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... | -272.14KJ |
[
{
"content": "Evaluate the limit: $$\\lim\\limits_{n\\to \\infty }\\left(\\sqrt[n]{\\left(\\frac{n!-1}{n!+1}\\right)^{\\left(n+1\\right)!}}\\right)$$",
"role": "user"
}
] | e^{-2} |
[
{
"content": "Let $a,$ $b,$ and $c$ be distinct real numbers. Simplify the expression\n\\[\\frac{(x + a)^3}{(a - b)(a - c)} + \\frac{(x + b)^3}{(b - a)(b - c)} + \\frac{(x + c)^3}{(c - a)(c - b)}.\\]",
"role": "user"
}
] | a + b + c + 3x |
[
{
"content": "Given a quadratic equation \\( ax^2 + bx + c = 0 \\), where \\( a, b, c \\) are positive integers in an arithmetic progression, and the roots \\( \\alpha \\) and \\( \\beta \\) are integers, find the value of \\( \\alpha + \\beta + \\alpha\\beta \\).",
"role": "user"
}
] | 7 |
[
{
"content": "Determine the values of $z$ for which the function $\\exp(-2 z\\sin^2 t)$ is the characteristic function of a discrete random variable.",
"role": "user"
}
] | z \geq 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... | 1.6 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... | $555.4 |
[
{
"content": "Given two random variables $X$ and $Y$, consider the following conditions:\n\n1. There exists a (not necessarily measurable) function $f: \\mathbb{R} \\to \\mathbb{R}$ such that $Y = f(X)$.\n2. There exists a Borel-measurable function $f: \\mathbb{R} \\to \\mathbb{R}$ such that $Y = f(X)$ almost s... | Yes |
[
{
"content": "Determine if it is possible for a triangle to be equilateral given that \\( \\sum \\left(\\frac{a}{b+c}\\right)^{2} \\) holds true.",
"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... | $1,600 |
[
{
"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... | 12.86 |
[
{
"content": "If $A$ and $B$ are closed subspaces of a Hilbert space $H$ such that $A^\\perp \\cap B^\\perp = \\{0\\}$, can we conclude that $A = B$? Provide a justification for your answer.",
"role": "user"
}
] | No |
[
{
"content": "Determine the intervals of convergence for the series \\(\\sum\\limits_{n=1}^{\\infty}(-1)^{n-1}\\frac{x^n}{n(n+1)}\\). Identify the values of \\(x\\) for which the series converges absolutely, converges conditionally, and diverges.",
"role": "user"
}
] | [-1, 1] |
[
{
"content": "Consider a decreasing sequence of bounded open sets \\(V_{n}\\) in \\(\\mathbb{R}^{m}\\) with \\(m \\geq 1\\). Suppose \\(\\cap V_{n} = \\emptyset\\) and \\(F := \\cap \\overline{V_{n}}\\) is connected. Is there an \\(N\\) such that each \\(x \\in F\\) belongs to the boundary of \\(V_{n}\\) for al... | 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... | 32.32% |
[
{
"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... | 8.22e-14 M |
[
{
"content": "Given a countably infinite set, what is the minimum number of infinite subsets that must be added to a cofinite topology to transform it into a discrete topology?",
"role": "user"
}
] | \aleph_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... | 0.0304 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... | 20.62r |
[
{
"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... | 15.87% |
[
{
"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... | 0.68 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... | 1. volume A (L)
2. moles A (multiply by the molarity of A)
3. moles B (multiply by the moles of B / moles of A)
4. volume B (L) (divide by the molarity of B) |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\searrow 0} \\frac{\\frac{\\pi}{6} - \\frac{1}{3} \\int_0^{1/x^3} \\frac{\\sin t}{t} \\,\\mathrm{d}t}{x} = 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... | $39667.5 |
[
{
"content": "In a connected network with 2008 computers, no two cycles share a common vertex. A hacker and an administrator play a game on this network. On the 1st move, the hacker selects and hacks one computer. On the 2nd move, the administrator selects and protects another computer. For every 2k+1th move (k... | 1004 |
[
{
"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... | 1.27 |
[
{
"content": "Determine whether the sequence \\( b_n = \\sum_{i=1}^n \\frac{1}{\\sqrt{n^2 + 2i}} \\) converges. If it converges, find its limit.",
"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... | 35.53 |
[
{
"content": "Consider a real-valued continuous function \\( f \\) satisfying \\( f(x+1) = f(x) \\) for all \\( x \\in \\mathbb{R} \\). Define:\n\\[ g(t) = \\int_{0}^{t} f(x) \\, dx \\]\n\\[ h(t) = \\lim_{n \\to \\infty} \\frac{g(t+n)}{n}, \\quad t \\in \\mathbb{R} \\]\nWhich of the following statements is true... | C |
[
{
"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... | 9.9 |
[
{
"content": "Consider the set $X=\\left\\{ \\left\\{x_n \\right\\}_{n=1}^{\\infty} \\mid x_n \\to 0 \\right\\}$, where $\\{x_n\\}$ is a real sequence, equipped with the metric $d(x_n, y_n)=\\sup_{n \\in \\mathbb{N}} |x_n - y_n|$. Define $E=\\left\\{ \\left\\{x_n \\right\\}_{n=1}^{\\infty} \\mid x_n \\in X, \\f... | B |
[
{
"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... | 19.89 kJ/mol |
[
{
"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... | Social Theory |
[
{
"content": "Let $F$ be a field and $\\langle a_1, \\ldots, a_n \\rangle \\subset F$. Given a non-zero polynomial $f \\in F[X_1, \\ldots, X_n]$, is it true that if $f(a_1, \\ldots, a_n) = 0$, then $(X_i - a_i)$ divides $f$ for some $i \\leq n$? Answer with \"True\" or \"False\".",
"role": "user"
}
] | False |
[
{
"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... | 8.21 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... | 2e-4 J |
[
{
"content": "Let $G$ be a unary recursive (total computable, on natural numbers) function. Define $F$ by the formula $F(x) = \\min_{y \\ge x} G(y)$. Does $F$ have to be recursive? Provide a justification for your answer.",
"role": "user"
}
] | No |
[
{
"content": "Let $X$ be a regular Lindelof space with a $G_\\delta$-diagonal. If there exists a one-to-one and onto continuous mapping $f: M \\to X$ from the Michael Line $M$, is the space $X$ submetrizable? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Calculate the convolution of the function \\( \\frac{\\sin(t)}{t} \\) with the constant function 1. Express your answer as a function or an expression.",
"role": "user"
}
] | \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... | 4.77 atm |
[
{
"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... | Php 205,181.93 |
[
{
"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... | 36.9J |
[
{
"content": "Find the largest positive integer \\( n \\) such that \\( 2^n \\) divides \\( 3^{4096} - 1 \\).",
"role": "user"
}
] | 14 |
[
{
"content": "Determine whether there exists a real number $b$, and integers $n$ and $k$, such that the sum of the powers of $b$ from $n$ to $n+k$ is a rational number.",
"role": "user"
}
] | Yes |
[
{
"content": "In an ideal gas undergoing a thermodynamic cycle with two isochoric and two adiabatic processes, the maximum absolute temperature is \\( T_{\\max} = 900 \\, \\mathrm{K} \\), the minimum absolute temperature is \\( T_{\\min} = 350 \\, \\mathrm{K} \\), and the cycle efficiency is \\( \\eta = 0.4 \\)... | \dfrac{54}{35} |
[
{
"content": "Derive the variance of a Bernoulli distribution using its moment generating function.",
"role": "user"
}
] | p(1 - p) |
[
{
"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... | 1.83 * 10^-9 |
[
{
"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... | $828.88 |
[
{
"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... | 2.54 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... | $20,400 |
[
{
"content": "Evaluate the contour integral \\( I = \\frac{1}{2\\pi i} \\oint_{\\gamma} z^7 \\cos\\left(\\frac{1}{z^2}\\right) dz \\) using the residue theorem, where \\( \\gamma = \\{z \\in \\mathbb{C} : |z| = 2\\} \\).",
"role": "user"
}
] | \dfrac{1}{24} |
[
{
"content": "Let \\((X,d)\\) be a complete metric space and \\(f: X \\rightarrow X\\) be a map. If \\(f^k\\) is a contraction for some positive integer \\(k\\), does \\(f\\) necessarily have a fixed point? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Given a ring $R$ and two distinct ideals $I$ and $J$ of $R$, is it possible for the quotient rings $R/I$ and $R/J$ to be isomorphic?",
"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... | 4.05e+06 N |
[
{
"content": "What is the sum of the positive whole number divisors of 210?",
"role": "user"
}
] | 576 |
[
{
"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... | $$p = p_0\left[1 - \dfrac{\gamma-1}{\gamma}\left(\frac{1}{\rho_0^{\gamma-1}} \right)\dfrac{gz}{k}\right]^{\frac{\gamma}{\gamma-1}}$$ |
[
{
"content": "Does there exist a left group that is not a right group?",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to-7} \\frac{[x]^2+15[x]+56}{\\sin(x+7)\\sin(x+8)}$$ where $[x]$ denotes the greatest integer less than or equal to $x$. Provide your answer in simplified form.",
"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... | $32,986.00 |
[
{
"content": "Compute the limit: \\[ \\lim_{x\\rightarrow 0} \\frac{x^{\\sin x} -1}{x} \\]",
"role": "user"
}
] | -\infty |
[
{
"content": "Mr. Mendez awards extra credit on quizzes to his students with quiz grades that exceed the class mean. Given that 107 students take the same quiz, what is the largest number of students who can be awarded extra credit?",
"role": "user"
}
] | 106 |
[
{
"content": "Given a sequence $\\alpha_n \\in \\mathbb{R}$ for which the following limit holds for all $t \\in \\mathbb{R}$:\n$$ \\lim_{n \\rightarrow \\infty}e^{i\\alpha_nt} = 1 $$ \nDoes it necessarily imply that $\\lim_{n \\rightarrow \\infty} \\alpha_n = 0$? Provide a justification for your answer.",
"... | Yes |
[
{
"content": "Compute the value of the complex integral \\( \\int_0^{2\\pi}\\dfrac{4ie^{it}}{4e^{it}-3}\\,\\mathrm{d}t \\).",
"role": "user"
}
] | 2\pi i |
[
{
"content": "Evaluate the limit using L'Hopital's rule: $$\\lim_{x\\to 0} \\frac{\\int_{0}^{x^4}(e^{u^{10}}-1)du}{x^{44}}$$ Apply L'Hopital's rule as needed to resolve the indeterminate form.",
"role": "user"
}
] | \dfrac{1}{11} |
[
{
"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... | 1.846e4 K |
[
{
"content": "Find the limit of \\( \\displaystyle{ \\lim \\limits_{n \\to \\infty} \\sqrt[2^n]{\\sqrt[n]{b}+1}} \\) given \\(b>0\\).",
"role": "user"
}
] | 1 |
[
{
"content": "Compute the integral \\( \\int_{\\gamma} \\frac{f(z)}{z^3}dz \\), where \\( f(z)=az^3+bz^2+cz+d \\) and \\( \\gamma(t)=e^{it} \\) for \\( t \\in [0, 4\\pi] \\).",
"role": "user"
}
] | 4\pi i b |
[
{
"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... | 8.92% |
[
{
"content": "Evaluate the limit: $$ \\lim_{(x,y)\\to(1,1)} \\frac{(x-1)^{4/3}-(y-1)^{4/3}}{(x-1)^{2/3}+(y-1)^{2/3}} $$",
"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... | -7.1 kJ |
[
{
"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... | 2.7300758 rad |
[
{
"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... | Adjusted balance per bank: $9,792
Adjusted balance per books: $9,792 |
[
{
"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... | $18.25 |
[
{
"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... | 3201.984 kJ/mol |
[
{
"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... | 2.34e2 m/s |
[
{
"content": "Find the derivative of the inverse function \\((f^{-1})'(y)\\) at \\(y = \\frac{1}{2} \\sqrt{2}\\) for \\(f(x) = \\cos x\\) in the interval \\([0, \\pi]\\).",
"role": "user"
}
] | -\sqrt{2} |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to 0} \\left(\\frac{\\cos x}{\\cos2x}\\right)^{\\frac{1}{x^2}}$$",
"role": "user"
}
] | e^{\frac{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... | 49.74 mi |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to 0} \\left(\\left(81+x\\right)^x-81^x\\right)^x$$",
"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... | 3440 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... | 0.021m |
[
{
"content": "Determine the set \\(\\bigcap_{x \\in A} \\bigcup_{n \\in \\Bbb N} \\left(\\frac{1}{n}, x-\\frac{1}{n^2}\\right)\\) where \\(A=\\{ x \\in \\Bbb R \\mid x > \\pi\\}\\).",
"role": "user"
}
] | (0, \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... | 0.182 kg |
[
{
"content": "Evaluate the integral \\( \\int_{0}^{\\infty} \\frac{\\cos(x)}{x^2 + 1} \\, dx \\) using complex analysis.",
"role": "user"
}
] | \dfrac{\pi}{2e} |
[
{
"content": "Given a set $E$ and a predicate $P$ such that for any subset $S \\subseteq E$, $P(S)$ is either true or false, and there exists a set $X \\subseteq E$ such that $P(X)$ is true, determine whether the collection $\\{S \\mid P(S)\\}$ always has a maximal element with respect to set inclusion.",
"... | No |
[
{
"content": "In a scalene triangle $ABC$, the incircle $\\Gamma$ touches $BC$ at $D$, $CA$ at $E$, and $AB$ at $F$. Let $r_A$ be the radius of the circle inside $\\triangle ABC$ which is tangent to $\\Gamma$ and the sides $AB$ and $AC$. Define $r_B$ and $r_C$ similarly. Given that $r_A = 16$, $r_B = 25$, and $... | 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... | $601,434 |
[
{
"content": "Given the equation $8iz^3 + 12z^2 - 18z + 27i = 0$, find the value of $4|z|^2$ for the complex number $z$.",
"role": "user"
}
] | 9 |
[
{
"content": "Let $a$, $b$, and $c$ be positive real numbers such that $a^2 + b^2 + c^2 = 2abc + 1$. Determine the maximum value of the expression \\((a - 2bc)(b - 2ca)(c - 2ab)\\).",
"role": "user"
}
] | \dfrac{1}{8} |
[
{
"content": "Evaluate the expression \\( \\sum_{k=0}^m \\binom{m}{k} a^k b^{m-k} \\sin(kB - (m-k)A) \\) in triangle \\( ABC \\).",
"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... | Assess competence of staff, bandwidth, and budget |
[
{
"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... | 15m |
[
{
"content": "Calculate the limit: \\[ \\lim_{n \\to \\infty} \\sqrt[n]{|\\sin n|} \\]",
"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... | $2,333,333.33 |
[
{
"content": "If \\( \\alpha, \\beta, \\gamma \\) are the roots of the equation \\( x^3 - x - 1 = 0 \\), find the value of the expression:\n\n\\[ \\frac{1+\\alpha}{1-\\alpha} + \\frac{1+\\beta}{1-\\beta} + \\frac{1+\\gamma}{1-\\gamma} \\]\n\nChoose the correct answer from the following options: \\( 1, 0, -7, -5... | -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... | average total cost |
[
{
"content": "Consider a bounded operator $T: c_0 \\to c_0$ represented by a double-infinite matrix $[T_{mn}]_{m,n \\geq 1}$. This operator acts on a sequence $a = [a_1, a_2, a_3, \\ldots] \\in c_0$ as follows:\n\\[ Ta = [T_{mn}][a_n] = \\left[ \\sum_{n=1}^\\infty T_{mn}a_n \\right] \\]\nSuppose $a = [a_1, a_2,... | 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... | 1.35 |
[
{
"content": "Find the derivative of the function \\( F(x) = \\int_0^x \\log(t) \\, dt \\) with respect to \\( x \\).",
"role": "user"
}
] | \log(x) |
[
{
"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... | 14.167 m/s |
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