instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
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|---|---|---|---|
Let z(x) = 2*x**3 - 9*x**2 + 7*x + 6. Let f = -735 - -739. Suppose f*r + 720 = 44*r. Calculate the least common multiple of z(6) and r.\n | 468\n | ibivibiv/math_instruct | |
How many micrometers are there in 99540.15nm?\n | 99.54015\n | ibivibiv/math_instruct | |
b"What is the oth term of 8016, 40711, 95196, 171465, 269512, 389331, 530916?\n" | -o**3 + 10901*o**2 - o - 2883\n | ibivibiv/math_instruct | |
Suppose 2 = 3*k - 1, c - k = 7. Let w = 5 - 0. Suppose w*r - 468 + 188 = 0. What is the greatest common divisor of r and c?\n | 8\n | ibivibiv/math_instruct | |
Find the common denominator of -197/13880040 and 127/12840.\n | 13880040\n | ibivibiv/math_instruct | |
Let t be 20/30 + 68/(-93). What is the third smallest value in -0.4, 1, t?\n | 1\n | ibivibiv/math_instruct | |
Solve -121*w + 114*w + 282*w = 14025 for w.\n | 51\n | ibivibiv/math_instruct | |
Solve 1 = 3*n + 2*d + 8, d + 4 = 2 for n.\n | -1\n | ibivibiv/math_instruct | |
Put 4/5, -25/7, -5, 1, 0, 3 in descending order.\n | 3, 1, 4/5, 0, -25/7, -5\n | ibivibiv/math_instruct | |
Let f be ((-8)/(-78))/(4/(-6)). Suppose -2*m = -b - 1, 1015*b = 1014*b - 5*m + 20. Sort -4, -1, f, b.\n | -4, -1, f, b\n | ibivibiv/math_instruct | |
What is the millions digit of 151106820?\n | 1\n | ibivibiv/math_instruct | |
Find r, given that 2*r**5/7 + 104*r**4/7 - 1704*r**3/7 + 1312*r**2 - 20864*r/7 + 16896/7 = 0.\n | -66, 2, 4\n | ibivibiv/math_instruct | |
Let g be (-1)/(-1) + 5 + 0. Let w = 2592 - 2592.5. What is the nearest to -1/3 in w, g, 3?\n | w\n | ibivibiv/math_instruct | |
Let z(c) = -c**2 - 5*c + 2. Let j be z(-4). Suppose 15 = -3*x, l - x = x + 12. Calculate the highest common factor of l and j.\n | 2\n | ibivibiv/math_instruct | |
Which is the fourth smallest value? (a) -0.1 (b) -1402 (c) 4 (d) 4/3\n | c\n | ibivibiv/math_instruct | |
Let g(m) be the second derivative of -m**7/7 + m**4/2 + 5*m. Find the third derivative of g(v) wrt v.\n | -360*v**2\n | ibivibiv/math_instruct | |
Put 0, 663781, -4, 4 in decreasing order.\n | 663781, 4, 0, -4\n | ibivibiv/math_instruct | |
Expand (-3*t + 2*t + 2*t)*(3*t**3 + 0*t**3 - t**3) - 2*t**4 + 0*t**4 + 4*t**4 + 4*t**4 - t**4 - t**4.\n | 6*t**4\n | ibivibiv/math_instruct | |
What is the greatest common factor of 45 and 191135?\n | 5\n | ibivibiv/math_instruct | |
Let z = -23379 + 67270. What is the thousands digit of z?\n | 3\n | ibivibiv/math_instruct | |
Is 989987 composite?\n | True\n | ibivibiv/math_instruct | |
Let r = 265.501 + 0.499. Let w = 279 - r. Which is the biggest value? (a) 0.2 (b) -0.5 (c) 0.3 (d) w\n | d\n | ibivibiv/math_instruct | |
Solve -3*r + 8*r - 32 = -3*p, 8*r = -40 for p.\n | 19\n | ibivibiv/math_instruct | |
Let t(p) = p**2 + p - 2. Let v be t(1). Solve -6*b - 5*k - 2 = -4*b, -2*b + 4*k - 2 = v for b.\n | -1\n | ibivibiv/math_instruct | |
Let c(n) = -1 + 1 - 1 + 3*n - 3. Let k be c(3). Find the third derivative of 4*b**k - 4*b**5 + 2*b**2 + b**6 wrt b.\n | 120*b**3\n | ibivibiv/math_instruct | |
What is the next term in -10911631, -10911633, -10911635, -10911637?\n | -10911639\n | ibivibiv/math_instruct | |
Suppose -5*g + g = -3*t - 26, -4*g + 2*t = -24. Suppose g*q - 5 = 10. Suppose -5*j + 309 = -q*u - 155, 2*j + 5*u = 198. List the prime factors of j.\n | 2, 47\n | ibivibiv/math_instruct | |
Factor 3*a**2 + a + a**2 + 0*a**2 - 5*a**2.\n | -a*(a - 1)\n | ibivibiv/math_instruct | |
Let g(u) = -4*u**2. Let q(s) = -301*s - 5. Let c(v) = -579*v - 12. Let y(n) = -2*c(n) + 5*q(n). Determine g(y(b)).\n | -481636*b**2 - 2776*b - 4\n | ibivibiv/math_instruct | |
Let q = -318766 - -318839.9918. Let c = -148 + 74. Let l = q + c. Round l to three decimal places.\n | -0.008\n | ibivibiv/math_instruct | |
Rearrange 15 - g**4 - 40*g**3 + 15 - 29 + (-5*g - g + g)*(-21*g**2 + 21*g**2 - 8*g**3) to k*g + h*g**4 + d*g**3 + o*g**2 + u and give h.\n | 39\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# Method of image charge for ellipse
If we put an external electron outside a elliptical metal described by: $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$, how do we determine the image charge or charges of that electron inside this... | The Method of Image Charges is a powerful technique used in electrostatics to simplify the solving of certain problems. It relies on the principle that if we have a conductor at zero potential with an external point charge placed near it, then there exists an equivalent system consisting only of charges for which the ... | ibivibiv/math_instruct | |
Expand -6*z**3 + 29*z**3 + 13*z**3 + (-1 - 2*z**2 + 1)*(-z + 10*z + 3*z).\n | 12*z**3\n | ibivibiv/math_instruct | |
Expand (-16 + 16 - 7*n)*(0*n - 6*n + 0*n).\n | 42*n**2\n | ibivibiv/math_instruct | |
What is the second derivative of -29636*t*z**3 - 3*t*z - 23*t + 913*z**4 - z**2 + 84*z - 637 wrt z?\n | -177816*t*z + 10956*z**2 - 2\n | ibivibiv/math_instruct | |
Put 5, 1.6, 3, -4 in increasing order.\n | -4, 1.6, 3, 5\n | ibivibiv/math_instruct | |
Let p(l) be the third derivative of 1/210*l**7 + 0*l - 9*l**2 + 0 + 5/6*l**3 + 0*l**4 + 0*l**6 + 0*l**5. Differentiate p(z) with respect to z.\n | 4*z**3\n | ibivibiv/math_instruct | |
-2 + 1 - (1 - (-6 + 6))\n | -2\n | ibivibiv/math_instruct | |
Put -0.5, 2, 2/9, 8, -3 in ascending order.\n | -3, -0.5, 2/9, 2, 8\n | ibivibiv/math_instruct | |
Let h(d) = -2*d**2 + 416*d + 10006. What is h(-22)?\n | -114\n | ibivibiv/math_instruct | |
Calculate the smallest common multiple of 4737989 and 746140.\n | 94759780\n | ibivibiv/math_instruct | |
Is 1175716 at most as big as 1175516?\n | False\n | ibivibiv/math_instruct | |
Which is greater: 6 or 4093?\n | 4093\n | ibivibiv/math_instruct | |
Solve -2 = -2*f + t, 3*f + 23*t - 7*t = -67 for f.\n | -1\n | ibivibiv/math_instruct | |
How many millilitres are there in fifty-one fifths of a litre?\n | 10200\n | ibivibiv/math_instruct | |
Let n = 4416.949 - 4419. Let f = n + 0.051. Let r = -14 - -113/8. Put f, r, -0.4, -2/7 in decreasing order.\n | r, -2/7, -0.4, f\n | ibivibiv/math_instruct | |
Let t(a) = 2*a + 6. Suppose 3*x = 3*u - 6*u - 12, 4*u = 2*x + 32. Let w = x + 3. Let c(s) be the second derivative of -s**2/2 - 2*s. Give w*c(f) - t(f).\n | -2*f - 1\n | ibivibiv/math_instruct | |
Is 134989 a prime number?\n | True\n | ibivibiv/math_instruct | |
Sort 31, -1, 7 in descending order.\n | 31, 7, -1\n | ibivibiv/math_instruct | |
b"What is the mth term of 6428, 13047, 19666, 26285?\n" | 6619*m - 191\n | ibivibiv/math_instruct | |
Calculate the remainder when 460 is divided by 6.\n | 4\n | ibivibiv/math_instruct | |
Let b be -6 - -4*(-15)/(-10). Is b bigger than 6/31?\n | False\n | ibivibiv/math_instruct | |
Solve 658 = 79*w + 105 for w.\n | 7\n | ibivibiv/math_instruct | |
Let z be (-3*(-10)/(-24))/((-25)/(-5100)). Do -255 and z have the same value?\n | True\n | ibivibiv/math_instruct | |
Expand (-11*m**2 - 2*m**2 + 2*m**2)*(12 - 2 + 15).\n | -275*m**2\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(25.616 - 75.714) / (-59.75 * 51.365) | 0.0163 | ibivibiv/math_instruct | |
Let m = -151/2 - -76. What is the nearest to 13 in -4/5, m, 0.3?\n | m\n | ibivibiv/math_instruct | |
Suppose 3*t = 3*m + 48, m + m - 52 = -5*t. Is 6 a factor of 286/t + (-1)/(-6)?\n | True\n | ibivibiv/math_instruct | |
Sort -3, -4, -2, 14 in increasing order.\n | -4, -3, -2, 14\n | ibivibiv/math_instruct | |
Let r = -18672 - -18641.806. What is r rounded to 1 dp?\n | -30.2\n | ibivibiv/math_instruct | |
Is 20 a factor of 2161?\n | False\n | ibivibiv/math_instruct | |
Let o(u) = -796*u**2 - 51*u - 32. Let k(h) = h**2 - 7*h + 3. Let t(c) = -6*k(c) + o(c). Find the second derivative of t(v) wrt v.\n | -1604\n | ibivibiv/math_instruct | |
Let d = -371 - -373. Suppose -2*g = 2 + d, p + 7 = -3*g. Let i be -1 + (-6)/(-4)*1. Which is the second biggest value? (a) -1/3 (b) i (c) p\n | a\n | ibivibiv/math_instruct | |
Let y(v) be the second derivative of -v**5/20 - 2*v**3/3 + v. Let z(q) = q**3 + 5*q. Let w(j) = -1 - 16*j + 14*j + 4. Let b be w(4). Give b*y(t) - 4*z(t).\n | t**3\n | ibivibiv/math_instruct | |
Find x, given that 2*x**4/9 - 16*x**3/3 - 214*x**2/9 - 92*x/3 - 112/9 = 0.\n | -2, -1, 28\n | ibivibiv/math_instruct | |
Let d be (3/(-6))/((-1)/2). Let n(i) be the first derivative of i**2/2 - 6. Let z(a) = 2. Determine d*z(p) - n(p).\n | -p + 2\n | ibivibiv/math_instruct | |
What is 24916 divided by -6229?\n | -4\n | ibivibiv/math_instruct | |
What are the prime factors of 3024854?\n | 2, 7, 216061\n | ibivibiv/math_instruct | |
What is the second smallest value in 3/2, -0.2, -6/7, -907, 1, -2/3?\n | -6/7\n | ibivibiv/math_instruct | |
Calculate the remainder when 2821 is divided by 83.\n | 82\n | ibivibiv/math_instruct | |
Collect the terms in 55*d - 2 + 5 - 21*d - 3 - 48*d + 11*d.\n | -3*d\n | ibivibiv/math_instruct | |
(-144)/42*(-91)/2*-23*(-39)/8970\n | 78/5\n | ibivibiv/math_instruct | |
Determine i, given that 16*i**2 + 2020*i + 504 = 0.\n | -126, -1/4\n | ibivibiv/math_instruct | |
((-275)/(-75)*(-324)/(-198))/(10/(-15))\n | -9\n | ibivibiv/math_instruct | |
Let y(l) = -4*l - 4. Let k(i) = -9*i - 7. Suppose -23*w = 14*w - 185. Calculate w*y(r) - 2*k(r).\n | -2*r - 6\n | ibivibiv/math_instruct | |
b"What is the ith term of 3, 0, -17, -54, -117, -212?\n" | -i**3 - i**2 + 7*i - 2\n | ibivibiv/math_instruct | |
What is 1666 to the power of 1/3, to the nearest integer?\n | 12\n | ibivibiv/math_instruct | |
Is 7864159207 prime?\n | True\n | ibivibiv/math_instruct | |
Round 0.00073863453 to seven dps.\n | 0.0007386\n | ibivibiv/math_instruct | |
b"What is the gth term of 4908873, 19634784, 44177969, 78538428, 122716161, 176711168?\n" | 4908637*g**2 + 236\n | ibivibiv/math_instruct | |
What are the prime factors of 70154?\n | 2, 7, 5011\n | ibivibiv/math_instruct | |
-1930b7 (base 16) to base 6\n | -55214531\n | ibivibiv/math_instruct | |
Let c = -1437/91 + 6197599/392483. What is the nearest to -2 in 3, -2, c?\n | -2\n | ibivibiv/math_instruct | |
What is the fifth smallest value in 0.1, -2/9, -343, 2/11, 0?\n | 2/11\n | ibivibiv/math_instruct | |
-3*-1441\n | 4323\n | ibivibiv/math_instruct | |
Let r be (8/6)/(7/(-3)). Let j = 0.02 + 5.28. Let d = j + -0.3. Which is the nearest to -1? (a) 0 (b) d (c) r\n | c\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 3440 and 120.\n | 40\n | ibivibiv/math_instruct | |
Let h(b) be the first derivative of b**4/144 + 7*b**3/72 + b**2/4 + 23*b + 69. Let z(l) be the first derivative of h(l). Find q, given that z(q) = 0.\n | -6, -1\n | ibivibiv/math_instruct | |
How many minutes are there between 12:27 AM and 8:01 AM?\n | 454\n | ibivibiv/math_instruct | |
Let m = 2727 - 720. What is the remainder when m is divided by 95?\n | 12\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 14196 and 168.\n | 84\n | ibivibiv/math_instruct | |
In base 3, what is -120 + -11?\n | -201\n | ibivibiv/math_instruct | |
What is the closest to 2/3 in -0.2, -108, -2/13?\n | -2/13\n | ibivibiv/math_instruct | |
What is -1b3da (base 14) in base 7?\n | -406163\n | ibivibiv/math_instruct | |
Factor -2*q**4/3 - 10*q**3/3 + 5542*q**2 - 185538*q.\n | -2*q*(q - 51)**2*(q + 107)/3\n | ibivibiv/math_instruct | |
Suppose 0*b + t + 101 = 5*b, -5 = 5*t. What are the prime factors of b?\n | 2, 5\n | ibivibiv/math_instruct | |
Simplify -2*((1 + (sqrt(1088) - (3 + sqrt(1088) - sqrt(1088))) + sqrt(1088))**2 - ((-3 + 4*sqrt(1088))**2 - sqrt(1088)) - (1*(3 + 5*(sqrt(1088) + -2)))**2).\n | -1392*sqrt(17) + 80620\n | ibivibiv/math_instruct | |
Calculate prob of sequence dr when two letters picked without replacement from prjjqjggqpqjdpqjqqqr.\n | 1/190\n | ibivibiv/math_instruct | |
Factor -4/9*i**2 + 1/9*i**3 + 4/9 - 1/9*i.\n | (i - 4)*(i - 1)*(i + 1)/9\n | ibivibiv/math_instruct | |
Let g(o) = -o**3 + 8*o**2 - 5*o - 3. Let k be g(7). Differentiate z**3 - 9*z**3 + k*z**3 - 10 wrt z.\n | 9*z**2\n | ibivibiv/math_instruct |
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