prompt list | ground_truth string |
|---|---|
[
{
"content": "Find the maximal volume of a rectangular box with a fixed surface area of 150 square units using the method of Lagrange multipliers.",
"role": "user"
}
] | 125 |
[
{
"content": "Given the equations:\n\\[ y = \\left\\lfloor\\frac{ x \\mod 790}{10}\\right\\rfloor + 48 \\]\n\\[ z = (x \\mod 790) \\mod 10 + 10\\left\\lfloor\\frac{x}{790}\\right\\rfloor + 48 \\]\nIf \\(y = 69\\) and \\(z = 60\\), find the value of \\(x\\).",
"role": "user"
}
] | 1002 |
[
{
"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... | 0.235 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... | 0.206 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... | 1.70293 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... | 6.08% |
[
{
"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... | 6.90e-6 m/s |
[
{
"content": "Find all the solutions to\n\\[\\sqrt{(2 + \\sqrt{3})^x} + \\sqrt{(2 - \\sqrt{3})^x} = 4.\\]Enter all the solutions, separated by commas.",
"role": "user"
}
] | 2,-2 |
[
{
"content": "If $x (x+y) = 27$ and $y (x+y) = 54$, what is the value of $(x+y)^2$?",
"role": "user"
}
] | 81 |
[
{
"content": "Prove that any group of order 63 must have an element of order 3, using only Lagrange's theorem and not Cauchy's or Sylow's theorems. Assume that the group cannot consist solely of the identity and elements of order 7. Provide a justification for why this is the case.",
"role": "user"
}
] | 3 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\to \\infty} \\frac{1}{n^4}\\left(\\frac{1}{a_1} + \\frac{2}{a_2} + \\frac{3}{a_3} + \\cdots + \\frac{n}{a_n}\\right) \\] where the sequence \\(a_n\\) is defined by \\(a_1 = 1\\) and \\(a_{n+1} = \\frac{a_n}{1 + n a_n}\\).",
"role": "user"
}
] | \dfrac{1}{8} |
[
{
"content": "Let $K_1$ and $K_2$ be parallel lines with line $K_3$ passing through both of them. Points $A$ and $H$ are not located on these lines. Points $C$ and $F$ are on line $K_3$. Draw lines $AG$, $AH$, and $AF$. Point $E$ is on line $AF$ such that $EC$ is perpendicular to $DC$. Find the measurement of t... | 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... | 9.9 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... | 2.85 M |
[
{
"content": "Find constants $A,$ $B,$ and $C$ so that\n\\[\\frac{x^2 - 7}{(x - 2)(x - 3)(x - 5)} = \\frac{A}{x - 2} + \\frac{B}{x - 3} + \\frac{C}{x - 5}.\\]Enter the ordered triple $(A,B,C).$",
"role": "user"
}
] | (-1,-1,3) |
[
{
"content": "One caterer charges a basic fee of $\\$100$ plus $\\$15$ per person. A second caterer charges a basic fee of $\\$200$ plus $\\$12$ per person. What is the least number of people for which the second caterer is cheaper?",
"role": "user"
}
] | 34 |
[
{
"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... | 22.4 |
[
{
"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... | $74,816 |
[
{
"content": "Determine the subset $A \\subset [0,8]^2$ with the largest Lebesgue measure such that $A$ and its translation by the vector $(3,4)$ do not intersect, i.e., $(A+(3,4)) \\cap A = \\emptyset$. What is the measure of this subset?",
"role": "user"
}
] | 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... | $839.62 |
[
{
"content": "Let \\( f, g \\in \\mathcal{L}(E) \\) where \\( E \\) is a complex vector space of dimension \\( n \\), satisfying the relation:\n\\[ f \\circ g - g \\circ f = f \\]\nDetermine the value of \\( \\det(f) \\).",
"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... | $111,480 |
[
{
"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... | 13.5% |
[
{
"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... | 5.286% |
[
{
"content": "Simplify the expression \\(\\lim_{x\\to 0+}\\exp\\left(\\frac{\\ln \\left( \\frac{\\cos(2x)}{2x} \\right)}{\\sin x}\\right)\\) using asymptotic equivalence.",
"role": "user"
}
] | \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... | 5.78 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... | 4.33 |
[
{
"content": "Determine the number of elements in the module \\(A = (\\mathbb{Z}[i]/I^{2014})\\otimes_{\\mathbb{Z}[i]}(\\mathbb{Z}[i]/J^{2014})\\), where \\(I\\) and \\(J\\) are the principal ideals of \\(\\mathbb{Z}[i]\\) generated by \\(7-i\\) and \\(6i-7\\), respectively.",
"role": "user"
}
] | 5^{2014} |
[
{
"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... | Cu |
[
{
"content": "Evaluate the integral \\(\\int_{-\\infty}^{\\infty} \\frac{\\cos (\\pi x)}{x^{2}-2 x+2} d x\\) using the residue theorem and a semicircular contour.",
"role": "user"
}
] | -\pi e^{-\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... | k |
[
{
"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... | 0.0049 |
[
{
"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... | $2,048,000 |
[
{
"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... | 84 m/s |
[
{
"content": "Determine the number of continuous functions \\( f: \\mathbb{R} \\to \\mathbb{R} \\) that satisfy the functional equation \\( f(f(x)) + f(x) + 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... | $S \to aSd \mid T$ $T \to bTd \mid U$ $U \to Ud \mid cU \mid c$ |
[
{
"content": "A rectangular cuboid \\(A B C D-A_{1} B_{1} C_{1} D_{1}\\) has dimensions \\(A A_{1} = 2\\), \\(A D = 3\\), and \\(A B = 251\\). The plane \\(A_{1} B D\\) intersects the lines \\(C C_{1}\\), \\(C_{1} B_{1}\\), and \\(C_{1} D_{1}\\) at points \\(L\\), \\(M\\), and \\(N\\) respectively. Calculate th... | 2008 |
[
{
"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... | $55.30 |
[
{
"content": "Evaluate the limit: $$\\lim_{(x,y)\\to(0,0)} \\left(\\frac{x+4x-4y^2}{4xy^2}\\right)^2+\\left(\\frac 1y-\\frac yx\\right)^2$$",
"role": "user"
}
] | \infty |
[
{
"content": "Let \\( A \\) be an \\( n \\times n \\) real matrix such that:\n\n1. \\( a_{ii} = 0 \\) for all \\( i \\), and \\( 1 > a_{ij} \\geq 0 \\) for all \\( i, j \\).\n2. \\( \\sum_{j=1}^n a_{ij} \\in (0,1] \\) for all \\( i \\).\n3. There exists at least one row \\( i_0 \\) such that \\( \\sum_{j=1}^n a... | 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... | 13.33% |
[
{
"content": "Find the real scalar value of $k$ such that the complex number \\( z = \\frac{2}{1+ki} - \\frac{i}{k-i} \\) lies on the line \\( y = 2x \\).",
"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... | 1.08 s |
[
{
"content": "Find a positive rational number such that its positive integer powers can be divided into two groups with equal sums.",
"role": "user"
}
] | \dfrac{1}{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... | 81730 |
[
{
"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... | 1.66e15 m/s^2 |
[
{
"content": "Calculate the value of the infinite series: \\[ \\sum_{k=1}^{\\infty} \\frac{k^2}{k!} \\]",
"role": "user"
}
] | 2e |
[
{
"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... | 7.400 MeV |
[
{
"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 = total cost / quantity of output |
[
{
"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... | 1.135keV |
[
{
"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... | Total costs = $16,800 + ($29.10 x Number of sales orders) |
[
{
"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... | 26.67 |
[
{
"content": "Determine whether the integral closure of a Noetherian integral domain is always Noetherian when the dimension of the domain is 2.",
"role": "user"
}
] | No |
[
{
"content": "Consider a set of $N$ points $X = (x_i)_{i=1}^N$. Define the score function $S: X \\rightarrow \\mathbb{N}$ as follows: \\[ S(X) = \\sum_{i=1}^N S(x_i) \\] where \\[ S(x_i) = 2 \\cdot \\left| \\{x_j; \\ |x_i-x_j| \\in [1,2]\\} \\right| + \\left| \\{x_j; \\ |x_i-x_j| \\in [2,3]\\} \\right| \\] and ... | 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... | mg/\mu_s |
[
{
"content": "Given the quadratic polynomials \\( f_{1}(x)=x^{2}-2 a x+3 \\), \\( f_{2}(x)=x^{2}+x+b \\), \\( f_{3}(x)=3 x^{2}+(1-4 a) x+6+b \\), and \\( f_{4}(x)=3 x^{2}+(2-2 a) x+3+2 b \\), let the differences between their roots be denoted as \\( A, B, C, \\) and \\( D \\) respectively. It is known that \\( ... | \dfrac{1}{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... | -0.4 |
[
{
"content": "Evaluate the integral \\( \\int_0^2 \\frac{2}{\\ln(x)} \\, dx \\) using the Fundamental Theorem of Calculus, given that \\( F'(x) = \\frac{1}{\\ln(x)} \\) and \\( F(0) = 1, F(1) = 2, F(2) = 5 \\).",
"role": "user"
}
] | 8 |
[
{
"content": "Determine whether the following statement is true or false: If $X, Y, Z$ are finite Abelian groups and $X \\oplus Y$ is isomorphic to $X \\oplus Z$, then $Y$ must be isomorphic to $Z$. Provide a justification for your answer.",
"role": "user"
}
] | True |
[
{
"content": "Evaluate the integral: \\( \\iiint \\delta(|\\mathbf{r}| - R)\\,\\mathrm{d}^{3}\\mathbf{r} \\).",
"role": "user"
}
] | 4\pi R^2 |
[
{
"content": "Consider the set $X = \\{ 1, 2, \\ldots, 10 \\}$. Find two disjoint nonempty subsets $A$ and $B$ of $X$ such that:\n\n1. $A \\cup B = X$;\n2. $\\prod_{x \\in A} x$ is divisible by $\\prod_{x \\in B} x$;\n3. The ratio $\\frac{\\prod_{x \\in A} x}{\\prod_{x \\in B} x}$ is as small as possible.",
... | 7 |
[
{
"content": "Let \\( f: \\mathbb{R} \\to \\mathbb{R} \\) be a differentiable function such that \\( f(0) = 0 \\) and \\( f(1) = 1 \\), with \\( |f'(x)| < 2 \\) for all \\( x \\in \\mathbb{R} \\). If \\( a \\) and \\( b \\) are real numbers such that the set of possible values of \\( \\int_0^1 f(x) \\, dx \\) i... | \dfrac{3}{4} |
[
{
"content": "Let $V$ be a finite-dimensional vector space and $W$ a subspace of $V$. Given a linear functional $f \\in W'$, prove that there exists a linear functional $g \\in V'$ such that $g$ restricted to $W$ is equal to $f$. Provide a justification for your answer.",
"role": "user"
}
] | 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... | $15,760.80 |
[
{
"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... | 10.24% |
[
{
"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... | 6352.5 J |
[
{
"content": "Given a smooth function \\( f: \\mathbb{R}^n \\rightarrow \\mathbb{R} \\) and a linear transformation \\( \\phi \\in GL(n) \\), find the Hessian matrix \\( H_{f \\circ \\phi} = \\left(\\frac{\\partial^2 (f \\circ \\phi)}{\\partial x_i \\partial x_j}\\right)_{ij} \\).",
"role": "user"
}
] | \phi^\top H_f(\phi(x)) \phi |
[
{
"content": "In how many different ways can the set \\( \\{1,2,\\dots, 2006\\} \\) be divided into three non-empty sets such that no set contains two successive numbers? Choose the correct answer from the options below:\n\\[\n\\textbf{(A)}\\ 3^{2006}-3\\cdot 2^{2006}+1 \\\\\n\\textbf{(B)}\\ 2^{2005}-2 \\\\\n\\... | 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... | 246.67 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... | 2.63 |
[
{
"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... | 0.53 mph |
[
{
"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... | {eq}Mn(OH)_2 + H_2O_2 \to MnO_2 + 2H_2O{/eq} |
[
{
"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... | 64.27m/s |
[
{
"content": "Find the smallest integer \\(x\\) such that \\(2^x \\equiv 166 \\pmod{330}\\).",
"role": "user"
}
] | 20 |
[
{
"content": "If \\(a, b, c\\) are distinct numbers such that \\(a^2 - bc = 2014\\), \\(b^2 + ac = 2014\\), and \\(c^2 + ab = 2014\\), compute \\(a^2 + b^2 + c^2\\). Choose the correct answer from the following options:\n\n(A) 4030 \n(B) 4028 \n(C) 4026 \n(D) 4000 \n(E) 2014",
"role": "user"
}
] | B |
[
{
"content": "Determine the rate of change of the function \\(x^2 + y^2\\) with respect to time for the system of differential equations given by \\(x' = -x + 4y\\) and \\(y' = -4x - y\\).",
"role": "user"
}
] | -2(x^2 + y^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... | 26.361 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... | 15.95% |
[
{
"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... | {"WHL TONE": 1.127294, "SMI TONE": 1.061741} |
[
{
"content": "A bee starts flying from point $P_0$. She flies 1 inch due east to point $P_1$. For $j \\ge 1$, once the bee reaches point $P_j$, she turns $30^{\\circ}$ counterclockwise and then flies $j+1$ inches straight to point $P_{j+1}$. When the bee reaches $P_{2015}$, she is exactly $a\\sqrt{b} + c\\sqrt{... | B |
[
{
"content": "Determine the number of possible rays that satisfy Snell's law in the lifeguard problem, given only the angle between the line connecting the two people and the normal.",
"role": "user"
}
] | 1 |
[
{
"content": "Calculate the limit of the sequence as \\( n \\to \\infty \\):\n\\[ \\lim_{n\\rightarrow\\infty}\\left( \\frac{1\\cdot3\\cdot5\\cdot\\ldots\\cdot(2n-1) }{ 2\\cdot4\\cdot6\\cdot\\ldots\\cdot(2n)}\\right)^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... | Culver City Lighting, Inc. Balance Sheet for the year ended December 31, 2006
Current Assets:
Cash and Cash Equivalents: $55,000
Inventories: $45,000
Accounts receivable: $39,000
Prepaid insurance: $15,000
Total Current Assets: $154,000
Fixed Assets:
Equipment: $100,000
Less: Accumulated depreciation-equipment: $34,000... |
[
{
"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... | 280 pm |
[
{
"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... | 6.370e-10 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... | 3200 J |
[
{
"content": "Determine whether there exists a natural number $n > 1$, which is not congruent to 3 modulo 4, such that there is a prime $p > 5$ for which both $3^{n^2-1} \\equiv 1 \\pmod{p}$ and $2^{n^2-1} \\equiv 1 \\pmod{p}$ hold true.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\to \\infty}{n\\left[\\left(1+\\frac{c}{n}\\right)^{n}-\\left(1-\\frac{c}{n}\\right)^{-n}\\right]} \\] without using L'Hopital's Rule.",
"role": "user"
}
] | -c^2 e^c |
[
{
"content": "The equation of the hyperbola shown below can be written as\n\\[\\frac{(y - k)^2}{a^2} - \\frac{(x - h)^2}{b^2} = 1.\\]Find $h + k + a + b.$\n\n[asy]\nunitsize(0.3 cm);\n\nreal upperhyper (real x) {\n return (2*sqrt((x - 6)^2/16 + 1) - 5);\n}\n\nreal lowerhyper (real x) {\n return (-2*sqrt((x - ... | 7 |
[
{
"content": "A rectangle has integer side lengths. One pair of opposite sides is increased by $30\\%$ and the other pair of sides is decreased by $20\\%$. The new side lengths are also integers. What is the smallest possible area, in square units, of the new rectangle?",
"role": "user"
}
] | 52 |
[
{
"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... | 2,600 million |
[
{
"content": "In \\(\\triangle ABC\\), \\(O\\) is the circumcenter. Given \\(|AB|=2\\), \\(|AC|=1\\), and \\(\\angle BAC = \\frac{2}{3} \\pi\\), let \\(\\overrightarrow{AB} = \\mathbf{a}\\) and \\(\\overrightarrow{AC} = \\mathbf{b}\\). If \\(\\overrightarrow{AO} = \\lambda_1 \\mathbf{a} + \\lambda_2 \\mathbf{b}... | \dfrac{13}{6} |
[
{
"content": "Given a positive $L^1$ function $f$ on $\\mathbb{R}^2$, determine if there exists a subset $A \\subseteq \\mathbb{R}^2$ such that \\( \\int_A f \\, d\\mu = \\int_{\\mathbb{R}^2 \\setminus A} f \\, d\\mu \\).",
"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 million |
[
{
"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... | 1.09 |
[
{
"content": "Determine the constant $c$ for the probability density function (pdf) given by \\( f(x, y) = c \\frac{2^{x+y}}{x ! y !} \\), where \\( x=0,1,2, \\ldots \\) and \\( y=0,1,2, \\ldots \\).",
"role": "user"
}
] | e^{-4} |
[
{
"content": "Determine the maximum possible order of a centralizer in a group of order 32.",
"role": "user"
}
] | 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... | 70 mEq/L |
[
{
"content": "In parallelogram \\(ABCD\\), point \\(M\\) is located on side \\(BC\\). Given that \\(\\angle A = 45^{\\circ}\\), \\(\\angle AMD = 90^{\\circ}\\), and the ratio \\(BM : MC = 2 : 3\\), determine the ratio of the lengths of the adjacent sides of the parallelogram.",
"role": "user"
}
] | \dfrac{2\sqrt{2}}{5} |
[
{
"content": "Find all natural number tuples \\((a, b, c)\\) that satisfy the following system of equations:\n\\[ a^2 + b^2 = c^3 \\]\n\\[ (a + b)^2 = c^4 \\]",
"role": "user"
}
] | (2, 2, 2) |
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