba0-4629-11e7-80b4-001018b5eb5c__mathematical-expression-and-equation_7.jpg |
- ( 1 8 3 ) - | 945e79cd-5570-4d87-963a-7a64a569e2ab__mathematical-expression-and-equation_0.jpg |
( \nabla \nu _ { * } ) ( X _ { x } , Y _ { x } , \xi _ { x } ) = \nabla ^ { V ^ { \perp } } _ { X _ { x } } v _ { * } ( Y , \xi ) = \Pi _ { V ^ { \perp } } ( \overline { \nabla } _ { X _ { x } } v _ { * } ( Y , \xi ) ) | 0c39dbd0-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_8.jpg |
- \frac { 1 } { I } \int ( \bar { x } v _ { 2 } - \bar { z } \lambda _ { 2 } ) ( \bar { y } v _ { 2 } - \bar { z } \mu _ { 2 } ) d w _ { y } - | 18c350a3-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_1.jpg |
E = \sqrt { B J } = E _ { i } | 0ecd69e3-3c62-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg |
R c \equiv P a + Q b | 66eea700-d034-11e3-93a3-005056825209__mathematical-expression-and-equation_3.jpg |
k _ { 1 } y + \psi \prime = \frac { \pi } { 4 } | 5da87cd5-435f-11dd-b505-00145e5790ea__mathematical-expression-and-equation_2.jpg |
- 0 , 0 0 2 x _ { 5 } + 0 , 0 5 4 0 6 x _ { 6 } - 0 , 0 1 5 5 9 x _ { 7 } + 0 , 0 0 0 0 8 x _ { 8 } + 0 , 0 0 0 0 2 x | 0a9e1690-b582-11ea-9b5d-005056825209__mathematical-expression-and-equation_3.jpg |
\frac { 1 } { 2 } l \times 4 = \frac { 4 } { 2 } l = 4 l : 2 = 2 l , | 12ed8617-3598-11ec-b695-001b63bd97ba__mathematical-expression-and-equation_1.jpg |
F ( \pi ) = \frac { \pi } { \sqrt { c ^ { 2 } - a ^ { 2 } - b ^ { 2 } } } | 29bd9d80-5d31-11e3-9ea2-5ef3fc9ae867__mathematical-expression-and-equation_1.jpg |
A _ { 1 } = 1 , | 442829cf-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_11.jpg |
\frac { \partial \Psi } { \stackrel { ( \alpha ) } { \partial C _ { K L } } } = 0 | 18c35029-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_18.jpg |
- u _ { z } + L _ { v } \frac { d ( i _ { d } - i _ { k } ) } { d t } + R _ { v } ( i _ { d } - i _ { k } ) + L _ { z } \frac { d i _ { d } } { d t } + | 23c01d88-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_2.jpg |
1 3 9 9 ) \sqrt { 6 2 9 2 6 9 3 6 0 2 2 5 } | 3f3f5f76-c060-11e6-855e-001b63bd97ba__mathematical-expression-and-equation_20.jpg |
N a _ { 2 } O + H _ { 2 } O = 2 N a O H + 3 5 \cdot 4 4 \text { K a l . } | 2c4c1e0e-901d-4119-9c63-cbeb0f2f4654__mathematical-expression-and-equation_2.jpg |
\epsilon _ { k l } = u _ { l , k } + \phi _ { k l } | 1ea66cac-3c62-11e1-3052-001143e3f55c__mathematical-expression-and-equation_13.jpg |
\psi ( z ) = \psi ( a t _ { 0 } + x ) | 0f9f61ce-3c62-11e1-1121-001143e3f55c__mathematical-expression-and-equation_11.jpg |
L = 1 8 9 3 0 0 0 c m \doteq 0 . 0 0 1 9 H . | 4b749f00-f0e4-11e2-9439-005056825209__mathematical-expression-and-equation_6.jpg |
C _ { p } = \Sigma ( P \sin \alpha ) , | 9755f628-1d00-11ea-b563-001999480be2__mathematical-expression-and-equation_7.jpg |
( i = 1 , 2 ) | 3855e372-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg |
C _ { 1 } = C \frac { S } { R + S } . | 7386ef2d-87a4-4e86-bdef-aafb150f113c__mathematical-expression-and-equation_0.jpg |
[ | \dot { v } | _ { L _ { p } ( \Omega ) ^ { 3 \times 3 } _ { p } } ^ { p } + | v | _ { L _ { 2 p / ( 3 - p ) } ( \Gamma ) ^ { 3 } } ^ { p } ] ^ { \frac { 1 } { p } } | 7997e1f5-a33a-4139-896c-bfae3ca0dfcd__mathematical-expression-and-equation_2.jpg |
Y _ { n } ( t ) = L _ { n } ( [ G t ] ) | 01d7e9fb-ac0b-11e1-7963-001143e3f55c__mathematical-expression-and-equation_9.jpg |
Q ( N ) = Q ( N - 1 ) . e ^ { A . Q ( N - 1 ) } | 0011ebbe-bc38-11e1-1211-001143e3f55c__mathematical-expression-and-equation_2.jpg |
2 S O _ { 2 } + 4 H _ { 2 } O + 4 J = 2 H _ { 2 } S O _ { 4 } + S + 4 H J ; | 6eef6120-2f96-4e3e-9803-3a577a717806__mathematical-expression-and-equation_5.jpg |
V = X _ { 0 } + X _ { 1 } \rho + X _ { 2 } \rho ^ { 2 } + X _ { 3 } \rho ^ { 3 } + \dots | 94d99eac-d0a2-4376-937c-bdf6f91c5702__mathematical-expression-and-equation_8.jpg |
a x ^ { 2 } + c y ^ { 2 } + f = 0 | 0d229550-860b-11e4-889a-5ef3fc9ae867__mathematical-expression-and-equation_11.jpg |
\alpha _ { 2 } = \frac { y _ { 1 } } { b } | 46067dd5-4027-42a4-9dbd-411449324eab__mathematical-expression-and-equation_13.jpg |
\frac { \xi } { 2 l } ( 1 + \eta ( \xi , \nu ) ) + \frac { g } { 1 6 l ^ { 2 } \nu ^ { 2 } } ( x _ { 0 } + \xi ) ^ { 2 } = 0 . | 0e4662d4-40e4-11e1-1121-001143e3f55c__mathematical-expression-and-equation_8.jpg |
\tan \delta = k \frac { C } { C _ { v } } \frac { 2 } { \pi } ( 1 + \kappa ) [ \frac { 1 } { U _ { m } } \int _ { x _ { m i n } } ^ { x _ { m a x } } ( a + b x ) d x - \frac { \kappa d } { \epsilon U _ { m } ^ { 2 } } \int _ { x _ { m i n } } ^ { x _ { m a x } } \frac { ( a + b x ) ^ { 2 } } { x } d x ] | 0c708f31-3c62-11e1-1586-001143e3f55c__mathematical-expression-and-equation_5.jpg |
u v x = x \implies v u x = x ; | 3855e30a-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg |
\rho \prime = a | 7fc14cf0-7aa3-11e4-964c-5ef3fc9bb22f__mathematical-expression-and-equation_13.jpg |
L _ { 1 } = 4 ( \sqrt { x ^ { 2 } + \rho ^ { 2 } } - \rho - x ) + 2 \rho ( \log 2 - 1 ) | 38efd020-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_7.jpg |
T ( b ) = \frac { \pi } { 2 } \frac { b ^ { 2 } R S } { \ln ^ { 2 } ( 1 - b ) } = \frac { \pi } { 2 } \frac { ( 1 + \frac { b } { \sqrt { 2 } } + \frac { b ^ { 2 } } { \sqrt { 3 } } + \dots ) ( 1 + \frac { b } { 2 \sqrt { 2 } } + \frac { b ^ { 2 } } { 3 \sqrt { 3 } } + \dots ) } { ( 1 + \frac { 1 } { 2 } b + \frac { 1 ... | 97198e4b-4334-11e1-8339-001143e3f55c__mathematical-expression-and-equation_7.jpg |
\tau \in U \implies | \phi ( \tau ) - \phi ( t ) | \ge \frac { c } { 2 } | \tau - t | | 4fbec42b-a8e1-4374-8c71-a9412f537717__mathematical-expression-and-equation_2.jpg |
\xi = v | 8ed54acb-d4a7-4dcc-b6ac-285aa5e55fbf__mathematical-expression-and-equation_8.jpg |
( J _ { x } ) = 2 v F \int _ { 0 } ^ { \frac { 1 } { 2 } } ( e _ { x } ^ { 2 } \delta z + z ^ { 2 } \delta z ) = 2 v F \int _ { 0 } ^ { \frac { 1 } { 2 } } ( e _ { x } ^ { 2 } \delta z + \delta \frac { z ^ { 3 } } { 3 } ) | 77cab820-d210-11e2-b081-5ef3fc9ae867__mathematical-expression-and-equation_2.jpg |
\frac { d \phi } { d t } = k \phi | 0fd8688d-ce3a-4fc1-9f0c-e5917a44fc2a__mathematical-expression-and-equation_12.jpg |
\bar { x } \in \bar { x } _ { \bar } { F } , Q . E . D . | 975b7ad0-ddff-11e2-b28b-001018b5eb5c__mathematical-expression-and-equation_8.jpg |
C = c A | 5bee98cc-2c4c-4434-a991-4b342d5ddf90__mathematical-expression-and-equation_2.jpg |
7 + 2 5 + 1 4 + 2 + 3 6 = 8 4 | 6258fd98-68bf-4041-a2fa-4b3c9be4c841__mathematical-expression-and-equation_5.jpg |
( x ^ { 3 } _ { - } p x - q ) = ( x - 2 w ) ( x + w \pm \sqrt { - ( 3 w ^ { 2 } - p ) } ) = x ^ { 3 } - p x - 2 w ( 4 w ^ { 2 } - p ) ( 1 7 | 7bc54945-b934-11e1-1154-001143e3f55c__mathematical-expression-and-equation_0.jpg |
J _ { s 2 } = \int _ { \omega d > \omega _ { d m i n } } ^ { \infty } \frac { \sin ( k _ { 8 } ) \sin ( k _ { 9 } ) } { \omega d [ \omega d - 4 \sqrt { ( 1 - k ) } ] ^ { 2 } } \cdot d ( \omega d ) | 2051ab73-3c62-11e1-8486-001143e3f55c__mathematical-expression-and-equation_4.jpg |
\sqrt { ( x - 3 ) ^ { 2 } } = 4 ( 3 + \sqrt { x - 3 } ) | 756aae96-f8cf-42f9-9987-0ced5291d2b9__mathematical-expression-and-equation_0.jpg |
C = \frac { \pi } { 4 } ( \frac { a } { 2 } - \frac { 1 } { M } + \frac { a } { 1 - e ^ { M \alpha } } ) | 772946ac-e1d5-4e67-8471-2f212dc27351__mathematical-expression-and-equation_1.jpg |
I _ { D T } = - 1 0 0 0 a _ { 1 } , A _ { D T } = 1 0 0 0 a _ { 0 } | 47030b49-420f-11e1-1431-001143e3f55c__mathematical-expression-and-equation_3.jpg |
a \{ 1 0 1 0 \} \infty P , c \{ 0 0 0 1 \} 0 P , | 5ee77e38-feb6-4f5f-a66c-905ca7a27053__mathematical-expression-and-equation_1.jpg |
r _ { A } ^ { B } \in \mathbb { R } | 0620b97b-570b-11e1-1090-001143e3f55c__mathematical-expression-and-equation_22.jpg |
Y _ { l } = 3 \text { f o r } A _ { l } < Q _ { l } | 3ef684ee-2e3b-4c7f-a00a-9cc4928fb8cd__mathematical-expression-and-equation_1.jpg |
= K _ { 3 } S b O _ { 3 } S + H _ { 2 } O + A g | 8403c89b-d366-4d70-951f-2d882d876e47__mathematical-expression-and-equation_1.jpg |
V = F ( \sum _ { 1 } ^ { n } \alpha _ { n } x _ { n } ) | 6fb4d981-c4d3-40a8-b6ed-f6bfffa8567a__mathematical-expression-and-equation_2.jpg |
H _ { 2 } O = H _ { 2 } + O , 1 8 = 2 + 1 6 , j e s t | 4c89e040-3241-11ec-a216-001b63bd97ba__mathematical-expression-and-equation_2.jpg |
X = \{ x \} \cup \{ a \in A - D : \Theta ( a , x ) \in S \} | 01d92527-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_2.jpg |
\lambda + i \int \frac { ( 1 - e ^ { 2 } ) d \phi } { ( 1 - e ^ { 2 } \sin ^ { 2 } \phi ) \cos \phi } = C | 54305b77-a30c-4216-8ae5-8bd44eff5aa9__mathematical-expression-and-equation_0.jpg |
\beta \prime _ { 2 } \sin \alpha \neq 0 , | 01d92666-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_6.jpg |
B _ { 1 } = E _ { 1 } | 9f429143-9992-4737-afcf-7a18999bff23__mathematical-expression-and-equation_19.jpg |
a _ { 1 } \rho \cup a _ { 1 } \rho ^ { 2 } \cup \dots \cup a _ { 1 } \rho ^ { n } = V | 046d3d26-570b-11e1-3052-001143e3f55c__mathematical-expression-and-equation_0.jpg |
\alpha = \alpha _ { 1 } \sqrt { \mu } + \alpha _ { 2 } \mu + \alpha _ { 3 } \mu \sqrt { \mu } | 5dabd88f-435f-11dd-b505-00145e5790ea__mathematical-expression-and-equation_7.jpg |
a = A r c T h \frac { Q } { p } | 04a81185-40e4-11e1-8339-001143e3f55c__mathematical-expression-and-equation_0.jpg |
h \prime - \alpha \prime = 0 | 3c0d74b6-8d77-497c-82ef-150607a2c508__mathematical-expression-and-equation_6.jpg |
2 A \prime A \prime \prime A \prime \prime \prime - A \prime \prime ^ { 3 } - A A \prime \prime \prime ^ { 2 } + A A \prime \prime A ^ { I V } - A \prime ^ { 2 } A ^ { I V } + | 5dbec47a-435f-11dd-b505-00145e5790ea__mathematical-expression-and-equation_6.jpg |
A _ { 0 } = ( a _ { 0 } , a _ { 1 } , a _ { 2 } , a _ { 3 } ) ( x , \gamma ) ^ { 3 } | 740f7fba-6bba-4285-b27b-b78f9132b19b__mathematical-expression-and-equation_11.jpg |
\sum _ { v = s + 1 } ^ { ( s , s \prime ) } \alpha _ { v } \mu _ { k } ^ { v } = \beta _ { 1 } ^ { ( s , s \prime ) } \mu _ { k } ^ { m - 1 } + \beta _ { 2 } ^ { ( s , s \prime ) } \mu _ { k } ^ { m - 2 } + \dots + \beta _ { m } ^ { ( s , s \prime ) } , ( k = 1 , 2 , \dots , m ) . | 3c10017d-3105-11e9-8847-005056a2b051__mathematical-expression-and-equation_8.jpg |
\gamma _ { v } = c _ { v } / R | 1cf70d96-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_0.jpg |
r _ { j } ( a , b ) = s _ { j } ( a _ { i } , b _ { i } ) | 0a7a7845-570b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_7.jpg |
2 C B \times B D = C B ^ { 2 } + B A ^ { 2 } | 206e85f6-6c3d-4abf-8ea8-6de04a7c7dd8__mathematical-expression-and-equation_0.jpg |
h = 4 . 9 5 4 c m | 875e7370-e3eb-11e2-b28b-001018b5eb5c__mathematical-expression-and-equation_16.jpg |
+ [ ( 1 + y ^ { 2 } ) d x ^ { 2 } + ( 1 + x ^ { 2 } ) d y ^ { 2 } - 2 x y d x d y ] / [ 2 \rho ^ { 2 } ( 1 + x ^ { 2 } + y ^ { 2 } ) ] | 39b0e032-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_3.jpg |
\rho ^ { 2 } = 2 a ^ { 2 } ( 1 + \cos \frac { 2 p } { p + 2 q } \phi ) | 49056faf-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_0.jpg |
( \frac { \tilde { \Delta y } } { \Delta t } ) = \frac { 1 } { n m T } ( \tilde { y } _ { n + 1 } - \tilde { y } _ { 1 } ) | 18c350ed-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_2.jpg |
0 . P r ( E ) \le 1 \cdot D ( 0 , 2 \pi ) C ( r ) | 72f9c221-ea40-486c-a654-3b2cf15389e4__mathematical-expression-and-equation_2.jpg |
\align* 9 3 \times 5 & = ( 9 2 + 1 ) 5 = 4 6 5 \\ 7 9 \times 5 & = ( 7 8 + 1 ) 5 = 3 9 5 \\ 5 7 \times 5 & = ( 5 6 + 1 ) 5 = 2 3 5 \align* | 3fbfdaa0-e709-11e8-9210-5ef3fc9bb22f__mathematical-expression-and-equation_3.jpg |
( \underbrace { A B : A C + B C } ) = a b : A B | 39d62109-332a-11ec-9f2d-001b63bd97ba__mathematical-expression-and-equation_3.jpg |
I _ { i } \sim O _ { i } \times k \times j \times \frac { e ^ { - ( \mu _ { 1 } x _ { 1 i } + \mu _ { 2 } x _ { 2 i } ) } } { X _ { i } ^ { 2 } } | 0a1c8fab-a0fd-4307-8967-6f76ee2bd00f__mathematical-expression-and-equation_0.jpg |
a = 3 x , b = 3 y , c = 3 z . | 098e7370-d3b8-11e2-b791-5ef3fc9bb22f__mathematical-expression-and-equation_14.jpg |
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