conversations listlengths 2 2 | id stringlengths 32 36 | source_dataset stringclasses 2
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[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nEvaluate the integral $\\int_{0}^{\\frac{\\pi}{4}} \\cos^{\\frac{3}{2}}(2x) \\cos(x) \\, dx$.",
"role": "user"
},
{
"content": "<think>We need answer only inside boxed. Need solve integ... | 1c09d2d8-1d5e-42c8-871a-7da50d297558 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nCompare \\( A = \\frac{2007^{2006} + 1}{2007^{2007} + 1} \\) and \\( B = \\frac{2007^{2007} + 1}{2007^{2008} + 1} \\).",
"role": "user"
},
{
"content": "<think>We need answer compare A ... | b51280d1-da6c-490a-9340-d870f781d23d | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"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": "user"
},
{
"content": "<think>We need to solve the integral ∫_0^∞ sin(x^2) dx. This is a classic Fresn... | da0cf3c2-5193-4cf1-860e-b51897df0f84 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nSolve the system of equations for \\(a, b, c \\in \\mathbb{R}\\):\n\n\\[\n\\begin{aligned}\na^2 + b^2 + c^2 &= \\frac{5}{3} \\\\\nabc &= 1\n\\end{aligned}\n\\]",
"role": "user"
},
{
"co... | 57215f6c-b07a-4bb8-ba8c-e95db666eb72 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"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.",
"role": "user"
},
... | 80eba578-3c17-4152-9bc5-5ab80236fbcc | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"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": "user"
},
{
"content": "<think>We need solve math. Ne... | 2643d7d5-a7f1-4935-9a19-3019db316140 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"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 numbers are divisible ... | 84214e90-ddd4-4f15-919b-43efa5d55975 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nSolve the equation \\(\\dfrac{1}{x+2009} + \\dfrac{2010}{y+2010} = 1\\) for natural numbers \\(x\\) and \\(y\\).",
"role": "user"
},
{
"content": "<think>The given equation is $\\frac{1... | 7a18cc3d-925a-4b77-b1d3-e7f27282eeac | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"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 the resulting functio... | dd9f82e0-8599-4153-8db3-1a7ed1692237 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nSolve the equation in real numbers:\n$$[x] + [2x] + [3x] + \\cdots + [2017x] = 1 + 2 + 3 + \\cdots + 2017$$",
"role": "user"
},
{
"content": "<think>The given equation is\n$$\\sum_{k=1}... | 09ff5c54-a9d5-4f2b-9ea2-9cfe78515250 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"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": "user"
},
{
"content": ... | 0f6d7264-59f0-4735-963d-4d024507d712 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nGiven that \\( n + m = 2014 \\), find the maximum and minimum values of \\( n! \\cdot m! \\).",
"role": "user"
},
{
"content": "<think>The problem asks for the maximum and minimum value... | 6947058d-b59c-498b-af59-7406de67308d | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"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": "user"
},
{
"content": "<think>The problem asks for all positive integers $N$ such that $N... | 755a1036-c6de-4650-b102-79295219c4f4 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"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 \\), where \\( p, q \\) are p... | 83dc3d80-867e-48cc-8644-c94f3d6c439f | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"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": "user"
},
{
"content": "<think>The problem asks for t... | 335e3b92-7061-4766-9939-275494c6ab67 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nGiven that \\( f(xy) = f(x) + f(y) + 1 \\) for \\( x, y > 0 \\) and \\( f(2) = 0 \\), find \\( f(2018) \\).",
"role": "user"
},
{
"content": "<think>The given equation is a functional e... | ddd6705f-4c2e-46d3-afd7-ddeaab88d3b9 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"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": "user"
},
{
"content": "<think>We need to evaluate the definite integral:\n\n\\[ I = \\int_0^1 (1 - \\... | cda83850-fbb6-447c-97fb-59c111a5596a | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nUse the Taylor Series found in part (a) to find the limit as \\( x \\) approaches 0 of \\( \\frac{1 - x^2 - f(x)}{x^4} \\).",
"role": "user"
},
{
"content": "<think>We need answer math ... | e8dc8fee-0cf2-4528-b0b1-c36115c2b815 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nSolve the following equations and inequalities: $\\sqrt {\\frac{x^2-2x-2}{x^2+4x+2}}+\\sqrt {\\frac{x^2+4x+2}{x^2-2x-2}}=2$.",
"role": "user"
},
{
"content": "<think>The equation is $\\... | 93e96799-12ce-4342-97ad-ea1f8cb41319 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nGiven a triangle with vertices \\((x_1, y_1)\\), \\((x_2, y_2)\\), and \\((x_3, y_3)\\), find the coordinates of the incenter of the triangle.",
"role": "user"
},
{
"content": "<think>W... | b6108e2b-cb0d-4e66-b608-31a324a9a07a | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\( P(x) \\) be a polynomial of degree 2010. What is the maximum degree of the polynomial \\( P(x-1) - 3P(x) + 3P(x+1) - P(x+2) \\)?",
"role": "user"
},
{
"content": "<think>The giv... | eaa17062-7cf5-4a2d-a507-bae3e384513c | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the coefficient of \\( a^8 b^4 c^9 d^9 \\) in the expansion of \\( (ab(c+d) + cd(a+b))^{10} \\).",
"role": "user"
},
{
"content": "<think>The problem asks for the coefficient of $a... | f8ad9798-62a7-46df-8615-dd0a3a3c52b4 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"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 book taking her 1 mor... | 481b8bf4-3e6a-4976-b2e8-f35f0c0b0e4a | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"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": "user"
},
{
"content": "<think>The problem asks for all primes $p ... | f8f6a5e4-f5a2-46da-b13b-7ec80a4b0b19 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet $a, b, c$, and $m$ be positive real numbers. Find for which $m$, independently of $a, b$, and $c$, at least one of the following three equations has real roots:\n\\[ ax^2 + bx + cm = 0, \\]\n\\... | 9e49d8ea-20a6-4447-bd4b-026b6e1539ca | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"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": "user"
},
{
"content": "<think>We need to find the nth derivative of $f(x) = \\frac{x^n}{1-x}$.\n\nWe need to com... | 7bd935f5-cfef-4008-b139-657db1e1506c | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nGiven the sequence defined by $a_{1}=0$ and $a_{n}=2a_{n-1} + (-1)^n$, find a closed-form expression for $a_n$ as a function of $n$.",
"role": "user"
},
{
"content": "<think>The problem... | e7e07d16-f237-4a9c-84e7-959058f5af77 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA right-angled triangle is inscribed in the parabola $y = x^2$, with its hypotenuse parallel to the $x$-axis. What can be the altitude of the triangle drawn to the hypotenuse?",
"role": "user"
... | c217d436-49fe-41ed-bffb-785359076471 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"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": "user"
},
{
"content": "<think>We need solve ... | eebc2658-77d3-458a-97fc-10be798908cd | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nEvaluate \\(\\lim_{n\\to\\infty} nI_n^2\\) where \\(I_n = \\int_0^{\\frac{\\pi}{2}} \\sin^n \\theta \\, d\\theta\\) for \\(n = 0, 1, 2, \\ldots\\).",
"role": "user"
},
{
"content": "<th... | add119fa-0233-434d-80f0-8d6b5cea765e | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA pipe is being carried down a hallway that is 8 ft wide. At the end of the hallway, there is a right-angled turn into a narrower hallway 7 ft wide. Find the length of the longest pipe that can be ... | 709bbc56-758d-4ba9-bfed-1984fee7ca3d | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFor the set \\( S_n = \\{1, 2, \\ldots, n\\} \\), find the maximum value of \\( m \\) such that there exist \\( m \\) different subsets \\( A_1, A_2, \\ldots, A_m \\) of \\( S_n \\) where for every... | 64c778b0-6b67-4995-800b-86dc786bb030 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn triangle \\(ABC\\), \\(\\angle B = 30^\\circ\\) and \\(\\angle C = 105^\\circ\\). Point \\(D\\) is the midpoint of side \\(BC\\). Find \\(\\angle DAC\\).",
"role": "user"
},
{
"conte... | bc830de9-c62b-459b-a967-ddddb1c4200f | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind \\( \\lim_{x \\to 1} \\frac{\\ln(x-1) + \\tan\\left(\\frac{\\pi x}{2}\\right)}{\\cot(\\pi x)} \\)",
"role": "user"
},
{
"content": "<think>We need solve limit x->1 of [ ln(x-1) + t... | 4fd18017-0f7d-47a1-9eb9-00e43ad0fcf6 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nSolve for \\( m \\) such that \\( K(m,3) = 64m^3 + 702046 \\), where \\( K(m,n) \\) is the smallest natural number exceeding \\( (\\sqrt{m+3} + \\sqrt{m+2})^{2n} \\).",
"role": "user"
},
{
... | fb3f0dc3-168e-454c-ab0b-7e1798e162aa | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nDetermine the remainder when \\( a_{83} = 6^{83} + 8^{83} \\) is divided by 49.",
"role": "user"
},
{
"content": "<think>The problem asks for the remainder when $a_{83} = 6^{83} + 8^{83... | fad2d2d3-857d-4b67-9d9f-826618590123 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFor \\( n \\geq 2 \\), let \\( a_n x + b_n \\) be the remainder when \\( x^n \\) is divided by \\( x^2 - 6x - 12 \\). Find, for each \\( n \\), all prime numbers that are common divisors of \\( a_n... | fa96221c-e2aa-4c76-b10a-739fa0afe29c | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn $\\triangle ABC$, points $M$, $I$, and $H$ are the feet of the median, bisector, and height, respectively, drawn from $A$. Given that $BC = 2$, $MI = 2 - \\sqrt{3}$, and $AB > AC$, determine $\\... | 91dfe08a-3dd4-4410-9d8e-7fd6890be226 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nEvaluate the integral $\\int \\frac{e^{x} ( x^{2} - x +2)}{(x+1)^{3}} \\ dx$.",
"role": "user"
},
{
"content": "<think>The integral to evaluate is:\n$\\int \\frac{e^{x} ( x^{2} - x +2)}... | 13776b95-1493-489d-9190-727d86fcfc71 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the volume of a doughnut (torus) with an inner diameter of 2 cm and a boundary diameter of 2 cm. Generalize the formula for the volume of a torus given its inner and boundary diameters.",
... | fc5e3b4a-b57e-4902-b518-09386baa25ee | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nGiven a square \\(ABCD\\), let \\(P, Q, R\\), and \\(S\\) be four variable points on the sides \\(AB, BC, CD\\), and \\(DA\\), respectively. Determine the positions of the points \\(P, Q, R\\), and... | ff090ac6-9b0f-4746-a385-ee71485ff348 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn the complex plane, let points \\( A(x) \\), \\( B(y) \\), and \\( C(z) \\) be such that \\( |x| = |y| = |z| = m \\) where \\( m \\in \\mathbb{R}^+ \\), and \\( m^2 (x + y + z) = xyz \\in \\mathb... | c134379a-b83f-4532-9616-0b4f8cf0015f | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet A be the point (7,4) and D be (-5,-3). What is the length of the shortest path ABCD, where B is a point (x, 2) and C is a point (x, 0)? This path consists of three connected segments, with the ... | 314c3abf-0ab1-4638-9967-867526e46383 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\(ABC\\) be a triangle with \\(AB=13\\), \\(BC=14\\), and \\(CA=15\\). The incircle of \\(ABC\\) meets \\(BC\\) at \\(D\\). Line \\(AD\\) meets the circle through \\(B\\), \\(D\\), and the ref... | 6c5a582e-3ac5-469b-be6d-ca2ab6cf3157 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nWhat is the difference between the largest and smallest value for \\( \\text{lcm}(a, b, c) \\), where \\( a, b \\), and \\( c \\) are distinct positive integers between 1 and 10, inclusive?",
"... | 77d6867f-b44b-4ac4-95ba-14ad89bf580b | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"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}{4}} x \\cos^{2} x \\, dx \\).",
"role": "user"
},
{
"content": "<think>We need solve integral 0 to pi/4 x cos^2 x dx. Need final only a... | 0860ca95-0298-436f-8f28-ef35b09d52b0 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nGiven various trapezoids whose two nonparallel sides and the smaller base are equal to $a$. Find the value of the greater base of the trapezoid which has the greatest area.",
"role": "user"
}... | 4038ba9f-6510-41cd-bee5-c9b86af2fc9c | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nWhat is the greatest integer of the product \\((1+1)(1+\\frac{1}{2})(1+\\frac{1}{4})(1+\\frac{1}{8})(1+\\frac{1}{16}) \\cdots (1+\\frac{1}{1024})(1+\\frac{1}{2048})\\)?",
"role": "user"
},
... | c2cbe525-9754-41c5-a937-f0e5f6685c28 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFor which \\( x \\in \\mathbb{R} \\) will the infinite series \\( \\sum_{n=0}^{\\infty} \\sin(nx) \\) be convergent?",
"role": "user"
},
{
"content": "<think>The given series is $\\sum_... | d7b93c1a-2913-49e3-b8f2-cc447bf3beca | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nEvaluate:\n\\[ \\sum_{n=1}^{\\infty} \\arctan \\left( \\frac{\\sqrt{3}}{1 + 3n + 3n^{2}} \\right) \\]",
"role": "user"
},
{
"content": "<think>The problem asks us to evaluate the sum:\n... | b7555a4d-c0aa-4e64-b7e3-52607e04aeea | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"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": "user"
},
{
"content": "<think>The problem asks for the number of... | 6f94e3aa-9fae-42cd-b917-69f8cbf6d7b0 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nSolve the system:\n\\[ x^3 + x(y - z)^2 = 2 \\]\n\\[ y^3 + y(z - x)^2 = 30 \\]\n\\[ z^3 + z(x - y)^2 = 16 \\]",
"role": "user"
},
{
"content": "<think>The given system of equations is:\... | a4182321-806e-4a08-a4ca-aad9d4520b2d | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all positive integers that have an even number of nice representations, where a nice representation of a positive integer \\( n \\) is defined as a sum of powers of 2 with at most two equal po... | 48876ccb-9607-4b09-906c-0bac32e385e8 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\(a, b, c, d\\) be the roots of the equation \\(t^4 - t^3 - 4t^2 + t + 1 = 0\\). Solve the system of equations:\n\n\\[\n\\begin{cases}\n\\frac{x}{a} + \\frac{y}{a-1} + \\frac{z}{a+1} + \\frac{... | 576d61fd-b2db-47b2-ae04-8d8ccc77ab72 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"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": "user"
},
{
"content": "<think>The given integral is:\n\\[ I = \\int_0^{\\frac{... | 66e86da1-fc54-4971-8eef-a7c5d065f0ac | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\(X, Y, Z\\) be independent random variables uniformly distributed on \\((0,1)\\). Define \\(Z_1 = \\max(X, Y)\\) and \\(Z_2 = \\min(Y, Z)\\). Find \\(E(Z_1, I(Z_1 = Z_2))\\).",
"role": "u... | 75c89fdd-81b2-4804-a01e-1c388bed3bec | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nEvaluate the definite integral $\\int_0^{\\frac{\\sqrt{3}}{2}} \\frac{t^2}{(1 - t^2)^{3/2}} \\, dt$.",
"role": "user"
},
{
"content": "<think>We need to evaluate the definite integral I... | 1d332a06-459b-43e1-a57b-d9ed49108df9 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the number of solutions in non-negative reals to the following system of equations:\n\\[\n\\begin{cases}\nx_1 + x_n^2 = 4x_n \\\\\nx_2 + x_1^2 = 4x_1 \\\\\n\\vdots \\\\\nx_n + x_{n-1}^2 = 4x_{... | 2ccf0d1b-7242-4c4b-8590-ff059da80715 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the area of the object generated by the intersection of two cylinders given by the equations \\(x^2 + y^2 = 1\\) and \\(x^2 + z^2 = 1\\).",
"role": "user"
},
{
"content": "<think>T... | c0dc2b31-8044-46a6-95f3-e5e0aecdc872 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA particular right prism has a rectangular octagonal base with each base edge measuring 4 cm and a height of 3 cm. Its volume can be expressed in the form \\(a(b + \\sqrt{c})\\) cubic cm, where \\(... | 9d795992-ae27-4c65-9eea-1a30b0ba5ec0 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn a casino game, a set of numbers $S$ is given, with some numbers possibly appearing twice. You must choose a number (which does not have to be in $S$). A number is then chosen randomly from $S$, ... | ca3f967f-50f0-45e9-9e6f-11299c0fb1e8 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nSolve the equation $\\lfloor x \\rfloor \\cdot \\lfloor y \\rfloor = x + y$.",
"role": "user"
},
{
"content": "<think>We need solve equation floor(x)*floor(y) = x + y. Need likely find ... | 6aab3e0e-42cb-4d7a-b372-cba7428f1808 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\( f(x) = \\sqrt{-x^2 + 20x + 400} + \\sqrt{x^2 - 20x} \\). How many elements in the range of \\( f \\) are integers?",
"role": "user"
},
{
"content": "<think>The given function is... | c586e857-a475-48c2-8993-63820a4d1410 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the number of four-digit numbers that contain at least one pair of consecutive threes in their digits.",
"role": "user"
},
{
"content": "<think>The problem asks for the number of f... | 35de7972-9948-4b7d-8e0b-8b02a57c3453 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nWhat is the value of $$\\sum_{b=5}^\\infty \\frac{15b^2+68b+120}{2^b(b^4+64)}$$?",
"role": "user"
},
{
"content": "<think>The problem asks for the sum:\n$$\\sum_{b=5}^\\infty \\frac{15b... | 06a0fb7e-258c-4fe2-a7e7-62a9b24e886f | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nConsider the 13 cards in a standard playing deck of cards that belong to the hearts suit. Let U be the set of all four card arrangements chosen from the hearts suit with replacement. For each heart... | fe36facf-d050-4bf0-9418-eb951c56b8d8 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nDetermine the quadrant in which the orthocenter of the triangle formed by the lines \\( x + y = 1 \\), \\( 2x + 3y = 6 \\), and \\( 4x - y + 4 = 0 \\) lies.",
"role": "user"
},
{
"conte... | 631f6953-8f92-4421-bf5d-410076333199 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nGiven that \\( x^2 + y^2 = \\sqrt{3} \\), find the minimum value of \\( \\frac{3}{xy} + \\frac{x}{y} - \\frac{y}{x} \\).",
"role": "user"
},
{
"content": "<think>The problem asks for th... | 0e6f1526-a2c4-4370-bffb-ec651ec06c1f | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nHow many odd seven-digit palindromic numbers are there in which every digit appears at most twice?",
"role": "user"
},
{
"content": "<think>The problem asks for the number of odd seven-... | 08732574-dbeb-4c0d-8507-01b4d3899874 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn a cyclic quadrilateral, each side has a length of either $6$ or $8$, and one of the diagonals has a length of $10$. Find the radius of its circumscribed circle.",
"role": "user"
},
{
... | 1875da7b-be60-4d4e-9ab6-98d9c52fdc04 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nThe integers \\(a, b, c, d, e, f, g\\) (none of which is negative) satisfy the following five simultaneous equations:\n\\[ a + b + c = 2 \\]\n\\[ b + c + d = 2 \\]\n\\[ c + d + e = 2 \\]\n\\[ d + e... | a0f14887-c257-42a0-8371-6b659ec98223 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nGiven 8 piles of bricks with different amounts of bricks, each pile can be removed and its bricks can be scattered to the other piles so that the remaining piles have the same number of bricks. Wha... | 2469ad83-7334-47a9-8a00-123b55812add | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nCompute the limit\n\\[\n\\lim_{x \\to 1} \\left( \\frac{H_x}{x(x-1)} - \\frac{1}{(x-1)(2x-1)} \\right),\n\\]\nwhere \\( H_x \\) represents the fractional harmonic number.",
"role": "user"
},
... | bb6a28db-5e02-4f4c-a93b-0ca9e82bfd1f | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nWhat is the number of ordered pairs $(m,n)$ of positive integers such that $3m^2+8mn+3n^2=383$?",
"role": "user"
},
{
"content": "<think>The given equation is $3m^2+8mn+3n^2=383$.\nWe w... | 7f602ef1-b7eb-471e-9d3a-7c5ca6f346eb | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nA fair, unbiased coin is tossed three times on Friday, four times on Saturday, and five times on Sunday. What is the probability that exactly one toss shows \"tails\" on at least one of the three d... | dc010a9b-854d-4bde-9928-bd405183b63c | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all functions \\( f\\colon \\mathbb{R}\\to\\mathbb{R} \\) such that \\( f(f(x)) - 4f^3(x) + 4f(x) = -12x^3 + 21x - 10 \\).",
"role": "user"
},
{
"content": "<think>The given equati... | f3a2f166-ff05-4d38-8941-5a12cf3e3b21 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet \\( x_0 = 0 \\) and the sequence be defined by \\( x_{n+1} = \\frac{1}{4^{x_n}} \\). Determine the limit of the sequence as \\( n \\to \\infty \\).",
"role": "user"
},
{
"content": ... | a3faf83b-1883-4d1e-957a-783e37ce89a0 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nNine tiles are numbered 1, 2, 3, ..., 9. Each of the three players randomly selects and keeps 3 of the tiles, and sums these values. Find the probability that all three players obtain an odd sum.",... | 8ecedd6e-e6b7-4ab6-838a-714674bc76db | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nDetermine the value of the expression $ \\sqrt {5 + \\sqrt {5^2 + \\sqrt {5^4 + \\sqrt {5^8 + \\ldots}}}}$.",
"role": "user"
},
{
"content": "<think>The problem asks for the value of th... | dbf511c7-5798-42ee-9d09-2248f7825ca0 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIn parallelogram $ABCD$, angles $B$ and $D$ are acute while angles $A$ and $C$ are obtuse. The perpendicular from $C$ to $AB$ and the perpendicular from $A$ to $BC$ intersect at a point $P$ inside ... | 236cfdd9-f4bc-448f-b57d-e002342dfe87 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\n$A$ and $B$ travel around a circular track at uniform speeds in opposite directions, starting from diametrically opposite points. If they start at the same time, meet first after $B$ has traveled $... | d76f7b33-8c1e-46de-870e-06638690c7a7 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nEvaluate the sum \\( \\sum_{n=1}^{\\infty} \\frac{1}{d(n)!} \\), where \\( d(n) \\) represents the number of digits of \\( n \\) in its decimal representation.",
"role": "user"
},
{
"co... | f960d93d-92ad-4f88-8590-245c109b0ff8 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nInside or on the faces of a tetrahedron with five edges of length $2$ and one edge of length $1$, there is a point $P$ having distances $a, b, c, d$ to the four faces of the tetrahedron. Determine ... | 86b43c99-93e5-4dc5-8db8-fec820963a72 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet $x$, $y$, and $z$ be real numbers such that $x + y + z = 1$ and $x^2 + y^2 + z^2 = 1$. Let $m$ denote the minimum value of $x^3 + y^3 + z^3$. Find $9m$.",
"role": "user"
},
{
"conte... | d24ec5e5-5712-4ca7-a897-bfd17ec3768b | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the minimum value of the expression:\n\\[ P = (\\sin x)^4 \\left[ (\\sin y)^4 + (\\cos y)^4 + \\frac{9}{8} (\\cos x)^2 (\\sin 2y)^2 \\right] + (\\cos x)^4. \\]",
"role": "user"
},
{
... | 81a3173c-2c80-4b31-a336-e52d45a1ad32 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nIf $z$ is a complex number such that $z^{23}=1$, find the value of $\\displaystyle \\sum^{22}_{k=1}\\frac{1}{1+z^{8k}+z^{16k}}$.",
"role": "user"
},
{
"content": "<think>The problem ask... | fc41990b-1d01-4cc5-8638-a8fe2644b9f9 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all polynomials \\( P(x) \\) such that \n\\[ xP(x-1) = (x-2017)P(x). \\]",
"role": "user"
},
{
"content": "<think>The problem asks for all polynomials $P(x)$ such that $xP(x-1) = (... | 90e15f6a-81e7-4e26-8192-99694ee069eb | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all prime numbers \\( p \\) and \\( q \\) such that \\( pq \\) divides \\( (5^p - 2^p)(5^q - 2^q) \\).",
"role": "user"
},
{
"content": "<think>The problem asks for all prime numbe... | 279ee59b-8a49-414b-934c-4eb3ec32f09a | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"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 all possible values o... | e91be8a0-1b54-4902-99a6-49a03efc3ab5 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"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 elements \\( a, b \\... | 2961b3c3-1414-4615-b02d-d3592c1c7cb6 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFor which values of $t \\in (0,2\\pi)$ does the inequality $(\\sin t)x^2 + 2(1+\\sin t)x + 9\\sin t + 4 < 0$ hold for all $x \\in \\mathbb{R}$?",
"role": "user"
},
{
"content": "<think>... | 77ced1d8-36b1-4ccb-a5a5-91fce8053366 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all functions \\( f: \\mathbb{Z} \\longrightarrow \\mathbb{R} \\) such that for every \\( k \\in \\mathbb{Z} \\setminus \\{0\\} \\),\n\\[ \\sum_{s \\in \\mathbb{Z}} f(s)f(s+k) = 0 \\quad \\tex... | 3351864f-c3cf-448a-a5a4-ef120514b425 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nGiven a triangle \\( \\triangle ABC \\) with \\( \\angle ACB = 60^\\circ \\) and \\( AC = BC \\). Point \\( M \\) is such that \\( AM = \\sqrt{2} \\), \\( BM = 2 \\), and \\( \\angle AMC = 15^\\cir... | b5e494e9-3c83-4d84-8c1c-dba4ff66f773 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all real numbers \\( a \\) such that there exists a function \\( f : \\mathbb{R} \\to \\mathbb{R} \\) satisfying the equation\n\\[ f(x + yf(x)) = axy + f(f(x)) \\]\nfor all \\( x, y \\in \\mat... | c5c31b1a-8dd4-43ab-8742-2916d6ffe08f | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind all pairs \\((m, n) \\in \\mathbb{N}^2\\) such that \\(n^{n^n} = m^m\\).",
"role": "user"
},
{
"content": "<think>The problem asks for all pairs $(m, n) \\in \\mathbb{N}^2$ such th... | e2bd671c-b2d2-47f3-b60d-a6f7932cff06 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the equivalent of the function \\( f(x) = \\sum_{n=1}^{\\infty} (-1)^{n-1} \\ln\\left(1 + \\frac{x}{n}\\right) \\) as \\( x \\) approaches 0.",
"role": "user"
},
{
"content": "<thi... | d97a935a-2b6b-49da-96ce-baa705ec40d9 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nFind the point on the ellipse given by the equation $\\frac{x^2}{a^2}+\\frac{y^2}{b^2}=1$ such that the triangle formed by the tangent at this point and the coordinate axes has the minimal area.",
... | 4ab33463-db25-4ced-a2bc-ad9a1ccbdcaa | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nGiven a tower with top P and foot Q on a horizontal plane, points A and B are on the plane such that AB = 32 meters and ∠QAB is a right angle. It is given that cot(∠PAQ) = 2/5 and cot(∠PBQ) = 3/5. ... | e6081eca-b853-4cd9-bdb9-e4f00e9beeb1 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nLet the product of the roots of \\( z^6 + z^4 + z^3 + z^2 + 1 = 0 \\) with positive imaginary part be \\( r(\\cos \\theta^\\circ + i \\sin \\theta^\\circ) \\). Find \\( \\theta \\).",
"role": "... | 04e41430-4770-4729-b4ae-809add19e4d0 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
[
{
"content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\nWhat is the value of \\( \\sum_{n=0}^{\\infty} \\dfrac{4^{2^{n-1}}}{1-4^{2^{n}}} \\)?",
"role": "user"
},
{
"content": "<think>We need solve math problem: sum n=0 to infinity 4^{2^{n-1}... | e999e50c-2417-4409-abb9-8ef5fbd4f757 | nvidia/Nemotron-Post-Training-Dataset-v2 | CC BY 4.0 | success |
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