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... | 0.5 pants per t-shirt |
[
{
"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... | -1.008% |
[
{
"content": "Consider the Cauchy problem given by:\n\\[ (PC_{a,b}) \\begin{cases} 3x^2y'' - 10xy' + 4y = 0 \\\\ y(2) = a \\\\ y'(2) = b \\end{cases} \\text{ with } a, b \\in \\mathbb{R} \\]\nDetermine under which condition(s) the solution can be uniquely extended to all of \\( \\mathbb{R} \\). Choose the corre... | A |
[
{
"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... | $47,619,047.62 |
[
{
"content": "Determine whether the following statement is true or false: Let \\(a_n\\) be an unbounded, non-decreasing sequence such that \\(\\sum \\frac{1}{\\log(a_n)}\\) converges. Then the series \\(\\sum \\frac{2^n}{a_n}\\) converges.",
"role": "user"
}
] | True |
[
{
"content": "Determine the values of \\( \\alpha \\) for which the set \\( S_{\\alpha} = \\{(x,y,z) \\in \\mathbb{R}^3 \\mid x^2 + y^2 = z^2, z - y + \\alpha = 0\\} \\) is a subspace of \\( \\mathbb{R}^3 \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Consider the Hilbert space $l_2[0,\\infty)$ with the right shift operator $S_r$ and the left shift operator $S_l$ defined as follows:\n\n$$S_r (x_0, x_1, x_2, \\dots) \\mapsto (0, x_0, x_1, \\dots)$$\n$$S_l (x_0, x_1, x_2, \\dots) \\mapsto (x_1, x_2, x_3, \\dots)$$\n\nThe combined operator $T = S_... | [-2, 2] |
[
{
"content": "Evaluate the integral \\(\\int _{|z|=1} \\left(\\frac{e^z}{z+2} - 3 \\bar{z}\\right) dz\\).",
"role": "user"
}
] | -6\pi i |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Non-Chain Motels |
[
{
"content": "Evaluate the integral \\( \\int_C{\\omega} \\) where \\( \\omega=\\frac{dx \\wedge dy}{x^2+y^2} \\) and \\( C(t_1,t_2)=(t_1+1)(\\cos(2\\pi t_2),\\sin(2\\pi t_2)) : I_2 \\rightarrow \\mathbb{R}^2 - \\text{{(0,0)}} \\).",
"role": "user"
}
] | 2\pi \ln 2 |
[
{
"content": "Determine whether the following statement is true or false: For any square matrix $A$, if $A^4 = \\text{Id}$, then $A^2 = -\\text{Id}$ or $A^2 = \\text{Id}$. Provide a justification for your answer.",
"role": "user"
}
] | False |
[
{
"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... | W = (12.06 - 38.45 * \rho_b) * V_b |
[
{
"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... | 0.1354 or 13.54% |
[
{
"content": "Determine whether the following statement is true or false: If a function $f$ is integrable on $[0,1]$ and $m(\\{x:f(x)>0\\})>0$, then $\\int_0^1 f >0$. Provide a justification for your answer.",
"role": "user"
}
] | B |
[
{
"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... | 113600 |
[
{
"content": "Find the number of ordered pairs \\((x, y)\\) that satisfy the equation \\(\\left\\lfloor\\frac{x}{2}\\right\\rfloor + \\left\\lfloor\\frac{2x}{3}\\right\\rfloor + \\left\\lfloor\\frac{y}{4}\\right\\rfloor + \\left\\lfloor\\frac{4y}{5}\\right\\rfloor = \\frac{7x}{6} + \\frac{21y}{20}\\), where \\(... | 4 |
[
{
"content": "Find the area of the largest triangle that can be formed in the first quadrant by a line tangent to the curve $y = e^{-x}$. Provide your answer as a single number.",
"role": "user"
}
] | \dfrac{2}{e} |
[
{
"content": "Given that $g: \\mathbb{R} \\to \\mathbb{R}$ is an odd function with respect to the point $x=2$, $g(6) = 7$, and $g(2+x) = -g(2-x)$, evaluate the integral $\\int_{-2}^6 xg'(x)\\,dx$. Provide your answer as a single number.",
"role": "user"
}
] | 28 |
[
{
"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 kg |
[
{
"content": "Suppose $a: \\mathbb{R}_+ \\to \\{-1,1\\}$ is a measurable function. Given $X_0 = \\frac{1}{2}$, consider a particle whose position $X_t$ on the $X$-axis evolves according to the integral equation $$X_t = X_0 + \\int_0^t a_s \\, ds$$ where the integral is a Lebesgue integral. Let $T = \\frac{1}{2}... | \ell(G) = \frac{1}{2} |
[
{
"content": "In triangle $ABC$, the measure of $\\angle A$ is $86$ degrees. The measure of $\\angle B$ is $22$ degrees more than three times the measure of $\\angle C$. What is the measure, in degrees, of $\\angle C$?",
"role": "user"
}
] | 18 \text{ degrees} |
[
{
"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... | 166.18 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... | $80 million |
[
{
"content": "Given the function \\( f: \\mathbb{R} \\rightarrow \\mathbb{R} \\) satisfying the equations \\( f(x+1) + f(x+2) = f(x-1) + f(x) \\) and \\( f(-x) = -f(x) \\), find the value of \\( f(2) \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Let $G$ be a locally compact abelian (LCA) group, and $H$ a topologically torsion group with a continuous group homomorphism $f: H \\rightarrow G$. Is the topological closure of the image of $f$ in $G$ a topologically torsion group?",
"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... | 3346.5 J |
[
{
"content": "Find the maximum value of the expression \\((1 - x)(2 - y)^2 (x + y)\\) given the constraints \\(x < 1\\), \\(y < 2\\), and \\(x + y > 0\\).",
"role": "user"
}
] | \dfrac{81}{64} |
[
{
"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... | -80.9 |
[
{
"content": "Let $X$ and $Y$ be normed linear spaces, and let $T : X \\to Y$ be a bijective linear map with a closed graph. Determine which one of the following statements is true:\n\n1. The graph of $T$ is equal to $X \\times Y$.\n2. $T^{-1}$ is continuous.\n3. The graph of $T^{-1}$ is closed.\n4. $T$ is cont... | 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... | 9.775 g |
[
{
"content": "Given that $\\alpha \\in \\mathbb{C}$ is a root of the irreducible polynomial $f(X) = X^3 + X + 3$, express $\\alpha^3$ in terms of the basis $\\{1, \\alpha, \\alpha^2\\}$ for the field extension $\\mathbb{Q}(\\alpha)$. Determine $\\alpha^3$ without explicitly finding the roots of $f(X)$. \\( \\al... | -\alpha - 3 |
[
{
"content": "Consider two elements $x$ and $y$ that are transcendental over a field $K$. If $y$ is a polynomial in $x$, determine whether $x$ is necessarily algebraic over $K(y)$. 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... | 41 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... | 0.13 L/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... | 10.8 |
[
{
"content": "Calculate the double integral \\( \\int_{\\mathbb{R}}\\left(\\int_{\\mathbb{R}} f(x,y) \\, dx\\right)dy \\) for the function \\( f(x,y) \\) defined as follows:\n\n\\[ f(x,y) = \\begin{cases} \n 1 & x\\geq 0, \\ x\\leq y\\leq 1+x \\\\\n -1 & x\\geq 0, \\ 1+x\\leq y\\leq 2+x \\\\\n 0 ... | 1 |
[
{
"content": "Solve for $x$ given the equations $4^{\\frac{x}{y} + \\frac{y}{x}} = 32$ and $\\log_3(x+y)+\\log_3(x-y)=1$. What is the value of $x$?",
"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... | $486.78 |
[
{
"content": "Find a closed formula, not involving summation notation, for the expression \\( \\sum_{k=0}^{n-1}\\binom{2n}{2k+1} \\).",
"role": "user"
}
] | 2^{2n-1} |
[
{
"content": "Find the sum of the series \\(\\sum_{n=1}^{\\infty}\\frac{n}{n^4+n^2+1}\\).",
"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... | 511 yr |
[
{
"content": "Kimberly borrows $1000$ dollars from Lucy, who charged interest of $5\\%$ per month (which compounds monthly). What is the least integer number of months after which Kimberly will owe more than twice as much as she borrowed?",
"role": "user"
}
] | 15 |
[
{
"content": "Determine the range of values of \\(\\alpha\\) such that the inequality \\((x_1)^2+(x_2)^2+(x_3)^2 - \\alpha (x_1x_2+x_1x_3+x_2x_3) \\geq 0\\) holds for all real numbers \\(x_1, x_2, x_3\\).",
"role": "user"
}
] | [-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... | 0.569 |
[
{
"content": "Let \\( f: \\mathbb{R}^2 \\to \\mathbb{R}^2 \\) be defined by \\( f(x,y) = (e^{2x+y}, e^{x+y}) \\). Compute the density function \\( \\frac{df[\\lambda_2]}{d\\lambda_2} \\) of the pushforward measure \\( f[\\lambda_2] \\), where \\( \\lambda_2 \\) is the Lebesgue measure on \\( \\mathcal{B}(\\math... | \dfrac{1}{uv} |
[
{
"content": "Determine the degree of the field extension \\(\\mathbb{Q}(\\sqrt{3}+(7)^{1/4})\\) over \\(\\mathbb{Q}\\). Use the hint that if \\(\\mathbb{Q} \\big( \\sqrt{a}, \\sqrt[b]{c} \\big)\\) has degree \\(ab\\) over \\(\\mathbb{Q}\\), then assuming \\(\\mathbb{Q} \\big( \\sqrt{a} + \\sqrt[b]{c} \\big) \\... | 8 |
[
{
"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... | 5.4 m/s |
[
{
"content": "What is the $x$-coordinate of the point on the $x$-axis that is equidistant from points $A( -2, 0)$ and $B(0,4)$?",
"role": "user"
}
] | 3 |
[
{
"content": "Let \\( a, b, c \\) be the sides opposite to the interior angles \\( A, B, C \\) of triangle \\( \\triangle ABC \\), and let the area of the triangle be \\( S = \\frac{1}{2} c^2 \\). If \\( ab = \\sqrt{2} \\), find the maximum value of \\( a^2 + b^2 + c^2 \\).",
"role": "user"
}
] | 4 |
[
{
"content": "Consider the limit \\( \\lim_{t \\to 0}\\int_t^x \\frac{1}{s} \\, ds \\). Analyze the behavior of this limit as \\( t \\to 0 \\).",
"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... | 443.33 nm |
[
{
"content": "Evaluate the integral \\( \\int_{|z| = 1}\\left(\\frac{z}{z - a}\\right)^n dz \\) for \\(|a| < 1\\) and \\(n > 1\\).",
"role": "user"
}
] | 2\pi i n a |
[
{
"content": "Find the remainder when $2^{2021}$ is divided by $2700$. Consider that $2700 = 3 \\times 9 \\times 100$ and use appropriate theorems to solve the problem.",
"role": "user"
}
] | 1652 |
[
{
"content": "Consider the stochastic processes $X$ and $X^{\\varepsilon}$, for $\\varepsilon > 0$, satisfying the following stochastic differential equations (SDEs) on $[0, T]$:\n\\[ dX = \\mu(t, X_t) \\, dt + \\sigma(t, X_t) \\, dW_t, \\]\n\\[ dX^{\\varepsilon} = \\mu(t, X^{\\varepsilon}_t) \\, dt + \\sigma_{... | Yes |
[
{
"content": "Given that $y(x)$ is a solution of the differential equation $y'' = y' + y$ with initial conditions $y(0) = 4$ and $y'(0) = 7$, find the value of $y^{(5)}(0)$, the fifth derivative of $y$ evaluated at zero.",
"role": "user"
}
] | 47 |
[
{
"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... | 0.166 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... | 0.16 or 16% |
[
{
"content": "Evaluate the limit \\( \\lim\\limits_{n\\to\\infty}\\int_{0}^{1}\\cos{(x^n)}dx \\) using integration by parts.",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\to\\infty} \\int_{\\{|x| > n\\}} X \\,dP \\] where $X$ is a random variable on the probability space $(\\Omega,\\mathbf{F},P )$ and $E|X|<+\\infty$. Determine the value of this limit.",
"role": "user"
}
] | 0 |
[
{
"content": "Find \\( \\lim_{x \\to 0} \\frac{x^2 \\sin\\left(\\frac{1}{x}\\right)}{\\sin x} \\).",
"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... | Land: $39,880
Common Stock: $17,280
Additional paid-in Capital: $22,600 |
[
{
"content": "On Monday, Jessica told two friends a secret. On Tuesday, each of those friends told the secret to two other friends. Each time a student heard the secret, he or she told the secret to two other friends the following day. On what day of the week will 1023 students know the secret?",
"role": "u... | \text{Tuesday} |
[
{
"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... | 2406 miles |
[
{
"content": "In a space with four non-coplanar points \\(A, B, C,\\) and \\(D\\), determine the ratio in which the plane passing through the intersection points of the medians of triangles \\(ABC\\), \\(ABD\\), and \\(BCD\\) divides the segment \\(BD\\).",
"role": "user"
}
] | 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... | $23.15 |
[
{
"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... | 6.55 |
[
{
"content": "Given that \\( A \\) is an antisymmetric matrix and \\( B \\) is a symmetric matrix, find the condition under which \\((A - B)^2\\) is antisymmetric.",
"role": "user"
}
] | A^2 + B^2 = 0 |
[
{
"content": "Evaluate the limit \\( \\lim\\limits_{n\\to\\infty}\\frac{\\sum_{i=1}^n (ni+i)}{n^{2}(n+1)^{2}} \\) using the concept of generalized harmonic numbers.",
"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... | 240.5 K |
[
{
"content": "Let $f$ be an analytic function such that the real part of $f$, denoted as $\\Re(f)$, is non-negative. Determine which of the following statements is true:\n\n1. $\\Im(f)$ is constant.\n2. $\\Im(f) \\ge 0$.\n3. $f$ is constant.\n4. $\\Re(f) = |z|$. \n\nSelect the correct statement.",
"role": "... | 3 |
[
{
"content": "Is there a countable collection of polynomials that is dense in the metric space of continuous functions on $[a,b]$?",
"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... | 0.1365 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... | 0.373 Kg |
[
{
"content": "Find the least positive integer \\( n \\) such that the matrix \\( A^n = I \\), where \\( A = \\begin{bmatrix} \\sin \\frac{\\pi}{18} & -\\sin \\frac{4\\pi}{9} \\\\ \\sin \\frac{4\\pi}{9} & \\sin \\frac{\\pi}{18} \\end{bmatrix} \\).",
"role": "user"
}
] | 9 |
[
{
"content": "Find the value of $a$ such that $$\\lim_{x\\to 0^+} \\ln(x \\ln(a))\\ln\\left(\\frac{\\ln(ax)}{\\ln(x/a)}\\right) = 6.$$",
"role": "user"
}
] | e^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... | 4.0e-5 |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^{0} \\frac{dx}{1+x^2} \\) using the residue theorem and a semicircular contour.",
"role": "user"
}
] | \dfrac{\pi}{2} |
[
{
"content": "Consider two possible events $a_1$ and $a_2$ with probabilities $p(a_1)$ and $p(a_2)$, where $p(a_1) + p(a_2) = 1$. A detector, affected by noise, has a probability $p^d(a_j \\to a_i)$ of observing $a_i$ given that the event was $a_j$. The probability of error for this detector is given by:\n\\[ p... | 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... | $11,868.77 |
[
{
"content": "Determine whether the following statement is generally true: \\(\\frac{\\mathrm d}{\\mathrm da} \\int_{-\\infty}^{a-y} f(x)\\, \\mathrm dx = f(a-y)\\), where \\(a\\) and \\(y\\) are constants.",
"role": "user"
}
] | 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... | 4.77 |
[
{
"content": "Determine whether the statement $S_n = \\langle (i_1,i_2),(i_2,i_3),(i_3,i_4),\\ldots,(i_{n-1},i_n)\\rangle$ is true, where $S_n$ is the symmetric group on $n$ letters and $i_k \\in \\{1,2,3,\\ldots,n\\}$ with $i_k \\neq i_l$ if $k \\neq l$. Answer with \"true\" or \"false.\"",
"role": "user"
... | true |
[
{
"content": "Determine the index of $K^{*n}$ in $K^*$ for an infinite extension field $K/\\mathbb{Q}_p$ where $p\\nmid n$.",
"role": "user"
}
] | 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... | 3.10% |
[
{
"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... | 0.10kg |
[
{
"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... | heuristic |
[
{
"content": "Evaluate the double limit: \\[ \\lim\\limits_{(x, y) \\rightarrow (+\\infty, +\\infty)} \\left(1 + \\frac{1}{xy}\\right)^{x\\sin y} \\]",
"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... | 54.35 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... | $7,750 (Unfavorable) |
[
{
"content": "Evaluate the limit: \\[ \\lim_{(x,y)\\to(0,0)} \\frac{\\cos( |x| + |y|) + |x|(e^y - 1)} {|x| + |y|} \\]",
"role": "user"
}
] | \infty |
[
{
"content": "Find the maximum value of the function \\( f(x, y, z) = x^2 + y^2 + z^2 \\) subject to the constraints given by the demand equation \\( z = x + y \\) and the ellipsoid equation \\( \\frac{x^2}{4} + \\frac{y^2}{5} + \\frac{z^2}{25} = 1 \\).",
"role": "user"
}
] | 10 |
[
{
"content": "Find \\( \\lim _{n \\rightarrow \\infty}\\left(a_{1}+a_{2}+\\cdots+a_{n}\\right) \\) for the sequence \\( \\{a_{n}\\} \\) with the general term \\( a_{n}=\\log _{3}\\left(1+\\frac{2}{n^{2}+3 n}\\right) \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Given a matrix $A \\in M_3(\\mathbb{R})$ with $\\text{tr}(A) = 2$, $\\det(A) = -2$, and $A\\alpha = \\alpha$ where $\\alpha = (1,-2,1)^T$, find the matrix $B = A^5 - A^4 - 2A^3 + I_3$. Provide your answer in terms of $A$.",
"role": "user"
}
] | A^2 - A - I_3 |
[
{
"content": "Let $X$ be a connected topological space and let $\\mathcal{O}$ be an open cover of $X$, excluding the empty set. Define a graph where the vertices are elements of $\\mathcal{O}$, and two vertices are connected by an edge if their intersection in $X$ is non-empty. Is the graph formed by $\\mathcal... | Yes |
[
{
"content": "Determine if the integral closure of the quotient ring $k[x,y]/(y^2-x^3-x^2)$ can be expressed as a polynomial ring over $k$.",
"role": "user"
}
] | Yes |
[
{
"content": "Let $P(x)$ be a polynomial with integer coefficients that satisfies $P(17)=10$ and $P(24)=17.$ Given that $P(n)=n+3$ has two distinct integer solutions $n_1$ and $n_2,$ find $n_1$ and $n_2$.\n\n(Give your answer as a comma-separated list, in either order; for example, \"2, 5\" or \"6, -3\".)",
... | 19, 22 |
[
{
"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... | 2.08% |
[
{
"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 increase in labor supply in Alaska from 1976 to 1977 can be attributed to several factors:
1. Lack of entry regulations or qualifications for the pipeline project lowered the barrier to entry for workers, thus increasing the labor supply.
2. The low working population in Alaska even after the initial influx of workers led to further migration of labor into the country, increasing the labor supply.
3. Doubling the wages attracted a greater inflow of workers, leading to a substantial increase in labor supply. |
[
{
"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... | 1.2e+05 Pa |
[
{
"content": "Let $X$ be a Banach space and $C\\subset X$ a bounded, closed, and convex set. Determine if the mapping \\(C\\mapsto d(x,C)\\) is continuous with respect to the Hausdorff distance.",
"role": "user"
}
] | Yes |
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