prompt list | ground_truth string |
|---|---|
[
{
"content": "Determine whether every subset of the extended real numbers has an infimum.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the values of \\( \\alpha \\in \\mathbb{R} \\) for which the integral \\( \\int_{2}^{+\\infty} \\frac{1}{x \\ln^\\alpha x} \\, dx \\) converges.",
"role": "user"
}
] | \alpha > 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... | 10227.17 |
[
{
"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... | Scanning electron microscope, Atomic absorption spectroscopy, Inductively coupled plasma-mass spectroscopy |
[
{
"content": "Provide an example of a continuous function \\( g: \\mathbb{R} \\rightarrow \\mathbb{R} \\) that is not an open mapping.",
"role": "user"
}
] | g(x) = 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... | 9.98e-2 kg |
[
{
"content": "Let $K$ be a number field with $[K:\\mathbf{Q}] = n$. Determine if the number of embeddings of $K$ into the algebraic closure of the rational numbers, $\\overline{\\mathbf{Q}}$, is equal to $n$. Provide a justification for your answer.",
"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... | Cost of goods manufactured = Total Manufacturing Cost + Beginning Work-in-Process Inventory - Ending Work-in-Process Inventory |
[
{
"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 flows from operating activities
Net Profit (Loss) 48,620
Adjustments for:
Depreciation 10,620
Working capital changes:
(Increase) / Decrease in trade and other receivables (5,100)
Increase / (Decrease) in trade payables 7,100
Net cash generated (used) from operating activities 61,240
Cash flows from investing activities
Purchase of property, plant, and equipment (19,100)
Net cash generated (used) in investing activities (19,100)
Cash flows from financing activities
Proceeds (Repurchase) from the issue of share capital 19,580
Dividends (29,720)
Net cash generated (used) in financing activities (10,140)
Net increase in cash and cash equivalents 32,000
Cash and cash equivalents at beginning of period 15,100
Cash and cash equivalents at end of period 47,100 |
[
{
"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... | 2.6 cm |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 46.875 rpm |
[
{
"content": "Does the definition of asymptotic normality imply that there exists an integer $n_0$ such that for all $n > n_0$, the random variables $X_n$ are normally distributed with parameters $(\\mu_n, \\sigma_n^2)$?",
"role": "user"
}
] | No |
[
{
"content": "Let $(u_{n})_{n},(v_{n})_{n}$ be two strictly positive real sequences satisfying the following condition: There exist a positive integer $N$ and a positive real number $a$ such that for all $n > N$, $$\\frac{u_{n}}{v_{n}} \\leq a.$$ Determine whether it is true that $$\\frac{u_{n}}{v_{n}} \\leq a ... | True |
[
{
"content": "Solve the following system of equations for \\(x\\) and \\(y\\):\n\\[\\begin{cases}\n2x^2+y^2=1,\\\\\nx^2 + y \\sqrt{1-x^2}=1+(1-y)\\sqrt{x}.\n\\end{cases}\\]",
"role": "user"
}
] | (0, 1) |
[
{
"content": "Evaluate the integral \\( \\int_0^{\\frac{\\pi}{2}} \\frac{\\mathrm{d}x}{1+\\tan^{2013}x} \\).",
"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... | TR = \frac{3000}{350}Q - \frac{1}{350}Q^2 |
[
{
"content": "In triangle ABC, the tangents of angles A, B, and C form a harmonic progression. Given that the length of side BC is 189 and the length of side AB is 459, find the length of side AC.",
"role": "user"
}
] | 351 |
[
{
"content": "Given that \\( m = 17 \\times 23 = 391 \\), an exponent \\( e = 3 \\), and an encrypted word \\( c = 21 \\), with a decrypting exponent \\( d = 235 \\), find the original word \\( w \\) such that \\( w \\equiv c^d \\pmod{m} \\).",
"role": "user"
}
] | 30 |
[
{
"content": "Evaluate the definite integral \\( \\int_0^{2\\pi} \\sqrt{2 + 2\\cos(x)} \\, dx \\).",
"role": "user"
}
] | 8 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | One should go about reconciling a bank statement by following the below-mentioned steps:
- Gather information of the records
- Check for uncleared dues
- Compare debit and credit sides
- Check for missing entries
- Correct and reverse the entries
- Prepare a bank reconciliation statement
- Add un-presented cheques and deduct un-credited cheques
- Make final changes and match accordingly |
[
{
"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... | Accrued Revenue |
[
{
"content": "In a 100 x 100 grid, Petya and Vasya play a game where Petya starts by coloring one cell black. On each subsequent turn, a player can color a vertical or horizontal white strip of size $1 \\times n$ black, where $n$ is either equal to or one more than the number of cells colored by the previous pl... | Vasya |
[
{
"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 mol |
[
{
"content": "Calculate the limit: \\[ \\lim_{x\\rightarrow 0}\\frac{\\sin(\\sin x) - \\cos(\\cos x)}{\\tan(\\tan x) - \\sin(\\sin x)} \\] using L'Hôpital's rule.",
"role": "user"
}
] | -\infty |
[
{
"content": "The points $P = (x_1,y_1)$ and $Q = (x_2,y_2)$ are the intersections of the parabola $y^2 = 4ax,$ where $a > 0,$ and a line passing through the focus of the parabola. Then the distance $PQ$ can be expressed in the form $c_1 x_1 + c_2 x_2 + c_3 a,$ where $c_1,$ $c_2,$ and $c_3$ are constants. Com... | 4 |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\rightarrow 0^+}\\int_0^1\\ln(1+\\sin(tx))\\,dt$$",
"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... | 607.2 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... | $135.69 |
[
{
"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... | 15.0 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... | 0.071 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... | Mg(s) + 2H^+(aq) \to Mg^{2+}(aq) + H_2(g) |
[
{
"content": "Determine whether the number of involutions in a finite abelian group uniquely determines its invariant factors. Answer with True or False.",
"role": "user"
}
] | False |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 7.013e-11 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... | 1.35e-2 W |
[
{
"content": "In triangle ABC, AB is not equal to AC. The angle bisector of angle A intersects the perpendicular bisector of side BC at point X. The line connecting the feet of the perpendiculars from X to sides AB and AC intersects BC at point D. Determine the ratio BD/DC.",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate the integral \\( \\int^{\\pi/2}_{-\\pi/2} \\frac{1}{1+e^{\\sin x}} \\, dx \\).",
"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... | 23.2 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... | v_{new}=v\sqrt{\frac{T_{new}}{T}} |
[
{
"content": "Let $c$ be a positive constant and let $f(t)=\\delta(t-c)$. Compute the convolution $f*g$. Express your answer in terms of $g(t)$. \\( \\boxed{} \\)",
"role": "user"
}
] | g(t - 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... | 26.0W |
[
{
"content": "The parabola \\(C_{1}: x^{2}=2 py\\) has its focus at \\(F\\). The hyperbola \\(C_{2}: \\frac{x^{2}}{a^{2}}-\\frac{y^{2}}{b^{2}}=1\\) has its left and right foci at \\(F_{1}\\) and \\(F_{2}\\). Point \\(P\\) is a common point of the two curves in the first quadrant. If points \\(P\\), \\(F\\), and... | \sqrt{2} |
[
{
"content": "Given the function \\( f(x) = x^2 - ax + \\frac{a}{2} \\) where \\( a > 0 \\) and \\( x \\in [0,1] \\), determine the minimum value \\( g(a) \\) of \\( f(x) \\) over the interval \\([0,1]\\). Then, find the maximum value of \\( g(a) \\) as \\( a \\) varies over all positive values.",
"role": "... | \dfrac{1}{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... | 0.561 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... | Classified Balance Sheet
as on 31st December, 2012
Particulars | Amount ($)
---|---
Assets: |
Current assets |
Cash | 3,000
Receivables | 58,000
Inventory | 54,000
Prepaid expenses | 2,000
Total Current Assets | 117,000
Fixed Assets: |
Building | 75,000
Machinery and equipment | 300,000
Land | 11,000
Total fixed assets | 386,000
Less: Accumulated Depreciation | 200,000
Net Fixed Assets | 186,000
Other assets | 7,000
Total assets | 310,000
Liabilities and Stockholder's equity |
Liabilities: |
Current liabilities: |
Accounts payable | 35,000
Other accrued expenses | 8,000
Accrued income tax | 3,000
Current portion of long-term debts | 7,000
Total current liabilities | 53,000
Long term liabilities: |
Long-term debts | 99,870
Deferred income tax liability | 24,000
Total long-term liabilities | 123,870
Shareholder's equity: |
Common stock | 3,180
Retained earnings | 129,950
Total stockholder's equity | 133,130
Total liabilities and equity | 310,000 |
[
{
"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... | Kb=[CH3OH][OH-]/[CH3O-] |
[
{
"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... | 0.11 Joule |
[
{
"content": "In a finite field $F_q$ with $q$ odd, determine the number of distinct roots of unity.",
"role": "user"
}
] | q - 1 |
[
{
"content": "Determine whether the following statement is true: If $g \\in G$ and $R: G \\rightarrow GL(V)$ is the matrix form of an irreducible representation of $G$, then $R^{-1}(g) = R(g^{-1})$. Here, the left-hand side corresponds to the matrix inversion of the irrep of $g$, and the right-hand side corresp... | True |
[
{
"content": "Given an integer $m$, choose integers $n \\le m$ and $x_1, x_2, \\ldots, x_n$ such that $\\sum_{i=1}^n x_i = m$ and $\\prod_{i=1}^n x_i$ is maximized. Is the maximum product $\\prod_{i=1}^n x_i$ polynomial in $m$?",
"role": "user"
}
] | No |
[
{
"content": "For a sequence of real numbers $(x_i)$ that satisfies $c i^{-\\alpha}<|x_i| < Ci^\\beta$ for some $c, C, \\alpha ,\\beta>0$, determine if the following product converges to $e$:\n\n$$\\prod_{i=1}^n \\left(1+\\frac{|x_i|^{\\frac{1}{n}}}{n}\\right)$$",
"role": "user"
}
] | e |
[
{
"content": "Evaluate the integral \\( \\int_0^\\infty \\int_0^t e^{-t}\\frac{\\sin(\\tau)}{\\tau}d\\tau \\, dt \\) using the Laplace transform.",
"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... | PCl_3 |
[
{
"content": "Let $A$ be an $R$-right module, $N$ be a submodule of an $R$-left module $M$, and let $\\pi: M \\rightarrow M/N$ be the natural epimorphism. Determine $\\ker(\\pi \\otimes 1_A)$. Provide your answer in terms of $M$, $N$, and $A$.",
"role": "user"
}
] | N \otimes_R A |
[
{
"content": "Find the function \\( f: \\mathbf{R} \\rightarrow \\mathbf{R} \\) such that for all \\( x, y \\in \\mathbf{R} \\), the equation \\( f(2x + f(y)) = x + y + f(x) \\) holds.",
"role": "user"
}
] | f(x) = x |
[
{
"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... | -2i |
[
{
"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... | {eq} \rm F = \sqrt{F_{x}^{2} + F_{y}^{2}} {/eq} |
[
{
"content": "Given three complex numbers $z$, $w$, and $u$ such that $|z|=1$, $|w|=2$, $|u|=3$, and $|z+w-u|=|u+z-w|$, determine the greatest possible value of $|z-u|$. Provide your answer as a single number.",
"role": "user"
}
] | \sqrt{14} |
[
{
"content": "Calculate the flux of the vector field \\( F(x,y,z) = (zy^2-2x, \\frac{1}{4}yz+z^2, xy+2x^2+2z) \\) exiting the region \\( \\Omega = \\{(x,y,z) \\in \\mathbb{R}^3 \\mid x^2 + y^2 + z^2 \\leq 16, z \\leq \\sqrt{x^2+y^2}\\} \\).",
"role": "user"
}
] | -8\pi |
[
{
"content": "Given a Poisson process \\(\\{N(t), t \\geq 0\\}\\) with rate \\(\\lambda\\), let \\(T_1\\) be the time of the first event. Find the probability \\(P[T_1 < s \\mid N(t) = 1]\\) for \\(s \\leq t\\).",
"role": "user"
}
] | \dfrac{s}{t} |
[
{
"content": "Compute the dimension of the spline space \\(\\mathcal{S}_\\Delta^{3,2}\\) on the interval \\([a,b]\\) with \\(n\\) subintervals, where \\(\\Delta\\) denotes the grid on \\([a,b]\\).",
"role": "user"
}
] | n + 3 |
[
{
"content": "Convert the boundaries of the set \\( \\Omega = \\{(x,y) \\in \\mathbb{R}^2: y \\leq x \\leq \\sqrt{y}, 0 \\leq y \\leq 1\\} \\) into polar coordinates and evaluate the integral: \n\\[ \\iint_{\\Omega}(x^2+y^2)\\ dxdy \\]",
"role": "user"
}
] | \dfrac{3}{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... | Cost of Merchandise sold
April 19: 2500 * $20 = $50,000
Sept 2: 4500 * $24 = $108,000
Inventory Balance
Jan 1: 4000 * $20 = $80,000
April 19: 1500 * $20 = $30,000
June 30: (1500 * $20) + (6000 * $24) = $30,000 + $144,000 = $174,000
Sept 2: (1500 * $20) + (1500 * $24) = $30,000 + $36,000 = $66,000
Nov 15: (1500 * $20) + (1500 * $24) + (1000 * $25) = $30,000 + $36,000 + $25,000 = $91,000 |
[
{
"content": "Can a surface with a fundamental group isomorphic to \\(\\mathbb{Z}_2\\) be embedded in \\(\\mathbb{R}^3\\) without self-intersections?",
"role": "user"
}
] | No |
[
{
"content": "Let $H$ be a Hilbert space and $T \\in B(H)$. Suppose that for any choice of orthonormal bases $\\{\\xi_j\\}$ and $\\{\\eta_j\\}$, the series $\\sum_{j=1}^\\infty \\langle T\\xi_j, \\eta_j \\rangle$ converges. Does this imply that $T$ is trace-class?",
"role": "user"
}
] | Yes |
[
{
"content": "Given the functions $f_0, f_1, \\ldots, f_n$ defined by $f_0(x) = \\frac{1}{x-2}$ and $f_{k+1}(x) = \\frac{1}{1-f_k(x)}$ for every $k = 0, 1, \\ldots, n-1$, evaluate $f_{2000}(2001)$. Provide your answer as a single value.",
"role": "user"
}
] | -1998 |
[
{
"content": "Let \\( \\triangle ABC \\) be a non-equilateral triangle with altitudes \\( AD, BE, CF \\). On the rays \\( AD, BE, CF \\), points \\( A', B', C' \\) are chosen such that \\( \\frac{AA'}{AD} = \\frac{BB'}{BE} = \\frac{CC'}{CF} = k \\). Determine all values of \\( k \\) such that \\( \\triangle A'B... | \dfrac{2}{3} |
[
{
"content": "If $\\{A_i\\}$ is a sequence in the endomorphism of $\\mathbb{R}^n$ such that $e^{A_i}$ converges to $e^A$, does it necessarily follow that $A_i$ converges to $A$? Answer yes or no.",
"role": "user"
}
] | No |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $20 |
[
{
"content": "Determine whether Euler's totient function, \\(\\phi(n)\\), takes on all possible values when \\(n\\) is an odd integer. Answer with 'True' or 'False'.",
"role": "user"
}
] | True |
[
{
"content": "Bag A contains $3$ white and $2$ red balls. Bag B contains $6$ white and $3$ red balls. One of the two bags will be chosen at random, and then two balls will be drawn from that bag at random without replacement. What is the probability that the two balls drawn will be the same color? Express your ... | \frac 9{20} |
[
{
"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... | 2.07e9 J |
[
{
"content": "Find the inverse polynomial \\( f^{-1}(x) \\) for \\( f(x) = x^6 + x^5 + 1 \\) in the quotient ring \\( \\frac{\\mathbb{Q}[x]}{(x+2)} \\).",
"role": "user"
}
] | \dfrac{1}{33} |
[
{
"content": "Determine the number of roots of the polynomial \\( P(z) = 2z^4 + z^3 - 5z^2 + z + 2 \\) that lie in the region where \\( \\operatorname{Re}(z) < 0 \\).",
"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... | 6 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... | 5.594 g |
[
{
"content": "Let $E$ be a Lebesgue measurable set in $\\mathbf{R}^{n}$ with $0 < m(E) < \\infty$, and let $f$ be a complex $L^{\\infty}$ function on $\\mathbf{R}^{n}$. For a given $0 < t < 1$, determine if there exists a Lebesgue measurable subset $A$ of $E$ such that:\n\\[\nm(A) = t \\cdot m(E), \\quad \\frac... | Yes |
[
{
"content": "Find the surface area of the region above the plane \\(x + 2z + 1 = 0\\) and below the surface defined by \\(\\sqrt{x^2 + y^2} + z = 1\\) using a double integral. The region of integration in the x-y plane is an ellipse. Express the surface area in terms of a double integral and evaluate it.",
... | 2\sqrt{6}\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... | deviant, distressful, and dysfunctional |
[
{
"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... | biological determinism |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\to 0^+} x^2 \\left(\\left[\\frac{1}{x}\\right]+\\left[\\frac{2}{x}\\right]+\\dots+\\left[\\frac{k}{x}\\right]\\right) \\] where \\( k \\in \\mathbb{N} \\) and \\([x]\\) denotes the integer part of \\( x \\).",
"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... | 8.34% |
[
{
"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... | 16.267% |
[
{
"content": "Consider the system of ordinary differential equations:\n$$\\begin{cases}\\frac{dx}{dt}=4x^3y^2-x^5y^4\\\\ \\frac{dy}{dt}=x^4y^5+2x^2y^3\\end{cases}$$\nDetermine which of the following statements is true:\n1. There exists a closed path in $\\{(x,y) \\in \\mathbb{R^2}|x^2+y^2 \\leq 5 \\}$.\n2. Ther... | D |
[
{
"content": "In a revolving restaurant, there are four round tables, each with three seats. How many different ways can 12 people be seated in this restaurant?",
"role": "user"
}
] | 5913600 |
[
{
"content": "Convert the polar equation \\(\\rho^{2} \\sin \\theta - \\rho \\cos^{2} \\theta - \\sin \\theta = 0\\) for \\(\\theta \\in (0, \\pi)\\) into its Cartesian coordinate system representation.",
"role": "user"
}
] | y = 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... | Additional noninterest expense |
[
{
"content": "Determine whether there exists an integer $n$ with exactly 2000 factors such that $n$ divides $2^n + 1$. In other words, does $n \\mid 2^n + 1$?",
"role": "user"
}
] | Yes |
[
{
"content": "Given a matrix $A$, let $B = AA$. Define matrix $C$ as $C = \\begin{pmatrix} A & 0 & 0 \\\\ 0 & A & 0 \\\\ 0 & 0 & A \\end{pmatrix}$ and matrix $D$ as $D = \\begin{pmatrix} B & 0 & 0 \\\\ 0 & B & 0 \\\\ 0 & 0 & B \\end{pmatrix}$. Prove or disprove that $D = CC$. Provide a justification for your an... | D = CC |
[
{
"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... | 35 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... | 1.89 m |
[
{
"content": "Verify the correctness of the following triple integral calculation in cylindrical coordinates:\n\\[ \\int\\limits_{0}^{2\\pi}\\int\\limits_{0}^{1}\\int\\limits_{r}^1 2zr \\, dz \\, dr \\, d\\theta. \\]\nThe calculation proceeds as follows:\n\\[ \\int\\limits_{0}^{2\\pi}\\int\\limits_{0}^{1}\\left... | \dfrac{\pi}{2} |
[
{
"content": "Evaluate the line integral \\( \\oint_{C} xy \\, ds \\) where \\( C \\) is the curve of intersection of the surfaces \\( x^2 + y^2 = 4 \\) and \\( y + z = 8 \\).",
"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... | 7.92 |
[
{
"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... | 22.83 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... | 0.024 L or 24 mL |
[
{
"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... | 2.74J |
[
{
"content": "Find the integer closest to the integral \\( \\int_{0}^{6} x^{\\{\\sqrt{x}\\}} \\, dx \\), where \\( \\{x\\} \\) denotes the fractional part of \\( x \\).",
"role": "user"
}
] | 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... | 4.47e3 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... | 0.254e10 N/C |
[
{
"content": "Given the integers \\( a, b, \\) and \\( c \\) satisfy:\n\\[\na + b + c = 3, \\quad a^3 + b^3 + c^3 = 3,\n\\]\nfind the maximum value of \\( a^2 + b^2 + c^2 \\).",
"role": "user"
}
] | 57 |
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