prompt list | ground_truth string |
|---|---|
[
{
"content": "Determine the number of integer values of \\( x \\) such that the expression \\( \\frac{4^n + 15n - 1}{x} \\) is an integer for every positive integer \\( n \\).",
"role": "user"
}
] | 6 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 7.6 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... | 43.33 barrels |
[
{
"content": "Determine whether a closed smooth manifold $M$ is diffeomorphic to the sphere $S^n$ if there exists a diffeomorphism between $M - \\{p\\}$ and $\\mathbb{R}^n$ for some point $p$ on $M$. Provide a justification for your answer.",
"role": "user"
}
] | No |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Through certain half-deserted streets, past cheap hotels and sawdust restaurants with oyster shells. |
[
{
"content": "Find the limit of \\( \\frac{{{k-1}\\choose n}}{{{n+k-1}\\choose n}} \\) as \\( n, k \\to \\infty \\) such that \\( \\frac{k}{n^2} \\to a > 0 \\).",
"role": "user"
}
] | e^{-1/a} |
[
{
"content": "Determine whether the statement is true: $X_n \\to X$ in distribution if and only if $X_n - X \\to 0$ in distribution.",
"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... | 3712.50 units |
[
{
"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... | imaginary audience |
[
{
"content": "Determine whether there are integer solutions to the equation \\(x^2 + y^2 - z^2 = 1\\).",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the value of the constant \\( c \\) such that the function \\( f(x,y) = c\\frac{2^{x+y}}{x!y!} \\) is a valid probability density function for the discrete random vector \\((X,Y)\\) over \\( \\mathbb{N}_0 \\times \\mathbb{N}_0 \\).",
"role": "user"
}
] | e^{-4} |
[
{
"content": "Calculate \\( \\int\\int_R xe^y \\, dA \\), where \\( R \\) is the region inside the circle \\( x^2 + y^2 = 1 \\) and outside the circle \\( x^2 + y^2 = 2y \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Given a topological space \\( E \\) with the topology \\( \\theta = \\{ G \\subseteq E \\mid \\text{card}(E \\setminus G) < \\infty \\} \\cup \\{ \\emptyset \\} \\), where \\( \\text{card}(E) = \\infty \\), find the interior \\( \\mathring{A} \\) of a set \\( A \\) such that \\( \\text{card}(A) = ... | \emptyset |
[
{
"content": "Determine all linear transformations \\( T: V \\to V \\) for a real vector space \\( V \\) of dimension \\( n > 1 \\) such that the matrix representation of \\( T \\) is independent of the basis. This means that for any invertible matrix \\( P \\), the condition \\( TP = PT \\) holds. Describe the... | T = \lambda I |
[
{
"content": "Determine whether the following statement is true or false: Every unbounded chain in a partially ordered set must be infinite.",
"role": "user"
}
] | True |
[
{
"content": "Is the topology on a compact connected Lie group metrizable? Specifically, if $G$ is a compact connected Lie group, does there exist a metric on $G$ that induces the underlying topology, ensuring $G$ is compact and connected with respect to this metric?",
"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... | 431 kJ |
[
{
"content": "Let $(\\Omega, \\mathcal{A}, \\operatorname{P})$ be a probability space, $(\\mathcal{F}_t)_{t \\geq 0}$ a filtration on $(\\Omega, \\mathcal{A})$, and $E$ a Banach space over $\\mathbb{R}$. Consider an $E$-valued process $(X_t)_{t \\geq 0}$ on $(\\Omega, \\mathcal{A}, \\operatorname{P})$ that is $... | 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... | 0.42 |
[
{
"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... | 1451 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... | Common Stock: $19,500
Retained Earnings: $13,000
Total Equity: $32,500 |
[
{
"content": "Evaluate the integral \\( \\frac{1}{2\\pi i}\\int_{\\gamma} \\frac{1}{z^2(e^{z}-1)}dz \\) where \\( \\gamma=\\{z: z=\\frac{1}{2}e^{2\\pi i t},0\\leq t\\leq1 \\} \\).",
"role": "user"
}
] | \dfrac{1}{12} |
[
{
"content": "In triangle \\(ABC\\), the median drawn from vertex \\(A\\) to side \\(BC\\) is four times shorter than side \\(AB\\) and forms a \\(60^\\circ\\) angle with it. Determine the measure of angle \\(A\\).",
"role": "user"
}
] | 150^\circ |
[
{
"content": "Find all eigenvalues of the linear transformation \\( L : P_3(\\mathbb{R}) \\rightarrow P_3(\\mathbb{R}) \\) defined by \\( L(p) = p' + p \\), where \\( p' \\) is the derivative of the polynomial \\( p \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Determine whether the bilinear form \\( \\langle f,g\\rangle =\\int^1_0f(x)g(x)xdx \\) is positive for all non-zero polynomials \\( f \\) and \\( g \\) in the vector space of polynomials of degree at most 2.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit \\(\\lim_{x \\to 0} \\frac{1}{x} \\left [ \\sqrt[3]{\\frac{1 - \\sqrt{1 - x}}{\\sqrt{1 + x} - 1}} - 1\\right ]\\) without using rationalization.",
"role": "user"
}
] | \dfrac{1}{6} |
[
{
"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... | 223 days |
[
{
"content": "If $\\omega$ is a faithful normal state on a von Neumann algebra $R$, and $P_1, P_2, \\ldots$ are projection operators in $R$ such that $\\omega(P_n) \\rightarrow 0$ as $n \\rightarrow \\infty$, determine whether the $P_n$ must converge to $0$ in the strong operator 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... | 6.892% |
[
{
"content": "Given a positive real number $l$, determine whether there exists a closed hyperbolic surface $X$ such that the injectivity radius of $X$ is not less than $l$. 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... | 475842.70 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... | 375 V |
[
{
"content": "Determine the number of spanning trees in a graph after contracting one edge in the middle of a triangle.",
"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... | 2.634e-19 J |
[
{
"content": "Determine whether the functions $p_1(z) = z^n$ and $p_2(z) = z^m$ from the unit circle $S^1$ to itself are homotopic, where $m$ and $n$ are fixed natural numbers.",
"role": "user"
}
] | m = 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... | 17.37% |
[
{
"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... | 73.14% |
[
{
"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... | 0.16% |
[
{
"content": "Let real numbers \\( x \\) and \\( y \\) satisfy the equation \\( 4x^2 - 5xy + 4y^2 = 5 \\). Define \\( S = x^2 + y^2 \\). Determine the maximum and minimum values of \\( S \\), denoted as \\( p \\) and \\( q \\) respectively. Calculate \\( \\frac{1}{p} + \\frac{1}{q} \\).",
"role": "user"
}... | \dfrac{8}{5} |
[
{
"content": "Given that \\(t^3\\) and \\(t e^t \\sin(t)\\) are solutions to an nth-order linear homogeneous differential equation with constant coefficients, determine the minimum possible value of \\(n\\).",
"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... | 245.88 |
[
{
"content": "Determine the values of $x$ for which the series \\(\\sum_{n=2}^\\infty \\Bigg|\\frac{x^n}{n(\\log n)^2}\\Bigg|\\) converges. Analyze the limit obtained from the Ratio Test:\n\\[ \\lim_{n\\to\\infty}(x)\\Bigg(\\frac{2\\log n + (\\log n)^2}{2\\log(n+1)+\\big(\\log(n+1)\\big)^2}\\Bigg) \\] to find t... | [-1, 1] |
[
{
"content": "Determine the rank of the elliptic curve given by the equation \\( y^2 = x^3 + p^3x \\) where \\( p \\) is a prime number such that \\( p \\equiv 7 \\pmod{16} \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Verify the formula \\( \\sum\\limits_{d|n} \\mu (d) \\lambda(d)= 2^{\\omega (n)} \\) for an integer \\( n \\geq 1 \\).",
"role": "user"
}
] | 2^{\omega(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... | -2.4 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... | -3.4 eV |
[
{
"content": "Can the action of $Spin(9)$ on the space of octonionic Hermitian $2 \\times 2$ matrices diagonalize any such matrix?",
"role": "user"
}
] | Yes |
[
{
"content": "Calculate the limit \\( \\lim_{n\\rightarrow\\infty} \\sum_{k=1}^{n}\\cos\\left( \\frac{2\\pi k}{2n+1} \\right) \\).",
"role": "user"
}
] | -\dfrac{1}{2} |
[
{
"content": "Select the false statement among the following options involving scalar fields and vector fields:\n\n1. For twice differentiable scalar fields \\(f\\) and \\(g\\), the Laplacian of their product satisfies: \\(\\nabla^2(fg) = f\\nabla^2g + g\\nabla^2f + 2\\nabla f \\cdot \\nabla g\\)\n2. There exis... | 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... | 18,18,000 |
[
{
"content": "Let $A$, $M$, and $C$ be nonnegative integers such that $A+M+C=12$. What is the maximum value of \\[A\\cdot M\\cdot C+A\\cdot M+M\\cdot\nC+C\\cdot A?\\]",
"role": "user"
}
] | 112 |
[
{
"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... | 18.55 m |
[
{
"content": "Without using a calculator, determine which is larger: $e^\\pi$ or $\\pi^e$.",
"role": "user"
}
] | e^\pi |
[
{
"content": "Solve the differential equation $f' = f$ using the Fourier transform method. Verify that the solution is $f(x) = e^x$.",
"role": "user"
}
] | e^x |
[
{
"content": "Evaluate the integral \\( \\oint_{|z|=1} z^4 \\cos(\\sin (1/z)) \\, dz \\) using the Residue Theorem.",
"role": "user"
}
] | 0 |
[
{
"content": "There are 2017 distinct points $A_{1}, A_{2}, \\ldots, A_{2017}$ marked on a circle. All possible chords connecting these points in pairs are drawn. A line passing through point $A_{1}$, which does not pass through any of the other points $A_{2}, \\ldots, A_{2017}$, is drawn. Determine the greates... | 1016064 |
[
{
"content": "Rewrite the expression \\(X^2 - 2X - 1 + \\frac{2}{X} + \\frac{1}{X^2}\\) in terms of \\(Y\\), given that \\(Y = X - \\frac{1}{X}\\).",
"role": "user"
}
] | (Y - 1)^2 |
[
{
"content": "Determine the number of ways to distribute 80 balls into 5 distinguishable bins such that no bin contains more than 24 balls.",
"role": "user"
}
] | 116371 |
[
{
"content": "Find the sum of the coefficients in the polynomial $3(3x^{7} + 8x^4 - 7) + 7(x^5 - 7x^2 + 5)$ when it is fully simplified.",
"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... | 22.21 |
[
{
"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... | 0.9999999999754c |
[
{
"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_0=sqrt(gR(cos(beta))^2/(2sin(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... | 65.85 degree 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... | $183,264.23 |
[
{
"content": "Find the power series solution for the differential equation \\((x-1)y'' - xy' + y = 0\\) with initial conditions \\(y(0) = -2\\) and \\(y'(0) = 6\\).",
"role": "user"
}
] | -2e^x + 8x |
[
{
"content": "Determine the number of models of the real numbers up to isomorphism.",
"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... | 8.56e-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... | 41 g NaNO_3 |
[
{
"content": "For any positive definite matrix $A$, does there exist some $m > 0$ such that $A - mI$ is positive semi-definite?",
"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... | 111.4% |
[
{
"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... | 93.5 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... | 5015.6kg |
[
{
"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... | 3.02E9 V |
[
{
"content": "Calculate \\( f^{(2001)}(0) \\) for the function \\( f(x) = e^{-x}\\sin(x) \\).",
"role": "user"
}
] | 2^{1000} |
[
{
"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... | 2.1 s |
[
{
"content": "Evaluate the expression \\(\\frac{z^{2012n} + z^{1006n}}{z^{2012n} + z^{1006n} + \\frac{1}{z^{2012n}} + \\frac{1}{z^{1006n}}}\\) for a given natural number \\( n \\), where \\( z \\) is a complex number satisfying the equation \\( z^5 + z^4 + z^3 + z^2 + z + 1 = 0 \\). Find the value of the expres... | \dfrac{1}{2} |
[
{
"content": "Compute the limit: \\[ \\lim_{T \\rightarrow \\infty} \\frac{1}{T} \\int_{0}^{T} \\sin(\\alpha x)\\cos(\\beta x) \\,dx \\] given that \\(|\\alpha| \\neq |\\beta|\\).",
"role": "user"
}
] | 0 |
[
{
"content": "Find all non-constant functions \\( g: \\mathbb{R} \\rightarrow \\mathbb{R} \\) that satisfy the functional equation \\( g(a+b) = g(a) + g(b) \\) and the condition \\( \\lim\\limits_{x\\rightarrow \\infty} g(x) = 0 \\).",
"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... | 3.88s |
[
{
"content": "Evaluate the definite integral \\( \\int_0^2 x^2 \\,d(x^2) \\). Determine whether the limits of integration should be applied to \\( x \\) or \\( x^2 \\).",
"role": "user"
}
] | 8 |
[
{
"content": "Determine whether the operator \\( L: \\mathbb{R}[X] \\rightarrow \\mathbb{R}[X] \\) defined by \\( L\\left(\\sum\\limits_n a_nX^n\\right)=\\sum\\limits_n a_{2n}X^{2n} \\) is bounded with respect to the norm \\( \\|p\\|=\\int\\limits_{-1}^{1}|p(t)|dt \\). If it is bounded, find its norm.",
"ro... | 1 |
[
{
"content": "Evaluate the contour integral \\( \\oint_{|z-i|=1/2} \\left( \\frac{z^2}{z-i} + \\ln\\frac{z+1}{z-1} \\right) \\, dz \\).",
"role": "user"
}
] | -2\pi i |
[
{
"content": "Evaluate the limit: $$\\lim_{h \\rightarrow 0} \\frac{\\tan(a+3h)-3\\tan(a+2h)+3\\tan(a+h)-\\tan a}{h}$$",
"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... | 208630.56 |
[
{
"content": "Evaluate the integral \\( \\int_{-\\pi/4}^{\\pi/4} (\\cos{t} + \\sqrt{1 + t^2}\\cos^3{(t)}\\sin^3{(t)})\\;\\mathrm{d}t \\).",
"role": "user"
}
] | \sqrt{2} |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\to\\infty} \\int_0^\\infty \\frac{\\sin(x/n)}{x+x^2}dx$$",
"role": "user"
}
] | 0 |
[
{
"content": "This circle passes through the points $(-1, 2)$, $(3,0)$ and $(9,0)$. The center of the circle is at $(h,k)$. What is the value of $h+k$?",
"role": "user"
}
] | 17 |
[
{
"content": "Determine the number of roots of the equation \\(x^3 + x^2 + 2x + \\sin x = 0\\) within the interval \\([-2\\pi, 2\\pi]\\).",
"role": "user"
}
] | 1 |
[
{
"content": "Find all pairs of real numbers \\((a, b)\\) such that for the function \\(f(x) = \\frac{x+a}{x+b}\\), the composition \\(f(f(x)) = -\\frac{1}{x}\\) holds for all real numbers \\(x\\) where \\(x \\neq 0\\) and \\(x \\neq -b\\).",
"role": "user"
}
] | (-1, 1) |
[
{
"content": "Can an inner product space have infinitely many dimensions?",
"role": "user"
}
] | Yes |
[
{
"content": "Let $V$ be a finite-dimensional complex vector space, $v \\in V$ be a nonzero vector, and $g$ be a linear functional on $V$. Define a linear operator $B: V \\to V$ by $B(x) = x - \\frac{g(x)}{g(v)}v$. Find the determinant of the operator $B$. \\( \\boxed{} \\)",
"role": "user"
}
] | 0 |
[
{
"content": "In neutral geometry, if opposite angles formed by intersecting lines are equal, does this imply that the lines are parallel? Answer true or false.",
"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... | 61.5 ft/s |
[
{
"content": "Consider two Gaussian distributions, where one has a variance of zero, effectively making it a unit impulse function. Determine the Overlapping Coefficient between these two distributions.",
"role": "user"
}
] | 0 |
[
{
"content": "Given points $A$, $B$, $C$, and $P$ in the plane such that no three are collinear, the areas of triangles $BPC$, $CPA$, and $APB$ are 13, 14, and 15, respectively. Compute the sum of all possible values for the area of triangle $ABC$. ",
"role": "user"
}
] | 84 |
[
{
"content": "Find the pointwise limit of the sequence of functions \\( f_n(x) \\), where \\( f_n(x) = 1 \\) if \\( x \\in [n, n+1] \\) and \\( f_n(x) = 0 \\) otherwise, as \\( n \\to \\infty \\).",
"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... | $229,000 |
[
{
"content": "Let $B$ be a real square matrix such that $BB^{T}=I$ and $\\det B > 0$. Find the determinant of the matrix $B - I$. \\( \\text{(Express your answer as a single number.)} \\)",
"role": "user"
}
] | 0 |
[
{
"content": "Find the limit of the sequence as \\( x \\to 1 \\) for \\( x > 1 \\):\n\\[ \\lim_{x\\to 1} \\frac{\\ln(x) - \\sin(\\pi x)}{\\sqrt{x -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... | Psychodynamic theory |
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