prompt list | ground_truth string |
|---|---|
[
{
"content": "Calculate the distance between two non-parallel hyperplanes in \\(\\mathbb{R}^n\\) given by the equations \\(a_1^Tx = b_1\\) and \\(a_2^Tx = b_2\\).",
"role": "user"
}
] | 0 |
[
{
"content": "Identify a polynomial \\( f(x) \\) such that the quotient ring \\( \\mathbb{R}[x]/(f(x)) \\) is isomorphic to \\( \\mathbb{C} \\).",
"role": "user"
}
] | x^2 + 1 |
[
{
"content": "Determine whether the functors $F: Sp \\cong Mod_{\\mathbb{S}}(Sp): U$ in the free-forgetful adjunction for the monoidal $\\infty$-categories $(Sp, \\wedge, \\mathbb{S})$ and $(Mod_{\\mathbb{S}}(Sp), \\otimes, \\mathbb{S})$ are strong monoidal, or equivalently, monoidal equivalences.",
"role":... | Yes |
[
{
"content": "Is there a connected topological space that is maximal compact, but not $T_2$? A space $(X,\\tau)$ is said to be maximal compact if for any topology $\\tau'$ on $X$ with $\\tau'\\supseteq \\tau$ and $\\tau'\\neq \\tau$, the space $(X,\\tau')$ is not compact.",
"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... | 8.91% |
[
{
"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... | 0.205 L |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 25.3 m/s |
[
{
"content": "Calculate the value of the Eisenstein series $G_2(\\Lambda)$ for the lattice $\\Lambda=\\mathbb{Z}[i]$ in the complex plane when $k=1$. Provide your answer as a complex number.",
"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... | $37,547.61 |
[
{
"content": "Evaluate the limit: \\( \\lim_{r \\to 0} I_1 (r) \\), where\n\n\\[ I_1(r)=\\int_{-r}^{r} \\int_{-\\sqrt{r-x^2}}^{\\sqrt{r-x^2}} \\frac{1} {(x^2+y^2) \\log^2\\big(\\frac{2}{\\sqrt{x^2+y^2}}\\big)}\\,dy\\,dx. \\]",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 944.0933 |
[
{
"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... | 708g |
[
{
"content": "Consider the function \\( f(x) = \\max \\{-11x - 37, x - 1, 9x + 3\\} \\) defined for all real \\( x. \\) Let \\( p(x) \\) be a quadratic polynomial tangent to the graph of \\( f \\) at three distinct points with \\( x \\)-coordinates \\( x_1, x_2, x_3. \\) Find \\( x_1 + x_2 + x_3. \\)",
"rol... | -\dfrac{11}{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... | 8.71e-4 us^-1 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\to 0}\\left(\\frac{1}{x}-\\frac{1}{e^{x}-1}\\right) \\] without using L'Hospital's Rule.",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 16.5Pa |
[
{
"content": "Let $X \\in M_n(\\mathbb{C})$ be a matrix and $m > n$ a positive integer. Does $X^m = O_n$ imply $X^n = O_n$? Answer 'yes' or 'no' and 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... | Date Particulars Debit Credit
1/01 Stock investment 152,000
To cash A/c 152,000
1/07 Cash 7,500
To dividend revenue A/c 7,500
1/12 Cash 32,000
To stock investment A/c 30,400
To gain on investment sold A/c 1,600
31/12 Cash 6,000
To dividend revenue A/c 6,000 |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to 0^+} \\frac{\\ln(x)}{x-\\sqrt{x}}$$",
"role": "user"
}
] | \infty |
[
{
"content": "Evaluate the limit: \\( \\lim_{{n\\to\\infty}} \\left(1+ \\sqrt{n+1} - \\sqrt{n}\\right)^{\\sqrt{n}} \\).",
"role": "user"
}
] | \sqrt{e} |
[
{
"content": "Evaluate the integral \\( \\int_2^{10} g(y) \\, dy \\), where \\( f(x) = x + x^3 \\), \\( g(y) = f^{-1}(x) \\), and \\( dy = 1 + 3x^2 \\).",
"role": "user"
}
] | \dfrac{51}{4} |
[
{
"content": "The quadratic $f(x) = x^2 + bx + c$ satisfies $f(2 + t) = f(2 - t)$ for all real numbers $t.$ Enter $f(1),$ $f(2),$ and $f(4)$ in increasing order. For example, if you think $f(4) < f(2) < f(1),$ then enter \"f(4), f(2), f(1)\".",
"role": "user"
}
] | f(2) < f(1) < f(4) |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\to 0} \\ln\\left(\\frac{\\cos x}{1+\\sin x}\\right)^{\\frac{1}{x}}$$.",
"role": "user"
}
] | -1 |
[
{
"content": "Let $a,b,c$ be continuous functions defined on $\\Bbb R^2$. Let $V_1,V_2,V_3$ be non-empty subsets of $\\Bbb R^2$ such that $V_1 \\cup V_2 \\cup V_3 =\\Bbb R^2$ and the PDE: $$a(x,y)u_{xx}+b(x,y)u_{xy}+c(x,y)u_{yy}=0$$ is elliptic in $V_1$, parabolic in $V_2$, and hyperbolic in $V_3$. Which of the... | B |
[
{
"content": "Find a constant $c$ such that the smallest eigenvalue $\\lambda_n$ of the matrix $AA^T$ satisfies the inequality:\n\\[ \\lambda_n(AA^T) \\ge c \\|A\\|_F^2 \\]\nwhere $A$ is a non-singular matrix and $\\|A\\|_F$ denotes the Frobenius norm of $A$. The matrix $A$ is not assumed to be symmetric.",
... | 0 |
[
{
"content": "Evaluate \\( \\frac{\\partial f}{\\partial s}(0,0) \\) for the function \\( f(s,t)=\\exp_{\\lambda (s)}tW(s) \\), where \\( \\lambda(s) \\) is a curve with \\( \\lambda(0)=\\gamma(0), \\lambda ' (0)=J(0) \\) and \\( W(s) \\) is a vector field along \\( \\lambda \\) such that \\( W(0)=\\gamma ' (0)... | J(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... | $74,700 |
[
{
"content": "Determine whether the statement \"$f(n)=o(f(\\frac{n}{2}))$ implies $f(n)=O(f(\\frac{n}{2}))$\" is true or false for asymptotically positive functions $f$. Provide a justification for your answer.",
"role": "user"
}
] | 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... | 0.389 kg |
[
{
"content": "Determine the number of distinct equivalence classes for logical statements composed of 5 variable letters, considering logical equivalence.",
"role": "user"
}
] | 2^{32} |
[
{
"content": "Determine whether positive definite matrices must be symmetric.",
"role": "user"
}
] | Yes |
[
{
"content": "What is the name of the algebraic structure where the additive group of a ring is non-abelian, and only right distributivity is required?",
"role": "user"
}
] | near-ring |
[
{
"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... | Cash Beginning 54,000
Net Income 56,000
Loss on Sale of Land 5,000
Depreciation Expense 57,000
Operating:
Increase in Accounts Receivables7,000
Decrease in Inventories-16,000
Decrease in Accounts Payable-2,000
Payment of Dividends-18,000
Net Cash Used in Operating Activities -29,000
Investing:
Increase in Common Stock30,000
Increase in Paid-in Capital2,000
Proceeds from Sale of Land15,000
Purchase of Equipment-125,000
Net Cash Used in Investing Activities -78,000
Cash, Ending 65,000 |
[
{
"content": "Calculate the limit: \\( \\lim_{n\\to \\infty } \\frac{n^n}{n!^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... | 5 cm behind the mirror |
[
{
"content": "Determine the fundamental group of the complex projective space \\( \\mathbb{P}^n(\\mathbb{C}) \\) for \\( n \\geq 1 \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Given a convergent series $\\sum a_n$ with positive terms, where $\\lim \\inf (na_n) = 0$, and the sequence $\\{a_n\\}$ is decreasing, determine if $\\lim (na_n) = 0$.",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the number of integers \\( n \\) such that the ideal \\( \\langle n, x \\rangle \\) in \\( \\mathbb{Z}[x] \\) is a principal ideal.",
"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... | 1450 mL |
[
{
"content": "The sum of 49 consecutive integers is $7^5$. What is their median?",
"role": "user"
}
] | 343 |
[
{
"content": "Calculate the flow of fluid through the closed surface S, which is the boundary of the region bounded by the half-spheres $z = -\\sqrt{4-x^{2}-y^{2}}$ and $z = \\sqrt{9-x^{2}-y^{2}}$, and the plane $z = 0$. The velocity field of the fluid is given by $\\vec{v}(x,y,z)= (y^{3}e^{-z^{2}} + x)\\vec{i}... | 70\pi |
[
{
"content": "Evaluate the integral \\( \\int_0^{\\infty}\\frac{\\sinh x}{1+\\cosh^2x}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... | 119.32 m/s |
[
{
"content": "Determine the number of roots of the polynomial \\( f(z) = z^6 - 5z^4 + 3z^2 - 1 \\) within the closed disk \\( |z| \\leq 1 \\).",
"role": "user"
}
] | 4 |
[
{
"content": "Determine whether the function \\( z(x,y) = \\ln(x^2 + y^2) \\) is harmonic by checking if it satisfies Laplace's equation.",
"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... | 61 months |
[
{
"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... | 0.651m |
[
{
"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 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... | 1.827e-34 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... | Transaction Assets Liabilities Owner's Equity
Received cash from owner as an additional investment + No Change + |
[
{
"content": "Let $A$ be a $3 \\times 3$ matrix with real entries. If $A$ commutes with all $3 \\times 3$ matrices with real entries, how many distinct real eigenvalues does $A$ have?",
"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... | Montoya, Inc.
Balance Sheet
As of December 31, 2014
\nAssets\nCurrent Assets\n\tCash $362,260\n\tNotes Receivable $447,960\n\tIncome Taxes Receivable $99,890\n\tInventory $242,060\n\tPrepaid Expenses $90,180\n\tEquity Investments (Trading) $123,260\n\tDiscount on Bonds Payable $15,466\n\tTotal Current Assets $1,381,076\n\nNon-Current Assets\n\tLand $482,260\n\tBuildings $1,642,260\n\tAccumulated Depreciation-Buildings -$270,666\n\tEquipment $1,472,260\n\tAccumulated Depreciation-Equipment -$292,466\n\tGoodwill $127,260\n\tTotal Non-Current Assets $3,160,918\n\nTotal Assets $4,541,994\n\nLiabilities and Stockholders' Equity\nCurrent Liabilities\n\tNotes Payable $267,260\n\tAccounts Payable $492,260\n\tPayroll Taxes Payable $179,851\n\tRent Payable (Short-Term) $47,260\n\tIncome Taxes Payable $100,622\n\tTotal Current Liabilities $1,087,253\n\nNon-Current Liabilities\n\tBonds Payable $302,260\n\tNotes Payable (Long-Term) $1,602,260\n\tRent Payable (Long-Term) $482,260\n\tTotal Non-Current Liabilities $2,386,780\n\nTotal Liabilities $3,474,033\n\nStockholders' Equity\n\tCommon Stock, $1 par value $202,260\n\tPreferred Stock, $10 par value $152,260\n\tRetained Earnings $713,441\n\tTotal Stockholders' Equity $1,067,961\n\nTotal Liabilities and Stockholders' Equity $4,541,994 |
[
{
"content": "Find the infimum of \\( \\left| z^2 - az + a \\right| \\) for \\( z \\in \\mathbb{C} \\) such that \\( |z| \\le 1 \\), where \\( a \\) is a real number in the interval \\([2+\\sqrt{2}, 4]\\).",
"role": "user"
}
] | 1 |
[
{
"content": "Let $f$ be a continuous function defined on $[0,1]$ such that \\( \\int_{0}^1f^2(x)dx=\\left(\\int_{0}^1f(x)dx\\right)^2 \\). Determine the range of $f$.",
"role": "user"
}
] | \{c\} |
[
{
"content": "Determine whether the limit \\( \\lim_{(x,y) \\to (0,0)} \\frac{xy}{\\sqrt{x^2+y^2}} \\) exists and, if so, find its value.",
"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... | 11.02 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... | 743 kg/m^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... | 1226 Hz |
[
{
"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... | $41,430 |
[
{
"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... | $46.17 |
[
{
"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... | 549.8 K |
[
{
"content": "Let $H$ be a Hilbert space and $(A_n)$ be a sequence of compact operators on $H$. If each $A_n$ has an eigenvalue $\\lambda_n$ with $|\\lambda_n| = 1$, can a subsequence of $A_n$ be extracted such that the corresponding eigenvalues have a limit point?",
"role": "user"
}
] | Yes |
[
{
"content": "Find the coefficient of \\(x^{12}\\) in the expansion of \\((1+x^{3} +x^{6} +x^{9} +\\ldots)^{7}\\).",
"role": "user"
}
] | 210 |
[
{
"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... | 566/18 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... | $401,492.13 |
[
{
"content": "Compute the total Gaussian curvature of the surface defined by the equation \\( x^2 + y^4 + z^6 = 1 \\).",
"role": "user"
}
] | 4\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... | C = \frac{4\pi \varepsilon _{0} ab}{b-a} |
[
{
"content": "Let $f$ be a bounded, measurable function defined on $[1, \\infty)$. Define $a_n = \\int_{[n, n+1)} f(x) \\, dx$. If $f$ is integrable over $[1, \\infty)$, does it follow that the series $\\sum_{n=1}^\\infty a_n$ converges?",
"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... | 5.34% |
[
{
"content": "In the National Basketball Association, there are 30 teams, each playing 82 games in the regular season. Can the teams be divided into Eastern and Western Conferences such that matches between teams from different conferences constitute exactly half of the total number of matches? Answer yes or no... | 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... | 34.44 m |
[
{
"content": "Let $f$ be a function such that for every real number $t$, \\( \\int_t^{f(t)} \\frac{x^4}{1+x^2} \\, dx = 2 \\). Calculate \\( \\lim_{x \\to \\infty} f'(x) \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Determine whether the function \\( h(x) = \\begin{cases} \\exp\\left(-\\frac{1}{x^2}\\right) & x \\neq 0 \\\\ 0 & x = 0 \\end{cases} \\) is differentiable at \\( x = 0 \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Find all positive integer solutions \\((x, y, z)\\) to the equation \\(2^x + 2^y + 1 = 3^z\\) where \\(x > y\\).",
"role": "user"
}
] | (6, 4, 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... | 47320 |
[
{
"content": "A quadrilateral is inscribed in a circle with radius 1, with two opposite sides being parallel. The difference between their lengths is \\( d > 0 \\). The distance from the intersection of the diagonals to the center of the circle is \\( h \\). Determine the supremum of \\( \\frac{d}{h} \\) and de... | 2 |
[
{
"content": "Let $V$ be the vector space of all polynomials over $\\mathbb{R}$, and let $W$ be the subspace of polynomials divisible by $x^4$. Find the dimension of the quotient space $V/W$. \\( \\text{Provide your answer as a single integer.} \\)",
"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... | 3.31e-31 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... | 118.85 m |
[
{
"content": "Calculate the expected value \\( \\mathbb{E}(e^{B(2)}) \\), where \\( B(t) \\) is a standard Brownian motion with \\( B(0) = 0 \\).",
"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... | 2Li + FeBr_2 rarr Fe + 2LiBr |
[
{
"content": "Determine whether it is possible to fit several non-overlapping squares inside a square with side length 1, such that the sum of the side lengths of these smaller squares equals 1992.",
"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... | mg/(m+M) |
[
{
"content": "Using Green's theorem, find the area enclosed by the curve \\(\\gamma(t) = \\begin{pmatrix} (1+\\cos t)\\cos t \\\\ (1+ \\cos t) \\sin t \\end{pmatrix}, \\qquad t \\in [0,2\\pi],\\) by choosing an appropriate vector field.",
"role": "user"
}
] | \dfrac{3\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... | $1,765.32 |
[
{
"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... | 6.66% |
[
{
"content": "Determine whether there exists a positive integer $n$ such that $n^n + (n + 1)^n$ is divisible by 1987.",
"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... | 42.43 |
[
{
"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... | Actual | Budget | Budget Variance | Variance %
---|---|---|---
Direct Materials | $16,140 | $15,000 | $1,140 U | 7.6% U
Direct Labor | 19,020 | 20,000 | 980 F | 4.9% F
Indirect Labor | 29,300 | 25,000 | 4,300 U | 17.2% U
Utilities | 13,110 | 12,000 | 1,110 U | 9.25% U
Depreciation | 19,000 | 19,000 | - | -
Repairs and Maintenance | 3,370 | 4,000 | 630 F | 15.75% F
Total | $99,940 | $95,000 | $4,940 U | 5.2% U |
[
{
"content": "Find a polynomial \\( g(t) \\) such that the linear map \\( g(T) \\) has the characteristic polynomial \\( p(t) = (11-t)^r(17-t)^{n-r} \\).",
"role": "user"
}
] | 17 - 6t |
[
{
"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... | 55.4J |
[
{
"content": "Determine whether every non-trivial finite group has a subgroup of prime-power index. Provide a justification for your answer.",
"role": "user"
}
] | No |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\to \\infty} [(x^3 + x^2 + 1)^{1/3} - (x^2 + x)^{1/2}].$$",
"role": "user"
}
] | -\dfrac{1}{6} |
[
{
"content": "Determine whether the following statement is true or false: A function with a Taylor expansion on an interval $I$ also has a Taylor expansion at every point of $I$ in the field of real numbers.",
"role": "user"
}
] | A |
[
{
"content": "Evaluate the limit \\( \\lim_{n\\rightarrow\\infty}\\frac{\\sum \\limits_{k=1}^n(k\\cdot a_k)}{n^2} \\) given that \\( \\lim_{n\\rightarrow\\infty}a_n = L \\). Express your answer in terms of \\( L \\).",
"role": "user"
}
] | \dfrac{L}{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... | 26.0e6 N |
[
{
"content": "Compute the limit: $$\\lim\\limits_{n\\to\\infty}\\frac{(2n)!\\sqrt{\\pi n}}{2^{2n}(n!)^2}.$$",
"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... | 6.00 rad/s |
[
{
"content": "Calculate the integral \\( \\int_\\Gamma (z-y)dx+(x-z)dy+(y-x)dz \\) using Stokes' Theorem, where \\( \\Gamma \\) is the surface obtained from the intersection of \\( x^2+y^2=1 \\) and \\( x+2z=1 \\).",
"role": "user"
}
] | 3\pi |
[
{
"content": "For how many ordered pairs of positive integers $(x,y),$ with $y<x\\le 100,$ are both $\\frac xy$ and $\\frac{x+1}{y+1}$ integers?",
"role": "user"
}
] | 85 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.