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... | a = \frac{5}{7}g\sin{\theta} |
[
{
"content": "Determine whether it is possible to construct an injective mapping from \\(\\mathbb{Z}^4\\) to \\(\\mathbb{Z}\\) that satisfies similar efficiency constraints as a known mapping for \\(\\mathbb{Z}^3\\).",
"role": "user"
}
] | Yes |
[
{
"content": "In three training matches, each lasting 90 minutes, exactly one of the seven players $A_{1}, A_{2}, \\cdots, A_{7}$ is on the field at any moment. The total playing time for each of players $A_{1}, A_{2}, A_{3}, A_{4}$ must be divisible by 7, and for players $A_{5}, A_{6}, A_{7}$, it must be divis... | 208806 |
[
{
"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... | 4.2 g |
[
{
"content": "Find an equivalent expression for the remainder of the converging series \\( R_n = \\sum_{k=n+1}^{\\infty} \\frac{1}{k^3} \\) given the series \\( \\sum_{n=1}^{\\infty} \\frac{1}{n^3} \\).",
"role": "user"
}
] | \dfrac{1}{2n^2} |
[
{
"content": "Find the limit of the integral \\( \\int_0^1 \\frac{ne^x\\cos x}{1 + n^2x^2} \\, dx \\) as \\( n \\rightarrow \\infty \\).",
"role": "user"
}
] | \dfrac{\pi}{2} |
[
{
"content": "Determine whether an infinite set can be partitioned into an infinite number of infinite sets.",
"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... | 77.9 mi |
[
{
"content": "Given a random variable \\( X \\) with the density function:\n\\[\nf(x; \\theta) = \\frac{\\theta + x}{\\theta + 1} \\cdot e^{-x}, \\quad \\text{if } x \\geq 0\n\\]\n\\[\nf(x; \\theta) = 0, \\quad \\text{if } x < 0\n\\]\nand the constraint \\( 0 \\leq \\theta \\leq 4 \\), determine the maximum lik... | 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... | $28.4 |
[
{
"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... | 2.42 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... | 14.18 |
[
{
"content": "Evaluate the expression \\(2016^{2016} + 2018^{2016} \\pmod{2017^{2016}}\\).",
"role": "user"
}
] | 2 |
[
{
"content": "Determine whether there exists a measurable function \\( g: \\mathbb{R}_+^n \\to \\mathbb{R}_+ \\) such that for any positive real numbers \\( x_1, x_2, \\ldots, x_n \\), the function satisfies \\( g(x_1 \\cdot x_2 \\cdot \\ldots \\cdot x_n) = \\min(g(x_1), g(x_2), \\ldots, g(x_n)) \\).",
"rol... | 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... | 9,000,000 |
[
{
"content": "Find the derivative of the function \\( f(x) = \\int_{-\\infty}^x e^{-(x-y)} \\eta(y) \\, dy \\). What is \\( \\frac{d}{dx}f(x) \\)?",
"role": "user"
}
] | \eta(x) - f(x) |
[
{
"content": "The scores on a $110$-point test were organized in the stem-and-leaf plot shown. $9 | 6$ represents $96$ points. What is the mode of the scores? \\begin{tabular}{c|lllllll}\n\\multicolumn{8}{c}{\\underline{Points on the Test}}\\\\\n5 &0 & 0 & & & & &\\\\\n6 &3 & & & & & &\\\\\n7 &7 & 8 & & & & &\\... | 89 |
[
{
"content": "Given the sets \\(A = \\{1, 2, 3, 4\\}\\) and \\(B = \\{1, 2, 3, 4, 5, 6, 7\\}\\), determine the number of one-to-one functions \\(f: A \\to B\\) such that \\(f(i) \\neq i\\) for all \\(i \\in A\\).",
"role": "user"
}
] | 465 |
[
{
"content": "Evaluate the integral \\( \\iiint \\limits _D z^3 \\, \\mathrm{d}V \\) over the region \\( D \\) bounded by the surface of the hemisphere \\( z = \\sqrt{1-x^2-y^2} \\) and the plane \\( z=0 \\) using spherical polar coordinates.",
"role": "user"
}
] | \dfrac{\pi}{12} |
[
{
"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... | 38 hours |
[
{
"content": "Given the pressure \\( p(x,y,z) = \\frac{x^2 + 2y^2}{1 + z^2} \\) and temperature \\( T(x,y,z) = 5 + xy - z^2 \\) at a point \\((x,y,z)\\), and the position of an airplane at time \\( t \\) is \\((x(t), y(t), z(t)) = (2t, t^2 - 1, \\cos t)\\), find \\( \\frac{\\mathrm{d}}{\\mathrm{d}t}(PT)^2 \\) a... | -16 |
[
{
"content": "A construction company plans to build a 100 km road from Arbatova to Chernomorsk. In the first month, they will build 1 km of the road. For each subsequent month, if $A$ km of the road is already completed at the beginning of the month, they will construct an additional $1 / A^{10}$ km during that... | 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... | 1492.47 million |
[
{
"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... | $27.06 |
[
{
"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... | 1885 V |
[
{
"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... | $6,465,000.00 |
[
{
"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... | $0.78 |
[
{
"content": "If $A$ and $B$ are compact and connected subsets of the complex plane, and there is a bijection $f$ that maps $A$ onto $B$, is $f$ necessarily continuous?",
"role": "user"
}
] | No |
[
{
"content": "Consider a sequence of functions \\((f_n(x))_n\\) that converges uniformly to a function \\(f(x)\\) on a domain \\(D\\). Can there exist an \\(N \\in \\mathbb{N}\\) such that \\(f_N(x)\\) is unbounded? Provide a justification or an example if possible.",
"role": "user"
}
] | Yes |
[
{
"content": "In a geometric progression, the first term is 3, and the sum of the first seven terms is 381. What is the common ratio of this progression?",
"role": "user"
}
] | 2 |
[
{
"content": "In triangle \\( \\triangle ABC \\), the circumradius is \\( R \\). Given the equation \\[ \\frac{a \\cos A + b \\cos B + c \\cos C}{a \\sin B + b \\sin C + c \\sin A} = \\frac{a + b + c}{9R}, \\] where \\( a, b, \\) and \\( c \\) are the lengths of the sides opposite to angles \\( A, B, \\) and \\... | 60^\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... | 1.91 rad/s |
[
{
"content": "Evaluate the limit: $$\\lim_{n \\to \\infty} \\left( \\lim_{x \\to 0} \\left(1+\\sin^2(x)+\\sin^2(2x)+\\cdots+\\sin^2(nx)\\right)^\\frac{1}{n^3\\cdot x^2}\\right)$$",
"role": "user"
}
] | e^{\frac{1}{3}} |
[
{
"content": "On a board, there are initially 34 ones written. Each minute, Karlson erases two random numbers from the board and writes their sum back on the board. He then eats a number of candies equal to the product of the two erased numbers. What is the maximum number of candies Karlson could eat in 34 minu... | 561 |
[
{
"content": "Given triangle \\( \\triangle ABC \\), if for any \\( t \\in \\mathbf{R} \\), \\( |\\overrightarrow{BA} - t \\overrightarrow{BC}| \\geqslant |\\overrightarrow{AC}| \\), determine the type of triangle \\( \\triangle ABC \\). Choose from the following options:\n\n(A) Acute triangle\n(B) Obtuse trian... | 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... | 21.3 N/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... | 10173056.86 lb/ft |
[
{
"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... | 5475.7 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... | Low, High |
[
{
"content": "Determine whether the complete graph $K_6$ can be embedded in three-dimensional space $\\mathbb{R}^3$ without any edges crossing.",
"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... | 0.315% |
[
{
"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... | 111.618 months |
[
{
"content": "Find the remainder when \\( (85^{70} + 19^{32})^{16} \\) is divided by 21.",
"role": "user"
}
] | 16 |
[
{
"content": "Evaluate the sum: \\[ \\sum_{r=1}^m \\frac{(m+1)(r-1)(m^{r-1})}{r\\binom{m}{r}} \\] where \\( \\binom{m}{r} \\) is the binomial coefficient.",
"role": "user"
}
] | m^m - 1 |
[
{
"content": "For any given \\(\\epsilon > 0\\), determine whether there always exist natural numbers \\(n\\) and \\(m\\) such that \\(e^n\\) is within \\(\\epsilon\\) of \\(m\\).",
"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... | The magnitude of the total acceleration is 0.2573 m/s^2 and the direction is 51 degrees west of north. |
[
{
"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... | p = m |
[
{
"content": "Find the limit of \\(\\left[(x^m + 1)^{1/n} - (x^m - 1)^{1/n}\\right]x^{(mn-m)/n}\\) as \\(x\\to\\infty\\), where \\(m\\) and \\(n\\) are natural numbers.",
"role": "user"
}
] | \dfrac{2}{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... | 511 g |
[
{
"content": "Compute the dimension of the Zariski cotangent space of the variety $V(Y-X^2)$ at the origin in $k^2$, where $k$ is an algebraically closed field. Use the definition of the Zariski cotangent space as the quotient $\\mathfrak{m}_{(0,0),V}/\\mathfrak{m}_{(0,0),V}^2$, where $\\mathfrak{m}_{(0,0),V}$ ... | 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... | g=GM/(R+100000)^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 |
[
{
"content": "In the figure, $AB \\perp BC, BC \\perp CD$, and $BC$ is tangent to the circle with center $O$ and diameter $AD$. In which one of the following cases is the area of $ABCD$ an integer?\n[asy] pair O=origin, A=(-1/sqrt(2),1/sqrt(2)), B=(-1/sqrt(2),-1), C=(1/sqrt(2),-1), D=(1/sqrt(2),-1/sqrt(2)); dra... | AB=9, CD=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... | 1.62e-3 cm |
[
{
"content": "Evaluate the double integral \\( \\int_{-\\infty}^\\infty \\int_{-\\infty}^\\infty e^{-(x-y)^2} \\, dy \\, dx \\).",
"role": "user"
}
] | \infty |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 19130.53 MJ/yr |
[
{
"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... | Black Pacer: Bbtt
Brown Trotter: bbTt
Offspring (Brown Pacer): bbtt |
[
{
"content": "Find the shortest distance from the point \\((1, -1, 1)\\) to the set of points defined by the equation \\(z = xy\\).",
"role": "user"
}
] | \sqrt{2} |
[
{
"content": "Find the limit of the sum of the areas of triangles formed by a line segment of length 1, with a ratio of 0.9, as the number of triangles approaches infinity.",
"role": "user"
}
] | \dfrac{9}{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... | 1693.7 |
[
{
"content": "A white cylindrical silo has a diameter of 30 feet and a height of 80 feet. A red stripe with a horizontal width of 3 feet is painted on the silo, as shown, making two complete revolutions around it. What is the area of the stripe in square feet?\n\n[asy]\nsize(250);defaultpen(linewidth(0.8));\n... | 240 |
[
{
"content": "Determine the minimum number of geostationary satellites required to ensure that at least three satellites are visible from any point on Earth at all times.",
"role": "user"
}
] | 7 |
[
{
"content": "Let $f$ be a Borel measurable nonnegative function such that $\\int_{E} f \\, dm < \\infty$ for all Lebesgue measurable sets $E$ with $m(E) < 1$. Prove that $\\lim_{n \\to \\infty} n \\cdot m(\\{f \\ge n\\}) = 0$. ",
"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... | 20.1983 N |
[
{
"content": "Find the derivative of the function \\( f(x) = \\arctan\\left(\\frac{\\sqrt{1+x^2}-\\sqrt{1-x^2}}{\\sqrt{1+x^2}+\\sqrt{1-x^2}}\\right) \\) with respect to \\( \\arccos(x^2) \\).",
"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... | 0.8168 EUR |
[
{
"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... | 4.33 years |
[
{
"content": "Let $n=2^{31}3^{19}.$ How many positive integer divisors of $n^2$ are less than $n$ but do not divide $n$?",
"role": "user"
}
] | 589 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $\frac{1}{2} R'(t_2)^2 - \frac{1}{2} R'(t_1)^2 = \frac{GM}{R(t_2)}- \frac{GM}{R(t_1)}$ . $\left ( \frac{dR}{dt} \right )^2$ is exactly what it looks like, the square of the rate of change of the radius. |
[
{
"content": "Consider two non-parallel/antiparallel real vectors $u$ and $v$ with equal norms, $\n u \\n = \\n v \\n$. Determine the number of orthogonal matrices $A$ with real entries such that $Au = v$. Provide your answer as a single integer.",
"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... | 410 Hz |
[
{
"content": "The points $A = (3,-4,2),$ $B = (5,-8,5),$ $C = (4,-3,0),$ and $D = (6,-7,3)$ in space form a flat quadrilateral. Find the area of this quadrilateral.",
"role": "user"
}
] | \sqrt{110} |
[
{
"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... | 2.97 m/s |
[
{
"content": "Find the generating function for the sequence \\( \\{c_n : n \\geq 0\\} \\) where \\( c_n \\) is the number of solutions to the equation \\( x_1 + x_2 + x_3 + x_4 = n \\) with the constraints: \\( x_1, x_2, x_3, x_4 \\geq 0 \\), \\( x_2 \\geq 2 \\), \\( x_3 \\) is a multiple of 4, and \\( 1 \\leq ... | 0 |
[
{
"content": "Given the equation \\(2^{a+1} + 2^{b+1} = 9 \\times 2^{\\frac{a+b-1}{2}}\\), find the absolute difference \\(|a-b|\\).",
"role": "user"
}
] | 3 |
[
{
"content": "Given the function $L(x) = x - \\frac{x^2}{4}$, let $a_n$ be the result of applying $L$ to itself $n$ times, starting with $\\frac{17}{n}$ as the initial value. Determine the limiting value of $n \\cdot a_n$ as $n$ approaches infinity.",
"role": "user"
}
] | \dfrac{68}{21} |
[
{
"content": "For a given value of $\\lambda$, determine if there exists a positive integer $n$ such that the inequality\n\n$$2^{10+\\lambda+n}-2^{10+\\lambda}-144759 \\equiv 13116 \\cdot 2^{-\\lambda} \\pmod{3^{10}}$$\nholds true.",
"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... | Total Product Total Fixed Cost Total Variable Cost Total Cost Marginal Cost
0 60 $0.00 60 -
1 60 $45.00 105 45
2 60 $85.00 145 40
3 60 $120.00 180 35
4 60 $150.00 210 30
5 60 $185.00 245 35
6 60 $225.00 285 40
7 60 270.00 330 45
8 60 $325.00 385 55
9 60 $390.00 450 65
10 60 $465.00 525 75 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\to 0}\\frac{1}{x^3}\\int_0^x\\frac{t^2}{t^4+1}dt \\]",
"role": "user"
}
] | \dfrac{1}{3} |
[
{
"content": "Find the value of \\( \\lim\\limits_{x \\to 0^{+}} \\lfloor \\frac{1}{\\ln x} \\rfloor \\).",
"role": "user"
}
] | -1 |
[
{
"content": "Compute the following limit without using l'Hopital's Rule:\n\n$$\\lim\\limits_{x\\to 0} \\frac{e^x-1-x-\\frac{1}{2}x^2}{x-\\sin{x}}$$",
"role": "user"
}
] | 1 |
[
{
"content": "Determine whether there exists a continuous function $g$ that maps an unbounded nonempty set of real numbers $E$ to the real numbers, such that $g$ is bounded but not uniformly continuous.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the value of the convergent series \\(\\sum_{n=1}^{\\infty}\\frac{n^2-n+1}{n!}\\) using the telescoping series property and the relationship with the exponential function.",
"role": "user"
}
] | 2e - 1 |
[
{
"content": "Determine the degree of the splitting field of the polynomial \\( f(x) = x^4 + 4 \\) over \\( \\mathbb{Q} \\).",
"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... | Given two colors \\(\\alpha = \\langle r_1, g_1, b_1\\rangle\\) and \\(\\beta = \\langle r_2, g_2, b_2\\rangle\\), a color \\(\\gamma = \\langle r_3, g_3, b_3\\rangle\\) lies on the gradient between them if there exists a \\(t \\in [0, 1]\\) such that \\(\\gamma = \\alpha + t(\\beta - \\alpha)\\) |
[
{
"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... | 112.14 m |
[
{
"content": "Determine the number of solutions to the equation \\(\\sqrt{3} \\cdot x = \\cos(xy)\\) for \\((x,y)\\) in the open interval \\((0,1)^2\\).",
"role": "user"
}
] | \infty |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | semblance |
[
{
"content": "Find the coefficient of \\(x^{24}\\) in the expansion of \\(\\left(\\frac{1}{1-x}\\right)^{2}\\left(\\frac{1}{1-x^3}\\right)\\) without using a calculator.",
"role": "user"
}
] | 117 |
[
{
"content": "Calculate the expected number of days it will take for two independent seeds to sprout, given that the probability of a seed not sprouting on day \\( n \\) is \\( \\frac{1}{2^n} \\).",
"role": "user"
}
] | \dfrac{8}{3} |
[
{
"content": "Evaluate the line integral \\(\\int^{(2,1,0)}_{(0,0,0)}(x^2y-xz)dx+(xy^2-yz)dy+(xz^2-xy)dz\\) along the straight line path from \\((0,0,0)\\) to \\((2,1,0)\\).",
"role": "user"
}
] | \dfrac{5}{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... | $675,903 |
[
{
"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... | 0.0204 m/s |
[
{
"content": "Calculate the conditional expectation \\( E(X^2 \\mid X+Y=1) \\) where \\( X \\) and \\( Y \\) are independent and identically distributed standard normal random variables.",
"role": "user"
}
] | \dfrac{3}{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... | Current Assets:
Cash: $97,650
Accounts Receivable: $203,600
Total Current Assets: $301,250
Non-Current Assets:
Equipment: $422,700
Total Non-Current Assets: $422,700
Total Assets: $723,950
Current Liabilities:
Accounts Payable: $114,340
Income Tax Payable: $4,010
Total Current Liabilities: $118,350
Non-Current Liab... |
[
{
"content": "Two concentric circles have radii 2006 and 2007. $ABC$ is an equilateral triangle inscribed in the smaller circle, and $P$ is a point on the circumference of the larger circle. A triangle with side lengths $PA, PB$, and $PC$ has an area of \\( \\frac{a \\sqrt{b}}{c} \\), where $a, b, c$ are positi... | 4020 |
[
{
"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... | 48.6% |
[
{
"content": "Given the functions \\( x = 4e^t \\) and \\( y = 3t \\), and the partial derivatives \\( f_x(4, 0) = 1 \\) and \\( f_y(4, 0) = 1 \\), find \\( \\frac{d}{dt} \\) at \\( t = 0 \\).",
"role": "user"
}
] | 7 |
[
{
"content": "Find the minimal polynomial of $\\sqrt[5]{2}$ over the field $\\mathbb{Q}(e^{2\\pi i/5})$. Provide your answer as a polynomial with rational coefficients.",
"role": "user"
}
] | x^5 - 2 |
[
{
"content": "Determine which of the following properties can be satisfied by a map \\( f: \\mathbb{Z} \\rightarrow \\mathbb{Q} \\):\n\n1. \\( f \\) is bijective and increasing.\n2. \\( f \\) is onto and decreasing.\n3. \\( f \\) is bijective and satisfies \\( f(n) \\geq 0 \\) if \\( n \\leq 0 \\).\n4. \\( f \\... | 3 |
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