instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Simplify (((1*sqrt(120)*-1)/(sqrt(32)/(sqrt(4)*1)))/(1*sqrt(363)*5*1))**2.\n | 1/605\n | ibivibiv/math_instruct | |
What is 659520.6 rounded to the nearest one hundred?\n | 659500\n | ibivibiv/math_instruct | |
Let t = -492 + 492.3. Let n = 34 - 139/4. Let b = 0 + 2. Put b, n, t in decreasing order.\n | b, t, n\n | ibivibiv/math_instruct | |
Suppose 3*s - 2 + 5 = -4*t, -4*t + 3*s - 21 = 0. Let d be (-18)/(-15)*(-5)/(-2). Let z be (-2)/(-8)*d/2. Which is the third smallest value? (a) z (b) 2 (c) t\n | b\n | ibivibiv/math_instruct | |
Suppose 10 = 4*u - 3*u. What is the highest common divisor of u and 4?\n | 2\n | ibivibiv/math_instruct | |
Factor 20*n**3 + 55*n**2 - 5*n - 70.\n | 5*(n - 1)*(n + 2)*(4*n + 7)\n | ibivibiv/math_instruct | |
Simplify (sqrt(192) + 0 + 1 + 2 + (sqrt(192) - -1*sqrt(192)) + -3)**2 - 3*-4*(sqrt(432) + sqrt(432) + 0 + -4).\n | 288*sqrt(3) + 1680\n | ibivibiv/math_instruct | |
Let i(n) be the first derivative of -2*n**7/7 + 32*n**3/3 + 26. Find the third derivative of i(z) wrt z.\n | -240*z**3\n | ibivibiv/math_instruct | |
Let d = 5 - 2. Let k = -2 + 2. Suppose -d*i + k = 15. Let c(j) = -j**3 - 5*j**2 + 2*j + 6. Calculate c(i).\n | -4\n | ibivibiv/math_instruct | |
Convert 7249.868 hours to minutes.\n | 434992.08\n | ibivibiv/math_instruct | |
Let d(w) = -w - 1. Let c = 280 - 275. Calculate the smallest common multiple of d(-5) and 8*((-28)/(-8) + 4 - c).\n | 20\n | ibivibiv/math_instruct | |
Rearrange -4*q**3 + 30 - 2*q - 16 - 14 + 3*q**4 to k*q**3 + p*q**2 + l*q + a + o*q**4 and give l.\n | -2\n | ibivibiv/math_instruct | |
Collect the terms in 41*d**3 - 99*d**3 + 63*d**3.\n | 5*d**3\n | ibivibiv/math_instruct | |
Is 5261287 a prime number?\n | False\n | ibivibiv/math_instruct | |
Let u(k) = 2*k - 1. Let t(l) = 2*l**2 - 18*l. What is t(u(g))?\n | 8*g**2 - 44*g + 20\n | ibivibiv/math_instruct | |
Let j(s) = -s**3 - 6*s**2 - 4*s + 7. Let c(m) = -m**3 + 8*m**2 - 8*m + 1. Let h be c(7). Does 13 divide j(h)?\n | False\n | ibivibiv/math_instruct | |
Is 194 a factor of 80972?\n | False\n | ibivibiv/math_instruct | |
Let w(q) = -4*q - 6. Let i be w(-4). List the prime factors of (28/(-10))/((-2)/i).\n | 2, 7\n | ibivibiv/math_instruct | |
What is the first derivative of -4*n - 2*n**2 - 5 + n - n + 40 wrt n?\n | -4*n - 4\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"Vectors differentiation formulas for Dot and Box Product! how?
1. Feb 3, 2012
abrowaqas
Let A ,B and C represent vectors.
we have
1) d/dt (A . B) = A. dB/dt + dA/dt .B
2) d/dt [ A . (BxC) ] = A . (Bx dC/dt) + A . ( dB/dt... | The derivation of the formulas provided by the original poster involves vectors and their derivatives with respect to time, specifically focusing on the dot product and the box product (also known as the scalar triple product). Before delving into the explanation of these formulas and addressing the confusion regardin... | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 70 and 208460.\n | 208460\n | ibivibiv/math_instruct | |
Let u(o) = -o - 8. Let k be u(-10). Let f = k - 1. Let z = -2 + f. Let g(h) = -3*h**2 + h + 1. Determine g(z).\n | -3\n | ibivibiv/math_instruct | |
Solve 3*z + 2*d = 109, 5*z + 38*d - 2230 = -300*d - 75*d for z.\n | 33\n | ibivibiv/math_instruct | |
What is the seventh biggest value in 2/3, -4, -50, 1/5, -0.2, 3/4, 8460?\n | -50\n | ibivibiv/math_instruct | |
Which is the closest to 707? (a) 3 (b) 793 (c) 4\n | b\n | ibivibiv/math_instruct | |
Let i(p) = -56. Let r(k) = k - 16. Let y(t) = 2*i(t) - 7*r(t). Let q(d) = -d - 4*d + 4*d. Give y(q(w)).\n | 7*w\n | ibivibiv/math_instruct | |
Suppose -2*u - 12*a + 9*a - 5 = 0, 2*a = 2*u - 10. Let x be u/3*(-29 - 1). Let p = 13 - x. Is p a multiple of 33?\n | True\n | ibivibiv/math_instruct | |
How many minutes are there between 8:36 AM and 10:57 AM?\n | 141\n | ibivibiv/math_instruct | |
What is the eighth root of 77815080 to the nearest integer?\n | 10\n | ibivibiv/math_instruct | |
Solve -t**5/5 + 7*t**4/5 + 22*t**3/5 - 34*t**2/5 - 21*t/5 + 27/5 = 0 for t.\n | -3, -1, 1, 9\n | ibivibiv/math_instruct | |
What is -101 divided by 196?\n | -101/196\n | ibivibiv/math_instruct | |
What is the tens digit of 911877597?\n | 9\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {t: 15, d: 3}. Give prob of sequence dd.\n | 1/51\n | ibivibiv/math_instruct | |
What is 7293 to the power of 1/9, to the nearest integer?\n | 3\n | ibivibiv/math_instruct | |
Calculate -40 divided by -112490.\n | 4/11249\n | ibivibiv/math_instruct | |
Sort 1, -7, 13, -4, 2, 7 in increasing order.\n | -7, -4, 1, 2, 7, 13\n | ibivibiv/math_instruct | |
Let n = -182048601415 + 182048600656.99999547. Let k = n + 758. Round k to 7 decimal places.\n | -0.0000045\n | ibivibiv/math_instruct | |
What is the hundred thousands digit of 177936531?\n | 9\n | ibivibiv/math_instruct | |
Let g(k) = -11*k**2 + 2*k + 4. Let i(f) = f**2 + f + 1. Let v(w) = -g(w) + 3*i(w). List the prime factors of v(-2).\n | 53\n | ibivibiv/math_instruct | |
Is 16727708981 composite?\n | True\n | ibivibiv/math_instruct | |
Let y = -3088 - -3350. Which is the third smallest value? (a) y (b) 4 (c) 0.5\n | a\n | ibivibiv/math_instruct | |
Solve -65661*d = -64739*d - 14752 for d.\n | 16\n | ibivibiv/math_instruct | |
What are the prime factors of 5567?\n | 19, 293\n | ibivibiv/math_instruct | |
In base 11, what is 776792 + -13?\n | 77677a\n | ibivibiv/math_instruct | |
Expand (-17*m + 17*m - 2*m**2)*(-30 - 357 - 161 + 81 - 851)*(2*m - 3 + 3).\n | 5272*m**3\n | ibivibiv/math_instruct | |
Let d = -58 - -61. Solve 3*x + 0*x = -d for x.\n | -1\n | ibivibiv/math_instruct | |
What is 27 minutes before 12:34 AM?\n | 12:07 AM\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 44574518 and 188.\n | 94\n | ibivibiv/math_instruct | |
What is the eighth root of 1137341866 to the nearest integer?\n | 14\n | ibivibiv/math_instruct | |
b"What is the sth term of -23018, -46038, -69060, -92084, -115110, -138138?\n" | -s**2 - 23017*s\n | ibivibiv/math_instruct | |
Suppose 0 = 9*k - 8*k - 16. Let o be (-9)/2*4/(-6). Suppose o*x = 2*x + 5. Solve b = 3*n - b + 4, -n + x*b + k = 0 for n.\n | -4\n | ibivibiv/math_instruct | |
Let b(c) = 2*c**3 - 19*c**2 + 18*c - 21. Let r be b(9). Let s(v) = v**2 + 9. Let n be s(-9). What is the highest common factor of r and n?\n | 30\n | ibivibiv/math_instruct | |
Calculate the common denominator of -109/12 and 9.\n | 12\n | ibivibiv/math_instruct | |
Let a = 102 - 98. Suppose -2*d - 18 + 94 = -2*i, -4*d + 152 = i. Sort a, -4, d, -2.\n | -4, -2, a, d\n | ibivibiv/math_instruct | |
Let k(z) be the third derivative of 0*z + 7/30*z**5 + 0*z**4 + 0 + 30*z**2 + 1/6*z**3. List the prime factors of k(3).\n | 127\n | ibivibiv/math_instruct | |
Let u = -10 - -16. Let i = 94 + -94. Suppose i = u*l - 10*l + 12. Does 2 divide l?\n | False\n | ibivibiv/math_instruct | |
Calculate prob of sequence wdd when three letters picked without replacement from {d: 7, w: 1}.\n | 1/8\n | ibivibiv/math_instruct | |
-2 + 8 - (-15 + 26)\n | -5\n | ibivibiv/math_instruct | |
Collect the terms in -90*k**3 + 41*k + 92*k**3 - 41*k.\n | 2*k**3\n | ibivibiv/math_instruct | |
Sort 3, -3/7, 8762.734.\n | -3/7, 3, 8762.734\n | ibivibiv/math_instruct | |
What is c in -8/5*c + 0*c**3 - 3/5 - 6/5*c**2 + 1/5*c**4 = 0?\n | -1, 3\n | ibivibiv/math_instruct | |
Let s = 26 + -132/5. Let h = 2 + -1.6. Let z = -15.9 - -16. Sort s, z, h.\n | s, z, h\n | ibivibiv/math_instruct | |
Does 13 divide 5202?\n | False\n | ibivibiv/math_instruct | |
What are the prime factors of 507450?\n | 2, 3, 5, 17, 199\n | ibivibiv/math_instruct | |
Simplify (y**0*y*y)**(1/6)*(y*y**0*y)**(-10/9) assuming y is positive.\n | y**(-17/9)\n | ibivibiv/math_instruct | |
Solve 5 = 3209*v - 3212*v - 2*z, -2*v - 5*z - 29 = 0 for v.\n | 3\n | ibivibiv/math_instruct | |
Let f = 425 + -226. Let r = 282 - f. What is r rounded to the nearest 100?\n | 100\n | ibivibiv/math_instruct | |
Is (-13)/(39/(-612)) + -1 a composite number?\n | True\n | ibivibiv/math_instruct | |
Simplify sqrt(104)/(3*sqrt(8))*4.\n | 4*sqrt(13)/3\n | ibivibiv/math_instruct | |
What is the value of 1/(-2)*70/7?\n | -5\n | ibivibiv/math_instruct | |
In base 5, what is -1424344200 + -10?\n | -1424344210\n | ibivibiv/math_instruct | |
What is 8381.2 rounded to the nearest 100?\n | 8400\n | ibivibiv/math_instruct | |
Factor -4802*m**2/3 - 9408*m - 13824.\n | -2*(49*m + 144)**2/3\n | ibivibiv/math_instruct | |
Suppose -11*t - 1 = -10*t. Let c(i) = -44*i - 1. List the prime factors of c(t).\n | 43\n | ibivibiv/math_instruct | |
Collect the terms in -432 + 27*w + 432.\n | 27*w\n | ibivibiv/math_instruct | |
Let d(c) = 30*c + 68. Let w(a) = 30*a + 90. Calculate 4*d(l) - 3*w(l).\n | 30*l + 2\n | ibivibiv/math_instruct | |
Simplify (-6*(2*-6*(sqrt(153) - (2*sqrt(153) + -4)) + 0)*2)**2.\n | -497664*sqrt(17) + 3504384\n | ibivibiv/math_instruct | |
Let -2*z**5/3 + 69800*z**4 - 5479369414*z**3/3 - 87723734648*z**2/3 + 1826456472*z + 87723525248/3 = 0. Calculate z.\n | -16, -1, 1, 52358\n | ibivibiv/math_instruct | |
What is 2/10*(-8 + (-3 - -12))?\n | 1/5\n | ibivibiv/math_instruct | |
What are the prime factors of 337716?\n | 2, 3, 53, 59\n | ibivibiv/math_instruct | |
Calculate the highest common factor of 5136 and 72.\n | 24\n | ibivibiv/math_instruct | |
What is prob of sequence ka when two letters picked without replacement from jvkjvja?\n | 1/42\n | ibivibiv/math_instruct | |
Expand 6 - 6 + 5*d**5 + ((-5*d**2 + 0*d**2 + 4*d**2)*(0*d**2 - d**2 - d**2) + 0 + d**4 + 0)*(4*d - 2*d + d).\n | 14*d**5\n | ibivibiv/math_instruct | |
What is the smallest common multiple of 15525697 and 14114270?\n | 155256970\n | ibivibiv/math_instruct | |
Multiply -261928 and -1.\n | 261928\n | ibivibiv/math_instruct | |
Solve -475*w = -472*w - 3*z + 72, 5*z = -2*w + 92 for w.\n | -4\n | ibivibiv/math_instruct | |
Let v(w) = -7. Let x(q) = 29*q**2 - 3*q + 43. What is 6*v(t) + x(t)?\n | 29*t**2 - 3*t + 1\n | ibivibiv/math_instruct | |
Let k(m) = m**3 - 29*m**2 + 25*m - 723. Let d be k(29). Solve 27*s + 5*r + 1 = 30*s, -4*r - 14 = d*s for s.\n | -3\n | ibivibiv/math_instruct | |
Suppose 3*i - 14 = i. Suppose -5*t = -i*t + 20. What is the remainder when (-13)/(1 + (-12)/8) is divided by t?\n | 6\n | ibivibiv/math_instruct | |
Do -2188 and -2189 have different values?\n | True\n | ibivibiv/math_instruct | |
Which is the third biggest value? (a) 8078 (b) 0.4 (c) 97 (d) -2/13\n | b\n | ibivibiv/math_instruct | |
What is ((-14)/(-8))/(516054/(-160848))?\n | -6/11\n | ibivibiv/math_instruct | |
Calculate prob of sequence qfqc when four letters picked without replacement from {i: 1, f: 1, q: 2, p: 1, c: 2, d: 1}.\n | 1/420\n | ibivibiv/math_instruct | |
What is (-2 + 5 - (26 - 28)) + (4 - -4)?\n | 13\n | ibivibiv/math_instruct | |
Find the common denominator of 7/262576 and -49/68.\n | 4463792\n | ibivibiv/math_instruct | |
Which is smaller: 4/4061685 or 1?\n | 4/4061685\n | ibivibiv/math_instruct | |
Let l = 3.6066 - -16.9104. Let z = l - 20.6. Let h = -0.08299894 - z. What is h rounded to 7 dps?\n | 0.0000011\n | ibivibiv/math_instruct | |
Simplify 5*((3 + sqrt(288))**2 + sqrt(288))*2 + (sqrt(512) - (sqrt(512) + 0))**2*-4.\n | 840*sqrt(2) + 2970\n | ibivibiv/math_instruct | |
Divide -12 by 2.\n | -6\n | ibivibiv/math_instruct | |
What is the value of (-10 - (-8 + 1)) + -4?\n | -7\n | ibivibiv/math_instruct |
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