prompt list | ground_truth string |
|---|---|
[
{
"content": "If $A$ and $B$ are subsets of $\\mathbb{N}$ with defined asymptotic densities, and $A \\cap B = \\emptyset$, is the asymptotic density of $A \\cup B$ also defined? Justify 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... | 303 K |
[
{
"content": "Let \\(a, b, c\\) be real numbers such that \\(\\frac{a+b}{1-ab}, b, \\frac{b+c}{1-bc}\\) are in arithmetic progression. If \\(\\alpha\\) and \\(\\beta\\) are the roots of the equation \\(2acx^2 + 2abcx + (a+c) = 0\\), find the value of \\((1+\\alpha)(1+\\beta)\\).",
"role": "user"
}
] | 1 |
[
{
"content": "Consider a rectangular board painted in three colors in a specific pattern: starting from a corner, one cell is painted with the first color, two adjacent cells with the second color, three adjacent cells with the third color, and then the pattern repeats with the first color. Determine if there e... | 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... | #v(t)=(dy)/(dt)=-1/((t+2)^2# |
[
{
"content": "Let $E_1$ and $E_2$ be two extensions of a field $F$ such that $[E_2:F]=2$ and $E_1\\cap E_2=F$. If $E_2=F(\\alpha)$, determine the degree $[E_1(\\alpha):E_1]$. \\( \\text{Provide your answer as a single integer.} \\)",
"role": "user"
}
] | 2 |
[
{
"content": "Evaluate the sum \\( I_1 + I_2 + I_3 + I_4 \\), where for a positive integer \\( n \\), \\( I_n = \\int_{-\\pi}^{\\pi} \\left(\\frac{\\pi}{2} - |x|\\right)\\cos nx\\ dx \\).",
"role": "user"
}
] | \dfrac{40}{9} |
[
{
"content": "Determine the nature of the roots of the quadratic equation \\( ax^2 + (b-c)x - 2b - c - a = 0 \\). Given that the expression \\( ax^2 + 2bx + c \\), where \\( a \\) is a non-zero real number, has the same sign as \\( a \\) for every real value of \\( x \\), choose the correct option:\n\n(A) real ... | 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... | 9420 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... | 2.17*10^4 N/C, directed vertically upward |
[
{
"content": "Determine whether the function \\( f(x) = e^{\\frac{x+1}{x}} \\) has a unique fixed point in the set of positive real numbers.",
"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... | The mass of the meter stick is 114.3g, and its center of gravity is located at 58.75cm. |
[
{
"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... | Zn^{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... | 1428.6 m^3 |
[
{
"content": "Find the value of \\( \\Phi \\), the infinite product of successive approximations to the golden ratio \\( \\phi \\), defined as \\[ \\Phi = \\frac{\\sqrt{1}}{\\phi} \\times \\frac{\\sqrt{1+\\sqrt{1}}}{\\phi} \\times \\frac{\\sqrt{1+\\sqrt{1+\\sqrt{1}}}}{\\phi} \\times \\dots \\]",
"role": "us... | \dfrac{1}{2} |
[
{
"content": "Let \\( \\{a_{n,k}\\}_{n\\in \\mathbb{N}} \\) be a sequence for some \\( k\\in \\mathbb{N} \\). Suppose that \\( \\lim_{n\\rightarrow \\infty} a_{n,k}=0 \\) for all \\( k=1,...,2n \\). Does this imply \\( \\lim_{n\\rightarrow \\infty} \\sum_{k=1}^{2n} a_{n,k}=0 \\)? Justify your answer.",
"rol... | No |
[
{
"content": "Let $S$ be the vector space of real $n \\times n$ skew-symmetric matrices. For a nonsingular matrix $A$, compute the determinant of the linear map $T_A : S \\rightarrow S$ where $T_A(X) = AXA^{T}$. What is the determinant of this map?",
"role": "user"
}
] | (\det A)^{n-1} |
[
{
"content": "Determine the form of the polynomial $P(x) \\in \\mathbb{R}[x]$ that satisfies the equation \\( P(x) \\cdot P(y) = P\\left(\\frac{x+y}{2}\\right)^2 - P\\left(\\frac{x-y}{2}\\right)^2 \\) for all real numbers $x$ and $y$. Provide your answer in terms of $P(x)$. ",
"role": "user"
}
] | P(x) = ax |
[
{
"content": "Let \\( n \\geq 3 \\) be a positive integer, and consider \\( n \\) numbers \\( a_{1}, a_{2}, \\cdots, a_{n} \\). Denote the sums of every pair of these numbers by \\( b_{ij} = a_{i} + a_{j} \\) for \\( i > j \\). If selecting any \\( k \\) numbers from these pairwise sums can uniquely determine t... | 2n - 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... | 145,566.702 L |
[
{
"content": "Maximize \\( \\int_{0}^{1} f(x)^5 \\, dx \\) over all functions \\( f: [0,1] \\to [-1,1] \\) such that \\( \\int_{0}^{1} f(x)^3 \\, dx = 0 \\) and \\( \\int_{0}^{1} f(x) \\, dx = 0 \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether the following limit is equal to 0:\n\n$$\\lim_{k\\to \\infty} \\sum_{i=1}^{k} a^{k-i} e_p(i+1)$$\n\nwhere $|a| < 1$ and $\\lim_{k\\to \\infty} e_p(k) = 0$. Provide a justification for your answer.",
"role": "user"
}
] | 0 |
[
{
"content": "Given a tetrahedron with one edge length \\( x \\) and the remaining edge lengths all equal to 1, the volume of the tetrahedron is represented by the function \\( F(x) \\). Determine which of the following best describes the behavior of \\( F(x) \\) within its domain:\n\nA. \\( F(x) \\) is an incr... | 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... | 0.0326 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... | 104.6 g of #Fe_2O_3# |
[
{
"content": "Given \\(\\alpha, \\beta \\in\\left(\\frac{3 \\pi}{4}, \\pi\\right)\\), \\(\\sin (\\alpha+\\beta)=-\\frac{3}{5}\\), and \\(\\sin \\left(\\beta-\\frac{\\pi}{4}\\right)=\\frac{12}{13}\\), find the value of \\(\\cos \\left(\\alpha+\\frac{\\pi}{4}\\right)\\).",
"role": "user"
}
] | -\dfrac{56}{65} |
[
{
"content": "Determine the number of elements in the field $F_2(a^2+a)$, where $F_{16} = F_2(a)$ and the minimal polynomial of $a$ over $F_2$ is $a^4 + a + 1$. Provide your answer as a single number.",
"role": "user"
}
] | 4 |
[
{
"content": "The line \\(\\frac{x}{4}+\\frac{y}{3}=1\\) intersects the ellipse \\(\\frac{x^{2}}{16}+\\frac{y^{2}}{9}=1\\) at points \\(A\\) and \\(B\\). Determine the number of points \\(P\\) on the ellipse such that the area of \\(\\triangle PAB\\) is 3.",
"role": "user"
}
] | 2 |
[
{
"content": "Let $E$ be a smooth curve, meaning it is a one-dimensional projective variety with a non-singular Jacobian matrix at any point. Suppose there is an isomorphism $\\phi$ that maps $E$ to another curve $E'$. Is $E'$ necessarily smooth?",
"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... | 2842.64 |
[
{
"content": "Given the smooth function $f(x,y)$ with partial derivatives $f_{x}(1,1)=2$ and $f_{y}(1,1)=-3$, and the parameterization $\\vec{r}(t)=(t,t^{2})$, determine if the derivative of the composite function $g(t)=(f\\circ \\vec{r})(t)=f(\\vec{r}(t))$ at $t=1$ is equal to $1$. State whether this is true o... | B |
[
{
"content": "Determine the time complexity of listing all triangles in a graph where the maximum degree of any vertex is 4.",
"role": "user"
}
] | O(n) |
[
{
"content": "Determine whether a random walk on the integers $\\mathbb{Z}$ with step $X_1$ is transient or recurrent, given that $P(X_1 = -2) = P(X_1 = 0) = P(X_1 = 3) = \\frac{1}{3}$. Provide your answer as either \"transient\" or \"recurrent\".",
"role": "user"
}
] | transient |
[
{
"content": "If $f(f(x)) = x$ for a function $f(x)$, does it imply that $f(x)$ is its own inverse? Determine whether this statement is never, sometimes, or always true.",
"role": "user"
}
] | 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... | 85.44 % |
[
{
"content": "Determine whether the general linear group $GL(2,\\mathbb{R})$ contains a cyclic subgroup of order 5, where $\\mathbb{R}$ denotes the set of all real numbers.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the maximum value of $z + x$ given the conditions: $x^2 + y^2 = 4$, $z^2 + t^2 = 9$, and $xt + yz \\geq 6$. Provide your answer in the form of a single number.",
"role": "user"
}
] | \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... | 1.6e6 W |
[
{
"content": "Given the matrix \\( A= \\begin{pmatrix} 0 & 1 & 2 \\\\ 0 & 0 & 1 \\\\ 0 & 0 & 0 \\\\ \\end{pmatrix} \\), determine the number of values \\( n \\) for which there exists a matrix \\( X \\) such that \\( X^n = A \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Let $g:\\mathbb{R} \\rightarrow \\mathbb{R}$ be a non-constant, twice differentiable function. If $g(1+\\frac{1}{n})+g(1-\\frac{1}{n})=2$ for all integers $n$, find $g''(1)$. \\( \\boxed{} \\)",
"role": "user"
}
] | 0 |
[
{
"content": "An 8 by 8 checkerboard has alternating black and white squares. How many distinct squares, with sides on the grid lines of the checkerboard (horizontal and vertical) and containing at least 5 black squares, can be drawn on the checkerboard?\n\n[asy]\ndraw((0,0)--(8,0)--(8,8)--(0,8)--cycle);\ndraw(... | 73 |
[
{
"content": "On an $8 \\times 8$ board, you can place several dominoes (each a $2 \\times 1$ rectangle) without overlapping. Let $N$ be the number of ways to place 32 dominoes to completely cover the board, and $S$ be the number of ways to place 16 dominoes. Determine which is greater: $N$ or $S$? Consider rot... | 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... | 8.87e8 J/mol |
[
{
"content": "Determine the number of distinct terms in the simplified expression \\((a+b+c)^{2006} + (a-b-c)^{2006}\\).",
"role": "user"
}
] | 1008016 |
[
{
"content": "Consider the bicomplex $(A_1^\\bullet, \\partial_1)$ and $(A_2^\\bullet, \\partial_2)$ of $\\mathbb{C}$-vector spaces, each equipped with an action of a discrete group $G$ that preserves the grading and commutes with the differentials. Assume $A_1$ is a free $\\mathbb{C}[G]$-module. Define the pro... | Yes |
[
{
"content": "Let $F$ be a field with $|F|=3^{2n+1}$, and let $r=3^{n+1}$. Find the number of elements $x \\in F$ that satisfy the equation $x^{r+1}=1$. Provide your answer as a single integer.",
"role": "user"
}
] | 2 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\to\\infty} \\int_{-1}^{1} \\cos^n(x)\\,dx. \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Calculate the work done by the force field \\( \\mathbf{F} = x^3\\,\\mathbf{i} + y^3\\,\\mathbf{j} \\) when an object is moved from point \\( P(1, 0) \\) to point \\( Q(2, 2) \\).",
"role": "user"
}
] | \dfrac{31}{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... | 1.12e-4 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... | 1693.06 psi |
[
{
"content": "In an inscribed quadrilateral \\(ABCD\\), diagonals intersect at point \\(O\\). Inside triangle \\(AOB\\), point \\(K\\) is chosen such that \\(KO\\) bisects angle \\(CKO\\). Ray \\(DK\\) intersects the circumcircle of triangle \\(COK\\) again at \\(L\\), and ray \\(CK\\) intersects the circumcirc... | 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... | 61250 lb-ft |
[
{
"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... | $\theta = {\cos ^{ - 1}}\left( {\frac{W}{{Td}}} \right)$ |
[
{
"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... | 1.77 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... | 10.18 |
[
{
"content": "Evaluate the definite integral \\( \\int_{1}^{3}{\\frac{1}{e^{-2x+4}+1}}dx \\).",
"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... | 240000 |
[
{
"content": "Determine the degree of the field extension \\(\\mathbb{Q}(\\sqrt{2}, \\sqrt[4]{2}, \\sqrt[8]{2})\\) over \\(\\mathbb{Q}\\). Choose the correct option: 4, 8, 14, 32.",
"role": "user"
}
] | 8 |
[
{
"content": "Evaluate the residue of the function \\( f(z) = (ze^{2-z}+(2-z)e^z)e^{(z-1)^{2}+(z-1)^{-2}} \\) at \\( z = 1 \\) using a method other than Laurent series expansion.",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether the following statement is true: For a bounded function $F: \\mathbb{R}_{\\ge 0} \\to \\mathbb{R}$, the condition \\( \\int_0^\\infty \\frac{x^k s}{(s^2 + x^2)^{(k+3)/2}} F(x) \\, dx = 0 \\) for all \\( s > 0 \\) implies \\( F \\equiv 0 \\), where \\( k \\in \\mathbb{N} \\) is a ... | 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... | -1,129.02 |
[
{
"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... | 2.88e-10 m |
[
{
"content": "Determine whether the set \\( V = \\left\\{ f \\in C^1[-1,1] \\mid f'(0) + \\int_{-1}^1 f(x) \\, dx = 0 \\right\\} \\) is a vector space.",
"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... | 63 mins |
[
{
"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... | m\sqrt{2g}(\sqrt{h_2} + \sqrt{h_1})/\Delta 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... | The magnitude of the net force is equal to the magnitude of the rubber weight of the ball. |
[
{
"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... | 29.45 |
[
{
"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... | 27.15e-3 psi |
[
{
"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... | 6.3s |
[
{
"content": "Given the recursive function \\( f(n+1) = (-1)^{n+1}n - 2f(n) \\) with the condition \\( f(1) = f(1986) \\), find the sum \\( f(1) + f(2) + f(3) + \\ldots + f(1985) \\).",
"role": "user"
}
] | 331 |
[
{
"content": "Determine the dimension of the vector space \\(\\mathbb{C}\\) over the field \\(\\mathbb{Q}\\).",
"role": "user"
}
] | 2^{\aleph_0} |
[
{
"content": "Evaluate the integral $$\\int_{-2}^2\\int_{-\\sqrt{4-x^2}}^{\\sqrt{4-x^2}}\\int_{-\\sqrt{4-x^2-y^2}}^{\\sqrt{4-x^2-y^2}}(z^3\\cos xyz-3)\\,dz\\,dy\\,dx$$ without using integration.",
"role": "user"
}
] | -32\pi |
[
{
"content": "Compute the area of an ideal triangle in the Poincaré disk model, where the triangle's vertices are on the boundary of the disk. One side of the triangle is a vertical geodesic that intersects a semicircle at the points (0,0) and (1,0). The semicircle is described by the equation \\((x-\\frac{1}{2... | \pi |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\rightarrow \\infty} \\frac{x^5 \\sin \\frac{1}{x} + \\cos x }{x^2 + x \\sin x}$$",
"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... | Hg_2Cl_2(s) + 2NH_3(aq) o Hg(s) + HgNH_2Cl(s) + NH_4^+(aq)+Cl^-(aq) |
[
{
"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... | {\Delta H = -1.12 \times 10^5 J, \Delta S = -120.6 J/mol \cdot K} |
[
{
"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... | 5.74 |
[
{
"content": "Find the area of the largest rectangle that can be inscribed in the ellipse \\(\\frac{x^2}{9} + \\frac{y^2}{4} = 1\\).",
"role": "user"
}
] | 12 |
[
{
"content": "Determine the function \\( f(x) \\) that satisfies the integro-differential equation: \\[ \\int_0^x f(u)du - f'(x) = x \\]",
"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... | 102858 |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\to \\infty}\\sin\\left(\\frac{\\pi}{3^{2}}\\right)\\sin\\left(\\frac{\\pi}{3^{3}}\\right)\\cdots\\sin\\left(\\frac{\\pi}{3^{n}}\\right)$$",
"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... | 53.6 m, 22.5 degrees South of West |
[
{
"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... | $14.84 |
[
{
"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... | -115.8 kJ |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 15.65 m/s |
[
{
"content": "Find the maximum value of \\(|\\sin z|\\) on the region \\([0,2\\pi] \\times [0,2\\pi]\\).",
"role": "user"
}
] | \cosh(2\pi) |
[
{
"content": "Given two full column rank matrices $A$ and $B$, where any non-zero linear combination of the columns of $A$ is not in the column space of $B$, determine if the matrix $[A, B]$, formed by concatenating $A$ and $B$, has full column rank.",
"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... | 46 mA |
[
{
"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... | 120% |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 90 |
[
{
"content": "Given the function \\( f(x) = \\left|\\log_{2} x\\right| \\), if the real numbers \\( a \\) and \\( b \\) (where \\( a < b \\)) satisfy \\( f(a) = f(b) \\), determine the range of values for \\( a + 2014b \\).",
"role": "user"
}
] | (2015, +\infty) |
[
{
"content": "Calculate the limit: \\[ \\lim_{x \\to 0^+} x^{x^{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... | 2.5e+04 N/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... | 1.24e-14 kg.m/s |
[
{
"content": "Evaluate the limit: $$ \\lim_{x\\to 0} \\left( \\frac{e\\cos(x)-e}{\\ln(1+\\ln(2-e^{\\sin^2(x)}))} \\right) $$",
"role": "user"
}
] | \dfrac{e}{2} |
[
{
"content": "Consider the logarithmic function with two branches, $f(z)$ and $g(z)$. If $f(z)$ has a branch cut along the positive real axis and $g(z)$ has a branch cut along the negative real axis, determine if it is possible for $f(z)$ and $g(z)$ to be equal for some $z$. Provide a justification for your ans... | Yes |
[
{
"content": "Consider a sequence of random variables \\((X_n)_{n \\in \\mathbb{N}^*}\\) defined as follows: for any \\(n \\in \\mathbb{N}^*\\), \\(X_n\\) has a probability mass function given by \\(\\mathbb{P}[X_n = \\frac{1}{n}] = 1 - \\frac{1}{n^2}\\) and \\(\\mathbb{P}[X_n = n] = \\frac{1}{n^2}\\). Determin... | 0 |
[
{
"content": "Determine the conditions on the function $F(x)$ such that the solution $u(x,t)$ to the partial differential equation $u_{t} - u_{xx} = F(x)$ on the interval $(0,\\pi)$ with homogeneous Neumann boundary conditions $u_{x} = 0$ for $x=\\{0,\\pi\\}$ has a limit as $t \\to \\infty$. Assume $F(x)$ is in... | c_0 = 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... | The percentages of Mg-24 and Mg-26 are 78.93% and 10.94%, respectively. |
[
{
"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... | 18246 |
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