conversations listlengths 2 2 | thinking stringclasses 1
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[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nEvaluate the definite integral $\\int_0^1(1-\\sqrt[2024]x)^{2024}\\,dx$."
},
{
"role": "assistant",
"content": "We need to evaluate the definite integral I = ∫_0^1 (... | on | success |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nDetermine the quadrant in which the point $(\\cos{B}-\\sin{A}, \\sin{B}-\\cos{A})$ lies, given that $\\triangle{ABC}$ is a triangle with three acute angles A, B, and C."
},
... | on | success |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nZoey read 15 books, one at a time. The first book took her 1 day to read, the second book took her 2 days to read, the third book took her 3 days to read, and so on, with each b... | on | success |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\( A \\) be the set of the 16 first positive integers. Find the least positive integer \\( k \\) such that in every \\( k \\)-subset of \\( A \\), there exist two distinct ... | on | success |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nHow many three-digit natural numbers have digits that sum to 13 and leave a remainder of 1 when divided by 4?"
},
{
"role": "assistant",
"content": "We need to count... | on | success |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the nth derivative of \\( f(x) = \\frac{x^n}{1 - x} \\)."
},
{
"role": "assistant",
"content": "We need to find the nth derivative of f(x) = x^n/(1-x). Actually... | on | success |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all the positive divisors of the integers:\ni) \\( A = p^k \\), where \\( p \\) is a prime number and \\( k \\) is a positive integer.\nii) \\( B = p^k \\cdot q^l \\), wher... | on | success |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nEvaluate the integral $\\displaystyle \\int^{\\infty}_{0}\\sin(x^2)dx$."
},
{
"role": "assistant",
"content": "We need to evaluate ∫_0^∞ sin(x^2) dx. This is a known... | on | success |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nGiven that \\(\\sin A + \\sin B = 1\\) and \\(\\cos A + \\cos B = 0\\), find the value of \\(12 \\cos 2A + 4 \\cos 2B\\)."
},
{
"role": "assistant",
"content": "We n... | on | success |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nThe regular octagon \\( ABCDEFGH \\) has an area of \\( n \\). Let \\( m \\) be the area of quadrilateral \\( ACEG \\). Calculate \\( \\frac{m}{n} \\)."
},
{
"role": "as... | on | success |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nSolve the equation $x(x^{2}+11) + 3(x^{2}-3) + (x-11) \\sqrt{3-x} = 0$."
},
{
"role": "assistant",
"content": "We are given the equation:\n\nx(x^2 + 11) + 3(x^2 - 3)... | on | success |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all values of \\( n \\) such that the equation \\( x^3 + y^3 + z^3 = n(x^2 y^2 z^2) \\) has non-trivial solutions in positive integers."
},
{
"role": "assistant",
... | on | success |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nEvaluate the integral \\( \\int_0^{\\frac{\\pi}{2}} (x \\cos x + \\sin^2 x) \\sin x \\, dx \\)."
},
{
"role": "assistant",
"content": "We are asked to evaluate the i... | on | success |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nSuppose \\( A = [a_{ij}] \\in \\mathbb{R}^{n \\times n} \\) has the property that there exist constant real numbers \\( c_1, c_2, \\cdots, c_n \\) such that\n\\[ \\sum_{i=1}^k a... | on | success |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all primes \\( p < q < r \\) such that \\( 25pq + r = 2004 \\) and \\( pqr + 1 \\) is a perfect square."
},
{
"role": "assistant",
"content": "We need to find a... | on | success |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nGiven two sinusoids with frequencies of $8 \\text{ kHz}$ and $3.5 \\text{ kHz}$, is the function obtained by summing these two sinusoids periodic? If so, what is the period of t... | on | success |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nSolve the system of equations $x + y + z = 1$ and $xyz = 1$ where $x, y, z$ are complex numbers with absolute value equal to $1$."
},
{
"role": "assistant",
"content... | on | success |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nDetermine all positive integers that are equal to 300 times the sum of their digits."
},
{
"role": "assistant",
"content": "We need to find all positive integers N s... | on | success |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA number is called flippy if its digits alternate between two distinct digits. For example, 2020 and 37373 are flippy, but 3883 and 123123 are not. How many five-digit flippy nu... | on | success |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nCalculate $\\lim_{n\\to \\infty} \\sqrt[n]{{nk}\\choose{n}}$, where $k$ is an arbitrarily fixed integer greater than $1$."
},
{
"role": "assistant",
"content": "We n... | on | success |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nWithout using a calculator, determine which is greater: $\\sin 28^\\circ$ or $\\tan 21^\\circ$."
},
{
"role": "assistant",
"content": "We are asked: \"Without using ... | on | success |
[
{
"role": "user",
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFor certain pairs $(m, n)$ of positive integers with $m \\ge n$, there are exactly 50 distinct positive integers $k$ such that $|\\log m - \\log k| < \\log n$. Find the sum of a... | on | success |
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