instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
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|---|---|---|---|
Suppose -2*i = 4*d - 8, 0 = 2*d + 4*i + 8 - 0. Suppose -g + 16 = g. What is the smallest common multiple of (2 - 1)/(2/d) and g?\n | 8\n | ibivibiv/math_instruct | |
What is 3944840680 to the power of 1/6, to the nearest integer?\n | 40\n | ibivibiv/math_instruct | |
Put -67139921, -5, 1/5, -0.1 in increasing order.\n | -67139921, -5, -0.1, 1/5\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 47993121 and 566.\n | 283\n | ibivibiv/math_instruct | |
In base 12, what is -1 + 7177a416?\n | 7177a415\n | ibivibiv/math_instruct | |
Factor -2*v**2/11 + 156*v/11 + 158/11.\n | -2*(v - 79)*(v + 1)/11\n | ibivibiv/math_instruct | |
What is the thousands digit of 3433?\n | 3\n | ibivibiv/math_instruct | |
Let x = -155 - -154. Let v(r) = -14*r + 20. Let s(q) = -5*q + 7. Let h(y) = 17*s(y) - 6*v(y). Let w(i) = -2*i**2 - 2*i - 3. Calculate x*w(b) + 3*h(b).\n | 2*b**2 - b\n | ibivibiv/math_instruct | |
Two letters picked without replacement from dddyddddddddd. Give prob of picking 1 y and 1 d.\n | 2/13\n | ibivibiv/math_instruct | |
b"What is the mth term of -16188, -16180, -16162, -16134, -16096?\n" | 5*m**2 - 7*m - 16186\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {j: 2, z: 1}. What is prob of sequence jj?\n | 1/3\n | ibivibiv/math_instruct | |
Rearrange (4 - 1 + 0)*(445 + 465 - 713 + 2*j) to w*j + f and give f.\n | 591\n | ibivibiv/math_instruct | |
What is the square root of 233204 to the nearest integer?\n | 483\n | ibivibiv/math_instruct | |
Let r(x) = x. Let t(h) = 66*h**2 + 88*h**2 - 2*h - 156*h**2. Let b(m) = -m - 1. Let q be b(5). Let z(y) = -y**2 - 7*y - 7. Let u be z(q). Give u*t(d) - 2*r(d).\n | 2*d**2\n | ibivibiv/math_instruct | |
Let i be (1*-2 - -4) + -2. Let j(o) be the second derivative of o**3/6 + 13*o**2/2 + 4*o. Let s be j(-9). Solve -5*k - 20 = 5*r, i*r = -2*r + s*k - 2 for r.\n | -3\n | ibivibiv/math_instruct | |
What is -0.0481330704 rounded to 3 dps?\n | -0.048\n | ibivibiv/math_instruct | |
Solve 3*m**3 + 78*m**2 + 147*m + 72 = 0 for m.\n | -24, -1\n | ibivibiv/math_instruct | |
Let o = -16 + 38. Let z = -7 + o. What is the remainder when 29 is divided by z?\n | 14\n | ibivibiv/math_instruct | |
What is the highest common factor of 826 and 218418?\n | 118\n | ibivibiv/math_instruct | |
Let c(h) = -3*h**2 + 11*h. Let o(u) = -14*u**2 + 61*u + 4. Let n(f) = 5*c(f) - o(f). Let d = -14 - -7. Calculate n(d).\n | -11\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"(arrows stand for vectors)
a) Find the T→ N B frame.
b) At the point ((√2)/4, (2)/4π) find the equations of the Osculating, Normal, and Rectifying planes.
c) Also at the point ((√2)/4, (2)/4π) find the equation (as a vecto... | We begin by defining some terms and establishing the necessary background information. A curve in three-dimensional space can be represented by a vector-valued function $\vec{r}(t)$, and its derivative $\vec{r}'(t)$ represents the tangent vector to the curve at the point $ \vec{r}(t)$. The unit tangent vector $\vec{T}... | ibivibiv/math_instruct | |
Which is the nearest to 7? (a) 0 (b) 13/4 (c) 7.5 (d) 4 (e) -5\n | c\n | ibivibiv/math_instruct | |
Sort 44, -0.2, 0.3, 67/3, -1 in increasing order.\n | -1, -0.2, 0.3, 67/3, 44\n | ibivibiv/math_instruct | |
Which is the second biggest value? (a) 0.5 (b) 3 (c) 3/5 (d) 3.3 (e) -0.3\n | b\n | ibivibiv/math_instruct | |
What is 5 + -6 - (-1 + 6 - 7)?\n | 1\n | ibivibiv/math_instruct | |
Expand (-5*f + 4*f + 3*f)*(5*f - 3*f + 0*f + 6*f).\n | 16*f**2\n | ibivibiv/math_instruct | |
Is 6397 a factor of 937749956?\n | False\n | ibivibiv/math_instruct | |
0 + 0.3245\n | 0.3245\n | ibivibiv/math_instruct | |
b"What is the zth term of -6294, -6605, -6916, -7227?\n" | -311*z - 5983\n | ibivibiv/math_instruct | |
Suppose -f - 1 = -5*a + 300, -2*a + 4*f = -124. Let v = 485 + a. Is 20 a factor of v?\n | False\n | ibivibiv/math_instruct | |
How many minutes are there between 3:35 AM and 5:18 AM?\n | 103\n | ibivibiv/math_instruct | |
What is the result of the following expression?
91.409 % (45.044 * 54.074) | 91.4090 | ibivibiv/math_instruct | |
Let b = 2058621770412084 + -3847564307252001871/1869. Let o = b - -116828158. Let a = -2/267 + o. What is the common denominator of a and -39?\n | 7\n | ibivibiv/math_instruct | |
Simplify 5 + (((-1*sqrt(84) - sqrt(84))*4)/(sqrt(36)/sqrt(3)*1) - (((sqrt(189) - sqrt(21)) + sqrt(21))*4)/(sqrt(3) - -3*-2*sqrt(3)))*5.\n | -28*sqrt(7) + 5\n | ibivibiv/math_instruct | |
How many millilitres are there in 3.651098 litres?\n | 3651.098\n | ibivibiv/math_instruct | |
What comes next: -3200, -6321, -9442, -12563, -15684?\n | -18805\n | ibivibiv/math_instruct | |
b"What is the fth term of 277, 304, 353, 424, 517, 632?\n" | 11*f**2 - 6*f + 272\n | ibivibiv/math_instruct | |
Collect the terms in -281*q**2 - 172*q**2 - 267 + 259.\n | -453*q**2 - 8\n | ibivibiv/math_instruct | |
Is -19921 greater than -19899?\n | False\n | ibivibiv/math_instruct | |
What is the units digit of 56852740?\n | 0\n | ibivibiv/math_instruct | |
Rearrange 1 + 151*d**2 - 94*d + 30*d + 0 + 30*d - 2*d**3 + 32*d to the form t*d**3 + a*d**2 + q*d + k and give q.\n | -2\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 4085 and 665.\n | 95\n | ibivibiv/math_instruct | |
Let l(m) = -195*m + 1367. Let s be l(7). Let g(c) be the first derivative of 0*c**s + 2*c**4 + 13 + 0*c + 2/5*c**5 + 8/3*c**3. Factor g(h).\n | 2*h**2*(h + 2)**2\n | ibivibiv/math_instruct | |
Does 187 divide 1164?\n | False\n | ibivibiv/math_instruct | |
Let q = 1189 + -1188. Which is the nearest to -3? (a) 5 (b) -4/5 (c) q\n | b\n | ibivibiv/math_instruct | |
Let q(r) = -3 - 2*r**2 - 6*r + 2*r**2 - r**2. Let x be q(-5). What is the second derivative of x*o + o - 2*o + o**5 wrt o?\n | 20*o**3\n | ibivibiv/math_instruct | |
What is the highest common factor of 506 and 12190?\n | 46\n | ibivibiv/math_instruct | |
Let i be -3*3/((-27)/84). Let q be i/(-30) - 8/20. Suppose 5*n + 0*n - 5*c = 50, 3*n = 5*c + 40. What is the second biggest value in q, -2/7, n?\n | -2/7\n | ibivibiv/math_instruct | |
What is the tens digit of 4380623?\n | 2\n | ibivibiv/math_instruct | |
List the prime factors of 274677071.\n | 47, 5844193\n | ibivibiv/math_instruct | |
Calculate -3 - (0 + 2) - (14 - 12).\n | -7\n | ibivibiv/math_instruct | |
List the prime factors of 32/16 + (-3)/((-6)/374).\n | 3, 7\n | ibivibiv/math_instruct | |
What is -43 divided by 43?\n | -1\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 1546 and 231290876?\n | 1546\n | ibivibiv/math_instruct | |
Evaluate (-7 - -12) + -5 + -13 + 7 + 1.\n | -5\n | ibivibiv/math_instruct | |
Convert -20 (base 5) to base 2.\n | -1010\n | ibivibiv/math_instruct | |
Suppose -4*h**3 + 31972*h**2 - 29934120*h = 0. Calculate h.\n | 0, 1083, 6910\n | ibivibiv/math_instruct | |
Let k(b) = -5059*b - 94 + 5092*b - b**2 - 22. Let o be k(4). Solve -6*g**4 + o + 16/7*g**2 - 250/7*g**3 + 24/7*g = 0 for g.\n | -6, -2/7, 0, 1/3\n | ibivibiv/math_instruct | |
What is 22.8177999 milliseconds in weeks?\n | 0.00000003772784375\n | ibivibiv/math_instruct | |
What is 162.46 rounded to the nearest one hundred?\n | 200\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 576 and 20088?\n | 72\n | ibivibiv/math_instruct | |
b"What is the vth term of 107400571, 107400570, 107400569?\n" | -v + 107400572\n | ibivibiv/math_instruct | |
Let x(v) = -v**3 - 19*v**2 - 24*v + 24. Let a(j) = 3*j**2 - 38*j + 6. Let h be a(12). Is x(h) a multiple of 12?\n | True\n | ibivibiv/math_instruct | |
Let k = 125 + -124. Let a = -2 + 1.5. What is the closest to -1 in 1/2, a, k?\n | a\n | ibivibiv/math_instruct | |
How many minutes are there between 10:19 PM and 4:03 AM?\n | 344\n | ibivibiv/math_instruct | |
What is the second biggest value in -0.1, -1, -0.29?\n | -0.29\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# uniform and pointwise convergence of $\sum_{n=1}^{+\infty} (x+1)^n \log(1+n^x)$
I study first the pointwise convergence :
1) if $$x=0$$ $$\sum_{n=1}^{+\infty} \log(2)$$ diverges
2) if $$x>0$$ using ratio test the series ... | Now let us examine the case when $x < -2.$ Recall our earlier result that $|x+1|^n \log(1+n^x) \sim_{+\infty} |x+1| n^x.$ When $x < -2,$ we have $|x+1| = (-x - 1) = \alpha$ for some $\alpha > 1.$ Thus, it suffices to analyze the behavior of the series $\sum \alpha^n \log(1+n^x).$
We proceed by finding a lower bound f... | ibivibiv/math_instruct | |
Let j(c) = 4625*c**3 + 12*c**2 - 4. Let b(g) = 144262999*g**3 + 374301*g**2 - 124767. Calculate 4*b(r) - 124767*j(r).\n | 4621*r**3\n | ibivibiv/math_instruct | |
What is the nearest to 0.1 in 1, -4324, -3/7, -0.2?\n | -0.2\n | ibivibiv/math_instruct | |
Calculate -24 + 1 + -5 + (-49 + 6 - -45).\n | -26\n | ibivibiv/math_instruct | |
Let h be (-22762)/(-570) + (-1)/(-15). Suppose -83*t = -73*t + h. Let z be 3/7*2/3. Which is the closest to 0? (a) -7 (b) z (c) t\n | b\n | ibivibiv/math_instruct | |
Solve 3*t - 1 - 11 = 0 for t.\n | 4\n | ibivibiv/math_instruct | |
Solve -r - 2*z - 525 = -520, 0 = 5*r + 2*z + 17 for r.\n | -3\n | ibivibiv/math_instruct | |
Let u = 0.03 + 2.97. Let b = -3.05 + u. Let a = b + -0.05. What is the second smallest value in a, 1/5, 5?\n | 1/5\n | ibivibiv/math_instruct | |
Solve 2*p + 5458*m + 66 = 5463*m, -2*m + 30 = -2*p for p.\n | -3\n | ibivibiv/math_instruct | |
What is 78454.9mm in nanometers?\n | 78454900000\n | ibivibiv/math_instruct | |
b"What is the gth term of -48432, -46588, -44744, -42900, -41056?\n" | 1844*g - 50276\n | ibivibiv/math_instruct | |
Let i = -10 + 10. Suppose 0 = u - i*u - 12. Solve -x + u = -3*f, 2*x + 4 + 2 = 0 for f.\n | -5\n | ibivibiv/math_instruct | |
Express 633*k**3 + 2*k**4 - 9 - 2*k - 323*k**3 - 309*k**3 + 4*k**2 as o*k**3 + d*k + q*k**2 + m + x*k**4 and give q.\n | 4\n | ibivibiv/math_instruct | |
What is the cube root of 511214551 to the nearest integer?\n | 800\n | ibivibiv/math_instruct | |
Simplify ((w/w**(-16))/(w/w**(-1/23)))/(w**(1/11)*w/(w*w*w/w**(5/4))) assuming w is positive.\n | w**(16815/1012)\n | ibivibiv/math_instruct | |
What is the next term in 3509, 4602, 5695, 6788, 7881, 8974?\n | 10067\n | ibivibiv/math_instruct | |
Let a(z) = 11 + 12 - 15 + 46*z + 28. What is the units digit of a(8)?\n | 4\n | ibivibiv/math_instruct | |
Calculate 3088874.69 - 14.1669.\n | 3088860.5231\n | ibivibiv/math_instruct | |
Divide 24 by 76.\n | 6/19\n | ibivibiv/math_instruct | |
Let q(r) be the second derivative of -277*r**7/21 + 185*r**4/12 - 2*r**2 - 170*r. Find the third derivative of q(h) wrt h.\n | -33240*h**2\n | ibivibiv/math_instruct | |
Let c = -41693/16 - -2606. Is 1/17 greater than or equal to c?\n | False\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 140 + 9/((-36)/(-16)) and 3760.\n | 33840\n | ibivibiv/math_instruct | |
Calculate the lowest common multiple of 33 and 2 + 62 - 2 - (-17)/17.\n | 693\n | ibivibiv/math_instruct | |
Is 437442223 a composite number?\n | True\n | ibivibiv/math_instruct | |
Put together 3527666 and 0.9.\n | 3527666.9\n | ibivibiv/math_instruct | |
What is 2/125 of a litre in millilitres?\n | 16\n | ibivibiv/math_instruct | |
Solve 2*l = 3*p - 33, -1923*p = -3*l - 1919*p - 45 for l.\n | -3\n | ibivibiv/math_instruct | |
Let a be 1059*-1 - (8 - 8). Let n be 2/5 - a/15. Let z = -50 + n. Is z composite?\n | True\n | ibivibiv/math_instruct | |
Sort 70, 1/6, 412 in decreasing order.\n | 412, 70, 1/6\n | ibivibiv/math_instruct | |
Let r(a) = -2*a + 2. What is the remainder when 27 is divided by r(-6)?\n | 13\n | ibivibiv/math_instruct | |
List the prime factors of 40969346.\n | 2, 11, 1862243\n | ibivibiv/math_instruct | |
Let u(c) = 18*c**2 + 4*c + 5. Determine u(-1).\n | 19\n | ibivibiv/math_instruct | |
Subtract 25084 from -10954258.\n | -10979342\n | ibivibiv/math_instruct | |
b"What is the hth term of -82, -345, -770, -1345, -2058?\n" | 2*h**3 - 93*h**2 + 2*h + 7\n | ibivibiv/math_instruct |
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