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... | double displacement reaction |
[
{
"content": "Determine whether the following statement is true or false: If there is a bijection between an infinite set $A$ and the Cartesian product $A \\times A$, then there exists an injective function from the set of natural numbers $\\mathbb{N}$ to $A$. Provide a justification for your answer.",
"rol... | True |
[
{
"content": "Consider a vector space $X$ over the reals with a separating family of seminorms $P$. For each $p \\in P$ and $\\epsilon > 0$, define the set \\( V(p, \\epsilon) = \\{ x \\in X : p(x) < \\epsilon \\} \\). If $P$ induces a locally convex topology $\\tau$ on $X$, is it true that the sets $V(p, \\eps... | Yes |
[
{
"content": "Determine the structure of the Galois group of the field extension \\( \\mathbb{Q}(\\sqrt[3]{5},\\omega):\\mathbb{Q} \\), where \\( \\omega = e^{2\\pi i/3} \\) is a primitive cube root of unity.",
"role": "user"
}
] | S_3 |
[
{
"content": "Let $X$ be a space, and consider a collection of subsets $\\{U_\\lambda\\}_{\\lambda \\in \\Lambda}$ of $X$. We wish to construct a topology $\\mathcal T$ in which the sets $U_\\lambda$ are all open. Define\n$$\\mathcal S=\\left\\{\\bigcap_{\\lambda \\in \\Gamma}U_\\lambda \\mid \\Gamma\\subset \\... | Yes |
[
{
"content": "Find the remainder when \\((1 \\cdot 2 \\cdot 3 \\cdots 102)^3\\) is divided by 105.",
"role": "user"
}
] | 0 |
[
{
"content": "Prove that a 20-degree angle is not constructible using a straightedge and compass.",
"role": "user"
}
] | 20^\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... | Shannon Company
Segmented Income Statement
For the period ended ...
North Division | South Division | Total
---|---|---|---
Sales Revenue | $180,000 | $300,000 | $480,000
Variable Costs | $45,000 | $147,000 | $192,000
Contribution Margin | $135,000 | $153,000 | $288,000
Traceable Fixed Costs | $53,000 | $115,000 | $16... |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Net Investment = (Capital Expenditure - Non-cash expenditure) |
[
{
"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... | 14.5 mJ |
[
{
"content": "Dr. Jones lives in a country with a progressive tax system. That is, he does not pay any taxes on the first $\\$20{,}000$ in income he makes, he pays $5\\%$ taxes on the next $\\$25{,}000$, he pays $10\\%$ taxes on the next $\\$35{,}000$, he pays $15\\%$ on the next $\\$50{,}000$, and he pays $20\... | \$115,000 |
[
{
"content": "Determine the minimum value of the function \\( g(x,y) = \\frac{(1-\\cos(\\pi x))(1-\\cos (\\pi y))}{x^2 y^2 \\sqrt{(1-\\cos(\\pi x))(2+\\cos(\\pi y))+(2+\\cos(\\pi x))(1-\\cos(\\pi y))}} \\) over the domain \\([0,1]^2\\).",
"role": "user"
}
] | 2 |
[
{
"content": "Given a quadratic equation with a discriminant $Z = 4(U^2 - V)$, where $U^2$ has a density function $f(t) = \\frac{1}{2}t^{-\\frac{1}{2}}\\mathsf{1}_{(0,1)}(t)$ and $V$ has a density function $g(t) = \\mathsf{1}_{(0,1)}(t)$, find the probability $\\mathbb{P}(Z > 0)$. Provide your answer as a proba... | \dfrac{1}{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... | 68.20 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... | 123.4 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... | $105 |
[
{
"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... | 9.43% |
[
{
"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... | -1.68e+04 V |
[
{
"content": "Let \\( l \\) and \\( m \\) be two skew lines. On line \\( l \\), there are points \\( A, B, \\) and \\( C \\) such that \\( AB = BC \\). From points \\( A, B, \\) and \\( C \\), perpendicular lines \\( AD, BE, \\) and \\( CF \\) are drawn such that they are perpendicular to \\( m \\), and the fee... | \sqrt{6} |
[
{
"content": "Can every graph be embedded in three-dimensional space, \\( \\mathbb{R}^3 \\)?",
"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... | Net Income - Dividends paid to the Shareholders |
[
{
"content": "Find the greatest common divisor of the 1960th and 1988th Fibonacci numbers.",
"role": "user"
}
] | 317811 |
[
{
"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... | 307.95 g |
[
{
"content": "Let $M$ and $N$ be smooth manifolds, let $p \\in M$, and let $L:T_p M \\rightarrow T_{f(p)} N$ be a linear map. Determine whether there always exists a smooth map $F:M \\rightarrow N$ on a neighborhood of $p$ such that $L$ is the differential map of $F$ at $p$. Provide a justification for your ans... | Yes |
[
{
"content": "Consider a sequence \\( V_N \\) of subspaces of \\( \\ell^N_1 \\) such that \\( \\dim V_N = N - n \\) and \\( n \\) is \\( \\mathsf{o}(N) \\). Determine if there exist constants \\( K_1, K_2 > 0 \\) such that for sufficiently large \\( N \\), the following holds:\n\\[\n\\sup_{x \\in V_N, \\|x\\|_1... | 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... | -200 |
[
{
"content": "Determine all natural numbers \\( n \\) such that the concatenation of \\( n^3 \\) and \\( n^4 \\) in decimal form contains each digit from 0 to 9 exactly once.",
"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... | [Ar]3d^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... | Machine Setups: $100 per set-up
Material Handling: $1.50 per unit of raw material
Quality Control Inspection: $50 per inspection
Other Overhead Cost: $8.00 per machine hour |
[
{
"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... | 72.35% |
[
{
"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... | 5.471e5 g/gal |
[
{
"content": "Calculate the value of the expression: \\( \\arctan \\frac{1}{3} + \\arctan \\frac{1}{5} + \\arcsin \\frac{1}{\\sqrt{50}} + \\arcsin \\frac{1}{\\sqrt{65}} \\).",
"role": "user"
}
] | \dfrac{\pi}{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... | 34.539 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... | $62 |
[
{
"content": "Let $(X,Y)$ be a random vector with a joint density function given by \\(f(x,y) = \\frac{6}{7}(x^2 + \\frac{xy}{2})\\) for \\(0 < x < 1\\) and \\(0 < y < 2\\). Given that the marginal density of \\(X\\) is \\(f_X(x) = \\frac{12}{7}x^2 + \\frac{6}{7}x\\) and \\(\\mathbb{P}(X > Y) = \\frac{15}{56}\\... | \dfrac{69}{80} |
[
{
"content": "Find all the solutions to\n\\[\\sqrt[3]{15x - 1} + \\sqrt[3]{13x + 1} = 4 \\sqrt[3]{x}.\\]Enter all the solutions, separated by commas.",
"role": "user"
}
] | 0, \frac{1}{14}, -\frac{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... | 15300 |
[
{
"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... | 1.16 nm |
[
{
"content": "In triangle \\(ABC\\) with \\(AC > AB\\), let \\(P\\) be the intersection of the perpendicular bisector of \\(BC\\) and the internal angle bisector of \\(\\angle A\\). Construct points \\(X\\) on \\(AB\\) (extended) and \\(Y\\) on \\(AC\\) such that \\(PX\\) is perpendicular to \\(AB\\) and \\(PY\... | 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... | #include <iostream>
#include <string.h>
using namespace std;
void toUpper(char str[]);
int main(int argc, char** argv) {
char s[100] = "My name is Sam North";
toUpper(s);
for (int i = 0; i < strlen(s); i++) {
cout << s[i];
}
return 0;
}
void toUpper(char str[]) {
int j = 0;
while (st... |
[
{
"content": "Let $G$ be an infinite, finitely generated group with one end. Consider a word-metric $d$ on the Cayley graph of $G$ with respect to some finite symmetric generating set $S$. Does there exist a good bi-infinite path $\\{g_i\\}_{i\\in\\mathbb{Z}}$ in $G$, where $d(g_i, g_{i+1})=1$ for all $i$ and $... | Yes |
[
{
"content": "Given that $g(x)$ is a differentiable function satisfying $(g(x))^2 - 2g(x) + x^2 = 1$ and $g(x) \\neq 1$, find the value of $|4g'(1)|$. Provide your answer as a single number.",
"role": "user"
}
] | 4 |
[
{
"content": "How many values of \\(x\\) in the interval \\([0,1]\\) satisfy the equation \\(f_7(x) = x\\), where the function \\(f(x)\\) is defined as \\(f(x) = 4x(1-x)\\)?",
"role": "user"
}
] | 128 |
[
{
"content": "In a linear space $X$ with $\\dim X = 6$, there are three linear subspaces $U$, $V$, and $W$ such that $\\dim U = 2$ and $U \\cap V = U \\cap W = \\{0\\}$. Determine whether the statement $U \\cap (V+W) = \\{0\\}$ is true or false.",
"role": "user"
}
] | False |
[
{
"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... | [Pb^2+] = 0.0020 M, [F-] = 0.0040 M |
[
{
"content": "Determine whether the statement \"All domains are commutative\" is true or false.",
"role": "user"
}
] | B |
[
{
"content": "The sum of the following seven numbers is exactly 19: $a_1 = 2.56,$ $a_2 = 2.61,$ $a_3 = 2.65,$ $a_4 = 2.71,$ $a_5 = 2.79,$ $a_6 = 2.82,$ $a_7 = 2.86.$ Each $a_i$ is approximated by some integer $A_i,$ for $1 \\le i \\le 7,$ such that the sum of the $A_i$'s is also $19.$ Let $M$ be the maximum of ... | 0.61 |
[
{
"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... | 9.6875 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... | $S \mapsto bA$
$A \mapsto aA | \Lambda$ |
[
{
"content": "Find the exact value of the series \\( \\sum_{n=0}^{\\infty} \\frac{(-1)^n}{(2n+1)^2} \\).",
"role": "user"
}
] | G |
[
{
"content": "Determine whether the sequence \\(u_n = \\frac{1}{n!}\\sum_{k=1}^n k!\\) converges or diverges.",
"role": "user"
}
] | 1 |
[
{
"content": "What is the expected number of Bernoulli trials required to achieve \\( k \\) successes, given that the probability of success in a single trial is \\( p \\) and the probability of failure is \\( q = 1 - p \\)?",
"role": "user"
}
] | \dfrac{k}{p} |
[
{
"content": "Find the area of the surface that is part of the cylinder \\(x^2+z^2=a^2\\) and lies inside the cylinder \\(x^2+y^2=a^2\\).",
"role": "user"
}
] | 8a^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... | 4.64e-8 s |
[
{
"content": "Find the largest positive integer \\( n \\) such that the intersection \\( A_1 \\cap A_2 \\cap \\cdots \\cap A_n \\neq \\emptyset \\), where \\( A_k = \\{ x \\mid 2^k < x^k + x^{k+1} < 2^{k+1} \\} \\) for \\( k = 1, 2, 3, \\ldots \\).",
"role": "user"
}
] | 3 |
[
{
"content": "Determine the value of \\( a \\) such that the following integral is equivalent to the given triple integral:\n\n\\[ \\iiint \\sqrt{x^2+y^2+z^2} \\,dx \\,dy \\,dz \\]\n\nwhere the region is bounded by \\( z=\\sqrt{x^2+y^2} \\) and \\( z=4 \\). After converting to spherical coordinates, the integra... | 128\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... | 99.9999 m |
[
{
"content": "In a round-robin Japanese chess tournament, each participant plays against 13 others, with no draws. Determine the maximum number of circular triples (where each of the three participants wins against one and loses to another) that can occur in the tournament.",
"role": "user"
}
] | 112 |
[
{
"content": "Compute the surface integral \\( \\int_M \\omega \\) where \\( \\omega = x^4 \\, dy \\wedge dz + y^4 \\, dz \\wedge dx + z^4 \\, dx \\wedge dy \\) and \\( M \\) is the sphere defined by \\( x^2 + y^2 + z^2 = R^2 \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the integral \\( \\int_{|\\vec{r}| \\le R} \\frac{y}{|\\vec{r} - \\vec{r}~'|} d^3V \\) over a sphere of radius \\( R \\), where \\( \\vec{r} \\) is a vector in three-dimensional space. Use cylindrical coordinates \\( (s, \\theta, z) \\) to express the integral and consider the symmetry of... | 0 |
[
{
"content": "Find the value of \\( k \\in \\mathbb{N} \\) such that the polynomial \\( x^{2k} + 1 + (x + 1)^{2k} \\) is not divisible by \\( x^2 + x + 1 \\).",
"role": "user"
}
] | 3 |
[
{
"content": "Let $T$ be a linear map defined on a subspace $S$ of a Euclidean vector space $V$, such that \\( d(T(v_1),T(v_2))\\leq d(v_1,v_2) \\) for all \\( v_1,v_2\\in S \\), where \\( d(v_1,v_2) \\) is the Euclidean distance on $V$. Does there always exist a linear map $T'$ defined on $V$ such that \\( d(T... | Yes |
[
{
"content": "Evaluate \\( \\lim_{n\\to\\infty}\\int_n^{n+1}\\cos^2(u^2) \\, du \\).",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Determine whether the following statement is true or false: If \\( \\{ a_{n} \\} \\) is a sequence and \\( A = \\sup(a_{n}) \\), then there exists a \\( K \\) such that for any \\( x > 0 \\), we have for all \\( m > K \\) that \\( |a_{m} - A| < x \\).",
"role": "user"
}
] | 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... | $70 |
[
{
"content": "Given that $\\tan x + 2\\tan y + 3\\tan z = 40$ for $x, y, z \\in \\left(\\frac{\\pi}{2}, \\frac{3\\pi}{2}\\right)$, find the minimum value of $\\tan^2 x + \\frac{\\tan^2 y}{4} + \\frac{\\tan^2 z}{9}$.",
"role": "user"
}
] | \dfrac{800}{49} |
[
{
"content": "Let \\( f(x) = 30 - 2x - x^3 \\). Determine the number of positive integral values of \\( x \\) that satisfy the inequality \\( f(f(f(x))) > f(f(-x)) \\).",
"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... | MC = 3Q + 4 |
[
{
"content": "Point $D$ is on side $\\overline{BC}$ of triangle $ABC.$ If $\\angle CAD = \\angle BAD = 60^\\circ,$ $AC = 3,$ and $AB = 6,$ then find $AD.$",
"role": "user"
}
] | 2 |
[
{
"content": "If $M$ is a martingale with respect to the filtration $(F_t)$, is the stopped process $M^T$ also a martingale with respect to the filtration $(F_{t \\wedge T})$?",
"role": "user"
}
] | Yes |
[
{
"content": "Can any 3x3 rotation matrix be represented as a linear combination of fewer than 9 constant basis matrices, such that \\( R = \\sum_{i = 1}^{n}\\lambda_i B_i \\) where \\( n < 9 \\), \\( R \\) is any 3x3 rotation matrix, \\( B_i \\) are constant basis matrices, and \\( \\lambda_i \\) are scalar we... | No |
[
{
"content": "Determine whether the following statement is true for a variety $X$ over an algebraically closed field: If the generic point of an irreducible closed subset $Y$ of $X$ is regular, then $Y$ contains a closed point that is also regular on $X$. Provide a proof or counterexample.",
"role": "user"
... | True |
[
{
"content": "The inscribed circle of triangle $ABC$ is tangent to $\\overline{AB}$ at $P,$ and its radius is $21$. Given that $AP=23$ and $PB=27,$ find the perimeter of the triangle.",
"role": "user"
}
] | 345 |
[
{
"content": "In triangle \\( ABC \\), the sides \\( AC = 14 \\) and \\( AB = 6 \\) are given. A circle with center \\( O \\), constructed on side \\( AC \\) as its diameter, intersects side \\( BC \\) at point \\( K \\). Given that \\(\\angle BAK = \\angle ACB\\), determine the area of triangle \\( BOC \\).",
... | 21 |
[
{
"content": "Compute the value of the summation:\n\\[1+\\frac{1}{2}+\\frac{1}{3}+\\cdots+\\frac{1}{2013}+\\frac{1}{1\\cdot2}+\\frac{1}{1\\cdot3}+\\cdots+\\frac{1}{2012\\cdot 2013}+\\frac{1}{1\\cdot2\\cdot3\\cdots2013}\\]",
"role": "user"
}
] | 2014 |
[
{
"content": "Determine whether it is possible to construct a sequence of functions $\\psi_n = \\psi \\circ f_n(r)$, where $\\psi \\in C^\\infty((0,\\infty); [0,1])$ is supported away from zero and identically one near $[1, \\infty]$, such that $\\int^\\infty_0 (\\partial_r \\psi_n)^2 r \\, dr \\to 0$ as $n \\t... | 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... | 588.6 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... | 0.3kgm^2s^-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... | 4.93% |
[
{
"content": "Let \\((a_n),(b_n)\\) be sequences of positive real numbers such that \\(na_n < b_n < n^2a_n\\) for all \\(n \\geq 2\\). If the radius of convergence of \\(\\sum a_n x^n\\) is 4, determine which of the following is true for \\(\\sum b_n x^n\\):\n\nA) converges for all \\(|x|<2\\)\nB) converges for... | A |
[
{
"content": "Determine whether there exists a permutation $a$ in $S_6$ such that $a^2 = (123)(456)$. 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... | 246.030 kW |
[
{
"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... | $6,404,494 |
[
{
"content": "In triangle $ABC$, where $AB=30$, $BC=51$, and $CA=63$, points $P$ and $Q$ are on $\\overline{BC}$, $R$ is on $\\overline{CA}$, and $S$ is on $\\overline{AB}$ such that $PQRS$ forms a parallelogram. The center of parallelogram $PQRS$ coincides with the centroid of $\\triangle ABC$. Determine the a... | 336 |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\to 0} \\frac{\\sin(e^{\\tan^2 x} - 1)}{\\cos^{\\frac{3}{5}}(x) - \\cos(x)}$$ without using L'Hôpital's rule or series expansion.",
"role": "user"
}
] | 5 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | [CO_2] = 0.24 M, [CO] = 0.00426 M, [O_2] = 0.00213 M |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -11,208.68 |
[
{
"content": "Evaluate the limit: $$ \\lim_{n \\to \\infty} \\frac{\\sqrt[n]{n\\cdot(n+1)\\cdots(2n)}}{n} $$",
"role": "user"
}
] | \dfrac{4}{e} |
[
{
"content": "Determine whether there exists a sequence of nowhere differentiable functions \\((f_n)\\) that converges uniformly to a function \\(f\\) that is everywhere differentiable. 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... | 343.5 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... | monthly |
[
{
"content": "Determine all continuous functions \\( f: \\mathbb{R} \\to \\mathbb{R} \\) such that \\( f(x) = f(\\sin x) \\) for every real number \\( x \\).",
"role": "user"
}
] | f(x) = 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... | 11.10% |
[
{
"content": "Calculate the arc length of the polar curve \\( r = 8\\sin^3\\left(\\frac{\\theta}{3}\\right) \\) over the interval \\( 0 \\leq \\theta \\leq \\frac{\\pi}{4} \\).",
"role": "user"
}
] | \pi - 3 |
[
{
"content": "Prove that \\(\\lim_{x \\to \\infty} \\frac{e^{e^{x}}}{x!} = \\infty\\).",
"role": "user"
}
] | \infty |
[
{
"content": "Is it necessary for the function $V(x)$ to be an even function if both $g(x)$ and $g(-x)$ are solutions to the differential equation $kf_{xx} + V(x)f(x) = cf(x)$, where $k$ is a negative constant and $c$ is a constant?",
"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... | 1114.6kg |
[
{
"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... | 1.09e5 m |
[
{
"content": "Let \\(ABCD\\) be a square with side length \\(x\\). If \\(P\\) is a point on the circumcircle of \\(ABCD\\), find all positive integers \\(n\\) such that the sum \\[ T^n(P) = PA^n - PB^n + PC^n - PD^n \\] is constant with respect to the point \\(P\\).",
"role": "user"
}
] | 2 |
[
{
"content": "In the Cartesian coordinate system, there are 50 different parabolas of the form \\( y = ax^2 + bx + c \\) and another 50 different parabolas of the form \\( x = a_1 y^2 + b_1 y + c_1 \\). Determine the maximum number of regions these 100 parabolas can divide the coordinate plane into.",
"role... | 15001 |
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