prompt list | ground_truth string |
|---|---|
[
{
"content": "Given a random variable $X$ with probability density function $f(x) = 0.5 e^{-|x-2|}$, calculate the conditional variance $\\text{Var}(X \\mid X > 8)$. Assume $E(X) = 2$ and $E(X^2) = 6$. Provide your answer in terms of a single numerical value.",
"role": "user"
}
] | 1 |
[
{
"content": "Let $A \\subset I_0$ be an arbitrary set such that $\\text{Int}(A) \\neq \\emptyset$. Is the outer measure $\\mu^*(A)$ always positive?",
"role": "user"
}
] | Yes |
[
{
"content": "Given the functional equation \\( P(P(x)-1) = 1 + x^{36} \\), find the value of \\( P(2) \\).",
"role": "user"
}
] | 65 |
[
{
"content": "Let \\( f(x,y): \\mathbb{R}^2 \\rightarrow \\mathbb{R} \\) be a smooth (\\( {\\cal C}^\\infty \\)) function such that \\( f(0,y)=0 \\) for all \\( y \\in \\mathbb{R} \\) and \\( f(x,y)>0 \\) for \\( x \\neq 0 \\). Determine whether there exists \\( y_0 \\in \\mathbb{R} \\), \\( \\varepsilon >0 \\)... | 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... | 1.06 rad/s |
[
{
"content": "Determine the number of distinct terms in the expansion of \\((1 + a^3 + a^{-3})^{100}\\).",
"role": "user"
}
] | 201 |
[
{
"content": "Determine whether the characteristic function of a normally distributed random variable is an analytic function on the complex plane.",
"role": "user"
}
] | Yes |
[
{
"content": "Let $f: (0,1) \\to \\mathbb{R}$ be a differentiable function such that $\\lim_{x\\to0^+}f(x) = A$ and $\\lim_{x\\to0^+}\\frac{f(x)}{x}=B$. Determine the value of $A$. \\(A\\) is a constant.",
"role": "user"
}
] | 0 |
[
{
"content": "Donna has $n$ boxes of doughnuts. Each box contains $13$ doughnuts.\n\nAfter eating one doughnut, Donna is able to rearrange the remaining doughnuts into bags so that each bag contains $9$ doughnuts, and none are left over. What is the smallest possible value of $n$?",
"role": "user"
}
] | 7 |
[
{
"content": "Find the indicial equation of the differential equation \\(t^2y''+ty'+(t^2-2)y=0\\) at \\(t=0\\).",
"role": "user"
}
] | r^2 - 2 = 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... | 1.60 mL |
[
{
"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... | 3.81e-6 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... | 25.63% |
[
{
"content": "Find the maximum value of the integral \\( \\int_0^1 f^3(x) \\, dx \\), where \\( f(x) \\) is a function satisfying \\( -1 \\le f(x) \\le 1 \\) and \\( \\int_0^1 f(x) \\, dx = 0 \\).",
"role": "user"
}
] | \dfrac{1}{4} |
[
{
"content": "Let \\( A \\) be an \\( n \\times n \\) real strictly upper triangular matrix. If the entry \\( a_{nn} \\) is changed to a non-zero real number \\( z \\), will the Jordan block sizes of the resulting matrix remain the same for all non-zero \\( z \\)? Answer with 'Yes' or 'No'.",
"role": "user"... | No |
[
{
"content": "Given two power series \\( g(x) = \\sum a_n x^n \\) and \\( h(x) = \\sum b_n x^n \\) with radii of convergence \\( R_1 \\) and \\( R_2 \\) respectively, such that \\( g(x) \\leq h(x) \\) for all \\( x \\) in \\( \\{|x| \\leq \\min \\{R_1, R_2\\}\\} \\). Does this imply that \\( R_1 \\leq R_2 \\)?"... | No |
[
{
"content": "Find the values of $a > 0$ for which the series $$\\sum_{n=1}^{\\infty} \\left(\\frac{a n+2}{3n+1}\\right)^{n}$$ converges.",
"role": "user"
}
] | (0, 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... | 18.2 degrees |
[
{
"content": "Determine if the surface defined by the equation \\(x^{4/3} + y^{4/3} + z^4 = 1\\) is closed.",
"role": "user"
}
] | Yes |
[
{
"content": "Calculate the limit: \\[ \\lim_{x \\to 0} \\left(\\frac{1+x2^x}{1+x3^x}\\right)^{\\frac{1}{x^2}}. \\]",
"role": "user"
}
] | \dfrac{2}{3} |
[
{
"content": "Find the ordered pair $(a,b)$ of integers such that\n\\[\\sqrt{9 - 8 \\sin 50^\\circ} = a + b \\csc 50^\\circ.\\]",
"role": "user"
}
] | (3,-1) |
[
{
"content": "Calculate the sum of the series: \\[ \\sum_{n \\geq 1} \\frac{C(n,0) + C(n,1) + C(n,2) + \\cdots + C(n,n)}{P(n,n)} \\] where \\( C(n,k) \\) is the binomial coefficient and \\( P(n,n) \\) is the number of permutations of \\( n \\) items. Express your answer in terms of known constants or functions.... | e^2 - 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... | 1.9e+19 |
[
{
"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... | Liver, heart, and muscles |
[
{
"content": "Evaluate \\(\\int\\int_{S} (\\text{curl}\\, \\vec{F}) \\cdot \\vec{n} \\, dS\\) using Stokes' Theorem, where \\(S\\) is the upper hemisphere of the sphere defined by \\(x^2 + y^2 + z^2 = 4\\) and oriented in the positive \\(y\\) direction. The vector field is \\(\\vec{F} = \\langle ze^y, x\\cos(y)... | -4\pi |
[
{
"content": "Find the value of $x$ such that $777^{777} \\equiv x \\pmod{100}$. Express your answer as a number in the form $\\boxed{x}$.",
"role": "user"
}
] | 97 |
[
{
"content": "Find all functions \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) such that for all \\( x, y \\in \\mathbb{R} \\), the following equation holds:\n\\[\nf(f(x+y))=f(x+y)+f(x) f(y)+\\alpha x y\n\\]where \\( \\alpha \\) is a nonzero real number.",
"role": "user"
}
] | f(x) = x |
[
{
"content": "Given that $a + b + c = 0$, prove that \\[ \\left(\\frac{a}{b-c} + \\frac{b}{c-a} + \\frac{c}{a-b}\\right) \\left(\\frac{b-c}{a} + \\frac{c-a}{b} + \\frac{a-b}{c}\\right) = 9. \\] Assume $a$, $b$, and $c$ are distinct.",
"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... | $6,431.00 |
[
{
"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... | mv/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... | 10.89 mm |
[
{
"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... | 23.466 ft |
[
{
"content": "Evaluate the integral of the function \\( f(z) = z^2 + 2z - 3 \\) over the ellipse defined by \\( |z-2i|+|z+2i|=12 \\), using the parametrization \\( z(t) = \\sqrt{35} \\sin t + 6i\\cos t \\).",
"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... | 118 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... | 9.01e-6 m |
[
{
"content": "Does the sequence $f_n(x) = \\frac{x}{n}$ converge weakly to $0$ in the normed space $C[0,1]$ with the supremum norm?",
"role": "user"
}
] | Yes |
[
{
"content": "Let \\( \\{ a_n \\} \\) be a sequence of non-negative real numbers such that the series \\( \\sum_{n=1}^{\\infty} a_n \\) is convergent. Determine the range of values of the real number \\( p \\) for which the series \\( \\sum_{n=1}^{\\infty} \\frac{\\sqrt{a_n}}{n^p} \\) diverges.",
"role": "u... | (-\infty, \frac{1}{2}] |
[
{
"content": "Find a generator of the ideal generated by $3$ and $2 - 2\\sqrt{-2}$ in the ring $\\mathbb{Z}[\\sqrt{-2}]$. The generator should be an element of the ideal with minimal norm. The norms of $3$ and $2 - 2\\sqrt{-2}$ are $9$ and $12$, respectively. Determine this generator.",
"role": "user"
}
] | 1 - \sqrt{-2} |
[
{
"content": "Compute the integral \\( \\int_C \\frac{e^z}{z} \\, dz \\), where \\( C \\) is the unit circle with positive orientation.",
"role": "user"
}
] | 2\pi i |
[
{
"content": "Evaluate the double integral \\( \\int \\int_R |xy| \\, dx \\, dy \\), where \\( R \\) is the region enclosed by \\( x^2+4y^2 \\geq 1 \\) and \\( x^2+y^2 \\leq 1 \\).",
"role": "user"
}
] | \dfrac{3}{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... | 4935.284 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... | 35 mol |
[
{
"content": "Determine the coefficient of $x^{11}$ in the expansion of the product $(1+x^2)^4(1+x^3)^7(1+x^4)^{12}$.",
"role": "user"
}
] | 1113 |
[
{
"content": "Determine whether a non-closed subspace of a separable Hilbert space can have a countable orthonormal basis, even though it is not a Hilbert space itself. Provide a justification for your answer.",
"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... | 45.56 |
[
{
"content": "Evaluate the integral \\( \\int _{|z|=3} \\frac{z^2 \\, dz}{(z^2+4)(z-2i)} \\) using Cauchy's Integral Formula.",
"role": "user"
}
] | 2\pi i |
[
{
"content": "Solve the differential equation \\( y'' - y' - 2y = 12 \\sin t \\, \\delta(t-\\pi) \\) with the initial conditions \\( y(0) = 1 \\) and \\( y'(0) = -1 \\).",
"role": "user"
}
] | e^{-t} |
[
{
"content": "Does the forgetful functor from the category of topological groups, \\( \\mathbf{TopGrp} \\), to the category of topological spaces, \\( \\mathbf{Top} \\), admit a left adjoint? Specifically, for an arbitrary topological space \\( X \\), can we find a topological group \\( \\Gamma X \\) and a cont... | Yes |
[
{
"content": "Are all topological vector spaces homeomorphic to each other?",
"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... | 0.0029 T |
[
{
"content": "Find all strictly positive integers $x, y, z$ such that $5^{x} - 3^{y} = z^{2}$.",
"role": "user"
}
] | (2, 2, 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... | Fluoro, difluoromethyl, and trifluoromethyl groups |
[
{
"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... | 15601 years |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $52,500 |
[
{
"content": "Let $PQ$ be a focal chord of the parabola $y^2= 4ax$. The tangents to the parabola at $P$ and $Q$ meet at a point lying on the line $y = 2x + a$, where $a > 0$. If the slope of chord $PQ$ is $m$, find the value of $m$.",
"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... | $65,548 |
[
{
"content": "Find \\( \\lim_{n \\to \\infty} n\\left[\\left(1+\\frac{1}{n}\\right)^n - e\\right] \\).",
"role": "user"
}
] | -\dfrac{e}{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... | H+(aq) + OH-(aq) -> H2O(l) |
[
{
"content": "Calculate the area under one arch of the cycloid defined by the parametric equations \\(x=6(t-\\sin(t))\\) and \\(y=6(1-\\cos(t))\\). The cycloid spans from \\(x=0\\) to \\(x=12\\pi\\). Set up and evaluate the integral to find the area.",
"role": "user"
}
] | 108\pi |
[
{
"content": "In the four-sided pyramid \\(SABCD\\), the lateral faces \\(SAB, SBC, SCD, SDA\\) have areas of 9, 9, 27, and 27 respectively. The dihedral angles at the edges \\(AB, BC, CD, DA\\) are equal, and the quadrilateral \\(ABCD\\) is inscribed in a circle with an area of 36. Find the volume of the pyram... | 54 |
[
{
"content": "Evaluate the limit of the product as \\( n \\) approaches infinity: \n\\[ P=\\lim_{n \\to \\infty}\\prod_{a=5}^{n}\\frac{a^3-64}{a^3+64} \\]",
"role": "user"
}
] | \dfrac{10}{259} |
[
{
"content": "Find a formula to calculate the sum of quadratic residues modulo a prime $q$ when $q \\equiv 1 \\pmod{3}$. Provide the formula.",
"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... | 240220.72 km |
[
{
"content": "Determine the minimum number \\( k \\) such that any subset of an \\( n \\times n \\) table with \\( k \\) elements contains an even subset, where an even subset is defined as a subset containing an even number of elements from each row and each column.",
"role": "user"
}
] | 2n |
[
{
"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... | 788 mi, 48.1 degrees north of east |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 635 mm Hg |
[
{
"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... | 0.01029 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... | -$17,800 |
[
{
"content": "For positive definite, diagonalizable, and finite-dimensional matrices A and B, does the positive definiteness of A + B imply that \\( \\det(A) < \\det(B) \\)? Answer yes or no and justify your answer.",
"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... | corporate profits |
[
{
"content": "Find the limit of \\(\\frac{e^{4\\pi i(x-2)}-1}{x-2}\\) as \\(x\\rightarrow 2\\) without using l'Hopital's rule.",
"role": "user"
}
] | 4\pi i |
[
{
"content": "Given real numbers $a, b, c$ such that $a + b + c = 2$ and $abc = 4$, find the minimum value of $|a| + |b| + |c|$.",
"role": "user"
}
] | 6 |
[
{
"content": "Find the length of the curve given by \\( y = \\frac{x^2}{8} - \\ln(x) \\) over the interval \\( 4 \\le x \\le 8 \\).",
"role": "user"
}
] | 6 + \ln 2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.395 m/s^2 |
[
{
"content": "In a normed vector space $X$, if the weak* topology on $X^*$ is not strictly weaker than the weak topology, does this imply that $X$ is reflexive? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the integral \\( \\int_{\\lvert z\\rvert = 2} \\frac{\\lvert dz\\rvert}{\\lvert z-1\\rvert^2} \\).",
"role": "user"
}
] | \dfrac{4\pi}{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... | Cash: $30,000,000
Total Assets: $100,000,000
Common Stock (40,000,000 shares outstanding, $0.50 par): $20,000,000
Additional Paid-in Capital: $5,000,000
Retained Earnings: $35,000,000 |
[
{
"content": "Determine whether the equation $LA = I$ implies $AL = I$ for non-square matrices.",
"role": "user"
}
] | No |
[
{
"content": "If $c$ is a nonzero constant such that $x^2+cx+9c$ is equal to the square of a binomial, then what is $c$?",
"role": "user"
}
] | 36 |
[
{
"content": "What is the smallest value of \\( n \\) such that the final digit of \\( 13^n \\) is one more than the digit adjacent to it?",
"role": "user"
}
] | 14 |
[
{
"content": "Calculate the limit: \\[ \\lim _{(x,y)\\to (1,2)} \\frac {\\arctan(x+y-3)}{\\ln(x+y-2)} \\]",
"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... | 2360.17 N |
[
{
"content": "Calculate the residue of \\( \\frac{e^{az}-1}{z^3} \\) at \\( z=0 \\), where \\( a \\) is a complex constant.",
"role": "user"
}
] | \dfrac{a^2}{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... | 54 * (64^0 + 64^1 + 64^2 + ... + 64^65534) = 54 * (64^65535-1)/(64-1) = 54/63 * (64^65535 - 1) |
[
{
"content": "Patty ordered a pizza to be delivered. The bill was $\\$$12.00. Patty pays $\\$$15 and tells the delivery person to keep the change as a tip. What percent tip did she give?",
"role": "user"
}
] | 25 |
[
{
"content": "In an acute triangle \\( ABC \\), a circle with diameter \\( BC \\) intersects sides \\( AB \\) and \\( AC \\) at points \\( D \\) and \\( E \\) respectively. Tangents to the circle at points \\( D \\) and \\( E \\) intersect at point \\( K \\). Determine the angle between the lines \\( AK \\) and... | 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... | Flexible Budget
Units|Materials|Labor|Variable Overhead|Fixed Overhead|Total
---|---|---|---|---|---
3,300|$49,500|$27,060|$13,200|$6,800|$96,560
3,800|$57,000|$31,160|$15,200|$6,800|$110,160
4,300|$64,500|$35,260|$17,200|$6,800|$123,760 |
[
{
"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... | 9.31 m/s |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\rightarrow \\infty}\\left(\\frac{1}{(2n+1)^2}+\\frac{1}{(2n+3)^2}+ \\ldots +\\frac{1}{(4n-1)^2}\\right). \\]",
"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... | 1559 pdl |
[
{
"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... | 9416.8 m/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... | nitroglycerin |
[
{
"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... | 5.57% |
[
{
"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... | 1953 |
[
{
"content": "Can the Ellipsoid method be used to find an optimal solution to a linear program?",
"role": "user"
}
] | Yes |
[
{
"content": "On an infinite chessboard, the distance between two cells is defined as the minimum number of moves needed for a king to move from one to the other. Three cells are chosen such that the pairwise distance between any two of them is 100. How many cells are there that are at a distance of 50 from eac... | 1 |
[
{
"content": "Given the function \\( f(x) = \\frac{2x^2 + \\sqrt{2} \\sin \\left(x + \\frac{\\pi}{4}\\right)}{2x^2 + \\cos x} \\), find the sum of its maximum and minimum values.",
"role": "user"
}
] | 2 |
[
{
"content": "Evaluate the limit: $$\\lim_{{x \\to 0}} \\frac{1 - \\cos{x}\\sqrt{\\cos{2x}}}{x\\sin{x}}$$",
"role": "user"
}
] | \dfrac{3}{2} |
[
{
"content": "Given that \\( \\begin{vmatrix} a_1 & a_2 & a_3 \\\\ b_1 & b_2 & b_3 \\\\ c_1 & c_2 & c_3 \\end{vmatrix} = -4 \\), find the determinant of the matrix \\( \\begin{vmatrix} 2a_3 & 2a_2 & 2a_1 \\\\ b_3-a_3 & b_2-a_2 & b_1-a_1 \\\\ c_3+3b_3 & c_2+3b_2 & c_1+3b_1 \\end{vmatrix} \\).",
"role": "user... | 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... | $3,576.74 |
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