instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
What is -101 (base 2) in base 3?\n | -12\n | ibivibiv/math_instruct | |
b"What is the ath term of 449, 771, 1093?\n" | 322*a + 127\n | ibivibiv/math_instruct | |
Let g be 2057/(-910) - 6/39. Let k = g - -27/10. Let a be (-1)/8*9/(-3). What is the second smallest value in a, -5, k, 4/7?\n | k\n | ibivibiv/math_instruct | |
Is 257695 composite?\n | True\n | ibivibiv/math_instruct | |
Product of 0 and -911030.\n | 0\n | ibivibiv/math_instruct | |
Let n = 240 + -163. Find the second derivative of -122*q**5 + n*q**5 - 1 + 0*q - 2*q**3 - 9*q wrt q.\n | -900*q**3 - 12*q\n | ibivibiv/math_instruct | |
Suppose -95*q = -99*q + 432. What is the units digit of 2/(-6) + 43452/q?\n | 2\n | ibivibiv/math_instruct | |
What are the prime factors of 25324?\n | 2, 13, 487\n | ibivibiv/math_instruct | |
Given a complex function $f(z) = \frac{z^3-1}{z^2+z}$,
(a) Find all the zeros of the function within the unit circle.
(b) Find all the poles of the function within the unit circle.
(c) State the order of each zero and pole.
(d) Find the Laurent series of $f(z)$ about $z=0$ and state the region of convergence. | (a) To find the zeros of the function, we need to solve the equation $z^3 - 1 = 0$. Using the fact that $z^3 - 1 = (z - 1)(z^2 + z + 1)$, we have:
1. $z = 1$ (outside the unit circle)
2. $z^2 + z + 1 = 0$
For the second equation, we can use the quadratic formula:
$z = \frac{-1 \pm \sqrt{1^2 - 4(1)(1)}}{2(1)} = \frac... | ibivibiv/math_instruct | |
Let o be (0 - 3) + 1 - -5. Sort -2, o, -3.\n | -3, -2, o\n | ibivibiv/math_instruct | |
Calculate prob of sequence jj when two letters picked without replacement from kdkkjkdjkkkkkkj.\n | 1/35\n | ibivibiv/math_instruct | |
-4.39 times -13082\n | 57429.98\n | ibivibiv/math_instruct | |
Suppose -3*c = 3, -2*d - 2*c - 3*c + 1 = 0. Solve -5*t + d = 3*m, m - 1 = 2*t - 0 for t.\n | 0\n | ibivibiv/math_instruct | |
Let p(h) = h**3 + 3*h**2 - 13*h - 13. Let s be p(-1). Let x = 3 - 0. Solve x*k = s*k for k.\n | 0\n | ibivibiv/math_instruct | |
Calculate the common denominator of -42/1343 and 63/439025.\n | 34682975\n | ibivibiv/math_instruct | |
Let c(g) = -g. Let f(l) = 37 - 62 + 29 - 9*l. Let j(y) = 4*c(y) - f(y). Give j(3).\n | 11\n | ibivibiv/math_instruct | |
Calculate the least common multiple of 1000 and 250.\n | 1000\n | ibivibiv/math_instruct | |
Round -0.23208 to 1 dp.\n | -0.2\n | ibivibiv/math_instruct | |
Add 0.001975 and 0.1.\n | 0.101975\n | ibivibiv/math_instruct | |
Suppose -1063 = -5*l + 2*z + 30686, -4*l + 2*z + 25398 = 0. Suppose l = 31*h - 2763. Does 1/2 = h?\n | False\n | ibivibiv/math_instruct | |
Multiply 0.77 and -0.3.\n | -0.231\n | ibivibiv/math_instruct | |
Let l(d) = d**3 - 89*d**2 - 1099*d + 17. Determine l(-11).\n | 6\n | ibivibiv/math_instruct | |
What is the value of (20/(-32))/((-99)/396)?\n | 5/2\n | ibivibiv/math_instruct | |
Find the second derivative of d*n**2*p - 7*d*n**2 + 9*d*n*p - d*p + 9*n**2*p - 6*n**2 + 24*n*p wrt n.\n | 2*d*p - 14*d + 18*p - 12\n | ibivibiv/math_instruct | |
What is -3340 (base 6) in base 3?\n | -1001220\n | ibivibiv/math_instruct | |
Suppose -3*f = -d - 12, -f - 7 = -3*d - 19. Let t be 6 + (-366)/42 + 2/(-7). Sort 0, t, f in decreasing order.\n | f, 0, t\n | ibivibiv/math_instruct | |
What is five quarters of a litre in millilitres?\n | 1250\n | ibivibiv/math_instruct | |
What is the second derivative of -211*b**4 + 9*b**3 - 1261*b**2 - 61229301*b?\n | -2532*b**2 + 54*b - 2522\n | ibivibiv/math_instruct | |
Simplify -3 + (sqrt(99))**2 + 2 + -4.\n | 94\n | ibivibiv/math_instruct | |
Which is the fifth smallest value? (a) 6/2075 (b) 0 (c) -1/11 (d) 10 (e) -1\n | d\n | ibivibiv/math_instruct | |
Simplify -4*(-5*sqrt(343)*4 - (sqrt(343) + 1 + (sqrt(343) + -1*sqrt(343) + sqrt(343))**2)).\n | 1376 + 588*sqrt(7)\n | ibivibiv/math_instruct | |
What is the result of the following expression?
-92.994 % 5.2453 | 1.4214 | ibivibiv/math_instruct | |
Which is smaller: -3532054/3 or -1177350?\n | -3532054/3\n | ibivibiv/math_instruct | |
Simplify (u**(-34)/u**(4/13))**(-10/7) assuming u is positive.\n | u**(4460/91)\n | ibivibiv/math_instruct | |
Collect the terms in 3525*a**3 - 4841006*a**2 + 4841006*a**2 - 3513*a**3.\n | 12*a**3\n | ibivibiv/math_instruct | |
Put -238112, -27, -1, -5, 5, -3 in decreasing order.\n | 5, -1, -3, -5, -27, -238112\n | ibivibiv/math_instruct | |
Let q = 1832 + -1829. Which is the third smallest value? (a) -0.07 (b) 478 (c) q\n | b\n | ibivibiv/math_instruct | |
Is 209489309 prime?\n | False\n | ibivibiv/math_instruct | |
Is 76 a factor of 912?\n | True\n | ibivibiv/math_instruct | |
Factor -2 - 3 - 696*b + 4 - 15138*b**2 - 7.\n | -2*(87*b + 2)**2\n | ibivibiv/math_instruct | |
Suppose -2*x + 4*x = -c - 3167, c = 2*x + 3161. Let p = x + 18965/12. Is -0.1 greater than or equal to p?\n | True\n | ibivibiv/math_instruct | |
Let c be (-152)/(-6) - (-1)/(-3). Let a be -1 - 0 - 0/(-2). What are the prime factors of a*c*2/(-5)?\n | 2, 5\n | ibivibiv/math_instruct | |
Let s = -2487.6 - -2488. Which is the closest to 2/3? (a) -0.19 (b) s (c) 125\n | b\n | ibivibiv/math_instruct | |
Collect the terms in 14 - w + 21 - 32 + 17 + 8 - 2*w.\n | -3*w + 28\n | ibivibiv/math_instruct | |
Calculate the remainder when 2288 is divided by 81.\n | 20\n | ibivibiv/math_instruct | |
What is 942 plus -11518?\n | -10576\n | ibivibiv/math_instruct | |
Evaluate (12/(-9))/(24/(-9) + 2).\n | 2\n | ibivibiv/math_instruct | |
b"What is the nth term of -109149, -218295, -327441, -436587, -545733?\n" | -109146*n - 3\n | ibivibiv/math_instruct | |
Let z(d) = d**3 - 7*d**2 - 4*d + 42. Let t be z(7). Calculate the remainder when 107 is divided by (t/(-21))/((-4)/162).\n | 26\n | ibivibiv/math_instruct | |
Expand -2*k - k + k + (-1 - 1 + 4)*(-k - 5 + 5) - 491*k + 433*k + 285*k.\n | 223*k\n | ibivibiv/math_instruct | |
Calculate the highest common divisor of 17469 and 1377.\n | 27\n | ibivibiv/math_instruct | |
Solve 0 = y - 23 + 24 for y.\n | -1\n | ibivibiv/math_instruct | |
Let n = 20 + -18. Let i be (-1 - 0)/(-1)*5. Suppose 2*o + 3*o - 5 = v, 5*o = -v - i. Which is the smallest value? (a) 3 (b) n (c) v\n | c\n | ibivibiv/math_instruct | |
Find the common denominator of -15/88 and 3/308.\n | 616\n | ibivibiv/math_instruct | |
Let w(f) = f - 2. Suppose q + 107 = 10. Let k = 146 + q. Let d = k + -55. Give w(d).\n | -8\n | ibivibiv/math_instruct | |
Let r(v) = v**2 - 7*v + 6. Let m be r(7). Let d be (-15)/(-6) - m/(-4). Find the second derivative of 2*x**5 - 4*x - x**5 + d*x**5 - x wrt x.\n | 100*x**3\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 1422 and 2724789?\n | 237\n | ibivibiv/math_instruct | |
Rearrange (-2 + 2 - a)*(-6*a**3 + 6*a**3 + 4*a**3) - 51*a**4 - 1 + 2*a**3 + 19646*a**2 - 19646*a**2 to the form d*a + y*a**2 + c*a**3 + t*a**4 + s and give t.\n | -55\n | ibivibiv/math_instruct | |
Let b(l) = l**3 + 9*l**2 - 10*l + 11. Calculate b(-10).\n | 11\n | ibivibiv/math_instruct | |
What is -2b7d01 (base 14) in base 5?\n | -342114411\n | ibivibiv/math_instruct | |
What is the second derivative of -4*l**2*v**4 - 230*l**2*v**2 - l**2*v - 1190*l**2 wrt v?\n | -48*l**2*v**2 - 460*l**2\n | ibivibiv/math_instruct | |
Let k be (6/21 + 88/(-112))*-8. Suppose -4*r - 15 = 5*t, -1 = r + k. Is -1/55 at least as big as t?\n | False\n | ibivibiv/math_instruct | |
Solve 5*l + 8*r = 29, 21137*r - 21141*r = -12 for l.\n | 1\n | ibivibiv/math_instruct | |
Let s(l) = l**2 + 4*l - 50. Let c be s(-10). Suppose 6*x = c*x - 60. Calculate the smallest common multiple of x and 30.\n | 30\n | ibivibiv/math_instruct | |
What is the second biggest value in -1, 596, -4, 0?\n | 0\n | ibivibiv/math_instruct | |
What is the closest to -75 in 0.4, 0.3, -7?\n | -7\n | ibivibiv/math_instruct | |
Let l be 23/21 + 2/(-3). Which is the biggest value? (a) 2 (b) l (c) 2/15\n | a\n | ibivibiv/math_instruct | |
What is the tens digit of 54099?\n | 9\n | ibivibiv/math_instruct | |
Calculate (5289/41)/(-43)*(-7)/((5/(-3))/5).\n | -63\n | ibivibiv/math_instruct | |
Suppose 0 = 2*g - 8*g - 60. Let l be (1 - (-1 + -1))/(g/5). Which is the smallest value? (a) l (b) 2 (c) 0.5\n | a\n | ibivibiv/math_instruct | |
What is the highest common divisor of 58 and 87?\n | 29\n | ibivibiv/math_instruct | |
Solve 20 = -6393*k + 6373*k for k.\n | -1\n | ibivibiv/math_instruct | |
Let t = 198 + -191. What is the second biggest value in 0, 4/3, t?\n | 4/3\n | ibivibiv/math_instruct | |
Let f(d) = -5*d + 7. Let m(y) = y. Calculate f(z) + 4*m(z).\n | -z + 7\n | ibivibiv/math_instruct | |
Let t = 237.27853 - 237.76. Let y = 0.31054 + t. Let u = -0.172 - y. What is u rounded to 3 decimal places?\n | -0.001\n | ibivibiv/math_instruct | |
Suppose 4*s = 5*o - 94, 2*s = -2*s - 4. Suppose 0 = -4*b - 3*r + 9, 23*b - 14 = o*b - r. Solve -13 = -4*n + b for n.\n | 4\n | ibivibiv/math_instruct | |
Let j(y) = 30*y + 20. Suppose 95 + 25 = 6*x. Let c be j(x). Suppose 309 = -4*f + 2*f - 3*d, 4*d = -4*f - c. What is f rounded to the nearest 10?\n | -160\n | ibivibiv/math_instruct | |
What is the hundreds digit of 31695?\n | 6\n | ibivibiv/math_instruct | |
Which is smaller: -6627/4 or -1657?\n | -1657\n | ibivibiv/math_instruct | |
20778138*3\n | 62334414\n | ibivibiv/math_instruct | |
Let 14 - 6*l - 3*l**2 - 7 - 7 = 0. What is l?\n | -2, 0\n | ibivibiv/math_instruct | |
Solve q**3/2 - 75*q**2/2 - 221400*q - 51516000 = 0.\n | -360, 795\n | ibivibiv/math_instruct | |
What is 4 take away -299153514.2113?\n | 299153518.2113\n | ibivibiv/math_instruct | |
Suppose -4*d = -3*d + 4. Let w = 463 + -461. Suppose -3*u - 20*n = -19*n + 3, -u - 6 = w*n. Sort u, 4, d in descending order.\n | 4, u, d\n | ibivibiv/math_instruct | |
Let n(h) = -3*h**3 - 22*h**2 + 14*h - 11. Let z be n(-8). Put z, -24, 4, 7 in descending order.\n | 7, z, 4, -24\n | ibivibiv/math_instruct | |
-4*-0.0505\n | 0.202\n | ibivibiv/math_instruct | |
Let r(q) = 4*q**2 - 5*q + 1. Let t be (-6)/(-33) - (-6)/(-33). Suppose 2*g - l + 11 = t, -15 = 3*g + l - 2*l. Is r(g) a multiple of 28?\n | False\n | ibivibiv/math_instruct | |
What is the closest to 3 in 294674, 0.4, -5, -0.04?\n | 0.4\n | ibivibiv/math_instruct | |
What is 4969 times -0.3?\n | -1490.7\n | ibivibiv/math_instruct | |
641931440 divided by 490024\n | 1310\n | ibivibiv/math_instruct | |
What is 570 minutes before 11:04 AM?\n | 1:34 AM\n | ibivibiv/math_instruct | |
Let w = -51 + 85. Let u = w - -53. Let a = u + -77.4. What is a rounded to zero decimal places?\n | 10\n | ibivibiv/math_instruct | |
Round 15112127 to the nearest one million.\n | 15000000\n | ibivibiv/math_instruct | |
Let j = -3036981464.00000997 + 3036981559. Let q = 95 - j. What is q rounded to 6 decimal places?\n | 0.00001\n | ibivibiv/math_instruct | |
What is the thousands digit of 148863779?\n | 3\n | ibivibiv/math_instruct | |
Let r = -14123746 - -14123746.7599951. Let n = -0.76 + r. What is n rounded to six dps?\n | -0.000005\n | ibivibiv/math_instruct | |
What is (-58)/84 + 3 + 660/(-210)?\n | -5/6\n | ibivibiv/math_instruct | |
What is the seventh root of 412124 to the nearest integer?\n | 6\n | ibivibiv/math_instruct | |
What is prob of picking 1 b and 1 h when two letters picked without replacement from {o: 2, j: 1, b: 4, h: 3, x: 2, a: 3}?\n | 4/35\n | ibivibiv/math_instruct | |
Let j = 25.5 - 25. Let b = -12 + 14.8. Let p = b + -3. What is the biggest value in p, -3, j?\n | j\n | ibivibiv/math_instruct |
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