prompt list | ground_truth string |
|---|---|
[
{
"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... | $31134.50 |
[
{
"content": "Find the global minimum of the function \\( f(x, y) = x^4 + y^4 + 4x^2 - xy + y^2 + 6 \\).",
"role": "user"
}
] | 6 |
[
{
"content": "Evaluate the line integral \\( \\int_{C} \\frac{x}{y} \\, \\mathrm{d}x + \\frac{y}{x} \\, \\mathrm{d}y \\) where \\( C \\) is the circle \\( x^2 + y^2 = 9 \\) traversed counterclockwise.",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the limit: \\[ \\lim \\limits_{h\\to \\infty} \\left(\\frac{f(10+\\frac{1}{h})}{f(10)}\\right)^h \\] given that \\( f(10) = 5 \\) and \\( f'(10) = 2 \\).",
"role": "user"
}
] | e^{\frac{2}{5}} |
[
{
"content": "Evaluate the limit: $$\\lim_{h\\to 0}\\frac{(h+1)-(1+h+h^2/2+O(h^3))}{h^2}-\\frac{2\\sin(h)^2}{h^2}$$",
"role": "user"
}
] | -\dfrac{5}{2} |
[
{
"content": "Find the closed-form expression for the determinant of the matrix \\( \\mathbf{G} \\), where\n\\[\\mathbf{G} = a\\mathbf{I} + b\\boldsymbol{ee}^T\\]\nin which \\(a\\) and \\(b\\) are constants, \\(\\boldsymbol{e}\\) is a column vector with all elements being \\(1\\), and \\((\\cdot)^T\\) denotes t... | a^{u-1}(a + bu) |
[
{
"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... | 8.214 rad/s |
[
{
"content": "Evaluate the divergence \\( \\nabla \\cdot (r^3 \\mathbf{v}) \\) in terms of \\( r \\), where \\( \\mathbf{v} \\) is the position vector and \\( r \\) is the magnitude of the position vector.",
"role": "user"
}
] | 6r^3 |
[
{
"content": "Find the limit: \\[ \\lim_{n \\to \\infty} \\frac{(-2)^n n!}{n^n} \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Find all real solutions (x, y) to the following system of equations:\n\\[ x^2 + 3x + \\ln(2x + 1) = y \\]\n\\[ y^2 + 3y + \\ln(2y + 1) = x \\]",
"role": "user"
}
] | (0, 0) |
[
{
"content": "Which of the following identities is correct when applying the secant method to $f(x)$ using the mean value theorem?\n\n(a) $\\xi - x_{k+1} = \\xi - x_k - \\left[\\frac{f'(\\eta_k)}{f'(\\theta_k)}\\right](\\xi - x_k)$, where $\\eta_k$ is between $x_k$ and $\\xi$, and $\\theta_k$ is between $x_k$ a... | 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... | Stimulus generalization |
[
{
"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... | 20 J/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... | C4H6O2 |
[
{
"content": "Let \\( S = \\{1, 2, \\cdots, 2016\\} \\). For any non-empty finite sets of real numbers \\( A \\) and \\( B \\), determine the minimum value of\n\\[ f = |A \\Delta S| + |B \\Delta S| + |C \\Delta S| \\]\nwhere\n\\[ X \\Delta Y = \\{a \\in X \\mid a \\notin Y\\} \\cup \\{a \\in Y \\mid a \\notin X... | 2017 |
[
{
"content": "Determine whether the statement $X^m = O_n$ implies $X^n = O_n$ for a complex square matrix $X \\in M_n(\\mathbb{C})$, where $m > n$ is a positive integer.",
"role": "user"
}
] | True |
[
{
"content": "Let \\( P_{1} \\) and \\( P_{2} \\) be any two different points on the ellipse \\(\\frac{x^{2}}{9}+\\frac{y^{2}}{4}=1\\). Let \\( P \\) be a variable point on the circle with diameter \\( P_{1} P_{2} \\). Determine the maximum area of the circle with radius \\( OP \\), where \\( O \\) is the origi... | 13\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... | 99.27cm/s |
[
{
"content": "Given that the elements of the second-order difference sequence \\(\\{a_{n}\\}\\) are all 16, and \\(a_{63} = a_{89} = 10\\), find the value of \\(a_{51}\\).",
"role": "user"
}
] | 3658 |
[
{
"content": "Find the radius of convergence of the power series \\( \\sum_{j=1}^\\infty \\frac{j!}{j^j}z^j \\).",
"role": "user"
}
] | e |
[
{
"content": "Given the recursive probability function defined as follows:\n\n\\[ p(1) = 0 \\]\n\\[ p(n+1) = (1-10^{-8}n)p(n)+10^{-8}n \\]\n\nDetermine the maximum integer \\( n \\) such that \\( p(n) \\leq 0.1 \\).",
"role": "user"
}
] | 4590 |
[
{
"content": "Let \\( p(x) \\) be the polynomial of degree 4 with roots 1, 2, 3, and 4, and leading coefficient 1. Let \\( q(x) \\) be the polynomial of degree 4 with roots 1, \\(\\frac{1}{2}\\), \\(\\frac{1}{3}\\), and \\(\\frac{1}{4}\\), and leading coefficient 1. Find \\(\\lim_{x \\rightarrow 1} \\frac{p(x)}... | -24 |
[
{
"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... | 3.36 years |
[
{
"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... | 0.357 |
[
{
"content": "Determine whether the flow with Lagrange path trajectories given by \\(x(\\alpha,t)=(\\alpha_1\\cos(t)+\\alpha_2\\sin(t),\\alpha_2\\cos(t)-\\alpha_1\\sin(t),\\alpha_3)\\) is incompressible. Calculate the divergence of the velocity field and state whether the flow is incompressible.",
"role": "... | 0 |
[
{
"content": "Suppose $f:[0,1]\\to [0,1]$ is a nondecreasing function with $f(0)=0$ and $f(1)=1$. Define $g:[0,1]\\to [0,1]$ by $g(y)=\\min\\{x\\in[0,1]\\mid f(x)\\ge y\\}$. If $g$ is strictly increasing, does it imply that $f$ is continuous? Answer 'yes' or 'no'.",
"role": "user"
}
] | yes |
[
{
"content": "A sequence $a_1$, $a_2$, $\\ldots$ of non-negative integers is defined by the rule $a_{n+2}=|a_{n+1}-a_n|$ for $n\\geq1$. If $a_1=999$, $a_2<999$, and $a_{2006}=1$, how many different values of $a_2$ are possible?",
"role": "user"
}
] | 324 |
[
{
"content": "In the inner product space $P([0,1])$ of all real polynomials on $[0,1]$ with inner product $\\langle f,g\\rangle=\\int_0^1f(x)g(x)dx$, consider $V=\\text{span}\\{t^2\\}$. Find $h(t) \\in V$ such that $\\|(2t-1)-h(t)\\| \\le \\|(2t-1)-x(t)\\|$ for any $x(t) \\in V$. Determine $h(t)$ from the optio... | 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... | Assets
Cash $6,350
Accounts Receivable $42,000
Inventory $(1,500)
Prepaid Rent $1,100
Fixtures and Equipment $5,937
Total $53,887
Liabilities & Owners' Equity
Accounts Payable $19,600
Interest Payable $21
Wages Payable $6,300
Notes Payable $5,000
Paid-in Capital $24,000
Retained Earnings $(1,034)
Total $53,887 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Year 1:
Preferred Total: $5,250
Preferred Per Share: $5.25
Common Total: $0
Common Per Share: $0
Year 2:
Preferred Total: $7,000
Preferred Per Share: $7.00
Common Total: $0
Common Per Share: $0
Year 3:
Preferred Total: $8,750
Preferred Per Share: $8.75
Common Total: $18,720
Common Per Share: $0.52 |
[
{
"content": "Find the sum of the infinite series \\( \\sum\\limits_{n=0}^{+\\infty}\\frac{n^2-2}{n!} \\).",
"role": "user"
}
] | 0 |
[
{
"content": "In an isosceles triangle \\( ACB \\), points \\( M \\) and \\( N \\) are the midpoints of sides \\( AC \\) and \\( CB \\), respectively. Point \\( L \\) is located on the median \\( BM \\) such that \\( BL : BM = 4 : 9 \\). A circle centered at \\( L \\) is tangent to line \\( MN \\) and intersect... | 4 + 2\sqrt{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... | $2,112.77 |
[
{
"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. Social Security
2. Healthcare
3. National Defense
4. Net investment |
[
{
"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... | 211.42 g |
[
{
"content": "Find the one's digit of the remainder when \\( |5555^{2222} + 2222^{5555}| \\) is divided by 7.",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether the following statement is true or false: In some inner product space $V$, there exist vectors $u, v \\in V$ such that $\\|u\\| = 3$, $\\|v\\| = 2$, and $\\langle u, v \\rangle = 5 + 4i$. Provide a justification for your answer.",
"role": "user"
}
] | False |
[
{
"content": "Let $R$ be a Noetherian domain of dimension at least 1, and let $T = R[[X]]$, where $X$ is an indeterminate. For each prime ideal $\\mathfrak{p}_i$ of height one in $R$, define $\\mathfrak{q}_i = \\mathfrak{p}_i[[X]]$. Consider the set $S = T \\setminus \\bigcup_{i \\ge 1} \\mathfrak{q}_i$. Determ... | 1 |
[
{
"content": "Evaluate the integral \\( \\int^{2\\pi}_0 (1+\\cos(x))\\cos(x)(-\\sin^2(x)+\\cos(x)+\\cos^2(x))~dx \\) using Euler's formula or other techniques to simplify the process.",
"role": "user"
}
] | \dfrac{3\pi}{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... | 86.48 cm |
[
{
"content": "If $a, b \\in \\mathbb{Z}$ and for every prime $p \\in \\mathbb{Z}$, there exists an integer $n_p$ such that $b \\equiv a^{n_p} \\ (\\text{mod } p)$, does it imply that there exists an integer $n$ such that $b = a^n$? Answer 'yes' or 'no'.",
"role": "user"
}
] | yes |
[
{
"content": "There is a total of 27 quarters stacked in four piles. The first pile has 5 fewer than the second pile. The second pile has 4 more than the third pile. The fourth pile has three times as many as the second pile. How many quarters are in the fourth pile?",
"role": "user"
}
] | 18 |
[
{
"content": "In a right triangle, the difference between the lengths of the two legs is 5, and the altitude to the hypotenuse measures 12. Determine the area of the triangle without solving a 4th-degree equation.",
"role": "user"
}
] | 150 |
[
{
"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... | 4.13 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... | (0, 0, 3/8) |
[
{
"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... | 2.00 |
[
{
"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... | simple |
[
{
"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... | Project 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... | 1035552 dyn/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... | $650,000 |
[
{
"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... | 1s^22s^22p^63s^23p^64s^2 |
[
{
"content": "Identify the only symmetric group that possesses a nontrivial outer automorphism group.",
"role": "user"
}
] | S_6 |
[
{
"content": "Let $G$ be an undirected, edge-weighted graph. Do all minimum spanning trees $T$ of $G$ have the same signature $S_T = \\{c(e) : e \\in T\\}$, where $c(e)$ denotes the weight of edge $e$?",
"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... | $3,400 + $14 per mile |
[
{
"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... | A Pedigree |
[
{
"content": "Let $X_n = \\{0,1,2\\}^n$ be the $n$-tuple Cartesian product of the ternary set. Define the subset $W_n$ as follows: \\[ W_n = \\{ y \\in X_n : y_1 \\leq 1, y_1 + y_2 \\leq 2, \\ldots, y_1 + \\cdots + y_{n-1} \\leq n-1, y_1 + \\cdots + y_n = n \\}. \\]\n\nConsider the polynomial \\[ P_n(x) = \\sum... | C_{n+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... | 3.80e5 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... | $9,876.10 |
[
{
"content": "Determine whether the following statement is true or false: If A is a proper subset of B, then the Lebesgue measure of A is strictly less than the Lebesgue measure of B.",
"role": "user"
}
] | B |
[
{
"content": "Find a lower bound for the expression \\( \\operatorname{Tr} \\bigl( \\bigl( (A+I )^{-1} \\bigr)^2\\bigr) \\), where \\( A \\in \\mathbb{R}^{n \\times n} \\) is a symmetric positive semi-definite matrix with \\( \\operatorname{Tr}(A) \\le n \\) and \\( I \\) is the identity matrix. Is it true that... | \dfrac{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... | 17 m/s^2 |
[
{
"content": "Calculate the limit: \\[ \\lim_{n \\to \\infty} n \\left( \\frac{3^{1+1/2+\\ldots+1/(n+1)}}{3^{1+1/2+\\ldots+1/n}} - 1 \\right) \\]",
"role": "user"
}
] | \ln 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... | $72,297.23 |
[
{
"content": "Calculate the residue of \\( \\frac{e^z-1}{1-\\cos z} \\) at \\( z=0 \\).",
"role": "user"
}
] | 2 |
[
{
"content": "Is the set $C^\\infty_c((0,1])$ of compactly supported smooth functions on the interval $(0,1]$ dense in the Sobolev space $H^1(0,1)$, restricted to functions that vanish at the origin, i.e., $\\{u \\in H^1(0,1): u(0) = 0\\}$?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the number of subgroups of order 3 in the symmetric group $S_6$. Provide your answer as a single integer.",
"role": "user"
}
] | 40 |
[
{
"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... | 100.1 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... | 4x |
[
{
"content": "Determine the dimension of the tangent space at a point \\((X_0, Y_0)\\) on the set of pairs \\((X, Y)\\) of real \\(n \\times k\\) matrices \\((k \\le n)\\) defined by the condition \\(X^T Y = I\\).",
"role": "user"
}
] | 2nk - k^2 |
[
{
"content": "Evaluate the integral \\( \\int_0^\\pi \\frac{(\\sin x + \\cos x)^2}{(1 + \\sin 2x)^{1/2}} \\, \\mathrm{d}x \\).",
"role": "user"
}
] | 2\sqrt{2} |
[
{
"content": "Let $B\\subset \\mathbb{R}^2$ be an open ball within a domain $\\Omega$. Consider $y_1, y_2 \\in H_0^1(\\Omega) \\cap H^2(\\Omega)$ satisfying:\n\\[ -\\Delta y_i = 1 \\text{ for } i=1,2 \\text{ on } B \\]\n\\[ 0 \\leq y_1(x) \\leq y_2(x) \\text{ on } \\bar{B} \\]\nIs there a point $x \\in \\bar{B}... | Yes |
[
{
"content": "A polygon has interior angles such that the difference between any two consecutive angles is 5 degrees. If the smallest angle is 120 degrees, determine the number of sides of the polygon.",
"role": "user"
}
] | 9 |
[
{
"content": "Find the candidate for a weak extremum for the functional \\( \\int_{0}^{1}\\sqrt{1+y'(x)^2}dx \\) subject to the constraint \\( y(1)=2 \\).",
"role": "user"
}
] | 2 |
[
{
"content": "Evaluate the integral \\( \\int_0^{2\\pi} \\frac{e^{|\\sin x|}\\cos(x)}{1+e^{\\tan x}} \\, dx \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the integral \\(\\int_{0}^{1}f(x)f'(x)(1+2(f'(x))^2+2f(x)f''(x))dx\\) for a function \\(f(x)\\) that has a continuous second derivative on the interval \\([0,1]\\), with the initial and boundary conditions: \\(f(0)=0\\), \\(f'(0)=0\\), \\(f(1)=1\\), and \\(f'(1)=3\\).",
"role": "user"... | \dfrac{19}{2} |
[
{
"content": "Evaluate the limit: \\[ \\lim_{h \\to 0} \\frac{\\sin\\left(\\frac{h}{2}\\right)-\\frac{h}{2}}{h\\sin\\left(\\frac{h}{2}\\right)} \\] without using l'Hospital's rule.",
"role": "user"
}
] | 0 |
[
{
"content": "An unbiased coin is tossed repeatedly. What is the expected number of tosses needed to obtain the sequence HT (one head followed by one tail) for the first time?",
"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... | $785,155.40 |
[
{
"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... | 1.5162 mm |
[
{
"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... | 3828.57 N |
[
{
"content": "Find all solutions to the inequality \\[\\frac{(2x-7)(x-3)}{x} \\ge 0.\\](Give your answer in interval notation.)",
"role": "user"
}
] | (0, 3] \cup [\tfrac72, \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... | 5.67e-21 J/K |
[
{
"content": "Let $C \\subset \\mathbb{P}_\\mathbb{C}^2$ be a projective curve, and $p \\in C$ a point of multiplicity $m$. If $\\mathcal{O}_p(C)$ is the local ring of $C$ at $p$, and $\\mathfrak{m} \\subset \\mathcal{O}_p(C)$ is its maximal ideal, find $\\text{dim}_\\mathbb{C} \\mathfrak{m}^k/\\mathfrak{m}^{k+... | \min(k + 1, m) |
[
{
"content": "In triangle \\(ABC\\), point \\(D\\) lies on side \\(BC\\) such that \\(BD = 2\\) and \\(DC = 6\\). Given that \\(AB = 4\\) and \\(\\angle ACB = 20^{\\circ}\\), determine the value of \\(\\angle BAD\\) using geometric principles without a calculator.",
"role": "user"
}
] | 20^\circ |
[
{
"content": "Evaluate the limit: $$\\lim\\limits_{x \\to 0} \\frac{\\ln(1+x^{144})-\\ln^{144}(1+x)}{x^{145}}$$",
"role": "user"
}
] | 72 |
[
{
"content": "In the rectangular parallelepiped $A B C D A_{1} B_{1} C_{1} D_{1}$, the lengths of the edges are $A B=54$, $A D=90$, and $A A_{1}=60$. A point $E$ is the midpoint of edge $A_{1} B_{1}$, and a point $F$ is the midpoint of edge $B_{1} C_{1}$. Calculate the distance between the lines $A E$ and $B F$... | \dfrac{216}{5} |
[
{
"content": "For each integer $n$, let $f(n)$ be the sum of the elements of the $n$th row (i.e. the row with $n+1$ elements) of Pascal's triangle minus the sum of all the elements from previous rows. For example, \\[f(2) = \\underbrace{(1 + 2 + 1)}_{\\text{2nd row}} - \\underbrace{(1 + 1 + 1)}_{\\text{0th and ... | 1 |
[
{
"content": "The points $(4, 0)$ and $(-4, 0)$ are two non-consecutive vertices of a rhombus with an area of $80$ square units. One of the other vertices is $(0, K)$ where $K > 0$. What is the value of $K$?",
"role": "user"
}
] | 10 |
[
{
"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... | $19,000 |
[
{
"content": "Determine all even natural numbers \\(n\\) such that the numbers \\(1, 2, \\ldots, n^2\\) can be divided into two equal sets \\(A\\) and \\(B\\) with \\(|A| = |B| = \\frac{n^2}{2}\\), and the sums of the elements in these sets, \\(S_A\\) and \\(S_B\\), satisfy \\(\\frac{S_A}{S_B} = \\frac{39}{64}\... | 206 |
[
{
"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... | 1904983 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... | 24.92% |
[
{
"content": "Find the surface area of an ideal tetrahedron in hyperbolic space $\\mathbb{H}^3$ as a function of its vertices, which are parametrized by four complex numbers $z_1, z_2, z_3, z_4$ on the boundary $\\mathbb{CP}^1$. Express the surface area in terms of $z_1, z_2, z_3, z_4$.",
"role": "user"
}... | 4\pi |
[
{
"content": "If $p, q, r,$ and $s$ are in continued proportion, find the minimum value of $\\frac{p-s}{q-r}$. Assume $qr > 0$. Provide your answer as a single number.",
"role": "user"
}
] | 3 |
[
{
"content": "Assume $f(x,y)$ is defined on $D=[0,1]\\times[0,1]$, and $f(x,y)$ is continuous in each variable separately. If $f(x,y)$ vanishes on a dense subset of $D$, does $f$ vanish on all of $D$? 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... | 2.408e+24 atoms and 4.816e+24 molecules |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n \\to \\infty} \\left(n^3 \\int_{n} ^{2n}\\frac{x \\, dx} {1+x^5}\\right) \\]",
"role": "user"
}
] | \dfrac{7}{24} |
[
{
"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... | 22.5 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... | N |
[
{
"content": "For each positive integer $n$, let $f(n) = n^4 - 360n^2 + 400$. What is the sum of all values of $f(n)$ that are prime numbers?",
"role": "user"
}
] | 802 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.