prompt list | ground_truth string |
|---|---|
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $37,811 |
[
{
"content": "Given the equations:\n\\[ x^{2} - 2px -5q = (x-m)(x-n) \\]\nand\n\\[ x^{2} - 2mx -5n = (x-p)(x-q) \\]\nwhere \\( p \\neq q \\neq m \\neq n \\), find the value of \\( p+q+m+n \\).",
"role": "user"
}
] | 30 |
[
{
"content": "Compute the integral of the 1-form \\( \\omega = \\frac{x\\,\\mathrm{d}y - y\\,\\mathrm{d}x}{x^2+y^2} \\) over the unit circle parameterized by \\( \\gamma(t) = (\\cos(t), \\sin(t)) \\) for \\( t \\in [0, 2\\pi] \\).",
"role": "user"
}
] | 2\pi |
[
{
"content": "Given a prime $q$ and an integer $n < q$, consider the finite field of $q^n$ elements. Let $s_n^k$ be the $k$-th elementary symmetric polynomial in $n$ variables, defined as $s_n^k(x_1, \\ldots, x_n) = \\sum_{i_1 < \\ldots < i_k} x_{i_1} \\cdot \\ldots \\cdot x_{i_k}$. Suppose for specific $c_1, \... | Yes |
[
{
"content": "Determine the number of ways to color the edges of a regular tetrahedron using \\( n \\) colors such that exactly two of the faces form monochromatic triangles.",
"role": "user"
}
] | 6n(n - 1) |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 6.3e-7 M |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 17.44% |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 28939.5 Pa |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -4 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $8,732.64 |
[
{
"content": "Find a single polynomial that generates the ideal $J = (h,k)$ in $\\mathbb{R}[x]$, where $h = (x^2 - 9)(x - 3)$ and $k = (x^4 - 81)(x + 2)$. Provide your answer as a polynomial expression.",
"role": "user"
}
] | x^2 - 9 |
[
{
"content": "Given the joint density function \\( f(x,y) = e^{-y} \\) for \\( 0 < x < y < \\infty \\), determine the joint density function for \\( W = X - Y \\).",
"role": "user"
}
] | e^{w} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $57,500 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $46,357.50 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.0e+3 m/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.32e13 J |
[
{
"content": "The dilation, centered at $-1 + 4i,$ with scale factor $-2,$ takes $2i$ to which complex number?",
"role": "user"
}
] | -3 + 8i |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $66,600 Unfavorable |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 940.4kg |
[
{
"content": "Determine whether there exists a natural number \\( n \\) such that \\( n^{2012} - 1 \\) is a power of two.",
"role": "user"
}
] | No |
[
{
"content": "If \\(z\\) is a complex number satisfying \\(|z^3+z^{-3}| \\le 2\\), what is the maximum possible value of \\(|z+z^{-1}|\\)?\n\n(A) \\(2\\)\n(B) \\(2^{1/3}\\)\n(C) \\(2\\sqrt{2}\\)\n(D) \\(1\\)",
"role": "user"
}
] | A |
[
{
"content": "In triangle \\( \\triangle ABC \\), \\( O \\) is the circumcenter of \\( \\triangle ABC \\), and \\( D \\) is the midpoint of \\( AC \\). It is given that \\( \\overrightarrow{OB} \\cdot \\overrightarrow{OD} = \\overrightarrow{OA} \\cdot \\overrightarrow{OC} \\). Determine the minimum value of \\(... | 1 |
[
{
"content": "Given the equation \\( x^3 + y^3 = (4x - 5y)y \\) for positive real numbers \\( x \\) and \\( y \\), find the maximum value of \\( y \\).",
"role": "user"
}
] | \dfrac{1}{3} |
[
{
"content": "A particle of mass \\(m\\) starts from rest at time \\(t=0\\) and is moved along the \\(x\\)-axis with constant acceleration \\(a\\) from \\(x=0\\) to \\(x=h\\) against a variable force of magnitude \\(F(t)=t^2\\). Find the work done in moving the particle from \\(x=0\\) to \\(x=h\\).",
"role"... | \dfrac{h^2}{a} |
[
{
"content": "Let $V$ be an open neighborhood of a point $y \\in \\mathbb{R}^n$. Suppose that $V$ is $C^k$ ($0 \\leq k \\leq \\infty$). Let $g:\\mathbb{R}^n \\rightarrow \\mathbb{R}^n$ be a $C^k$ diffeomorphism. Is $g^{-1}(V)$ also a $C^k$ open neighborhood?",
"role": "user"
}
] | Yes |
[
{
"content": "Let $A$ and $B$ be $n \\times n$ matrices over $\\mathbb{R}$ with minimal polynomials $x^2 - 1$ and $x^2 + 1$, respectively. If $A$ and $B$ commute, find the minimal polynomial of the matrix $AB$. \\(AB = BA\\)",
"role": "user"
}
] | x^2 + 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.33 years |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 6.56 m/s^2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Br2O5 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -32.77 cm |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.30 moles |
[
{
"content": "Determine the number of independent 3-cycles in a complete graph $K_n$, where $n \\ge 3$. Independent 3-cycles form a minimal set that can generate any cycle within $K_n$. Prove that the number of such 3-cycles is given by $\\binom{n-1}{2}$.",
"role": "user"
}
] | \dbinom{n-1}{2} |
[
{
"content": "Find the smallest positive common difference of a 6-term arithmetic progression consisting entirely of positive prime numbers.",
"role": "user"
}
] | 30 |
[
{
"content": "Find all natural number solutions $(m, n)$ to the equation $5^m = 2 + 3^n$.",
"role": "user"
}
] | (1, 1) |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -0.046 C |
[
{
"content": "A coin is tossed repeatedly until either two heads or two tails appear consecutively. The game ended with two tails. What is the probability that the game started with a head? Express your answer as a fraction.",
"role": "user"
}
] | \dfrac{1}{3} |
[
{
"content": "Evaluate the integral \\( \\int_{0}^{a} \\frac{dx}{x + \\sqrt{a^{2} - x^{2}}} \\) where \\( a \\) is a positive constant.",
"role": "user"
}
] | \dfrac{\pi}{4} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.22e-13 C |
[
{
"content": "The roots of a quadratic equation with a mistaken constant term are \\(-17\\) and \\(15\\), and with a mistaken leading coefficient, the roots are \\(8\\) and \\(-3\\). Find the actual roots of the quadratic equation.",
"role": "user"
}
] | -1 \pm \dfrac{\sqrt{215}}{5}i |
[
{
"content": "Fido's leash is tied to a stake at the center of his yard, which is in the shape of a regular hexagon. His leash is exactly long enough to reach the midpoint of each side of his yard. If the fraction of the area of Fido's yard that he is able to reach while on his leash is expressed in simplest ra... | 18 |
[
{
"content": "Determine whether the sequence \\( \\left( \\frac{\\sum_{j=1}^n (-1)^j j^k}{\\sum_{j=1}^n j^k} \\right)_{n \\in \\mathbb{N}} \\) converges or diverges for some \\( k \\in \\mathbb{N} \\). Justify your answer.",
"role": "user"
}
] | 0 |
[
{
"content": "Find the minimum value of the expression \\[ \\frac{x(1+y)+y(1+z)+z(1+x)}{(xyz)^{\\frac{1}{2}}} \\] where \\(x, y, z\\) are positive integers.",
"role": "user"
}
] | 6 |
[
{
"content": "Consider an $n \\times n$ array where each site is either open or blocked. A fluid falls from the top, and a site becomes \"full\" if it has fluid. Fluid can only move downwards and stops at blocked sites. The array percolates if fluid reaches the bottom row in at least one column. If each site is... | 1 - (1 - p^n)^n |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 6-ethyl-2,2-dimethylheptane |
[
{
"content": "Find the minimum value of $f(b)$, where $f(b)$ is the maximum value of $g(x)$, and $g(x) = \\left|\\sin x + \\frac{2}{3 + \\sin x} + b\\right|$. Provide your answer as a single number.",
"role": "user"
}
] | \dfrac{3}{4} |
[
{
"content": "Determine whether there exists a field extension $E$ containing $S$ such that $E$ has finite dimension when considered as a vector space over $S$. Here, $S$ is a subset of the positive real numbers $\\mathbb{R}^+$, and $(S, \\times)$ is a group. Additionally, $(S, \\times, *)$ is a field with the ... | Yes |
[
{
"content": "Find the remainder when \\(x^{1000000}\\) is divided by \\(x^3 + x + 1\\) in \\(\\mathbb{Z}_2[x]\\).",
"role": "user"
}
] | x |
[
{
"content": "Determine whether the Fourier inversion theorem holds for a function $f$ such that $\\int_{-\\infty}^{\\infty}|f(x)|dx<\\infty$. Specifically, is it true that for almost every $x\\in\\mathbb{R}$, the Fourier transform of $f$, denoted by $\\hat{f}$, satisfies $$f(x)=\\lim_{R\\rightarrow+\\infty}\\i... | No |
[
{
"content": "Evaluate the integral \\( \\int_C \\frac{z^2 \\, dz}{z^2+4} \\) where \\( C \\) is the square with vertices at \\( 2, -2, 2+4i, -2+4i \\). Use the Cauchy integral formula to find the value of the integral.",
"role": "user"
}
] | -2\pi |
[
{
"content": "If $f$ is a uniformly continuous function and $\\{x_n\\}$ and $\\{y_m\\}$ are Cauchy sequences in $D$, does it follow that $f(x_n)$ and $f(y_m)$ are also Cauchy sequences?",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.35% |
[
{
"content": "The center of the circle with equation $x^2+y^2=-2x-10y-16$ is the point $(x,y)$. What is $x+y$?",
"role": "user"
}
] | -6 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2500 V |
[
{
"content": "Evaluate the limit of the line integral \\( \\int_\\mathrm{arc} \\frac{\\exp(iz)}{z+1} \\, dz \\) as the radius \\( R \\) of the semi-circular arc in the upper half complex plane goes to infinity. Does the integral converge to a fixed constant? If so, calculate this constant.",
"role": "user"
... | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $3,423,791.48 |
[
{
"content": "Determine whether the number of intersection points of two distinct piecewise differentiable simple closed curves in \\(\\mathbb{R}^2\\) is necessarily finite.",
"role": "user"
}
] | No |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.78 M |
[
{
"content": "Determine whether the following limit converges to 0:\n\\[ \\lim_{N \\to \\infty} e^N \\int_{N}^{\\infty} \\frac{e^{-x}}{\\log(x)} \\, dx \\]",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -3.96 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | The weight of Stock D is 0.2213, and the weight of Stock I is 0.7787. |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 589.56 N |
[
{
"content": "Determine whether the ideal generated by $y$ in the integer ring $\\mathcal{O_k}$ of the number field extension $\\mathbb{Q}(y)$, where $y^{2}=3$, is prime, given that the norm of $y$ is 3.",
"role": "user"
}
] | Yes |
[
{
"content": "Compute the limit: \\[ \\lim_{x \\to 0^{+}} \\frac{4^{-1/x}+4^{1/x}}{4^{-1/x}-4^{1/x}} \\] without using L'Hopital's rule.",
"role": "user"
}
] | -1 |
[
{
"content": "How many distinct Boolean algebras can be formed with the six elements $0, 1, a, b, c, d$?",
"role": "user"
}
] | 0 |
[
{
"content": "Calculate the limit: $$\\lim_{n \\to \\infty} \\ln \\left(\\frac{n!^{\\frac{1}{n}}}{n}\\right)$$",
"role": "user"
}
] | -1 |
[
{
"content": "A deck of $n$ cards numbered $1, 2, \\ldots, n$ is shuffled. Determine the probability that exactly one card remains in its original position. What is the limit of this probability as $n$ approaches infinity?",
"role": "user"
}
] | \dfrac{1}{e} |
[
{
"content": "Given a continuous function $f:[-2,8]\\rightarrow\\mathbb{R}$ such that $f(6-x)=f(x)$ for all $x\\in[-2,8]$, and knowing that \\(\\int_{-2}^8f(x)dx=10\\), find the value of \\(\\int_{-2}^8xf(x)dx\\).",
"role": "user"
}
] | 30 |
[
{
"content": "Find the volume of the region bounded between the surfaces defined by the equations \\( z^2 = x^2 + y^2 \\) and \\( z = x^2 + y^2 \\).",
"role": "user"
}
] | \dfrac{\pi}{6} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | HCl, H2SO3, HF, HOCl |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -1.5 m/s |
[
{
"content": "Calculate the residue of the function \\( \\frac{z^9}{z^{10} -1} \\) at infinity.",
"role": "user"
}
] | -1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4/3m/s and 40/3m/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1092 g/mL |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5.65e+22 atoms |
[
{
"content": "Given positive numbers $a$, $b$, and $c$ such that $\\frac{a}{2} + b + 2c = 3$, determine the maximum value of $\\min\\left\\{ \\frac{1}{2}ab, ac, 2bc \\right\\}$.",
"role": "user"
}
] | 1 |
[
{
"content": "Determine whether the set \\(\\{(m, -m)| m\\in\\mathbb{Z}\\}\\) with the operation \\((m, -m) + (n, -n) = (m+n, -(m+n))\\) is isomorphic to the set \\(\\mathbb{Z}\\) with the operation of addition. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the limit of the sequence \\( \\lim_{n\\to\\infty}\\frac{(n!)^{1/n}}{n} \\) using the Gamma function.",
"role": "user"
}
] | \dfrac{1}{e} |
[
{
"content": "Solve for \\( x \\) in the equation: \\[ 5^{x+2} + 2^{x+1} = 2^{x+5} + 13 \\cdot 5^x \\]",
"role": "user"
}
] | 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 16023000 |
[
{
"content": "Determine which of the following expressions correctly calculates the number of permutations of the numbers 1, 2, ..., 1392, such that exactly 696 of these numbers are in their natural positions:\n\n(a) \\(\\frac{1392!}{696!}\\sum_{k=0}^{696} \\frac{(-1)^k}{k!}\\)\n\n(b) \\(\\binom{1392}{696}\\sum... | a |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 18.2 g |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 8.51% |
[
{
"content": "The sum of the $x$-coordinates of the vertices of a triangle in the Cartesian plane equals $\\sqrt{13}$. Let $S$ equal the sum of the $x$-coordinates of the midpoints of the sides of the triangle. Find $S^2$.",
"role": "user"
}
] | 13 |
[
{
"content": "Adam and Simon start on bicycle trips from the same point at the same time. Adam travels east at 8mph and Simon travels south at 6mph. After how many hours are they 60 miles apart?",
"role": "user"
}
] | 6 |
[
{
"content": "Given the transition matrix of a Markov chain:\n\\[\n\\begin{bmatrix} \n\\frac{1}{5} & \\frac{4}{5} & 0 & 0 & 0 \\\\\n\\frac{1}{2} & \\frac{1}{2} & 0 & 0 & 0 \\\\\n\\frac{1}{5} & \\frac{1}{5} & \\frac{1}{5} & \\frac{1}{5} & \\frac{1}{5} \\\\\n0 & \\frac{1}{3} & \\frac{1}{3} & \\frac{1}{3} & 0 \\\\... | \dfrac{5}{13} |
[
{
"content": "Let \\( f(x) \\) be a non-negative continuous function on \\( \\mathbb{R} \\) such that \\( f(x) + f(x+\\frac{1}{3}) = 5 \\). Calculate the value of the integral \\( \\int_0^{1200} f(x) \\, dx \\).",
"role": "user"
}
] | 3000 |
[
{
"content": "Does there exist an increasing function \\( g \\) such that \\( g' = 0 \\) almost everywhere, but \\( g \\) is not constant on any open interval?",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1095.92 nm |
[
{
"content": "Determine the exact number of real roots of the equation \\(x^{2016} - x^{2011} + x^{2006} - x^{2001} + 1 = 0\\).",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $115,066.26 plus closing costs |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.2e-5 g/L |
[
{
"content": "A sphere with an initial radius of $24$ cm has its volume decreasing at a rate of three times its surface area per unit time. How long does it take for the volume to be reduced to one-eighth of its original size?",
"role": "user"
}
] | 4 |
[
{
"content": "Find an asymptotic equivalent of the sequence \\((u_n)_{n \\in \\mathbb{N}^*}\\) defined by:\n\\[ u_1 = 1, \\quad u_{n+1} = 1 + \\frac{n}{u_n} \\]\nas \\(n\\) approaches infinity. Provide a proof for your proposed equivalent.",
"role": "user"
}
] | \sqrt{n} |
[
{
"content": "Calculate the sum \\( \\sum^{20}_{k=1}\\frac{1}{x_k-x_k^2} \\) where \\( x_k \\) are the roots of the polynomial \\( P(x)=x^{20}+x^{10}+x^5+2 \\).",
"role": "user"
}
] | 7 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.87e5 m/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.7J |
[
{
"content": "Determine the values of $a$ for which the improper integral \\( \\int_{0}^{\\infty} \\frac{\\sin x}{x^a} \\, dx \\) converges.",
"role": "user"
}
] | (0, 2) |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Four forces act on the jet: weight, normal force, thrust, and drag. |
[
{
"content": "Determine the real values of \\( k \\) for which the matrix \\( B = \\begin{bmatrix} 1 & k^2+k & 1 \\\\ -k & k^2 & k \\\\ k & k & -k \\end{bmatrix} \\) is equivalent by rows to a matrix of the form \\( \\begin{bmatrix} 1 & 0 & a \\\\ 0 & 1 & b \\\\ 0 & 0 & 0 \\end{bmatrix} \\).",
"role": "user... | -1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $276.84 |
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