prompt list | ground_truth string |
|---|---|
[
{
"content": "Determine the number of integer pairs \\((x, y)\\) that satisfy the following system of inequalities:\n\n\\[\\begin{cases} y \\geq 2^{x} + 3 \\cdot 2^{34} \\\\ y < 76 + 2(2^{32} - 1)x \\end{cases}\\]",
"role": "user"
}
] | 3985729651808 |
[
{
"content": "In triangle $ABC$, points $K$ and $N$ are located on segments $AB$ and $BC$, respectively, such that $BK = 2AK$ and $CN = 2BN$. Let $Q$ be the intersection of lines $AN$ and $CK$. Calculate the ratio $\\frac{S_{\\triangle ABC}}{S_{\\triangle BCQ}}$. \\(\\text{Express your answer as a simplified fr... | \dfrac{7}{4} |
[
{
"content": "Given a hyperbola with foci $F_{1}$ and $F_{2}$, and vertices $M$ and $N$, if the vertex $P$ of triangle $\\triangle P F_{1} F_{2}$ lies on the hyperbola, determine the position of the point where the incircle of $\\triangle P F_{1} F_{2}$ touches side $F_{1} F_{2}$. Choose from the following opti... | 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... | 54.8 |
[
{
"content": "Find the partial derivative \\( f_x(0,0) \\) of the function \\( f(x, y) = \\frac{5x^2y}{x^4+y^2} \\), given that \\( f(0,0) = 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... | 24.52% |
[
{
"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 annealing temperature is calculated as Tm - 5C, where Tm = (4 x (G+C)) + (2 x (A+T)). This temperature is the same for the first and last cycle. |
[
{
"content": "In an equilateral triangle $ABC$, a point $M$ is located inside the triangle. Let $D$, $E$, and $F$ be the orthogonal projections of $M$ onto sides $AB$, $BC$, and $AC$, respectively, with $MD = 1$, $ME = 2$, and $MF = 3$. Determine the side length of triangle $ABC$.",
"role": "user"
}
] | 4\sqrt{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... | 11,036 |
[
{
"content": "Find the coefficient of \\(x^5\\) in the expansion of \\((1+2x+3x^2+4x^3)^5\\).",
"role": "user"
}
] | 1772 |
[
{
"content": "Let $a$ and $b$ be two 12th roots of unity, not necessarily distinct. Find the number of different possible values of $(a + b)^{12}.$",
"role": "user"
}
] | 7 |
[
{
"content": "Determine whether the following statement is true or false: If the set of limit points of a set $X$, denoted by $X'$, is finite or countable, then the set $X$ is also finite or countable.",
"role": "user"
}
] | B |
[
{
"content": "Given the quadratic function \\( y = x^2 + 2mx - 3m + 1 \\), where the variable \\( x \\) and real numbers \\( p \\) and \\( q \\) satisfy:\n\\[ 4p^2 + 9q^2 = 2, \\]\n\\[ \\frac{1}{2}x + 3pq = 1, \\]\nand the minimum value of \\( y \\) is 1. Find the value of \\( m \\).",
"role": "user"
}
] | -3 |
[
{
"content": "Consider a tetrahedron where one edge has a length of \\( x \\) and the remaining edges have a length of 1. The volume of this tetrahedron is given by the function \\( F(x) \\). Determine the nature of the function \\( F(x) \\) over its domain:\n\n(A) It is an increasing function but has no maximu... | D |
[
{
"content": "Evaluate the definite integral \\( \\int_4^6 \\sin^4 (\\pi x) \\cdot \\cos^2 (2 \\pi x) \\,\\mathrm{d}x \\) using reduction formulae or other appropriate methods.",
"role": "user"
}
] | \dfrac{7}{16} |
[
{
"content": "In rhombus \\(ABCD\\), a point \\(M\\) is located on the extension of side \\(AB\\) beyond \\(B\\) such that \\(MD = MC\\) and \\(\\angle MDC = \\arctan \\frac{8}{5}\\). Determine the ratio \\(\\frac{MA}{MB}\\).",
"role": "user"
}
] | 11 |
[
{
"content": "Let $U$ be an open set of the Riemann sphere, and let $z_i$ be $n$ distinct points in $U$. Consider $E$, the vector space of meromorphic functions on $U$ with poles of order no more than 2, and $F$, the subspace of $E$ consisting of functions that are holomorphic in a neighborhood of each $z_i$. D... | 2n |
[
{
"content": "Evaluate the limit: $$\\lim\\limits_{x\\to 0}{\\frac{ \\sqrt{x+\\sqrt{x+\\sqrt{x}}} }{ 2\\sqrt{x}+4\\sqrt[8]{x}}}$$ After simplifying the expression, determine the value of the limit as \\(x\\) approaches 0.",
"role": "user"
}
] | \dfrac{1}{4} |
[
{
"content": "Find the vector $\\mathbf{v}$ such that\n\\[\\begin{pmatrix} 2 & 3 & -1 \\\\ 0 & 4 & 5 \\\\ 4 & 0 & -2 \\end{pmatrix} \\mathbf{v} = \\begin{pmatrix} 2 \\\\ 27 \\\\ -14 \\end{pmatrix}.\\]",
"role": "user"
}
] | \begin{pmatrix} -2 \\ 3 \\ 3 \end{pmatrix} |
[
{
"content": "A finite set of points in the plane has the property that for any two points A and B in the set, there exists a point C in the set such that triangle ABC is equilateral. Determine the maximum number of points that such a set can contain.",
"role": "user"
}
] | 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... | $87.57 |
[
{
"content": "Calculate the limit \\(\\lim_{N\\to\\infty} \\frac{N!}{(N-k)!N^{k}}\\) for any integer \\(k\\) between \\(0\\) and \\(N\\).",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate the integral \\( \\int_0^{+\\infty} \\frac{\\sin^4{x}}{x^4} \\, dx \\).",
"role": "user"
}
] | \dfrac{\pi}{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... | 11.37 |
[
{
"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... | 14.12 kV |
[
{
"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... | 0.1141 M |
[
{
"content": "Count the number of functions \\( f: \\{1, 2, \\ldots, 12\\} \\rightarrow \\{1, 2, \\ldots, 12\\} \\) such that if \\((a, b, c)\\) is a multiplication pair, then \\((f(a), f(b), f(c))\\) is also a multiplication pair.",
"role": "user"
}
] | 7776 |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\to \\infty } \\frac {1^3+4^3+7^3+...+(3n-2)^3}{[1+4+7+...+(3n-2)]^2}$$",
"role": "user"
}
] | 3 |
[
{
"content": "If two acute angles $\\alpha$ and $\\beta$ satisfy $(\\sin \\alpha + \\cos \\alpha)(\\sin \\beta + \\cos \\beta) = 2$, find the value of $(\\sin 2\\alpha + \\cos 3\\beta)^2 + (\\sin 2\\beta + \\cos 3\\alpha)^2$. \\(\\boxed{\\text{Your answer here}}\\)",
"role": "user"
}
] | 3 - 2\sqrt{2} |
[
{
"content": "The trip from Carville to Nikpath requires $4\\frac 12$ hours when traveling at an average speed of 70 miles per hour. How many hours does the trip require when traveling at an average speed of 60 miles per hour? Express your answer as a decimal to the nearest hundredth.",
"role": "user"
}
] | 5.25 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 19.6 m |
[
{
"content": "Is the trace of a sum of nilpotent matrices always zero?",
"role": "user"
}
] | Yes |
[
{
"content": "Find a closed form for the limit:\n\\[ f(m) = \\lim_{n\\to\\infty} \\left(\\prod_{i=1}^n \\frac{m+i}{n}\\right)^{1/n} \\]\nAssume \\(m\\) is a positive real number.",
"role": "user"
}
] | \dfrac{1}{e} |
[
{
"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... | $15,020 |
[
{
"content": "Evaluate the limit \\( \\lim_{n\\to\\infty}\\int_{0}^{\\infty}\\frac{x}{\\sqrt[n]{1+x^{3n}}}dx \\). Determine whether the limit converges or diverges.",
"role": "user"
}
] | \dfrac{3}{2} |
[
{
"content": "Compute the Krull dimension of the ring \\( k[x,y,z]/(xz, yz) \\).",
"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... | 5.5 moles |
[
{
"content": "Find a closed-form expression for the series: \\( \\sum_{k=0}^{\\infty} \\frac{z^k}{(k!)^2} \\).",
"role": "user"
}
] | I_0(2\sqrt{z}) |
[
{
"content": "Given that the absolute value of the difference of the two roots of $ax^2 + 5x - 3 = 0$ is $\\frac{\\sqrt{61}}{3}$, and $a$ is positive, what is the value of $a$?",
"role": "user"
}
] | 3 |
[
{
"content": "What is the coproduct in the category of commutative rings?",
"role": "user"
}
] | A \otimes_{\mathbb{Z}} 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... | 0.067 ton/Litre |
[
{
"content": "Find the last two digits of the integer \\( \\left[\\frac{10^{93}}{10^{31}+3}\\right] \\). Write the tens digit first, followed by the units digit, where \\([x]\\) denotes the greatest integer less than or equal to \\(x\\).",
"role": "user"
}
] | 08 |
[
{
"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... | 1.347e+6 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... | 290K |
[
{
"content": "If two regular unit speed curves have the same non-vanishing curvature and torsion, are the curves necessarily congruent?",
"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... | 1447 J |
[
{
"content": "Find the splitting field $F$ of the polynomial $x^5 + x + 1$ over $\\mathbb{Z}_2$, and determine the degree $[F: \\mathbb{Z}_2]$. Given that $x^5 + x + 1$ factors as $(x^2 + x + 1)(x^3 + x^2 + 1)$ over $\\mathbb{Z}_2$, and both factors are irreducible, calculate the degree of the field extension."... | 6 |
[
{
"content": "Calculate the limit \\(\\lim_{n \\to \\infty}\\frac{(2x+1)n^n}{(n-1)^n(n+1)}\\).",
"role": "user"
}
] | 0 |
[
{
"content": "In right $\\Delta ABC$, $\\angle CAB$ is a right angle. Point $M$ is the midpoint of $\\overline{BC}$. What is the number of centimeters in the length of median $\\overline{AM}$? Express your answer as a decimal to the nearest tenth. [asy] pair A,B,C,M;\nA = (0,0); B = (4,0); C = (0,3); M = (B+C)/... | 2.5 |
[
{
"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... | 2.705646236e-4 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... | 111.06 N |
[
{
"content": "Determine whether the following statement is true or false: If a sequence $(u_n)$ in $L^p \\cap L^q$ converges to $u$ in $L^p$ and to $v$ in $L^q$, then $u = v$ almost everywhere.",
"role": "user"
}
] | True |
[
{
"content": "Compute the flux of the vector field \\( F = \\langle 4x, 4y, 0 \\rangle \\) through the surface \\( S \\), which is the part of the surface \\( z = 25 - (x^2 + y^2) \\) above the disk of radius 5 centered at the origin, oriented upward.",
"role": "user"
}
] | 2500\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... | 30 W/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... | 4.6 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... | 1.8 |
[
{
"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... | a/(2rg) |
[
{
"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... | 0.031 s^-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... | TUBE 1 - {eq}H_2SO_4{/eq}
TUBE 2 - {eq}NaOH{/eq}
TUBE 3 - {eq}K_2CO_3{/eq} |
[
{
"content": "Determine whether the following statement is true or false: If the derivative of a function $f$ at $0$ does not exist, then the right-hand derivative $f'_+(0)$, defined as $\\lim\\limits_{n\\to \\infty}n\\left[f\\left(\\dfrac{1}{n}\\right)-f(0)\\right]$ for $n \\in \\mathbb{N}$, may not exist eith... | A |
[
{
"content": "Find an element of order 5 in the field \\( \\mathbb{Z}_3[x]/\\langle x^4 + x + 2 \\rangle \\).",
"role": "user"
}
] | 2x^3 + x + 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... | 7.86e-6 m |
[
{
"content": "Find all integer solutions \\((x, y, z)\\) to the equation \\(x^3 + 2y^3 = 4z^3\\).",
"role": "user"
}
] | (0, 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... | $71,148 |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\to \\pi/2} (\\sin x)^{\\tan x}$$",
"role": "user"
}
] | 1 |
[
{
"content": "Determine the radius of convergence of the power series \\( \\sum_{n=0}^{\\infty} n!x^n \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether every compact infinite non-abelian topological group with a nontrivial topology has at least three distinct closed subgroups.",
"role": "user"
}
] | Yes |
[
{
"content": "Let \\(a, b, c\\) be non-negative real numbers such that \\(a^2 + b^2 + c^2 = 1\\). Determine the maximum value of the expression \\(2\\sqrt{6}ab + 8bc\\).",
"role": "user"
}
] | \sqrt{22} |
[
{
"content": "Determine the rational numbers \\( n \\) for which \\( \\sin(\\pi n) \\) is an algebraic number.",
"role": "user"
}
] | \mathbb{Q} |
[
{
"content": "Evaluate the integral \\( \\int_0^\\pi \\frac{\\sin{mt}\\sin{nt}}{a+b\\cos{nt}}dt \\) for positive integers \\(m, n\\), and real numbers \\(a, b\\) with \\(a > 0\\), \\(b < 0\\), \\(|a| > |b|\\), and \\(n > 1\\). Assume that \\(m\\) is significantly larger than \\(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... | $7,898 |
[
{
"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... | 193880.3 Joules |
[
{
"content": "Verify if the conclusion that the minimum of $x^TAy$ is 0, based on the given KKT conditions, is correct.",
"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... | 0.0568 m^3/kg |
[
{
"content": "Given a binary matrix $A$, determine the maximum possible difference between the rank of $A$ and the rank of NOT$(A)$. Provide your answer as a single integer.",
"role": "user"
}
] | 1 |
[
{
"content": "Determine if there is a closed form for the integral \\( \\int_0^{\\pi/2} \\frac{1}{1+\\tan^{s} x} \\, dx \\).",
"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... | 4.61 kg |
[
{
"content": "Prove that for any integer \\( n \\), the expression \\( n^{9^9} + 4 \\) is not divisible by 37.",
"role": "user"
}
] | n^{9^9} + 4 |
[
{
"content": "Let $N$ be a positive integer, and let $p$ and $q$ be distinct positive integers less than $N$. If the number of distinct remainders when multiples of $p$ are divided by $N$ is equal to the number of distinct remainders when multiples of $q$ are divided by $N$, does it imply that the two sets of r... | Yes |
[
{
"content": "Evaluate the integral: \\[ \\int_{-\\infty}^{+\\infty}\\frac{1}{\\sqrt{4\\pi}}e^{x}e^{-\\frac{x^2}{4}}dx \\]",
"role": "user"
}
] | e |
[
{
"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... | $4048.75 |
[
{
"content": "In an acute-angled triangle \\( ABC \\), the altitudes from vertices \\( B \\) and \\( C \\) are 7 and 9, respectively, and the median \\( AM \\) is 8. Points \\( P \\) and \\( Q \\) are symmetric to point \\( M \\) with respect to sides \\( AC \\) and \\( AB \\), respectively. Calculate the perim... | 32 |
[
{
"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... | Q = 90 - 1.5p |
[
{
"content": "Find all pairs of prime numbers \\((p, q)\\) such that \\(p^2 + 3pq + q^2 = 5^t\\) for some integer \\(t\\).",
"role": "user"
}
] | (5, 5) |
[
{
"content": "Let $X, Y, Z, T$ be independent random variables each following a standard normal distribution $N(0,1)$. Consider two circles centered at the origin with radii $\\sqrt{X^2 + Y^2}$ and $\\sqrt{Z^2 + T^2}$, respectively. Let $A$ be the area of the annulus formed by these two circles. Calculate the e... | 2\pi |
[
{
"content": "Determine whether the set \\((e_n)_{n>0}\\) is a basis for the sequence Hilbert space \\(l^2\\).",
"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... | 11289 J |
[
{
"content": "Evaluate the integral: \\[ \\int_0^\\infty \\frac{\\ln(1+x^2)}{1+x^2} \\, dx \\]",
"role": "user"
}
] | \pi \ln 2 |
[
{
"content": "Let \\( \\alpha \\) be an element in an algebraic closure of \\( GF(64) \\) such that \\( \\alpha^4 = \\alpha + 1 \\). Determine the value of \\( r \\in \\mathbb{N} \\) for which the field extension \\( GF(64)[\\alpha] \\) is isomorphic to \\( GF(2^r) \\).",
"role": "user"
}
] | 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... | artificial active immunity |
[
{
"content": "Given the matrices \\( A = \\begin{bmatrix} 0 & 1-i \\\\ -1-i & i \\end{bmatrix} \\) and \\( B = A^T \\overline{A} \\), determine which of the following statements is true:\n\n(A) An eigenvalue of \\( B \\) is purely imaginary.\n(B) An eigenvalue of \\( A \\) is zero.\n(C) All eigenvalues of \\( B... | 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... | 27.3 m/s |
[
{
"content": "Determine the greatest integer $A$ such that in any permutation of the numbers $1, 2, \\ldots, 100$, there exist ten consecutive numbers whose sum is at least $A$. What is $A$?",
"role": "user"
}
] | 505 |
[
{
"content": "Given real numbers \\(x, y, z\\) that are not all zero, determine all possible values of the expression:\n\\[ A = \\frac{|x+y|}{|x|+|y|} + \\frac{|y+z|}{|y|+|z|} + \\frac{|z+x|}{|z|+|x|}. \\]",
"role": "user"
}
] | [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... | 0.02754M |
[
{
"content": "Determine the number of distinct cyclic subgroups of order 10 in the group \\( \\mathbb{Z}_{30} \\oplus \\mathbb{Z}_{120} \\). Identify the generators of these subgroups by locating elements with order 10, ensuring to account for duplicates that generate the same subgroup.",
"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... | 274 km/hr |
[
{
"content": "Evaluate the limit \\( \\lim\\limits_{n \\to \\infty}(e-1)\\sum_{k=1}^n \\frac{1}{n+k(e-1)} \\).",
"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... | 0.84c |
[
{
"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 cash flow from operating activities = 94,500
Cash inflow from investing activity = (25,000)
Cash flow from financing activity = (40,000)
Net cash flow for the year = (35,000) |
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