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ddrg
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math_formulas

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32,460
30 = 2220422932^3 + \left(-2218888517\right)^3 + (-283059965) \cdot (-283059965) \cdot (-283059965)
9,583
\left(\sqrt{z + d}\right)^2 = \sqrt{G + m} * \sqrt{G + m}\Longrightarrow G + m = z + d
-6,693
80/100 + 3/100 = 8/10 + \dfrac{1}{100}\times 3
-14,550
1 + 5 \cdot 7 = 1 + 35 = 1 + 35 = 36
15,023
\dfrac{x - y}{x^2 - y \cdot y} = \frac{1}{y + x}
-5,133
\dfrac{66.6}{1000} = \frac{66.6}{1000}
26,406
\tfrac{6}{35} = 3/5*\frac{2}{7}
20,175
\frac{1}{54}\cdot 4 = \frac{\dfrac{1}{2}}{2}\cdot 8\cdot \frac{1}{27}
17,157
i^{-1} = i^{1 + 2 \times (-1)} = \dfrac{i}{i^2} = i/(-1) = -i
6,302
0 = k\cdot 3 + (-1) \Rightarrow k = 1/3
1,448
m = 3/2*y rightarrow 2/3*m = y
2,443
\left\lfloor{\frac{90000}{35}}\right\rfloor = 2571
2,919
\frac{1}{20} = \frac14 - \frac{1}{5}
40,555
\frac{1}{3}*3 = 1 = 3 + 2\left(-1\right)
10,843
y\cos(a) = \sin(a) x \Rightarrow -x^2 \sin^2(a)*2 = -y^2 \cos^2(a)*2
17,016
\mathbb{E}[\sum_{l=1}^x X_l] = \sum_{l=1}^x \mathbb{E}[X_l]
13,601
0 = x^3 + b^3 + h \cdot h \cdot h - 3 \cdot x \cdot b \cdot h = (x + b + h) \cdot \left(x^2 + b^2 + h^2 - x \cdot b - b \cdot h - h \cdot x\right)
7,202
2 + 2 + 2 + 2 + \dotsm = -\frac12
-7,793
\frac{1}{-4}\cdot (20\cdot i - 20) = -\frac{20}{-4} + i\cdot 20/\left(-4\right)
28,915
z^6 + z^5 + z^4 + z^3 = (z^3 + z) \cdot \left(z^2 + z^3\right)
7,100
90/100 \cdot \left(1 - \frac{75}{100}\right) = \frac{25}{100} \cdot 90 \cdot \frac{1}{100} = 9/40
27,794
m \cdot 0 = m + (-1)^m \cdot 0 = m = 0 + \left(-1\right)^0 \cdot m = 0 \cdot m
-26,432
16 = 24 \times 2/3
45,561
195 = 3*5*13
37,180
t^2 + 2\cdot y\cdot t + \left(-1\right) = 0 \Rightarrow -y ± \sqrt{1 + y^2} = t
11,270
1 = (1^{1.5})^{\frac{1}{2}}
46,411
\sin{4 \cdot x}/\sin{x} = \dfrac{1}{e^{i \cdot x} - e^{-i \cdot x}} \cdot \left(e^{4 \cdot i \cdot x} - e^{-4 \cdot i \cdot x}\right) = e^{3 \cdot i \cdot x} + e^{i \cdot x} + e^{-i \cdot x} + e^{-3 \cdot i \cdot x} = 2 \cdot \cos{x} + 2 \cdot \cos{3 \cdot x}
-21,055
6/8 = \frac34\cdot 2/2
3,552
E(T_1) + \cdots + E(T_x) = E(T_1 + \cdots + T_x)
6,773
\cos{6z} = \cos(5z + z)
-30,916
3 \cdot b + 6 = 3 \cdot b + 6
21,852
\alpha \times |Z|^2 + \beta \times |Z^2| = \alpha \times |Z|^2 + \beta \times |Z|^2 = (\alpha + \beta) \times |Z|^2
18,533
\dfrac{D\cdot x}{D} = 1 \Rightarrow x\cdot D = D
-18,319
\frac{42 + y^2 - y\cdot 13}{y^2 - 7\cdot y} = \frac{(y + 6\cdot \left(-1\right))\cdot (y + 7\cdot (-1))}{(y + 7\cdot (-1))\cdot y}
-4,552
-\frac{5}{x + 2} - \frac{1}{x + (-1)} = \frac{3 - 6*x}{x^2 + x + 2*\left(-1\right)}
-19,342
\frac48\tfrac13 = \tfrac{1}{\dfrac143 \cdot 8}
1,050
21 \cdot z/20 = \frac{z}{5} \cdot 4 + \dfrac{z}{4}
23,389
Y_2\cdot A_1 = A_1\cdot Y_2
23,629
(\tfrac{u}{2} + w/2)*2 = u + w
-20,651
\frac{t\cdot (-18)}{3\cdot t + 30\cdot (-1)} = \tfrac33\cdot \frac{(-6)\cdot t}{t + 10\cdot (-1)}
15,532
b = \arcsin{h} rightarrow \sin{b} = h
-15,685
\frac{1}{s^{12}*x^{15}*(\frac{1}{x^5*s^4})^4} = \frac{\tfrac{1}{x^{15}}*\frac{1}{s^{12}}}{\dfrac{1}{x^{20}}*\frac{1}{s^{16}}}
-19,488
\phantom{\dfrac{1}{9} \times \dfrac{8}{5}} = \dfrac{1 \times 8}{9 \times 5} = \dfrac{8}{45}
24,708
1 - \sin^2{z} = \cos^2{z} = (1 + \cos{2*z})/2
-12,428
\frac{1}{2}*116 = 58
-12,117
1/6 = \frac{x}{6*\pi}*6*\pi = x
-10,267
-\tfrac{45 \cdot (-1) + 45 \cdot y}{y \cdot 15 + 60 \cdot (-1)} = 15/15 \cdot \left(-\frac{1}{4 \cdot (-1) + y} \cdot (3 \cdot y + 3 \cdot (-1))\right)
-154
\frac{10!}{(3(-1) + 10)!} = 10\cdot 9\cdot 8
29,559
-1/24 = \dfrac{1}{2} + 2/2 + \dots
23,145
1! + 2! + \dots + n! + (n + 1)! \leq 2n! + (n + 1)! = \left(n + 3\right) n! \leq 2(n + 1) n!
11,212
\binom{-1}{q} = (\left(-1\right)*\left(-2*\dotsm*(-1 - q + 1)\right))/q! = (-1)^q
-20,622
5/5 \cdot \frac{1}{i \cdot 6} \cdot (-8 \cdot i + 4 \cdot (-1)) = \dfrac{1}{30 \cdot i} \cdot (20 \cdot (-1) - i \cdot 40)
2,647
x*x^N = x^{1 + N}
18,294
-z^2 \cdot 2 + (z^2 + 1) \cdot (z^2 + 1) = z^4 + 1
1,039
(1/4)^{1/2} = \dfrac{1}{2}
-19,575
7\cdot \frac{1}{3}/9 = 7/(9\cdot 3) = 7/27
-20,825
\frac{1}{\left(-1\right) + n} \cdot ((-4) \cdot n) \cdot 7/7 = \frac{1}{7 \cdot n + 7 \cdot (-1)} \cdot (n \cdot (-28))
-11,646
22\cdot i - 15 + 8 = -7 + 22\cdot i
6,332
n = n + (-1) + 1 = n + 2\cdot (-1) + 2 = \dotsm = (n + 1)/2 + (n + (-1))/2
-16,690
-5\cdot y = -5\cdot y\cdot \left(-5\cdot y\right) + -5\cdot y\cdot \left(-7\right) = 25\cdot y^2 + 35\cdot y = 25\cdot y^2 + 35\cdot y
-29,144
18 = 4\cdot 4 + 1\cdot 2
-19,683
20/9 = \frac{4}{9} \cdot 5
8,496
4 \lt z \cdot z \implies 0 \lt (2 + z) \cdot (z + 2 \cdot \left(-1\right))
51,751
1 = i^0
29,559
1/2 + \frac{2}{2} + ... = -1/24
-12,841
3/4 = 18/24
28,679
2\cdot 5\cdot \dfrac{5!}{2!} = 600
-20,286
\frac13 \cdot 3 \cdot (-10/7) = -30/21
7,844
-\frac{1}{1 + x} + 1/x = \dfrac{1}{x + x \times x}
-3,338
6\times \sqrt{2} = \sqrt{2}\times \left(4 + 3 + (-1)\right)
-1,423
-\frac{8}{3}\cdot 3/5 = ((-8)\cdot \frac13)/(5\cdot 1/3)
-2,886
7*\sqrt{2} = (5 + 4 + 2*\left(-1\right))*\sqrt{2}
808
\cos(x) = (e^{ix} + e^{-ix})/2 = \overline{\cos(x)} = \frac{1}{2}\left(e^{-ix} + e^{ix}\right)
20,064
(a - b)/(b*a) = -1/a + 1/b
29,492
4! \binom{5}{4}*4! = 5!*4!
-20,665
\frac33 \frac16(y + 9(-1)) = \frac{1}{18}(y*3 + 27 \left(-1\right))
-10,491
\dfrac{20}{z \cdot z\cdot 16} = 2/2\cdot \dfrac{10}{8\cdot z^2}
1,688
(x + (-1))*\left(x + 2*\left(-1\right)\right)*(x + 3*\left(-1\right)) = x^3 - 6*x^2 + x*11 + 6*(-1)
1,332
\tfrac{\tfrac{F'}{F}\cdot \frac{K}{F}}{K \cap F'/F} = K\cdot F'/F
22,322
4\cdot3/2=6
13,205
x + 4x = 1x + 4x = (1+4)x = 5x
5,313
1/2 + \tfrac{1}{3} + 1/3 = 7/6
-20,083
\frac{1}{4(-1) + z*4}\left(-14 z + 10 (-1)\right) = \frac122 \frac{5\left(-1\right) - 7z}{2(-1) + 2z}
26,714
|c| \cdot c/|c| = c
29,605
(2^d)^3 = 8^d
17,826
\sin(x + g + d) = \sin(d + g + x)
-15,507
\frac{1}{k^{20} \times (\dfrac{q}{k^4})^2} = \frac{1}{k^{20} \times \dfrac{1}{k^8} \times q^2}
9,579
5/27 = 6/27\cdot 5/6
-5,785
\frac{2}{20 + z \cdot 4} = \frac{1}{(5 + z) \cdot 4} \cdot 2
6,255
\sqrt{7}\cdot 2 = \sqrt{7} + \sqrt{2} + \sqrt{7} - \sqrt{2}
26,707
128 = (1 + 1) \cdot (1 + 1) \cdot (1 + 1) \cdot (3 + 1) \cdot (1 + 3)
-9,354
2*3*11 + x*11 = 11 x + 66
23,744
g\cdot p = g\cdot p\cdot g = p\cdot g
14,441
y^{b + c} = y^b*y^c
-1,560
\frac{9}{4} = \frac14 \cdot 9
-18,264
\tfrac{1}{(k + 6)\times k}\times (k + 6)\times (9\times \left(-1\right) + k) = \frac{54\times \left(-1\right) + k^2 - 3\times k}{k\times 6 + k^2}
15,028
((x - b)^2 + (-d + b)^2 + (-x + d)^2)/2 = -d*x + x^2 + b^2 + d^2 - b*x - b*d
8,916
14.5 = \cos{z} + 5 \implies 9.5 = \cos{z}
-13,377
2 + \frac{1}{8}72 = 2 + 9 = 2 + 9 = 11
274
\binom{1/2}{m} = \frac{1}{2 \cdot (\frac12 + \left(-1\right)) \cdot (\frac{1}{2} + 2 \cdot (-1)) \cdot \dots \cdot (1/2 - m + 1) \cdot m!}