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... | 2.4e-6 degC^-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... | 25.33 rpm |
[
{
"content": "Find the outward flux of the vector field \\( V = x(x^2+y^2+z^2)^{-3/2}\\mathbf{i} + y(x^2+y^2+z^2)^{-3/2}\\mathbf{j} + z(x^2+y^2+z^2)^{-3/2}\\mathbf{k} \\) through the boundary of the rectangular box \\( R \\), where \\( R \\) consists of all points \\((-1 \\leq x \\leq 1, -1 \\leq y \\leq 1, -1 ... | 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... | 0.02919 rad/s |
[
{
"content": "In triangle \\( \\triangle ABC \\), the sides are given as \\( AB = 7 \\), \\( BC = 8 \\), and \\( AC = 9 \\). A circle is drawn such that it is tangent to side \\( AC \\) and the extensions of sides \\( AB \\) and \\( BC \\). Let \\( D \\) be the center of this circle. Calculate \\( BD^2 \\).",
... | 224 |
[
{
"content": "Is it possible to construct a sequence of continuous functions that converges pointwise to a continuous function but does not converge uniformly?",
"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... | N |
[
{
"content": "Find the maximum value of the function \\( f(z) = \\int_0^z \\sqrt{x^4 + (z - z^2)^2} \\, dx \\) for \\( 0 \\leq z \\leq 1 \\).",
"role": "user"
}
] | \dfrac{1}{3} |
[
{
"content": "Given the power series expansion \\(\\frac{1}{1-x-x^{2}-x^{3}}=\\sum_{n=0}^{\\infty} a_{n} x^{n}\\), find the set of possible values for \\(n\\) such that \\(a_{n-1}=n^{2}\\).",
"role": "user"
}
] | \{1, 9\} |
[
{
"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... | 2.48e5 Pa |
[
{
"content": "Evaluate the triple integral \\( \\iiint_K (x^2 + y^2) \\, dx \\, dy \\, dz \\) over the region \\( K \\) defined by the inequalities \\( 0 \\leq x^2 + y^2 \\leq z^2 \\) and \\( 0 \\leq z \\leq 1 \\).",
"role": "user"
}
] | \dfrac{\pi}{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... | 1/3 |
[
{
"content": "Let $X_i$ be copies of the standard real Gaussian random variable $X$. Let $b$ be the expectation of $\\log |X|$. Assume that the correlations $EX_iX_j$ are bounded by $\\delta_{|i-j|}$ in absolute value, where $\\delta_k$ is a fast decreasing sequence. Is there a constant $C$, depending only on t... | 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... | 7.094 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... | 14.2244 nF |
[
{
"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... | 8030.55 sec |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\rightarrow\\infty}\\left(\\Gamma\\left(\\frac{1}{x}\\right)\\right)^{-1}\\int_{0}^{x}\\frac{|\\sin\\left(t\\right)|}{t}\\:dt$$",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the number of ways to express the polynomial $x^{2n} + 1$ as a product of $n$ quadratic polynomials with real coefficients, given $n \\in \\mathbb{N}$. Provide your answer as a single integer.",
"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... | 68.5 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... | Assets = Liabilities + Equity, where Equity is increased by Revenues and decreased by Expenses |
[
{
"content": "Find the spectrum of the operator \\( T \\in \\mathcal{B}(\\ell^2) \\) given by \\( T(x_1, x_2, x_3, x_4,...) = (-x_2, x_1, -x_4, x_3,...) \\).",
"role": "user"
}
] | \{i, -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... | C = (2m{eq}_1R + m{eq}_1L)/(2(m{eq}_1 + m{eq}_2)) |
[
{
"content": "Determine whether the assertion about the geometrical interpretation of the line integral of a function $f$ along a curve $C$ with respect to $x$ is true or false.",
"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... | Date Particular Amount debited (USD) Amount credited (USD)
Mar 3 Account Receivable A/c ( USD 94 X 5) 470
To Sales A/c 470
Mar 3 Cost of goods sold A/c ( 5 x USD 40) 200
To Inventory A/c 200
Mar 10 Inventory A/c ( USD 48 X 16) 768
To Account Payable A/c 768
Mar 12 Account Receivable A/c ( USD 96 X 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... | 9.04 percent |
[
{
"content": "Evaluate the integral \\( \\int_{\\mathbb{R}} e^{-(x+iy)^2} \\, dx \\) for a fixed \\( y \\in \\mathbb{R} \\).",
"role": "user"
}
] | \sqrt{\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... | Changes in Equity - Changes in Common Stock - Dividends Declared = Net Income |
[
{
"content": "In a Lie algebra generated by $n$ elements, determine if the number of linearly independent elements is always less than or equal to $n+1$. 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... | (1.42 x 10^-3 m, -8.2 x 10^-4 m) |
[
{
"content": "Find the smallest positive integer \\( n \\) such that for any integer \\( p \\geq n \\), a square can be partitioned into \\( p \\) non-congruent smaller squares.",
"role": "user"
}
] | 21 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $4 |
[
{
"content": "Given two matrices $x$ and $y$ of the same rank, does there exist a pair of matrices $(g_1, g_2) \\in GL(m,k) \\times GL(n,k)$ such that $g_1 x g_2^{-1} = y$?",
"role": "user"
}
] | Yes |
[
{
"content": "Given a sequence of real numbers $(s_n)_{n\\geq 0}$ and the corresponding Hankel matrix $H_n=(s_{i+j})_{0\\leq i,j\\leq n}$, if $\\det H_n>0$ for all $n\\geq 0$, does it imply that $H_n$ is positive semi-definite as well? Justify 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... | Kr < CO2 < Ne < He |
[
{
"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... | 15.64% |
[
{
"content": "What is the area, in square units, of triangle $ABC$? [asy]\nunitsize(0.15inch);\npath X = (-6.5, 0)--(5.5, 0);\npath Y = (0, -3.5)--(0, 7.5);\ndraw(X); draw(Y);\n\nfor(int n=-6; n <= 5; ++n)\nif( n != 0 )\ndraw( (n,0.25)--(n,-0.25) );\nfor(int n=-3; n <= 7; ++n)\nif( n != 0 )\ndraw( (0.25,n)--(-0... | 19 |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\to 0} \\frac{\\left(\\int_{0}^{x} e^{t^2}dt\\right)^2}{\\int_{0}^{x} e^{2t^2}dt}$$",
"role": "user"
}
] | 0 |
[
{
"content": "Let $X$ be a locally compact Hausdorff space. Does the diagonal $\\Delta X \\subset X \\times X$ have a closed neighborhood $N$ such that the canonical projection maps $N \\to X$ are proper?",
"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 moles |
[
{
"content": "Determine the values of \\(\\alpha\\) for which there exists a non-constant function \\(f: \\mathbb{R} \\rightarrow \\mathbb{R}\\) satisfying the equation:\n\n\\[ f(\\alpha(x+y)) = f(x) + f(y) \\]",
"role": "user"
}
] | 1 |
[
{
"content": "Calculate the surface area of the portion of the cone \\( 3z^2 = x^2 + y^2 \\) that is below the plane \\( z = \\sqrt{3} \\) and above the xy-plane. Express your answer in terms of \\( \\pi \\).",
"role": "user"
}
] | 6\sqrt{3}\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... | Cellular respiration and Active transport |
[
{
"content": "Given a Hermitian positive semidefinite matrix $\\textbf{X}$ of rank $N$, determine if it is possible to decompose it into a matrix $\\textbf{F}$ with rank $M \\leq N$ such that $\\textbf{X} = \\textbf{F} \\textbf{F}^H$. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the equation of the plane tangent to the surface $z = \\sqrt{2x^2+y^4+1}$ that is parallel to the plane $x-y-z=0$.",
"role": "user"
}
] | x - y - z = 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... | 71.25 m/s |
[
{
"content": "Let \\(\\alpha\\) be a non-real fifth root of unity and \\(\\beta\\) be a non-real fourth root of unity. Evaluate the expression \\((1+\\alpha)(1+\\beta)(1+\\alpha^2)(1+\\beta^2)(1+\\alpha^3)(1+\\beta^3)(1+\\alpha^4)\\).",
"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... | 43 Ohms |
[
{
"content": "Determine the number of ways to color a grid using T-tetrominos, given that the grid is symmetrical and the orientation of the tetrominos matters. Ensure that there are no red-green colorings in the grid.",
"role": "user"
}
] | 2 |
[
{
"content": "Given a polynomial $f(x)$ that is irreducible over $\\mathbb{Q}$ by Eisenstein's criterion and has only two real roots, determine if it can be solved by radicals, given that its Galois group is isomorphic to a subgroup of $S_4$. Provide your answer as \"Yes\" or \"No\".",
"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... | $17,849.65 |
[
{
"content": "Evaluate the integral: $$\\int_{-\\infty}^{\\infty} \\frac{1}{\\sqrt{2\\pi}} xe^{\\displaystyle\\frac{-x^{2}}{2}}dx$$",
"role": "user"
}
] | 0 |
[
{
"content": "Consider the Collatz Conjecture, where for a given non-zero natural number, if it is even, you divide it by 2, and if it is odd, you multiply it by 3 and add 1. This process is repeated, and the number of transformations needed for a number to first reach 1 is called its path length. Calculate the... | 1572 |
[
{
"content": "Find the limiting value of the ratio \\( \\lim_{r\\to\\infty}\\frac{f(r)}{r^2} \\), where \\( f(r) \\) is the number of integer lattice points contained within a circle of radius \\( r \\) centered at the origin.",
"role": "user"
}
] | \pi |
[
{
"content": "Determine the number of real solutions for the equation \\( \\sin^5 x - \\cos^5 x = \\frac{1}{\\cos x} - \\frac{1}{\\sin x} \\) given that \\( \\cos x \\neq \\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... | 6.42 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... | 0.265 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... | $52.09 |
[
{
"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... | $55,338.75 |
[
{
"content": "Given real numbers $a, b, c, d, e$ such that $a+b+c+d+e=8$ and $a^2+b^2+c^2+d^2+e^2=16$, determine the minimum value of the expression $\\sum_{cyc} (t-a)^2$ for $t \\in \\mathbb{R}$ and find the values of $a, b, c, d, e$ for which this minimum occurs.",
"role": "user"
}
] | \dfrac{16}{5} |
[
{
"content": "Spot's doghouse has a regular hexagonal base that measures one yard on each side. He is tethered to a vertex with a two-yard rope. What is the area, in square yards, of the region outside the doghouse that Spot can reach? Express your answer in terms of $\\pi$.",
"role": "user"
}
] | 3\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... | 6.77e-4 W/m^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... | 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... | 1.11 mm |
[
{
"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... | s = uT + 1/2 * a * T^2 |
[
{
"content": "Let $E$ be a smooth vector bundle over a manifold $M$ with dimension greater than 1, equipped with a metric. Consider a metric connection $\\nabla$ on $E$. Suppose there exists a non-zero section $\\sigma \\in \\Gamma(E)$ such that $\\sigma$ lies in $\\ker R(X,Y)$ for all $X,Y \\in \\Gamma(TM)$. D... | 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... | 202.3 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... | Polonium (Po) |
[
{
"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... | 50% type O and 50% heterozygous type 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... | 1.06 kJ |
[
{
"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... | $1,436,000 |
[
{
"content": "Determine whether the following statement is true or false: If the derivative of a function approaches zero as \\( x \\) approaches infinity, then the ratio of the function to \\( x \\) also approaches zero as \\( x \\) approaches infinity.",
"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... | $56.40 |
[
{
"content": "Given integers $a_1, a_2, \\ldots, a_n \\geq 0$, let $E$ be the number of ways to choose $(x_1, x_2, \\ldots, x_n)$ such that $0 \\leq x_i \\leq 2a_i$ and $\\sum_{i=1}^n x_i$ is even, and let $O$ be the number of ways such that $\\sum_{i=1}^n x_i$ is odd. Prove that $E - O = 1$. ",
"role": "us... | 1 |
[
{
"content": "Consider a complete graph $K_n$ on $n$ vertices, where $n$ is even and greater than 2. Let $G$ be a spanning subgraph of $K_n$, and $G'$ be its complement in $K_n$. The edges of $G$ and $G'$ form two color classes in an edge 2-coloring of $K_n$. Prove that the number of paths of length 2 with exac... | even |
[
{
"content": "Find the value of the infinite series \\( \\sum\\limits_{n=0}^{\\infty}\\frac{n^2}{n!} \\).",
"role": "user"
}
] | 2e |
[
{
"content": "Find the limit of \\((\\sin x)^{\\frac{1}{\\ln x}}\\) as \\(x\\) approaches 0 from the right.",
"role": "user"
}
] | e |
[
{
"content": "Find the volume of the region in \\(\\mathbb{R}^n\\) defined by the constraints \\(x_i \\geq 0\\) for all \\(i\\) and \\(\\sum_{i=1}^n x_i \\leq a\\), where \\(a\\) is a positive constant.",
"role": "user"
}
] | \dfrac{a^n}{n!} |
[
{
"content": "Find an entire function whose real part is given by \\( x^4 - 6x^2y^2 + y^4 \\).",
"role": "user"
}
] | z^4 |
[
{
"content": "There exist constants $a_1,$ $a_2,$ $a_3,$ $a_4,$ $a_5$ such that\n\\[\\cos^5 \\theta = a_1 \\cos \\theta + a_2 \\cos 2 \\theta + a_3 \\cos 3 \\theta + a_4 \\cos 4 \\theta + a_5 \\cos 5 \\theta\\]for all angles $\\theta.$ Find $a_1^2 + a_2^2 + a_3^2 + a_4^2 + a_5^2.$",
"role": "user"
}
] | \frac{63}{128} |
[
{
"content": "Express the empty set $∅$ using only the set $A$, the operation $*$, and parentheses if necessary.",
"role": "user"
}
] | A * 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... | Telex Inc.\nBalance Sheet\nDecember 31, 20Y7\nStockholders' Equity:\nPaid-in capital:\nPreferred 2% stock, $80 par, (125,000 shares authorized and issued) $10,000,000\nExcess of issue price over par $500,000\nPaid-in capital, preferred stock $10,500,000\nCommon stock, $20 par (1,000,000 shares authorized, 825,000 share... |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to\\infty}\\left(\\frac{3x^2-x+1}{2x^2+x+1}\\right)^\\left(\\frac{x^3}{1-x}\\right)$$",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | {
"Sales Volume Variance": {
"Units": 14300,
"Sales Revenue": 100100,
"Variable Expenses": 31460,
"Contribution Margin": 68640
},
"Flexible Budget Variance": {
"Units": 14300,
"Sales Revenue": 50050,
"Variable Expenses": 1430,
"Contribution Margin": 48620,
"Fixed Expenses": 2000,... |
[
{
"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... | $23,599.80 |
[
{
"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... | h-(1/8g) |
[
{
"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... | 6.57 bounces |
[
{
"content": "Determine whether two non-commuting diagonalizable linear operators can have a common eigenvector in a finite-dimensional Hilbert space.",
"role": "user"
}
] | Yes |
[
{
"content": "If $\\alpha \\neq 1$ and $\\alpha^6 = 1$, find the value of $|x|$, where $x$ is defined as:\n$$x = \\sum_{r=1}^6 {^6}C_r\\alpha^{r-1}$$\nGiven that $\\alpha$ is a non-principal $6$th root of unity, determine $|x|$.",
"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... | 2080 m^3 |
[
{
"content": "In a regular 4000-gon, let $X$ be the foot of the altitude from $A_{1986}$ onto diagonal $A_{1000}A_{3000}$, and let $Y$ be the foot of the altitude from $A_{2014}$ onto $A_{2000}A_{4000}$. Given that $XY = 1$, find the area of square $A_{500}A_{1500}A_{2500}A_{3500}$. \n\n*Proposed by Evan Chen*"... | 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... | P = $12, Q = 18,000 |
[
{
"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... | Machining: $189,111.11
Assembly: $215,555.56
Finishing: $105,333.33 |
[
{
"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... | $9,000,000 |
[
{
"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... | 0.222 s |
[
{
"content": "Determine the smallest integer $n$ such that the Simpson's Rule approximation for the integral \\( \\int_0^1 9e^{x^2} \\, dx \\) is accurate to within 0.0001.",
"role": "user"
}
] | 18 |
[
{
"content": "Determine the radius of convergence of the power series \\( \\sum_{n=0}^{\\infty} a_n z^n \\), where the sequence \\( (a_n) \\) is defined recursively by \\( a_{n+3} = a_{n+2} + a_{n+1} - a_n \\) for \\( n \\in \\mathbb{N}_0 \\), with initial terms \\( a_0, a_1, a_2 \\in \\mathbb{C} \\).",
"ro... | 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... | 18.4 kJ |
[
{
"content": "Calculate the value of \\( R = \\frac{1}{\\lim\\limits_{n \\to \\infty} \\sup \\frac{1}{\\sqrt[n]{n!}}} \\). Explain why \\( \\sqrt[n]{n!} \\to +\\infty \\) as \\( n \\to \\infty \\).",
"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... | 26.57 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\rightarrow+\\infty}(\\sqrt[5]{x^5-x^4}-x) \\]",
"role": "user"
}
] | -\dfrac{1}{5} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.