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... | By changing the volume of the container, by changing the molar quantity of the gas in question, or by increasing the temperature |
[
{
"content": "Evaluate the integral: $$\\int_0^1 \\left(\\sqrt[5]{1-x^9} - \\sqrt[9]{1-x^5}\\right)\\;dx$$",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether the statement $\\pi_n(D^{n+1}) = 0$ holds true for all $n \\in \\mathbb{N}$, where $D^n$ is the $n$-dimensional disk and $\\pi_n$ is the $n$-th homotopy group.",
"role": "user"
}
] | Yes |
[
{
"content": "Let \\( \\sum_{n=1}^\\infty a_n, \\ a_n > 0 \\) be a convergent series. Consider the following statements:\n\n- **P:** The series \\( \\sum_{n=1}^\\infty \\sqrt{a_n} \\) is always convergent.\n- **Q:** The series \\( \\sum_{n=1}^\\infty \\frac{a_1 + a_2 + \\ldots + a_n}{n} \\) is always divergent.... | D |
[
{
"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... | 13.83 J by the force of gravity |
[
{
"content": "How many positive integer divisors of $2004^{2004}$ are divisible by exactly 2004 positive integers?",
"role": "user"
}
] | 54 |
[
{
"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... | $4,500 |
[
{
"content": "Evaluate the complex integral \\( \\int_{|z-1|=1}\\frac{1}{z^2-1}dz \\) over the circle centered at 1 with radius 1 in the complex plane.",
"role": "user"
}
] | \pi i |
[
{
"content": "In a regular tetrahedron with edge length $a$, find the angle subtended at the centroid by the line segment connecting the midpoint of an edge to the centroid of the tetrahedron.",
"role": "user"
}
] | 90^\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... | v = \sqrt{\frac{2qEd}{m}} |
[
{
"content": "Determine whether there exists a nowhere continuous function \\( f: \\mathbb{R} \\to \\mathbb{R} \\) such that the functional equation \\( f(f(x)) = (f(x))^2 \\) holds for all \\( x \\in \\mathbb{R} \\).",
"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... | <img>https://useruploads.socratic.org/lT0EmGCRpa7yT6ZYPRfv_%28R%29-3-Methylhexan-3-ol%20Fischer.jpg</img> |
[
{
"content": "As the area of a hyperbolic triangle in the open upper half complex plane becomes arbitrarily large, what happens to the sum of its angles?",
"role": "user"
}
] | 0 |
[
{
"content": "Given a concave twice continuously differentiable function $g : (0, 1) \\to (0, +\\infty)$, maximize the growth of the ratio \\( f(x) := -\\frac{g''(x)}{g(x)} \\) as \\( x \\to 0 \\). For example, if \\( g(x) = x^p \\) with \\( p \\in (0, 1) \\), then \\( f(x) = \\frac{p(1 - p)}{x^2} \\), which is... | \sqrt{x} |
[
{
"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 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... | Work-in-Process: $196,560
Over-Applied Direct Labor: $2,148
Direct Labor: $198,708 |
[
{
"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 m/s^2 |
[
{
"content": "Given a vector space $V$ with two ordered bases $\\beta = \\{v_i\\}_{i \\in I}$ and $\\beta' = \\{v'_i\\}_{i \\in I}$, where each vector $v \\in V$ can be uniquely expressed as a linear combination of vectors from both bases, with corresponding coefficients $\\alpha_i$ and $\\alpha'_i$ respectivel... | \beta = \beta' |
[
{
"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... | Adjusted Cash Balance per Books: $20,642
Adjusted Cash Balance per Bank: $20,642 |
[
{
"content": "Given the equation \\( \\int_0^1 (1+\\cos^8 x)(ax^2+bx+c) \\, dx = \\int_0^2 (1+\\cos^8 x)(ax^2+bx+c) \\, dx \\), determine the interval in which the root of the quadratic equation \\( ax^2 + bx + c = 0 \\) lies, where \\( a, b, \\) and \\( c \\) are non-zero numbers.",
"role": "user"
}
] | (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... | $116,304 |
[
{
"content": "Evaluate the infinite series: \\[ \\sum_{n=0}^{\\infty}\\frac{1}{2^n(n+1)} \\]",
"role": "user"
}
] | 2 \ln 2 |
[
{
"content": "In an acute-angled scalene triangle $ABC$, point $T$ is located inside the triangle such that $\\angle ATB = \\angle BTC = 120^\\circ$. A circle centered at point $E$ passes through the midpoints of the sides of $\\triangle ABC$. Given that points $B, T, E$ are collinear, determine the measure of ... | 60 |
[
{
"content": "The equation $y = \\frac{x + A}{Bx + C}$, where $A,B,$ and $C$ are integers, is shown below. What is $A + B + C$?\n\n[asy]\nimport graph; size(8.14cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-2.52,xmax=5.62,ymin=-4.28,ymax=3.32;\n\npen cqcqcq=rg... | -3 |
[
{
"content": "Evaluate the limit: $$\\lim_{(x,y)\\to(0,0)}\\frac{x^2y^2}{\\sqrt{x^2y^2+(x-y)^2}}.$$",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -3.33% |
[
{
"content": "Determine whether there exists a perfect square whose leading digits are a given finite string of numbers. For example, can a perfect square have leading digits 123456?",
"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... | 86 m |
[
{
"content": "Let \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) be a non-constant, thrice differentiable function such that \\( f(1+1/n)=1 \\) for all \\( n \\in \\mathbb{Z} \\). Determine the value of \\( f''(1) \\).",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 15/24 MR^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... | 11 g NO2 |
[
{
"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... | supply; left; increase; decrease |
[
{
"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... | 864231 |
[
{
"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... | 3.12 hours |
[
{
"content": "If $y>0$, find the range of all possible values of $y$ such that $\\lceil{y}\\rceil\\cdot\\lfloor{y}\\rfloor=42$. Express your answer using interval notation.",
"role": "user"
}
] | (6,7) |
[
{
"content": "Let $X$ be a random variable with an absolutely continuous cumulative distribution function $F(x)$. Determine the distribution of the random variable $Y = \\log(1 - F(X))$. Provide the probability density function of $Y$.",
"role": "user"
}
] | e^y |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $35,630,000 |
[
{
"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... | $480,769.96 |
[
{
"content": "Can every positive definite real symmetric matrix $S$ be expressed as $S = A^T A$ for some matrix $A$? Provide a simple proof if possible.",
"role": "user"
}
] | Yes |
[
{
"content": "Given a set \\( S \\) of size 100, find the maximum size of a collection \\( G \\) of subsets of \\( S \\), each of size 5, such that any two different subsets in \\( G \\) have different intersections of size 4. What is the maximum size of \\( G \\)?",
"role": "user"
}
] | 2800 |
[
{
"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... | 12/49 Ohms |
[
{
"content": "Find the number of digits in the smallest positive integer \\( s \\) such that both the digit sum of \\( s \\) and the digit sum of \\( s + 1 \\) are divisible by 19.",
"role": "user"
}
] | 20 |
[
{
"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 m/s^2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 14.955% |
[
{
"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... | 0.116 g CH3COOH per mL |
[
{
"content": "Determine whether the inequality $nt + (1-t^n) - n > 0$ can be satisfied for $n > 1$ and $t \\in [0,1]$. Provide a justification for your answer.",
"role": "user"
}
] | No |
[
{
"content": "Evaluate the integral: \\[ I = \\int_0^{2\\pi} \\frac{e^{|\\sin x|} \\cos x}{1+e^{\\tan x}} \\,dx \\]",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2012: 4.9%
2013: 10.0%
2014: 12.7% |
[
{
"content": "Find all natural number pairs \\((a, b)\\) that satisfy the equation \\(2^a + 5 = b^2\\).",
"role": "user"
}
] | (2, 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... | 108.3N |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 41 N downwards |
[
{
"content": "Determine the number of solutions to the equation \\( x^2 - \\lfloor x^2 \\rfloor = \\{x\\}^2 \\) within the interval \\([1, m]\\), where \\( m \\) is a positive integer. Choose the correct answer from the following options:\n\nA. 0\n\nB. \\( m(m-1) + 1 \\)\n\nC. \\( m^2 \\)\n\nD. Infinitely many"... | 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... | 3069 nm |
[
{
"content": "Let $A$ be a $2 \\times 2$ matrix with eigenvalues $1$ and $-1$. Find the determinant of the matrix $S = 2A + A^{-1} - I$. \\( \\text{(Note: } I \\text{ is the identity matrix.)} \\)",
"role": "user"
}
] | -8 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.6e-8 F |
[
{
"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... | 42.1 g |
[
{
"content": "Calculate \\( \\limsup\\limits_{j\\to\\infty} |a_j|^{1/j} \\), where\n\\[ a_j = \\sum_{j=1}^\\infty \\frac{(1+1/j)^{2j}}{e^j} \\]",
"role": "user"
}
] | \dfrac{1}{e} |
[
{
"content": "Evaluate the line integral \\( \\int_{C} xydx + (x+y)dy \\) along the curve \\( y = x^2 \\) from \\((-2, 4)\\) to \\((1, 1)\\).",
"role": "user"
}
] | -\dfrac{21}{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... | 0.34 W/K |
[
{
"content": "Consider the number field extension $L = \\mathbb{Q}(\\alpha)$ where $\\alpha$ is a root of the polynomial $p(X) = X^3 + 2X + 1$. The ring of integers of $L$ is $\\mathbb{Z}[\\alpha]$. Given that the discriminant of $L$ is $-59$, determine whether the prime number 3 remains prime in the field $L$.... | 3 |
[
{
"content": "Let \\( \\psi \\neq 1 \\) be a non-trivial character of the finite field \\( \\mathbb{F}_p \\). Define the Gauss sum \\( G(\\psi) = \\sum_{x \\in \\mathbb{F}_p} \\psi(x^2) \\). Prove that \\( |G(\\psi)|^2 = p \\).",
"role": "user"
}
] | p |
[
{
"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... | Treasury Inflation-Protected Security or index funds |
[
{
"content": "Let the set \\( P = \\{1, 2, \\ldots, 2014\\} \\) and \\( A \\subseteq P \\). If the difference between any two numbers in the set \\( A \\) is not a multiple of 99, and the sum of any two numbers in the set \\( A \\) is also not a multiple of 99, what is the maximum number of elements that the se... | 50 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 50 min |
[
{
"content": "Let \\(\\{a_{n}\\}\\) be an integer sequence such that for any \\(n \\in \\mathbf{N}^{*}\\), the condition \\((n-1) a_{n+1} = (n+1) a_{n} - 2 (n-1)\\) holds. Additionally, \\(2008 \\mid a_{2007}\\). Find the smallest positive integer \\(n \\geqslant 2\\) such that \\(2008 \\mid a_{n}\\).",
"ro... | 501 |
[
{
"content": "Determine the dimension of the vector space $V$ defined by $$ V = \\{P \\in \\mathbb{R}_n [X] : P (X^3)-( X^{n+1} + 1) P (X) =0\\} $$ for $n \\in \\mathbb {N}$. \\( \\mathbb{R}_n [X] \\) denotes the space of real polynomials of degree at most \\( n \\).",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | (15.9m) 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... | 10.16 F |
[
{
"content": "Find all integer pairs \\((x, y)\\) such that \\(4y^2 = x^7 + 1\\).",
"role": "user"
}
] | (-1, 0) |
[
{
"content": "Let \\(a_1, a_2, a_3, a_4\\) be positive integers such that it is impossible to arrange them around a circle where all neighbors are coprime. Determine the maximum number of triples \\((i, j, k)\\) with \\(i, j, k \\in \\{1, 2, 3, 4\\}\\) and \\(i \\neq j\\), \\(j \\neq k\\), \\(k \\neq i\\) for w... | 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... | 12.57 ft^3 |
[
{
"content": "Consider the polynomial \\(P(z)=\\sum_{k=0}^n a_k z^k\\) of degree \\(n\\), and let \\(z_k\\) (for \\(1 \\leq k \\leq n\\)) be the \\(n\\)th roots of \\(-1\\). Evaluate the truth of the following modified inequality for \\(\\theta = 0\\):\n\\[|P'(e^{i\\theta})| \\leq \\frac{4}{n} \\sum_{k=1}^n \\l... | True |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $5,501.93 |
[
{
"content": "In the figure, $\\angle ABC$ and $\\angle ADB$ are each right angles. Additionally, $AC = 17.8$ units and $AD = 5$ units. What is the length of segment $DB$? [asy]\nimport olympiad; import geometry; size(150); defaultpen(linewidth(0.8));\ntriangle t = triangle((0,0),(sqrt(89),0),(sqrt(89),-8/5*sqr... | 8 |
[
{
"content": "Given a positive integer $x$, let $x_n$ denote the remainder when $x$ is divided by $n$. Compute the sum of all elements in the solution set of the equation:\n\n$$x^5(x_5)^5 - x^6 - (x_5)^6 + x(x_5) = 0,$$\n\nwhere $x_5$ is restricted to the interval $[0, 4]$. What is the sum of all such $x$?",
... | 1300 |
[
{
"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... | 1.90e-5 A/t |
[
{
"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... | 0.036 eV |
[
{
"content": "Let $H$ and $K$ be two subgroups of a group $G$, each of finite order. Can the subgroup generated by $H$ and $K$, denoted as $HK$, be infinite?",
"role": "user"
}
] | Yes |
[
{
"content": "Consider a sequence of independent random variables \\(X_n \\sim U (1, 1+ 1/n)\\). Determine whether this sequence converges almost surely.",
"role": "user"
}
] | 1 |
[
{
"content": "Determine the smallest positive integer \\( m \\) such that the symmetric group \\( S_n \\) can be embedded into the general linear group \\( GL_m(F) \\), where \\( F \\) is a field.",
"role": "user"
}
] | n - 1 |
[
{
"content": "Given an irrational number \\( r \\in \\mathbb{R} \\), determine whether the set \\( r\\mathbb{Z} \\) is dense in the topological space \\( \\mathbb{R}/\\mathbb{Z} \\).",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit: \\[ \\lim_{k \\to 0^{+}} \\gamma(k) \\] where \\( \\gamma(k) = \\frac{(k+1)A-3kA+2A^3}{(k-A^2)^{\\frac{3}{2}}} \\) and \\( A = -\\sqrt{2} \\frac{\\Gamma(\\frac{k+1}{2})}{\\Gamma(\\frac{k}{2})} \\), with \\( \\Gamma \\) being the Gamma function.",
"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... | 7.85 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... | $5,045 |
[
{
"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... | mg/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... | 2p-2p overlapping |
[
{
"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... | 8e-13 F |
[
{
"content": "Determine whether the points $P(x, y)$ and $P^{\\prime}(x^{\\prime}, y^{\\prime})$, which satisfy the system of equations \\( x^{\\prime} = 3x + 2y + 1 \\) and \\( y^{\\prime} = x + 4y - 3 \\), can move along the same straight line.",
"role": "user"
}
] | Yes |
[
{
"content": "Let $G$ be a group with generators $a, b \\in G$. Define $\\mathrm{len}:G\\to\\mathbb{Z}_{\\geq 0}$ by sending $g$ to the minimum length of a word in $a, b, a^{-1}, b^{-1}$ equal to $g$. Assume that for all $g \\neq e \\in G$, there are infinitely many $n \\in \\mathbb{Z}_{\\geq 0}$ such that $\\m... | Yes |
[
{
"content": "Determine whether there exists an isometric embedding of the space $L^1(a,b;H^*)$ into the dual space of $L^{\\infty}(a,b;H)$, where $H$ is a separable Hilbert space and $H^*$ denotes its dual.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the integral \\( \\int_0^{2\\pi} \\frac{dx}{3-2\\cos x + \\sin x} \\).",
"role": "user"
}
] | \pi |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 44310845 |
[
{
"content": "Find the distance from the point $(1,-1,2)$ to the line passing through $(-2,2,1)$ and $(-1,-1,3).$",
"role": "user"
}
] | \sqrt{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... | <img>/cimages/multimages/16/se_lewis7678446189679546676.png</img> |
[
{
"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 m/s |
[
{
"content": "Let $m$ be a constant not equal to $0$ or $1.$ Then the graph of \\[x^2 + my^2 = 4\\]is a conic section with two foci. Find all values of $m$ such that the foci both lie on the circle $x^2+y^2=16.$\n\nEnter all possible values of $m,$ separated by commas.",
"role": "user"
}
] | \frac{1}{5}, -\frac{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... | 9.01% |
[
{
"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... | 1.39e-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... | 11 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... | sqrt(2qEz/m) |
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