prompt list | ground_truth string |
|---|---|
[
{
"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... | 1.930 nm |
[
{
"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 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... | The major factors that determine the marginal propensity to expend are the availability of credit, the confidence level of consumers and the tax rates, and economic policies by the government. |
[
{
"content": "Given that \\( S > 0 \\) and \\( \\frac{1}{S(S-1)} + \\frac{1}{(S+1) S} + \\cdots + \\frac{1}{(S+20)(S+19)} = 1 - \\frac{1}{R} \\), determine the value of \\( S \\).",
"role": "user"
}
] | 2 |
[
{
"content": "Solve for $p$: $\\frac 56 = \\frac n{72} = \\frac {m+n}{84}= \\frac {p - m}{120}$.",
"role": "user"
}
] | 110 |
[
{
"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... | 810 |
[
{
"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... | 1.22 eV |
[
{
"content": "Calculate the area $A$ enclosed by the closed loop $\beta$ formed by the curve defined by the vector function $\\vec r(t) = (1 - t^2)\\hat{i} + (t - t^3)\\hat{j}$, where $t \\in [0, 1]$. Use Green's theorem to find $A$:\n\n$$A = \\frac{1}{2} \\int_{0}^{1} \\left((1 - t^2)(1 - 3t^2) - (t - t^3)(-2t... | \dfrac{4}{15} |
[
{
"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... | 5/3 ohm |
[
{
"content": "Determine the number of ways to distribute 20 pencils among 4 students such that each student receives an odd number of pencils and at least 1 pencil. Use generating functions to solve the problem.",
"role": "user"
}
] | 165 |
[
{
"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... | -1368 kJ/mol |
[
{
"content": "Evaluate the limit: \\( \\lim_{x\\to 0^+}(x^{x}-1)\\ln(x) \\) using L'Hospital's rule.",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the maximum value of \\( x(G) \\), the chromatic number of a graph \\( G \\) with \\( n \\) vertices, where adjacent vertices share a common color and non-adjacent vertices have no common colors.",
"role": "user"
}
] | \left\lfloor \dfrac{n^2}{4} \right\rfloor |
[
{
"content": "Evaluate the integral \\( \\int_{0}^{\\pi/4}\\frac{\\sin(8x) \\cos^2(4x)}{\\sin(2x)}\\,\\dd x \\).",
"role": "user"
}
] | \dfrac{18}{35} |
[
{
"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... | 4.512 g O |
[
{
"content": "Find the value of \\( \\frac{S}{t} \\) if \\( S = \\sum_{k=1}^{\\infty} \\frac{1}{k^2} \\) and \\( t = \\sum_{k=1}^{\\infty} \\frac{(-1)^{k+1}}{k^2} \\).",
"role": "user"
}
] | 2 |
[
{
"content": "Given a vector space \\( \\mathbb{C}^n \\) over \\( \\mathbb{R} \\) and a linear operator \\( T : \\mathbb{C}^n \\rightarrow \\mathbb{C}^n \\), determine the field to which an eigenvalue \\( \\lambda \\) of \\( T \\) belongs.",
"role": "user"
}
] | \mathbb{R} |
[
{
"content": "Circles are drawn passing through the origin O to intersect the coordinate axes at points P and Q such that \\((m)(OP)+(n)(OQ)=k\\). Determine the fixed point that satisfies all such circles. \n\n(A) \\((m,n)\\) \n(B) \\(\\left(\\dfrac{m^2}{k},~\\dfrac{n^2}{k}\\right)\\) \n(C) \\(\\left(\\dfrac{... | C |
[
{
"content": "In triangle ABC, the areas of the shaded regions are denoted as \\( S_1 \\) and \\( S_2 \\). Given that \\( S_1 \\cdot S_2 = 16 \\text{ cm}^4 \\), calculate the length of segment \\( MN \\).",
"role": "user"
}
] | 4 |
[
{
"content": "Determine whether the ring $R$ of all functions $f : \\Bbb{R} \\to \\Bbb{R}$, which are continuous outside $(-1,1)$, is isomorphic to the ring $S$ of all functions $f : \\Bbb{R} \\to \\Bbb{R}$, which are continuous outside a bounded open interval containing zero. Is $R \\cong S$?",
"role": "us... | R \not\cong 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... | Avoidable costs, incremental costs, opportunity costs, and future cash flows |
[
{
"content": "For $n > 1$, determine whether the complement of a hypersurface in $\\mathbb{A}^n$ is an algebraic variety. Answer with 'Yes' or 'No'.",
"role": "user"
}
] | No |
[
{
"content": "Suppose $f(x)$ is a continuous function with derivative $f'(x)$ on the interval $(0, \\infty)$. If $f'(x) \\rightarrow \\infty$ as $x \\rightarrow \\infty$, does it necessarily follow that $f(x) \\rightarrow \\infty$ as $x \\rightarrow \\infty$? Answer yes or no.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine whether the following statement is true or false: For any $n \\times n$ matrix $B$, $B^n$ can be expressed as a linear combination of $B$ and the identity matrix $I_n$. Provide a proof or counterexample to support your answer.",
"role": "user"
}
] | False |
[
{
"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... | 0.70 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... | $3,030 |
[
{
"content": "Evaluate the definite integral \\( \\int_0^\\pi \\sin t \\cdot \\sin^{11}(\\cos t) \\, dt \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Find the largest natural number \\( n \\leq 100 \\) such that the polynomial \\( Q(x) = x^{624} + x^{524} + x^{424} + x^{324} + x^{224} + x^{124} + x^{n} \\) is divisible by \\( P(x) = x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + 1 \\) without a remainder.",
"role": "user"
}
] | 94 |
[
{
"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... | 3.065e+23 Na atoms |
[
{
"content": "What is the greatest product obtainable from two integers whose sum is 1998?",
"role": "user"
}
] | 998001 |
[
{
"content": "Suppose a function \\( f:\\mathbb{R}\\rightarrow\\mathbb{R} \\) is analytic at 0, meaning it is represented by its Taylor series in a neighborhood \\( U \\) of 0. Is it necessarily true that \\( f \\) is analytic at every point in \\( U \\)? Answer yes or no.",
"role": "user"
}
] | Yes |
[
{
"content": "Let \\( H \\) be a Hilbert space and \\( A \\) and \\( B \\) be closed subspaces of \\( H \\) such that \\( A^{\\perp} = B^{\\perp} \\). Determine if \\( A = B \\).",
"role": "user"
}
] | A = B |
[
{
"content": "Evaluate the limit \\( A = \\lim_{n\\to\\infty}(6^{1/n}+4^{1/n}-3^{1/n})^n \\).",
"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... | $83,000 |
[
{
"content": "Are all faces of a closed convex cone in finite dimensions closed? Let $C$ be a convex closed cone in $\\mathbb{R}^n$. A face of $C$ is a convex sub-cone $F$ such that whenever $\\lambda x + (1-\\lambda)y\\in F$ for some $\\lambda \\in (0,1)$ and $x,y\\in C$, it holds that $x,y\\in F$. Determine i... | Yes |
[
{
"content": "Find the limit: \\( \\lim_{n \\to \\infty} \\left( \\sqrt{n^3 + 6n - 1} - \\sqrt{n^3 - 10n - 11} \\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... | 1.5 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... | 3/2 sqrt 3 m |
[
{
"content": "Determine whether the following statement is true or false: Given a double series $\\{a_{mn}\\}$ with $a_{mn} > 0$ for all $m, n \\in \\mathbb{N}$, if both $\\sum\\limits_{i=1}^\\infty a_{ik}$ and $\\sum\\limits_{j=1}^\\infty a_{hj}$ converge for all $k, h \\in \\mathbb{N}$, then the double series... | 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... | 21.3 degrees |
[
{
"content": "In terms of $\\pi$, what is the area of the circle defined by the equation $2x^2+2y^2+10x-6y-18=0$?",
"role": "user"
}
] | \frac{35}{2} \pi |
[
{
"content": "In a 7x7 grid, each unit square can be part of a Swiss cross shape consisting of 5 unit squares. Determine the minimum number of squares that must be marked on the grid so that every possible placement of a Swiss cross covers at least one marked square.",
"role": "user"
}
] | 5 |
[
{
"content": "Evaluate the line integral \\(\\int_C (x+y) \\, dx + (x-y) \\, dy\\) using Green's Theorem, where \\(C\\) is the circle with center at the origin and radius \\(2\\).",
"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... | 31.2m/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... | Perihelion = a (1 - e), where a is the semi-major axis and e is the eccentricity |
[
{
"content": "Find the fundamental group $\\pi_1(\\mathbb{R}\\backslash\\{0\\},1)$. Express your answer in terms of a well-known group, if possible.",
"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... | 13.262 |
[
{
"content": "Determine the radius of convergence of the power series \\( \\sum_{n=1}^\\infty \\frac{(-1)^n}{n} z^{n(n+1)} \\).",
"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... | Projects B and 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... | x(t) = 14t^2 - 32t - 5 |
[
{
"content": "Let $f : \\mathbb{R} \\to \\mathbb{R}$ be a measurable function such that $F(x) = \\int_0^x f(y)\\ \\mathrm{d}y$ exists and is bounded, i.e., $\\|F\\|_\\infty = M$. Must $F$ be continuous? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the value of \\( \\alpha \\) that satisfies the equation: \\( \\sin^{-1}(2 \\alpha) \\sin^{-1}(60^{\\circ} - 2 \\alpha) \\sin^{-1}(60^{\\circ} + 2 \\alpha) = 4 \\sin^{-1}(6 \\alpha) \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the integral \\( \\int_{-2}^2 \\frac{x^3}{\\sqrt{4-x^2}} \\, dx \\) and determine if it exists and is finite. If it does, find its value.",
"role": "user"
}
] | 0 |
[
{
"content": "Determine all positive integers $n$ for which the expression \\( \\frac{1}{1+p_{n}}+\\sum_{k=1}^{n-1}\\frac{1}{p_k} \\) is an integer, where \\( p_n \\) denotes the \\( n \\)-th prime number.",
"role": "user"
}
] | 3 |
[
{
"content": "Seth and Cain play a game where they take turns choosing a pair of integers from 1 to 50. In each pair, one integer must be twice the other, and no integer can be reused. The first player unable to choose a valid pair loses. If Seth starts, which player has a winning strategy?",
"role": "user"... | Seth |
[
{
"content": "Find the smallest integer \\( n \\geq 2 \\) such that there exist permutations \\( \\alpha, \\beta, \\gamma, \\delta \\) of the set \\( \\{1, 2, \\ldots, n\\} \\) satisfying the equation: \\[ \\sum_{i=1}^n \\alpha(i) \\beta(i) = \\frac{19}{10} \\sum_{i=1}^n \\gamma(i)\\delta(i). \\]",
"role": ... | 28 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Labor: 20-50%
Raw materials: 10-50%
Transportation: 13-25%
Sales and Distribution: 5-10% |
[
{
"content": "Evaluate the double integral \\( \\iint_D x^6y^6 \\, dx \\, dy \\) where the domain \\( D = \\{ (x,y) : x^{2}\\le y\\le x^{1/8} \\} \\).",
"role": "user"
}
] | \dfrac{5}{441} |
[
{
"content": "Evaluate the limit \\( \\lim_{n \\to \\infty} \\sum_{k=0}^{2n+1} \\frac{n}{n^2 + k} \\).",
"role": "user"
}
] | 2 |
[
{
"content": "Given the curves $x^2 = 4ay$ and $x^2 + y^2 = \\lambda^2$, find a condition under which $y_1 + y_2 \\neq 0$, where $y_1$ and $y_2$ are the roots of the equation $y^2 + 4ay - \\lambda^2 = 0$. Provide your answer in terms of $a$ and $\\lambda$. ",
"role": "user"
}
] | a \neq 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... | 1.6 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... | 0.1*g*L^-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... | -$146,575,000 |
[
{
"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... | 3.06e15 J |
[
{
"content": "Consider non-negative real numbers \\(a, b,\\) and \\(c\\) such that \\(a \\leq b + c\\). For which positive real values of \\(n\\) does the inequality \\(a^n \\leq b^n + c^n\\) hold?",
"role": "user"
}
] | (0, 1] |
[
{
"content": "Determine whether the following assertion is true or false: For any finite abelian group $G$, there exists an integer $m$ such that $G$ is isomorphic to a subgroup of the units $U(\\mathbb{Z}_m)$, where $U(\\mathbb{Z}_m)$ represents the units of integers modulo $m$. Provide a proof or counterexamp... | True |
[
{
"content": "Evaluate the integral \\(I = \\int_0^2 (3x^2 - 3x + 1) \\cos(x^3 - 3x^2 + 4x - 2) \\, dx\\). If \\(I\\) can be expressed as \\(p(\\sin q)\\), where \\(p, q \\in \\mathbb{N}\\), find the value of \\(p + q - 1\\).",
"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... | 2.035 |
[
{
"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... | 2.34 s^(-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... | 637 N |
[
{
"content": "What is the smallest number of subsets, $n$, into which the set of all integers can be partitioned such that none of the subsets contain an infinite arithmetic progression?",
"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... | 40800 J |
[
{
"content": "Find the limit \\( \\lim_{t \\rightarrow \\infty} tx(t) \\) where \\( x = x(t) \\) is the least positive root of the equation \\( x^2 + \\frac{1}{2} = \\cos(tx) \\).",
"role": "user"
}
] | \dfrac{\pi}{3} |
[
{
"content": "Let $h(4x-1) = 2x + 7$. For what value of $x$ is $h(x) = x$?",
"role": "user"
}
] | 15 |
[
{
"content": "Let $p(x)$ be quadratic with rational coefficients. If $p(\\sqrt{7}) = 22$ and $p(\\sqrt{11}) = 30,$ then find $p(\\sqrt{17}).$",
"role": "user"
}
] | 42 |
[
{
"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... | 15 W |
[
{
"content": "Solve for $x$ if \\( \\frac{1}{2x} + \\frac{1}{2}\\left(\\frac{1}{2x} + \\frac{1}{2}\\left(\\frac{1}{2x} + \\cdots\\right)\\right) = y \\).",
"role": "user"
}
] | \dfrac{1}{y} |
[
{
"content": "Is the rank of a symmetric or skew-symmetric matrix equal to the number of its non-zero eigenvalues?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the number of zeroes of the function \\( f(z) = z^4 + e^z \\) within the unit disc \\( |z| < 1 \\).",
"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... | Business continuity plan (BCP) |
[
{
"content": "Find the minimum distance between the curves $y = e^x$ and $y = \\ln x$.",
"role": "user"
}
] | \sqrt{2} |
[
{
"content": "Evaluate the series: \\[ \\sum_{k=1}^{\\infty}\\frac{1}{k(k+1)^2k!} \\]",
"role": "user"
}
] | 3 - 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... | 333,333,333.33 |
[
{
"content": "Determine the value of \\( \\liminf f_n \\) for the sequence of functions \\( f_n = \\chi_{[n, n+1]} \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n \\to +\\infty} \\left ( 2\\sqrt[n]{x} - 1 \\right )^n \\] for a real number \\( x \\geq 1 \\).",
"role": "user"
}
] | x^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... | $427,945 |
[
{
"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... | 2.45e3 N/C, upwards |
[
{
"content": "Determine all primitive Pythagorean triples \\((a, b, c)\\) that form an arithmetic progression, where \\(a^2 + b^2 = c^2\\) and \\(\\gcd(a, b, c) = 1\\).",
"role": "user"
}
] | (3, 4, 5) |
[
{
"content": "Find a line that is tangent to the curve \\( y = x^4 - 4x^3 \\) at two distinct points.",
"role": "user"
}
] | y = -8x - 4 |
[
{
"content": "In the group of units \\( G = ( \\mathbb{Z} / 133 \\mathbb{Z} )^{\\times} \\), determine the number of elements that have an order of 9.",
"role": "user"
}
] | 18 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.4 m/s |
[
{
"content": "Let $g$ be a function such that $$ \\sqrt {x + \\sqrt { x - g(x) } } = g(x) , $$ for $x > 1$. If $g(x)$ has the form $\\frac{p+\\sqrt{qx+r}}{s},$ where $p,q,r,s$ are integers and $p,s$ are relatively prime, find $p+q+r+s$. Determine the value of $p+q+r+s$. \\( \\boxed{} \\)",
"role": "user"
... | 4 |
[
{
"content": "Evaluate the surface integral \\( \\iint_S \\frac{X}{Y}\\sqrt{9Z^2 - 4} \\, dS \\) over the portion of the hyperboloid \\( Z=2\\sqrt{X^2+Y^2+1} \\) that lies within the cylinder \\( X^2+Y^2=4 \\).",
"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... | 10 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... | 33.16 billion |
[
{
"content": "Determine the value of $f(550)$ if $f: \\mathbb{Z} \\to \\mathbb{Z}$ is a function satisfying $f(11) = 1$ and the property $f(a)f(b) = f(a + b) + f(a - b)$ for all integers $a$ and $b$. Given that $f(0) \\neq 0$, find $f(550)$.",
"role": "user"
}
] | -1 |
[
{
"content": "Given that $xyz = (1-x)(1-y)(1-z)$ with $x, y, z \\in (0,1)$, find the minimum value of the expression $x(1-z) + y(1-x) + z(1-y)$. Use the AM-GM inequality to determine this minimum value.",
"role": "user"
}
] | \dfrac{3}{4} |
[
{
"content": "Let the numbers \\(x\\) and \\(y\\) satisfy the conditions \\(\\begin{cases} x^2 + y^2 - xy = 2 \\\\ x^4 + y^4 + x^2y^2 = 8 \\end{cases}\\). Determine the value of \\(P = x^8 + y^8 + x^{2014}y^{2014}\\). Choose the correct answer from the following options:\n\n(A) \\(46\\), (B) \\(48\\), (C) \\(50... | 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... | $14,400 |
[
{
"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... | 8.19% |
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