prompt list | ground_truth string |
|---|---|
[
{
"content": "Determine the coefficient of \\(x^{17}\\) in the expansion of \\((3x^7 + 2x^5 -1)^{20}\\).",
"role": "user"
}
] | -41040 |
[
{
"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... | Total $36,000=$16,000+$20,000 |
[
{
"content": "In a city, there are 2019 metro stations, and some pairs of stations are connected by tunnels, allowing travel between any two stations. The mayor wants to organize several metro lines such that each line includes multiple distinct stations connected sequentially by tunnels, and each station is pa... | 1008 |
[
{
"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... | 9.4 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... | 3.64*10^29 kg |
[
{
"content": "Find the maximum value of the function \\( f(x,y) = (x+y)^4 + y^4 \\) subject to the constraint \\( x^4 + y^4 = 1 \\) using the method of Lagrange multipliers.",
"role": "user"
}
] | \dfrac{17}{2} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9.25% |
[
{
"content": "Determine the values of \\(p\\) for which the inequality \\(-9 < \\frac{3x^2 + px - 6}{x^2 - x + 1} < 6\\) holds for all real numbers \\(x\\).",
"role": "user"
}
] | (-3, 6) |
[
{
"content": "Determine the maximal compact interval for which the series \\( \\sum_{n=0}^{\\infty}(-1)^n\\frac{x^{2n+1}}{2n+1} = \\arctan(x) \\) converges. Provide your answer as an interval.",
"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... | 8.14 |
[
{
"content": "Determine whether the following statement is true or false: An absolutely continuous function, defined on a closed interval in \\(\\mathbb{R}\\), with a non-negative derivative almost everywhere, is necessarily monotone increasing (but not necessarily strictly increasing).",
"role": "user"
}... | A |
[
{
"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... | $900 |
[
{
"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... | 0.02748 m |
[
{
"content": "Evaluate the infinite series:\n\\[ \n\\sum_{n=1}^{\\infty} \\frac{\\left(\\frac{3}{2}\\right)^{f(n)} + \\left(\\frac{3}{2}\\right)^{-f(n)}}{\\left(\\frac{3}{2}\\right)^{n}},\n\\]\nwhere \\( f(n) \\) is the integer nearest to \\( \\sqrt{n} \\).",
"role": "user"
}
] | 5 |
[
{
"content": "Let \\( C \\) be the ellipse \\( \\frac{x^2}{4} + \\frac{y^2}{9} = 1 \\) traversed once in the positive direction. Define the function\n\\[\nG(z) := \\int_C \\frac{\\zeta^2-\\zeta+2}{\\zeta-z}\\, d\\zeta \\quad \\text{(for \\( z \\) inside \\( C \\))}\n\\]\nFind \\( G''(-i) \\).",
"role": "use... | 4\pi i |
[
{
"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... | 0.0023 |
[
{
"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... | 0.0883 m |
[
{
"content": "Solve the congruence \\(x^3 + x^2 - 5 \\equiv 0 \\pmod{7^3}\\) using Hensel's lemma.",
"role": "user"
}
] | 23 |
[
{
"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... | Comparative research |
[
{
"content": "Evaluate the line integral \\( \\int_C \\mathbf{f} \\cdot d\\mathbf{r} \\) where \\( \\mathbf{f} = (\\sin y, x\\cos y) \\), and the curve \\( C \\) is any closed circle.",
"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... | The value of equity is 120, and the value of debt is 40. |
[
{
"content": "In triangle ABC, where AB = AC = 25 and BC = 14, point P is located such that the perpendicular distances from P to each of the three sides of the triangle are equal. Determine the length of this equal distance.",
"role": "user"
}
] | \dfrac{21}{4} |
[
{
"content": "Suppose $\\sqrt{1 + \\sqrt{2y-3}} = \\sqrt{6}$; find $y$.",
"role": "user"
}
] | 14 |
[
{
"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 |
[
{
"content": "Calculate the condition number of the matrix product $X \\cdot Y$ with respect to the Frobenius norm, where $X \\in \\mathbb{R}^{M \\times N}$ and $Y \\in \\mathbb{R}^{N \\times P}$. Provide your answer as a single numerical value.",
"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... | 12.70% |
[
{
"content": "Given the function \\( f(x) = \\frac{x}{\\sqrt{1+x^2}} \\), find the value of \\( f^{(99)}(1) \\), where \\( f^{(n)}(x) \\) denotes the function \\( f \\) applied \\( n \\) times to \\( x \\).",
"role": "user"
}
] | \dfrac{1}{10} |
[
{
"content": "Let \\(ABC\\) be a triangle with area \\(\\Delta\\). The triangle \\(A'B'C'\\) is formed by the altitudes \\(h_a, h_b, h_c\\) of \\(ABC\\) as its sides, and has an area \\(\\Delta' = 30\\). The triangle \\(A''B''C''\\) is formed by the altitudes of \\(A'B'C'\\) and has an area \\(\\Delta'' = 20\\)... | 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... | $16,237.55 |
[
{
"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... | 232.33 |
[
{
"content": "Given a world population model with an initial population of 6 billion at time 0, increasing towards a limiting population of 30 billion, the rate of population growth at time $t \\geq 0$ is modeled by $\\frac{Ae^t}{(.02A+e^t)^2}$ billion people per year. Determine the time (to the nearest 0.1) wh... | 0.3 |
[
{
"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... | On April 1, 2015:
Debit Bonds Payable $1,181,475
Debit Discount on Bonds Payable $43,254
Credit Common Stock $626,400
Credit Paid-in Capital in Excess of Par $598,329 |
[
{
"content": "Given a probability space \\((\\Omega, \\mathcal{F}, \\mathbb{P})\\) where \\(\\Omega = (0,1]\\), \\(\\mathcal{F} = \\mathcal{B}((0,1])\\), and \\(\\mathbb{P}\\) is the Lebesgue measure \\(\\lambda\\), consider the following random variables:\n\n- \\(X_1(\\omega) = 0\\) for all \\(\\omega \\in \\O... | 0 |
[
{
"content": "Let $h(x)$ be a function defined as follows:\n\n$$h(x) = \\begin{cases}1, & 0 \\leq x \\leq 1\\\\ 0, & x < 0 \\text{ or } x > 1\\end{cases}$$\n\nShow that:\n\n$$\\int_{0}^{1} \\left|\\frac{1}{2 \\epsilon}\\int_{x-\\epsilon}^{x+\\epsilon}h(t) \\, dt \\right|\\, dx \\leq \\int_{0}^{1}|h(x)|\\, dx$$"... | \int_{0}^{1} \left|\frac{1}{2 \epsilon}\int_{x-\epsilon}^{x+\epsilon}h(t) \, dt \right|\, dx \leq \int_{0}^{1}|h(x)|\, dx |
[
{
"content": "Determine the real parameter \\(m\\) such that the substitution \\(y = z^m\\) transforms the differential equation \\(2x^4yy' + y^4 = 4x^6\\) into a first-order homogeneous differential equation.",
"role": "user"
}
] | \dfrac{3}{2} |
[
{
"content": "Let $A$, $B$, $C$, and $D$ be points in the plane with $AB=AC=BC=BD=CD=36$ and such that $A \\neq D$. Point $K$ lies on segment $AC$ such that $AK=2KC$. Point $M$ lies on segment $AB$, and point $N$ lies on line $AC$, such that $D$, $M$, and $N$ are collinear. Let lines $CM$ and $BN$ intersect at ... | 1632 |
[
{
"content": "Determine whether the statement is true or false: All subspaces of metrizable spaces are metrizable.",
"role": "user"
}
] | A |
[
{
"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... | 479 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... | 18.2 m/s |
[
{
"content": "Determine the set of cluster points of the set \\( \\left\\{\\frac{m}{10^n} : m \\in \\mathbb{Z}, n \\in \\mathbb{N}\\right\\} \\).",
"role": "user"
}
] | \mathbb{R} |
[
{
"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... | 1.71 s |
[
{
"content": "Given that \\(X\\) and \\(Y\\) are independent and identically distributed standard normal random variables, calculate the probability \\( P(X > 0 \\mid X + Y > 0) \\).",
"role": "user"
}
] | \dfrac{3}{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... | 2.97 |
[
{
"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... | 1.874M |
[
{
"content": "Determine the value of $k$ such that $n$ points located at the vertices of a convex $n$-gon and $k$ additional points inside the $n$-gon form isosceles triangles with any three of the $n+k$ points.",
"role": "user"
}
] | 1 |
[
{
"content": "Verify the correctness of the following solution for the expectation $E[e^{2 \\sqrt{2}(W_T-W_t)}]$, where $W_s$ is a Wiener process, $t$ is fixed, and $T > t$. Using Ito's lemma, the differential equation for $m(T) = E(Z_T)$ is derived as:\n\n$$m'(T) = 2\\sqrt{2}m(T)$$\n$$m(t) = 1$$\n\nThe propose... | e^{4(T - t)} |
[
{
"content": "Compute \\( \\sum_{k=0}^n \\binom{2n}{k} \\binom{n}{k} \\) using generating functions.",
"role": "user"
}
] | \dbinom{3n}{n} |
[
{
"content": "Determine whether it is possible to construct the fourth root of two using only a compass and straightedge. If it is possible, describe the construction process.",
"role": "user"
}
] | \sqrt[4]{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... | 961 Hz |
[
{
"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... | 0.419 |
[
{
"content": "Determine the cardinality of the quotient ring of Gaussian integers when factored by a non-zero element with relatively prime components.",
"role": "user"
}
] | a^2 + b^2 |
[
{
"content": "Determine the range of values for the parameter $a$ such that the inequality \\( x^{-3} e^{x} - a \\ln x \\geq x + 1 \\) holds for all \\( x \\in (1, +\\infty) \\).",
"role": "user"
}
] | (-\infty, -3] |
[
{
"content": "Determine whether the sequence of functions $v_n''(x)$, where $v_n(x)=\\frac{x^{2n}}{2n(2n+1)}$, converges to a continuous function in $L^2([0,1])$ as $n \\to \\infty$. Provide a justification for your answer.",
"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... | 72.7 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... | 87.825 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... | The magnitude is 28.44 and the direction is 7.5 degrees above the x-axis. |
[
{
"content": "Evaluate the infinite nested radical: \\(\\sqrt{1+ 2 \\sqrt{1+3 \\sqrt{1+\\dots\\infty}}}\\).",
"role": "user"
}
] | 3 |
[
{
"content": "Given a sequence $(a_n)$ of positive real numbers where $\\sum_{n=1}^\\infty a_n$ diverges and $\\lim_{n \\rightarrow \\infty} a_n = 0$, determine if it is possible to construct a subsequence $(a_{n_k})$ such that $\\sum_{k =1}^\\infty a_{n_k}$ converges to any arbitrary positive real number $a$. ... | Yes |
[
{
"content": "Calculate the Generalized Directional Derivative (Clarke Derivative) of the function \\( f(x) = -|x| \\) at the point \\( x = 0 \\).",
"role": "user"
}
] | |v| |
[
{
"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... | 192.5636 g/mol |
[
{
"content": "There are 7 dwarfs, D1 through D7, and 7 tasks, T1 through T7, in a mine. Each dwarf can perform exactly one task. However, D1 cannot perform T1, D4 cannot perform T2, D5 cannot perform T6, and D6 cannot perform T3 or T7. Determine the number of ways to assign the tasks to the dwarfs under these c... | 2364 |
[
{
"content": "Find the steady-state solution of the differential equation \\( \\frac{\\partial^2u}{\\partial x^2}+\\gamma^2(u-T)=\\frac{1}{k}\\frac{\\partial u}{\\partial t} \\) for \\( 0<x<a, \\ t>0 \\), with boundary conditions \\( u(0,t)=T \\), \\( u(a,t)=T \\) for \\( 0<t \\), and initial condition \\( u(x,... | T |
[
{
"content": "Evaluate the integral \\( I = \\int_{0}^{\\infty} \\delta(\\sin(\\pi x)) \\cdot 2^{-x} \\, dx \\), where \\( \\delta(b(x)) \\) is the Dirac delta function with \\( b(x) = \\sin(\\pi x) \\).",
"role": "user"
}
] | \dfrac{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... | 3.76% |
[
{
"content": "Calculate the surface integral \\( \\iint_{S} \\text{curl}(\\vec{F}) \\cdot \\vec{dS} \\) for the vector field \\( \\vec{F} = -y\\vec{i} + x\\vec{j} + xyz\\vec{k} \\), where \\( S \\) is the part of the sphere \\( x^2 + y^2 + z^2 = 25 \\) below the plane \\( z = 4 \\) and is oriented positively. T... | -18\pi |
[
{
"content": "In a volleyball tournament, there are \\( n \\) teams from city \\( A \\) and \\( 2n \\) teams from city \\( B \\). Each team plays exactly one game with every other team. The ratio of the number of wins by the teams from city \\( B \\) to the number of wins by the teams from city \\( A \\) is \\(... | 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... | 1.1782e5 |
[
{
"content": "Evaluate the integral \\( \\int_{|z+1|=2} \\frac{z^2}{4-z^2}dz \\) using the residue theorem.",
"role": "user"
}
] | 2\pi i |
[
{
"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... | 1.06 m |
[
{
"content": "Given the function \\(f(x) = \\frac{1}{2}(x + \\sqrt{x^2 + 4})\\), find the value of \\(f^{-1}(x) + f^{-1}(\\frac{1}{x})\\) for \\(x \\neq 0\\).",
"role": "user"
}
] | 0 |
[
{
"content": "Find the minimum value of the function \\(g(x) = \\sqrt{x + 16} + \\sqrt{25 - x} + \\sqrt{x - 9}\\) for \\(9 \\leq x \\leq 25\\) without using calculus or a calculator.",
"role": "user"
}
] | 9 |
[
{
"content": "Find the 2002th term of a binary sequence defined as follows: Start with $S_1 = 0$. For $k \\ge 2$, obtain $S_k$ from $S_{k-1}$ by replacing every 0 with 01 and every 1 with 001. The sequence satisfies $S_k = S_{k-1}S_{k-2}S_{k-1}$ for all $k \\ge 3$. What is the 2002th term of this sequence?",
... | 0 |
[
{
"content": "Two people enter adjacent lines in a grocery store. The service time for person A is exponentially distributed with a mean of 4 minutes, and the service time for person B is exponentially distributed with a mean of 6 minutes. What is the probability that person A finishes their service before pers... | \dfrac{3}{5} |
[
{
"content": "Given the probability density function (PDF) of a random variable X as:\n\n$$f(x) = \\begin{cases} e^{-x} & x > 0, \\\\ 0 & x \\leq 0, \\end{cases}$$\n\nfind the PDF of the random variable Y, where $Y = X^{1/2}$. Provide the expression for the PDF of Y.",
"role": "user"
}
] | 2y e^{-y^2} |
[
{
"content": "A regular tetrahedron is a pyramid with four faces, each of which is an equilateral triangle.\n\nLet $ABCD$ be a regular tetrahedron and let $P$ be the unique point equidistant from points $A,B,C,D$. Extend $\\overrightarrow{AP}$ to hit face $BCD$ at point $Q$. What is the ratio $PQ/AQ$ ?",
"r... | \frac{1}{4} |
[
{
"content": "Verify if the inequality \\( \\pi(100 + 200) - \\pi(200) \\leq \\pi(100) \\) holds true.",
"role": "user"
}
] | True |
[
{
"content": "Determine whether an absolutely convergent series can always be split into its even and odd components without affecting the sum.",
"role": "user"
}
] | Yes |
[
{
"content": "A father went for a walk with his sons and mentioned that the age of the oldest son is equal to the sum of the ages of his two other brothers. The sons replied that the product of their ages and the father's age equals the sum of the cube of the number of sons, multiplied by a thousand, and ten ti... | 34 |
[
{
"content": "Given the system of equations for real numbers \\(x, y, z\\):\n\\[ x + y + z = 3 \\]\n\\[ x^2 + y^2 + z^2 = 9 \\]\n\\[ xyz = -2 \\]\nFind the value of \\(x^4 + y^4 + z^4\\).",
"role": "user"
}
] | 57 |
[
{
"content": "Find the least number \\( c \\) such that \\( \\sum_{i=1}^n x_i^2 \\leq cn \\) for all real numbers \\( x_1, x_2, \\ldots, x_n \\) where each \\( x_i \\geq -1 \\) and \\( \\sum_{i=1}^n x_i^3 = 0 \\).",
"role": "user"
}
] | \dfrac{4}{3} |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\rightarrow 0} e^{-\\frac{1}{x^2}}\\cdot \\frac{2}{x^3}$$",
"role": "user"
}
] | 0 |
[
{
"content": "Find the product of all the solutions of the equation \\(x^{1+\\log_{10}x} = 100000x\\).",
"role": "user"
}
] | 1 |
[
{
"content": "Calculate the mass of an object in the $x$-$y$ plane that lies above the disk $x^2 + y^2 \\leq 1$ and below the sphere $x^2 + y^2 + z^2 = 4$, with a density function $\\rho(x, y, z) = 2z$. Express the mass as $\\iiint_R 2z\\,dV$, where $R$ is the region of the object. Determine the limits for inte... | \dfrac{7\pi}{2} |
[
{
"content": "Given that on the interval \\([1,2]\\), the functions \\( f(x) = x^2 + px + q \\) and \\( g(x) = x + \\frac{1}{x^2} \\) attain the same minimum value at the same point, determine the maximum value of \\( f(x) \\) on this interval. Choose the correct answer from the options below:\n\nA. \\( 4 + \\f... | 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... | 412 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... | $542.16 |
[
{
"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 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... | Normal stress in steel: 3144.8Pa
Normal stress in concrete: 470.4Pa |
[
{
"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... | $10.00 |
[
{
"content": "Evaluate the limit: \\[ \\lim \\limits_{x \\to \\infty} x\\int_{0}^{x}e^{t^2-x^2}dt \\]",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Let $G$ be a finite group, $N$ a normal subgroup of $G$, and $K$ a characteristic subgroup of $N$. Given that $Z(G/N) = 1$ and $Z(G) = 1$, determine if it follows that $Z(G/K) = 1$.",
"role": "user"
}
] | No |
[
{
"content": "Consider two Sobolev spaces $H^s(\\mathbb{R}^n)$ and $H^t(\\mathbb{R}^n)$ where $s > t$. Let $V$ be a linear subspace of $H^s(\\mathbb{R}^n)$ such that there exists a constant $C$ for which $\\|f\\|_{H^s} \\leq C\\|f\\|_{H^t}$ for any $f \\in V$. Is $V$ necessarily finite-dimensional?",
"role"... | 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... | T=mb^2/r |
[
{
"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... | I = (1/6)ma^2 |
[
{
"content": "Let $p(x)$ be a fifth-degree polynomial such that $p(x)+1$ is divisible by $(x-1)^3$ and $p(x)-1$ is divisible by $(x+1)^3$. Find the value of the definite integral $\\int_{-10}^{10}p(x)\\,dx$. \\( \\text{Express your answer as a single number.} \\)",
"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... | 9.05 degrees Celsius |
[
{
"content": "Let $E$ be a compact subset of an open subset $U$ of the Euclidean plane. Is there a radius $r > 0$ such that for each point $z \\in E$, the closed disc $\\bar{D}(z, r)$ is contained in $U$?",
"role": "user"
}
] | Yes |
[
{
"content": "There are \\( n \\) people, and any two of them can have at most one phone call between them. The total number of phone calls among any \\( n-2 \\) of these people is \\( 3^m \\), where \\( m \\) is a natural number. Determine all possible values of \\( n \\).",
"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... | 34.9 degrees |
[
{
"content": "Find the limit of the sequence of functions as \\( n \\to \\infty \\):\n\n\\[ \\lim_{n\\to\\infty}\\sup_{x\\in[0,1]}\\left|\\frac{x}{x^2+(n^2+1)}-\\frac{1}{2\\sqrt{n^2+1}}\\right| \\]",
"role": "user"
}
] | 0 |
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