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math_formulas

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-556
\pi \cdot \frac{1}{3} \cdot 38 - \pi \cdot 12 = 2/3 \cdot \pi
8,561
0 = (i*\pi*2 - 2*\pi*i)/(i*2)
-23,451
\frac{2}{15} = 2 \cdot \frac15/3
10,931
\sin(π\times 19/2) = \sin(\frac{21\times π}{2}\times 1 - \frac{2\times π}{2})
13,531
13!/7! - 12!/7! = 1140480
-20,236
\frac{1}{-2\cdot z + 4\cdot (-1)}\cdot (4\cdot (-1) - 2\cdot z)\cdot (-\tfrac{1}{10}\cdot 3) = \frac{1}{-20\cdot z + 40\cdot (-1)}\cdot (12 + 6\cdot z)
1,573
\tan\left(\frac{1}{z_2} \cdot z_1\right) = \theta \Rightarrow \operatorname{atan}(\theta) = \dfrac{z_1}{z_2}
5,837
\frac{1}{\beta^{-k}*\frac{1}{k!}} = k!*\beta^k
18,909
60/2\cdot 2/3\cdot 4/5 = 16
-12,606
16 = \dfrac{32}{2}
2,292
\frac{f_x}{f_x + 1} = \dfrac{\dfrac{1}{f_x}\cdot f_x}{\frac{1}{f_x} + 1}
5,561
\dfrac{1}{2\cdot n}\cdot ((-1) + n\cdot 2) = g_n \implies 1 - \frac{1}{2\cdot n} = g_n
-4,551
\dfrac{-x-13}{x^2-2x-3} = \dfrac{3}{x+1} + \dfrac{-4}{x-3}
19,197
R*2 = \dfrac{a}{\sin\left(a\right)} \Rightarrow a/(2*R) = \sin\left(a\right)
-6,637
\frac{4}{8 + z^2 + 9*z} = \frac{1}{(z + 8)*(z + 1)}*4
-18,744
\left(-1\right) \cdot 0.0401 + 0.9332 = 0.8931
-5,778
\frac{x \cdot 2}{\left(x + 4 \cdot (-1)\right) \cdot (x + 3 \cdot \left(-1\right))} = \dfrac{x \cdot 2}{12 + x^2 - 7 \cdot x}
25,578
Z \cdot X = I_l \Rightarrow I_l = X \cdot Z
13,915
\pi/4 + \pi = \dfrac{5}{4}\cdot \pi
10,233
y^3 = 2 + 11\cdot i + 2 - 11\cdot i + 3\cdot ((2 + 11\cdot i)\cdot (2 - 11\cdot i))^{\frac{1}{3}}\cdot y = 4 + 15\cdot y
5,557
\mathbb{E}(Q_2^2) = \mathbb{E}(Q_1^2) \mathbb{E}((1 + Q_2) * (1 + Q_2)) = \mathbb{E}(Q_1) (1 + 2\mathbb{E}(Q_2) + \mathbb{E}(Q_2^2))
-5,041
36.8\cdot 10^{4 - 2} = 36.8\cdot 10^2
30,739
\frac{1}{32}\cdot 64 = 2
-22,368
z^2 - 7z + 10 = (z + 5(-1)) (2(-1) + z)
-29,150
2*3 + 3*0 = 6
22,471
0 + \frac{1}{x + 2}*\left(x^4*2 + 1\right) = \dfrac{1}{2 + x}*(1 + x^4*2)
36,625
18 = 21 + 3\cdot \left(-1\right)
13,586
\binom{4}{2}*\binom{12}{3} = \binom{23}{3} - \binom{13}{3} - \binom{11}{3}
28,591
\frac{1}{-\frac{1}{d_1} + \dfrac{1}{d_1 - \tfrac{1}{d_2}}} = d_1 d_2 d_1 - d_1
28,300
14 + (3 + u)^2 = 23 + u^2 + 6u
-2,662
2\sqrt{7} = \sqrt{7}\cdot (5 + 3\left(-1\right))
-796
7723/10000 = 0 + \frac{7}{10} + \frac{7}{100} + \frac{2}{1000} + \dfrac{1}{10000}3
-5,013
0.94\cdot 10^3 = 10^{3\cdot (-1) + 6}\cdot 0.94
18,766
(a^2 + c \cdot a + c \cdot c) \cdot (a - c) = -c^3 + a^3
-20
1 = 3 \left(-1\right) + 4
24,138
\frac{n \cdot 9}{7 + n} \cdot 1 = \tfrac{9}{\frac7n + 1}
928
(2 \cdot 13)^4 + 13^4 \cdot 239 + 13^4 = (2 \cdot 2 \cdot 13)^4
28,703
\log_e(1 + 1/2) = \log_e(3/2)
-3,849
6t \cdot t/11 = 6/11 t^2
-11,524
1 + 21 i = 21 i - 9 + 10
18,570
z^{g_1 + g_2} = z^{g_2} z^{g_1}
-6,351
\frac{1}{r\cdot 5 + 50} = \frac{1}{5(10 + r)}
13,603
a = f = \frac{1}{2}(a + f)
-5,690
\frac{1}{9 + n^2 + 10*n} = \dfrac{1}{(9 + n)*(n + 1)}
3,197
672 = \frac{20160}{3\cdot 5\cdot 2}\cdot 1
205
-(e*i*y/2 - e^{((-1)*i*y)/2})^2 = -(2*i)^2*\sin^2{\frac{y}{2}} = 4*\sin^2{y/2}
-30,578
35 \cdot z + 14 \cdot (-1) = (2 \cdot \left(-1\right) + 5 \cdot z) \cdot 7
24,083
-q \cdot p \cdot 2 + (q + p)^2 = p^2 + q \cdot q
20,620
2\cdot y + 5 + (y + 2\cdot (-1))\cdot \left(2 + y^2 + 2\cdot y\right) = y \cdot y^2 + 1
11,569
a \cdot b = \frac{1}{\frac1a \cdot 1/b} = \dfrac{1}{\frac1b \cdot 1/a} = b \cdot a
29,370
\mathbb{Var}[C \cdot Z] = \mathbb{E}[(C \cdot Z)^2] - \mathbb{E}[C \cdot Z] \cdot \mathbb{E}[C \cdot Z] = \mathbb{E}[(C \cdot Z)^2] - \left(\mathbb{E}[C] \cdot \mathbb{E}[Z]\right)^2
17,634
A = (x + J)^{\frac{1}{2}} \Rightarrow A = x + J
23,497
0/1 + 2 = \frac{2}{1}
22,752
1/\tan(\theta) = \tan\left(\dfrac12*\pi - \theta\right)
15,743
x^2 + \left(x + 4\right)^2 + (x + 6) \cdot (x + 6) + (x + 10)^2 + (x + 12)^2 = 296 + 5 \cdot x^2 + 64 \cdot x
5,249
C_2 - G - C_1 - x = C_2 - C_1 - G - x
-3,178
\sqrt{16} \sqrt{7} - \sqrt{7} \sqrt{9} = \sqrt{7}*4 - 3 \sqrt{7}
34,712
324 = (4 + 12 + 2) \cdot 3! \cdot 3
37,739
\frac{(\frac1m\cdot l) \cdot (\frac1m\cdot l)}{m}\cdot \tfrac{1}{1 + (\frac{l}{m})^2 \cdot (l/m)} = \frac{l \cdot l}{m^3 + l^3}
36,032
\cos{\theta*3} = -\cos{\theta}*3 + \cos^3{\theta}*4
48,278
c_{n+1} = 3\cdot x + 4^n - x \implies c_{n+1} = x\cdot 2 + 4^n
17,533
(x - 2 \cdot R) \cdot (x - 2 \cdot R) = x - 4 \cdot R + 4 \cdot R \cdot R = x - 4 \cdot (R - R \cdot R)
16,647
6/27 = \frac{4}{6^3}\times 3\times 2^2
29,574
(x^2 + y^2)^2 = x^4 + 2 x^2 y^2 + x^4 \geq x^4 + y^4
-2,460
\sqrt{7} \cdot \left(2 \cdot \left(-1\right) + 4\right) = 2 \cdot \sqrt{7}
24,106
\frac{4*6*5}{6} = 20
7,870
\frac{5^n + 3^n}{7^n + (-2)^n} = \dfrac{(\tfrac{5}{7})^n + (3/7)^n}{1 + (-2/7)^n}
-4,844
\frac{1.6}{10} = 1.6/10 \cdot 10 \cdot 10 = 1.6 \cdot 10^1
16,157
\vartheta c + xb = xb + c\vartheta + xc
28,986
\tan{x} = \cot(-x + \frac{1}{2} \cdot \pi)
5,511
a*k*x*k' = k'*x*k*a
27,519
l = l + (x^2 - l^2)/2 \Rightarrow |x| = l
5,418
d/dz (z\ln(z)) = 1 + \ln\left(z\right)
3,758
\cos^2(w*x) = (1 + \cos(2*w*x))/2 = 1/2 + \dfrac{1}{2}*\cos(2*w*x)
2,726
\cos(dz + b) d = \frac{\partial}{\partial z} \sin(dz + b)
34,129
-\frac14*33 = -\dfrac{33}{4}
871
3\cdot i = (a + b\cdot i)^2 = a^2 - b^2 + 2\cdot a\cdot b\cdot i
-7,959
\left(-180 - 20*i + 225*i + 25*\left(-1\right)\right)/41 = \frac{1}{41}*(-205 + 205*i) = -5 + 5*i
-1,126
(1/8*(-3))/(1/2*7) = \frac{2}{7}*\left(-\frac{1}{8}*3\right)
16,312
\frac{1}{2^{-\sqrt{n}}} \cdot n^2 = n^2 \cdot 2^{\sqrt{n}}
31,027
n = 3 \cdot m + 2 rightarrow \frac{n^2}{3} \cdot 1 = 1 + m \cdot m \cdot 3 + 4 \cdot m
23,600
r/s + a/b = \frac{1}{s \cdot b} \cdot (b \cdot r + a \cdot s)
4,140
b = 4\cdot \left(-1\right) + \frac{a^2}{2} \Rightarrow a^2 = 2\cdot (b + 4) = 2\cdot b + 8
21,638
\left(1 + y\right)\cdot (y + \left(-1\right)) = y \cdot y + \left(-1\right)
13,607
\tan(h) = \frac{1}{\cos\left(h\right)}*\sin(h)
6,050
\lambda\cdot I = \lambda\cdot I\cdot \frac1Z\cdot Z = \frac{1}{Z}\cdot I\cdot Z\cdot \lambda
-20,699
\tfrac{1}{(-1) + a} \cdot ((-7) \cdot a) \cdot 9/9 = \dfrac{\left(-63\right) \cdot a}{9 \cdot (-1) + a \cdot 9}
-12,113
\frac{14}{15} = \dfrac{1}{6*\pi}*s*6*\pi = s
33,558
60 = 160 + 100\cdot (-1)
35,249
x/dx = \dfrac{1}{dx \cdot \frac1x}
-11,521
10 + 4 \cdot \left(-1\right) + 22 \cdot i = 6 + 22 \cdot i
14,633
-2^2 + 5 \cdot 5 = 11^2 - 10^2
-18,300
\frac{1}{a^2 + 9 \cdot a} \cdot (9 + a^2 + 10 \cdot a) = \frac{1}{(9 + a) \cdot a} \cdot (a + 9) \cdot (1 + a)
-20,518
\dfrac{1}{9}2\cdot 10 s/(10 s) = 20 s/(90 s)
13,942
1680 = \frac{1}{3! \cdot 3! \cdot 3!} 9!
15,871
14 = \left\lfloor{\frac{1}{2}((-1) + 30)}\right\rfloor
38,503
4 \cdot \frac{3!}{2!} = 12
5,764
((-1) + \vartheta)! = \frac{1}{\vartheta}\vartheta!
38,974
\dfrac16*4 = 2/3
30,264
a + h \neq 0 rightarrow -a \neq h