prompt list | ground_truth string |
|---|---|
[
{
"content": "Determine the number of parameters needed to completely define a 2D n-gon without over-specifying, given that the n-gon is defined by its side lengths and internal angles.",
"role": "user"
}
] | 2n - 3 |
[
{
"content": "Consider the sequence \\(\\{a_n\\}\\) defined recursively by \\(a_1 = 3\\) and \\(a_{i+1} = 3^{a_i}\\) for \\(i > 0\\). Determine which integers between 00 and 99, inclusive, appear as the last two digits in the decimal expansion of an infinite number of terms \\(a_i\\).",
"role": "user"
}
] | 87 |
[
{
"content": "Let \\( m = 30030 \\) and let \\( M \\) be the set of its positive divisors which have exactly 2 prime factors. Determine the smallest positive integer \\( n \\) such that for any choice of \\( n \\) numbers from \\( M \\), there exist three numbers \\( a \\), \\( b \\), and \\( c \\) among them s... | 11 |
[
{
"content": "Evaluate the integral \\( \\int_0^{2\\pi} e^{e^{ix}} \\, dx \\).",
"role": "user"
}
] | 2\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... | -2.2361 feet per second |
[
{
"content": "Given \\( n > 8 \\), let \\( a = \\sqrt{n} \\) and \\( b = \\sqrt{n+1} \\). Determine which is greater: \\( a^b \\) or \\( b^a \\)?",
"role": "user"
}
] | a^b |
[
{
"content": "Find the orthogonal matrix that aligns the axes of a given rotation matrix with the standard coordinate axes.",
"role": "user"
}
] | R^\top |
[
{
"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... | 0.4*mol*dm^-3 |
[
{
"content": "Calculate the total mass of a thin plate with the shape defined by the region bounded by the line $y = x - 1$ and the parabola $y^{2} = 2x + 6$, given that the density of the plate is $\rho(x,y) = xy$.",
"role": "user"
}
] | 36 |
[
{
"content": "Consider a square matrix $A_n$ with dimensions $n \\times n$ where $n \\geq 2$, and it satisfies the equation $A^2 + 2A = 0$. Determine which of the following statements is true:\n\n1. $A$ is singular.\n2. $A$ is nonsingular.\n3. 0 and -2 are eigenvalues of $A$.\n4. Either 0 or -2 is not an eigenv... | E |
[
{
"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... | 12.22% |
[
{
"content": "Find the smallest odd integer \\( n > 1 \\) such that the Mersenne number \\( 2^n - 1 \\) is divisible by twin primes \\( p \\) and \\( q \\) with \\( p < q \\).",
"role": "user"
}
] | 315 |
[
{
"content": "Find the limit: \\( \\lim_{\\alpha\\rightarrow0} \\left(\\alpha\\log^2{\\alpha}\\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... | 174 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... | $v=\frac{Q}{4\pi r^2}$ |
[
{
"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... | 416 nm |
[
{
"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 ft/lb |
[
{
"content": "Evaluate $i^6+i^{16}+i^{-26}$.",
"role": "user"
}
] | -1 |
[
{
"content": "Evaluate the integral \\( \\int _{-\\infty} ^{+\\infty} \\exp(-(x+i)^2) \\, dx \\) using complex integration techniques.",
"role": "user"
}
] | \sqrt{\pi} |
[
{
"content": "Find the exponential generating function for the sequence defined by \\( a_n = (-1)^n \\sum_{k=0}^{n} k \\binom{n}{k} \\).",
"role": "user"
}
] | -x e^{-2x} |
[
{
"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... | $3,928.68 |
[
{
"content": "Find the minimum value of the function \\(f(x)=12x^2\\int_0^1yf(y)dy+ 20x\\int_0^1y^2f(y)dy+4x\\).",
"role": "user"
}
] | -1 |
[
{
"content": "In a locally compact Hausdorff space, let \\( \\mu \\) be a Borel measure that is finite on compact sets, outer regular with respect to open sets, and inner regular with respect to compact sets. Must an atom of such a measure be a singleton, up to a set of zero measure?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine whether there exists a strictly decreasing sequence \\((x_n)_{n \\in \\mathbb{N}}\\) that approaches zero, such that the ratio \\(\\frac{x_{n+1}}{x_n}\\) converges to 1.",
"role": "user"
}
] | Yes |
[
{
"content": "In Fisher's lady tasting tea experiment, consider a scenario where the lady can correctly guess the type of each cup with a probability of 90% (i.e., \\( P(\\text{guess } A|\\text{true } A) = P(\\text{guess } B|\\text{true } B) = 0.9 \\)). Given a total of \\( N = 8 \\) cups, with \\( n = 4 \\) cu... | 0.831 |
[
{
"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... | 8.32e28 m/s^2 |
[
{
"content": "Find the approximate value of $x$ in the equation \\(36^x + 6^x = 42\\) using Taylor expansions and series reversion.",
"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... | 8.02 g |
[
{
"content": "Evaluate the integral analytically: $$\\int^{\\pi/2}_{0}\\frac{\\sin(2x)^x(\\ln(\\sin(x))+\\ln(\\cos(x))-x(\\tan(x)-\\cot(x)))}{2^x}\\,dx$$ and verify that it equals -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... | 1.2e4 m/s |
[
{
"content": "Determine the closure of the set \\( S \\) in the real numbers \\( \\mathbb{R} \\), where \\[ S = \\left\\{ \\frac{a}{p^n} \\in \\mathbb{R} \\mid a \\in \\mathbb{Z}, n \\in \\mathbb{N} \\right\\}, \\] given that \\( p \\) is a fixed prime number in the set of natural numbers \\( \\mathbb{N} \\), a... | \mathbb{R} |
[
{
"content": "Find \\( f^{\\prime}(0) \\) for the function defined by:\n\n\\[\nf(x) = \\begin{cases}\n1 - \\cos \\left(x \\sin \\frac{1}{x}\\right), & x \\neq 0 \\\\\n0, & x = 0\n\\end{cases}\n\\]",
"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... | 26e9 |
[
{
"content": "Given two triangles $\\triangle ABC$ and $\\triangle A'B'C'$ with side lengths $a, b, c$ and $a', b', c'$ respectively, where $\\angle B = \\angle B'$ and $\\angle A + \\angle A' = 180^\\circ$, prove that $a a' = b b' + c c'$.",
"role": "user"
}
] | a a' = b b' + c c' |
[
{
"content": "In triangle ABC, where AB = 10 cm and AC = 12 cm, the incenter (I) and the centroid (G) lie on a line parallel to side BC. Determine the length of side BC.",
"role": "user"
}
] | 11 |
[
{
"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... | 3.4 m/s |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\to \\infty}\\int_0^{\\pi/2}\\sqrt[n]{\\sin^n{x}+\\cos^n{x}}\\,dx \\]",
"role": "user"
}
] | \sqrt{2} |
[
{
"content": "Determine the values of $a$ for which the function \\( g(u,v) = u_1v_1 + 5u_2v_2 + au_3v_3+ 2(u_1v_2+u_2v_1)+3(u_1v_3+u_3v_1)+4(u_2v_3+u_3v_2) \\) defines a scalar product in \\( \\mathbb{R}^3 \\).",
"role": "user"
}
] | a > 13 |
[
{
"content": "A spider starts at vertex A of a cube and moves randomly along the edges of the cube. Vertex B is the vertex opposite to A. Calculate the expected number of moves the spider will make to reach vertex B for the first time.",
"role": "user"
}
] | 10 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | E = \frac{\rho L}{4\pi \epsilon_o a(L+a)} |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\to\\infty}\\frac{1}{\\sqrt{n}}\\int\\limits_0^{\\frac{\\pi}{2}}\\ln\\left(1+2\\sin x\\cos\\frac{x}{n}\\right) \\, dx.$$",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the number of solutions in natural numbers \\((x, y)\\) to the equation \\(\\frac{1}{x} + \\frac{1}{y} = \\frac{1}{2023}\\) such that \\(x + y\\) is a multiple of 101.",
"role": "user"
}
] | 0 |
[
{
"content": "Let $P(x)=ax^{2015}-bx^{2014}+1$ and $Q(x)=x^2-2x+1$ be polynomials where $a$ and $b$ are real numbers. If $P(x)$ is divisible by $Q(x)$, find the value of $b-a$.",
"role": "user"
}
] | 1 |
[
{
"content": "Use Stokes' Theorem to evaluate the line integral \\( \\int_C \\mathbf{F} \\cdot d\\mathbf{r} \\), where \\( \\mathbf{F} = (-y^2, x, z^2) \\) and \\( C \\) is the curve of intersection of the plane \\( y+z=2 \\) and the cylinder \\( x^2+y^2=1 \\). The curve \\( C \\) should be oriented anticlockwi... | \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... | -$47,894.29 |
[
{
"content": "Find the indicial equation in terms of \\( r \\) for the differential equation \\( xy'' - 4y' + 5xy = 0 \\), given that \\( x=0 \\) is a regular singular point.",
"role": "user"
}
] | r(r - 5) = 0 |
[
{
"content": "Find the residue at $z=0$ for the complex function $f(z) = \\frac{1}{z^2 \\sin z}$.",
"role": "user"
}
] | \dfrac{1}{6} |
[
{
"content": "A motorist approaches a toll bridge and counts 50 vehicles waiting in a queue to pay the toll. Only one toll booth is in operation. The times in minutes needed to collect the tolls from motorists crossing a toll bridge follow the probability density function \\( f(x)=2\\exp(-2x), x\\in[0,\\infty) ... | 0.5 |
[
{
"content": "If two finite groups are isomorphic, do they have the same character table?",
"role": "user"
}
] | Yes |
[
{
"content": "Did Frobenius generalize Cayley's result for the characteristic polynomial of a matrix from $3\\times 3$ to $n\\times n$?",
"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... | 2.353 s |
[
{
"content": "In a basis for $\\Bbb R^d$ that includes the vector with the first $k$ coordinates equal to $1$ and the vectors with $1$ as the first component and $-1$ as the $i$th component for $2 \\leq i \\leq k$, determine the number of linearly independent vectors such that the sum of their first $k$ compone... | 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... | 1.82e4 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... | $361,350.50 |
[
{
"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... | 1.1e-4 T |
[
{
"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... | 0.6g |
[
{
"content": "Joan tries to solve a really hard problem once each day. She has a 1/4 probability of solving it each day. What is the probability that she will solve it before her sixth try?",
"role": "user"
}
] | \frac{781}{1024} |
[
{
"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... | 596.87 km/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... | 0.250 m/s |
[
{
"content": "Evaluate the surface integral \\( \\iint_S \\mathbf{F} \\cdot d\\mathbf{S} \\) for the vector field \\( \\mathbf{F}(x,y,z) = x\\mathbf{i} + y\\mathbf{j} + 5\\mathbf{k} \\). The surface \\( S \\) is the boundary of the region enclosed by the cylinder \\( x^2 + z^2 = 1 \\) and the planes \\( y = 0 \... | 4\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... | 9.38 |
[
{
"content": "Let $P(x)$ be a polynomial with non-negative integer coefficients such that $P(0)=33$, $P(1)=40$, and $P(9)=60,000$. Find the value of $P(2)$. \\( \\boxed{} \\)",
"role": "user"
}
] | 87 |
[
{
"content": "Using the implicit function theorem, determine if the equation $x\\cos(x-y) = 0$ implicitly defines $y$ as a function of $x$ near the point $(\\pi/2, \\pi/2)$. If it does, calculate the derivative $\\frac{dy}{dx}$ at $x=\\pi/2$. Provide your answer as a single value.",
"role": "user"
}
] | 1 |
[
{
"content": "Consider a sequence of real numbers $\\{a_n\\}$ such that the series $\\sum _{n=1}^{\\infty }\\left|a_n-a_{n-1}\\right|$ is convergent. Determine the convergence of the power series $\\sum_{n=1}^\\infty a_nx^n$ for $x \\in \\mathbb{R}$. Choose the correct option:\n\n(a) Convergent nowhere on $\\ma... | 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... | 398 A/m^2 |
[
{
"content": "Consider a classical knot diagram $K$ that is colored by a finite quandle $X$ such that only one element in the quandle is used to color the knot $K$. This coloring is termed trivial. Determine if the following statement is true: If the knot admits only trivial coloring by any finite quandle, then... | 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... | D=gr^2/GV |
[
{
"content": "Find an integer x such that:\n\\[ x^{17} \\equiv 7 \\pmod{53} \\]\nand\n\\[ x^{17} \\equiv 1 \\pmod{61} \\]",
"role": "user"
}
] | 123 |
[
{
"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... | 6.72 m/s |
[
{
"content": "Calculate the volume of the solid bounded by the surfaces $x^2 + y^2 - 2y = 0$, $z = x^2 + y^2$, and $z = 0$ using triple integrals.",
"role": "user"
}
] | \dfrac{3\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... | 32,787 |
[
{
"content": "If $A$ is a function field in one variable over $\\mathbb{C}$, and $B$ is a finite extension of $A$ with degree $[B : A]$, such that $B$ is isomorphic to $\\mathbb{C}(x)$ over $\\mathbb{C}$, does it follow that $A$ must also be isomorphic to $\\mathbb{C}(x)$ over $\\mathbb{C}$? Consider the proper... | Yes |
[
{
"content": "Determine the set of points in the complex plane where the function \\( f(z) = ze^{\\overline{z}} \\) is differentiable.",
"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... | 10.8 g |
[
{
"content": "Determine whether the extension \\( \\mathbb{Q}(e^{i2\\pi/7})/\\mathbb{Q} \\) is a Galois extension.",
"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... | 2.65 * 10^4 |
[
{
"content": "Does there exist a finite nonoriented graph whose automorphism group is transitive but not generously transitive, meaning it is not true that each pair \\((x,y)\\) of vertices can be interchanged by some automorphism?",
"role": "user"
}
] | Yes |
[
{
"content": "Let \\( f(x+y) = f(x)f(y) \\) for all \\( x, y \\in \\mathbb{R} \\), with \\( f(5) = 2 \\) and \\( f'(0) = 3 \\). Find \\( f'(5) \\).",
"role": "user"
}
] | 6 |
[
{
"content": "Use Green's Theorem to evaluate the line integral \\( \\int_C 2xy^{3} \\, dx + 4x^{2}y^{2} \\, dy \\), where \\( C \\) is the boundary of the triangular region in the first quadrant, enclosed by the x-axis, the line \\( x=1 \\), and the curve \\( y=x^{3} \\).",
"role": "user"
}
] | \dfrac{2}{33} |
[
{
"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... | 6.21% |
[
{
"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... | 60.2 m |
[
{
"content": "Let $R$ be a ring and $a \\in R$. If $a$ is a root of a polynomial $F$ in $R[X]$, does there exist a polynomial $G$ in $R[X]$ such that $F = (X-a)G$? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Consider a sequence of step functions $(f_n)$ that converges pointwise to a function $f$. If $f$ is also in $L^1$, does the sequence $(f_n)$ converge to $f$ in the $L^1$ norm? Provide a justification for your answer.",
"role": "user"
}
] | No |
[
{
"content": "Determine the limit of the following integral as \\( \\varepsilon \\to 0 \\):\n\\[\n\\lim_{\\varepsilon\\rightarrow 0}\\frac{1}{\\varepsilon}\\int_{D(\\varepsilon)}\\frac{1 + \\sin(x) + \\sin(y)}{\\sqrt{x^2 + y^2}} \\, d(x,y)\n\\]\nwhere \\( D(\\varepsilon) = \\{ (x,y) \\in \\mathbb{R}^2 \\mid 0 <... | 2\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... | 83.8 A |
[
{
"content": "A particle is placed at the center of an interval on a 1-D axis. The particle moves according to the following rules: it chooses its direction freely and randomly, and the span of each step is chosen with equal probability from the range (0, r]. The total number of steps is unlimited. Determine th... | 1 |
[
{
"content": "Given a real number $x$ and the matrix $M_x = \\begin{pmatrix} 1 & x+1 & 0 & 0 \\\\ 0 & x & x-1 & 0 \\\\ 0 & x-1 & x & 0 \\\\ 1 & 0 & x+1 & x \\end{pmatrix}$, find the value(s) of $x$ for which $M_x$ is diagonalizable. The eigenvalues of $M_x$ are $\\lambda_1 = 1$, $\\lambda_2 = x$, and $\\lambda_... | -1 |
[
{
"content": "Let $a=\\frac{3}{5}$ and let $b=\\frac{2}{3}$. Compute $a^{2}b^{-3}.$",
"role": "user"
}
] | \frac{243}{200} |
[
{
"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... | 1163000 |
[
{
"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... | 407.65 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... | The operating income for 2010 is $2,600,000 and the operating income for 2011 is $3,219,500. |
[
{
"content": "For integers $a$ and $b$, with $a$ odd and $b$ even, if the equation $a^4+4a^3b-4ab^3-4b^4 = w^2$ holds for some integer $w$, does it necessarily follow that $a$ divides $b$? Answer yes or no.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine a suitable substitution to simplify the integral \\( \\iint_R (x+y+1) \\, dy \\, dx \\), where the region \\( R \\) is bounded by the curves \\( y=1-x \\), \\( y=2-x \\), \\( y=1+x \\), and \\( y=-1+x \\).",
"role": "user"
}
] | u = x + y, v = y - x |
[
{
"content": "Find the number that is the product of three prime numbers, where the sum of the squares of these primes is 2331, there are 7560 numbers less than it that are coprime with it, and the sum of all its divisors is 10560.",
"role": "user"
}
] | 8987 |
[
{
"content": "Determine the quotient space of \\( C[0,1] / C_{0}[0,1] \\), where \\( C_{0}[0,1] = \\{ x \\in C[0,1] : x(0) = 0 \\} \\). Is the quotient space isomorphic to \\( \\mathbb{R} \\)?",
"role": "user"
}
] | \mathbb{R} |
[
{
"content": "Evaluate the double integral \\( \\iint_D e^{2(x+y)}(1+e^y) \\, dx \\, dy \\), where \\( D \\) is the region defined by \\( \\{(x,y) \\in \\mathbb{R}^2: e^y - 2 \\leq x \\leq e^y, -y - 1 \\leq x \\leq -y + 1\\} \\). Consider using the change of coordinates \\( u = x - e^y \\) and \\( v = x + y \\)... | e^2 - e^{-2} |
[
{
"content": "Calculate the residue of the function \\( f(z) = \\frac{e^z +1}{\\sin^2(iz)} \\) at the point \\( z = i\\pi \\).",
"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... | 3.71 |
[
{
"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... | 41.52% |
[
{
"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... | oxygen gas |
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