prompt list | ground_truth string |
|---|---|
[
{
"content": "Evaluate the line integral \\(\\int_C (x+y)dx-(x-y)dy\\) along the ellipse defined by \\(\\frac{x^2}{a^2}+\\frac{y^2}{b^2}=1\\), where \\(a\\) and \\(b\\) are positive constants, using a parameterization of the curve.",
"role": "user"
}
] | -2\pi ab |
[
{
"content": "In a right triangle \\( \\triangle ABC \\) with hypotenuse \\( AB \\), construct a point \\( X \\) on \\( AB \\) such that \\( \\frac{XA}{XB} = \\frac{BC^2}{AC^2} \\).",
"role": "user"
}
] | X |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.63 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... | 1.27 g |
[
{
"content": "Given that the function $f(x+y) = f(x)f(y)$ for all $x, y \\in \\mathbb{R}$, $f(10) = 4$, and $f'(0) = 3$, find the value of $f'(10)$. \\( \\boxed{} \\)",
"role": "user"
}
] | 12 |
[
{
"content": "Given the matrix \\( M = \\begin{bmatrix} 1 & 0 & 0 & 0 & 1 \\\\ 0 & 1 & 1 & 1 & 0 \\\\ 0 & 1 & 1 & 1 & 0 \\\\ 0 & 1 & 1 & 1 & 0 \\\\ 1 & 0 & 0 & 0 & 1 \\end{bmatrix} \\), find the product of its positive eigenvalues.",
"role": "user"
}
] | 6 |
[
{
"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... | 5.545e-25 J |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 12.2 g |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n \\to \\infty} \\left( \\sqrt[3]{\\frac{\\sin n}{n} + n^3 - n^2} - \\sqrt[3]{n^3 + n} \\right) \\]",
"role": "user"
}
] | -\dfrac{1}{3} |
[
{
"content": "Let $X_1, X_2, \\ldots$ be i.i.d. random variables with $E[X_i] = 0$ and $E[X_i^2] = \\sigma^2 > 0$. Define $S_n = X_1 + \\cdots + X_n$. Let $N_n$ be a sequence of nonnegative integer-valued random variables and $a_n$ a sequence of integers such that $a_n \\to \\infty$ and $N_n/a_n \\to 1$ in prob... | \chi |
[
{
"content": "There are two different isosceles triangles whose side lengths are integers and whose areas are $120.$ One of these two triangles, $\\triangle XYZ,$ is shown. Determine the perimeter of the second triangle.\n\n[asy]\ndraw((0,0)--(30,0)--(15,-8)--cycle,black+linewidth(1));\nlabel(\"$X$\",(0,0),W);\... | 50 |
[
{
"content": "What is the expected number of fair coin flips needed to obtain the sequence HTT? Use the conditional expectation technique to solve this problem.",
"role": "user"
}
] | 8 |
[
{
"content": "Determine whether all real symmetric matrices with non-negative entries and a positive determinant are guaranteed to be positive definite.",
"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... | 0.0551 mg/ 100g |
[
{
"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... | 3.97e5 J |
[
{
"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... | 26.2 N/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... | 8.839e-14 g Fe2O3 |
[
{
"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... | -D a sin(ka) |
[
{
"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... | $106,000 |
[
{
"content": "Determine if the function $f(x) = x^2$ is Riemann-Stieltjes integrable with respect to the function $g(x)$ defined as $g(x) = 3x$ for $x \\in [0,1)$ and $g(1) = 4$. If it is integrable, find the value of the integral $\\int_0^1 f(x) \\, d(g(x))$. Assume $h(x) = g(x) - 3x$ and use the partition $P ... | 2 |
[
{
"content": "Determine the value of $y_0$ such that the solution to the initial value problem $y'+\\frac{2x^2-4xy-y^2}{3x^2}=0, \\ x>0, \\ y(1)=y_0$ has a limit of $y'(x)$ as $x$ approaches 0 that is not equal to 2.",
"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... | -$75 |
[
{
"content": "Calculate the Lebesgue integral of the function defined as 1 for irrational numbers and 0 for rational numbers over the interval \\([0, 2]\\).",
"role": "user"
}
] | 2 |
[
{
"content": "Let $z_1,$ $z_2,$ $\\dots,$ $z_{20}$ be the twenty (complex) roots of the equation\n\\[z^{20} - 4z^{19} + 9z^{18} - 16z^{17} + \\dots + 441 = 0.\\]Calculate $\\cot \\left( \\sum_{k = 1}^{20} \\operatorname{arccot} z_k \\right).$ Note that the addition formula for cotangent is still valid when wor... | \frac{241}{220} |
[
{
"content": "Find the sum of the series \\(\\sum_{n=0}^\\infty \\frac{n^{2}}{2^{n}}.\\)",
"role": "user"
}
] | 6 |
[
{
"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... | $24,208 |
[
{
"content": "Given that \\( f(x) \\) is a function defined on \\( \\mathbf{R} \\) with \\( f(1) = 1 \\) and for any \\( x \\in \\mathbf{R} \\) it holds that \\( f(x+5) \\geq f(x)+5 \\) and \\( f(x+1) \\leq f(x)+1 \\), find the value of \\( g(2002) \\) where \\( g(x) = f(x) + 1 - x \\).",
"role": "user"
}... | 1 |
[
{
"content": "Determine the values of \\(a > 0\\) for which the expected value of the random variable \\(X_1\\), with distribution \\(\\mathbb{P}(X_k \\geq x) = \\frac{1}{x^a}\\) for \\(x \\in \\mathbb{N}\\), is finite.",
"role": "user"
}
] | a > 1 |
[
{
"content": "Find the inverse Fourier Transform of the function $2\\pi \\delta(x-\\omega)$, where $\\omega$ is a real parameter and $x \\in \\mathbb{R}$. Express your answer in terms of $\\omega$.",
"role": "user"
}
] | e^{i\omega t} |
[
{
"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... | 31.17 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... | Magnitude = 95.29, Direction = 79.53 degrees |
[
{
"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... | 64950 |
[
{
"content": "Given the system of equations:\n\\[ x^3 - 3xy^2 = 2010, \\]\n\\[ y^3 - 3x^2y = 2009, \\]\nwhere \\((x_1, y_1), (x_2, y_2), (x_3, y_3)\\) are the solutions, find the value of:\n\\[ \\left(1 - \\frac{x_1}{y_1}\\right) \\left(1 - \\frac{x_2}{y_2}\\right) \\left(1 - \\frac{x_3}{y_3}\\right). \\]",
... | \dfrac{2}{2009} |
[
{
"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... | 649.4 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... | 8.32 |
[
{
"content": "Let $a, b, c \\ge 0$ such that $a + b + c = 3$. Find the maximum value of \\[ P = \\frac{1}{\\sqrt{a^2 - 3a + 3}} + \\frac{1}{\\sqrt{b^2 - 3b + 3}} + \\frac{1}{\\sqrt{c^2 - 3c + 3}}. \\]",
"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... | 9.8e4 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... | 720 |
[
{
"content": "Six-digit integers will be written using each of the digits $1$ through $6$ exactly once per six-digit integer. How many different positive integers can be written such that all pairs of consecutive digits of each integer are relatively prime? (Note: $1$ is relatively prime to all integers.)",
... | 72 |
[
{
"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... | 9.999 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... | 84.0ft |
[
{
"content": "Determine the values of $p$ for which the improper integral \\( \\int_0^\\infty \\frac{\\log(x)}{1+x^p} \\, dx \\) converges.",
"role": "user"
}
] | p > 1 |
[
{
"content": "Evaluate the integral \\( \\oint_{|z| = 3} \\frac{\\mathrm{d}z}{\\sqrt{z^2 - 1}} \\) using a branch of the function that is analytic outside the interval \\([-1, 1]\\) and positive on \\((1, \\infty)\\).",
"role": "user"
}
] | 2\pi i |
[
{
"content": "Calculate the expected value \\( \\mathbb{E}(e^{M_n}) \\), where \\( M_n = \\max(X_1, X_2, \\ldots, X_n) \\) and \\( X_1, \\ldots, X_n \\) are iid random variables each with distribution \\( \\mathcal{Exp}(1) \\). The cumulative distribution function of \\( M_n \\) is given by \\( F_{M_n}(x) = (1 ... | \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... | _{18}^{37}Ar + e_{-1}^{0}\rightarrow _{17}^{37}Ar + \nu _{e} |
[
{
"content": "In an equilateral triangle divided into smaller equilateral triangles with side length 1 by lines parallel to its sides, each side is divided into $n$ parts. Determine the maximum number of segments of length 1 that can be marked such that no triangle has all its sides marked. Assume $n=5$ in the ... | 30 |
[
{
"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... | 3.7 |
[
{
"content": "Calculate the line integral \\( \\int_{dA} (x^2 \\, dx + y^2 \\, dy) \\) over the region \\( A = \\{(x, y) \\in \\mathbb{R}^2 : -\\frac{\\pi}{2} \\leq x \\leq \\frac{\\pi}{2}, \\ -1 \\leq y \\leq \\cos(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... | 8.77 |
[
{
"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... | 5.7 L/minute |
[
{
"content": "There are 15 students, with 3 students each from 5 different high schools. Five admission officers, each from a different college, will each select 3 students to attend their college. In how many ways can the officers select the students such that no officer selects all 3 students from the same hi... | 159252480 |
[
{
"content": "Determine the number of 2-Sylow subgroups of the group $S_4 \\times S_4$. Assume that any such subgroup is isomorphic to $\\mathbb{Z}_{2} \\times \\mathbb{Z}_{2}$. Provide your answer as a single number.",
"role": "user"
}
] | 9 |
[
{
"content": "In \\(\\triangle{ABC}\\) with side lengths \\(AB = 13\\), \\(AC = 12\\), and \\(BC = 5\\), let \\(O\\) and \\(I\\) denote the circumcenter and incenter, respectively. A circle with center \\(M\\) is tangent to the legs \\(AC\\) and \\(BC\\) and to the circumcircle of \\(\\triangle{ABC}\\). What is... | 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... | 9.28 m/s^2 |
[
{
"content": "Find the natural number \\( n \\) such that \\( 2^{2^{2^{2n-1}}} \\equiv 16 \\pmod{127} \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Determine the number of solutions to the equation \\( x^{10} = \\begin{bmatrix}1 & 0 \\\\ 0 & 1 \\end{bmatrix} \\) in the set of 2x2 real matrices \\( M_{2}(\\mathbb{R}) \\). Provide a brief explanation for your answer.",
"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... | 151 V |
[
{
"content": "Let $A$ and $B$ be two $n \\times n$ real matrices with strictly positive real eigenvalues. Determine if the matrix $A + B$ can have a strictly negative eigenvalue.",
"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... | 0.39 |
[
{
"content": "Evaluate the product: $$\\log_8 9 \\cdot \\log_9 10 \\cdot \\dots \\cdot \\log_n(n+1) \\cdot \\log_{n+1}8$$",
"role": "user"
}
] | 1 |
[
{
"content": "Let $g$ be a non-negative function defined on the interval $[0, \\pi]$. Given that \\( \\int_0^x \\cos g'(t) \\, dt = \\int_0^x g(t) \\, dt \\) for \\(0 \\leq x \\leq \\pi\\) and \\(g(0) = 0\\), determine the possible values of \\(g\\left(\\frac{\\pi}{2}\\right)\\).",
"role": "user"
}
] | 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.06e+02 J |
[
{
"content": "Find the minimum value of the expression \\(8x^3 + 36x + \\frac{54}{x} + \\frac{27}{x^3}\\) for positive real numbers \\(x\\). Express your answer in simplest radical form.",
"role": "user"
}
] | 48\sqrt{6} |
[
{
"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... | temperature |
[
{
"content": "Calculate the surface integral of the vector field \\(\\mathbf{v}(x,y,z) = (y^2, -xz, z)\\) over the surface of the rectangular prism with vertices \\((0,0,0), (2,0,0), (0,3,0), (0,0,1), (2,3,0), (0,3,1), (2,0,1), (2,3,1)\\) using direct calculation.",
"role": "user"
}
] | 6 |
[
{
"content": "Let $R$ be a commutative ring with unity, $M$ be an $R$-module, and $I$ be an ideal of $R$ such that $IM$ is not a finitely generated submodule. Let $J \\subseteq I$ be a finitely generated ideal such that $JM$ is a finitely generated submodule. Does there exist $a \\in I$ such that $JM \\subsetne... | Yes |
[
{
"content": "Fedia has three sticks. If it is impossible to form a triangle with them, Fedia shortens the longest stick by the sum of the lengths of the other two. If the length of the stick does not become zero and the triangle still cannot be formed, Fedia repeats the operation. Determine if this process can... | No |
[
{
"content": "If an orbit $G \\cdot x$ is closed in the standard topology on a finite-dimensional complex vector space $V$, where $G$ is a complex linear algebraic group acting linearly on $V$, is the orbit also Zariski-closed?",
"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... | 0.0018 m/s |
[
{
"content": "Euler discovered that the polynomial $p(n) = n^2 - n + 41$ yields prime numbers for many small positive integer values of $n$. What is the smallest positive integer $n$ for which $p(n)$ and $p(n+1)$ share a common factor greater than $1$?",
"role": "user"
}
] | 41 |
[
{
"content": "Let $a_1,$ $a_2,$ $\\dots,$ $a_{12}$ be positive real numbers such that $a_1 + a_2 + \\dots + a_{12} = 1.$ Find the minimum value of\n\\[\\frac{1}{a_1} + \\frac{1}{a_2} + \\dots + \\frac{1}{a_{12}}.\\]",
"role": "user"
}
] | 144 |
[
{
"content": "Determine the limit of the sequence defined by the recurrence relation \\(x_{n+1} = \\frac{1}{2} x_n^2 - 1\\) with the initial condition \\(x_1 = \\frac{1}{3}\\).",
"role": "user"
}
] | 1 - \sqrt{3} |
[
{
"content": "Determine whether the converse of the statement \"If a function f is convex (or strictly convex) on [a, c] and on [c, b], then f is convex (or strictly convex) on [a, b]\" is true or false.",
"role": "user"
}
] | True |
[
{
"content": "Find the value of \\(a\\) for which the limit \\[ L = \\lim_{n \\to \\infty} \\frac{1^a + 2^a + \\cdots + n^a}{(n+1)^{a-1} [(na+1) + (na+2) + \\cdots + (na+n)]} = \\frac{1}{60}. \\]",
"role": "user"
}
] | 7 |
[
{
"content": "Determine the values of \\( n \\in \\mathbb{N} \\) for which the proposition \\( \\exists x\\;\\exists y:(xy \\notin n\\mathbb{N}) \\land (x \\notin n\\mathbb{N}) \\land (y \\notin n\\mathbb{N}) \\) is false.",
"role": "user"
}
] | 1 |
[
{
"content": "Calculate \\(\\displaystyle\\lim_{x\\rightarrow 0}\\frac{1}{x}\\int_{0}^{x}e^{t^{2}}{\\rm d}t\\).",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate the expression: \\[ \\frac{2012!}{2^{2010}} - \\sum_{k=1}^{2010} \\frac{k^2 k!}{2^k} - \\sum_{k=1}^{2010} \\frac{k \\cdot k!}{2^k} \\]",
"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... | 160 Hz |
[
{
"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... | 784.03 m/s |
[
{
"content": "Evaluate the integral \\( \\oint_{\\gamma} \\frac{z}{\\cos z} \\, dz \\), where \\( \\gamma \\) is the circle \\( |z|= 5 \\) oriented counterclockwise.",
"role": "user"
}
] | 4\pi^2 i |
[
{
"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... | $528,180 |
[
{
"content": "Determine whether the function \\( f(x,y) = (1+x)^t(1+y)^{1-t} - x^ty^{1-t} \\), where \\( t \\in [0,1] \\), satisfies \\( f(x,y) \\geq 1 \\) for all \\( x, y \\geq 0 \\).",
"role": "user"
}
] | f(x,y) \geq 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... | 0.293 nm |
[
{
"content": "Find the rate of change of the function \\( f(x,y,z) = \\frac{x}{z} + \\frac{y}{z} \\) with respect to \\( t \\) along the curve \\( r(t) = \\sin^2{t} \\mathbf{i} + \\cos^2{t} \\mathbf{j} + \\frac{1}{2t} \\mathbf{k} \\).",
"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... | 110.647 kJ/mol |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | The profit-maximizing price in the US market is $14, and the profit-maximizing price in the overseas market is $7.5. |
[
{
"content": "Given a vector $y = \\begin{bmatrix} R(t) & F(t) \\end{bmatrix}^{T}$ representing the populations of rabbits $R(t)$ and foxes $F(t)$, the populations follow the system of differential equations $ \\dot y = Ay$, where $$ A = \\begin{bmatrix} 98 & -1170 \\\\ 7 & -83 \\end{bmatrix}$$. If the rabbit p... | 4100 |
[
{
"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... | -$10,725 |
[
{
"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 machine's power (510.12 W) is 227.5 times greater than the man's power (2.242 W). |
[
{
"content": "Given that $a_2 = 2$ and $a_{mn} = a_m a_n$ for coprime integers $m$ and $n$, prove that $a_n = n$ for all natural numbers $n$.",
"role": "user"
}
] | a_n = 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... | {eq}4\pi\varepsilon_0\frac{R_1R_2}{R_1-R_2}{/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... | 5.334 m/s |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^{\\infty}\\frac{\\sin^3{x}}{x^3}dx \\) using contour integration.",
"role": "user"
}
] | \dfrac{3\pi}{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... | $2,417.44 |
[
{
"content": "The length of the median to the hypotenuse of an isosceles, right triangle is $10$ units. What is the length of a leg of the triangle, in units? Express your answer in simplest radical form.",
"role": "user"
}
] | 10\sqrt{2} |
[
{
"content": "A cone is formed from a 300-degree sector of a circle of radius 18 by aligning the two straight sides. [asy]\nsize(110);\ndraw(Arc((0,0),1,0,300));\ndraw((1,0)--(0,0)--(.5,-.5*sqrt(3)));\nlabel(\"18\",(.5,0),S); label(\"$300^\\circ$\",(0,0),NW);\n[/asy] What is the result when the volume of the co... | 225\sqrt{11} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 248.16 m |
[
{
"content": "Evaluate the integral \\(\\int_{S^2} \\frac{dS}{\\sqrt{(x-a)^2 + y^2 + z^2}}\\) over the unit sphere \\(S^2\\), given that \\(a > 1\\), using only multivariable calculus techniques.",
"role": "user"
}
] | \dfrac{4\pi}{a} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 22.35 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... | 350000 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.