instruction_seed stringlengths 5 2.9k | response_seed stringlengths 3 9.55k | input stringclasses 1
value | _source stringclasses 1
value |
|---|---|---|---|
Let n(f) be the first derivative of -19*f**2/2 + 16*f - 1. What is the first derivative of n(w) wrt w?\n | -19\n | ibivibiv/math_instruct | |
Which is the closest to 598/7? (a) 1/4 (b) 2/7 (c) -8\n | b\n | ibivibiv/math_instruct | |
What is 0.05900580114 rounded to five dps?\n | 0.05901\n | ibivibiv/math_instruct | |
Let w(r) = -2*r**2 - 9*r - 6. Calculate w(-6).\n | -24\n | ibivibiv/math_instruct | |
Suppose 6*y - y - 245 = -5*v, -5*y - 91 = -2*v. What is the greatest common divisor of v and 6?\n | 6\n | ibivibiv/math_instruct | |
Collect the terms in -225*b**2 - 9792 - 9816 + 19608.\n | -225*b**2\n | ibivibiv/math_instruct | |
-5 - (-4 + 5) - (-19 - 18)\n | 31\n | ibivibiv/math_instruct | |
What is the tens digit of 2026?\n | 2\n | ibivibiv/math_instruct | |
What comes next: 6630, 13288, 19950, 26616?\n | 33286\n | ibivibiv/math_instruct | |
Calculate the greatest common divisor of 475 and 20.\n | 5\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"Lemma 15.97.4. Let $A$ be a ring and $I \subset A$ an ideal. Suppose given $K_ n \in D(A/I^ n)$ and maps $K_{n + 1} \to K_ n$ in $D(A/I^{n + 1})$. Assume
1. $A$ is $I$-adically complete,
2. $K_1$ is a perfect object, and
3... | We will delve into Lemma 15.97.4, which discusses some properties of objects in the derived category of a commutative ring with an ideal. The lemma combines results from two other lemmas (15.97.3 and 15.97.2) to establish claims about the derived completion property of certain complexes constructed using a given seque... | ibivibiv/math_instruct | |
What is prob of picking 1 z, 1 v, and 1 n when three letters picked without replacement from {n: 3, v: 9, z: 2, s: 3}?\n | 27/340\n | ibivibiv/math_instruct | |
Calculate the highest common factor of 43660 and 4220.\n | 20\n | ibivibiv/math_instruct | |
What is the closest to -0.1 in -0.5, -4, 1.6, -27876, 3/4?\n | -0.5\n | ibivibiv/math_instruct | |
Let p(o) = -32*o - 104. Calculate the least common multiple of p(-5) and 48.\n | 336\n | ibivibiv/math_instruct | |
What is the greatest common divisor of 280770 and 882?\n | 294\n | ibivibiv/math_instruct | |
Let u(p) be the second derivative of 0 - p + 0*p**2 + 0*p**4 - 5/6*p**3 - 1/40*p**5. Let a(l) be the second derivative of u(l). Let i(b) = b. Determine i(a(x)).\n | -3*x\n | ibivibiv/math_instruct | |
Collect the terms in -2*l - 6*l + 13*l.\n | 5*l\n | ibivibiv/math_instruct | |
Let x(q) = 7*q**3 + 2*q**2 + 8*q + 2. Let b(z) = -z**3 - z - 1. What is -6*b(i) - x(i)?\n | -i**3 - 2*i**2 - 2*i + 4\n | ibivibiv/math_instruct | |
Suppose -547*k + 15570464 = -26241178 - 1392606. What is the units digit of k?\n | 4\n | ibivibiv/math_instruct | |
Calculate the common denominator of -77/19563592 and 103/105032.\n | 371708248\n | ibivibiv/math_instruct | |
Solve 2*z - 36*z = 136, -40 = -4*b + 295*z - 291*z for b.\n | 6\n | ibivibiv/math_instruct | |
Let v(q) = q. Let l(g) = 79*g**2 - g + 15184. What is v(l(j))?\n | 79*j**2 - j + 15184\n | ibivibiv/math_instruct | |
What is (1 - -49) + -110 + (-118 - -208)?\n | 30\n | ibivibiv/math_instruct | |
What is 1*(81/15)/9*5?\n | 3\n | ibivibiv/math_instruct | |
Let m(h) be the first derivative of -h**3/3 + 2*h**2 + 4*h + 1. Suppose 0 = -4*k - 41 + 57. Calculate m(k).\n | 4\n | ibivibiv/math_instruct | |
Factor 14*w**3/5 + 234*w**2/5 + 104*w - 168/5.\n | 2*(w + 3)*(w + 14)*(7*w - 2)/5\n | ibivibiv/math_instruct | |
Calculate the remainder when 430 is divided by 11 - 2/(-3 + (-13)/(-5)).\n | 14\n | ibivibiv/math_instruct | |
Simplify (2*-2*sqrt(171))**2 + (sqrt(190) - (sqrt(190) + ((sqrt(190) - (sqrt(190)*2*2 + sqrt(190))) + sqrt(190) - sqrt(190))))/sqrt(10).\n | 4*sqrt(19) + 2736\n | ibivibiv/math_instruct | |
Find the second derivative of -4857363*z**2 + 1366173*z.\n | -9714726\n | ibivibiv/math_instruct | |
Let -5*a**4/3 - 15760940*a**3 - 49681445936720*a**2 - 156605257704377543360*a/3 = 0. What is a?\n | -3152188, 0\n | ibivibiv/math_instruct | |
Let d = 10621 + -10621. Determine u, given that d*u + 6/13*u**3 + 2/13*u**4 - 20/13*u**2 + 0 = 0.\n | -5, 0, 2\n | ibivibiv/math_instruct | |
Suppose -121*n = -125*n. Let h(m) be the third derivative of 5*m**4/24 + 5*m**3/2 + 13*m**2. What is the tens digit of h(n)?\n | 1\n | ibivibiv/math_instruct | |
Calculate the greatest common factor of 374 and 22.\n | 22\n | ibivibiv/math_instruct | |
Suppose 0 = -3*l + 52 - 1. Calculate the remainder when (-4)/14 + 219/7 is divided by l.\n | 14\n | ibivibiv/math_instruct | |
What is 4 (base 15) in base 12?\n | 4\n | ibivibiv/math_instruct | |
Suppose 0 = 23*n - 21*n - 110. Calculate the highest common factor of n and 5.\n | 5\n | ibivibiv/math_instruct | |
Let p(h) = -3*h + h**2 + 1 + 9*h - 3*h. Let q be p(-4). Suppose -q*l + 346 = -74. What is the tens digit of l?\n | 8\n | ibivibiv/math_instruct | |
What is the cube root of 167036 to the nearest integer?\n | 55\n | ibivibiv/math_instruct | |
Simplify ((p**(3/2)/p**33)**(3/5))**(-5) assuming p is positive.\n | p**(189/2)\n | ibivibiv/math_instruct | |
Let h be ((-2)/3)/((-14)/189). Suppose -228*t = -236*t + 144. What is the highest common divisor of t and h?\n | 9\n | ibivibiv/math_instruct | |
Let r = -145 + 324. What are the prime factors of r?\n | 179\n | ibivibiv/math_instruct | |
Let i be (42/420*(10 + -1))/((-1)/2). Is i at least as big as -13/3?\n | True\n | ibivibiv/math_instruct | |
Let g be (-14)/(-35)*(-1 - 9). Let b be 4*1 - (-8)/g. Let h be -2 + 0 - (-10 - -3). What is the greatest common divisor of b and h?\n | 1\n | ibivibiv/math_instruct | |
Which is the second biggest value? (a) 0 (b) 0.3 (c) -18\n | a\n | ibivibiv/math_instruct | |
Calculate (-27)/3 + 2 - (-28)/14.\n | -5\n | ibivibiv/math_instruct | |
4301 (base 7) to base 11\n | 1162\n | ibivibiv/math_instruct | |
Solve -5*f - l = -0*l + 11, 2*f - 10 = -4*l for f.\n | -3\n | ibivibiv/math_instruct | |
What is 586 minutes before 12:18 AM?\n | 2:32 PM\n | ibivibiv/math_instruct | |
Which is the closest to 1? (a) -2 (b) -0.2 (c) 1/2 (d) -0.3\n | c\n | ibivibiv/math_instruct | |
What is 2 + -4 + (1 - -3) + -3?\n | -1\n | ibivibiv/math_instruct | |
Let k = 9 - 5. Let y = 2 - k. Let d = y - -2.2. What is the second biggest value in d, 5, 3/7?\n | 3/7\n | ibivibiv/math_instruct | |
Is 55183006 composite?\n | True\n | ibivibiv/math_instruct | |
Work out 229296.403 - -2305127.\n | 2534423.403\n | ibivibiv/math_instruct | |
What is the next term in 1, -4, -9, -14, -19, -24?\n | -29\n | ibivibiv/math_instruct | |
Does 156 divide 171805608?\n | True\n | ibivibiv/math_instruct | |
What is the value of ((-1450)/125)/(-15*(-30)/3375)?\n | -87\n | ibivibiv/math_instruct | |
Let s = -1 + 6. What is the units digit of s?\n | 5\n | ibivibiv/math_instruct | |
Calculate the remainder when 8405182 is divided by 16.\n | 14\n | ibivibiv/math_instruct | |
Let f = 1.432 + -1.362. Let d be 26918/(-92) - 2/4. Let s = 293 + d. Which is the third biggest value? (a) s (b) f (c) 5/6\n | a\n | ibivibiv/math_instruct | |
1 (base 16) to base 10\n | 1\n | ibivibiv/math_instruct | |
Which is the nearest to 0.0535? (a) -1/2 (b) -3/4 (c) 1/11 (d) 11 (e) -1/7\n | c\n | ibivibiv/math_instruct | |
Suppose 0*f - 54 = -3*f. Let k be f/15*20/8. What is the third derivative of -t**2 - 2*t**3 - 5*t**3 + 12*t**k wrt t?\n | 30\n | ibivibiv/math_instruct | |
Suppose -3*f + 5*v = 5, 0 = v - 1 - 3. What is the remainder when 13 is divided by f?\n | 3\n | ibivibiv/math_instruct | |
Let j(n) = -3*n**2 + 2*n**2 - n**3 + 0*n**2 + n. Let b(v) be the first derivative of -5*v**4/4 - 2*v**3 + 3*v**2 + 3. Give b(q) - 6*j(q).\n | q**3\n | ibivibiv/math_instruct | |
What is 444 minutes after 10:37 PM?\n | 6:01 AM\n | ibivibiv/math_instruct | |
Solve -40*s = 31*s + 22*s - 3255 for s.\n | 35\n | ibivibiv/math_instruct | |
Let g = -17711 - -17711.3. Is g at least as big as 1029?\n | False\n | ibivibiv/math_instruct | |
Solve 88 = -4277*c + 4264*c + 231 for c.\n | 11\n | ibivibiv/math_instruct | |
Is 2356 a factor of 343612842?\n | False\n | ibivibiv/math_instruct | |
Let x = 105844 - 39507. Is x prime?\n | True\n | ibivibiv/math_instruct | |
Find the second derivative of -2*b**2*m*z + 2*b**2*z**3 + 882*b**2*z**2 + 2*b*m - 816*m*z**3 + 2*m wrt b.\n | -4*m*z + 4*z**3 + 1764*z**2\n | ibivibiv/math_instruct | |
Let i(m) = -22*m**3 + 2*m - 2. Let q(z) = z - 1. Determine -i(a) + 2*q(a).\n | 22*a**3\n | ibivibiv/math_instruct | |
In base 3, what is 10 + -21021?\n | -21011\n | ibivibiv/math_instruct | |
What is the third smallest value in 2/25, 16, 0.3?\n | 16\n | ibivibiv/math_instruct | |
What comes next: 1309, 1306, 1293, 1264, 1213, 1134, 1021, 868?\n | 669\n | ibivibiv/math_instruct | |
Is 125 a factor of 606175?\n | False\n | ibivibiv/math_instruct | |
Let o = -13 - -8. Let d(v) = v**3 + 4*v**2 - 6*v + 1. Is d(o) prime?\n | False\n | ibivibiv/math_instruct | |
Find the third derivative of 776*h**6 + 8*h**3 - 160897*h**2 wrt h.\n | 93120*h**3 + 48\n | ibivibiv/math_instruct | |
Let l be 0*5/(-20)*1. Suppose l = -7*u + u + 966. Is u composite?\n | True\n | ibivibiv/math_instruct | |
Expand (-2 + 2 - 3)*(-3*b**4 + 2*b**4 + 14*b**4).\n | -39*b**4\n | ibivibiv/math_instruct | |
Which is the smallest value? (a) -2/25 (b) 20 (c) -4/107\n | a\n | ibivibiv/math_instruct | |
-1762 divided by 881\n | -2\n | ibivibiv/math_instruct | |
Suppose 18*t + 4*t - 2178 = 0. Let l be t*(115/23 + (-32)/6). Put 0.1, l, 4 in increasing order.\n | l, 0.1, 4\n | ibivibiv/math_instruct | |
Calculate ((-364)/312)/((-3)/(-36)).\n | -14\n | ibivibiv/math_instruct | |
In base 8, what is -556475 + -76?\n | -556573\n | ibivibiv/math_instruct | |
Simplify (g**(-2/21)*(g**(-2/11)*g)/g)/((g/g**(1/9))/g*g**(-7)) assuming g is positive.\n | g**(4736/693)\n | ibivibiv/math_instruct | |
b"What is the qth term of 223955, 447944, 671933, 895922?\n" | 223989*q - 34\n | ibivibiv/math_instruct | |
Which is the closest to 2? (a) -0.2 (b) 0.4 (c) 53 (d) 2 (e) 4140\n | d\n | ibivibiv/math_instruct | |
Calculate 18/10*1060/318.\n | 6\n | ibivibiv/math_instruct | |
Let s(u) = -16*u**2 - 5*u + 11. Let w(d) = -3*d**2 - d + 2. Let y(h) = 2*s(h) - 11*w(h). Factor y(k).\n | k*(k + 1)\n | ibivibiv/math_instruct | |
Write an educational piece suited for college students related to the following text snippet:
"# 数学代写|微积分代写Calculus代写|MATH7000
## 数学代写|微积分代写Calculus代写|Limit of a Function
Definition of a Limit:
Let $f(x)$ be defined for all $x$ in an interval about $x=a$, but not necessarily at $x=a$. If there is a number $L$ such th... | Limits of a function are fundamental concepts in calculus which describe how a function approaches a certain value as the input (or variable) gets arbitrarily close to a specified value. In this discussion, we will delve into the definition of limits, its properties, and two crucial trigonometric limits. We'll also pr... | ibivibiv/math_instruct | |
What is 676 minutes before 5:15 AM?\n | 5:59 PM\n | ibivibiv/math_instruct | |
Which is the second biggest value? (a) -0.5 (b) 1 (c) 1238 (d) -578\n | b\n | ibivibiv/math_instruct | |
Suppose q - 4 = 2*m, -12 = 3*m + 3*q + 12. Put m, -2, -1 in decreasing order.\n | -1, -2, m\n | ibivibiv/math_instruct | |
Let a = 4.37279 - -3.06416. Let t = a - 7.48. Round t to 3 dps.\n | -0.043\n | ibivibiv/math_instruct | |
Let o be 8*(-4)/(-8) - (-8)/(-2). Suppose 11 + o = l. Suppose -8*h = -l*h + 5523. Is h a prime number?\n | False\n | ibivibiv/math_instruct | |
Let y = 2721505 + -2721638.172992. Let i = -131.173 - y. Let p = 2 - i. Round p to five decimal places.\n | 0.00001\n | ibivibiv/math_instruct | |
What is the result of the following expression?
(-7.33 + -6.57) % (-6.13 - -2.34) | -2.53 | ibivibiv/math_instruct | |
Two letters picked without replacement from ffwififfw. Give prob of picking 2 w.\n | 1/36\n | ibivibiv/math_instruct |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.