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... | E= \frac{\lambda}{2\pi r\epsilon_0} |
[
{
"content": "Consider all real sequences \\( x_0, x_1, \\ldots, x_{100} \\) satisfying the following conditions:\n1. \\( x_0 = 0 \\).\n2. For any integer \\( i \\) where \\( 1 \\leq i \\leq 100 \\), we have \\( 1 \\leq x_i - x_{i-1} \\leq 2 \\).\n\nFind the greatest positive integer \\( k \\leq 100 \\) such th... | 67 |
[
{
"content": "Find all positive real numbers $x$ such that the inequality $x^{n+1} - x^n + 2x \\geq 0$ holds for all even natural numbers $n$.",
"role": "user"
}
] | (0, \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... | 1.71e+26 |
[
{
"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... | $19,963.85 |
[
{
"content": "Calculate $2023^{4046} \\mod 1547$ using the Chinese Remainder Theorem.",
"role": "user"
}
] | 714 |
[
{
"content": "Find the limit of the difference between the prime zeta function $P(s)$ and the natural logarithm of the Riemann zeta function $\\ln(\\zeta(s))$ as $s$ approaches 1. Given that $M = \\gamma + \\sum_{n=2}^{\\infty} \\mu(n) \\frac{\\ln(\\zeta(n))}{n}$, $P(s) = \\sum_{n=1}^{\\infty} \\mu(n) \\frac{\\... | M - \gamma |
[
{
"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... | 196 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... | A company's cash availability influences its choice between cash and accrual methods. The cash method recognizes income upon cash receipt, ensuring tax payments align with available funds. The accrual method recognizes income when earned, regardless of cash receipt, potentially leading to tax liabilities before cash is... |
[
{
"content": "Determine if there exists a constant \\(K\\) such that for all positive numbers \\(a\\) and \\(b\\), the inequality \\(|a-b|^p \\leq K |a^p - b^p|\\) holds, where \\(p > 1\\). If such a constant exists, find its explicit form.",
"role": "user"
}
] | 1 |
[
{
"content": "Given that \\( f(0) = 0 \\), \\( f(1) = 2 \\), and \\( \\int_0^1 f(x) \\, dx = 3 \\), find the value of \\( \\int_0^1 x f(x) \\, dx \\).",
"role": "user"
}
] | \dfrac{5}{3} |
[
{
"content": "Given a matrix $A$ such that $A^2 = A - I$, where $I$ is the identity matrix, determine $A^{15}$. Express your answer in terms of $A$ and $I$.",
"role": "user"
}
] | -I |
[
{
"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... | 1.02e5 m/s |
[
{
"content": "Determine the value of \\( a \\) such that the equation \\( \\ln(x) = ax^4 \\) has exactly one real root.",
"role": "user"
}
] | \dfrac{1}{4e} |
[
{
"content": "Determine whether the first-order predicate formula \\((A \\land B) \\Rightarrow C\\) is valid, where:\n\n- \\(A = \\forall a (\\neg P(a,a))\\)\n- \\(B = \\forall a \\forall b \\forall c (P(a,b)\\wedge P(b,c)\\Rightarrow P(a,c))\\)\n- \\(C = \\forall a \\forall b (P(a,b)\\Rightarrow \\neg P(b,a))\... | Valid |
[
{
"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 torque, for the rod rotating about the center, is =75.4Nm. The torque, for the rod rotating about one end, is =301.6Nm |
[
{
"content": "Rational Man and Irrational Man both buy new cars, and they decide to drive around two racetracks from time $t = 0$ to $t = \\infty.$ Rational Man drives along the path parameterized by\n\\begin{align*}\nx &= \\cos t, \\\\\ny &= \\sin t,\n\\end{align*}and Irrational Man drives along the path para... | \frac{\sqrt{33} - 3}{3} |
[
{
"content": "Determine whether the following statement is true or false: If $B^A$ and $A^B$ are both countable, then $A$ and $B$ are both countable.",
"role": "user"
}
] | B |
[
{
"content": "According to the data shown, how much cheaper, in cents, is the cheaper store's price for Camera $X$ compared to the more expensive? \\begin{tabular}{|l|l|}\n\\hline\n\\textbf{Store}& \\textbf{Sale Price for Camera $X$} \\\\ \\hline\nSuper Savers & $\\$9$~off the list price~$\\$39.96$ \\\\ \\hline... | 99 |
[
{
"content": "In a separable Hilbert space $H$ with an inner product $(\\cdot, \\cdot)$, determine whether there exists a countable family $\\{w_n\\} \\subset H$ such that for any vector $u \\in H$, the norm can be expressed as $||u|| = \\sup_{n \\in \\mathbb{N}} \\, (u, w_n)$, given that $H$ has an orthonormal... | 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... | 302.60 J |
[
{
"content": "Let $X$ be a projective variety and $F \\in \\overline{NE}(X)$ an extremal face. A morphism $f: X \\longrightarrow Y$ is called the contraction of $F$ if the following conditions hold:\n\n- $f(C) = \\text{point}$ for an irreducible curve $C \\subset X$ if and only if $[C] \\in F$.\n- $f_*(\\mathca... | Yes |
[
{
"content": "A regular 100-sided polygon is placed on a table, with the numbers $1, 2, \\ldots, 100$ written at its vertices. These numbers are then rewritten in order of their distance from the front edge of the table. If two vertices are at an equal distance from the edge, the left number is listed first, fo... | 5050 |
[
{
"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... | 11.974 meter/second |
[
{
"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... | 12.87% |
[
{
"content": "Six positive integers are written on the faces of a cube. Each vertex is labeled with the product of the three numbers on the faces adjacent to the vertex. If the sum of the numbers on the vertices is equal to $1001$, then what is the sum of the numbers written on the faces?",
"role": "user"
... | 31 |
[
{
"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 determinants of resource demand include the productivity of that specific resource, quality of the resource, and the technology in which the resource will be employed. |
[
{
"content": "Find the formula for the derivative of the function \\( g: M_{n\\times n}(\\mathbb{R}) \\rightarrow M_{n\\times n}(\\mathbb{R}) \\) defined by \\( g(A) = A^{-1} + A^3 \\) at the identity matrix \\( I \\). Specifically, determine \\( Dg(I)(H) \\), where \\( I \\) is the identity matrix and \\( H \\... | 2H |
[
{
"content": "Given \\( 0 \\leqslant \\alpha \\leqslant \\beta < \\gamma \\leqslant 2\\pi \\) and\n\\[ \\cos \\alpha + \\cos \\beta + \\cos \\gamma = 0, \\]\n\\[ \\sin \\alpha + \\sin \\beta + \\sin \\gamma = 0, \\]\nwhat is the value of \\( \\beta - \\alpha \\)?\n\nA. \\( \\frac{\\pi}{3} \\)\n\nB. \\( \\frac{2... | B |
[
{
"content": "Two points rotate uniformly around two concentric circles. One completes a revolution 5 seconds faster than the other, resulting in two additional revolutions per minute. Initially, the rays from the center of the circles to these points coincide. Calculate the magnitude of the angle between the r... | \dfrac{\pi}{15} |
[
{
"content": "Determine whether there exists an uncountably infinite subset $X \\subseteq \\mathbb{R}$ such that $\\mathbb{R}$ cannot be generated by $X$ as a field, i.e., $\\mathbb{R} \\neq \\langle X \\rangle$. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the value(s) of the parameter \\( a \\) for which it is possible to find explicit formulas (without integrals) for the solution to the differential equation:\n\\[ \\frac{dy}{dt} = aty + e^{-t^2} \\]",
"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... | -6.785 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... | 418897 Pa |
[
{
"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... | $5,151.70 |
[
{
"content": "Let $X\\subset\\mathbb{R}^n$ be a nonempty convex set with a nonempty interior, and let $f:X\\rightarrow \\mathbb{R}$ be a continuous function. If $f$ is convex on the interior of $X$, is $f$ convex on the entire set $X$?",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the double integral \\( \\int\\int_{D} [x\\sin(x^4+y)+1] \\, dx \\, dy \\), where \\( D \\) is the circle centered at the origin with radius 1.",
"role": "user"
}
] | \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... | Cash flows from operating activities:
Net income: $30,000
Depreciation expense: $30,000
Decrease in accounts receivable: $10,000
Increase in inventory: -$19,000
Increase in accounts payable: $5,000
Net cash provided by operating activities: $56,000
Cash flows from investing activities:
Purchase of PPE: -$5,000
Net cash... |
[
{
"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... | 0.72 |
[
{
"content": "Point \\(P\\) is located inside a square \\(ABCD\\) with side length 10. Let \\(O_1, O_2, O_3\\), and \\(O_4\\) be the circumcenters of \\(\\triangle PAB, \\triangle PBC, \\triangle PCD\\), and \\(\\triangle PDA\\), respectively. Given that \\(PA + PB + PC + PD = 23\\sqrt{2}\\) and the area of qua... | 16902 |
[
{
"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... | 0.0302 or 3.02% |
[
{
"content": "Determine whether the polynomial \\(a_{0}x^{4}+a_{1}x^{3}+a_{2}x^{2}+a_{3}x+a_{4}=0\\), with \\(a_{4}\\neq0\\), has at least one root in the interval \\([0,1]\\) given that \\(\\frac{a_{0}}{5}+\\frac{a_{1}}{4}+\\frac{a_{2}}{3}+\\frac{a_{3}}{2}+a_{4}=0\\).",
"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... | 17.9 cm |
[
{
"content": "Determine the number of values of \\( a \\) for which the polynomials \\( x^3 + ax + 1 = 0 \\) and \\( x^4 + ax^2 + 1 = 0 \\) have at least one common root.",
"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... | 0.37 eV |
[
{
"content": "The vectors $\\mathbf{a},$ $\\mathbf{b},$ and $\\mathbf{c}$ satisfy $\\|\\mathbf{a}\\| = \\|\\mathbf{b}\\| = 1,$ $\\|\\mathbf{c}\\| = 2,$ and\n\\[\\mathbf{a} \\times (\\mathbf{a} \\times \\mathbf{c}) + \\mathbf{b} = \\mathbf{0}.\\]If $\\theta$ is the angle between $\\mathbf{a}$ and $\\mathbf{c},$ ... | 150^\circ |
[
{
"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... | phi = V_o*x/d |
[
{
"content": "Find the exact value of the limit \\( A_\\infty \\) for the sequence defined by \\( A_1 = x \\) and \\( A_j = \\cos(\\sin A_{j - 1}) \\) for all \\( j \\geq 2 \\), where \\( x \\in \\mathbb{R} \\).",
"role": "user"
}
] | \cos(\sin A_\infty) |
[
{
"content": "Two players are playing a game. One player thinks of a set of integers \\( x_{1}, x_{2}, \\ldots, x_{n} \\), where each \\( x_i \\) is a single-digit positive or negative number. The second player can ask for the sum \\( a_{1} x_{1} + \\ldots + a_{n} x_{n} \\) using any chosen set of coefficients ... | 1 |
[
{
"content": "Determine the value of $A$ such that the function $f(x) = \\lfloor{x}\\rfloor \\cos(Ax)$ is continuous for all $x \\in \\mathbb{R}$.",
"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... | 0.3973 BTU/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... | {eq}\vec{E} = \dfrac{\rho r}{2\epsilon_0} \hat{r}{/eq} |
[
{
"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: January 2
Debit: Equipment $48,750
Credit: Common Stock $20,000
Credit: Paid-in Capital in Excess of Par $28,750 |
[
{
"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... | 8.61% |
[
{
"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(t) = (e^(-9t) * (5sin(5t) - 9cos(5t)) + 9)/106 + q(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... | discretionary spending |
[
{
"content": "Evaluate the limit: \\( \\lim_{x \\to -\\infty} \\frac{x^2 - \\sqrt{x^4 + 1}}{x^3 - \\sqrt{x^6 + 1}} \\) without using L'Hôpital's Rule.",
"role": "user"
}
] | 0 |
[
{
"content": "Find a closed form for the sequence $a_n$, defined as \\( a_n := \\sum_{k=0}^{n}\\binom{n}{k}(n-k)^n(-1)^k \\), using generating functions.",
"role": "user"
}
] | n! |
[
{
"content": "Find the value of $f''(1)$ for the function \\( f(x) = \\frac{e^{(x-1)^2}-1}{(x-1)^{2}} \\) using its Taylor series expansion about $x=1$. Express your answer as a single number.",
"role": "user"
}
] | 1 |
[
{
"content": "If \\(a\\) is the largest root of the equation \\(x^2(x-5) + 2 = 0\\), find the value of \\([a^4]\\), where \\([x]\\) denotes the greatest integer less than or equal to \\(x\\).",
"role": "user"
}
] | 584 |
[
{
"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... | 616 N |
[
{
"content": "A bus departs from station $A$ and travels along the road, reaching each of the bus stops $B, C, \\ldots, I$ exactly once before finally returning to station $A$. Determine the number of different sequences of bus stops that the bus can take.",
"role": "user"
}
] | 40320 |
[
{
"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... | 91.1s |
[
{
"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 true NPVs for project F and G are $5,160.48 and -$3,327.45, respectively. |
[
{
"content": "Determine whether it is possible to construct a function $y(x)$ such that $y(a) \\neq 0$, $y'(a) = 0$, and $y''(a) = 0$ given that $g(x)$ has a first derivative at $a$. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "How many $4 \\times 4$ matrices with entries from the set $\\{0, 1\\}$ have an odd determinant?",
"role": "user"
}
] | 20160 |
[
{
"content": "A miner is trapped in a mine with three identical doors. The first door leads to safety in 2 hours. The second door leads back to the starting point in 3 hours. The third door leads to a maze, returning to the starting point in 5 hours on the first entry, and 1 hour on subsequent entries. The mine... | 8 |
[
{
"content": "The sum of 18 consecutive positive integers is a perfect square. What is the smallest possible value of this sum?",
"role": "user"
}
] | 225 |
[
{
"content": "Determine the pointwise convergence of the series \\( \\sum_{n=1}^{+\\infty}(-1)^n\\frac{nx^3}{n^2+x^2} \\).",
"role": "user"
}
] | \mathbb{R} |
[
{
"content": "Derive the critical region for the likelihood ratio test (LRT) statistic for the following hypothesis test: Let $X$ be a random variable with pdf $f(x; \\theta) = \\theta x^{\\theta - 1}$ where $0 < x < 1$ and $\\theta > 0$. Consider the null hypothesis $H_0: \\theta = 1/2$ versus the alternative ... | 0.0025 |
[
{
"content": "If $T : B \\rightarrow B$ is a linear continuous operator and $B$ is a Banach space, is $T$ a closed operator?",
"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... | Higher atmospheric pressure and lower temperature |
[
{
"content": "Evaluate the limit \\( \\lim_{n \\to \\infty} \\frac{a_n}{\\frac{\\ln(n)}{n^{2-x}}} \\), where \\( a_n = n^x(n^{1/n^2} - 1) \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Sisyphus has three boxes of stones. He moves stones one by one between the boxes. Each time he moves a stone, Zeus gives him coins equal to the difference between the number of stones in the destination box and the source box (excluding the moved stone). If the difference is negative, Sisyphus ret... | 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... | -32.36 |
[
{
"content": "Determine whether the following statement is true or false: If a function $F$ is continuous on a closed interval, then the epigraph of its convex envelope $\\hat{F}$ is equal to the convex hull of the epigraph of $F$. Provide a justification for your answer.",
"role": "user"
}
] | True |
[
{
"content": "Let \\( R = k[x_{1}, \\ldots, x_{n}] \\) where \\( k \\) is a field, and let \\( I \\) be a homogeneous ideal. Consider the graded minimal free resolution \\( \\cdots \\to R_{1} \\to R_{0} \\to R/I \\to 0 \\) of \\( R/I \\). Is it always true that \\( R_{0} = R \\)?",
"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... | $5,498.65 |
[
{
"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... | 9.05% |
[
{
"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... | 67.6 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... | 21396 min |
[
{
"content": "Consider two sets of real numbers: \\( A = \\{ a_1, a_2, \\cdots, a_{100} \\} \\) and \\( B = \\{ b_1, b_2, \\cdots, b_{50} \\} \\). Let \\( f \\) be a mapping from \\( A \\) to \\( B \\) such that every element in \\( B \\) has a preimage and \\( f(a_1) \\leq f(a_2) \\leq \\cdots \\leq f(a_{100})... | D |
[
{
"content": "A complex number \\( w \\) has modulus \\( r \\). Given that \\( w \\) satisfies the equation \\( \\frac{500}{w} = 3|w| + 40i \\), find the value of \\( r \\) using a non-calculator method.",
"role": "user"
}
] | 10 |
[
{
"content": "Let $R$ be a commutative Noetherian ring with unity, and let $I$ be an ideal of $R$ such that $R/I \\cong R$. Is it true that $I = (0)$?",
"role": "user"
}
] | (0) |
[
{
"content": "Determine the range of the expression \\[ \\frac{|x-y|}{|x|+|y|} + \\frac{|y-z|}{|y|+|z|} + \\frac{|z-x|}{|z|+|x|} \\] for real numbers $x, y, z$ such that no two of $x$, $y$, and $z$ are equal.",
"role": "user"
}
] | (0, 3] |
[
{
"content": "Evaluate the integral \\( \\int_0^1 r(x) \\, dx \\), where \\( r(x) \\) is defined as follows: \\[ r(x) = \\begin{cases} 1 & \\text{if } x \\text{ is rational}, \\\\ 0 & \\text{if } x \\text{ is irrational}. \\end{cases} \\]",
"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... | 27 revolutions per minute |
[
{
"content": "Find all functions \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) such that for all real numbers \\( x \\) and \\( y \\), the following equation holds:\n\\[ f\\left(f(y)+x^{2}+1\\right)+2x = y + f^{2}(x+1). \\]",
"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... | 3.5 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... | -0.0079 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... | 1.30*10^-23 A.m^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... | $2.13 million |
[
{
"content": "Determine whether all complex matrices $A$ that satisfy $A^2 = A$ are necessarily diagonalizable.",
"role": "user"
}
] | Yes |
[
{
"content": "In a Poisson process with a rate of 0.1 observations per minute, calculate the expected time of the 2nd arrival, given that the 2nd arrival occurs within the first 2.5 minutes.",
"role": "user"
}
] | 1.63 |
[
{
"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... | $65,000 |
[
{
"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... | 0.0104L |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\to \\infty}\\ln{\\left(\\frac{x+\\sqrt{x^2+1}}{x+\\sqrt{x^2-1}}\\right)}\\cdot \\left(\\ln{\\left(\\frac{x+1}{x-1}\\right)}\\right)^{-2}$$",
"role": "user"
}
] | \dfrac{1}{8} |
[
{
"content": "In a triangle $\\Delta ABC$ with side lengths $a = 3$, $b = 4$, and $c$, the circumradius $R$ is at least $2$. Determine the maximum possible value of $\\lfloor 2rR \\rfloor$, where $r$ is the inradius and $\\lfloor . \\rfloor$ denotes the greatest integer function.",
"role": "user"
}
] | 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... | 22590.66 m |
[
{
"content": "In a directed graph with 2013 vertices, there is exactly one edge between any two vertices, and for every vertex, there exists an edge outwards from this vertex. Given that from every vertex, you can reach exactly k vertices using at most two edges, determine the maximum value of k.",
"role": ... | 2012 |
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