instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
What is the closest to -2/3 in -58194, -5, 3?\n | 3\n | ibivibiv/math_instruct | |
What is the result of the following expression?
-11.4927 - (89.5395 % 66.1273) | -34.9049 | ibivibiv/math_instruct | |
Rearrange 6*r - 4 - 4 - 2*r**3 + 6 - r**2 - r to o*r**3 + u*r**2 + w*r + p and give w.\n | 5\n | ibivibiv/math_instruct | |
Expand 0*a**4 - 3*a**4 + 0*a**4 + (7*a**2 + 158*a**2 + 435*a**2)*(-a**2 + 6*a**2 - 3*a**2) - a**4 - 4*a**3 + 4*a**3.\n | 1196*a**4\n | ibivibiv/math_instruct | |
Find the first derivative of 52249*o**2 - 24496.\n | 104498*o\n | ibivibiv/math_instruct | |
Let p = 50 + -41.9. Let i = p + -8. Let f = 23 + -29. Are f and i nonequal?\n | True\n | ibivibiv/math_instruct | |
Let t be -1*(4 + 18/6). Let z = 2 - 6. Sort -1, z, t in descending order.\n | -1, z, t\n | ibivibiv/math_instruct | |
What is the common denominator of 86/135 and 82/45?\n | 135\n | ibivibiv/math_instruct | |
How many minutes are there between 9:54 PM and 11:24 PM?\n | 90\n | ibivibiv/math_instruct | |
What is -11442755 minus -4?\n | -11442751\n | ibivibiv/math_instruct | |
(2/(-4))/((1/10)/1)\n | -5\n | ibivibiv/math_instruct | |
What is the units digit of 8684?\n | 4\n | ibivibiv/math_instruct | |
Is 27245180977 a prime number?\n | False\n | ibivibiv/math_instruct | |
Let b(t) = -t**3 - 3*t**2 + 3*t - 1. Let j be b(-5). What is the derivative of 34*g**2 - j*g**2 - 1 - 2*g**3 wrt g?\n | -6*g**2\n | ibivibiv/math_instruct | |
What are the prime factors of 353?\n | 353\n | ibivibiv/math_instruct | |
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"# What are the contributions by heron in the field of mathematics?
• -21
Not much good
• -21
Here are some of the books that he wrote:
Baroulkos
Berlopoeica (in Greek and Roman Artillery, Technical Treatises, 1971)
Catopt... | Heron of Alexandria was a renowned mathematician, engineer, and inventor who lived during the 1st century AD in ancient Greece. He made significant contributions to various fields, including geometry, physics, pneumatics, and mechanics. This piece will delve into the mathematical works of Heron, highlighting the impor... | ibivibiv/math_instruct | |
Express 2 + 2*t**2 - 4 - 6*t**3 + 0 + 1 as g + l*t**2 + c*t**3 + w*t and give c.\n | -6\n | ibivibiv/math_instruct | |
Let x(t) = -t - 2. Let i be x(2). Let n(g) = g**3 + 4*g**2 - g + 1. Give n(i).\n | 5\n | ibivibiv/math_instruct | |
What is the closest to -0.7 in 20.3, 1/8, 6?\n | 1/8\n | ibivibiv/math_instruct | |
What is 6.106748t in milligrams?\n | 6106748000\n | ibivibiv/math_instruct | |
Find the second derivative of -1954208*v**2 - 7287*v + 34.\n | -3908416\n | ibivibiv/math_instruct | |
What is 3/25 of a millennium in months?\n | 1440\n | ibivibiv/math_instruct | |
What is 13367 to the power of 1/2, to the nearest integer?\n | 116\n | ibivibiv/math_instruct | |
Collect the terms in -372*o**2 + 3300*o + 372*o**2 + 1 - 286*o**3 - 3300*o.\n | -286*o**3 + 1\n | ibivibiv/math_instruct | |
Simplify sqrt(240)/(sqrt(30)/sqrt(6)).\n | 4*sqrt(3)\n | ibivibiv/math_instruct | |
Find the second derivative of -l**3 - 1484*l**2*z - 2*l**2 + l*z + 3580*l wrt l.\n | -6*l - 2968*z - 4\n | ibivibiv/math_instruct | |
What is (9/(-135)*-42)/(7/(-35))?\n | -14\n | ibivibiv/math_instruct | |
Calculate prob of sequence zz when two letters picked without replacement from zzzgwmwz.\n | 3/14\n | ibivibiv/math_instruct | |
Calculate (((-7)/(28/80))/(3048/(-381)))/(5/16).\n | 8\n | ibivibiv/math_instruct | |
Two letters picked without replacement from {a: 4, j: 2, p: 2}. What is prob of picking 2 p?\n | 1/28\n | ibivibiv/math_instruct | |
Is 33 a factor of 222321?\n | True\n | ibivibiv/math_instruct | |
Two letters picked without replacement from pklwqwwpkkppwplp. What is prob of sequence kk?\n | 1/40\n | ibivibiv/math_instruct | |
Let o be 16/6 + 3*(-2)/9. Find the second derivative of 6*m**o - 9*m**2 - 13*m**2 - 27*m wrt m.\n | -32\n | ibivibiv/math_instruct | |
Two letters picked without replacement from kkkt. Give prob of sequence kk.\n | 1/2\n | ibivibiv/math_instruct | |
Solve 1507*s = 57806 + 5488 for s.\n | 42\n | ibivibiv/math_instruct | |
42495 divided by -14165\n | -3\n | ibivibiv/math_instruct | |
Simplify ((r*r**(3/4))/r**(-11))**(-48)*((r*r**2)**(-13/6))**(-43) assuming r is positive.\n | r**(-665/2)\n | ibivibiv/math_instruct | |
Find the third derivative of 8728*u**3 - 29182*u**2 - 11*u.\n | 52368\n | ibivibiv/math_instruct | |
Suppose -65 = -3*s - 8. Let y = s - 22. Calculate the common denominator of 13/3 and (-4)/(-12)*y + 35/(-24).\n | 24\n | ibivibiv/math_instruct | |
Find the second derivative of -465*i**2*u**3 + 3*i*u**3 + 60*i*u**2 - i wrt i.\n | -930*u**3\n | ibivibiv/math_instruct | |
Let k = -16242.7299799 + 16227.4853699422. Let s = k - -0.2446098678. Let i = 15 + s. What is i rounded to 7 decimal places?\n | -0.0000001\n | ibivibiv/math_instruct | |
Let w(i) = -i**3 - 8*i**2 + 7*i - 5. Give w(-8).\n | -61\n | ibivibiv/math_instruct | |
Let x = -943/5 + 188. Let u = -0.13 - -4.13. Which is the third biggest value? (a) -1 (b) x (c) u\n | a\n | ibivibiv/math_instruct | |
Collect the terms in -2*y**3 + 18*y**3 - 44*y**3.\n | -28*y**3\n | ibivibiv/math_instruct | |
Evaluate (-5)/(-2*4/8).\n | 5\n | ibivibiv/math_instruct | |
Subtract 140252 from 116633964.\n | 116493712\n | ibivibiv/math_instruct | |
Is 2075719 prime?\n | False\n | ibivibiv/math_instruct | |
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"# Differentiating a Vector and a Matrix w.r.t. a Vector [Matrix Calculus]
I am studying matrix calculus for linear regression and machine learning and I would like to know exactly if the following calculations are correct:
... | Now, let's dive deeper into the concept of differentiating vectors and matrices with respect to a vector. This topic is crucial in various fields such as machine learning, physics, engineering, and more. Specifically, in linear regression and machine learning, this skill allows us to optimize models by finding gradien... | ibivibiv/math_instruct | |
Collect the terms in 2*j**3 + 277*j + 285*j - 838*j + 276*j.\n | 2*j**3\n | ibivibiv/math_instruct | |
Let u(o) = -3*o**2 + o. Let w(k) = 19*k**2 - 3*k + 25. Let j(t) = 6*u(t) + w(t). Is j(6) a composite number?\n | False\n | ibivibiv/math_instruct | |
What is 0.1 + -4494?\n | -4493.9\n | ibivibiv/math_instruct | |
Suppose 0 = -2*a + a + 180. Suppose -3*s - 2*s + a = 0. Suppose -5*r + s = -44. What is the remainder when r is divided by 6?\n | 4\n | ibivibiv/math_instruct | |
Rearrange (-62*i**2 + 62*i**2 - 9*i**3)*(-3*i - i + 3*i) - 2*i**2 - i**4 + 2*i**4 - 4*i**2 to g*i + h*i**3 + y*i**2 + t + l*i**4 and give y.\n | -6\n | ibivibiv/math_instruct | |
Let y(m) = -m + 3. Let w(l) = -6*l. Calculate w(y(a)).\n | 6*a - 18\n | ibivibiv/math_instruct | |
Calculate the remainder when 478737 is divided by 412.\n | 405\n | ibivibiv/math_instruct | |
Suppose f + p - 1 + 2 = 0, 0 = -f + 2*p - 4. Let y be (6/(-4))/((-1)/f). Is 2 - -1*(2 - y) composite?\n | False\n | ibivibiv/math_instruct | |
Calculate the highest common factor of 188 and 7541056.\n | 188\n | ibivibiv/math_instruct | |
Let w = -6462 - -6464. Let n be (3/6)/(2/12). Suppose -d + 3*k = -23, n*d - k = -0*d + 61. Calculate the least common multiple of d and w.\n | 20\n | ibivibiv/math_instruct | |
Solve -2*v + 69*l - 57*l = -164, 2*v + 9 - 30 = l for v.\n | 4\n | ibivibiv/math_instruct | |
Let s = -17 - -27. Let a(o) = 50 - 3*o - s + 5 + 2*o. What is the tens digit of a(0)?\n | 4\n | ibivibiv/math_instruct | |
Calculate the lowest common multiple of 121 and 55.\n | 605\n | ibivibiv/math_instruct | |
What is 195.6789 weeks in milliseconds?\n | 118346598720\n | ibivibiv/math_instruct | |
Which is smaller: 26875 or 26877?\n | 26875\n | ibivibiv/math_instruct | |
Calculate -12 + 10 + 1 + -7 + 5 - -9.\n | 6\n | ibivibiv/math_instruct | |
Simplify (4*sqrt(32)/sqrt(4))/(2*sqrt(196)) + 5*(sqrt(20) + sqrt(80)*1)/sqrt(10).\n | 107*sqrt(2)/7\n | ibivibiv/math_instruct | |
What is 1.378 + -6630552?\n | -6630550.622\n | ibivibiv/math_instruct | |
Sort -5, 3, 1.2 in decreasing order.\n | 3, 1.2, -5\n | ibivibiv/math_instruct | |
Evaluate (4/(-6))/(22/66).\n | -2\n | ibivibiv/math_instruct | |
Sort 4, -1, 95295 in increasing order.\n | -1, 4, 95295\n | ibivibiv/math_instruct | |
In base 3, what is 1101001212101 + -20102?\n | 1101001121222\n | ibivibiv/math_instruct | |
Let t(q) = -40*q - 243. Let n = 305 + -314. Let k be t(n). Calculate the highest common factor of k and 195.\n | 39\n | ibivibiv/math_instruct | |
Which is the smallest value? (a) -513/13855 (b) 0.5 (c) -1\n | c\n | ibivibiv/math_instruct | |
38*2.1\n | 79.8\n | ibivibiv/math_instruct | |
Express (-b + 3*b - 4*b)*(-16*b - 23*b + 93*b) as r*b + x*b**2 + g and give x.\n | -108\n | ibivibiv/math_instruct | |
How many minutes are there between 8:58 PM and 8:40 AM?\n | 702\n | ibivibiv/math_instruct | |
Suppose 13*y - 22*y = -36. Let v(q) be the first derivative of 2*q - 1 + 0*q**2 + 9/4*q**y + 0*q**3. Differentiate v(k) with respect to k.\n | 27*k**2\n | ibivibiv/math_instruct | |
Let l(h) = -55*h**3 + 29*h**2 - h - 10. Let i(t) = -47*t**3 + 28*t**2 - t - 12. Let d(j) = -7*i(j) + 6*l(j). Give d(-22).\n | 2\n | ibivibiv/math_instruct | |
Let d = 19 + -10. Suppose -5*g + 1 = -d. Suppose 4*y + 3*q - 17 - 11 = 0, g*q - 12 = -y. What is the smallest common multiple of y and 2?\n | 4\n | ibivibiv/math_instruct | |
Let w(u) = u**2 + 2*u + 4. Suppose a - 20 + 54 = 5*v, -4*v = 3*a - 31. Is w(v) a composite number?\n | False\n | ibivibiv/math_instruct | |
Divide -20714112 by -64.\n | 323658\n | ibivibiv/math_instruct | |
Work out -63930 + -3.1.\n | -63933.1\n | ibivibiv/math_instruct | |
What is the value of (-17 - (-17 + -4)) + 8 + -7 + 26?\n | 31\n | ibivibiv/math_instruct | |
b"What is the th term of 18370, 73466, 165292, 293848?\n" | 18365*b**2 + b + 4\n | ibivibiv/math_instruct | |
Let n(l) = 4*l**3 - 5*l**2 - 8*l + 3. List the prime factors of n(5).\n | 2, 13\n | ibivibiv/math_instruct | |
What is 11286 to the power of 1/10, to the nearest integer?\n | 3\n | ibivibiv/math_instruct | |
Let o = 5161 - 5155. Solve -o*r = -35*r + 58 for r.\n | 2\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(-94.6079 + -14.3754) + 45.3745 | -63.6088 | ibivibiv/math_instruct | |
Simplify (sqrt(405) + 1)**2*-2*5 + 6*(sqrt(180) + (sqrt(180) - ((sqrt(180) - (3 + sqrt(180)*-2)**2) + sqrt(180))) + sqrt(180)).\n | -576*sqrt(5) + 314\n | ibivibiv/math_instruct | |
Let v(b) be the first derivative of 2*b**3 + 21*b**2 + 9*b - 127. What are the prime factors of v(-10)?\n | 3, 7\n | ibivibiv/math_instruct | |
Suppose 0*c - 3*c - 621 = 0. Let g = 406 + c. Is g composite?\n | False\n | ibivibiv/math_instruct | |
Round -22538.81107 to the nearest 100.\n | -22500\n | ibivibiv/math_instruct | |
Let t(i) = 6*i**2. Let c = -17 - -10. Let s = c + 7. Let f(p) = -p**2 - p**2 + s*p**2. Determine t(f(v)).\n | 24*v**4\n | ibivibiv/math_instruct | |
Calculate the remainder when 56453 is divided by 731.\n | 166\n | ibivibiv/math_instruct | |
Suppose 0 = 3*v + 313 - 1861. What are the prime factors of v?\n | 2, 3, 43\n | ibivibiv/math_instruct | |
Let c be 60/8 + 2/4. Let z(n) = -n**3 + 36*n**2 - 2*n + 80. Let m be 36*(8/32)/((-3)/(-12)). Let w be z(m). Calculate the greatest common divisor of w and c.\n | 8\n | ibivibiv/math_instruct | |
Let p(f) = -39*f + 120. Let v be p(3). Solve -v*d = 4*c - 35, 4*c - 30 = -d - c for d.\n | 5\n | ibivibiv/math_instruct | |
Let s = 7405 + -5312. Calculate the smallest common multiple of 2 and s.\n | 4186\n | ibivibiv/math_instruct | |
Simplify (4*(sqrt(144) - sqrt(36)))/((sqrt(18)*-2 + sqrt(2))*5).\n | -12*sqrt(2)/25\n | ibivibiv/math_instruct | |
Let k = -1 - 2. Let x(n) = -5*n - 2. What is the tens digit of x(k)?\n | 1\n | ibivibiv/math_instruct | |
Let l be 2 + 2 + 4 + -4. Factor 3*y**2 + 11*y**l - 12*y**4 + y**3 - 3*y**2.\n | -y**3*(y - 1)\n | ibivibiv/math_instruct |
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