prompt list | ground_truth string |
|---|---|
[
{
"content": "Consider the hyperbola \\( C: \\frac{x^{2}}{a^{2}}-\\frac{y^{2}}{b^{2}}=1 \\) with eccentricity \\(\\frac{5}{3}\\). A line \\( l \\) passes through the left focus \\( F_{1} \\) and is tangent to the circle \\( x^{2}+y^{2}=a^{2} \\) at point \\( T \\). The line \\( l \\) also intersects the right b... | 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... | 5.58 sec |
[
{
"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... | 0.78 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... | 0.175 |
[
{
"content": "Determine the values of \\( \\alpha \\in (0,1) \\) for which the operator \\( A: L_2[0,1]\\rightarrow L_2[0,1] \\), defined by \\((Ax)(t) = \\int_0^1 \\frac{x(s)}{|t-s|^{\\alpha}}ds\\), is compact.",
"role": "user"
}
] | (0,1) |
[
{
"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... | 87.86 m |
[
{
"content": "Determine whether the intersection of the nested sequence of sets \\( B_{2^n}^k = \\left[\\frac{k}{2^n},\\frac{k+1}{2^n}\\right) \\), where \\( n \\in \\mathbb{N} \\) and \\( k = 2^{n+1}-2 \\), is a singleton or empty.",
"role": "user"
}
] | \emptyset |
[
{
"content": "Consider a locally compact Hausdorff topological group \\( G \\) with a left Haar measure \\( \\mu \\) that is not right-invariant. Does there exist a Borel subset \\( B \\) of \\( G \\) and an element \\( g \\) of \\( G \\) such that the closure of \\( B \\) is compact, and for \\( C = \\{ h \\in... | 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... | 9.87 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... | 4.85 |
[
{
"content": "Consider a deck of $N$ cards, numbered from $1$ to $N$. Perform the following operation: look at the number on the top card, say it is $K$, and reverse the order of the first $K$ cards in the deck. If $N$ is an even number, will this process eventually stop?",
"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... | 3.3882e-5 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... | 1.898 s |
[
{
"content": "Evaluate the limit: $$ \\lim_{n \\to\\infty} \\int_{0}^1 nxe^{-nx} \\, dx $$",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 513 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... | ClO_3^(-)+3SO_2(g) +6HO^(-) rarr 3SO_4^(2-) + Cl^(-) +3H_2O |
[
{
"content": "Find a polynomial \\( p(x) \\) of degree \\( \\le 2 \\) that approximates \\( f(x) = x^{1/3} \\) and minimizes the error \\[ E = (f(-1)-p(-1))^2 + \\int_{-1}^1 (f(x)-p(x))^2 \\, dx + (f(1)-p(1))^2. \\]",
"role": "user"
}
] | \dfrac{15}{14}x |
[
{
"content": "Calculate the limit as \\( n \\to \\infty \\) for the expression: \\[ \\lim\\limits_{n\\to \\infty} \\sqrt [n]{\\frac{(3n)!}{n!(2n+1)!}} \\]",
"role": "user"
}
] | \dfrac{27}{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... | 2.07 T |
[
{
"content": "Find all positive integers that are coprime with every term of the sequence \\(a_{n}=2^{n}+3^{n}+6^{n}-1\\) for \\(n=1,2,3,\\ldots\\).",
"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... | L= \frac{\mu _{0} Na^{2}}{2 R} |
[
{
"content": "Given a complex number \\( z \\) such that \\( |z| = 1 \\), determine the maximum value of \\( u = \\left| z^3 - 3z + 2 \\right| \\).",
"role": "user"
}
] | 3\sqrt{3} |
[
{
"content": "Determine whether the following statement is true or false: Let $R$ be a ring with identity and $f$ be a ring homomorphism from $R$ to a ring $S$. The left ideals of the ring $f(R)$ are exactly of the form $f(I)$, where $I$ is a left ideal of $R$. Provide a justification for your answer.",
"ro... | True |
[
{
"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... | $24.23 |
[
{
"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... | 1.67e-5 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... | 8041.6 |
[
{
"content": "Find the Taylor series representation of the function \\( f(x) = \\frac{x}{4+x^2} \\) centered at \\( x = 0 \\). Determine the radius of convergence using the \\( n \\)-th root test.",
"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... | $52,662.04 |
[
{
"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... | 0.054 rad/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... | $1,168.33 |
[
{
"content": "Find the residue of the function \\( f(z) = \\frac{1}{z - \\sin(z)} \\) at \\( z = 0 \\).",
"role": "user"
}
] | \dfrac{3}{10} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Output (Units) | Total Cost ($) | ATC
---|---|---
0 | 100 | -
10 | 240 | 24
20 | 340 | 17
30 | 420 | 14
40 | 520 | 13
50 | 660 | 13.2
60 | 860 | 14.33 |
[
{
"content": "Let $f(n)$ return the number of distinct ordered pairs of positive integers $(a, b)$ such that for each ordered pair, $a^2 + b^2 = n$. Note that when $a \\neq b$, $(a, b)$ and $(b, a)$ are distinct. What is the smallest positive integer $n$ for which $f(n) = 3$?",
"role": "user"
}
] | 50 |
[
{
"content": "Let $\\mathcal{A}$ be an abelian category and $\\mathbb{K}(\\mathcal{A})$ the homotopy category of complexes of $\\mathcal{A}$. Consider a functor $F: \\mathbb{K}(\\mathcal{A}) \\to \\mathbb{E}$, where $\\mathbb{E}$ is a triangulated category, such that $F$ takes quasi-isomorphisms to isomorphisms... | No |
[
{
"content": "What is the base ten equivalent of $12345_{6}$?",
"role": "user"
}
] | 1865 |
[
{
"content": "Evaluate $\\log_432$.",
"role": "user"
}
] | \frac{5}{2} |
[
{
"content": "Determine whether there exists a Riemann integrable function \\( f: [a,b] \\to \\mathbb{R} \\) that satisfies the following conditions:\n\n1. \\( f \\) is a positive function, meaning \\( f(x) \\geqslant 0 \\) for all \\( x \\in [a,b] \\).\n2. There exists an infinite subset \\( E \\) of \\( [a, b... | 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... | 16.28% |
[
{
"content": "Calculate the limit: \\[ \\lim_{n\\to\\infty}\\left(\\left(\\frac{9}{4}\\right)^n+\\left(1+\\frac{1}{n}\\right)^{n^2}\\right)^{\\frac{1}{n}} \\]",
"role": "user"
}
] | e |
[
{
"content": "Determine the constant \\( c \\) such that the function \\( f(x, y) = c \\frac{2^{x+y}}{x! y!} \\) is a valid probability density function for \\( x = 0, 1, 2, \\ldots \\) and \\( y = 0, 1, 2, \\ldots \\).",
"role": "user"
}
] | e^{-4} |
[
{
"content": "Given that $a$ and $b$ are positive integers and that $a+b=24$, what is the value of $ab$ if $2ab + 10a = 3b + 222$?",
"role": "user"
}
] | 108 |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to0}\\frac{x\\sin{(\\sin{x})}-\\sin^2{x}}{x^6}$$",
"role": "user"
}
] | \dfrac{1}{18} |
[
{
"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... | [A] = 0.0190 M, [B] = 0.329 M, [C] = 0.012 M |
[
{
"content": "Given two power series \\(\\sum_{n=0}^{\\infty} a_nx^n\\) and \\(\\sum_{n=0}^{\\infty} b_nx^n\\) with radii of convergence \\(R_{1}\\) and \\(R_{2}\\) respectively, where \\(R_{1} < R_{2}\\), determine the radius of convergence of the series \\(\\sum_{n=0}^{\\infty} (a_n+b_n)x^n\\).",
"role": ... | R_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... | (sigma_(2s))^2 (sigma_(2s)^"*")^2 (sigma_(2p_z))^2 (pi_(2p_x))^2 (pi_(2p_y))^2 (pi_(2p_x)^"*")^2 (pi_(2p_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... | $1,155,555.56 |
[
{
"content": "Determine the interval of convergence for the series \\(\\sum_{n=1}^{\\infty} \\left(1 + \\frac{1}{2} + \\frac{1}{3} + \\cdots + \\frac{1}{n}\\right)x^n\\) using the Cauchy Root Test.",
"role": "user"
}
] | (-1, 1) |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 221 |
[
{
"content": "Let $g_n:[0,1] \\to \\mathbb{R}$ be defined by \\( g_n(x) = \\frac{nx}{1+n^2 x^q} \\) for \\( q > 0 \\). Determine the values of \\( q \\) for which the sequence \\( g_n \\) converges uniformly to its point-wise limit.",
"role": "user"
}
] | (0, 2) |
[
{
"content": "Evaluate the limit of the sequence as \\( n \\to \\infty \\): \\[ \\lim_{n \\to \\infty} \\frac{n! - n^3}{n^5 - e^n + 3} \\]",
"role": "user"
}
] | -\infty |
[
{
"content": "Suppose \\(\\phi\\) is a simple function such that \\(0 \\leq \\phi \\leq f\\), where \\(f\\) is a measurable function. If \\(f = 0\\) almost everywhere, is it true that \\(\\phi = 0\\) almost everywhere?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine whether there exists a function $f$ such that $f$ is not in the $L^1$ space, but its Fourier transform $\\hat{f}$ is in the $L^1$ 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... | NH4+(aq) + H2O(l) <-> H3O+(aq) + NH3(aq) |
[
{
"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... | 1.9e-10 |
[
{
"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... | 114.74 |
[
{
"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... | 3.31e-4 |
[
{
"content": "Find all real solutions to $x^4+(2-x)^4=34$. Enter all the solutions, separated by commas.",
"role": "user"
}
] | 1 + \sqrt{2}, 1 - \sqrt{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... | {\frac{\sqrt 3 \mu_{0}I }{ \pi a }} |
[
{
"content": "Let $a$ be a positive integer such that $\\cos\\left(\\frac{a\\pi}{6}\\right)=\\frac{\\sqrt{3}}{2}$ and $\\cos(\\theta+a\\cdot\\beta)=\\cos(\\theta+\\beta)$ for any $\\theta,\\beta \\in \\mathbb{R}$. Calculate the limit:\n\\[ \\lim_{x\\to\\pi/6}\\frac{2\\cos(ax)-\\sqrt{3}}{\\pi-6x} \\]",
"role... | \dfrac{1}{6} |
[
{
"content": "Find the variance of the distribution of the number of Bernoulli trials needed to achieve 100 successes, given that the probability of success in each trial is 0.01.",
"role": "user"
}
] | 990000 |
[
{
"content": "Determine the number of roots of the polynomial \\( z^5 + 4z^2 + 1 \\) that lie in the annulus defined by \\( 1 < |z| < 2 \\).",
"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... | 1.99 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... | Sales revenue: $276,000
Cost of Goods Sold:
Direct material: $46,000
Direct labor: $69,000
Variable manufacturing overheads: $34,500
Fixed manufacturing overheads: $18,400
Total Cost of Goods Sold: $167,900
Gross Profit: $108,100
Less Selling and administrative expenses:
Variable selling and administrative ex... |
[
{
"content": "Calculate the expected number of coin tosses required to obtain the sequence H-T-H-T-T-H with a fair coin.",
"role": "user"
}
] | 66 |
[
{
"content": "Let $f : [0, 1] \\rightarrow \\mathbb{R}$ be a twice differentiable function such that $f(0) = f(1) = 0$ and $f''(x) - 2f '(x) + f(x) \\geq x$ for $x \\in [0, 1]$. Determine which of the following is true for $0 < x < 1$:\n1) $0 < f(x) < \\infty$\n2) $-1/2 < f(x) < 1/2$\n3) $-1/4 < f(x) < 1$\n4) $... | 3 |
[
{
"content": "Determine whether there exists a power of 2, when expressed in base 3, that contains only even digits, excluding the case of \\(2^0 = 1_3\\).",
"role": "user"
}
] | Yes |
[
{
"content": "In a bank with 1000 customers, the number of withdrawal requests per month follows a Poisson distribution with an average of 60 requests. Each withdrawal amount is exponentially distributed with an average of 700 euros. Calculate the probability that the total amount withdrawn in a given month exc... | 0.149 |
[
{
"content": "Evaluate the limit: $$\\lim_{h\\to0} \\frac{f(e^{2h} + h) - f(1)}{h}$$ given that $f'(1) = 3$.",
"role": "user"
}
] | 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... | $45,000 reduction |
[
{
"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... | 4.09 ton |
[
{
"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... | 0.57 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... | 8.28 |
[
{
"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... | 9.42 |
[
{
"content": "Determine the number of sequences of 6 positive integers \\(a_1, a_2, a_3, a_4, a_5, a_6\\) such that \\(a_1 = 1\\), \\(a_6 = 2000\\), and for each \\(2 \\leq n \\leq 6\\), \\(a_n\\) is divisible by \\(a_{n-1}\\).",
"role": "user"
}
] | 2450 |
[
{
"content": "Do two $n \\times n$ matrices, $A$ and $B$, with the same column space necessarily have the same row space? Answer yes or no.",
"role": "user"
}
] | No |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 68.72 m |
[
{
"content": "Given positive numbers $a$ and $b$ such that $a + b = 1$, find the minimum value of the expression \\((a + \\frac{1}{a})^2 + (b + \\frac{1}{b})^2\\).",
"role": "user"
}
] | \dfrac{25}{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... | $318,748.4 |
[
{
"content": "Let $R$ be an integral domain and $F$ be a subfield of $R$. If $\\alpha \\in R$ is algebraic over $F$, does it imply that $\\frac{1}{\\alpha}$ is also algebraic over $F$? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine whether the following statement is true or false: If \\( p(x) \\) and \\( q(x) \\) are real-coefficient polynomials such that \\( p(p(x)) = q(x)^2 \\) for all real \\( x \\), then there exists a real-coefficient polynomial \\( r(x) \\) such that \\( p(x) = r(x)^2 \\) for all real \\( x \... | True |
[
{
"content": "Let $p$ be a prime number, $p \\ge 5$, and $k$ be a digit in the $p$-adic representation of positive integers. Determine the maximal length of a non-constant arithmetic progression whose terms do not contain the digit $k$ in their $p$-adic representation.",
"role": "user"
}
] | p-1 |
[
{
"content": "Let $X$ be a real random variable, and consider a real number $x \\in \\mathbb{R}$ such that $X$ is centrally symmetric with respect to $x$, meaning $X - x$ has the same distribution as $x - X$. Determine if $|X - x|$ has the same distribution as $|x - X|$. Justify your answer.",
"role": "user... | Yes |
[
{
"content": "Find the number of distinct elements in the group defined by the presentation \\( \\langle x,y \\mid x^3=y^2=(xy)^3=e \\rangle \\) by determining a normal form for its elements.",
"role": "user"
}
] | 12 |
[
{
"content": "Calculate \\( \\frac{dF(x)}{dx} \\bigg|_{x=0} \\) for the function \\( F(x) = \\int_0^2 \\sin(x+l)^2\\ dl \\).",
"role": "user"
}
] | \sin(4) |
[
{
"content": "Evaluate the limit: \\( \\displaystyle\\lim_{z\\to3i}\\frac{-3z}{z^2-9-6iz} \\). Determine whether the limit is \\( \\infty \\) or does not exist.",
"role": "user"
}
] | \infty |
[
{
"content": "If the line \\(mx + ny = 3\\) is normal to the hyperbola \\(x^2 - y^2 = 1\\), find the value of \\(\\frac{1}{m^2} - \\frac{1}{n^2}\\).",
"role": "user"
}
] | \dfrac{4}{9} |
[
{
"content": "Solve for $x$: $3x-(1-x)=5$. Express your answer as a common fraction in simplest form.",
"role": "user"
}
] | \frac32 |
[
{
"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... | 36.23 kgm^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... | 8.62% |
[
{
"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... | 3.3e-8 M |
[
{
"content": "The points $(0,0)\\,$, $(a,11)\\,$, and $(b,37)\\,$ are the vertices of an equilateral triangle. Find the value of $ab\\,$.",
"role": "user"
}
] | 315 |
[
{
"content": "If $y - x,$ $y - 2x,$ and $y - kx$ are all factors of\n\\[x^3 - 3x^2 y + p_1 xy^2 + p_2 y^3,\\]then find $k$.",
"role": "user"
}
] | \frac{2}{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... | 115 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... | 13.0208 |
[
{
"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... | m/(dV) |
[
{
"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... | 60 mH |
[
{
"content": "Determine whether there exists a natural number \\( n \\) such that the sum of the digits of \\( n \\) is 1000, and the sum of the digits of \\( n^2 \\) is equal to the sum of the digits of \\( 1000^2 \\).",
"role": "user"
}
] | No |
[
{
"content": "Is it possible to select 2016 integers such that their product is 9 and their sum is zero?",
"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... | 890.641 cm^3/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... | 3.23e+08 L |
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