prompt list | ground_truth string |
|---|---|
[
{
"content": "Determine whether a set with infinite Lebesgue measure in \\(\\mathbb{R}^n\\) can consist solely of boundary points.",
"role": "user"
}
] | Yes |
[
{
"content": "If $K$ is a weakly compact set in a Banach space $E$, and $Y = \\operatorname{span}(K)$, is the unit ball $B_Y$ weakly compact in $Y$?",
"role": "user"
}
] | No |
[
{
"content": "A computer science laboratory has 15 workstations and 10 servers. A cable can be used to directly connect a workstation to a server, with only one direct connection to each server active at any time. Determine the minimum number of direct connections required to ensure that any set of 10 or fewer ... | 60 |
[
{
"content": "Consider the vector field \\( F(x,y,z) = \\begin{pmatrix} x^{2}+5y+3yz \\\\ 5x +3xz -2 \\\\ 3xy -4z \\end{pmatrix} \\) and the curve \\( \\kappa: [0, 2\\pi] \\to \\mathbb{R}^{3} \\) defined by \\( \\kappa(t) = \\begin{pmatrix} \\sin t \\\\ \\cos t \\\\ t \\end{pmatrix} \\). Compute the line integr... | -8\pi^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... | $94,100 |
[
{
"content": "Evaluate the integral \\( I = \\int_{0}^{2\\pi} e^{\\cos x} \\cos (\\sin x)\\,dx \\). Verify if the solution process leads to \\( I = 0 \\).",
"role": "user"
}
] | 2\pi |
[
{
"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 A/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... | 1.37e5 J |
[
{
"content": "Evaluate the limit \\( \\lim_{x\\to 0}\\frac{(\\tan x)^{2008}-(\\arctan x)^{2008}}{x^{2009}} \\) without using Taylor series.",
"role": "user"
}
] | 0 |
[
{
"content": "Given that $X$ and $Y$ are independent and identically distributed standard normal random variables, calculate the covariance $Cov(XY|X+Y>0)$. Provide your answer as a single value.",
"role": "user"
}
] | -\dfrac{1}{\pi} |
[
{
"content": "Consider a dice game played with a fair $n$-sided die. On the first roll, a roll of $n$ wins, while a roll of $1$ loses. For any other result, the player rolls again. On the second roll, a roll of $n$ wins, while a roll of $1$ or $2$ loses. The game continues similarly, where on roll $k$, the play... | 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... | 5.0e4 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... | 8.86e-5 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... | 11 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... | 5.601 L |
[
{
"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... | 1.6e6 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... | 2.3e+03 V |
[
{
"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... | Pb(s) + 2H_2SO_4(aq) + PbO_2(s) -> 2PbSO_4(s) + 2H_2O |
[
{
"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... | -0.083 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... | 282.7Nm |
[
{
"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... | 1475.297 J |
[
{
"content": "Calculate the length of the curve given by the equation \\(6xy = 3 + x^4\\) from \\(x = 1\\) to \\(x = 2\\).",
"role": "user"
}
] | \dfrac{17}{12} |
[
{
"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... | $4,765,410 |
[
{
"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... | TC = p1(x1 + (1/3)sqrt(x2)) |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\to 1}\\frac{\\left(1-\\sqrt{x}\\right)\\left(1-\\sqrt[3]{x}\\right)...\\left(1-\\sqrt[n]{x}\\right)}{\\left(1-x\\right)^{\\left(n-1\\right)}}$$ as \\(x\\) approaches 1.",
"role": "user"
}
] | \dfrac{1}{n!} |
[
{
"content": "Evaluate the integral \\( \\int_0^{2\\pi} \\frac{1}{5+3 \\cos x} \\, dx \\) using the substitution \\( t = \\tan \\frac{x}{2} \\).",
"role": "user"
}
] | \dfrac{\pi}{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... | 0.8960 J |
[
{
"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... | 1.7 m/s |
[
{
"content": "At a certain university, the division of mathematical sciences consists of the departments of mathematics, statistics, and computer science. There are two male and two female professors in each department. A committee of six professors is to contain three men and three women and must also contain ... | 88 |
[
{
"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 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... | 1060 km |
[
{
"content": "Find the minimum value of \\( \\sum_{1\\le i<j\\le 6}[a_{i}+a_{j}] \\) where \\( a_{1},a_{2},\\cdots,a_{6} \\) are real numbers such that \\( a_{1}+a_{2}+a_{3}+a_{4}+a_{5}+a_{6}=2014 \\) and \\( [x] \\) denotes the greatest integer less than or equal to \\( x \\).",
"role": "user"
}
] | 10060 |
[
{
"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... | (-r/sqrt(2r^2+1))i + (r/sqrt(2r^2+1))j - (1/sqrt(2r^2+1))k |
[
{
"content": "Use Stoke's Theorem to evaluate the line integral \\( \\int_{C} \\mathbf{F} \\cdot \\mathrm{d}\\mathbf{r} \\), where \\( \\mathbf{F}(x,y,z) = -x^2\\mathbf{i} + xz\\mathbf{j} + yx\\mathbf{k} \\) and \\( C \\) is the boundary of the surface \\( S \\), which is the graph of \\( f(x,y) = 4x - 8y + 30 ... | 160 |
[
{
"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... | 1.13e-10 N/C, upwards |
[
{
"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... | 7.5e-16 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... | 4.7 |
[
{
"content": "Identify the tensor product $H \\otimes_{\\mathbb{R}} \\mathbb{C}$, where $H$ is the algebra of Hamiltonian quaternions, $\\mathbb{C}$ is the field of complex numbers, and $\\mathbb{R}$ is the field of real numbers. Express your answer in familiar mathematical terms.",
"role": "user"
}
] | M_2(\mathbb{C}) |
[
{
"content": "Determine the degree of the splitting field of the polynomial \\( f(x) = x^7 - 6 \\) over \\( \\mathbb{Q} \\).",
"role": "user"
}
] | 42 |
[
{
"content": "Given the joint probability density function of random variables $X$ and $Y$:\n\\[\nf(x,y)=\\begin{cases}\n24xy, & 0<x<1, 0<y<1, x+y<1 \\\\\n0, & \\text{elsewhere}\n\\end{cases}\n\\]\nCalculate the probability $P(X+Y<\\frac{1}{2})$. Determine the appropriate limits for the double integral to find ... | \dfrac{1}{16} |
[
{
"content": "Is a complex symmetric matrix with a positive definite real part necessarily diagonalizable? Let \\( M \\in \\mathbb{C}^{n \\times n} \\) be a complex-symmetric matrix. If the real part of \\( M \\) is positive-definite, determine whether \\( M \\) is diagonalizable.",
"role": "user"
}
] | Yes |
[
{
"content": "Given a 2 by 2 matrix $B$ with eigenvalues $\\frac{4}{5}$ and $\\frac{7}{3}$, determine if there exists a non-zero vector $w$ such that $\\|Bw\\|^2 = 2\\|w\\|^2$. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "In triangle \\( \\triangle ABC \\), the sides \\( AB \\) and \\( AC \\) have lengths 16 and 5, respectively. The angle bisectors of \\( \\angle ABC \\) and \\( \\angle BCA \\) intersect at point \\( P \\) inside the triangle. If \\( AP = 4 \\), determine the length of side \\( BC \\).",
"role"... | 14 |
[
{
"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... | Basic: $155.16
Dominator: $300.67 |
[
{
"content": "Calculate the expected value of \\( \\ln(X) \\) where \\( X \\) is a random variable following a Beta\\(\\frac{1}{y}, 1\\) distribution.",
"role": "user"
}
] | -y |
[
{
"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... | 3.9932e-3 |
[
{
"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... | $7304 |
[
{
"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... | $129,688.17 |
[
{
"content": "Evaluate the limit: $$\\lim_{n \\to \\infty} \\sqrt[n]{\\frac{n!}{\\sum_{m=1}^n m^m}}$$",
"role": "user"
}
] | \dfrac{1}{e} |
[
{
"content": "Find the area of the surface enclosed between the sphere \\(x^2+y^2+z^2=4a^2\\) and the cylinder \\(x^2+(y-a)^2=a^2\\). The answer should be \\((8\\pi-16)a^2\\).",
"role": "user"
}
] | (8\pi - 16)a^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... | 12 rad/s |
[
{
"content": "For how many integer values of $a$ does the equation $$x^2 + ax + 8a = 0$$ have integer solutions for $x$?",
"role": "user"
}
] | 8 |
[
{
"content": "Calculate Spearman's rho for the comonotonicity copula, defined as \\( C_m(u_1, u_2) = \\min(u_1, u_2) \\). Spearman's rho is given by the formula \\( \\rho = 12 \\int_{0}^{1}\\int_{0}^{1} C(u_1,u_2) \\, du_1 \\, du_2 - 3 \\). Evaluate this integral.",
"role": "user"
}
] | 1 |
[
{
"content": "Compute the distance between a unilateral shift operator $S$ on a separable, infinite-dimensional Hilbert space $\\mathcal{H}$ and the set of compact operators on $\\mathcal{H}$, denoted by $\\mathbb{K}(\\mathcal{H})$. Find $d(S, \\mathbb{K}(\\mathcal{H}))=\\inf\\{\\|S-K\\|: K\\in \\mathbb{K}(\\ma... | 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... | 6.74% |
[
{
"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... | 3.7323 |
[
{
"content": "Consider a complete probability space $(\\Omega,\\mathcal{F},\\mathbb{P})$, where $X$ is an $E$-valued random variable and $Y$ is an $F$-valued random variable, with $E$ and $F$ being Polish spaces. Determine whether the following statement is true: If $X$ is $\\overline{\\sigma(Y)}$-measurable, t... | True |
[
{
"content": "Evaluate the expression: $$[(\\nabla \\times \\nabla)\\cdot \\nabla](x^2 + y^2 + z^2)$$",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the unit digit of the sum of all divisors of \\(20^{90} + 1\\) that are of the form \\(2^{p} \\cdot 5^{q}\\), where \\(p\\) and \\(q\\) are positive integers.",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the integral of the cardinal sine function over the entire real line:\n\\[ \\int_{-\\infty}^{\\infty} \\frac{\\sin(a)}{a} \\, {\\rm d} a \\]",
"role": "user"
}
] | \pi |
[
{
"content": "Evaluate \\( \\lim_{n \\to \\infty} a_n \\), where \n\\[ a_n = \\frac{ e^{-1} }{2^{n^2}} \\sum_{k = 0}^\\infty{\\frac{n^k}{k!}} \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Is 1 a regular value of the function \\( g: TM \\to \\mathbb{R} \\) defined by \\( g(p,v) = \\langle v,v \\rangle \\), where \\( T^1M \\) is the unit tangent bundle of a submanifold \\( M \\) of \\( \\mathbb{R}^n \\)?",
"role": "user"
}
] | Yes |
[
{
"content": "Let $L(X)$ denote the Banach algebra of all bounded linear operators on a Banach space $X$. If $T \\in L(X)$ is invertible, is it true that $||T^{-1}|| = ||T||^{-1}$? Provide a justification for your answer.",
"role": "user"
}
] | No |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\to\\infty}\\frac{\\sum_{k=1}^n \\frac 1k}{\\sum_{k=1}^{n+1} \\frac{1}{2k-1} }$$.",
"role": "user"
}
] | 2 |
[
{
"content": "Evaluate the limit: $$\\lim_{(x, y) \\to(0, 0)}\\frac{(\\sin y)(2^x - 1)}{xy}$$",
"role": "user"
}
] | \ln 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... | 122.7 km/hr |
[
{
"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... | 9.44g |
[
{
"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... | -$2,473,418 |
[
{
"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... | 3.08 mc^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... | $64.10 |
[
{
"content": "Let $S$ be the set of integers $n > 1$ for which $\\tfrac1n = 0.d_1d_2d_3d_4\\ldots$, an infinite decimal that has the property that $d_i = d_{i+12}$ for all positive integers $i$. Given that $9901$ is prime, how many positive integers are in $S$? (The $d_i$ are digits.)",
"role": "user"
}
] | 255 |
[
{
"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... | -0.26 |
[
{
"content": "Is the infinite product space \\(\\Pi_{i = 1}^{\\infty}\\mathbb{N}_n\\) compact, where each \\(\\mathbb{N}_n\\) is equipped with the discrete topology and is compact for finite \\(n\\)?",
"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... | 3.6 cm |
[
{
"content": "Evaluate the limit \\( \\lim_{k \\to \\infty} \\int_0^k x^n \\left(1 - \\frac{x}{k} \\right)^k \\, \\mathrm{d} x \\) for a fixed integer \\( n \\).",
"role": "user"
}
] | 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... | 7.72 nm^-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... | 228 J |
[
{
"content": "Find \\(\\lim_{x \\to \\infty} x^2\\big(\\ln(x\\cot^{-1}(x))\\).",
"role": "user"
}
] | -\dfrac{1}{3} |
[
{
"content": "If the sides of a convex pentagon are extended to form 5 equal triangles, is the pentagon necessarily regular?",
"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... | 9.08kg |
[
{
"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... | 6470.53 minutes |
[
{
"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... | 14 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... | -3.93 F/hr |
[
{
"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... | 32.92% |
[
{
"content": "Is the number of irreducible components $m$ of an analytic hypersurface in a complex manifold always finite?",
"role": "user"
}
] | No |
[
{
"content": "Let \\( S \\subsetneq \\mathbb{Z} \\) be an infinite set. Does there always exist a prime \\( p \\) such that the closure of \\( S \\) in the \\( p \\)-adic integers, \\( \\mathbb{Z}_p \\), contains a rational integer \\( n \\notin S \\)? In other words, does there exist a prime \\( p \\) and \\( ... | Yes |
[
{
"content": "Determine whether the limit \\( e^{-x}\\sum_{n=0}^N \\frac{(-1)^n}{n!}x^n \\to e^{-2x} \\) as \\( N\\to\\infty \\) is uniform on \\([0,+\\infty)\\).",
"role": "user"
}
] | Yes |
[
{
"content": "Let $Q(b)$ denote the right-tail probability of a standard Gaussian random variable. Suppose that $X$ and $Y$ are jointly-distributed Gaussian random variables with $X \\sim N(3, 8)$ and $Y \\sim N(10, 5)$. If the correlation coefficient between $X$ and $Y$ is 0.8, find the value of $b$ such that ... | -7.453 |
[
{
"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... | $24,942 |
[
{
"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... | 30.1 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... | 7.2e-3 Wb |
[
{
"content": "Determine whether for any three distinct natural numbers \\( a \\), \\( b \\), and \\( c \\), there exists a quadratic polynomial with integer coefficients and a positive leading coefficient that takes the values \\( a^3 \\), \\( b^3 \\), and \\( c^3 \\) at some integer points.",
"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... | $29,244.86 |
[
{
"content": "Find the 2-norm of the eigenvalue \\( \\lambda = a + bi \\) of the matrix \\( A = I - \\frac{2}{u^T u} uu^T \\), where \\( u \\) is a non-zero vector in \\( \\mathbb{R}^n \\) and \\( A \\in \\mathbb{R}^{n \\times n} \\). The 2-norm is given by \\( \\left\\|\\lambda\\right\\|_2 = \\sqrt{a^2 + b^2} ... | 1 |
[
{
"content": "Evaluate the limit: $$\\lim_{t\\to 0}\\left(\\frac{\\left[\\ln \\left(e\\left(1+t\\right)^{1-\\frac{1}{t}}\\right)\\right]}{t}\\right)$$ without using Taylor series expansion.",
"role": "user"
}
] | \dfrac{3}{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... | 31.29 m/s to the east |
[
{
"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 after-tax yield on the municipal bond is 8%, while the after-tax yield on the corporate bond is 7.5%. |
[
{
"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... | Quorum Health Group: 12.80%, Beverly Enterprises: 14.90%, HEALTHSOUTH Corporation: 16.65%, United Healthcare: 18.40% |
[
{
"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... | $210.87 |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\rightarrow0^{+}} \\frac {\\ln(e^{x} - 1)} {x^{-0.3}}$$",
"role": "user"
}
] | 0 |
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