prompt list | ground_truth string |
|---|---|
[
{
"content": "Find the terminating polynomial series solution for the differential equation \\((1-x^2)y''-xy'+4y=0\\) using the series form \\(y(x) = x^q \\sum_{n=0}^\\infty a_n x^n\\) with \\(q = 0, 1\\) and the recurrence relation \\(a_{n+2} = \\frac{(n+q)^2-4}{(n+q+1)(n+q+2)} a_n\\).",
"role": "user"
}... | 1 - 2x^2 |
[
{
"content": "Calculate the mass of a half disc of radius $R$ centered at the origin $(0,0)$, with $y>0$, given that the density is \\( \\rho = \\frac{\\rho_oy}{\\sqrt{x^2+y^2}} \\) for \\( y>0 \\), where \\( \\rho_o \\) is a constant with units of \\( \\text{kg.m}^{-3} \\).",
"role": "user"
}
] | \rho_o R^2 |
[
{
"content": "Triangle \\(ABC\\) has side lengths \\(AB=2\\sqrt{5}\\), \\(BC=1\\), and \\(CA=5\\). Point \\(D\\) is on side \\(AC\\) such that \\(CD=1\\), and \\(F\\) is a point such that \\(BF=2\\) and \\(CF=3\\). Let \\(E\\) be the intersection of lines \\(AB\\) and \\(DF\\). Find the area of quadrilateral \\... | \dfrac{22}{35} |
[
{
"content": "Estimate the number of ways to choose integers \\( x_1, x_2, \\ldots, x_k \\) such that \\( 1 \\leq x_j \\leq p \\) for each \\( j \\), and there are at most \\( n-1 \\) distinct integers among them. Show that this number is at most \\( n^k p^{n-1} \\).",
"role": "user"
}
] | n^k p^{n-1} |
[
{
"content": "An equilateral triangle and a square both have perimeters of 48 inches. What is the ratio of the length of the side of the triangle to the length of the side of the square? Express your answer as a common fraction.",
"role": "user"
}
] | \frac43 |
[
{
"content": "Find the coefficient of \\(x^7\\) in the Taylor series expansion of \\(\\arcsin(x)\\) around \\(x=0\\).",
"role": "user"
}
] | \dfrac{5}{112} |
[
{
"content": "Determine the number of zeros of the function \\( f(z) = z^5 + iz^3 - 4z + i \\) within the annular region \\( \\{1 < |z| < 2\\} \\).",
"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... | $3,787.92 |
[
{
"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... | 104 rpm |
[
{
"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... | 14.47 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... | 7.96 m/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... | $41,394 |
[
{
"content": "For positive integers \\( n \\) and \\( k \\) (excluding \\( n = 1 \\)), does \\( \\frac{(n+k)!}{n!} \\) ever equal \\( n! \\)?",
"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... | [Year 0: -$1,620,000, Year 1: $540,000, Year 2: $540,000, Year 3: $540,000, Year 4: $540,000, Year 5: $900,000] |
[
{
"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... | Assets:
Current assets: 17,663
Non-current assets: 6,984
Total assets: 24,647
Liabilities and equity:
Current liabilities: 8,350
Non-current liabilities: 10,943
Total liabilities: 19,293
Equity: 5,354
Total liabilities and equity: 24,647 |
[
{
"content": "Determine whether the limit \\( \\lim_{(x,y)\\to (0,0)} \\frac {x^3y^2}{x^4+y^6} \\) exists.",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the splitting field of the polynomial \\(x^4 + x + 1\\) over the finite field \\(\\mathbb{F}_2\\).",
"role": "user"
}
] | \mathbb{F}_{2^4} |
[
{
"content": "Find the value of $x+y+z$ given that $x, y, z \\in \\mathbb{Z}^+$ and \\( x^{y^z} \\cdot y^{z^x} \\cdot z^{x^y} = 3xyz. \\)",
"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... | s = 40/t, where t can be determined experimentally from the video recording |
[
{
"content": "Find the slope of the tangent line to the curve given by the equation \\(2(x^2 + y^2)^2 = 25(x^2 - y^2)\\) at the point (3, 1).",
"role": "user"
}
] | -\dfrac{9}{13} |
[
{
"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... | 5.148e3 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... | 8450 |
[
{
"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... | 3.14 L Ar |
[
{
"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... | Phytochemicals |
[
{
"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... | 3.45 m/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... | 1.83 m/s at 37.0 degrees West of South |
[
{
"content": "Evaluate the double sum \\( \\sum_{x=-\\infty}^{\\infty} \\sum_{y=-\\infty}^{\\infty} e^{-\\frac{x^2+y^2}{2}} \\).",
"role": "user"
}
] | 2\pi |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -5.86 x 10^3 kJ |
[
{
"content": "Evaluate the integral \\( \\int\\limits_{L} z \\cos(2\\pi z \\bar{z}) \\, dz \\), where \\( L = \\{|z| = 1; \\quad 0 \\le \\arg z \\le \\pi \\} \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the double integral: \\[ \\int_0^\\infty\\int_0^\\infty xye^{-(x^2+y^2)}\\,dx\\,dy \\]",
"role": "user"
}
] | \dfrac{1}{4} |
[
{
"content": "Evaluate the limit \\(\\lim_{{x, y \\to 0}}(x^2+y^2)^{x^2y^2}\\) using polar coordinates.",
"role": "user"
}
] | 1 |
[
{
"content": "In a building with 120 apartments and 119 tenants, an apartment is considered overcrowded if at least 15 people live in it. Each day, if there is an overcrowded apartment, all the tenants from that apartment move to different apartments. Will there eventually be a day when no apartments are overcr... | Yes |
[
{
"content": "Given a function $f$ with derivatives of all orders, a table of values for $f$ and its first four derivatives at $x=0$, and the inequality $|f^{(5)}(x)|\\leq160$ for all $x$ in the interval $[0, 2]$, find the maximum value of $f(3/2)$. Use Taylor's theorem with remainder to justify your answer.",
... | \dfrac{81}{8} |
[
{
"content": "Is it possible to construct a probabilistic prime test with sub-logarithmic runtime complexity for generic integers?",
"role": "user"
}
] | No |
[
{
"content": "Find the length of the plane curve parameterized by \\( x(t)=\\int_{t}^{\\infty} \\frac{\\cos u}{u} \\, du \\) and \\( y(t)=\\int_{t}^{\\infty} \\frac{\\sin u}{u} \\, du \\) for \\( 1 \\leq t \\leq 2 \\).",
"role": "user"
}
] | \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... | 23.0 N |
[
{
"content": "Octagon $ABCDEFGH$ is equiangular. Given that $AB=1$, $BC=2$, $CD=3$, $DE=4$, and $EF=FG=2$, compute the perimeter of the octagon.",
"role": "user"
}
] | 20+\sqrt{2} |
[
{
"content": "Determine if there exists a bound on the exponent $a$ such that $x^a = x^b$ holds for all $x$ in any ring $R$, independent of the ring $R$.",
"role": "user"
}
] | a = b |
[
{
"content": "Determine whether there exists a non-zero holomorphic function $g(z)$ that satisfies $|g(z)| = |z|^b$ for some real number $b$ in an annulus centered at the origin.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine whether the following inequality is true for $a > 1$:\n\\[ \\left| \\int_{a}^{\\infty} \\{x\\} \\frac{1 - \\log x}{x^2} dx \\right| \\le 2 \\int_{a}^{\\infty} \\frac{\\log x}{x^2} dx \\]\nwhere $ \\{ x \\} $ denotes the fractional part of a real number $ x $. Provide a justification for ... | True |
[
{
"content": "Determine all values of \\( \\alpha \\) for which the improper integral \\( \\int_0^{+ \\infty } \\frac{e^x \\arctan(xe^{-x})}{(x+ \\sqrt[3]{x})^ \\alpha } \\, dx \\) converges.",
"role": "user"
}
] | (2, 6) |
[
{
"content": "Given the sequence \\( \\{a_{n}\\} \\) defined by \\( a_{1} = 0 \\), \\( a_{2} = 1 \\), and for \\( n \\geq 3 \\), \\( a_{n} = \\frac{1}{2} n a_{n-1} + \\frac{1}{2} n(n-1) a_{n-2} + (-1)^{n} \\left(1-\\frac{n}{2}\\right) \\), find the simplest expression for \\( f_{n} = \\sum_{k=0}^{n-1} (k+1) C_{... | 2n! - n - 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... | $152,059 |
[
{
"content": "Given positive integers $a$ and $b$ with $\\gcd(a,b)$ divisible by exactly 7 distinct primes and $\\mathop{\\text{lcm}}[a,b]$ divisible by exactly 28 distinct primes, where $a$ has fewer distinct prime factors than $b$, find the maximum number of distinct prime factors that $a$ can have.",
"ro... | 17 |
[
{
"content": "Evaluate the integral \\( \\int_{|z|=1}(z^2+2z)^{-1}dz \\) and determine if the result is \\( \\pi i \\).",
"role": "user"
}
] | \pi i |
[
{
"content": "Determine the tight big-O bound for the recurrence relation \\( T(n) = T(n^{1/2}) + 1 \\).",
"role": "user"
}
] | O(\log \log n) |
[
{
"content": "Let $f: X \\rightarrow X$ be a bijective map between topological spaces such that $f \\circ f = \\text{id}$. Does this imply that $f$ is a continuous map and hence a homeomorphism?",
"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... | 1.76 g |
[
{
"content": "In the expansion of \\((1 + x + x^2)^{1000}\\), the coefficients are given by \\(a_0 + a_1 x + a_2 x^2 + \\cdots + a_{2000} x^{2000}\\). Calculate the sum of the coefficients where the powers of \\(x\\) are multiples of 3, i.e., find the value of \\(a_0 + a_3 + a_6 + a_9 + \\cdots + a_{1998}\\).",... | 3^{999} |
[
{
"content": "Consider the differential equation: \\( x y'' -\\frac{2}{x(x-2)}y'+x^2y = 0 \\). Determine which of the following statements is true:\n\n(a) \\(x=0\\) is a regular singular point of this equation.\n(b) \\(x=0\\) is an irregular singular point of this equation.\n(c) \\(x=0\\) is an ordinary point o... | 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... | 1.02 kg |
[
{
"content": "Calculate the sum: \\[ \\sum_{k=1}^n (-1)^k {n\\choose k}\\frac{1}{k+1} \\]",
"role": "user"
}
] | -\dfrac{n}{n + 1} |
[
{
"content": "Find the remainder when the binomial coefficient \\( \\binom{40}{12} \\) is divided by 7.",
"role": "user"
}
] | 5 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 20.3 < V < 30.1 |
[
{
"content": "In a country with 1985 airfields, each airfield sends a plane to the airfield farthest from it. Assuming the Earth is flat and all pairwise distances between airfields are different, is it possible for all 1985 planes to end up at only 50 airfields?",
"role": "user"
}
] | Yes |
[
{
"content": "Let $G$ be the special linear group $SL(2,F_q)$ where $F_q$ is a finite field of order $q$. Determine whether all matrices of the upper triangular group (or a conjugate of it) of $G$ have a common eigenvector.",
"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... | 9e+2 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... | 18.86 |
[
{
"content": "Find the smallest positive integer \\( n \\) such that \\( 1 + 5u_nu_{n+1} = k^2 \\), where \\( k \\) is a natural number, given the sequence \\( \\{u_n\\} \\) defined by:\n\\[\\begin{cases}u_1=20;\\\\u_2=30;\\\\ u_{n+2}=3u_{n+1}-u_{n},\\; n \\in \\mathbb{N}^*.\\end{cases}\\]",
"role": "user"
... | 3 |
[
{
"content": "Suppose there is a group homomorphism $\\phi: G \\to G_0$ where $|G|$ and $|G_0|$ are coprime, and $G$ is a simple group. Determine the image of an element $g \\in G$ under $\\phi$. Provide a justification for your answer.",
"role": "user"
}
] | e_{G_0} |
[
{
"content": "Given the differential equation $y' = y + 10\\sin y$ with the initial condition $y(0) = a$, find $\\frac{\\partial y}{\\partial a} \\Big|_{a=0}$. Evaluate this derivative at $a = 0$.",
"role": "user"
}
] | e^{11t} |
[
{
"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... | 3.66e-10 M |
[
{
"content": "Given any uncountable subset $S$ of the unit interval $[0, 1]$, does $S$ have an accumulation point that also lies in $S$? Provide a proof or counterexample.",
"role": "user"
}
] | Yes |
[
{
"content": "Calculate the limit: \\[ \\lim _{x \\rightarrow 1}\\left(\\frac{2 x-1}{x}\\right)^{1 /(\\sqrt[5]{x}-1)} \\]",
"role": "user"
}
] | e^5 |
[
{
"content": "Evaluate the definite integral \\( \\int_{0}^{\\pi/4}\\frac{\\tan^{2}{x}}{\\cos^{4}{x}}dx \\).",
"role": "user"
}
] | \dfrac{8}{15} |
[
{
"content": "Let \\( A \\) be a \\( 3 \\times 3 \\) real matrix satisfying \\( A^8 = I \\). Determine which of the following statements is true:\n\n1. The minimal polynomial of \\( A \\) is of degree 3.\n2. The minimal polynomial of \\( A \\) is of degree 2.\n3. \\( A = I \\) or \\( A = -I \\).\n4. There are u... | 4 |
[
{
"content": "Consider the differential equation \\( \\frac{dy}{dx} = y^2 - 1 + \\cos x \\) with the initial condition \\( y(0) = 0 \\). Determine which of the following statements is correct about the solution \\( y(x) \\) on the open interval \\((-c, c)\\), where \\(c\\) is a positive real number:\n\n(A) \\( ... | 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... | 11.999 cm |
[
{
"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... | 13.7 $rad/s^2$ |
[
{
"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... | 2.3 s |
[
{
"content": "Determine the number of functions \\( f: \\{1, 2, \\cdots, 12\\} \\rightarrow \\{1, 2, \\cdots, 12\\} \\) such that for every multiplication pair \\((a, b, c)\\), the triplet \\((f(a), f(b), f(c))\\) is also a multiplication pair.",
"role": "user"
}
] | 7776 |
[
{
"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... | Year Particulars Debit Credit
2011 Gain on sale of equipment 75,000
Equipment 150,000
Accumulated depreciation 225,000
Accumulated depreciation 15,000
Depreciation expense 15,000
2012 Retianed earnings-Pike 67,500
Non-controlling interest 7,500
Equipment 150,000
Accumulated depreciation 225,000
Accumulated depreciation 30,000
Depreciation expense 15,000
Beginning retained earnings-Pike 13,500
Non-controlling interest 1,500 |
[
{
"content": "Given a polynomial $p(x)$ in $R[x]$ such that $p(0)=1$, $p(x) \\ge p(1)$, and $\\lim_{x \\rightarrow \\infty} p''(x)=4$, find the value of $p(2)$. \\( \\boxed{} \\)",
"role": "user"
}
] | 1 |
[
{
"content": "Given a $2\\pi$ periodic function defined as $f(t) = t$ for $0 \\leq t < \\pi$ and $f(t) = 0$ for $\\pi \\leq t < 2\\pi$, find the value of its complex Fourier series representation at $t = \\pi$. The complex Fourier series is given by:\n\\[ f(t) = \\frac{\\pi}{4} + \\sum_{k \\neq 0} \\frac{1}{2\\... | \dfrac{\pi}{2} |
[
{
"content": "Suppose \\( \\int_{0}^{a}f(x)dx = 1 \\). Determine if it is true that for every \\( b>0 \\), the inequality \\( \\int_{0}^{a}\\frac{e^{bx}}{b}\\left(f(x)\\right)^2dx \\ge 1 \\) holds.",
"role": "user"
}
] | True |
[
{
"content": "Compute the volume of the convex polyhedron with vertices \\((0,0,0)\\), \\((1,0,0)\\), \\((0,2,0)\\), \\((0,0,3)\\), and \\((10,10,10)\\) using a triple integral.",
"role": "user"
}
] | \dfrac{110}{3} |
[
{
"content": "Determine the number of integer solutions \\((x, y, z)\\) for the system of equations:\n\\[\n\\begin{align*}\nx + 2y + 4z &= 9 \\\\\n4yz + 2xz + xy &= 13 \\\\\nxyz &= 3\n\\end{align*}\n\\]\nsuch that at least two of the variables \\(x, y, z\\) are integers.",
"role": "user"
}
] | 5 |
[
{
"content": "Find the remainder when \\(3^{234}\\) is divided by 234, given that \\(234 = 2 \\times 9 \\times 13\\).",
"role": "user"
}
] | 27 |
[
{
"content": "Determine if there exists an entire function $g(z)$ such that $g(1/n) = \\frac{1}{n^2}$ for all positive integers $n$. If such a function exists, find $g'(0)$.",
"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... | 2AgNO_3(aq) +CuCl_2(aq) rarr Cu(NO_3)_2(aq) + 2AgCl(s)darr |
[
{
"content": "Determine whether the following statement is true or false: If $A$ is a real symmetric matrix of order $n (\\geq 2)$, then there exists a symmetric matrix $B$ such that $B^{2k+1} = A$. Justify your answer.",
"role": "user"
}
] | 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... | 8.06 N |
[
{
"content": "Determine the closure of the set \\( S = \\left\\{ \\frac{a}{p^n} \\in \\mathbb{R} \\mid a \\in \\mathbb{Z}, n \\in \\mathbb{N} \\right\\} \\) in \\( \\mathbb{R} \\) with respect to the usual topology, where \\( p \\) is a fixed prime number.",
"role": "user"
}
] | \mathbb{R} |
[
{
"content": "Determine the nature of the singularity at the point \\( z = \\pi/2 \\) for the function \\( f(z) = \\tan^2 z \\). Specifically, identify if it is a regular point, an essential singularity, or a pole, and if it is a pole, state its degree.",
"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... | 24041.00 |
[
{
"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... | 0.388 A |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\to\\infty} (-x +\\sqrt{x^2+1})^{1/\\ln x} \\]",
"role": "user"
}
] | \dfrac{1}{e} |
[
{
"content": "Simplify the radical $\\sqrt{2940}$.",
"role": "user"
}
] | 14\sqrt{15} |
[
{
"content": "Let \\( \\{a_n\\}_{n=1}^{\\infty} \\) be a sequence defined by \\( a_1 = 1, a_2 = 1 \\), and \\( a_{n+2} = 2a_{n+1} + a_n \\) for all \\( n \\ge 1 \\). Calculate the value of \\( 47 \\sum_{n=1}^{\\infty} \\frac{a_n}{2^{3n}} \\).",
"role": "user"
}
] | 7 |
[
{
"content": "Find the volume of the region enclosed by the plane \\( z = 3 - 2y \\) and the paraboloid \\( z = x^2 + y^2 \\). The intersection of these surfaces is the circle \\( x^2 + (y + 1)^2 = 4 \\).",
"role": "user"
}
] | 8\pi |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $85,015 |
[
{
"content": "Consider a 2D grid with \\( n \\) rows and \\( m \\) columns. You can fill this grid with numbers ranging from 1 to \\( k \\) (inclusive). The condition is that for each number \\( r \\) such that \\( 1 \\leq r \\leq k \\), no two rows can have exactly the same number of the number \\( r \\). Dete... | 0 |
[
{
"content": "In a parallelepiped $A B C D A_{1} B_{1} C_{1} D_{1}$, point $X$ is located on edge $A_{1} D_{1}$ such that $A_{1} X = 5$, and point $Y$ is located on edge $B C$ such that $B Y = 3$. Given that $B_{1} C_{1} = 14$, the plane $C_{1} X Y$ intersects ray $D A$ at point $Z$. Determine the length of $D ... | 20 |
[
{
"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... | 7.24 |
[
{
"content": "Is the theory $Th(C)$ of the class of finite sets with at least $n$ elements axiomatized by the sentence that states there are at least $n$ elements?",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit: $$\\lim _{x\\to \\infty \\:}\\left(\\sqrt[3]{3x^2+4x+1}-\\sqrt[3]{3x^2+9x+2}\\right)$$",
"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... | ^{13}_6 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... | 19.05% |
[
{
"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... | 10.80% |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 148,500 |
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