prompt list | ground_truth string |
|---|---|
[
{
"content": "Determine the condition on the matrix $C$ such that the linear map $\\varphi_C : V \\to V$, defined by $A \\mapsto CA$, is selfadjoint with respect to the scalar product $\\langle A, B \\rangle = \\operatorname{tr}(A^t B)$, where $V = M_{n\\times n}(\\mathbb{R})$. Provide your answer in terms of p... | C = C^\top |
[
{
"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... | 11.4mT out of the plane |
[
{
"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... | 0.105 N |
[
{
"content": "Suppose $p, q, r$ are prime numbers such that $pqx, qry, rpz$ are within a factor of $2$ of each other. Determine the number of distinct integers that the expression $pqx + qry + rpz$ can represent, where $x, y, z$ are integers satisfying $0 < x < (pq)^\\alpha$, $0 < y < (qr)^\\alpha$, and $0 < z ... | 7 |
[
{
"content": "Let \\((r_k)_{k \\in \\mathbb{N}}\\) be an enumeration of \\(\\mathbb{Q}\\). Define \\(U_{1/p} = \\bigcup_{k \\in \\mathbb{N}} \\left(r_k - \\frac{1/p}{2^k}, r_k + \\frac{1/p}{2^k}\\right) \\subset \\mathbb{R}\\). Determine the set \\(\\bigcap_{p \\in \\mathbb{N}^*} U_{1/p}\\).",
"role": "user... | \mathbb{Q} |
[
{
"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... | 161 mph |
[
{
"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... | 11129.67 sec |
[
{
"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 ft/s |
[
{
"content": "Compute the limit \\(\\lim_{(x,y) \\to (1,0)} \\frac{\\cos{\\sqrt{xy}}-1}{y}\\).",
"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... | 1.455 cm |
[
{
"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... | 2.83 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... | 760.44 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... | 9.05 |
[
{
"content": "Let $A$ be an $n \\times n$ matrix over $\\mathbb{C}$ for which every nonzero vector in $\\mathbb{C}^n$ is an eigenvector. Determine which of the following statements is true:\n\n1. All eigenvalues of $A$ are equal.\n2. All eigenvalues of $A$ are distinct.\n3. $A = \\lambda I$ for some $\\lambda \... | 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... | 511.11 N/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... | 90 km/hr |
[
{
"content": "[asy] fill(circle((4,0),4),grey); fill((0,0)--(8,0)--(8,-4)--(0,-4)--cycle,white); fill(circle((7,0),1),white); fill(circle((3,0),3),white); draw((0,0)--(8,0),black+linewidth(1)); draw((6,0)--(6,sqrt(12)),black+linewidth(1)); MP(\"A\", (0,0), W); MP(\"B\", (8,0), E); MP(\"C\", (6,0), S); MP(\"D\... | 1:4 |
[
{
"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... | $19,220 |
[
{
"content": "Calculate the sum \\( \\sum_{n=1}^{\\infty} \\frac{2}{n(n+1)} \\).",
"role": "user"
}
] | 2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.523 J |
[
{
"content": "Evaluate the integral \\( \\int_0^{\\pi} \\frac{1}{1 + 3\\sin^2x}dx \\).",
"role": "user"
}
] | \dfrac{\pi}{2} |
[
{
"content": "Solve the logarithmic equation: \\[ 1 - \\dfrac{1}{x} + \\ln x = 0 \\] without assuming that \\( \\ln(1)=0 \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Given a signal $s(t)$ sampled at $1000$ observations, where $h(k) = s(k\\Delta t + t_0)$ for $k = 0, 1, \\dots, 999$, with $\\Delta t = 1/200$ and $t_0 = -2$ seconds, the discrete Fourier transform $|\\hat{h}(m)|$ has its largest values at $m = 193$ and $m = 807$. What is the corresponding positiv... | 39 |
[
{
"content": "Determine whether the ring $R = K[X]/(X^n)$ consists of all polynomials of degree less than $n$. Justify your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "A rhombus has an area of 108 square units. The lengths of its diagonals have a ratio of 3 to 2. What is the length of the longest diagonal, in units?",
"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... | $2 million |
[
{
"content": "Given the system of equations \\(a x + b y = 1\\) and \\(x^{2} + y^{2} = 50\\), determine the number of real pairs \\((a, b)\\) such that there is at least one solution, and all solutions \\((x, y)\\) are integer solutions.",
"role": "user"
}
] | 72 |
[
{
"content": "Determine whether it is possible to partition the unit interval $[0, 1]$ into subsets, each containing exactly three elements.",
"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... | 210.15 N/m |
[
{
"content": "Evaluate $\\left\\lceil-\\sqrt{\\frac{49}{4}}\\right\\rceil$.",
"role": "user"
}
] | -3 |
[
{
"content": "Determine whether there exist infinite groups whose center is trivial but have non-trivial characteristic subgroups.",
"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... | 2.13e+27 kg |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1. Differences in fiscal policies (e.g., Reagan tax cuts in the US vs. conservative fiscal policies in some European countries)
2. Interaction between macroeconomic recessions and technological change (e.g., impact on skilled labor demand, supply, and wages)
3. Differences in job search methods (e.g., active job search... |
[
{
"content": "Determine whether the following statement is true or false: If $f(x,y)$ is a continuous function on $\\mathbb{R}^2$ with $f(x,y) > 0$ for all $(x,y)\\in\\mathbb{R}^2$, then for any continuous function $g(a)$ on $\\mathbb{R}$, there exists a unique continuous function $h(a)$ on $\\mathbb{R}$ such t... | 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... | 631 N |
[
{
"content": "Determine the number of distinct ways to label the vertices of a cube with the integers 1 through 8, without repetition, such that the sum of the numbers on the four vertices of each face is the same. Arrangements that can be obtained through rotations of the cube are considered identical. How man... | 6 |
[
{
"content": "Suppose $f \\in R := \\mathbb{C}[[z_1, \\dots, z_n]]$ is a formal power series in several variables such that $f(0) \\neq 0$. If $f$ converges absolutely in a neighborhood of $0$, does the formal inverse $\\frac{1}{f}$ also converge absolutely in a neighborhood of $0$?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the smallest natural number \\( n \\) such that for any prime number \\( p \\), if \\( n \\) is divisible by \\( p-1 \\), then \\( n \\) is also divisible by \\( p \\).",
"role": "user"
}
] | 1806 |
[
{
"content": "Given the coordinates of the points $P_1, P_2, \\ldots, P_n$, which are the vertices of a regular n-gon, determine if these points lie on an ellipse.",
"role": "user"
}
] | Yes |
[
{
"content": "Find all pairs of natural numbers \\((x, y)\\) such that \\(5^x + 3^y\\) is a perfect square.",
"role": "user"
}
] | \emptyset |
[
{
"content": "Evaluate the limit of the function \\( f(x) = \\frac{\\tan(\\pi x)}{2x - 1} + \\frac{2}{\\pi(2x - 1)^2} \\) as \\( x \\to \\frac{1}{2} \\). Determine whether the limit exists or if the function diverges at this point.",
"role": "user"
}
] | \dfrac{\pi}{6} |
[
{
"content": "Find the maximum value of $k$ such that \\( \\frac{1001 \\cdot 1002 \\cdot \\cdots \\cdot 2005 \\cdot 2006}{11^{k}} \\) is an integer, where $1 \\le k$ is a natural number.",
"role": "user"
}
] | 101 |
[
{
"content": "Given a probability space $(\\Omega, \\Sigma, P)$, where $X: \\Omega \\to \\mathbb{R}$ and $Y: \\Omega \\to \\mathbb{R}$ are jointly continuous random variables with marginal density functions $f_X$ and $f_Y$ and joint density function $f_{X,Y}$. The conditional density function of $X$ given $Y$ i... | 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... | 13.8% |
[
{
"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... | 1.8 cm |
[
{
"content": "The average age of 33 fifth-graders is 11. The average age of 55 of their parents is 33. What is the average age of all of these parents and fifth-graders?",
"role": "user"
}
] | 24.75 |
[
{
"content": "Each solution to $x^2 + 5x + 8 = 0$ can be written in the form $x = a + b i,$ where $a$ and $b$ are real numbers. What is $a + b^2$?",
"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... | 632,285 |
[
{
"content": "Given an $n$-dimensional lattice $L$ and its Voronoi cell $\\mathcal{V}$, defined as $\\{x\\in \\mathbb{R}^n: ||x|| \\le ||x-v||, \\text{ for all } v\\in L\\}$, determine whether there always exists a Voronoi relevant vector $v$ such that $||v|| < ||\\lambda||$, for an arbitrary non-Voronoi releva... | 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... | 327.5 degrees |
[
{
"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... | 63.5571 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... | 1) Closing inventory Dr. $4,994
Trading account Cr. $4,994
(Being closing inventory recorded)
2) closing inventory Dr. $ 4,994
Purchase account Cr. $4,994
( being closing inventory recorded) |
[
{
"content": "Find the maximal value of the sum \\( \\sum_{n=0}^{\\infty} a_n \\), where \\( a_n \\) is the distance from a real number \\( a \\) to the nearest number of the form \\( \\frac{m}{2^n} \\) with \\( m \\in \\mathbb{Z} \\).",
"role": "user"
}
] | \dfrac{2}{3} |
[
{
"content": "If \\( \\theta: R \\to S \\) is an isomorphism of topological rings, does the restriction \\( \\theta|_{R^{\\times}}: R^{\\times} \\to S^{\\times} \\) result in a topological group isomorphism when restricted to their groups of units?",
"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... | 352.28 |
[
{
"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... | 12.037% |
[
{
"content": "Let \\(f(z)\\) be an analytic function on the domain \\(D = \\{(x,y) : |x| \\leq a, |y| \\leq b, a \\geq b\\}\\). If \\(|f(z)| \\leq M\\) on the boundary of \\(D\\), which of the following can be taken as the upper bound for \\(|f'(0)|\\)?\n\n(A) \\(\\frac{2M(a+b)}{\\pi ab}\\)\n\n(B) \\(\\frac{2\\... | A |
[
{
"content": "Minimize the function \\( f(x, y) = 2x + xy + 3y \\) subject to the constraints:\n\\[ \\begin{cases} x^2 + y \\geq 3 \\\\ x \\geq 0 \\\\ y \\geq 0 \\end{cases} \\]\nDetermine the minimum value of \\( f(x, y) \\) and the corresponding values of \\( x \\) and \\( y \\).",
"role": "user"
}
] | 2\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... | 27000 light years from the center of the Milky Way Galaxy |
[
{
"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... | 61 |
[
{
"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... | Sales: 1,920,000
Cost of goods sold: 1,000,000
Variable administrative expense: 300,000
Variable selling expense: 100,000
Total variable expenses: 1,400,000
Contribution margin: 520,000
Fixed selling expense: 86,000
Fixed administrative expense: 57,000
Total fixed expenses: 143,000
Net income: 377,000 |
[
{
"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... | 61.39 |
[
{
"content": "Determine all real numbers \\( a_0 \\) such that the sequence \\( a_0, a_1, a_2, \\ldots \\) defined by the recurrence relation \\( a_{n+1} = 2^n - 3a_n \\) for \\( n \\geq 0 \\) is strictly increasing.",
"role": "user"
}
] | \dfrac{1}{5} |
[
{
"content": "Evaluate the limit: $$\\lim_{N\\to\\infty}N^2\\sum^{N-1}_{k=1}\\left(\\frac{k}{N}\\right)^{N\\ln N}$$",
"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... | 12470 |
[
{
"content": "Does there exist a function that is continuous everywhere except on a countable dense subset and is bounded, meaning the supremum of the function is a finite number?",
"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... | 0.4995 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... | $25,500.20 |
[
{
"content": "Given the quartic equation \\(x^4 + kx^2 + 90x - 2009 = 0\\) with roots \\(x_1, x_2, x_3, x_4\\), where \\(x_1x_2 = 49\\), find the value of \\(k\\) using Vieta's formulas.",
"role": "user"
}
] | 7 |
[
{
"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 cm |
[
{
"content": "Let $H$ be a Hilbert space and $\\{a_n\\}$ be a sequence in $H$. If $a_n$ converges weakly to $a$ but $\\lVert a_n \\rVert \\nrightarrow \\lVert a \\rVert$, does it follow that $a_n$ does not converge to $a$ in the norm topology?",
"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... | 3.3e-3 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... | 55 feet |
[
{
"content": "Given a smooth curve \\(\\alpha:I\\to \\mathbb{R}^3\\) with \\([a,b]\\subset I\\), if the equation \\(|\\alpha(b)-\\alpha(a)| = \\int_a^b |\\alpha'(t)|dt\\) holds, does this imply that the curve is a line segment between the points \\(\\alpha(a)\\) and \\(\\alpha(b)\\)? Justify your answer.",
... | Yes |
[
{
"content": "Evaluate the limit of the infinite product as \\( n \\) approaches infinity:\n\n\\[\n\\lim_{n \\to \\infty} \\left(1 - \\frac{2}{3}\\right)^{\\frac{3}{n}} \\left(1 - \\frac{2}{4}\\right)^{\\frac{4}{n}} \\left(1 - \\frac{2}{5}\\right)^{\\frac{5}{n}} \\ldots \\left(1 - \\frac{2}{n+2}\\right)^{\\frac... | e^{-2} |
[
{
"content": "Find the closest point on the parabola given by the equation \\(2x^2 - 4xy + 2y^2 - x - y = 0\\) to the line \\(9x - 7y + 16 = 0\\). Use the distance formula \\(d = \\frac{|ax_0 + by_0 + c|}{\\sqrt{a^2 + b^2}}\\) to determine the distance from a point \\((x_0, y_0)\\) to the line \\(ax + by + c = ... | (3, 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... | 214.74 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... | 1.3e-6 N |
[
{
"content": "Let \\( f : \\mathbb{R} \\to \\mathbb{R} \\) be a function such that \\( f(f(x - y)) = f(x) f(y) - f(x) + f(y) - xy \\) for all real numbers \\( x \\) and \\( y \\). Find the sum of all possible values of \\( f(1) \\).",
"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... | Work-in-Progress $21,580 (Debit)
Standard Overhead Applied $20,000 (Credit)
Volume Variance $2,080 (Debit)
Spending Variance $150 (Debit)
Efficiency Variance $650 (Credit) |
[
{
"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... | -$1,323,825 |
[
{
"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... | $84,500 |
[
{
"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... | PbCl_2(s) |
[
{
"content": "Determine the radius of convergence for the power series \\( \\sum_{n=0}^{\\infty} 2^{2n} x^{n^2} \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Given a transition function \\( \\delta : (Q \\setminus F) \\times \\Gamma \\to Q \\times \\Gamma \\times \\{L, R, S\\} \\), where \\( \\Sigma = \\{0, 1\\} \\) and \\( \\Gamma = \\{0, 1, \\flat\\} \\), and \\( |Q| = t \\), determine why the number of possible functions \\( \\delta \\) is \\((9t)^{... | (9t)^{3t} |
[
{
"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... | 61.037 g |
[
{
"content": "Differentiate the function \\( \\log(\\Gamma(x + r)) \\) with respect to \\( r \\). Express your answer in terms of the digamma function.",
"role": "user"
}
] | \psi(x + 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... | 1032ft |
[
{
"content": "Compute the circulation of the vector field \\( \\mathbf{a} = y e^{x y} \\mathbf{i} + x e^{x y} \\mathbf{j} + x y z \\mathbf{k} \\) along the path \\( L \\), which is the intersection of the cone \\( x^{2} + y^{2} = (z-1)^{2} \\) with the coordinate planes.",
"role": "user"
}
] | 0 |
[
{
"content": "Calculate the genus of the projective curve given by the equation \\(3x^{3}+4y^{3}+5z^{3} = 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... | 887.325 Joules |
[
{
"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... | 1.983 |
[
{
"content": "Let $x_i \\in [-11, 5]$ for $i = 1, 2, \\ldots, 2014$, and suppose $x_1 + x_2 + \\cdots + x_{2014} = 0$. Determine the maximum value of $x_1^2 + x_2^2 + \\cdots + x_{2014}^2$. \\(\\text{Express your answer as a single number.}\\)",
"role": "user"
}
] | 110710 |
[
{
"content": "Solve the inequality: $$5 \\times \\frac{3^{x-2}}{3^{x} - 2^{x}} \\geq 1 + \\left(\\frac{2}{3}\\right)^x$$",
"role": "user"
}
] | (0, 1] |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -37.368 kJ/mol |
[
{
"content": "Determine which of the following functions is entire: \\(\\sin(\\sqrt{z})\\) and \\(\\cos(\\sqrt{z})\\).",
"role": "user"
}
] | \cos(\sqrt{z}) |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.03% |
[
{
"content": "In triangle $ABC$, $AB = 13$, $AC = 15$, and $BC = 14$. Let $I$ be the incenter. The incircle of triangle $ABC$ touches sides $BC$, $AC$, and $AB$ at $D$, $E$, and $F$, respectively. Find the area of quadrilateral $AEIF$.\n\n[asy]\nimport geometry;\n\nunitsize(2 cm);\n\npair A, B, C, D, E, F, I... | 28 |
[
{
"content": "A construction set consists of rectangular parallelepipeds that fit into a box of the same shape. If one dimension of each parallelepiped is reduced, is it always possible to reduce one dimension of the box while still fitting all the parallelepipeds inside, assuming their edges remain parallel to... | No |
[
{
"content": "What is the minimum value of \\( n \\) such that when 160 pigeons are distributed into \\( n \\) holes according to the rule that the \\( i \\)-th pigeon goes to the \\(((i^2) \\mod n)\\)-th hole, each hole contains at most one pigeon?",
"role": "user"
}
] | 331 |
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