prompt list | ground_truth string |
|---|---|
[
{
"content": "The integers \\( a \\) and \\( b \\) are such that the expression \\( \\frac{2n^3 + 3n^2 + an + b}{n^2 + 1} \\) is an integer for every integer \\( n \\). Determine the value of this expression when \\( n = 4 \\).",
"role": "user"
}
] | 11 |
[
{
"content": "Let \\( g(t) = t \\) for all \\( t \\in [-1,1] \\). Consider the linear operator \\( T: C[-1,1] \\rightarrow \\mathbb{R} \\) defined by\n\\[ T(f) = \\int_{-1}^1 t f(t) \\, dt \\]\nwhere the norm of \\( f \\) is given by \\( \\|f\\| = \\max_{t \\in [-1,1]} |f(t)| \\). Given \\( f(t) = t^{\\frac{1}{... | 1 |
[
{
"content": "In a parallelogram \\(ABCD\\), let \\(K\\) and \\(L\\) be the midpoints of \\(BC\\) and \\(CD\\), respectively. Given that \\(\\angle BAD = \\frac{\\pi}{3}\\) and the points \\(A\\), \\(B\\), \\(K\\), and \\(L\\) lie on a common circle, find \\(\\angle ADB\\).",
"role": "user"
}
] | \dfrac{\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... | $3.54 |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\to\\infty}\\left(\\frac{\\sqrt{n^2+n}-1}{n}\\right)^{2\\sqrt{n^2+n}-1}$$.",
"role": "user"
}
] | \dfrac{1}{e} |
[
{
"content": "In a right square prism $A B C D A_{1} B_{1} C_{1} D_{1}$, the height is half the length of the side of the base. Determine the maximum value of the angle $A_{1} M C_{1}$, where $M$ is a point on the edge $A B$. Provide your answer in degrees.",
"role": "user"
}
] | 90 |
[
{
"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... | 7.69e-3 J/m^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... | 10.303 |
[
{
"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... | 22/3 s |
[
{
"content": "Given that $f(x)= \\lim\\limits_{n\\to\\infty} n(x^{1/n} - 1)$, find the value of $f(xy)$. ",
"role": "user"
}
] | \ln(xy) |
[
{
"content": "Determine whether the norm on an infinite dimensional Hilbert space is weakly lower-semicontinuous.",
"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... | $64,000 |
[
{
"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... | A |
[
{
"content": "Evaluate the limit as \\( n \\to \\infty \\) of the expression:\n\\[ I = \\left(\\frac{\\sin\\left(\\frac{1}{n^2}\\right) + \\binom{n}{1}\\sin\\left(\\frac{2}{n^2}\\right) + \\binom{n}{2}\\sin\\left(\\frac{3}{n^2}\\right) + \\cdots + \\binom{n}{n}\\sin\\left(\\frac{n+1}{n^2}\\right)}{\\cos\\left(\... | \sqrt{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... | $28,308.61 |
[
{
"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... | 44.96 |
[
{
"content": "Evaluate the integral \\( \\int_{0}^{\\frac{\\pi}{2}} \\frac{1}{1+\\tan(x)^{\\sqrt{2}}} \\, dx \\).",
"role": "user"
}
] | \dfrac{\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... | 0.095 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... | 266.658 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... | 142148198.4 lbs |
[
{
"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... | Campa: $11,600
St. Edith's: $12,900 |
[
{
"content": "Determine whether there exists an order-complete field.",
"role": "user"
}
] | \mathbb{R} |
[
{
"content": "Below is a drawing of all $26$ letters in the English alphabet. As drawn below, some of these letters could be portions of the graph of a function, and some cannot. For example, the $\\textsf{O}$ resembles an ellipse, which cannot be part of the graph of a function.\n\nAs drawn below, which of the... | \text{VW} |
[
{
"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... | 2.25e5 N/C |
[
{
"content": "Let $R$ be a commutative Noetherian ring such that for every $R$-module $M$ with finite projective dimension, every submodule of $M$ also has finite projective dimension. Given that $R$ is regular, does $R$ have finite global dimension?",
"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... | 0.7 s |
[
{
"content": "Evaluate the integral \\( \\int_{-\\pi/4}^{\\pi/4}\\left(\\cos x+ \\sqrt {1+x^2}\\sin^3x \\cos^3x \\right)\\, dx \\).",
"role": "user"
}
] | \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... | 1.04 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... | $f(yx + \theta) = R(yx + \theta) - R(yx + \theta - 1)$ |
[
{
"content": "Given a sequence of functions $\\{f_n(x)\\}$ in $L^2[0,1]$, where $\\lim_{n\\to\\infty} f_n(x) = f(x)$ almost everywhere and $f(x)\\in L^2[0,1]$, determine the limit of the following integral as $n$ tends to infinity: $$\\lim_{n\\to\\infty} \\int_0^1 f_n(x)\\sin (nx)dx.$$",
"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... | $112,500 |
[
{
"content": "Compute the expected value of the random variable X given that the sum of two independent geometrically distributed random variables X and Y, both with parameter p, is k. That is, find \\( E(X|X+Y=k) \\) for all \\( k = 2, 3, \\ldots \\).",
"role": "user"
}
] | \dfrac{k}{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... | 1.56 |
[
{
"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... | 10.82 |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\rightarrow \\infty}\\left(\\frac{\\pi}{2}-\\tan^{-1}x\\right)^{\\Large\\frac{1}{x}}$$ without using L'Hopital's rule.",
"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... | 29.85 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... | 12.2567 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | (33/4, 11/2) |
[
{
"content": "Determine the limit of the sequence \\(x_n=\\frac{1}{n}\\left(n+\\frac{n-1}{2}+\\frac{n-2}{3}+\\dots+\\frac{2}{n-1}+\\frac{1}{n}-\\log(n!)\\right)\\).",
"role": "user"
}
] | \gamma |
[
{
"content": "In \\(\\triangle XYZ\\), point \\(A\\) is on segment \\(YZ\\) such that \\(XA\\) is perpendicular to \\(YZ\\). Let \\(M\\) and \\(N\\) be the incenters of triangles \\(XYA\\) and \\(XZA\\), respectively. Given \\(YZ = 28\\), \\(XA = 24\\), and \\(YA = 10\\), find the length of \\(MN\\).",
"rol... | 2\sqrt{26} |
[
{
"content": "Determine the largest topology on a set $X$ that contains a given family of subsets $\\mathcal{S}$.",
"role": "user"
}
] | \mathcal{P}(X) |
[
{
"content": "Find the residue of \\(\\frac{\\cosh z}{z^4}\\) at \\(z=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... | 0.615 W/m^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... | 923.93 F |
[
{
"content": "In a triangular pyramid \\( P-ABC \\), \\(\\angle APB = \\angle BPC = \\angle CPA = 90^\\circ\\). \\(M\\) is a point on the base \\(ABC\\), \\(\\angle APM = \\alpha\\), \\(\\angle BPM = \\beta\\). Given \\(\\sin \\alpha = \\frac{\\sqrt{6}}{3}\\) and \\(\\cos \\beta = \\frac{\\sqrt{6}}{6}\\), find ... | B |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $25.20253 |
[
{
"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... | $2,565 |
[
{
"content": "Evaluate the integral \\( \\iiint_E 1 \\, dx \\, dy \\, dz \\) where \\( E = \\{(x,y,z) \\mid |x| + |y| + |z| \\leq 1\\} \\).",
"role": "user"
}
] | \dfrac{4}{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... | 37.9 cm |
[
{
"content": "Determine the number of zeros (counting multiplicities) of the polynomial \\(f(z) = z^{100} + 8z^{10} - 3z^3 + z^2 + z + 1\\) within the closed unit disc \\(|z| < 1\\).",
"role": "user"
}
] | 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... | 45 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... | 123123.95 |
[
{
"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... | 7.39J |
[
{
"content": "Determine whether the integral \\( Y = \\int_{0}^\\infty Ae^{-B\\sqrt{t}}\\mathrm{d}t \\) can be solved, where \\( A \\) and \\( B \\) are constants.",
"role": "user"
}
] | \dfrac{2A}{B^2} |
[
{
"content": "Let $A \\in M_n$ be a normal matrix with its polar decomposition $A = PU$, where $U$ is a unitary matrix and $P$ is a positive semidefinite matrix. Determine whether it holds that $PU = UP$. Justify your answer.",
"role": "user"
}
] | PU = UP |
[
{
"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... | $0 = \partial^\alpha {\gamma_\alpha}^\mu - {1\over2} \partial^\mu \gamma$ |
[
{
"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... | See the image. Note: only chromosome 4 is shown, but all other chromosomes are also present in two copies. |
[
{
"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... | -5.76 m/s |
[
{
"content": "Determine the values of \\(\\alpha\\) for which the improper integral \\(\\iint_{\\Bbb R^2}\\frac{dxdy}{(1+x^2+xy+y^2)^\\alpha}\\) converges.",
"role": "user"
}
] | \alpha > 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... | 26.19 g |
[
{
"content": "A tangent to the circle \\(x^2 + y^2 = 9\\) is drawn from the left focus \\(F\\) of the hyperbola \\(\\frac{x^2}{9} - \\frac{y^2}{16} = 1\\), with the point of tangency being \\(T\\). The line segment \\(FT\\) is extended to intersect the right branch of the hyperbola at point \\(P\\). Let \\(M\\)... | 1 |
[
{
"content": "In triangle ABC, points B' and C' are located on sides AB and AC such that BB' = CC'. Let O and O' be the circumcenters of triangles ABC and AB'C', respectively. The line OO' intersects lines AB' and AC' at points B'' and C'', respectively. Given that AB = \\( \\frac{1}{2} \\) AC, determine the re... | AB'' = AC'' |
[
{
"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... | 1.03 times |
[
{
"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... | 31.12 degrees |
[
{
"content": "Find the smallest ordinal \\( \\beta \\) such that \\( \\omega + \\beta = \\beta \\).",
"role": "user"
}
] | \omega^2 |
[
{
"content": "In triangle ABC, points E and F divide sides AC and AB respectively such that \\( \\frac{AE}{EC} = 4 \\) and \\( \\frac{AF}{FB} = 1 \\). Let D be a point on side BC, and G be the intersection of lines EF and AD. If \\( \\frac{AG}{GD} = \\frac{3}{2} \\), determine the ratio \\( \\frac{BD}{DC} \\)."... | \dfrac{4}{5} |
[
{
"content": "Suppose $R$ is a unique factorization domain (UFD) and $a, b \\in R$ are distinct irreducible elements. Determine which of the following statements is true:\n\n1. The ideal $\\langle 1+a \\rangle$ is a prime ideal.\n2. The ideal $\\langle a+b \\rangle$ is a prime ideal.\n3. The ideal $\\langle 1+a... | 4 |
[
{
"content": "In a graph $G = (V,E)$, each vertex $v \\in V$ is randomly assigned a unique integer identifier. An edge $(u,v)$ is directed from $u$ to $v$ if $u < v$. What is the expected number of vertices that have an in-degree of 0 or an out-degree of 0?",
"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... | 1.14e27 |
[
{
"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... | 4.55e-14 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... | Income tax expense: $6,020,000
Deferred tax asset: $20,000
Income tax payable: $6,000,000 |
[
{
"content": "Let $X$ be a topological space of infinite cardinality that is homeomorphic to $X \\times X$. Determine which of the following statements is true:\n\n(a) $X$ is not connected.\n(b) $X$ is not compact.\n(c) $X$ is not homeomorphic to a subset of $\\mathbb{R}$.\n(d) None of the above.",
"role": ... | D |
[
{
"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... | 245.25 rad/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... | Cash Flow from Operating Activity: 343875
Cash Flow from Investing Activities: -90390
Cash Flow from Financing Activities: -58950
Net Increase In Cash and Equivalents: 194535 |
[
{
"content": "Determine whether the equation \\(a^3 + b^3 + c^3 \\equiv 5 \\pmod{9}\\) has any integer solutions.",
"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... | D - I - G - A - B - F - E - H - C |
[
{
"content": "In the Cartesian coordinate system, a point whose both coordinates are rational numbers is called a rational point. If \\( a \\) is an irrational number, determine which of the following statements is true for lines passing through the point \\((a, 0)\\):\n\n(A) There are infinitely many lines, ea... | C |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to\\pi/2}(\\sin x)^{\\tan x}$$",
"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... | 255 s |
[
{
"content": "Find the minimum value of the real number \\( A \\) such that the inequality \\( \\left|f^{\\prime}(0)\\right| \\leq A \\) holds for all quadratic functions \\( f(x) \\) satisfying \\( |f(x)| \\leq 1 \\) for \\( 0 \\leq x \\leq 1 \\).",
"role": "user"
}
] | 8 |
[
{
"content": "Find all prime numbers \\( x \\) such that \\( x^x + x \\) is a factorial.",
"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... | 59.72 g CaSO4 |
[
{
"content": "Find the maximum value of the function \\( f(x) = 12x^2\\int_0^1 yf(y) \\, dy + 20x\\int_0^1 y^2 f(y) \\, dy + 4x \\).",
"role": "user"
}
] | \dfrac{1}{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... | 2/3 of the height of the building |
[
{
"content": "Find the complete solution set for the inequality \\([\\sin^{-1}x] > [\\cos^{-1}x]\\), where \\([\\cdot]\\) denotes the greatest integer function.",
"role": "user"
}
] | [\sin 1, 1] |
[
{
"content": "Given that $z = -1 + i$ is a root of the polynomial $z^7 + az^3 + 2b$, find the value of $a + b$.",
"role": "user"
}
] | 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... | $332,340 |
[
{
"content": "The line $y = \\frac{-12x + 74}{5}$ is parameterized in the form\n\\[\\begin{pmatrix} x \\\\ y \\end{pmatrix} = \\mathbf{v} + t \\mathbf{d},\\]so that for $x \\le 7,$ the distance between $\\begin{pmatrix} x \\\\ y \\end{pmatrix}$ and $\\begin{pmatrix} 7 \\\\ -2 \\end{pmatrix}$ is $t.$ Find $\\ma... | \begin{pmatrix} -5/13 \\ 12/13 \end{pmatrix} |
[
{
"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... | 259.2 hours |
[
{
"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... | $16.66 |
[
{
"content": "In triangle \\( \\triangle ABC \\), the sides opposite to angles \\( A \\), \\( B \\), and \\( C \\) are \\( a \\), \\( b \\), and \\( c \\) respectively. Given that \\( c - a = 2a \\cdot \\cos B \\), determine the minimum possible value of \\( \\frac{3a + c}{b} \\).",
"role": "user"
}
] | 2\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... | $9,930 |
[
{
"content": "Determine the number of subgroups of the group $Z_{p^2} \\oplus Z_{p^2}$ that are isomorphic to $Z_{p^2}$, where $p$ is a prime number.",
"role": "user"
}
] | p(p + 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... | 1.425e-6 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... | 4.64e-11 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... | $947.49 |
[
{
"content": "Given the conditional cumulative distribution function (CDF) of the lifetime $X$ of a machine, given the event $C = \\{X > t\\}$, find the corresponding conditional probability density function (PDF) for $x < t$.",
"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... | $2,589.52 |
[
{
"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... | 277.97 atm |
[
{
"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... | 122.5 Joule |
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