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ddrg
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math_formulas

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-4,814
1.8/1000 = \dfrac{1}{1000}1.8
-25,510
\frac{d}{dx} (\frac{1}{2 + x} 4) = -\frac{1}{\left(2 + x\right)^2} 4
31,873
\cos{x} + \sin{x} = Y \cdot \sin(x + x_0) = Y \cdot \sin{x} \cdot \cos{x_0} + Y \cdot \cos{x} \cdot \sin{x_0}
23,589
\left(S + 2 \times (-1)\right) \times 2^n = 0 = (S + 1) \times (-1^n)
21,659
h\cdot h + g\cdot h + h\cdot g + g\cdot g = (h + g)^2
5,670
2\cdot b \cdot b - b\cdot 2 + (-1) = 0\Longrightarrow b = \frac12\cdot (1 \pm 3^{1/2})
12,437
(-1)^{1/n} = \left(e^{\pi\cdot i}\right)^{\frac{1}{n}} = e^{\pi\cdot i/n}
494
z^3 - \gamma^3 = (z^2 + \gamma\cdot z + \gamma^2)\cdot (z - \gamma)
-19,626
\frac{1}{3}*8/(7*1/5) = 5/7*\frac{8}{3}
34,091
\dfrac{x}{y} = 1/\left(\frac1x y\right)
-6,628
\frac{3}{5 \cdot (n + 4)} = \tfrac{3}{n \cdot 5 + 20}
7,356
z^4 \cdot 7 + 4 \cdot z^3 + z^2 \cdot 8 + 11 \cdot z - z^4 \cdot 7 - 3 \cdot z \cdot z \cdot 2 - 2 \cdot (z \cdot 5 + 2 \cdot z^3 + z \cdot z) = z
35,924
2*z*y^2*z*2 = y * y*z^2*4
20,821
a a - b b = (a - b) (a + b)
-1,810
-\frac{1}{6}\pi + \frac{\pi}{6} = 0
10,823
2100/9 = 700/3 = 699/3 + \frac13 = 233 + \dfrac{1}{3}
-742
(e^{\frac{11}{6} \times \pi \times i})^{11} = e^{\dfrac{1}{6} \times \pi \times 11 \times i \times 11}
-5,619
\frac{1}{(6\cdot (-1) + y)\cdot (y + 5)}\cdot 2 = \frac{2}{30\cdot \left(-1\right) + y^2 - y}
-20,978
\dfrac{15 - 12\times x}{-21\times x + 12} = 3/3\times \tfrac{-4\times x + 5}{-7\times x + 4}
-7,298
\frac27\cdot 0 = 0
-471
(e^{\frac{5}{12} \cdot \pi \cdot i})^{12} = e^{\dfrac{5}{12} \cdot \pi \cdot i \cdot 12}
13,388
(1 + l)^2 = 1 + l \cdot l + 2\cdot l
37,797
2 \cdot z + x - z = z + x
-20,953
\dfrac{64}{s\cdot 40}\cdot s = \frac{8}{5}\cdot s\cdot 8/(8\cdot s)
12,661
(b + c) a = ac + ba
19,325
(1/4)^2 + (1/2)^2 + (1/4) \cdot (1/4) = \frac{3}{8} = 0.375
-10,266
\frac{3}{3} (-\frac{4}{5x + 10}) = -\frac{12}{30 + 15 x}
-1,581
\dfrac{23}{12} \pi + \pi/6 = \pi \cdot 25/12
960
\dfrac{2101}{3125} = 1 - (\frac154)^5
6,398
\binom{2}{0}\times \binom{2}{1}\times \binom{4}{1} = 8
17,935
25 + 20 \cdot \left(-1\right) = 5
8,719
150 = 5!/(2!*3!) \binom{6}{4}
-12,344
\sqrt{7} \cdot 3 = \sqrt{63}
-9,269
y*y*2*2 + y*y*2*2*y = 4*y^2 + y^3*4
-21,059
2/4 = \frac48
-20,160
\dfrac{24}{-12 x + 36 (-1)} = \frac{6}{-x \cdot 3 + 9 (-1)} \frac{4}{4}
8,184
\frac{1}{p! \times \left(-p + n\right)!} \times n! = \binom{n}{p}
7,329
d^2*I_k + I_k*x^2 = I_k*(d^2 + x^2)
21,322
3 = 11 - 4k \Rightarrow 2 = k
14,844
27 + D \cdot 26 + x = 26 \cdot (1 + D) + x + 1
8,406
\left(\frac{y}{b}\right)^2 = (y/b)^2
-11,962
2/5 = s/\left(4\pi\right)*4\pi = s
14,209
\dfrac{2}{2^n} = \frac{1}{2^{n + \left(-1\right)}}
-22,288
(1 + r)\cdot \left(9 + r\right) = 9 + r^2 + 10\cdot r
-17,690
38\cdot \left(-1\right) + 56 = 18
8,694
z^{2^{n + 1}} = (z^{2^n})^2
20,345
y \cdot y - 2 \cdot y + 3 \cdot \left(-1\right) = (y + 1) \cdot (y + 3 \cdot (-1))
-20,745
\dfrac{1}{-8} \cdot (5 - 10 \cdot x) \cdot \dfrac{9}{9} = (-90 \cdot x + 45)/(-72)
3,693
10 = 4l \implies \frac52 = l
18,224
\left\lfloor{\frac{1}{4} \cdot (300/3 + 2)^2}\right\rfloor = 2601
-2,184
\frac{3}{11} - 2/11 = \frac{1}{11}
25,964
108124016 = \left(2002\cdot (-1) + 15504\right)\cdot (6006 + 2002)
4,981
{5 \choose 2} {5 \choose 3} = 100
42,468
2^4 + 3^2 = 5^2
8,888
(-1) + n^2 = \left(n + 1\right) \left(n + (-1)\right)
4,608
x - N + (-1) = x - N + 1
-12,593
3 = \dfrac{31.5}{10.5}
8,257
x \cdot x + x \cdot 2 - -7 \cdot x + x^2 = 9 \cdot x
-9,529
27 = 3\cdot 9
27,048
12/17\cdot 2/3 = \frac{8}{17}
12,228
x^2 + 2*y^2 + B^2 + 2*y^2 = x^2 + 4*y^2 + B^2
6,186
c^{\dfrac{1}{2}\cdot 3}/(\frac1c) = c^{3/2}\cdot c = c^{5/2}
-4,464
20 \cdot (-1) + Y^2 - Y = (Y + 4) \cdot (Y + 5 \cdot (-1))
1,747
\left(3 + n\right) \cdot (\left(-1\right) + n) = n \cdot n + n \cdot 2 + 3 \cdot \left(-1\right)
16,182
\sin(1 + m) = \sin(m) \cos\left(1\right) + \sin\left(1\right) \cos(m)
26,801
8315 = 21 \times 21 \times 5 \times 3 + 5^2 \times 21 \times 3 + 5^3
-555
\dfrac{1}{12} \pi = 169/12 \pi - \pi*14
33,703
1 = \sin(\theta) \implies \theta = \pi/2
31,822
-(m^2 + (-1)) + m^2 \cdot 2 = m^2 + 1
18,173
x^2 = ((-1) + x)^2 + x\cdot 2 + (-1)
34,442
\sqrt{-1 + \sqrt{2}\cdot 2} = \sqrt{2\cdot \sqrt{2} - 1}
29,746
\frac{1}{z^2}(C_1 + zC_2) = \frac{C_2}{z} + \frac{C_1}{z^2}
20,018
1/60 = \dfrac18\cdot (\dfrac13 - 1/5)
32,141
4\times 3! = 24
43,577
-3\cdot 4 + 48 = 36
-7,732
\left(40 + 16 \cdot i + 100 \cdot i + 40 \cdot (-1)\right)/29 = \tfrac{1}{29} \cdot (0 + 116 \cdot i) = 4 \cdot i
13,522
0 = Iy \Rightarrow I = 0\text{ or }y = 0
1,698
\sin(H + B) = \cos(B) \cdot \sin(H) + \sin(B) \cdot \cos(H)
15,111
( x, B*y*\Phi(f)) = ( x, y*B*\Phi(f))
1,936
\pi\cdot 3/2 + \cos{\dfrac{3}{2}\cdot \pi} = y + 1 \Rightarrow 2\cdot (-1) + \pi\cdot 3/2 = y
2,703
\left(z + 5 \cdot (-1) \geq 0 \Rightarrow z + 5 \cdot (-1) = 1\right) \Rightarrow z = 6
43,809
965 = 5 \cdot 193
12,661
ha + ag = a\cdot (g + h)
27,463
1260 = 2 \cdot 2\cdot 3 \cdot 3\cdot 5\cdot 7
1,052
(a + g)\times (a \times a - a\times g + g^2) = a^3 - a^2\times g + a\times g^2 + a \times a\times g - a\times g^2 + g^3 = a \times a \times a + g^3
8,149
2 + 2*z = 2*\left(z + 1\right)
37,383
P(x) = X^x\cdot B = B\cdot X^x
30,608
47 = 2*(-1) + (1 + 2*3) * (1 + 2*3)
-29,563
\dfrac{1}{z} \cdot (2 \cdot \left(-1\right) + 3 \cdot z^3 - z) = -2/z + \frac{3}{z} \cdot z^3 - z/z
30,849
2\cdot (-1) + n = -\left(3 + (-1)\right) + n
13,108
0 = T * T - \lambda * \lambda = \left(T - \lambda\right)*(T + \lambda) = (T - \lambda)*\left(T - -\lambda\right)
32,148
\infty + 2(-1) = \infty
5,993
\left(-x_0^{1/2} + x^{1/2}\right) (x_0^{1/2} + x^{1/2}) = x - x_0
-27,416
667 + 10 = 677
5,223
(a \times b)^2 = (b \times a)^2
-5,159
0.81\cdot 10^{6 + 2\cdot (-1)} = 0.81\cdot 10^4
31,498
(g \cdot g + a^2 + g\cdot a)\cdot 4 = \left(g + 2\cdot a\right)^2 + 3\cdot g^2
-10,630
\frac{25}{t\times 15} = 5/5\times \frac{5}{t\times 3}
-7,967
(-21 + 72 \cdot i + 28 \cdot i + 96)/25 = (75 + 100 \cdot i)/25 = 3 + 4 \cdot i
11,942
(A+B)x = 0 \implies Ax + Bx = 0