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... | -$73,930 |
[
{
"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... | Development stage: 40%-60%
Startup-stage: 30%-50%
Survival-stage: 25%-45%
Early growth stage ventures: 25%-35% |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 57.56 N |
[
{
"content": "Evaluate the contour integral \\( \\oint \\limits_C \\frac{z^2+1}{(2z-i)^2}dz \\) using the residue theorem, where \\( C:|z|=1 \\) is a circle with positive orientation.",
"role": "user"
}
] | -\dfrac{\pi}{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... | 107.3^oC |
[
{
"content": "Let $p$ be an odd prime number and $M$ be a set derived from $\\frac{p^2 + 1}{2}$ square numbers. Determine whether it is possible to select $p$ elements from this set such that their arithmetic mean is an integer.",
"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... | 25c 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... | 162.7 mL |
[
{
"content": "Is the quotient space $S^1 \\times [-1, 1] / \\sim$ compact, where $\\sim$ is defined by $(a, b) \\sim (c, d)$ if and only if $(a, b) = (c, d)$, $b = d = 1$, or $b = d = -1$?",
"role": "user"
}
] | Yes |
[
{
"content": "Find the limit of the sequence: \\( \\lim \\limits_{n\\to \\infty}\\dfrac{n^3}{{((3n)!)^\\frac{1}{n}}} \\).",
"role": "user"
}
] | \dfrac{e^3}{27} |
[
{
"content": "Find the smallest nonnegative value of the sum \\( \\sum_{k=1}^{1985} e_k k^5 \\), where each \\( e_k = \\pm 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... | 0.237 L |
[
{
"content": "The sum of an infinite geometric series is $27$ times the series that results if the first three terms of the original series are removed. What is the value of the series' common ratio?",
"role": "user"
}
] | \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... | 10.3986 m/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... | 155.75 mL |
[
{
"content": "Determine whether there exists a $C^{\\infty}$ function $f$ such that the radius of convergence of the Taylor series \\( \\sum_{n=0}^\\infty \\frac{f^{(n)}(x_0)}{n!} (x-x_0)^n \\) is zero.",
"role": "user"
}
] | Yes |
[
{
"content": "Let $Q_n$ and $Q$ be compact positive and symmetric operators. Define $A_n = {Q_n}^{\\frac12}$ and $A=Q^{\\frac12}$. If $Q_n$ converges to $Q$ with respect to the operator norm, does $A_n$ converge to $A$?",
"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... | -$400 |
[
{
"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... | selenium difluoride |
[
{
"content": "Rectangle $ABCD$ has area $2006.$ An ellipse with area $2006\\pi$ passes through $A$ and $C$ and has foci at $B$ and $D$. What is the perimeter of the rectangle?",
"role": "user"
}
] | 8\sqrt{1003} |
[
{
"content": "Find the function \\( f: \\mathbf{R} \\rightarrow \\mathbf{R} \\) that satisfies the equation \\( f[x^{2}+f(y)]=y+[f(x)]^{2} \\) for all \\( x, y \\in \\mathbf{R} \\).",
"role": "user"
}
] | f(x) = x |
[
{
"content": "Find the limit: \\( \\lim_{{n\\rightarrow \\infty}} \\frac{(n!)^2}{(2n)!} \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether the following equality holds true: \\[ \\sqrt[3]{\\frac{1}{2} \\left(56-\\sqrt{\\frac{84640}{27}}\\right)} + \\sqrt[3]{\\frac{1}{2} \\left(\\sqrt{\\frac{84640}{27}}+56\\right)} = 4. \\] Provide a proof suitable for an oral examination if the equality is true.",
"role": "user"... | 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... | -$6,668 |
[
{
"content": "Is the wedge sum operation associative? Specifically, is the wedge sum $X \\vee Y \\vee Z$ homeomorphic to $(X \\vee Y) \\vee Z$? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "If $\\hat{\\theta}$ is a consistent estimator based on an i.i.d. random sample $X_1, \\ldots, X_n$ with $\\text{var}(\\hat{\\theta}) < \\infty$ for all $n$, does it follow that $\\lim_{n\\to\\infty} \\text{var}(\\hat{\\theta}) = 0$?",
"role": "user"
}
] | No |
[
{
"content": "Determine the number of solutions to the congruence $x^5 \\equiv 7 \\pmod{p}$, where $p$ is a prime of the form $10k+3$. How many solutions exist?",
"role": "user"
}
] | 1 |
[
{
"content": "Determine whether there exist rational numbers $x, y, z$ with $xyz \\neq 0$ such that $y^2 = x^3 + z^{4k}$ for some integer $k > 1$. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the number of distinct abelian groups of order $8^4$ up to isomorphism.",
"role": "user"
}
] | 77 |
[
{
"content": "Determine whether there exists a non-abelian nilpotent Lie algebra \\( \\mathfrak{n} \\) over \\( \\mathbb{R} \\) and an automorphism \\( \\alpha: \\mathfrak{n} \\to \\mathfrak{n} \\) such that \\( \\alpha \\) is periodic, the fixed subspace of \\( \\alpha \\) is the origin, and there is an \\( \\... | Yes |
[
{
"content": "Evaluate the integral \\( \\int_{L} z \\cos(2\\pi z \\bar{z}) \\, dz \\), where \\( L \\) is the contour defined by \\( |z| = 1 \\) and \\( 0 \\leq \\arg(z) \\leq \\pi \\).",
"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... | 100.33 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... | 4093704959 |
[
{
"content": "Let $X$ be an exponential random variable with rate parameter $\\lambda = 5$, and let $Y$ be a uniformly distributed random variable on the interval $(-3, X)$. Calculate the expected value $\\mathbb{E}(Y)$. Use the law of total expectation and conditional expectations to find the solution.",
"... | -\dfrac{7}{5} |
[
{
"content": "Evaluate the limit: $$\\lim_{(x,y) \\to (0,0)} \\frac{\\ln(1+x^3+y^3)}{\\sqrt{x^2+y^2}}$$",
"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... | -$2,636.38 |
[
{
"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... | 3.27e-18 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... | 1.96 g |
[
{
"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... | 0.014mm |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to \\infty} \\left( \\frac{e}{\\left( 1 + \\frac {1}{x} \\right)^x} \\right)^x. \\]",
"role": "user"
}
] | \sqrt{e} |
[
{
"content": "Compute the line integral of the vector field \\( \\vec{F}(\\vec{x}) = \\begin{pmatrix} x_1^2 + 2x_3 \\\\ x_1x_2 \\\\ x_3^2 - 2x_1 \\end{pmatrix} \\) along the straight line path \\( C \\) from the origin to the point \\( P(1, 2, 3) \\).",
"role": "user"
}
] | \dfrac{32}{3} |
[
{
"content": "For a rectangle with dimensions $n \\times m$, where $n \\geq 3$ and $m \\geq 3$, determine the maximum possible sum of numbers in the rectangle. Each unit square contains a number between 0 and 1, and the sum of numbers in any sub-rectangle must be less than or equal to 1.",
"role": "user"
... | 1 |
[
{
"content": "A convex dodecagon is inscribed in a circle. Six sides of the dodecagon have a length of \\(\\sqrt{2}\\), and the other six sides have a length of \\(\\sqrt{24}\\). Determine the radius of the circle.",
"role": "user"
}
] | \sqrt{38} |
[
{
"content": "Find the minimum distance between the point \\((1,1,1)\\) and the surface defined by the equation \\(z - xy = 10\\).",
"role": "user"
}
] | 3\sqrt{2} |
[
{
"content": "Determine whether the statement \"If $\\mathbb{Z}[x] / I$ is an integral domain, then $\\mathbb{Z}[x] / I$ is a field\" is true or false.",
"role": "user"
}
] | B |
[
{
"content": "Let \\( n \\) be the largest 12-digit prime number. Find the product of all integers \\( j \\) less than \\( n \\) such that for each \\( j \\), all numbers from 1 to \\( n-1 \\) can be expressed as a power of \\( j \\) in modulo-\\( n \\) arithmetic. Compute this product in modulo-\\( n \\) arith... | 1 |
[
{
"content": "Determine the dimension of the subspace of $M_n(\\mathbb{C})$ consisting of matrices $B$ such that $AB = BA$, where $A$ is a fixed matrix in $M_n(\\mathbb{C})$. Provide your answer as a single integer.",
"role": "user"
}
] | 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... | 5225 ft. lb |
[
{
"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... | hypobromous acid |
[
{
"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(n-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... | $24,342.10 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.124 m/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... | 7.431e+3 J/mol |
[
{
"content": "Let $g(x)$ be a strictly increasing and twice-differentiable function over the interval $[a,b]$. Suppose $f(x)$ is another twice-differentiable function such that for all $x \\in (a,b)$, the inequality $g'(x) f'(x) \\geq 0$ holds. Given that $g'(x) \\geq 0$ for all $x$ and $g'(x) > 0$ except possi... | 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... | 0.985 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... | - 490.5 m/s^2 |
[
{
"content": "In triangle \\(ABC\\), medians \\(BD\\) and \\(CE\\) are equal in length. Given that \\(\\angle BAC = 80^\\circ\\), determine the measure of \\(\\angle BDC\\).",
"role": "user"
}
] | 100^\circ |
[
{
"content": "Calculate the work done by the force \\( \\vec{F}(x,y) = (x^2 - y^2) \\ \\vec{i} + 2xy \\ \\vec{j} \\) in moving a particle counterclockwise around the square with corners \\((0,0)\\), \\((a,0)\\), \\((a,a)\\), \\((0,a)\\), where \\(a > 0\\).",
"role": "user"
}
] | 2a^3 |
[
{
"content": "Find the value of the expression \\( \\left(\\frac{i+\\sqrt{3}}{2}\\right)^{200} + \\left(\\frac{i-\\sqrt{3}}{2}\\right)^{200} \\), given that \\( \\left(\\frac{i+\\sqrt{3}}{2}\\right)^{100}\\left(\\frac{i-\\sqrt{3}}{2}\\right)^{100} = 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... | 2.1e-4 |
[
{
"content": "Express the function \\( f \\) as a Taylor series centered at 0, given that \\( f'(x) = 2xf(x) \\) and \\( f(0) = 1 \\). Determine the radius of convergence for this series.",
"role": "user"
}
] | \infty |
[
{
"content": "Evaluate the limit of \\( \\frac{x^x}{x!} \\) as \\( x \\to \\infty \\).",
"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... | 3355.92 |
[
{
"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... | 4514kg |
[
{
"content": "The average age of the 40 members of a computer science camp is 17 years. There are 20 girls, 15 boys, and 5 adults. If the average age of the girls is 15 and the average age of the boys is 16, what is the average age of the adults?",
"role": "user"
}
] | 28 |
[
{
"content": "Given that for real numbers $a, b, c$, the condition $\\frac{a}{b+c}+\\frac{b}{c+a}+\\frac{c}{a+b}=1$ holds, find the possible value of the expression $\\frac{a^2}{b+c}+\\frac{b^2}{c+a}+\\frac{c^2}{a+b}$.",
"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... | 62.16 meters |
[
{
"content": "Evaluate the limit: $$\\lim_{n \\to \\infty} \\frac{x^{n+1}}{1-x}\\int_0^1 \\left (\\frac{1-s}{1-xs}\\right )^n\\,ds$$ where $x \\in (-1,1)$. ",
"role": "user"
}
] | 0 |
[
{
"content": "The scores on Trisha's first three tests were 88, 73 and 70. After two more tests, the mean score for all five tests was 81. Each test score was less than 90, and all of Trisha's test scores were different integer values. List Trisha's five test scores from the greatest to the least, separated by ... | 89, 88, 85, 73, 70 |
[
{
"content": "Let $(M, \\omega)$ be a symplectic manifold and $N$ an isotropic submanifold. For a point $p \\in N$, determine if it is always possible to find coordinates $(x_1, \\ldots, x_n, y_1, \\ldots, y_n)$ in a neighborhood $U$ of $p$ such that both $\\omega = \\sum dx_i \\wedge dy_i$ (Darboux coordinates... | 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... | $1,714,285.71 |
[
{
"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... | 6.70% |
[
{
"content": "In triangle $ABC$, $AX = XY = YB = BC$ and the measure of angle $ABC$ is 120 degrees. What is the number of degrees in the measure of angle $BAC$?\n\n[asy]\npair A,X,Y,B,C;\nX = A + dir(30); Y = X + dir(0); B = Y + dir(60); C = B + dir(-30);\ndraw(B--Y--X--B--C--A--X);\nlabel(\"$A$\",A,W); label(\... | 15 |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\to 0} \\frac{x - \\sin x \\cos x}{\\tan x - x}$$ without using L’Hospital’s rule and without using series expansion.",
"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... | 0.2205 or 22.05% |
[
{
"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... | 6.33e-7 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... | Date Particulars Debit Credit
Jan 1, 2017 Accumulated Depreciation $61,700
Equipment $61,700
June 30, 2017 Depreciation Expense $4,200
Accumulated Depreciation $4,200
June 30, 2017 Accumulated Depreciation $25,200
Loss on Sale of Equipment $2,800
Cash $14,000
Equipment $42,000
Dec 31, 2017 Depreciation Expense... |
[
{
"content": "Evaluate the integral \\( \\int_{-1}^{1} \\frac{x^2 \\, dx}{1 + e^x} \\).",
"role": "user"
}
] | \dfrac{1}{3} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 10.37% |
[
{
"content": "What is the difference between the sum of the first 2003 even counting numbers and the sum of the first 2003 odd counting numbers?",
"role": "user"
}
] | 2003 |
[
{
"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 revenue cycle affects Sales, Accounts Receivable, Allowance for Doubtful Accounts, Bad Debt Expense, Cash, Commission on Sales, Warranty Expense, and Sales Return and Allowance accounts. These accounts are interrelated, for example, Sales are linked to Cash, Accounts Receivable, Sales Returns and Allowances, Warra... |
[
{
"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... | 23.83% |
[
{
"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 cost of capital represents the return a company needs to earn on its investments to satisfy its investors. It's calculated using the Weighted Average Cost of Capital (WACC), which considers both the cost of equity and the cost of debt based on the company's capital structure. WACC is the average rate a company is ... |
[
{
"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... | 24.65 J/s |
[
{
"content": "Determine the disc of convergence for the series \\( \\sum_{n=0}^\\infty z^{n^3} \\).",
"role": "user"
}
] | \{ z \in \mathbb{C} \mid |z| < 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... | {\frac{72}{g*100}} or {\frac{\ln(2)}{\ln(1 + g)}} |
[
{
"content": "Find the limit \\( \\lim_{x \\to \\infty} f(x) \\) for the function \\( f(x) \\) defined by \\( f(x) = -\\ln(f(x)) - x + 1 \\).",
"role": "user"
}
] | 0 |
[
{
"content": "In coordinate space, $A = (-2,3,5),$ $B = (7,0,-1),$ $C = (-3,-2,-5),$ and $D = (3,4,7).$ Find the intersection point of lines $AB$ and $CD.$",
"role": "user"
}
] | (1,2,3) |
[
{
"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... | 8.63% |
[
{
"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... | 2302.82 kJ |
[
{
"content": "Determine all positive integers \\( k \\) such that for any positive numbers \\( a, b, c \\) satisfying \\( k(ab + bc + ca) > 5(a^2 + b^2 + c^2) \\), there exists a triangle with side lengths \\( a, b, c \\).",
"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... | 0.21 T |
[
{
"content": "Show that the function \\( g(x) = \\frac{4^x + x^2 - \\ln(2) \\cdot x - 1}{\\tan(2x)} \\) is continuous at \\( x = 0 \\), given that \\( g(0) := \\ln(\\sqrt{2}) \\). The function \\( g(x) \\) is defined on the intervals \\( \\left(\\frac{-\\pi}{2}, 0\\right) \\cup \\left(0, \\frac{\\pi}{2}\\right)... | \ln(\sqrt{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... | Outstanding checks and deposits in transit |
[
{
"content": "Consider the function $g : \\mathbb{R}^3 \\to \\mathbb{R}$ defined by $g(x,y,z) = x^3 - 2y^2 + z^4$. Determine the values of $w$ for which $g^{-1}(w)$ is a submanifold of $\\mathbb{R}^3$.",
"role": "user"
}
] | w \neq 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... | a=20/9 m/s^2 or a=-20/9 m/s^2 |
[
{
"content": "For a grid graph \\(M_{n,n}\\), determine the smallest value of \\(\\alpha > 0\\) such that an \\(\\alpha\\)-Spanning Tree exists. An \\(\\alpha\\)-Spanning Tree \\(H = (V_H, E_H)\\) of \\(G\\) is defined as a subgraph where \\(V_H = V\\), \\(E_H \\subseteq E\\), and the shortest path distance in ... | 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... | 7.83*10^4 mL |
[
{
"content": "Evaluate the line integral \\( \\oint_C (x-z) \\, dx + (x + y) \\, dy + (y+z) \\, dz \\) where \\( C \\) is the ellipse formed by the intersection of the plane \\( z=y \\) with the cylinder \\( x^2 + y^2 = 1 \\), oriented counterclockwise as viewed from above, using Stokes' Theorem.",
"role": ... | 2\pi |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^{\\infty} \\frac{\\sin (3x)}{\\cosh^3(x)} \\, dx \\) using complex integration techniques.",
"role": "user"
}
] | 0 |
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