prompt list | ground_truth string |
|---|---|
[
{
"content": "Determine the smallest integer $a$ such that the inequality \\(x^2 - ax - \\ln x + e^{\\sin x} - 1 < 0\\) is satisfied for at least one positive value of $x$. Provide your answer as an integer.",
"role": "user"
}
] | 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... | 2.2e-5 |
[
{
"content": "Compute the expected value \\( \\text{E}[X] \\) of a random variable \\( X \\sim \\mathcal{N}(\\mu, \\sigma^2) \\) using the density function \\( f_X(x) = \\frac{1}{\\sigma \\sqrt{2\\pi}} \\exp\\left(-\\left(\\frac{x-\\mu}{\\sigma\\sqrt{2}}\\right)^2\\right) \\). Use the substitution \\( y = \\fra... | \mu |
[
{
"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... | -5156.34 J |
[
{
"content": "Determine the number of real roots of the equation \\(3^{x^{22}} + 28^{(1-x)^2} = 2020\\) by analyzing the monotonicity of the functions involved.",
"role": "user"
}
] | 2 |
[
{
"content": "A Markov chain $X_0,X_1,X_2,\\ldots$ has the transition probability matrix:\n$$P=\\begin{Vmatrix}\n0.3 & 0.2 & 0.5\\\\\n0.5 & 0.1 & 0.4 \\\\\n0 & 0 & 1\n\\end{Vmatrix}$$\nand starts in state $X_0=0$. Eventually, the process will end up in state 2. What is the probability that the time $T=\\text{mi... | \dfrac{90}{133} |
[
{
"content": "Evaluate the limit: $$ \\lim_{x \\to \\infty} \\left(\\frac{x + \\log9}{x - \\log9}\\right)^x $$.",
"role": "user"
}
] | 81 |
[
{
"content": "Let $a > 1$ be a fixed positive integer and $f(x)$ be a polynomial with integer coefficients and a positive leading coefficient. Define the set $S$ as follows:\n\\[\nS = \\{ n \\in \\mathbb{Z}^+ : n \\mid a^{f(n)} - 1 \\}.\n\\]\nDetermine the density of the set $S$, i.e., compute\n\\[\n\\lim_{n \\... | 0 |
[
{
"content": "Find the largest positive integer \\( m \\) such that the series \\( \\sum_{n=1}^{\\infty} \\frac{f(n)}{m^{\\left\\lfloor \\log_{10} n \\right\\rfloor}} \\) is an integer, where \\( f(n) \\) is the product of the digits of \\( n \\).",
"role": "user"
}
] | 2070 |
[
{
"content": "Let $a, b, c$ be positive integers such that $0 < a, b, c < 11$. They satisfy the following congruences: \\[ 3a + b + c \\equiv abc \\pmod{11} \\] \\[ a + 3b + c \\equiv 2abc \\pmod{11} \\] \\[ a + b + 3c \\equiv 4abc \\pmod{11} \\] Find the sum of all possible values of $abc$.",
"role": "user... | 198 |
[
{
"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... | 5870 photons/s |
[
{
"content": "Evaluate the limit: $$ \\lim_{x\\rightarrow \\infty}\\frac{\\ln(1+\\sin(2x))}{x} $$",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether the set of numbers $x > 1$ for which the set $\\{\\sin(x^n) \\mid n \\in \\mathbb{N}\\}$ is dense in $[-1, 1]$ is meager or has cardinality $2^{\\aleph_0}$.",
"role": "user"
}
] | 2^{\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... | 90*10^-5J |
[
{
"content": "In an isosceles triangle \\( ABC \\) with vertex angle \\( A \\), let \\( M \\) be the midpoint of \\( BC \\). Reflect point \\( M \\) over segment \\( AC \\) to obtain point \\( D \\). If \\( x \\) is the measure of angle \\( \\widehat{BAC} \\), find the measure of angle \\( \\widehat{MDC} \\) as... | \dfrac{x}{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... | Compensating variation |
[
{
"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... | 33.0 L |
[
{
"content": "Determine whether the following statement is true or false: If $M$ is a non-orientable $C^{\\infty}$ manifold and $p \\in M$, then $M - \\{p\\}$ is orientable.",
"role": "user"
}
] | 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... | 0.0103 N, 18.2 degrees from the +x-axis |
[
{
"content": "Is the inclusion map between two normed linear spaces always continuous when one space is a subspace of the other and inherits its norm from the larger space?",
"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... | Sympathetic and parasympathetic |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^\\infty \\frac{1}{\\left(x^2+1\\right)^2}\\,dx \\) using contour integration.",
"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... | -0.647e-5 T |
[
{
"content": "Polygon $ABCDEF$ is a regular hexagon. What is the measure in degrees of angle $ABF$?",
"role": "user"
}
] | 30 |
[
{
"content": "Given the sequence defined by the recursive relation \\(\\left\\{\\begin{matrix}u_{0}\\in [-1;1], \\quad u_{0}\\neq 0 \\\\ u_{n+1}=2^{u_{n}}-u_{n}-1 \\end{matrix}\\right.\\), determine the limit of the sequence \\(u_{n}\\). Assume \\(-1< u_{n}< 1\\) for all \\(n\\).",
"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... | The molarity of sodium cation is 0.6 M and the molarity of sulfate anion is 0.3 M. |
[
{
"content": "Simplify the vector equation:\n\n$$ (p^2 + q^2 |\\mathbf{P}|^2 + (\\mathbf{P} \\bullet \\mathbf{Q})^2)\\mathbf{X} + (\\mathbf{Q} \\bullet \\mathbf{X})(|\\mathbf{P}|^2 \\mathbf{Q} - (\\mathbf{P} \\bullet \\mathbf{Q})\\mathbf{P}) + (\\mathbf{P} \\bullet \\mathbf{X})(|\\mathbf{Q}|^2 \\mathbf{P} - (\\... | \mathbf{X} |
[
{
"content": "Let $a,b,$ and $c$ be real numbers such that \\[a + b + c = 2\\]and \\[a^2+b^2+c^2=12.\\]What is the difference between the maximum and minimum possible values of $c$?",
"role": "user"
}
] | \tfrac{16}3 |
[
{
"content": "How many degrees are there in the measure of angle $P?$\n\n[asy]\nsize (5cm,5cm);\npair A,B,C,D,E;\n\nA=(0,1.1);\nB=(4.5,0);\nC=(6.4,1.7);\nD=(4.2,5);\nE=(0.5,4.2);\n\ndraw (A--B--C--D--E--A,linewidth(1));\n\nlabel(\"$P$\",A,SW);\nlabel(\"$128^\\circ$\",shift(0,0.6)*B);\n\nlabel(\"$92^\\circ$\",C,... | 96^\circ |
[
{
"content": "Among the integers from 1 to \\(8 \\cdot 10^{20}\\) (inclusive), determine which are more numerous: those containing only even digits or those containing only odd digits. Additionally, calculate the difference in their quantities.",
"role": "user"
}
] | \dfrac{5^{21} - 5}{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... | 2060500 |
[
{
"content": "Can symmetric matrices alone form a basis for the vector space of all \\( n \\times n \\) matrices over \\( \\mathbb{R} \\)?",
"role": "user"
}
] | No |
[
{
"content": "Prove that there exists a constant \\( C > 0 \\) such that for the function \\( R: \\text{Mat}(n, \\mathbb{R}) \\to \\mathbb{R} \\) defined by \\[ R(H) = \\det(I+H) - 1 - \\text{Tr}(H) \\] the inequality \\( |R(H)| \\leq C ||H||^2 \\) holds for all \\( H \\in \\text{Mat}(n, \\mathbb{R}) \\) with \... | 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... | -1.66e-7 V |
[
{
"content": "Calculate the mass of the surface defined by \\( z = xy \\) that lies inside the cylinder \\( x^2 + \\frac{y^2}{4} = 1 \\), given the density function \\( \\rho = \\frac{|z|}{\\sqrt{1 + x^2 + y^2}} \\).",
"role": "user"
}
] | 2 |
[
{
"content": "What is the remainder when $18!$ is divided by 437?",
"role": "user"
}
] | 436 |
[
{
"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... | 111743 |
[
{
"content": "What is the ratio of the area of a square inscribed in a semicircle with radius $r$ to the area of a square inscribed in a circle with radius $r$? Express your answer as a common fraction.",
"role": "user"
}
] | \dfrac{2}{5} |
[
{
"content": "In triangle \\(ABC\\), let \\(J\\) be the center of a semicircle that touches side \\(BC\\) at \\(A_1\\) and the extensions of sides \\(AC\\) and \\(AB\\) at \\(B_1\\) and \\(C_1\\) respectively. The line \\(A_1B_1\\) intersects line \\(AB\\) at right angles at \\(D\\). Let \\(E\\) be the projecti... | 90^\circ |
[
{
"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... | Expected return = 8%, standard deviation = 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... | 187.6 ft/s |
[
{
"content": "Let $W = \\{W_t : t \\geq 0\\}$ be a Brownian motion. Find $\\mathbb{E}(W_t(W_{t+1} + W_{t+2}))$. ",
"role": "user"
}
] | 2t |
[
{
"content": "How many unique 7-tuples of integers (1, 2, or 3) exist such that the sum of the integers is 12, and two tuples are considered equivalent if one can be obtained by circularly shifting the other?",
"role": "user"
}
] | 38 |
[
{
"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... | 1.56 T along the negative Z-direction |
[
{
"content": "Determine the possible values of the greatest common divisor of $n^5 + 6$ and $n^5 + 2$ given that $n^5 + 4$ is a perfect square.",
"role": "user"
}
] | 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... | -0.6m/s |
[
{
"content": "Evaluate the limit \\( \\lim_{n \\to \\infty}\\int_{0}^{1}nx^ne^{x^2}dx \\).",
"role": "user"
}
] | e |
[
{
"content": "Determine the number of ways to distribute 6 distinguishable objects into 4 indistinguishable boxes such that each box contains at least one object.",
"role": "user"
}
] | 65 |
[
{
"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... | 156.50 |
[
{
"content": "Given two real polynomials $f(x)$ and $g(x)$ with degrees $m \\geq 2$ and $n \\geq 1$ respectively, such that \\(f(x^2+1)=f(x) g(x)\\) for all real numbers \\(x\\), determine the correct conclusion about the real roots of $f(x)$:\n\n(A) $f$ has exactly one real root $x_0$ with $f'(x_0) \\neq 0$\n(... | D |
[
{
"content": "Find the limit: \\[ \\lim_{x \\to +\\infty} \\tan \\left( \\left( \\frac{\\pi x}{2x+1} \\right)^{1/x} \\right) \\]",
"role": "user"
}
] | \tan 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... | 0.12 M |
[
{
"content": "In triangle $\\Delta ABC$, where $a \\ge b \\ge c$, it is given that \\( \\frac{a^3+b^3+c^3}{\\sin^3 A+\\sin^3 B+ \\sin^3 C}=7 \\). Determine the maximum value of $a$. \\( \\text{Express your answer as a single number.} \\)",
"role": "user"
}
] | \sqrt[3]{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... | 1.0e5 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... | $5,500 |
[
{
"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... | -240.8 kg.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... | $2537.12 |
[
{
"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... | 0.0941 M |
[
{
"content": "Determine the number of different nonzero real values of $k$ for which there exist nonzero real numbers $x$, $y$, and $z$ satisfying the equations: \\[ \\frac{x+y}{z} = \\frac{y+z}{x} = \\frac{z+x}{y} = k. \\]",
"role": "user"
}
] | 2 |
[
{
"content": "Consider a tetrahedron with one edge length \\( x \\) and all other edge lengths equal to 1. The volume of this tetrahedron is given by the function \\( F(x) \\). Determine the behavior of the function \\( F(x) \\) over its domain:\n\n(A) \\( F(x) \\) is an increasing function but has no maximum v... | D |
[
{
"content": "In a regular $2n$-gon with vertices alternately colored red and black, two players, A and B, take turns drawing diagonals between vertices of the same color. The diagonals must not intersect any of the diagonals previously drawn by the same player. Player A goes first. Determine which player has a... | B |
[
{
"content": "Determine whether the group \\((\\mathbb{Z}_p)^m\\) requires at least \\(m\\) elements to generate it.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit \\( \\lim_{n \\to \\infty} \\frac{1}{n} \\sum_{r=1}^n r^{\\frac{1}{r}} \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Determine whether the following inequality holds for a function $f(t):[0,t]\\rightarrow \\mathbb{R}$, where $s\\leq t$:\n\\[\\left|\\max\\limits_{0\\leq v\\leq t}\\left(\\int_{0}^{v}f(u)du\\right)-\\max\\limits_{0\\leq w\\leq s}\\left(\\int_{0}^{w}f(u)du\\right)\\right|\\leq \\max\\limits_{s\\leq ... | 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... | 6.9% |
[
{
"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... | 6.65% |
[
{
"content": "What is the smallest two-digit positive integer such that the product of its two digits is one-half the integer?",
"role": "user"
}
] | 36 |
[
{
"content": "Evaluate the expression: $$\\lim_{n\\to \\infty}\\int_0^{\\pi}\\sin^{2n+1}x\\cos x \\, dx -\\int_0^{\\pi}(\\lim_{n\\to \\infty}\\sin^{2n+1}x\\cos x)\\, dx$$",
"role": "user"
}
] | 0 |
[
{
"content": "Find the minimum value of the product \\( ab \\) if the roots of the cubic equation \\( x^3 - ax^2 + bx - 2 = 0 \\) are all positive.",
"role": "user"
}
] | 18 |
[
{
"content": "Determine the range of values for $a$ such that the inequality \\(x^{-3} e^{x} - a \\ln x \\geq x + 1\\) is satisfied for all \\(x \\in (1, +\\infty)\\).",
"role": "user"
}
] | (-\infty, -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... | 88.385 m |
[
{
"content": "Find the interval of values for the parameter \\( a \\) such that the expression \\( \\sqrt{\\log_4(\\log_3(\\log_2(x^2-2x+a)))} \\) is defined for all real numbers \\( x \\).",
"role": "user"
}
] | [9, \infty) |
[
{
"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... | Date: 31-Dec-07
Dr. Cost of goods sold: 1,500
Cr. Allowance to reduce inventory value to NRV: 1,500
Date: 31-Dec-08
Dr. Cost of goods sold: 1,000
Cr. Allowance to reduce inventory value to NRV: 1,000 |
[
{
"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... | 10.42 |
[
{
"content": "Find the degree of the field extension \\( \\mathbb{Q}(i, \\sqrt[4]{3}, \\sqrt[6]{3}) \\) over \\( \\mathbb{Q} \\).",
"role": "user"
}
] | 24 |
[
{
"content": "Evaluate the following double integral to find the constant $k$ in terms of $a$ and $b$, where $a, b > 0$:\n\n$$\\int_{0}^{\\infty}\\int_{0}^{\\infty}k.e^{-(ax+by)}dxdy = 1$$\n\nDetermine the value of $k$.",
"role": "user"
}
] | ab |
[
{
"content": "If $A$ is an angle such that $\\tan A + \\sec A = 2,$ enter all possible values of $\\cos A,$ separated by commas.",
"role": "user"
}
] | \frac{4}{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... | 381.13K |
[
{
"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... | 79.21 |
[
{
"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... | 0.0147Radian/second |
[
{
"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... | $26.20 |
[
{
"content": "Given two games with the same number of players, each having a set of equilibria, consider the following probabilities:\n\n1. \\( Pr(\\text{players pick } Y_1 \\text{ in game 1}| \\text{the set of equilibria of game 1 is } \\mathcal{A}) \\)\n2. \\( Pr(\\text{players pick } X_1 \\text{ in game 2}| ... | Yes |
[
{
"content": "Let \\( f(x) \\) be a polynomial of degree 8 such that \\( f(r) = \\frac{1}{r} \\) for \\( r = 1, 2, 3, \\ldots, 9 \\). Find \\( \\frac{1}{f(10)} \\).",
"role": "user"
}
] | 5 |
[
{
"content": "Determine the number of roots of the complex function \\( f(z) = z^6 - 5z^4 + 8z - 1 \\) within the domain \\( |z| < 2 \\) using Rouché's theorem.",
"role": "user"
}
] | 4 |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^\\infty \\frac{x^2}{(1+x^2)^3} \\, dx \\).",
"role": "user"
}
] | \dfrac{\pi}{8} |
[
{
"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... | number of cells in given phase/total number of cells observed X length of cell cycle = length of given phase |
[
{
"content": "Evaluate the limit \\( \\lim_{ x\\to 0 } \\frac { \\sin(x^2) - x^2 }{ x^4 - \\sin^2(x) }.\\)",
"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... | 5782.62 kg |
[
{
"content": "Determine the number of analytic functions that satisfy the condition \\( f\\left(\\frac{1}{n\\pi}\\right)=1 \\) for \\( n\\in\\mathbb{N} \\) within a domain \\( D \\), where \\( D \\) is a disk centered at \\( z = a \\) with radius \\( r \\), and \\( 0 \\notin D \\).",
"role": "user"
}
] | \infty |
[
{
"content": "Determine the order of the group of homomorphisms from the dihedral group $D_{2n}$ to the multiplicative group of complex numbers $\\mathbb{C}^*$, where $n$ is an odd integer.",
"role": "user"
}
] | 2 |
[
{
"content": "Is there an uncountable subset of the interval \\([0,1]\\) that is not dense in any open interval but is not scattered?",
"role": "user"
}
] | Yes |
[
{
"content": "Compute the flux of the vector field \\( F(x,y,z) = (2x-y^2) \\mathbf{i} + (2x - 2yz) \\mathbf{j} + z^2 \\mathbf{k} \\) through the surface consisting of the side and bottom of the cylinder of radius two and height two, i.e., \\( \\{(x,y,z) \\mid x^2+y^2 = 4, 0 \\le z \\le 2\\} \\). Note that this... | 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... | qA = 2.16e-8 C, qB = 6.44e-9 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... | 13400 kg |
[
{
"content": "The volume of a cylinder is 60 cubic centimeters. What is the number of cubic centimeters in the volume of the sphere it circumscribes?",
"role": "user"
}
] | 40 |
[
{
"content": "Find an element of order 5 in the field \\( \\mathbb{Z}_3[x]/\\langle x^4 + x + 2 \\rangle \\).",
"role": "user"
}
] | 2x^3 + x + 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... | 23935 |
[
{
"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... | 5.42e-11 m |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\rightarrow \\infty} \\frac{(x - 2)^{3/4} \\sqrt{x^x}}{\\sqrt{{(x - 2)^x}{(x - 1)}{\\sqrt{x}}}}$$ and show that it converges to \\(e\\).",
"role": "user"
}
] | e |
[
{
"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... | 22.31 mL |
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