prompt list | ground_truth string |
|---|---|
[
{
"content": "Determine whether the sequence \\( \\sqrt[n]{1+a^n} \\), where \\( 0<a<1 \\), converges to 1. Provide a rigorous proof of your conclusion.",
"role": "user"
}
] | 1 |
[
{
"content": "Given that \\(0 < x < 1\\) and \\(a > 0, a \\neq 1\\), determine whether \\(p = \\left|\\log_a(1 - x)\\right|\\) is greater than, less than, or equal to \\(q = \\left|\\log_a(1 + x)\\right|\\).",
"role": "user"
}
] | p > q |
[
{
"content": "Calculate the flux of the vector field \\( F = y\\hat{i} + z\\hat{k} \\) across the surface of the solid cone defined by \\( 0 \\le z \\le 1 - \\sqrt{x^2 + y^2} \\) using the divergence theorem.",
"role": "user"
}
] | \dfrac{\pi}{3} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $75.13 |
[
{
"content": "Determine the number of positive integers less than or equal to $10^9$ that are neither perfect squares, perfect cubes, nor perfect seventh powers.",
"role": "user"
}
] | 999967395 |
[
{
"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... | Government subsidization of the sale of produce |
[
{
"content": "Let $\\mathbb{F}$ be an ordered field, and let $a, b, q, r \\in \\mathbb{F}$ with $a < b$. Consider the polynomial $f(x) = x^3 + qx + r$. Given that $f(a) > 0$, $f(b) > 0$, and the discriminant $\\Delta = -4p^3 - 27q^2$ of $f$ is negative, determine if $f(x) > 0$ for all $x \\in [a, b]$. Is this s... | 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... | 0.2286 |
[
{
"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... | $25,735 |
[
{
"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... | 7.38e5 C |
[
{
"content": "Evaluate the integral \\( \\int_{0}^{a}\\frac{1}{1+f(x)}\\,dx \\) given that \\( f(x)f(a-x)=1 \\), \\( a>0 \\), and \\( f(x) \\) is continuous and positive on \\([0,a]\\). Use the fact that the integral is independent of \\( f(x) \\) to find the answer.",
"role": "user"
}
] | \dfrac{a}{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... | 17.4 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... | 9952.94 |
[
{
"content": "Find the limit, if it exists: $$\\lim_{x\\to\\infty } \\left(\\sqrt{e^{2x}+e^{x}}-\\sqrt{e^{2x}-e^{x}}\\right)$$",
"role": "user"
}
] | 1 |
[
{
"content": "When \\( a \\) and \\( b \\) are two distinct positive numbers, which of the following algebraic expressions has the largest value?\n\n1. \\( \\left( a + \\frac{1}{a} \\right) \\left( b + \\frac{1}{b} \\right) \\)\n2. \\( \\left( \\sqrt{ab} + \\frac{1}{\\sqrt{ab}} \\right)^2 \\)\n3. \\( \\left( \\... | D |
[
{
"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... | see-saw |
[
{
"content": "Four packages are delivered to four houses, one to each house. If these packages are randomly delivered, what is the probability that exactly two of them are delivered to the correct houses? Express your answer as a common fraction.",
"role": "user"
}
] | \frac{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... | 681.3 Hz |
[
{
"content": "Given the parabola $y = x^2$, three points $P$, $Q$, and $R$ lie on it, and a fourth point $S$ is such that $PQRS$ forms a square. Determine the area of the smallest possible square that can be formed.",
"role": "user"
}
] | 2 |
[
{
"content": "In the Galois field \\( GF(8) \\), let \\( \\alpha \\) be a root of the polynomial \\( x^3 + x + 1 \\). Determine \\( \\gamma \\) as a function of \\( \\alpha \\), where \\( \\gamma \\) is a root of the polynomial \\( x^3 + x^2 + x + 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... | A: $170
B: $220
C: $150
D: $130
E: $80 |
[
{
"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... | 9.98e4 L |
[
{
"content": "Determine the number of subsets of the set \\( A = \\{1, 2, 3, \\ldots, 35\\} \\) that have exactly 26 elements and whose sum is divisible by 5.",
"role": "user"
}
] | 14121492 |
[
{
"content": "Determine whether it is possible to construct a sequence of continuous, non-negative functions $f_n: H \\to \\mathbb{R}$, for $n \\in \\mathbb{N}$, such that $f_n$ converges pointwise to $\\mathbf{1}_U$ and $f_n \\in C_b(\\mathbb{R}^d)$ for each $n$, where $d=d_n$ is allowed to depend on $n$. Prov... | 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... | 1.51 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... | -12634.81 N |
[
{
"content": "Find the limit of the sequence \\(z_n\\) defined by \\(z_1=1\\) and \\(z_n=T(z_{n-1})\\) for \\(n\\geq 2\\), where \\(T(z)=\\dfrac{7z+15}{-2z-4}\\).",
"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... | Year 3 |
[
{
"content": "Let $F:(0,\\infty) \\to [0,\\infty)$ be a continuous function satisfying $F(1)=0$, which is strictly increasing on $[1,\\infty)$, and strictly decreasing on $(0,1]$. Suppose also that $F|_{(1-\\epsilon,1+\\epsilon)}$ is convex and smooth for some $\\epsilon>0$. Is it true that $F$ is convex at eve... | 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... | new or full moon |
[
{
"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... | 6.6 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... | 19.9 L |
[
{
"content": "Determine the number of positive integers that are multiples of 2013 and have exactly 2013 divisors.",
"role": "user"
}
] | 6 |
[
{
"content": "Determine whether there exist matrices of the form $M^k$, where $k$ is a positive integer greater than 2, that have an LU decomposition.",
"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... | -3242 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... | 1392 rad |
[
{
"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... | Sales: CD $300,000, DVD $450,000, Total $750,000; Less: Variable Expenses: CD $120,000, DVD $315,000, Total $435,000; Contribution: CD $180,000, DVD $135,000, Total $315,000; Less: Traceable fixed expenses: CD $138,000, DVD $45,000, Total $183,000; Income before common fixed expenses: CD $42,000, DVD $90,000, Total $132,000; Less: Common fixed expenses: $105,000; Net Income: $27,000 |
[
{
"content": "Compute the surface integral \\( \\iint_S G \\cdot dS \\) where \\( S \\) is the boundary of the solid inside the cylinder \\( x^2 + y^2 = 4 \\), bounded above by the plane \\( z = x \\) and below by the \\( xy \\)-plane. The vector field is given by \\( G(x,y,z) = \\langle x + \\cos z, y + y \\si... | 16 |
[
{
"content": "Let $g(x)$ be a function piecewise defined as \\[g(x) = \\left\\{\n\\begin{array}{cl}\n-x & x\\le 0, \\\\\n2x-41 & x>0.\n\\end{array}\n\\right.\\] If $a$ is negative, find $a$ so that $g(g(g(10.5)))=g(g(g(a)))$.",
"role": "user"
}
] | a=-30.5 |
[
{
"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... | 30.667 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... | 0.12 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... | 0.0271 L |
[
{
"content": "Determine whether the interval $(0,1)$ with the usual topology can be equipped with a complete metric. Answer \"True\" if it can, and \"False\" if it cannot.",
"role": "user"
}
] | A |
[
{
"content": "An archipelago consists of $N \\geqslant 7$ islands. Any two islands are connected by at most one bridge. It is known that no more than 5 bridges lead from each island, and among any 7 islands, there are always at least two connected by a bridge. What is the maximum possible value of $N$?",
"r... | 36 |
[
{
"content": "Given that $g$ is bounded, determine whether $\\lim_{x\\rightarrow \\infty}u(x)=0$ can be concluded.",
"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... | 1650 gm |
[
{
"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... | 60.0 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... | 4143.5 J |
[
{
"content": "Find the sum of the series \\(\\sum_{n=1}^{\\infty} b_n\\), where \\(b_1 = 1\\) and \\(\\frac{b_{n+1}}{b_n} = \\frac{5}{6}+\\frac{(-1)^n}{3}\\).",
"role": "user"
}
] | \dfrac{18}{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... | decrease by $195,000 |
[
{
"content": "What is the distance between the two intersections of $y=x^2$ and $x+y=1$?",
"role": "user"
}
] | \sqrt{10} |
[
{
"content": "Given that $\\frac{a}{b} + \\frac{b}{c} + \\frac{c}{a} = 5$ and $\\frac{a}{c} + \\frac{c}{b} + \\frac{b}{a} = 6$, determine the value of $\\frac{a^3}{b^3} + \\frac{b^3}{c^3} + \\frac{c^3}{a^3}$, where $a, b, c \\neq 0$. \\( \\boxed{} \\)",
"role": "user"
}
] | 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... | 71.88 degrees Celcius |
[
{
"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... | 15.8 m/s, 60 degrees south of east |
[
{
"content": "Let $f_n(x) = \\sin(2^n x)$ for $n \\in \\mathbb{N}$. Show that the distance function \\( d(f_n, f_m) = \\sup_{x \\in [0, 2\\pi]} \\{|f_n(x) - f_m(x)|\\} \\) satisfies \\( d(f_n, f_m) \\geq 1 \\) when \\( n \\neq m \\).",
"role": "user"
}
] | d(f_n, f_m) \geq 1 |
[
{
"content": "How many one-thirds are in one-sixth?",
"role": "user"
}
] | \frac{1}{2} |
[
{
"content": "Determine if $3 = 2 + 1$ is the only case where equality holds in the inequality:\n\\[ p_{n} \\leq p_{1}p_{2} \\cdots p_{n-1} + 1 \\]\nwhere $p_{r}$ denotes the $r^{th}$ prime number.",
"role": "user"
}
] | Yes |
[
{
"content": "Let $x$ be an infinite set and let $\\text{Part}(x)$ be the collection of all partitions of $x$. For a partition $P \\in \\text{Part}(x)$ and a subset $t \\subseteq x$, define $P_{[t]} = \\{p \\in P : p \\cap t \\neq \\emptyset\\}$. The tiling relation on $\\text{Part}(x)$ is defined by $P \\trian... | Yes |
[
{
"content": "The first term of a given sequence is 1, and each successive term is the sum of all the previous terms of the sequence. What is the value of the first term which exceeds 5000?",
"role": "user"
}
] | 8192 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\to 0^+} \\int_0^\\infty \\frac{e^{-xt}}{\\sqrt{t^2 +t}} \\, dt \\]",
"role": "user"
}
] | \infty |
[
{
"content": "Consider the set \\( Y:=\\{x\\in[0,1]|(0.x_{1}x_{2}...),x_{i}\\in\\{0,1\\},x_{2j+1}=1 \\text{ for some } j\\in\\mathbb{N}\\} \\). Determine the measure of \\( Y \\).",
"role": "user"
}
] | 1 |
[
{
"content": "In the Zariski topology on \\(\\mathbb{R}\\), is every point a limit point of the sequence \\(x_n = n\\)?",
"role": "user"
}
] | Yes |
[
{
"content": "Suppose $X$ is a manifold embedded in $\\mathbb{R}^m$ and $Y$ is a subset of $X$ such that every point in $X$ has an open neighborhood in $\\mathbb{R}^m$ that intersects $Y$ in a set that is not contained in $X$. Can $Y$ be a manifold embedded in $\\mathbb{R}^m$? Provide a justification for your a... | No |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to\\infty}\\left(\\frac{3x^2-x+1}{2x^2+x+1}\\right)^\\left(\\frac{x^3}{1-x}\\right)$$",
"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... | La Brava Veterinary Clinic
Balance Sheet
As of September 30
Assets
Cash $17,331
Accounts Receivable $5,974
Supplies $600
Equipment $7,388
Total Assets $31,293
Liabilities
Accounts Payable $2,046
Note Payable - Short Term $12,064
Equity
Common Stock $13,641
Retained Earnings $5,542
Total Liabilities and Equity $31,293 |
[
{
"content": "Consider the Dirichlet problem for the open unit disk \\( \\omega = \\{(x,y) : x^2 + y^2 < 1\\} \\) in \\( \\mathbb{R}^2 \\) with boundary condition \\( u(x,y) = 1 - 2y^2 \\) on \\( \\delta\\omega \\). If \\( u(x,y) \\) is the solution to the problem:\n\\[\n\\begin{cases} \n u_{xx} + u_{yy} = 0 &... | D |
[
{
"content": "Evaluate the integral \\( \\int_0^\\frac{\\pi}{2} \\int_0^1 r^3\\cos\\theta\\sin\\theta(r^2)^{\\frac{1}{2}}\\ dr\\ d\\theta \\) without using polar coordinates.",
"role": "user"
}
] | \dfrac{1}{10} |
[
{
"content": "If \\(x_1, x_2, \\ldots, x_{2019}\\) are roots of \\(P(x) = x^{2019} + 2019x - 1\\), find the value of \\(\\sum_{i=1}^{2019}\\frac{x_i}{x_i - 1}\\).",
"role": "user"
}
] | 2017 |
[
{
"content": "What is the sum of the distinct prime factors of 315?",
"role": "user"
}
] | 15 |
[
{
"content": "Is the identity map the only function \\( f: \\mathbb{Z}_{+} \\to \\mathbb{Z}_{+} \\) that satisfies the following properties?\n\n1. \\( f(mn) = f(m)f(n) \\) for all positive integers \\( m \\) and \\( n \\).\n2. \\( f(m) < f(n) \\) whenever \\( m < n \\).\n3. \\( f(p) \\) is prime for any prime n... | 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... | -2\sqrt{\frac{4GM}{15R}}, \sqrt{\frac{4GM}{15R}} |
[
{
"content": "Does the additive group of rational numbers \\( \\mathbb{Q} \\) have a basis as a \\( \\mathbb{Z} \\)-module?",
"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... | 5.747 kW |
[
{
"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... | 1.87 L |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to 0} \\frac{\\ln(x+1) + 1 - e^x}{x^2} \\] without using L'Hospital's rule or series expansion.",
"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... | 3.6 mm |
[
{
"content": "Suppose $Y$ is a multivariate random variable taking values in $\\mathbb{R}^k$, where $k \\geq 3$. If the marginal distribution function of each coordinate of $Y$ can only take values 0 and 1, does it imply that $Y$ is constant almost surely? Answer 'yes' or 'no'.",
"role": "user"
}
] | yes |
[
{
"content": "Given the polynomial \\( f(x) = ax^2 - bx + c \\) where \\( a, b, \\) and \\( c \\) are positive integers, and \\( f(p) = f(q) = 0 \\) for \\( 0 < p < q < 1 \\), find the minimum possible value of \\( a \\). The vertex of the polynomial is at \\( \\frac{b}{2a} \\) and lies between 0 and 1. Additio... | 5 |
[
{
"content": "Solve the equation \\( \\frac{4}{3} \\left( \\frac{1}{x} - \\lfloor \\frac{1}{x} \\rfloor \\right) = x \\) for a rational number \\( x \\) such that \\( 0 < x < 1 \\). Here, \\( \\lfloor \\cdot \\rfloor \\) denotes the floor function.",
"role": "user"
}
] | \dfrac{2}{3} |
[
{
"content": "Use Cauchy's integral formula to compute the contour integral \\( \\int \\limits_{\\Gamma} \\frac{e^{-z}}{z-1}dz \\), where \\( \\Gamma \\) is the square with sides parallel to the axes, centered at \\( i \\), and with side length 5, traversed in the anticlockwise direction.",
"role": "user"
... | \dfrac{2\pi i}{e} |
[
{
"content": "Determine whether the following inequality holds for all \\( |x| \\neq 0 \\) in \\( \\mathbb{R}^3 \\) with \\( \\lambda > 0 \\):\n\\[\n\\frac{|e^{i\\sqrt{\\lambda+i\\varepsilon}|x|}-e^{i\\sqrt{\\lambda}|x|}|^2}{|x|^2} \\leq \\frac{C}{|x|^2}\n\\]\nwhere \\( \\sqrt{\\lambda+i\\varepsilon} = \\sqrt{\... | 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... | 10891.64 |
[
{
"content": "Does there exist a finite topological space with a fundamental group isomorphic to the infinite cyclic group $\\mathbb{Z}_2$?",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | v= -12.7 m/s x-40.7 m/s y |
[
{
"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... | 10.38 |
[
{
"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... | crude oil |
[
{
"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... | 1.376kgm^2s^-1 |
[
{
"content": "Find the closed form of the infinite series: \\[ \\sum_{k=1}^{\\infty} \\frac{(-1)^{k+1}}{\\left\\lfloor \\sqrt{k} \\right\\rfloor} \\]",
"role": "user"
}
] | \ln 2 |
[
{
"content": "Let $x$ and $y$ be nonzero real numbers such that\n\\[xy(x^2 - y^2) = x^2 + y^2.\\]Find the minimum value of $x^2 + y^2.$",
"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... | Date | Cash Received | Interest Revenue | Premium Amortized | Carrying Amount of Bonds
---|---|---|---|---|
Jan. 1, 2020 | | | | $390,329.57
Jan. 1, 2021 | $28,800 | $23,419.77 | $5,380.23 | $384,949.34
Jan. 1, 2022 | $28,800 | $23,096.96 | $5,703.04 | $379,246.30
Jan. 1, 2023 | $28,800 | $22,754.78 | $6,045.22 | $373,201.08
Jan. 1, 2024 | $28,800 | $22,392.06 | $6,407.94 | $366,793.14
Jan. 1, 2025 | $28,800 | $22,007.59 | $6,792.41 | $360,000.00 |
[
{
"content": "In how many ways can a commander issue a series of 8 orders to a row of 2018 soldiers, where each order instructs either all soldiers in even positions or all soldiers in odd positions to leave the formation, such that exactly 7 soldiers remain in formation?",
"role": "user"
}
] | 30 |
[
{
"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... | 748 torr |
[
{
"content": "Evaluate the integral \\( \\int_{-4}^{4} \\cos{x} \\delta(\\sin{x}) \\,{\\rm d} x \\).",
"role": "user"
}
] | -1 |
[
{
"content": "Suppose \\( a \\) is a real number such that \\( \\sin(\\pi \\cdot \\cos a) = \\cos(\\pi \\cdot \\sin a) \\). Evaluate \\( 35 \\sin^2(2a) + 84 \\cos^2(4a) \\).",
"role": "user"
}
] | 21 |
[
{
"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... | 1.9e6 N/m^2 |
[
{
"content": "The number 42524 is a palindrome, because it reads the same backwards as forward. How many integer palindromes are between 10,000 and 70,000, and are even?",
"role": "user"
}
] | 300 |
[
{
"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... | 4.23 m |
[
{
"content": "Find the value of the infinite product: \\[ 2^{\\frac{1}{4}} \\cdot 4^{\\frac{1}{8}} \\cdot 8^{\\frac{1}{16}} \\cdots \\]",
"role": "user"
}
] | 2 |
[
{
"content": "Find the maximum value of the function \\( F(x,y,z) = 2x+y-z \\) subject to the constraint \\( 4x^2 + 2y^2 + z^2 = 40 \\).",
"role": "user"
}
] | 10 |
[
{
"content": "Determine the values of \\( k \\) for which the equation \\( x^3 - 3x^2 + 6x + k = 0 \\) has three real roots.",
"role": "user"
}
] | \emptyset |
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