prompt list | ground_truth string |
|---|---|
[
{
"content": "Calculate the sum: $$\\sum_{k=1}^{n} \\frac{(-1)^{k+1}}{k} {n \\choose k}.$$",
"role": "user"
}
] | H_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... | +0.101 |
[
{
"content": "$ABCD$ is a trapezoid with the measure of base $\\overline{AB}$ twice the measure of the base $\\overline{CD}$. Point $E$ is the point of intersection of the diagonals. The measure of diagonal $\\overline{AC}$ is 11. Find the length of segment $\\overline{EC}$. Express your answer as a common frac... | \dfrac{11}{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... | The acceleration at t=2 is a(t) = (-1/4, 4), whose magnitude is sqrt(257)/4 and the direction is 93.576 degrees with respect to the x-axis. |
[
{
"content": "Let \\(\\kappa\\) and \\(\\lambda\\) be infinite cardinals. Consider a random function \\(\\phi: \\kappa \\times \\lambda \\rightarrow \\{0,1\\}\\) constructed by flipping a fair coin for each element of the domain. Determine the probability \\(P(\\kappa, \\lambda)\\) that there exists an \\(\\alp... | 0 |
[
{
"content": "Determine whether the statement \"$a^b + b^c + c^a$ is a multiple of 8 if and only if $a + b + c$ is a multiple of 8\" is true for odd natural numbers $a$, $b$, and $c$.",
"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... | Ba + 2H -> Ba^(2+) + 2H^(-) |
[
{
"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... | 438.6 N |
[
{
"content": "Let \\(\\varepsilon \\in (0,1)\\). Consider the functions \\(f_\\varepsilon(n)\\) and \\(g_\\varepsilon(n)\\) defined for all \\(n \\geq 2\\) as follows:\n\\[f_\\varepsilon(n) = \\left(\\frac{1-\\varepsilon}{1+\\varepsilon}\\right)\\left(\\frac{n^2}{\\ln(n^2)} + \\frac{(n+1)^2}{\\ln((n+1)^2)}\\rig... | Yes |
[
{
"content": "Determine the transcendence degree of the field \\( \\mathbf{Q}(x,y,\\exp(x),\\exp(y)) \\) using the Lindemann-Weierstrass Theorem.",
"role": "user"
}
] | 4 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.58*10^9 yr |
[
{
"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... | 1.01 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... | 212.3 |
[
{
"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... | -$43,020 |
[
{
"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... | 6,363 shares |
[
{
"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... | 103 nC |
[
{
"content": "Determine the real number $a$ for which the integral \\( \\int_0^{\\infty} \\frac{1-\\cos x}{x^a} \\, dx \\) converges.",
"role": "user"
}
] | (1, 3) |
[
{
"content": "Calculate the surface integral of the function \\( f(x, y, z) = x^2 + y^2 + z^2 \\) over the upper hemisphere of the sphere defined by \\( x^2 + y^2 + (z - 1)^2 = 1 \\).",
"role": "user"
}
] | 6\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... | 3.642*10^12 kWh |
[
{
"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... | 53 K |
[
{
"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... | 110.61 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... | 725.202*10^3 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... | 118 Hz |
[
{
"content": "Determine whether the Kolmogorov Extension Theorem holds without any assumptions on the topology of the state space. Answer with True or False.",
"role": "user"
}
] | False |
[
{
"content": "Find the differential of the integral \\( \\int_0^t B_s \\, ds \\) when interpreted as an Itô integral, where \\( B_s \\) is standard Brownian motion.",
"role": "user"
}
] | B_t \, dt |
[
{
"content": "Find the maximum value of \\( \\sum_{i=1}^n x_i \\) subject to the constraint \\( \\sum_{i=1}^n x_i^2 \\leq c \\), where \\( c \\) is a given constant.",
"role": "user"
}
] | \sqrt{nc} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 41.90 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... | 7.21% |
[
{
"content": "Evaluate the limit \\( \\lim_{x \\to 0} \\frac{e^x-1}{e^{2x}-1} \\) using the \\( \\delta - \\varepsilon \\) definition of a limit.",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Evaluate the limit if it exists: $$\\lim_{h\\to 0}\\frac{f(a+2h)-f(a-2h)}{h}$$ given that the function $f:\\mathbb{R}\\mapsto \\mathbb{R}$ satisfies $\\lim_{x\\to a}{\\frac{f(x)-f(a)}{x-a}}=2$. Provide your answer in a simplified form.",
"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... | 1.75 moles |
[
{
"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... | 0.1318 |
[
{
"content": "Minimize the expression: $$ \\left[\\cos ^{2}\\left(\\frac{\\theta }{2}\\right) + \\sqrt{1 - \\gamma}\\,\\sin^{2}\\left(\\frac{\\theta }{2}\\right)\\right] ^{2} + \\frac{\\gamma }{4}\\,\\sin^{2}\\left(\\theta\\right) $$ where $0 \\le \\gamma \\le 1$. Use half-angle formulas and differentiation to ... | 1 - \gamma |
[
{
"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... | 11129 |
[
{
"content": "Let $C \\subset \\mathbb{R}^2$ be an algebraic curve defined by an irreducible polynomial $P$. Suppose $Q \\in \\mathbb{R}[x,y]$ is another polynomial such that $Q(x,y) = 0$ on a set $A \\subset C$ where $A$ has a limit point. Does it follow that $P$ divides $Q$?",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\rightarrow \\infty}\\left \\{ \\frac{\\left ( n+1 \\right )\\left ( n+2 \\right )...3n}{n^{2n}} \\right \\}^{\\frac{1}{n}}$$",
"role": "user"
}
] | \dfrac{27}{e^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... | $66,300 |
[
{
"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... | 3216N |
[
{
"content": "Determine whether the limit \\( \\lim_{x \\to 0} \\frac{\\sin\\left(\\int_{x^3}^{x^2}\\left(\\int_{0}^{t}g(s^2)ds\\right)dt\\right)}{x^8} \\) converges, given that the function \\( g(x) \\) is differentiable for all \\( x \\in [-1,1] \\) and satisfies \\( g(0) = 0 \\) and \\( g'(0) = 1 \\).",
... | \dfrac{1}{12} |
[
{
"content": "Determine the largest interval around \\(x=0\\) where the function \\(f(x) = x^5 - 5x + 3\\) is invertible.",
"role": "user"
}
] | (-1, 1) |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\rightarrow\\infty}\\frac{n!}{(n-i)!}\\left(\\frac{c}{n}\\right)^{n-i} \\] where \\(c\\) and \\(i\\) are constants.",
"role": "user"
}
] | 0 |
[
{
"content": "Define the function $f(x) = 2x - 5$. For what value of $x$ is $f(x)$ equal to $f^{-1}(x)$?",
"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... | 483 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... | $17,335 |
[
{
"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... | 469.1Nm |
[
{
"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... | -52.99*10^{15} N/m |
[
{
"content": "Let \\(A\\) be a matrix in \\(\\mathbb{R}^{n \\times k}\\) with orthonormal columns. Determine the rank of the matrix \\(I_n - AA^T\\).",
"role": "user"
}
] | n - k |
[
{
"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... | 5.5436e-4 L |
[
{
"content": "Consider a linear transformation $B$ that maps a four-dimensional subspace $L$ of a five-dimensional vector space $V$ to a vector space $W$. If the intersection of the kernel of $B$ with $L$ is 0-dimensional, determine the possible dimensions of the image of $L$ under $B$. Provide your answer as a... | \{4\} |
[
{
"content": "In a cooperative game with symmetric players, is it possible for the core to contain allocations where the symmetric players receive unequal payoffs? Provide a yes or no answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Let $F = \\mathbb{Z}_2$ and consider the polynomial $f(x) = x^3 + x + 1 \\in F[x]$. Suppose $a$ is a root of $f(x)$ in some extension of $F$. Determine the number of elements in the field $F(a)$ and express each element of $F(a)$ in terms of $a$.",
"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... | $909.187 million |
[
{
"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... | 2333 g |
[
{
"content": "Construct a polynomial with integer coefficients such that \\( f(i + \\sqrt{2}) = 0 \\). The polynomial should be of even degree greater than 2.",
"role": "user"
}
] | x^4 - 2x^2 + 9 |
[
{
"content": "Evaluate the integral \\( \\int_{0}^{2\\pi} \\sin(c\\sin (dx))~dx \\) where \\(c\\) and \\(d\\) are constants.",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the cardinality of the set represented by \\( \\omega \\uparrow^\\omega \\omega \\), where \\( \\uparrow \\) denotes Knuth's up-arrow notation.",
"role": "user"
}
] | \aleph_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... | 0.063 |
[
{
"content": "Let \\( \\{A_n\\} \\) and \\( A \\) be bounded operators on a Hilbert space \\( H \\). Suppose:\n\n1. \\( A_n f \\to A f \\) for any \\( f \\in H \\).\n2. \\( \\|A_n\\| \\to \\|A\\| \\).\n\nIs it true that \\( A_n \\to A \\) in the operator norm on \\( \\mathcal{L}(H) \\)?",
"role": "user"
}... | No |
[
{
"content": "Find the Fourier Transform of the derivative of a function $f(t)$, given that the Fourier Transform of $f(t)$ is $F(s) = \\int_{-\\infty}^{\\infty} e^{-2 \\pi i s t} f(t) \\, dt$. Express the Fourier Transform of $f'(t)$, denoted as $G(s)$, in terms of $F(s)$. What is $G(s)$?",
"role": "user"
... | 2\pi i s F(s) |
[
{
"content": "Determine the principal period of the function \\( g(x) = \\frac{\\cos ^{2n}(x)}{\\cos ^{2n}(x)+\\sin ^{2n}(x)} \\), where \\( n \\in \\mathbb{N}^* \\) is a fixed positive integer.",
"role": "user"
}
] | \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... | $1,112.15 |
[
{
"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... | NaOH > NH4NO3 > Ba(NO3)2 > Al(NO3)3 > HNO3 |
[
{
"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... | 17.45 |
[
{
"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... | 2.37% |
[
{
"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... | 55.8 cm^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... | u = \sqrt{\frac{g(R^2+16H^2)}{8H}} |
[
{
"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... | clockwise |
[
{
"content": "A round pizza is $\\frac13$ of an inch thick and has a diameter of 12 inches. It is cut into 12 congruent pieces. What is the number of cubic inches in the volume of one piece? Express your answer in terms of $\\pi$.",
"role": "user"
}
] | \pi |
[
{
"content": "In convex quadrilateral $ABCD$, $AB=BC=13$, $CD=DA=24$, and $\\angle D=60^\\circ$. Points $X$ and $Y$ are the midpoints of $\\overline{BC}$ and $\\overline{DA}$ respectively. Compute $XY^2$ (the square of the length of $XY$).",
"role": "user"
}
] | \frac{1033}{4}+30\sqrt{3} |
[
{
"content": "Find the value of \\(a\\) in the interval \\((2, \\infty)\\) such that \\[ \\int_{0}^{1}\\frac{x^8-x^2}{x^{12}+ax^6+1}dx=-\\frac{\\pi}{24}. \\]",
"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... | 50.0 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... | 14459.53 |
[
{
"content": "Calculate the limit: $$\\lim_{x \\to 0}{(1+2x)}^{\\cot x}$$ without using logarithms.",
"role": "user"
}
] | e^2 |
[
{
"content": "Determine the minimum number of steps required to reach $2^{2018}$ starting from $1$, using only the operations of multiplying by $2$ or squaring the current number.",
"role": "user"
}
] | 17 |
[
{
"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... | $528.67 |
[
{
"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. $2,000 in cash
2. 100 shares of google stock
3. a $10.000 treasury bill
4. a 10,000 square foot office building |
[
{
"content": "Let $a$ be a zero of the polynomial $x^3 + x^2 + 1$ in some extension of $\\mathbb{Z}_2$. Find the multiplicative inverse of $a+1$ in this extension.",
"role": "user"
}
] | a^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... | 18.9 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... | 1592 kHz |
[
{
"content": "Evaluate the contour integral \\( \\oint_{|z|=1} \\frac{f(z)}{z^4} \\, dz \\), where \\( f(z) = \\sum_{k=0}^\\infty \\frac{k^3}{3^k}z^k \\).",
"role": "user"
}
] | 2\pi i |
[
{
"content": "Let \\( x, y, \\) and \\( z \\) be three positive real numbers whose sum is 1. If none of the numbers is greater than twice the sum of the other two, find the minimum value of the product \\( xyz \\). Choose from the following options:\n\n(A) \\( \\frac{1}{32} \\)\n(B) \\( \\frac{1}{36} \\)\n(C) \... | E |
[
{
"content": "When the graph of $y = 2x^2 - x + 7$ is shifted four units to the right, we obtain the graph of $y = ax^2 + bx + c$. Find $a + b + c$.",
"role": "user"
}
] | 28 |
[
{
"content": "Let $\\mathcal{H}$ be a Hilbert space. If $T \\in \\mathcal{L}(\\mathcal{H})$ is compact, is the set $\\{ x \\in S_{\\mathcal{H}} \\; |\\; \\| Tx\\| =\\| T\\| \\}$ nonempty, where $S_{\\mathcal{H}}$ denotes the unit sphere?",
"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... | $0.13 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.644 min |
[
{
"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... | 35% |
[
{
"content": "Find the smallest possible value of \\(|2011^m - 45^n|\\) for positive integers \\(m\\) and \\(n\\).",
"role": "user"
}
] | 14 |
[
{
"content": "Given $a+b+c=0$, simplify the expression:\n\\[ \\frac{(a^3-abc)^3+(c^3-abc)^3+(b^3-abc)^3}{(c^2-ab)(b^2-ac)(a^2-bc)} \\]",
"role": "user"
}
] | 3abc |
[
{
"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 tension in the left cord is 35 N, and the tension in the right cord is 25 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... | 1.02e3 m/s |
[
{
"content": "In a regular tetrahedron \\(ABCD\\), where \\(AC = 1\\), let \\(M\\) be the midpoint of \\(AC\\) and \\(N\\) be the centroid of \\(\\triangle BCD\\). If \\(DE \\perp AB\\) and \\(E\\) is the foot of the perpendicular, find the angle between the skew lines \\(MN\\) and \\(DE\\). Choose the correct ... | B |
[
{
"content": "Determine the Lebesgue measure of the set $A$ within the interval [0,1], where $A$ consists of numbers whose continued fraction expansions contain an infinite subsequence such that each term is divisible by its predecessor.",
"role": "user"
}
] | 1 |
[
{
"content": "Let $p(x)=\\sqrt{-x}$, and $q(x)=8x^2+10x-3$. The domain of $p(q(x))$ can be written in the form $a\\le x \\le b$. Find $b-a$.",
"role": "user"
}
] | \frac{7}{4} |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\to\\infty} \\frac{1}{n} \\left(\\frac{(2n+1)^{2n}}{2^{2n-1}}+\\frac{(2n+2)^{2n+1}}{2^{2n}}\\right)$$",
"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... | {\frac{1}{2}}\frac{{\left( {{a_1}{t_1} - {a_2}{t_2}} \right)^2}}{{{t_1} - {t_2}\left( {{a_1} - {a_2}} \right)}} |
[
{
"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... | Patent: $2,000
Trade name: $0
Internet domain name: $2,500
Goodwill: $0
Total: $4,500 |
[
{
"content": "Evaluate the limit: \\[ L_1 = \\lim_{x\\to 0}\\frac{\\text{erf}(x^2)}{\\text{erf}(x)}. \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Given that complex numbers $z_1$ and $z_2$ satisfy the equation $z+\\bar{z}=2|z-1|$, and $\\arg(z_1-z_2)=\\frac{\\pi}{4}$, find the value of $\\Im(z_1+z_2)$. Express your answer as a single number.",
"role": "user"
}
] | 2 |
[
{
"content": "The product $N$ of three positive integers is $6$ times their sum, and one of the integers is the sum of the other two. Find the sum of all possible values of $N$.",
"role": "user"
}
] | 336 |
[
{
"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... | 7.80 liters |
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