prompt list | ground_truth string |
|---|---|
[
{
"content": "Given that $g(x)$ is a polynomial function satisfying the equation $g(x)g(y) = g(x) + g(y) + g(xy) - 2$ for all real numbers $x$ and $y$, and that $g(2) = 5$, find the value of $g(3)$. ",
"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... | 6.25e18 N/C to the east |
[
{
"content": "Is it possible to construct a function \\( g(a,b) \\) such that it is computationally feasible to determine \\( b \\) from \\( g(a,b) \\), but computationally infeasible to determine \\( a \\) from \\( g(a,b) \\)?",
"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... | 3.53 mA |
[
{
"content": "Determine the singularities of the function \\( f(z) = \\sin\\left(\\frac{3}{2-z}\\right) \\) and find the radius of convergence of its Maclaurin series.",
"role": "user"
}
] | 2 |
[
{
"content": "The Great Kingdom is a rectangular island divided into smaller rectangular landscapes. Each landscape has a road running along one of its diagonals. These roads form a closed loop that does not intersect itself. If the Great Kingdom has an odd number of landscapes, what is the minimum number of la... | 5 |
[
{
"content": "Compute the limit: $$\\lim_{x \\to 0^+} \\frac{\\sqrt{e^x-1}-e^x\\sqrt{x}}{x}.$$",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether the limit \\( \\lim\\limits_{(x,y)\\rightarrow (0,0)}\\frac{\\sin(xy)}{y} \\) exists.",
"role": "user"
}
] | 0 |
[
{
"content": "Solve the equation \\( 2021 \\cdot \\sqrt[202]{x^{2020}} - 1 = 2020x \\) for \\( x \\geq 0 \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Find the maximum value of the function \\( f(x) = \\sqrt{(x-3)^2 + (x^2-2)^2} - \\sqrt{x^2 + (x^2-1)^2} \\), where \\( P(x, x^2) \\) is a point on the parabola \\( y = x^2 \\).",
"role": "user"
}
] | \sqrt{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... | 7.64 J |
[
{
"content": "Let $\\Omega$ be a smoothly open bounded domain in $\\mathbb{R}^{n}$. Assume that $u \\in W^{1,2}(\\Omega)$ and $v \\in W^{1,2}_{0}(\\Omega)$. Determine if the following integration by parts formula is always true:\n\n$$ \\int_{\\Omega}(\\partial_{i}u) v + (\\partial_{i}v) u \\, dx = \\int_{\\part... | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.095 V |
[
{
"content": "Find the greatest common divisor (GCD) of \\(7^{3001} - 1\\) and \\(7^{3000} + 1\\).",
"role": "user"
}
] | 2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 25091264.42 |
[
{
"content": "Calculate the limit: $$\\lim_{x \\to \\infty} \\left(\\frac{\\ln(x\\ln(\\gamma) )}{\\ln(x\\ln(\\gamma)+\\ln(\\frac{\\gamma-1}{\\gamma}))}\\right)^{1/2},$$ where $\\gamma >10$ is a constant.",
"role": "user"
}
] | 1 |
[
{
"content": "Let $F$ be a global field with ring of integers $o$. Suppose $x \\in F$ satisfies $|x|_v = 1$ for all non-archimedean valuations $v$ of $F$. Does this imply that $x \\in o^\\times$?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the number of components in the graph $C_{9}$, where the vertices represent all binary strings of length nine, and two strings are adjacent if and only if they differ in exactly three positions.",
"role": "user"
}
] | 1 |
[
{
"content": "Consider a regular $9$-gon with symmetry group $D_9$. There are three distinct equilateral triangles that can be formed using the nine vertices. Identify the subgroup of $D_9$ that acts trivially on the set of these three triangles.",
"role": "user"
}
] | C_3 |
[
{
"content": "Evaluate the integral of the function \\( f(x, y) = 1 + xy \\) over the region \\( D = \\{(x, y) \\in \\mathbb{R}^2 : 1 \\leq x^2 + y^2 \\leq 2 \\text{ and } y \\geq 0\\} \\). Use polar coordinates to perform the integration.",
"role": "user"
}
] | \dfrac{3\pi}{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... | $1,840 |
[
{
"content": "In a relay race from Moscow to Petushki, two teams of 20 people each participate. Each team divides the distance into 20 segments, assigning one segment to each participant. Each participant runs at a constant speed, but speeds may vary between participants. The first participants of both teams st... | 380 |
[
{
"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... | 8.16 min |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\to 0} \\dfrac{e^{-\\frac{1}{x^2}}}{\\sin x} \\]",
"role": "user"
}
] | 0 |
[
{
"content": "In an acute triangle \\(ABC\\) with \\(AB \\neq AC\\), let \\(H\\) be the foot of the altitude from \\(A\\). Points \\(P\\) and \\(Q\\) are taken on the extensions of sides \\(AB\\) and \\(AC\\) respectively, such that \\(HP = HQ\\) and the points \\(B, C, P, Q\\) are concyclic. Determine the rati... | 1 |
[
{
"content": "Find all continuous functions $f: \\mathbb{R} \\to \\mathbb{R}$ such that $f(0) = 0$ and satisfy the inequalities $f(2x) \\geq x + f(x)$ and $f(3x) \\leq 2x + f(x)$ for all $x \\in \\mathbb{R}$. Are there any functions other than $f(x) = |x|$ that satisfy these conditions?",
"role": "user"
}... | f(x) = 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... | 30.84 degree Celsius |
[
{
"content": "Evaluate the limit using L'Hopital's rule: $$\\lim_{x \\to 0}\\frac{\\int_0^{2x}\\ln(1+t)\\,dt}{\\int_{x^4}^{x^2}\\frac{\\sin t}{t}\\,dt}$$",
"role": "user"
}
] | 2 |
[
{
"content": "Let $C([0,1])$ be the space of all real-valued continuous functions $f:[0,1]\\to \\mathbb{R}$. Consider the norm $$||f||=\\left(\\int_0^1 |f(x)|^2\\right)^{1/2}$$ and the subspace $$C=\\{f\\in C([0,1]):f(0)=0\\}.$$ Determine the closure of $C$ in this normed space.",
"role": "user"
}
] | C([0,1]) |
[
{
"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... | $21.28 million |
[
{
"content": "Evaluate the limit \\( \\lim_{n \\rightarrow \\infty} \\sum_{k=1}^{\\infty} k^{1/2} n^{-1} (1 - \\cos(n^2 k^{-2})) \\) and determine if it equals infinity.",
"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... | U = \frac{\sigma q d}{2 \epsilon_{o}} |
[
{
"content": "Let $X$ and $Y$ be topological spaces such that $A \\subset X \\subset Y$. If $A$ is a connected subspace of $Y$, does it imply that $A$ is also a connected subspace of $X$? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the value of the constant $K$ such that the function \\( u(x,t) = \\frac{2}{\\sqrt{\\pi}}\\int_{0}^\\frac{x}{\\sqrt{t}} e^{-s^2}ds \\) satisfies the partial differential equation \\( \\frac{\\partial u}{\\partial t} = K\\frac{\\partial^2u}{\\partial x^2} \\).",
"role": "user"
}
] | \dfrac{1}{4} |
[
{
"content": "Let the quadratic function \\( f(x) = a x^2 + b x + c \\) (where \\( a, b, c \\in \\mathbb{R} \\) and \\( a \\neq 0 \\)) satisfy the following conditions:\n1. For all \\( x \\in \\mathbb{R} \\), \\( f(x-4) = f(2-x) \\), and \\( f(x) \\geq x \\);\n2. For all \\( x \\in (0, 2) \\), \\( f(x) \\leq \\... | 9 |
[
{
"content": "Compute the complex integral \\( \\int_{|z|=1}\\frac{1}{z^2+1}dz \\) given that both \\( i \\) and \\( -i \\) lie on the contour \\( |z|=1 \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Consider a sequence of $n$ independent and identically distributed (i.i.d.) random variables $X_1, X_2, \\ldots, X_n$, each following a uniform distribution on the interval $(0, 1)$. Determine the limit as $n$ approaches infinity of the probability that the sum of these random variables is less th... | 1 |
[
{
"content": "The sum of three different numbers is 67. The two larger numbers differ by 7 and the two smaller numbers differ by 3. What is the value of the largest number?",
"role": "user"
}
] | 28 |
[
{
"content": "Find a continuous function \\( f \\) that satisfies the equation:\n\n\\[ f(x) = 1 + \\frac{1}{x}\\int_1^x f(t) \\, dt \\]",
"role": "user"
}
] | 1 + \ln 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... | 7.953 kg |
[
{
"content": "Given the sequence \\( \\{a_n\\} \\) defined by \\( a_1 = 1 \\) and \\( a_{n+1} = (1 + a_1)(1 + a_2)\\cdots(1 + a_n) \\), find the value of \\( \\sum_{n=1}^\\infty \\frac{1}{1 + a_n} \\).",
"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... | 100342.5 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... | 9.498 days |
[
{
"content": "Evaluate the integral \\( \\int_{0}^{\\infty} f(x) g(x) \\, dx \\), where \\( f(x) = x - \\frac{x^3}{2} + \\frac{x^5}{2 \\cdot 4} - \\frac{x^7}{2 \\cdot 4 \\cdot 6} + \\cdots \\) and \\( g(x) = 1 + \\frac{x^2}{2^2} + \\frac{x^4}{2^2 \\cdot 4^2} + \\frac{x^6}{2^2 \\cdot 4^2 \\cdot 6^2} + \\cdots \\... | \sqrt{e} |
[
{
"content": "Consider the system of equations given by \\( \\frac{dx(t)}{dt} = -A(x(t) - y) \\) where \\(x(t), y \\in \\mathbb{R}^p\\) and \\(A \\in \\mathbb{R}^{p \\times p}\\) are known. Given \\(x(0)\\), determine which of the following solutions is correct:\n\n1. \\(x(t) = \\exp(-At)[x(0) - Ay] + Ay\\)\n2.... | 2 |
[
{
"content": "Find the derivative of the expression \\( \\text{trace} (\\Sigma^{\\frac{1}{2}} S^{-1}\\Sigma^{\\frac{1}{2}}) \\) with respect to the matrix \\( \\Sigma \\), where both \\( \\Sigma \\) and \\( S \\) are positive definite matrices.",
"role": "user"
}
] | S^{-1} |
[
{
"content": "Find all positive integer pairs \\((j, k)\\) such that \\(2^j + 3 = 7^k\\).",
"role": "user"
}
] | (2, 1) |
[
{
"content": "In a nonempty set $S$, the binary operation $\\cdot$ is associative and cancellable. The set of powers of any element in $S$ is finite, implying that every element has finite order. Does this necessarily mean that $S$ forms a group?",
"role": "user"
}
] | Yes |
[
{
"content": "Find the limit of the function \\( g(x) = \\left[\\left(\\frac{1}{2e}\\right)\\left(1-\\frac{1}{x}\\right)^x\\right]^x \\) as \\( x \\to \\infty \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Find the minimum area of the image of a univalent function $g: \\mathbb{D} \\rightarrow \\mathbb{C}$ with $g(0) = 0$ and $|g'(0)| = k$, where $k$ is a positive constant.",
"role": "user"
}
] | \pi k^2 |
[
{
"content": "Determine whether the polynomial $x^2-15$ can be factorized into linear factors in the ring $\\mathbb{Z}_{2023}$.",
"role": "user"
}
] | Yes |
[
{
"content": "In a heptagon $A_1A_2A_3A_4A_5A_6A_7$, the diagonals $A_1A_3, A_2A_4, A_3A_5, A_4A_6, A_5A_7, A_6A_1$, and $A_7A_2$ are congruent to each other, and the diagonals $A_1A_4, A_2A_5, A_3A_6, A_4A_7, A_5A_1, A_6A_2$, and $A_7A_3$ are also congruent to each other. Is the polygon necessarily regular?",
... | Yes |
[
{
"content": "Determine whether the following statement is true: If $A \\times B$ is an element of a product $\\sigma$-algebra $\\mathcal{A} \\times \\mathcal{B}$, then $A \\in \\mathcal{A}$ and $B \\in \\mathcal{B}$. 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... | $3,627,639.69 |
[
{
"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... | An additional capacitor of 7.94 nF and a resistor of 685 \\Omega connected in series are needed. |
[
{
"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... | 14000 |
[
{
"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... | 32J |
[
{
"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... | $82,296.77 |
[
{
"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... | 191880 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... | 4.7e4 kg |
[
{
"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... | 8.02 |
[
{
"content": "Find the limit as \\( h \\) approaches 0 of the expression:\n\\[ \\frac{e^{x(h+2)^2} - e^{4x}}{h} \\]",
"role": "user"
}
] | 4x e^{4x} |
[
{
"content": "Find the sum of the series \\( \\sum_{n=1}^{\\infty} \\frac{n^2}{n!} \\).",
"role": "user"
}
] | 2e |
[
{
"content": "Let $M_n$ be the $n \\times n$ matrix with entries as follows: for $1 \\le i \\le n$, $m_{i,i} = 10$; for $1 \\le i \\le n - 1$, $m_{i+1,i} = m_{i,i+1} = 3$; all other entries in $M_n$ are zero. Let $D_n$ be the determinant of matrix $M_n$. Find\n\\[\\sum_{n=1}^{\\infty} \\frac{1}{8D_n+1}.\\]Note:... | \frac{1}{72} |
[
{
"content": "Let \\( \\alpha \\) be a solution to the equation \\( |x| = e^{-x} \\). Define \\( I_n = \\int_0^{\\alpha} (xe^{-nx} + \\alpha x^{n-1}) \\, dx \\) for \\( n = 1, 2, \\ldots \\). Find \\( \\lim_{n \\to \\infty} n^2 I_n. \\)",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to 0} \\frac{1 - x^2 - f(x)}{x^4} \\] where \\( f(x) = 1 - x^2 + \\frac{x^4}{2!} - \\frac{x^6}{3!} + \\frac{x^8}{4!} + \\cdots + \\frac{(-1)^n x^{2n}}{n!} \\).",
"role": "user"
}
] | -\dfrac{1}{2} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.255 cm^3 |
[
{
"content": "A $\\textit{palindrome}$ is a positive integer which reads the same forward and backward, like $12321$ or $4884$.\n\nHow many $4$-digit palindromes are there?",
"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... | 1.88E-4 M s^-1 |
[
{
"content": "Compute the limit of the sequence \\(a_n\\) as \\(n\\) approaches infinity, where \\[a_n=\\int_n^{2n} \\frac{1}{x}e^\\frac{1}{x} \\,dx\\].",
"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... | 4.4e-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... | -0.283% |
[
{
"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... | 5.9 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 230.946 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... | 3.09e30 kg |
[
{
"content": "A tangent to the incircle of a triangle is drawn parallel to one of the sides and intersects the other two sides at points X and Y. Given that the triangle has a perimeter of \\( p \\), determine the maximum possible length of the segment XY.",
"role": "user"
}
] | \dfrac{p}{8} |
[
{
"content": "Verify if the following integral correctly represents the volume of the region in the first octant under the surfaces $z=4-x^2$ and $y=4-x^2$, where the projection of the region $R$ onto the $xy$-plane is bounded by $0 \\leq y \\leq 4$ and $0 \\leq x \\leq \\sqrt{4-y}$, and the cylinders intersect... | \dfrac{256}{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... | Number of atoms of acid = (mass of acid in grams * (1 mole / molar mass of acid in grams)) * (6.022e23 atoms / mole) |
[
{
"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... | 82.90 |
[
{
"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... | 9.66e6 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... | Managers may employ income-decreasing accounting policies instead of income-increasing ones for several reasons:
1. To reduce tax burden: Lower reported income leads to lower taxes payable.
2. For labor negotiations: Reporting lower income can weaken the position of labor unions demanding higher wages.
3. To reduce re... |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to0}\\left(\\frac{1}{x^3}\\int_0^x\\sin(t^2)\\,dt-\\frac{1}{2x^2}+\\frac{1}{x}\\right)$$",
"role": "user"
}
] | -\infty |
[
{
"content": "Determine whether there exists a decreasing sequence of sets \\( \\{A_n\\} \\) of real numbers, where \\( A_{n+1} \\subseteq A_n \\) for all \\( n \\in \\mathbb{N} \\), such that \\( m^*(A_n) < \\infty \\) for all \\( n \\in \\mathbb{N} \\) and \\( m^*(\\cap_{n\\in \\mathbb{N}} A_n) < \\lim_{n\\to... | 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... | 2.13e7 L |
[
{
"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... | 4.472 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... | 42.73 m |
[
{
"content": "Consider a line $y = kx + b$ where $k < 0$ and $b > 0$, which is tangent to the parabola $y = x^2 - 4x + 4$. Find the maximal area of the region bounded by the lines $y = kx + b$, $y = 0$, and $x = 0$. Provide your answer as a single numerical value.",
"role": "user"
}
] | \dfrac{64}{27} |
[
{
"content": "Solve the congruence equation: \\(x^{257} \\equiv 5 \\pmod{2016}\\).",
"role": "user"
}
] | 101 |
[
{
"content": "Find the values of $x$ for which the series \\( \\sum_{n=1}^{\\infty}\\frac{x^n}{1-x^n} \\) converges absolutely.",
"role": "user"
}
] | (-1, 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... | 1.069 |
[
{
"content": "Determine whether the following statement is true: If a CW complex $X$ is $(n-1)$-connected, then its suspension $SX$ is $n$-connected.",
"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... | $151,500.00 |
[
{
"content": "Find the singular point \\(x = a\\) of the solution to the differential equation \\(y' - \\left(\\frac{6}{17}\\sin x\\right)y = \\frac{5}{32} x^4 y^2\\) with the initial condition \\(y(0) = 1\\). (Hint: Consider the behavior of \\(y(x)\\) when \\(y \\gg 1\\).)",
"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... | 152,200 |
[
{
"content": "Let \\( G \\) be a finite group, and consider the commuting graph \\( X(G) \\) where vertices are the elements of \\( G \\), and two distinct vertices \\( x \\) and \\( y \\) are connected by an edge if and only if \\( xy = yx \\). If \\( c \\) denotes the chromatic number of \\( X(G) \\), does \\... | Yes |
[
{
"content": "Find the Lebesgue measure of the set \\( \\{(x_1,\\ldots,x_n)\\in \\mathbb{R}^n: x_1+x_2+\\cdots+x_n\\leq1, x_i\\geq0 \\text{ for all } i\\} \\).",
"role": "user"
}
] | \dfrac{1}{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... | The lighter piece acquires 5500 J and the heavier piece acquires 4000 J |
[
{
"content": "Let $A$ be a ring and $M$ an $A$-module. Suppose $M_1$ and $M_2$ are submodules of $M$ such that $M_1$ is flat and $M_1 \\cap M_2$ is not flat. Does this imply that $M_2$ is not flat? Provide a justification for your answer.",
"role": "user"
}
] | No |
[
{
"content": "A line with an inclination angle of \\(\\frac{\\pi}{4}\\) intersects the ellipse \\(\\frac{x^{2}}{4} + y^{2} = 1\\) at points \\(A\\) and \\(B\\). Determine the equation of the locus of the midpoint of the line segment \\(AB\\).",
"role": "user"
}
] | x + 4y = 0 |
[
{
"content": "If \\( x + \\sqrt{x^2 - 1} + \\frac{1}{x - \\sqrt{x^2 - 1}} = 20 \\), find the value of the expression:\n\\[ x^2 + \\sqrt{x^4 - 1} + \\frac{1}{x^2 + \\sqrt{x^4 - 1}} \\]\nChoose the correct answer:\n(A) 5.05 \n(B) 20 \n(C) 51.005 \n(D) 61.25 \n(E) 400",
"role": "user"
}
] | C |
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