prompt list | ground_truth string |
|---|---|
[
{
"content": "How many distinct labeled simple undirected graphs with 10 vertices can be constructed if each vertex has an even degree?",
"role": "user"
}
] | 2^{36} |
[
{
"content": "In an equilateral triangle \\( \\triangle ABC \\), a point \\( M \\) is located inside the triangle such that \\( |MA|^2 = |MB|^2 + |MC|^2 \\). Determine the measure of \\( \\angle BMC \\).",
"role": "user"
}
] | 150^\circ |
[
{
"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... | -166 kcal |
[
{
"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... | 7.6 m/s |
[
{
"content": "Given the vector \\( v = \\left( \\frac{1}{2}, \\frac{1}{2}, \\frac{1}{2} \\right) \\) and the sequence of vectors defined by:\n\\[\n\\begin{aligned}\nw_1 &= (e, e+2, e-2), \\\\\nw_n &= v \\times w_{n-1} + (2, -4, 2) \\quad (n \\geq 2),\n\\end{aligned}\n\\]\nwhere \\( e \\) is Euler's number, find... | 12 |
[
{
"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... | 3/4 |
[
{
"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... | 0.012 |
[
{
"content": "Is it possible for a finitely generated module of constant finite rank over a non-semisimple ring to be non-free?",
"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... | The initially right moving glider moves left with velocity 3.36 m/s and the initially left moving glider moves left with velocity 0.29 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... | April: 75,100
May: 87,900
June: 111,800
Total: 274,800 |
[
{
"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... | 1.8 * 10^-8 mol/L |
[
{
"content": "Determine the values of $C$ for which the integral \\( \\int_0^{\\infty}\\left(\\frac{7x}{x^2+1}-\\frac{7C}{3x+1}\\right)dx \\) converges.",
"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... | 3 i + 8 j 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... | 0.415L from the 2.2 micro coulomb charge and 1.415L from the 4.4 micro coulomb charge |
[
{
"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... | 568.96 cm/sec |
[
{
"content": "An ellipse whose axes are parallel to the coordinate axes is tangent to the $x$-axis at $(4, 0)$ and tangent to the $y$-axis at $(0, 1).$ Find the distance between the foci of the ellipse.",
"role": "user"
}
] | 2\sqrt{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... | 1.69 |
[
{
"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... | 6.7 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... | 0.0168 m^3 |
[
{
"content": "Suppose that \\( \\ell_\\phi \\) is a reflexive Orlicz sequence space such that its dual space \\( \\ell_\\phi^* \\) is isomorphic to \\( \\ell_\\phi \\). Is \\( \\ell_\\phi \\) isomorphic to \\( \\ell_2 \\)?",
"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... | ```matlab
clc; close all
a=3*exp(j*0); b=4*exp(j*pi/6); c=a+b; vet=[a b c];
figure(1)
Vet=compass(vet)
set(Vet(2),{'xdata'},{get(Vet(2),'xdata')+real(vet(1))})
set(Vet(2),{'ydata'},{get(Vet(2),'ydata')+imag(vet(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... | 25.512 m |
[
{
"content": "Let \\( f: S^1 \\rightarrow S^1 \\) be the mapping defined by \\( f(z) = z^k \\) for some integer \\( k \\). Describe the induced homomorphism \\( f_*: \\pi(S^1, 1) \\rightarrow \\pi(S^1, 1) \\) in terms of the isomorphism \\( \\pi(S^1, 1) \\cong \\mathbb{Z} \\).",
"role": "user"
}
] | k |
[
{
"content": "Does the punctured non-orientable surface of genus $g$ deformation retract to a wedge of $g$ circles? Consider $N_g$, the non-orientable surface of genus $g$, obtained by gluing pairs of adjacent sides in a $2g$-gon. Let $X$ be the space $N_g$ without a point. Determine if $X$ deformation retracts... | 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... | 2.0e-9 M OH- |
[
{
"content": "Find the remainder when \\( \\sum_{r=0}^{1008}{2016 \\choose 2r}{3^{2016-2r}8^r} \\) is divided by 2017.",
"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... | 15 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... | 8 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... | -1.61e+2 J |
[
{
"content": "In a country with 100 cities connected by a road network, any city can be reached from any other city in only one way without any turns. The network's layout is known, and not all junctions and intersections necessarily represent cities. Any dead-end branch of the network always ends in a city. If... | 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... | MnO_4^- + 8H^+ + 5e^- \rightarrow Mn^{2+} + 4H_2O |
[
{
"content": "Determine the genus $g$ of a closed Riemann surface if its tangent bundle $T$ is trivial, given that the degree of the tangent bundle is given by the formula $\\deg(T) = 2 - 2g$. What is the value of $g$?",
"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... | 508.65 m |
[
{
"content": "Find the function $f(x)$ such that $f(0) = 1$ and \\[ f(x) = f'(x) + f''(x) + f'''(x) + \f''''(x) + \text{...} \\] where the series continues indefinitely.",
"role": "user"
}
] | e^{x/2} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 32.01% |
[
{
"content": "Given two polynomials $p(x)$ of degree $m$ and $q(x)$ of degree $k$, where the equation $p(x) = q(x)$ has at least $n+1$ distinct solutions, and $n \\geq m$ and $n \\geq k$, determine the relationship between $p(x)$ and $q(x)$. Provide a justification for your conclusion.",
"role": "user"
}
... | p(x) = q(x) |
[
{
"content": "In the floating point number system \\( F(10,10,-98,100) \\), calculate the number of significant decimal digits lost when subtracting \\( \\sqrt{1001} \\) from \\( \\sqrt{1002} \\).",
"role": "user"
}
] | 3 |
[
{
"content": "Given two random variables $X$ and $Y$, where $X$ follows a uniform distribution $U(1, 2)$, and the conditional distribution of $Y$ given $X$ is an exponential distribution $\\operatorname{Exp}(X)$, find the joint distribution of $X$ and $Y$ conditioned on the event $X \\leq 1.5$. Provide your ans... | 2x e^{-xy} |
[
{
"content": "Expand the function \\( f(z) = \\frac {2(z + 2)} {z^2 - 4z + 3} \\) in a Laurent series about the point \\( z = 1 \\) and determine the annulus \\( R \\) inside of which the series converges.",
"role": "user"
}
] | 0 < |z - 1| < 2 |
[
{
"content": "Compute the least squares polynomial of degree three for the function \\( f(x) = x^3 \\) on the interval \\((0, \\infty)\\) with respect to the weight function \\( w(x) = e^{-x} \\) using the Laguerre polynomials \\( L_1(x) = x - 1 \\), \\( L_2(x) = x^2 - 4x + 2 \\), and \\( L_3(x) = x^3 - 9x^2 + ... | x^3 |
[
{
"content": "Given integers \\( a, b, c > 1 \\) and \\( N > 1 \\), satisfying the equation \\( \\sqrt[a]{N \\sqrt[b]{N \\sqrt[c]{N}}} = \\sqrt[36]{N^{25}} \\), determine the value of \\( b \\).",
"role": "user"
}
] | 3 |
[
{
"content": "Given that $X$ is normally distributed with mean $0$ and variance $1$ ($X \\sim N(0,1)$), and for a given $X = x$, $Y$ follows a normal distribution with mean $x$ and variance $1$ ($Y \\sim N(x,1)$), determine the covariance between $X$ and $Y$. Provide your answer as a single numerical value.",
... | 1 |
[
{
"content": "Compute the covariance between $X_i$ and $Y = \\sum_{k=-\\infty}^{\\infty} a_k X_k$, where $X_i$, $i \\in \\mathbb{Z}$, are independent and identically distributed Gaussian variables with mean $0$ and variance $\\sigma_i^2$, $X_i \\sim \\mathcal{N}(0,\\sigma_i^2)$. The random variable $Y$ is distr... | a_i \sigma_i^2 |
[
{
"content": "Use the Divergence Theorem to evaluate the surface integral \\( \\iint\\limits_S F\\cdot dS \\) where \\( F(x,y,z)=xi+y^2j+(z+y)k \\) and \\( S \\) is the boundary of the region enclosed by the cylinder \\( x^2+y^2=4 \\) and the planes \\( z=x \\) and \\( z=8 \\).",
"role": "user"
}
] | 64\pi |
[
{
"content": "Determine the range of $p$ values in $1 \\leq p \\leq \\infty$ for which the function $f(x) = e^{-|x|^2}$ belongs to the $L^p(\\mathbb{R}^d)$ space, where integration is with respect to the $d$-dimensional Lebesgue measure.",
"role": "user"
}
] | [1, \infty] |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\to 0}\\dfrac{e^{-x^2/2}-\\cos(x)}{x^3\\sin(x)} \\]",
"role": "user"
}
] | \dfrac{1}{12} |
[
{
"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... | 2.8 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... | 1.25e-7 N in the negative y-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... | 1.52 s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.193 L |
[
{
"content": "Determine whether there exists an entire function $g(z)$ such that $|g(z) - e^{z}| \\leq 5|z|$ for all $z \\in \\mathbb{C}$.",
"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... | 638 g of NaHCO3 and 84.0 g of Na2CO3 |
[
{
"content": "Find the generator of the kernel of the homomorphism \\(\\phi : \\mathbb{R}[x] \\to \\mathbb{C}\\) defined by \\(f(x) \\mapsto f(2+i)\\).",
"role": "user"
}
] | x^2 - 4x + 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... | 16h_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... | 0.78 minutes |
[
{
"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... | 97.7 cm |
[
{
"content": "At an international meteorological conference, each participant announced the average monthly temperature in their hometown. All other participants recorded the product of their own city's temperature and the announced temperature. A total of 68 positive and 64 negative numbers were recorded. What... | 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... | 7 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... | 8.95 Mev/nucleon |
[
{
"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 m/s^2 |
[
{
"content": "Find the minimum value of \\[ A = \\frac{1}{\\sqrt{a^2+b^2+c^2+1}} - \\frac{2}{(a+1)(b+1)(c+1)} \\] for \\( a, b, c > 0 \\).",
"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... | $311.72 |
[
{
"content": "Given that \\( xy = 1 \\), find the maximum value of \\( A \\) such that the inequality \n\\[ ((x+y)^2+4)\\cdot ((x+y)^2-2) \\ge A\\cdot(x-y)^2 \\]\nholds true for all \\( x \\) and \\( y \\).",
"role": "user"
}
] | 18 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9.53% |
[
{
"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 |
[
{
"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... | 1.3 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... | 13.65% |
[
{
"content": "Let $A$ and $B$ be Hermitian matrices in $\\mathbf{M}_{n \\times n}(\\mathbb{C})$. If for every vector $v$ such that $v^*Av = 1$, it follows that $v^*Bv = 1$, does it necessarily mean that $A = B$? Assume that there exists a vector $v$ for which $v^*Av = 1$. Provide a justification for your answer... | A = B |
[
{
"content": "Find the maximum integer $k$ such that \\((7!)!\\) is divisible by \\((7!)^{k!} \\cdot (6!)!\\).",
"role": "user"
}
] | 6 |
[
{
"content": "Let \\( Y_1, Y_2, \\ldots, Y_n \\) be i.i.d. random variables with mean \\( \\mu \\) and variance \\( \\sigma^2 \\). Define the sample mean as \\( \\bar{Y}_n = \\frac{1}{n} \\sum_{i=1}^n Y_i \\). Consider the function \\( g(z) = z^2 \\). To what value does \\( g(\\bar{Y}_n) \\) converge in probabi... | \mu^2 |
[
{
"content": "Find the limit \\( \\lim_{n\\to\\infty} \\frac{a_1 b_n + a_2 b_{n-1} + \\cdots + a_n b_1}{n} \\) given that \\( \\lim_{n\\to\\infty} a_n = a \\) and \\( \\lim_{n\\to\\infty} b_n = b \\).",
"role": "user"
}
] | ab |
[
{
"content": "Consider the function \\( f(x) = 2 + x^{-2} \\) on the interval \\([2, \\infty)\\). Using the contraction mapping principle, determine the number of iterations required for the fixed-point iteration starting at \\( x_0 = 2 \\) to approximate the fixed point to three decimal places. The contraction... | 5 |
[
{
"content": "Evaluate the integral \\( \\int_{0}^1 \\binom{300}{10} x^{290}(1-x)^{10} \\, dx \\) using the method of adding the integral to itself after replacing \\( x \\) with \\( 1-x \\).",
"role": "user"
}
] | \dfrac{1}{301} |
[
{
"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... | 326759.50 |
[
{
"content": "Determine whether the function \\( g(x) = \\int_x^{x^2} \\frac{1}{\\ln t} \\, dt \\) has a finite limit as \\( x \\to 1 \\), given the inequalities \\( t - \\frac{t^2}{2} \\leq \\ln(1+t) \\leq t \\) and \\( \\frac{1}{t - \\frac{t^2}{2}} = \\frac{1}{t} + \\frac{\\frac{1}{2}}{1 - \\frac{t}{2}} \\)."... | \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... | 0.42 J |
[
{
"content": "Let $f_k(s) = \\frac{\\sin^2(ks)}{s^2}$ for $k \\geq 1$ and $s \\in (0, 1]$. Suppose there exists a constant $M$ such that \\( \\sum_{k=1}^\\infty f_k(s) p_k \\leq M \\) for all $s \\in (0, 1]$, where $p_k \\geq 0$. Can we conclude that \\( \\sum_{k=1}^\\infty k^2 p_k \\) is finite?",
"role": ... | 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... | 0.034 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... | 2.5 ft/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... | realitivistic |
[
{
"content": "Compute the volume of the solid bounded by the cone \\( z = 3\\sqrt{x^2 + y^2} \\), the plane \\( z = 0 \\), and the cylinder \\( x^2 + (y-1)^2 = 1 \\).",
"role": "user"
}
] | \dfrac{32}{3} |
[
{
"content": "Evaluate the integral \\( I = \\int_\\gamma \\frac{1}{z^2} \\, dz \\), where \\( \\gamma \\) is the upper half of the unit circle in the complex plane.",
"role": "user"
}
] | 2 |
[
{
"content": "Evaluate the limit \\( \\lim_{x \\to 0}\\left(\\frac{e^{ax}-e^{bx}}{\\sin(ax)-\\sin(bx)}\\right) \\) for any constants \\( a \\) and \\( b \\) without using L'Hopital's rule.",
"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... | 42.9 m/s at 21.1 degrees South of East |
[
{
"content": "Evaluate the integral \\( \\iint_D \\left[3-\\frac{1}{2}\\left( \\frac{x^2}{a^2}+\\frac{y^2}{b^2}\\right)\\right] \\, dx \\, dy \\) where \\( D \\) is the region defined by \\( \\frac{x^2}{a^2}+\\frac{y^2}{b^2} \\le 4 \\). Use a change of variables to simplify the integration.",
"role": "user"... | 8\pi ab |
[
{
"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. May 1, 2013:
Note Receivable: $6,900
Accounts Receivable: $6,900
(To record note received in exchange for accounts receivable)
2. Dec 31, 2013:
Interest Receivable: $276
Interest Revenue: $276
(To record accrued interest revenue on note)
3. May 1, 2014:
Cash: $7,314
Note Receivable: $6,900
Interest Receivable: $276
Interest Revenue: $138
(To record collection of principal and interest) |
[
{
"content": "Let \\(f: \\mathbb{R} \\to \\mathbb{R}\\) be a continuous, differentiable function such that \\(f(x) = 0\\) for any \\(x \\le 0\\) and \\(f(x) > 0\\) for \\(x > 0\\). Determine if there exists a positive real number \\(a\\) such that for any \\(x \\in (0, a]\\), \\(f'(x) > 0\\).",
"role": "use... | 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... | 783.31 |
[
{
"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... | $2,200U |
[
{
"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... | 0.02585 mg |
[
{
"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... | 0.440 m |
[
{
"content": "Let $f : \\mathbb{R} \\to \\mathbb{R}$ be a continuous function such that $f(1000) = 999$ and $f(x)f(f(x)) = 1$ for all real $x$. Determine the value of $f(500)$. \\( \\boxed{} \\)",
"role": "user"
}
] | \dfrac{1}{500} |
[
{
"content": "Find the minimum value of the expression \\(\\frac{ab}{c} + \\frac{bc}{a} + \\frac{ca}{b}\\), given that \\(a^2 + b^2 + c^2 = 1\\) and \\(a, b, c > 0\\).",
"role": "user"
}
] | \sqrt{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... | Cash Flow Statement Using Indirect Method
Cash Flow from Operating Activities
Net Profit 40,120
Adjustments
Depreciation 17,120
Loss on investment 10,120
Increase in accounts receivable -20,800
Decrease in account payable 10,000
Net Cash flow from operating activities 56,560
Cash Flow From Investing Activities
Sales on Investment 21,880
Purchase on land -43,120
Net Cash flow from Investing activities -21,240
Cash flow from Financing activities:
Proceeds from capital issued 30,000
Paid Cash dividend -15,120
Net Cash flow from financing activities 14,880
Net cash flow from all activities 50,200
Beginning Cash balance 25,120
Ending Cash Balance 75,320 |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\to 0} \\frac{e^{\\tan x} - e^x + \\ln(\\sec x + \\tan x) -x }{\\tan x - x}$$",
"role": "user"
}
] | \dfrac{3}{2} |
[
{
"content": "Given that the error sum of squares (SSE) is defined as \\(SSE = \\sum\\limits_{i}\\sum\\limits_{j} (X_{ij} - \\bar{X})^2\\) and follows \\(SSE/\\sigma^2 \\sim \\chi^2\\) with \\(I(J-1)\\) degrees of freedom, deduce that \\(E(SSE/I(J-1)) = \\sigma^2\\).",
"role": "user"
}
] | \sigma^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... | 2200 kJ/mol |
[
{
"content": "Determine whether the following statement is true or false: If every linear operator on a normed space $X$ is bounded, then $X$ is finite dimensional.",
"role": "user"
}
] | A |
[
{
"content": "In a group of nine people each person shakes hands with exactly two of the other people from the group. Let $N$ be the number of ways this handshaking can occur. Consider two handshaking arrangements different if and only if at least two people who shake hands under one arrangement do not shake ha... | 16 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\rightarrow \\infty} \\frac{\\sqrt{1}+\\sqrt{2}+\\sqrt{3}+\\ldots+\\sqrt{n}-\\frac{2}{3}n\\sqrt{n}}{\\sqrt{n}}. \\]",
"role": "user"
}
] | \dfrac{1}{2} |
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