instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
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|---|---|---|---|
Simplify -4 + sqrt(128) + sqrt(128) + -1 - (sqrt(128) + ((sqrt(128) - (0 + sqrt(128))) + 1)**2).\n | -6 + 8*sqrt(2)\n | ibivibiv/math_instruct | |
Let q be (-16)/(-12)*(-9)/102. What is the smallest value in q, 2/125, 4, -5, 1?\n | -5\n | ibivibiv/math_instruct | |
Which is the nearest to -2? (a) 10 (b) -3 (c) 1/18 (d) 2\n | b\n | ibivibiv/math_instruct | |
What is -873208.75 rounded to the nearest 1000?\n | -873000\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 329 and 3525?\n | 47\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"MAT244-2014F > Quiz 2
Quiz 2 Problem 1 (night sections)
(1/1)
Chang Peng (Eddie) Liu:
3.2 #17
If the Wronskian $W$ of $f$ and $g$ is $3e^{4t}$ , and if $f (t) = e^{2t}$ , find $g(t)$.
Can anyone type solution? - V.I.
Ro... | The Wronskian is a fundamental concept in the study of differential equations, which provides a method for determining whether two functions are linearly independent or dependent. Given two differentiable functions f(t) and g(t), the Wronskian W is defined as follows:
W = det \ begin{bmatrix} f(t) & g(t) \\ f'(t) & g... | ibivibiv/math_instruct | |
Let w = 12 - 9. Suppose -w*t = 41 + 43. Calculate the lowest common multiple of 130/8 - (-7)/t and 4.\n | 16\n | ibivibiv/math_instruct | |
What is the result of the following expression?
-42.8377 * 65.2317 | -2794.3760 | ibivibiv/math_instruct | |
What is the value of (3/(-7))/((-594)/1848)?\n | 4/3\n | ibivibiv/math_instruct | |
What is 6136616.383 rounded to the nearest 1000?\n | 6137000\n | ibivibiv/math_instruct | |
Is 581107 a composite number?\n | True\n | ibivibiv/math_instruct | |
Round 781.6 to the nearest ten.\n | 780\n | ibivibiv/math_instruct | |
Divide -87 by 29.\n | -3\n | ibivibiv/math_instruct | |
Calculate -2 + (3 - -8) + (10 - 21).\n | -2\n | ibivibiv/math_instruct | |
What are the prime factors of 24531?\n | 3, 13, 17, 37\n | ibivibiv/math_instruct | |
Is (0 - 1)/(1/(-751)) a prime number?\n | True\n | ibivibiv/math_instruct | |
Solve -67220*k + 67 = -67219*k + 5*f, -k - 24 = -2*f for k.\n | 2\n | ibivibiv/math_instruct | |
Let n = 0 + 15. Suppose 3*o - 4*i = 26, -2*i = -0*i + 4. What is the highest common divisor of n and o?\n | 3\n | ibivibiv/math_instruct | |
b"What is the rth term of 143, 186, 227, 266, 303?\n" | -r**2 + 46*r + 98\n | ibivibiv/math_instruct | |
What is the nearest to 1/6 in -7, 0.4, 1/9, -1?\n | 1/9\n | ibivibiv/math_instruct | |
What is 1.978831 litres in millilitres?\n | 1978.831\n | ibivibiv/math_instruct | |
Simplify (-1 + sqrt(847))**2 + -1.\n | -22*sqrt(7) + 847\n | ibivibiv/math_instruct | |
Sort -233, 2, -1, 14373 in increasing order.\n | -233, -1, 2, 14373\n | ibivibiv/math_instruct | |
Let d be 6/39 - (-3)/(-2). Let n = -50/13 - d. Which is the biggest value? (a) n (b) 6 (c) 2\n | b\n | ibivibiv/math_instruct | |
Let o = 2787 - 2787.089. Which is smaller: o or 0.16?\n | o\n | ibivibiv/math_instruct | |
Let 3/7*c**2 - 3/7*c + 3/7*c**3 + 0 - 3/7*c**4 = 0. Calculate c.\n | -1, 0, 1\n | ibivibiv/math_instruct | |
Which is smaller: 126233 or 126198?\n | 126198\n | ibivibiv/math_instruct | |
Solve -4070*d + 174059 + 21972 = -15609 for d.\n | 52\n | ibivibiv/math_instruct | |
What is the units digit of ((-636)/48 + 12)*-2204?\n | 5\n | ibivibiv/math_instruct | |
What is prob of sequence ukeu when four letters picked without replacement from {e: 3, q: 3, u: 3, k: 1}?\n | 1/280\n | ibivibiv/math_instruct | |
Let s = -14 - -4. Let k = -7 - s. Suppose 3*o = -f - o + 4, 10 = -k*f - o. Let n(m) = -m**3 - 3*m**2 + m - 4. Give n(f).\n | 8\n | ibivibiv/math_instruct | |
Which is the nearest to 2/29? (a) -1 (b) -4 (c) -1/4 (d) -2/13\n | d\n | ibivibiv/math_instruct | |
Solve 517*g - 89 - 12961 = 67*g for g.\n | 29\n | ibivibiv/math_instruct | |
Simplify ((j*j/(j*j/((j/(j**(4/13)/j))/j*j))*j)**8/(j**(-10)*j*j**(-10)/j*j))**(-3/11) assuming j is positive.\n | j**(-1581/143)\n | ibivibiv/math_instruct | |
Evaluate (-8)/(12400/93)*35/84.\n | -1/40\n | ibivibiv/math_instruct | |
Suppose -3*f - 97 - 77 = 0. Let w = f + 53. What is the remainder when (w - -4)/((-1)/67) is divided by 24?\n | 19\n | ibivibiv/math_instruct | |
Solve -1984 = 2*p + 198*v, -2*p - 1110*v + 1106*v - 44 = 0 for p.\n | -2\n | ibivibiv/math_instruct | |
Simplify (2*(-3 + sqrt(1053)))**2 + 3.\n | -216*sqrt(13) + 4251\n | ibivibiv/math_instruct | |
Suppose 0 = -g + 3*o + 695 - 100, 0 = -4*o. What are the prime factors of g?\n | 5, 7, 17\n | ibivibiv/math_instruct | |
What is the smallest value in 1.5, 4, 0, -1/5, 1/4?\n | -1/5\n | ibivibiv/math_instruct | |
What is the smallest common multiple of 63572 and 325647570?\n | 651295140\n | ibivibiv/math_instruct | |
Factor -2*i**5/15 - 82*i**4/15 - 146*i**3/5 - 42*i**2.\n | -2*i**2*(i + 3)**2*(i + 35)/15\n | ibivibiv/math_instruct | |
Let h(s) = s**3 + s**2 - s + 1. Let r(o) = -26*o**3 - 9*o**2 + 6*o - 8. Let v(k) = -8*k**3. Let w(f) = -r(f) + 3*v(f). What is 6*h(l) - w(l)?\n | 4*l**3 - 3*l**2 - 2\n | ibivibiv/math_instruct | |
What comes next: 1592, 3182, 4772?\n | 6362\n | ibivibiv/math_instruct | |
b"What is the ith term of 851, 1706, 2555, 3398, 4235, 5066, 5891?\n" | -3*i**2 + 864*i - 10\n | ibivibiv/math_instruct | |
What is 0.44782 rounded to 3 decimal places?\n | 0.448\n | ibivibiv/math_instruct | |
What is next in -8608, -17173, -25678, -34099, -42412, -50593, -58618, -66463?\n | -74104\n | ibivibiv/math_instruct | |
-343807535428 - -743\n | -343807534685\n | ibivibiv/math_instruct | |
Suppose -3*q = -0*q. Let y(v) = 2*v - 9. Let g be y(6). Factor 1/2*u**4 + 1/2*u**2 + q*u - u**g + 0.\n | u**2*(u - 1)**2/2\n | ibivibiv/math_instruct | |
((-460)/(-2277))/((3040/57)/(-40))\n | -5/33\n | ibivibiv/math_instruct | |
Let v(b) = 10*b**2 - 6*b + 4. Let o(w) = w**2 - w - 4. Let s(z) = -1. Let m(h) = o(h) - 5*s(h). Determine -6*m(x) + v(x).\n | 4*x**2 - 2\n | ibivibiv/math_instruct | |
What is five quarters of a meter in millimeters?\n | 1250\n | ibivibiv/math_instruct | |
What is the fifth root of 1796039007 to the nearest integer?\n | 71\n | ibivibiv/math_instruct | |
In base 6, what is -1134 + 1?\n | -1133\n | ibivibiv/math_instruct | |
-6 (base 10) to base 2\n | -110\n | ibivibiv/math_instruct | |
Let n be -2*(-3)/12*8. Suppose n*c - 7*c = 0. Let t = -79053/14 - -11293/2. Is c greater than or equal to t?\n | True\n | ibivibiv/math_instruct | |
Simplify f**(2/17)/f**(-3/16) assuming f is positive.\n | f**(83/272)\n | ibivibiv/math_instruct | |
Suppose -6 = -9*m + 6*m. Suppose 2*r - 4 = -m. Is -1/10 > r?\n | False\n | ibivibiv/math_instruct | |
What is the distance between -10.92 and 0.012791306?\n | 10.932791306\n | ibivibiv/math_instruct | |
What is 228739 to the power of 1/2, to the nearest integer?\n | 478\n | ibivibiv/math_instruct | |
What is the nearest to 3 in -10, -4, 42, 0, 4, 38?\n | 4\n | ibivibiv/math_instruct | |
Suppose -39 + 131 = 4*s. Let w(l) = 3*l**2 - 2*l - 3. Let i be w(4). Suppose s + i = 4*h. List the prime factors of h.\n | 3, 5\n | ibivibiv/math_instruct | |
(4 + -11 - -10) + -15 - -10\n | -2\n | ibivibiv/math_instruct | |
What is ((-9)/24)/(378/(-280))*3?\n | 5/6\n | ibivibiv/math_instruct | |
Collect the terms in 209*n**3 + 4 - 67*n**3 - 60*n**3 - 46*n**3 - 58*n**3.\n | -22*n**3 + 4\n | ibivibiv/math_instruct | |
Find the second derivative of -19*q - 794 - 8486*q**3 - 189*q**3 - 24*q + 47*q wrt q.\n | -52050*q\n | ibivibiv/math_instruct | |
Let v = -11489 - -11496. Solve -k = 5*u - 21, 3*k + v*u - 11 = 5*u for k.\n | 1\n | ibivibiv/math_instruct | |
Is 2984 greater than 2900?\n | True\n | ibivibiv/math_instruct | |
Convert 0.0314536km to centimeters.\n | 3145.36\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 899539 and 34976.\n | 1093\n | ibivibiv/math_instruct | |
Let i be -2 + (2 - 16/(-4)). Let n(k) = -15*k**2 + 4. Let p(w) = -16*w**2 + 5. What is i*p(h) - 5*n(h)?\n | 11*h**2\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 1498 and 187678.\n | 214\n | ibivibiv/math_instruct | |
Let w = -12179 - -12142. Which is the closest to -1? (a) w (b) -10 (c) 0.1\n | c\n | ibivibiv/math_instruct | |
What is the closest to 16 in 5, 0.5, -938/13?\n | 5\n | ibivibiv/math_instruct | |
Put -3, 1, -10419, 2, 17 in descending order.\n | 17, 2, 1, -3, -10419\n | ibivibiv/math_instruct | |
((-102)/22)/(-17)*((-4)/(-1))/8\n | 3/22\n | ibivibiv/math_instruct | |
Let p(o) = -2*o**2 - 5*o + 3. Let q(a) = -3*a - 2*a + 1 - a + 5*a. Calculate -p(n) + 5*q(n).\n | 2*n**2 + 2\n | ibivibiv/math_instruct | |
b"What is the cth term of -246, -245, -244?\n" | c - 247\n | ibivibiv/math_instruct | |
What is the value of -20 + 38 + 18 - (-10 + 1) - -7?\n | 52\n | ibivibiv/math_instruct | |
Suppose -26*z = 3*z - 3915. Sort 0, 1, z in ascending order.\n | 0, 1, z\n | ibivibiv/math_instruct | |
Let k(o) be the third derivative of -8*o**4/3 - 2830*o**2. Let p(d) = 4*d - 3. Calculate p(k(j)).\n | -256*j - 3\n | ibivibiv/math_instruct | |
Simplify (0 + sqrt(171))*-4 + 2*(sqrt(19) - sqrt(38)/sqrt(2))*6.\n | -12*sqrt(19)\n | ibivibiv/math_instruct | |
Suppose -1960819 = -46*u + 131307. Is u a prime number?\n | True\n | ibivibiv/math_instruct | |
Solve 2*x - 9 = 1 for x.\n | 5\n | ibivibiv/math_instruct | |
Let i(c) be the first derivative of -c**6/1080 - 17*c**5/360 + c**4/4 + 26*c**3/3 + 72. Let g(s) be the third derivative of i(s). Factor g(f).\n | -(f - 1)*(f + 18)/3\n | ibivibiv/math_instruct | |
Which is smaller: 3255570 or 16277846/5?\n | 16277846/5\n | ibivibiv/math_instruct | |
What is the third root of 1005565170 to the nearest integer?\n | 1002\n | ibivibiv/math_instruct | |
Let x = 10 - 7. Suppose -4*r + x*r = 3*i - 1038, -5*r + 360 = i. Suppose -4*f - i = f. Round f to the nearest 10.\n | -70\n | ibivibiv/math_instruct | |
What is -18 divided by 9?\n | -2\n | ibivibiv/math_instruct | |
What is the remainder when (45/30)/(1/6) is divided by 6?\n | 3\n | ibivibiv/math_instruct | |
Let u(y) be the third derivative of -y**6/120 - y**5/60 + y**4/24 + 7*y**3/6 + y**2. Let m = 3 - 16. Let c = 13 + m. What is u(c)?\n | 7\n | ibivibiv/math_instruct | |
Suppose -6*t + 9*t - 6 = 0. Calculate the greatest common divisor of t and 10.\n | 2\n | ibivibiv/math_instruct | |
Let r(j) = 60*j + 17. Let g(t) = -180*t - 60. Give -4*g(y) - 13*r(y).\n | -60*y + 19\n | ibivibiv/math_instruct | |
Which is the second smallest value? (a) 2/7 (b) 78 (c) 1702 (d) -4\n | a\n | ibivibiv/math_instruct | |
(-10 + 2 - -3)/(470/564) - 37\n | -43\n | ibivibiv/math_instruct | |
Suppose -23*a + 205 = 182. Put 8, 13, a, 5, -5 in increasing order.\n | -5, a, 5, 8, 13\n | ibivibiv/math_instruct | |
Suppose 2*x + 15 = -q, -4*q + 12 = 6*x - 10*x. Let n(l) = -l**2 - 7*l - 6. Determine n(x).\n | 0\n | ibivibiv/math_instruct | |
What is the units digit of 12146?\n | 6\n | ibivibiv/math_instruct | |
Put -28, 5, 3 in increasing order.\n | -28, 3, 5\n | ibivibiv/math_instruct | |
Let w = -7 + 9. Suppose w*m + 1 = -9. Let d be (-2)/1*(-10)/4. Sort d, 3, m in descending order.\n | d, 3, m\n | ibivibiv/math_instruct |
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