prompt list | ground_truth string |
|---|---|
[
{
"content": "In an exchange economy with two types of goods and n consumers, half of the consumers have a utility function given by \\( U(x) = 5\\ln{x} + m \\) and the other half have \\( U(x) = 3\\ln{x} + m \\). Each consumer has an initial endowment of 20 units of good \\( x \\) and 10 units of good \\( m \\... | 25 |
[
{
"content": "Determine the theoretical maximum average compression rate for a reversible function \\( f(s) \\), where \\( f'(f(s)) = s \\), when applied to a random bit sequence \\( s \\). Consider the impact of pattern identification and mapping in modern compression algorithms on this rate.",
"role": "us... | 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... | 40 m/s |
[
{
"content": "Compute \\(4^{11112} \\mod 683\\) using the prime factorization of \\(p-1\\), where \\(p = 683\\) is a prime number and \\(p-1 = 2 \\cdot 11 \\cdot 31\\).",
"role": "user"
}
] | 16 |
[
{
"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... | 11.18 MPa |
[
{
"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... | 0.19 m |
[
{
"content": "Let \\(f\\) be a continuous function on \\(\\mathbb{R}\\). Consider the sequence of functions defined recursively as follows:\n\\[ F_1(x) = \\int_0^x xf(t)\\,dt \\]\n\\[ F_2(x) = \\int_0^{F_1(x)} xf(t)\\,dt \\]\n\\[ F_3(x) = \\int_0^{F_2(x)} xf(t)\\,dt \\]\nGiven that \\(\\int_0^1 f(t)\\,dt = 1\\)... | 2^{n+1} - 1 |
[
{
"content": "Calculate the volume of the solid bounded by the surfaces $z = a + x$, $z = -a - x$, and the cylinder $x^2 + y^2 = a^2$. Express your answer in terms of $a$. \\( \\boxed{V} \\)",
"role": "user"
}
] | 2\pi a^3 |
[
{
"content": "Given the joint probability density function (PDF) \\( f_{XY}(x,y) = 8xy \\) for \\( 0 < x < 1 \\) and \\( 0 < y < x \\), find the probability density function \\( f_Z(z) \\) where \\( Z = \\frac{Y}{X} \\). Determine the bounds of integration needed to calculate the cumulative distribution functio... | 2z |
[
{
"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... | Precipitation reaction |
[
{
"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... | 2.77 ppb |
[
{
"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... | 325.949 kPa |
[
{
"content": "What is the coefficient of $x^2y^2$ in the expansion of $(x+y)^4+(x+2y)^4$?",
"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... | 3.0e-3 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... | 21.3 L |
[
{
"content": "Evaluate the contour integral \\( \\oint_{|x+i|=\\rho} \\frac{1}{(x^2+4) \\sqrt{ x^2+4}} \\, dx \\) as \\( \\rho \\rightarrow 0 \\) using the residue theorem.",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate \\( \\lim_{n\\rightarrow\\infty}\\int_0^1 x^n f(x)\\,dx \\), where \\( f \\) is a continuous function on \\([0,1]\\). Use the Weierstrass Approximation Theorem to find this limit.",
"role": "user"
}
] | 0 |
[
{
"content": "Is there a winning strategy for you to secure more pieces of pepperoni than your enemy when sharing a pepperoni pizza sliced into an odd number of pieces, given that you choose first and each subsequent choice must be adjacent to the last chosen slice?",
"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... | 4.05e6 V |
[
{
"content": "A plane passes through vertex \\( C \\) of tetrahedron \\( ABCD \\) and the midpoints of edges \\( AD \\) and \\( BD \\). Determine the ratio in which this plane divides the segment \\( MN \\), where \\( M \\) and \\( N \\) are the midpoints of edges \\( AB \\) and \\( CD \\) respectively.",
"... | 2:1 |
[
{
"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... | 0.0697 or 6.97% |
[
{
"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. Debit Fees Earned $690,500, Credit Income Summary $690,500.
To close Revenue to Income Summary.
2. Debit Income Summary $553,350, Credit Wages Expense $410,000, Credit Rent Expense $75,000, Credit Supplies Expense $48,650, Credit Miscellaneous Expense $19,700.
To close expenses to Income Summary.
3. Debit Income Sum... |
[
{
"content": "Evaluate the integral \\( \\iint_{D} \\frac{\\mathrm{d}x\\,\\mathrm{d}y}{\\sqrt{1 - x^{2} - y^{2}}} \\), where \\( D = \\{(x,y) \\mid x^{2} + 4y^{2} \\leq 1\\} \\).",
"role": "user"
}
] | \dfrac{2\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... | 479 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... | Gold nucleus, Gold atom, Gold coin |
[
{
"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... | 1.1 g/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... | $38.45 |
[
{
"content": "Evaluate the limit \\(\\lim_{n\\rightarrow\\infty} \\left(\\left(\\frac{1}{n}\\right)^n+\\left(\\frac{2}{n}\\right)^n+\\left(\\frac{3}{n}\\right)^n+\\cdots+1^n\\right)^{1/n}\\).",
"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... | 0.11625 m^3/kg |
[
{
"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... | C6H14 |
[
{
"content": "If a function $f$ has partial derivatives $f_x$ and $f_y$ at a point $P$, and these partial derivatives are continuous at $P$, does this imply that $f$ has a tangent plane at $P$? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Accrued expenses |
[
{
"content": "Let $C$ be an abelian category and let $X$ be an object with finite length. Consider a composition series $$0=X_0<X_1< \\cdots <X_n=X$$ where $X_i/X_{i-1}$ is simple for $i=1, \\dots, n$. Is it true that $X = X_0 \\oplus X_1/X_0 \\oplus \\cdots \\oplus X_n/X_{n-1}$?",
"role": "user"
}
] | No |
[
{
"content": "Given the series \\(a = 1 + \\frac{w^2x^2}{2!} + \\frac{w^4x^4}{4!} + \\cdots\\) and \\(b = -x - \\frac{w^2x^3}{3!} - \\frac{w^4x^5}{5!} - \\cdots\\), where \\(w\\) is a non-real complex cube root of unity, find the value of \\((a^2 - b^2w^2)\\).",
"role": "user"
}
] | 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | <img>https://useruploads.socratic.org/mQaE2Y7XSgGXexHmYsBh_Screenshot%20%2854%29.png</img> |
[
{
"content": "For a positive integer $m,$ let $f(m) = m^2 + m + 1$. Find the largest positive integer $n$ such that\n\\[1000 f(1^2) f(2^2) \\dotsm f(n^2) \\ge f(1)^2 f(2)^2 \\dotsm f(n)^2.\\]",
"role": "user"
}
] | 31 |
[
{
"content": "Find the limit of the sequence \\(a_k = \\left(\\dfrac{k^4 11^k + k^9 9^k}{7^{2k} +1}\\right)\\).",
"role": "user"
}
] | 0 |
[
{
"content": "In triangle $\\triangle ABC$, point $D$ is on $AC$ such that $D$ divides $AC$ in the ratio $1:2$. Point $E$ is on $AB$ such that line $CE$ divides $BD$ in the ratio $2:1$. Determine the ratio $AB:EB$. \\(\\text{Express your answer as a simplified ratio.}\\)",
"role": "user"
}
] | 7:4 |
[
{
"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... | Density |
[
{
"content": "Determine the maximum value of the expression \\( |\\ldots|\\left|x_{1}-x_{2}\\right|-x_{3}|\\ldots-x_{1990}\\right| \\), where \\( x_{1}, x_{2}, \\ldots, x_{1990} \\) are distinct natural numbers from 1 to 1990.",
"role": "user"
}
] | 995 |
[
{
"content": "The edges of a rectangular parallelepiped are in the ratio $3: 4: 12$. A diagonal cross-section is made through the largest edge. Calculate the sine of the angle between the plane of this cross-section and the diagonal of the parallelepiped that does not lie in that plane.",
"role": "user"
}... | \dfrac{24}{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... | 9.44e18 electrons/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... | octane |
[
{
"content": "Can two distinct formulas or series of formulas have the same Gödel number?",
"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... | 41.46 psi |
[
{
"content": "Consider an open complete manifold $M$ with Ricci curvature $\\ge 0$. Let $p$ be a fixed point in $M$ and $B(p, r)$ be the distance ball of radius $r$ in $M$. For any given $R>0$, determine whether there exists a constant $c=c(p,R)>0$ such that $\\text{Area}(\\partial B(p, r)) \\ge c(p,R)$ for any... | Yes |
[
{
"content": "In triangle \\( ABC \\), points \\( C_1, A_1, \\) and \\( B_1 \\) are located on sides \\( AB, BC, \\) and \\( AC \\) respectively, such that \\( AC_1 : C_1B = BA_1 : A_1C = CB_1 : B_1A = 2 : 1 \\). If the area of triangle \\( ABC \\) is 1, find the area of the triangle formed by the intersections... | \dfrac{1}{7} |
[
{
"content": "A triangle \\( \\triangle A_0A_1A_2 \\) in the plane has side lengths \\( A_0A_1 = 7 \\), \\( A_1A_2 = 8 \\), \\( A_2A_0 = 9 \\). For \\( i \\ge 0 \\), given \\( \\triangle A_iA_{i+1}A_{i+2} \\), let \\( A_{i+3} \\) be the midpoint of \\( A_iA_{i+1} \\) and let \\( G_i \\) be the centroid of \\( \... | 422 |
[
{
"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... | {\psi} = {\left( {\frac{2}{{{\pi ^3}{{\rm{a}}^3}}}} \right)^{\frac{1}{4}}}\exp \left( { - \frac{{{{\rm{r}}^2}}}{{\rm{a}}}} \right) |
[
{
"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... | 350 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... | 1.7e10 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\to\\ \\frac{\\pi}{2}^-}\\left(\\frac{1}{x-\\frac{\\pi}{2}} + \\tan x\\right) \\] as \\( x \\) approaches \\( \\frac{\\pi}{2} \\) from the left.",
"role": "user"
}
] | 0 |
[
{
"content": "Given the function \\( f(x) = \\prod_{n=1}^{100} (x-n)^{n(101-n)} \\), find the value of \\( \\frac{f(101)}{f'(101)} \\). Choose the correct answer from the following options:\n\n\\((A)\\) 5050\n\n\\((B)\\) \\(\\frac{1}{5050}\\)\n\n\\((C)\\) 10010\n\n\\((D)\\) \\(\\frac{1}{10010}\\)",
"role": ... | B |
[
{
"content": "Given \\( n \\) vectors \\( a_1, \\ldots, a_n \\) in \\( \\mathbb{R}^{d} \\), determine the maximum number of these vectors that can be linearly independent if their first \\( k \\) entries sum to zero.",
"role": "user"
}
] | d - 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... | ontology |
[
{
"content": "Evaluate the integral: \\[ \\int_0^\\pi \\frac{\\sin\\left(n+\\frac{1}{2}\\right)x}{\\sin \\frac{x}{2}} \\, dx \\]",
"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... | 9236282.40155 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... | 0.33% |
[
{
"content": "Evaluate the improper integral \\( \\int_0^\\infty \\left( \\frac{x^{10}}{1+x^{14}} \\right)^{2} \\, dx \\).",
"role": "user"
}
] | \dfrac{\pi}{28} |
[
{
"content": "Is it possible to determine the sum of the factors of a composite integer \\(x\\) by adding a random integer \\(n\\) to all of its factors and multiplying the resulting numbers, without factorizing \\(x\\)?",
"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... | 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... | $32,323.10 |
[
{
"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... | 26 cm/s |
[
{
"content": "In triangle \\( \\triangle ABC \\), the interior angles \\( A, B, C \\) satisfy \\( \\sin A = \\cos B = \\tan C \\). Determine the value of \\( \\cos^3 A + \\cos^2 A - \\cos A \\).",
"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... | 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... | 27.5 g |
[
{
"content": "Suppose for two operators $X$ and $Y$, it is given that $e^X e^Y = e^{X + Y}$. Does this imply that $X$ and $Y$ commute, i.e., $[X,Y] = 0$?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the fixed point of the operator \\( T(f) = \\int_0^x f(y) \\left(\\frac{1}{2} + \\frac{y}{2}\\right) \\, dy \\) using the Banach fixed point theorem.",
"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... | 91.94 C |
[
{
"content": "Let \\( f \\in \\mathbb{R}[x_1, \\ldots, x_n] \\) be a homogeneous real polynomial. Suppose there exists a polynomial \\( h \\in \\mathbb{R}[x_1, \\ldots, x_n] \\) such that \\( f = h \\cdot (x_1 + \\cdots + x_n - 1) \\). Is it necessarily true that \\( f = 0 \\)? Justify your answer.",
"role"... | 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... | 30578 Btu/h |
[
{
"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... | 320 N |
[
{
"content": "Evaluate the integral \\( \\int_{3}^{\\infty}\\frac{1}{x(x^2-9)^{1/2}}dx \\) using an appropriate substitution method.",
"role": "user"
}
] | \dfrac{\pi}{6} |
[
{
"content": "If a subset of \\(\\mathbb{R}\\) is closed and bounded with respect to a metric equivalent to the Euclidean metric, must it be compact? Justify your answer.",
"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... | 201L |
[
{
"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... | $11,223.34 |
[
{
"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... | 40cm |
[
{
"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... | 7.5e9 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... | 3.29*10^-18 J |
[
{
"content": "Let $X_1, X_2, \\ldots, X_n$ be independent and identically distributed random variables, each following an exponential distribution with mean $\\frac{1}{\\lambda}$. Define $S_n = X_1 + X_2 + \\cdots + X_n$ and let $N = \\inf\\{n \\geq 1 : S_n > 1\\}$. Determine the variance of $N$, $\\operatornam... | 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... | 23/6 |
[
{
"content": "Two circles, each with a radius of 12 cm, intersect at points X and Y. The distance between the centers of the circles is 18 cm, and the angle at which the circles intersect is 60 degrees. Calculate the length of the chord XY.",
"role": "user"
}
] | 6\sqrt{7} |
[
{
"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... | 1.048 |
[
{
"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... | 1.53 g/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... | v=4(1-e^{-t/2}) |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.06e-4 Wb |
[
{
"content": "Find the first coefficient, \\( k_1 \\), in the Taylor series expansion of the function \\( F(c) = \\int_0^1 \\sqrt{x^{2p} + c^2} \\, dx \\) at \\( c = 0 \\). The series is given by:\n\\[ F(c) = \\frac{1}{p+1} + k_1c + k_2c^2 + \\cdots \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to \\frac{\\pi}{2}} \\biggl|\\frac{1}{(1+\\sin x)\\log(\\sin x)}+\\frac{1}{\\cos^2x} \\biggl| \\]",
"role": "user"
}
] | \dfrac{1}{4} |
[
{
"content": "Find the limit of \\( \\frac{x^x - (\\sin x)^x}{x^3} \\) as \\( x \\to 0 \\).",
"role": "user"
}
] | \dfrac{1}{6} |
[
{
"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... | Bad debt expense = $12,375 |
[
{
"content": "Suppose $F$ is a finite field and $F^{\\times}$ denotes the group of all non-zero elements of $F$ under multiplication. If $F^{\\times}$ has a subgroup with order 17, what is the smallest possible order of the field $F$?",
"role": "user"
}
] | 103 |
[
{
"content": "Given a figure with an incircle of radius $R$, find the length of the segment $IN$.",
"role": "user"
}
] | R |
[
{
"content": "Is it possible for a continuous and injective function to have a domain that is not open, even if its image is an open interval? Provide a justification for your answer.",
"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... | 82.9 m |
[
{
"content": "If 2 cards from a standard deck are selected randomly, what is the probability that either two kings or at least 1 ace occurs? (There are 4 Aces, 4 kings and 52 total cards in a standard deck.)",
"role": "user"
}
] | \frac{2}{13} |
[
{
"content": "Compute the residue of the function \\( g(z) = \\frac{e^z - 1}{z^3} \\) at \\( z = 0 \\).",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Suppose $g:\\Bbb R\\to \\Bbb R$ is a continuous function such that $\\int _{-\\infty}^\\infty g(x)\\text{dx}$ exists. If $\\lim _{x\\to -\\infty } g(x)$ exists, does it follow that $\\lim_{x\\to -\\infty} g(x)=0$? Answer yes or no.",
"role": "user"
}
] | Yes |
[
{
"content": "Given a matrix $B$ with an eigenvalue of $-5$ having algebraic multiplicity $m$, and satisfying the equation $B^4 = 0$, determine the determinant of $B$. \\( \\boxed{0} \\)",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the improper integral \\( \\int_0^{\\infty}\\frac{e^{-x}-e^{-2x}}{x}dx \\).",
"role": "user"
}
] | \ln 2 |
[
{
"content": "Calculate the probability \\( P(X > Y+Z, X > Y) \\), where \\( X, Y, \\) and \\( Z \\) are independent and identically distributed exponential random variables with rate 1.",
"role": "user"
}
] | \dfrac{1}{4} |
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