prompt list | ground_truth string |
|---|---|
[
{
"content": "Suppose $p_i$ is an odd prime for all $i=1,\\cdots,r$ and there is an integer $m$ such that $2$ divides $m$. Can $m$ be written as $m=\\prod_{i=1}^{r}{p_i}^{a_i}$ where $a_i$ is a power of primes and $r$ denotes the number of distinct primes? Answer with \"Yes\" or \"No.\"",
"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... | 36.036 kHz |
[
{
"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 years |
[
{
"content": "Calculate the radius of convergence of the power series \\( S(x) = \\sum_{n=1}^\\infty \\left(\\frac{n^2+4n+3}{5n(n+2)}\\right)^n \\cdot x^n \\).",
"role": "user"
}
] | 5 |
[
{
"content": "Find the natural number \\(a\\) such that \\(a^4 + 4\\) is a prime number.",
"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... | Outlandish Novelties must produce 6,420 units in July and 4,360 units in August. |
[
{
"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... | 7.06% |
[
{
"content": "Find the last three digits of the number \\(8^{8^8}\\).",
"role": "user"
}
] | 656 |
[
{
"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... | 72 mL of 0.100 M benzoic acid and 28 mL of 0.160 M sodium benzoate |
[
{
"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... | 0.51*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... | Carbon |
[
{
"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... | 11.99% |
[
{
"content": "Determine whether the integral \\( \\int_{0}^{1} |\\ln (x)|^n \\, dx \\) converges for an arbitrary natural number \\( n \\).",
"role": "user"
}
] | Converges |
[
{
"content": "Determine the minimum value of \\( \\frac{a^2+b^2+c^2}{d^2} \\) where \\(a, b, c, d\\) are the sides of a quadrilateral.",
"role": "user"
}
] | \dfrac{1}{3} |
[
{
"content": "Evaluate the triple integral \\( \\int_{0}^{6} \\int_{0}^{12-2y} \\int_{0}^{4-\\frac{2y}{3}-\\frac{x}{3}} x \\, dz \\, dx \\, dy \\).",
"role": "user"
}
] | 144 |
[
{
"content": "Let \\( f: \\mathbb{R} \\to \\mathbb{R} \\) be a function satisfying the conditions \\( f(10-x) = f(x) \\) and \\( f(2-x) = f(2+x) \\) for all \\( x \\in \\mathbb{R} \\). Given that \\( f(0) = 101 \\), determine the minimum possible number of values of \\( x \\) in the interval \\([0, 30]\\) such ... | 11 |
[
{
"content": "Let $A$ be a finite abelian group and $p$ a prime number. Define $A^p = \\{pa : a \\in A\\}$ and $A_p = \\{a \\in A : pa = 0\\}$. Prove that $A/A^p \\cong A_p$ by finding a surjective homomorphism $f: A \\to A_p$ with kernel $A^p$.",
"role": "user"
}
] | A/A^p \cong A_p |
[
{
"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 1: $141,471, $848,529; Year 2: $242,451, $606,078; Year 3: $173,151, $432,927; Year 4: $123,651, $309,276; Year 5: $88,407, $220,869; Year 6: $88,308, $132,561; Year 7: $88,407, $44,154; Year 8: $44,154, $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... | 260 km/h at an angle of 22.619 degrees with the east direction |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 24.2N |
[
{
"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... | Hydrogen |
[
{
"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... | Two factors that can help to facilitate knowledge sharing are organizational culture and information technology. The ideal response would be information technology. |
[
{
"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... | 8KClO_3 + C_{12}H_{22}O_{11} \rightarrow 8KCl + 11H_2O + 12CO_2 |
[
{
"content": "Below is a portion of the graph of an invertible function, $y=f(x)$:\n\n[asy]\nimport graph; size(8cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-3.25,xmax=3.25,ymin=-6.25,ymax=7.25;\n\npen cqcqcq=rgb(0.75,0.75,0.75);\n\n/*grid*/ pen gs=linewidth(... | -2 |
[
{
"content": "Consider a set of points in the plane such that only two distinct Manhattan distances occur between all pairs of distinct points. What is the maximal number of points in such a set?",
"role": "user"
}
] | 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... | 200 nm |
[
{
"content": "Is it true that the ultraproduct of non-commutative $L^p$-spaces, \\( \\prod_{\\mathcal U}L^p(M_i,\\tau_i) \\), can be identified as \\( L^p(M,\\tau) \\) for some von Neumann algebra \\( M \\) with \\( \\tau \\) being a normal faithful semifinite trace on \\( M \\)?",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit: $$ \\lim_{x \\rightarrow \\infty, y \\rightarrow \\infty} \\left( \\frac{xy}{x^2 + y^2}\\right)^{x^2} $$",
"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... | 8.46% |
[
{
"content": "Find the minimal real number \\(c\\) such that the inequality \\(x+y-(xy)^c \\geq 0\\) holds for all \\(x, y \\in [0, 1]\\).",
"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... | 6.0 W |
[
{
"content": "Let \\(n\\) and \\(k\\) be positive integers, and let \\(G\\) be a group with \\(k\\) cyclic subgroups of order \\(n\\). Determine the number of elements of order \\(n\\) in \\(G\\).",
"role": "user"
}
] | k \phi(n) |
[
{
"content": "Determine whether the function \\( f(x) = x + A e^{Bx} \\), where \\( A \\) and \\( B \\) are known constants, is invertible.",
"role": "user"
}
] | AB \geq 0 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\rightarrow\\infty} \\frac{1}{n}\\left[\\log\\left( \\frac{\\sqrt{2\\pi n} (x-p) - p(1-p) e^{-\\frac{n}{2}(\\frac{x-p}{p(1-p)})^2}}{\\sqrt{2\\pi n} (x-p)} \\right)\\right] \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Let \\( a_k \\) be a sequence defined by:\n\\[ a_k = \\begin{cases} \\frac{(-1)^n}{\\ln(n)} & \\text{if } k = 3n-1, \\\\ 0 & \\text{otherwise.} \\end{cases} \\]\nFind \\( \\limsup \\sqrt[k]{|a_k|} \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Is a function $f: A \\subset \\mathbb{R}^n \\rightarrow \\mathbb{R}$ necessarily continuous almost everywhere if it is Riemann integrable on $A$?",
"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... | 3.93e9 nuclei/year |
[
{
"content": "Evaluate the limit: \\[ \\lim_{(x,y) \\to (0,0)}\\frac{\\cos(x^2+y^2)}{\\ln(2x^2y^2+1)} \\]",
"role": "user"
}
] | \infty |
[
{
"content": "Consider the sequence of numbers defined recursively by \\(t_1=1\\) and for \\(n>1\\) by \\(t_n=1+t_{(n/2)}\\) when \\(n\\) is even and by \\(t_n=\\frac{1}{t_{(n-1)}}\\) when \\(n\\) is odd. Given that \\(t_n=\\frac{19}{87}\\), find the sum of the digits of \\(n\\).",
"role": "user"
}
] | 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... | 54,999.33 |
[
{
"content": "In the hyperbolic plane, is it possible for a geodesic to intersect orthogonally two distinct geodesics $L$ and $L'$ that do not intersect each other at infinity?",
"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... | 1.16 m |
[
{
"content": "Find all positive integer solutions to the equation: \\[ 3x^2 - 7y^2 + 1 = 0 \\]",
"role": "user"
}
] | (3, 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... | 15.2 m |
[
{
"content": "Is every finite-dimensional normed space complete?",
"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... | 0.074 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... | 13.98 dB |
[
{
"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 MPa |
[
{
"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... | NaCl: 43.0%, KCl: 57% |
[
{
"content": "Consider two compact, connected, and orientable manifolds $X$ and $Y$ of equal dimension, such as $X = Y = \\mathbb{CP}^n$. Given a surjective analytic map $f: X \\to Y$, determine if the mapping degree of $f$ can be defined. Specifically, does there exist an integer $d$ such that each point $y \\... | 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... | profit = 625,000 * max(0, exchange rate at expiration - 1.5) - 3,125 |
[
{
"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 days |
[
{
"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... | <img>/cimages/multimages/16/nitrogen_trichloride1595132841648652502.png</img> |
[
{
"content": "If $13^{3n}=\\left(\\frac{1}{13}\\right)^{n-24}$, find $n$.",
"role": "user"
}
] | 6 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 164.3 kJ |
[
{
"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... | 2.0e+3 |
[
{
"content": "A boy has the following seven coins in his pocket: $2$ pennies, $2$ nickels, $2$ dimes, and $1$ quarter. He takes out two coins, records the sum of their values, and then puts them back with the other coins. He continues to take out two coins, record the sum of their values, and put them back. How... | 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... | 1.66 |
[
{
"content": "Determine the number of positive integer solutions (a, b) for the equation \\(a^{2014} + 2015 \\cdot b! = 2014^{2015}\\).",
"role": "user"
}
] | 0 |
[
{
"content": "Solve the differential equation: \\((x^2-y^2)dx+2xydy=0\\).",
"role": "user"
}
] | x^2 + y^2 = Cx |
[
{
"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... | 0.2776 rad/s^2 |
[
{
"content": "Determine whether there exist two square matrices \\( M \\) and \\( N \\) such that \\( MN + NM = 0 \\), where \\( 0 \\) is the zero matrix.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the coordinates of the closest point on the cylinder defined by the equation \\(y^2 + z^2 = 25\\) to the point \\((2,9,12)\\) using Lagrange multipliers.",
"role": "user"
}
] | (2, 3, 4) |
[
{
"content": "Determine whether every bounded Borel function on a compact set is the pointwise limit of continuous functions. Provide a justification for your answer.",
"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... | two |
[
{
"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... | Two factors: (i) nuclear charge; and (ii) shielding by other electrons. |
[
{
"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... | 4546 |
[
{
"content": "Provide an example of a group that cannot be expressed as the direct product of its Sylow subgroups.",
"role": "user"
}
] | S_3 |
[
{
"content": "Given that the random variable $X$ follows a uniform distribution on the interval $(0,1)$, $X\\sim\\text{Unif}(0,1)$, and the conditional distribution of $Y$ given $X$ is a binomial distribution with parameters $n$ and $p = x$, $Y\\mid X = x\\sim\\text{Binom}(n, p = x)$, compute the expected value... | \dfrac{n}{2} |
[
{
"content": "Given the inequalities $3 > b > 0$ and $a + b = 3$, find the minimum value of the expression $(3^a + 3^{2b} + 3^{2-b})^3$. Use calculus to determine the minimum value.",
"role": "user"
}
] | 8748 |
[
{
"content": "Find the smallest positive integer $n$ with the property that the polynomial $x^4 - nx + 63$ can be written as a product of two nonconstant polynomials with integer coefficients.",
"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... | The direct materials budget for the third quarter of 2017 is as follows:
July: Direct materials purchases = 118,880 pounds, Cost of purchases = $1,188,800
August: Direct materials purchases = 101,280 pounds, Cost of purchases = $1,012,800
September: Direct materials purchases = 120,960 pounds, Cost of purchases = $1,20... |
[
{
"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... | 0.27 |
[
{
"content": "Anna thinks of a sequence of natural numbers \\((a_{1}, a_{2}, a_{3}, a_{4})\\). Béla names a sequence of natural numbers \\((b_{1}, b_{2}, b_{3}, b_{4})\\), and Anna responds with the sum \\(a_{1} b_{1} + a_{2} b_{2} + a_{3} b_{3} + a_{4} b_{4}\\). Béla can name new sequences. What is the minimum... | 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... | 222.83 nm |
[
{
"content": "If $m+\\frac{1}{m}=8$, then what is the value of $m^{2}+\\frac{1}{m^{2}}+4$?",
"role": "user"
}
] | 66 |
[
{
"content": "Find the limit of the sequence \\( \\{x_n\\} \\) defined by the following recurrence relations: \\[ x_1 = \\sqrt[2022]{\\frac{2022}{2021}} \\] \\[ x_{n+1} = \\frac{n+2}{3n+11}(\\sqrt{x_n} + \\sqrt[3]{7+x_n}), \\quad \\forall n \\in \\mathbb{N}^* \\]",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate the double integral \\( \\iint_G (x^{4}-y^{4})xy\\,dxdy \\), where \\( G \\) is the region defined by \\( 0 \\leq x \\), \\( 1 \\leq x^{2}-y^{2} \\leq 2 \\), and \\( 1 \\leq xy \\leq 2 \\).",
"role": "user"
}
] | \dfrac{9}{8} |
[
{
"content": "Calculate the sum of the series \\( \\sum_{n=0}^{\\infty} \\frac{n^2 - 2}{n!} \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the number of homomorphisms from the ring of Gaussian integers \\( \\mathbb{Z}[i] \\) onto the ring \\( \\mathbb{Z}_{13}(i) \\).",
"role": "user"
}
] | 2 |
[
{
"content": "Determine whether a closed ball \\(B\\) centered at the origin within an open ball \\(W\\) centered at the origin in \\(\\mathbb{C}^n\\) is holomorphically convex in \\(W\\).",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the type of singularity at the point $z=0$ for the function $f(z)=\\sin\\left(\\cos\\left(\\frac{1}{z}\\right)\\right)$. Choose one of the following options:\n(a) Removable singularity\n(b) Pole\n(c) Essential singularity\n(d) Non-isolated singularity",
"role": "user"
}
] | 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... | 805280 |
[
{
"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... | Six isomers: But-1-ene, cis-But-2-ene, trans-But-2-ene, 2-Methylpropene, Cyclobutane, Methylcyclopropane |
[
{
"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... | $57.70 |
[
{
"content": "Determine the number of distinct topological group structures that can be defined on the unit circle $S^1$ with its usual topology.",
"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... | 0.541 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... | 1.16e-18 kg |
[
{
"content": "Find the largest value of \\( a \\) such that there exist real numbers \\( b \\) and \\( c \\) satisfying the equations \\( a^2 - bc - 8a + 7 = 0 \\) and \\( b^2 + c^2 + bc - 6a + 6 = 0 \\).",
"role": "user"
}
] | 9 |
[
{
"content": "Consider the system of differential equations given by:\n\\[ x' = ax + ay \\]\n\\[ y' = ax - (a + 2b)y \\]\nwhere \\(a\\) and \\(b\\) are real numbers. Which of the following conditions ensures that each solution \\(\\begin{pmatrix}x(t)\\\\y(t)\\end{pmatrix}\\) satisfies \\(\\lim_{t\\to \\infty}x(... | C |
[
{
"content": "The points \\( K, L, M, N \\) are the centers of the circles inscribed in the faces \\( S A B, S A C, S B C, \\) and \\( A B C \\) of the tetrahedron \\( S A B C \\). Given that \\( A B = S C = 5 \\), \\( A C = S B = 7 \\), and \\( B C = S A = 8 \\), find the volume of the tetrahedron \\( K L M N ... | 0.66 |
[
{
"content": "Given that a scalar random variable \\( y = z + v \\), where the probability density function (pdf) of \\( v \\) is \\( p_{v}(t) = \\frac{t}{4} \\) on the interval \\([0,4]\\), and the pdf of \\( z \\) is \\( p_{z}(t) = t \\) on the interval \\([0,2]\\), both densities are zero elsewhere. If a sin... | \dfrac{3}{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... | 0.122 |
[
{
"content": "Given \\( x, y \\in \\mathbf{R} \\) such that\n\\[\\begin{cases}\n(x-1)^{2003}+2002(x-1)=-1, \\\\\n(y-2)^{2003}+2002(y-2)=1 .\n\\end{cases}\\]\n\nFind \\( x + y \\).",
"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... | 0.35 or 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... | 1.337e-7 |
[
{
"content": "Find the minimum value of the function \\( g(x) = \\frac{\\ln(x)}{\\ln(\\ln(x))} \\).",
"role": "user"
}
] | 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... | 335J |
[
{
"content": "Determine the number of 2-order partitions of an $n$-element set $S_n$. A 2-order partition is defined as a way to divide $S_n$ into two non-empty subsets.",
"role": "user"
}
] | 2^{n-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... | 1.95*10^-4 g/L |
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