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... | 1786 mL |
[
{
"content": "Determine whether the function \\( f(z) = \\frac{\\log(z)}{z} \\), where \\( \\log(z) \\) is the principal branch of the logarithm defined on \\((-\\pi, \\pi]\\), is analytic on the domain \\( \\Sigma = \\mathbb{C} - ((-\\infty, 0]) \\).",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n \\to \\infty} \\frac{1}{n} \\cdot \\left((m+1)(m+2) \\ldots (m+n)\\right)^{\\frac{1}{n}} \\] where \\( m \\) is a fixed positive integer.",
"role": "user"
}
] | \dfrac{1}{e} |
[
{
"content": "Determine the number of non-isomorphic tournaments (directed cliques) with 5 vertices.",
"role": "user"
}
] | 12 |
[
{
"content": "Calculate the value of the expression \\( \\frac{t^{4012}+37}{2} \\), where \\( t \\) is given by:\n\\[ t = \\sqrt[4012]{55+12\\sqrt{21}} \\times \\sqrt[2006]{3\\sqrt{3} - 2\\sqrt{7}}. \\]",
"role": "user"
}
] | 19 |
[
{
"content": "Find the value of \\(\\alpha^5 + \\beta^5 + \\gamma^5\\), where \\(\\alpha\\), \\(\\beta\\), and \\(\\gamma\\) are the roots of the polynomial equation \\(x^3 - x^2 + 1 = 0\\).",
"role": "user"
}
] | -4 |
[
{
"content": "If $ a$, $ b$, $ c$, $ d$, and $ e$ are constants such that every $ x > 0$ satisfies\n\\[ \\frac{5x^4 - 8x^3 + 2x^2 + 4x + 7}{(x + 2)^4} \n = a + \\frac{b}{x + 2} + \\frac{c}{(x + 2)^2} \n + \\frac{d}{(x + 2)^3} + \\frac{e}{(x + 2)^4} \\, ,\\]then what is the value of $ a + b + c + d + e... | 18 |
[
{
"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... | 5.56e-5 T at 36.7 degrees with the right toward the out of the page |
[
{
"content": "Evaluate the definite integral: \\[ \\int_0^{4\\pi} \\frac{dx}{5+4\\cos x} \\]",
"role": "user"
}
] | \dfrac{4\pi}{3} |
[
{
"content": "Determine all positive integers \\( n \\) such that \\( n = p_1^2 + p_2^2 + p_3^2 + p_4^2 \\), where \\( p_1, p_2, p_3, \\) and \\( p_4 \\) are the four smallest distinct positive divisors of \\( n \\).",
"role": "user"
}
] | 130 |
[
{
"content": "Given a set of unique numbers \\(\\{1, 2, 3, \\ldots, n\\}\\), determine the number of binary search trees (BSTs) that can be formed with a height not exceeding a given height \\(h\\). For instance, if \\(n = 4\\) and \\(h = 2\\), calculate the number of BSTs with height at most 2.",
"role": "... | 6 |
[
{
"content": "Determine whether the recursive sequence defined by \\( b_{n+1} = 2b_n - c(b_n)^2 \\) is convergent, where \\( c > 0 \\) is a constant and \\( b_0 \\in \\left(0, \\frac{1}{c}\\right) \\). If the sequence is convergent, find its limit.",
"role": "user"
}
] | \dfrac{1}{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... | 23.76% |
[
{
"content": "Bob rolls a fair six-sided die each morning. If Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal. If he rolls a 1, then he rolls again. In a non-leap year, what is the expected value of the difference between the number of days Bob eats... | 73 |
[
{
"content": "Find all possible solutions of the form \\(x = \\frac{m}{n}\\) (with \\(m, n\\) coprime) for the equation: \\[ x + \\lfloor x \\rfloor = 2013x\\cdot\\lfloor x \\rfloor + 2013^{-1} \\] where \\(\\lfloor x \\rfloor\\) is the integer part of \\(x\\).",
"role": "user"
}
] | \dfrac{1}{2013} |
[
{
"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... | 37.24 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... | April: 88,300
May: 95,700
June: 123,650
Quarter Total: 307,650 |
[
{
"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... | 13.328 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... | 2.1e-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... | 5.78 m/s |
[
{
"content": "Find the sum\n\\[0.1 + 0.02 + 0.003 + 0.0004 + \\dots + \\frac{n}{10^n} + \\dotsb.\\]",
"role": "user"
}
] | \frac{10}{81} |
[
{
"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... | 0.83s |
[
{
"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 m/s |
[
{
"content": "Evaluate the limit \\( \\lim_{x\\rightarrow \\infty}\\frac{f^{-1}(1000 x)-f^{-1}(x)}{x^{\\frac{1}{3}}} \\), where \\( f(x) = 27x^3 + (\\cos 3 + \\sin 3)x \\) and \\( f^{-1}(x) \\) is the inverse of \\( f(x) \\).",
"role": "user"
}
] | 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... | 0.0548 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... | 10.572% |
[
{
"content": "Given the real part \\( u(x, y) = x^2 - y^2 + 2x \\) of a differentiable function \\( f(z) \\), find the function \\( f(z) \\).",
"role": "user"
}
] | z^2 + 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... | $84,000 |
[
{
"content": "Determine the maximum possible order of an element in the multiplicative group \\( \\mathbb{Z}_{2^k}^* \\) for \\( k \\ge 3 \\).",
"role": "user"
}
] | 2^{k-2} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | NaCH3COO(aq) + HCl(aq) -> CH3COOH(aq) + NaCl(aq) |
[
{
"content": "In the coordinate plane, set \\( A \\) is defined by the equation \\( x^2 + y^2 = 2x + 2y + 23 \\). Set \\( B \\) is defined by the equation \\( |x - 1| + |y - 1| = 5 \\). Set \\( C \\) is the intersection of sets \\( A \\) and \\( B \\). Determine the maximum value of the product of the lengths o... | 1250 |
[
{
"content": "Is second countability a topological invariant?",
"role": "user"
}
] | Yes |
[
{
"content": "$A$, $B$, $C$, and $D$ are points on a circle, and segments $\\overline{AC}$ and $\\overline{BD}$ intersect at $P$, such that $AP=8$, $PC=1$, and $BD=6$. Find $BP$, given that $BP < DP.$\n\n[asy]\n\nunitsize(0.6 inch);\n\ndraw(circle((0,0),1));\ndraw((-0.3,0.94)--(0.3,-0.94));\ndraw((-0.7,-0.7)--(... | 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. Child care division of labor
2. Contribution to the food supply |
[
{
"content": "Given that event $A$ is independent of the events $B$, $B \\cap C$, and $B \\cup C$, determine the probability $P(A \\cap C)$. Provide your answer in terms of $P(A)$, $P(B)$, and $P(C)$. \\( \\boxed{} \\)",
"role": "user"
}
] | P(A)P(C) |
[
{
"content": "Solve the differential equation \\( y'' + (y')^2 \\cdot e^x = 0 \\) with the initial conditions \\( y(0) = 1 \\) and \\( y'(0) = 1 \\). Find \\( y(x) \\).",
"role": "user"
}
] | 2 - e^{-x} |
[
{
"content": "Provide an example of a non-compact operator in the Hilbert space $l^2$. Explain why the operator you chose is not compact.",
"role": "user"
}
] | 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... | 0.234 |
[
{
"content": "Determine whether every linear code has an encoding function that is a linear transformation. Answer with 'yes' or 'no'.",
"role": "user"
}
] | yes |
[
{
"content": "Determine whether there exists a fraction \\( \\frac{r}{s} \\), with integers \\( r \\) and \\( s \\), such that \\( \\frac{p}{q} < \\frac{r}{s} < \\frac{p+1}{q} \\) and \\( s < q \\) for all \\( 0 < p < q-1 \\) where \\( p, q \\in \\mathbb{Z} \\).",
"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... | 119 g |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n \\to \\infty} \\frac{{n^2 \\choose n}}{{n^2+n-1 \\choose n}}. \\]",
"role": "user"
}
] | \dfrac{1}{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... | $5,656.5 |
[
{
"content": "Determine whether the integral \\( \\int_{0}^\\infty x^{4n-1}\\sin(x)e^{-x}dx \\) equals zero for all positive integers \\(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... | 2.257e-34 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... | $875.38 |
[
{
"content": "Determine whether the sequence \\((1+\\frac{2i}{n})^n\\) converges as \\(n\\) approaches infinity.",
"role": "user"
}
] | e^{2i} |
[
{
"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... | 32663.06 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Period cost |
[
{
"content": "Let $f$ be a nonnegative function defined on the power set of positive integers with the following properties:\n1. $f(X) \\leq f(Y)$ if $X \\subseteq Y$ and $f(\\mathbf{N}) = 1$.\n2. $f(X \\cup Y) \\leq f(X) + f(Y)$ for all $X$ and $Y$.\n3. For each $X$ and each $y \\in [0, f(X)]$, there exists $Y... | yes |
[
{
"content": "Given positive numbers $a, b, c$, find the minimum value of the expression:\n\\[ \\max\\left(\\dfrac{1}{ac}+b,\\dfrac{1}{a}+bc,\\dfrac{a}{b}+c\\right) \\]",
"role": "user"
}
] | 2 |
[
{
"content": "Evaluate the limit \\( \\lim_{w\\to 0} \\frac{\\cos (2m+1)w}{\\cos w/2} \\) as \\( m \\) approaches infinity.",
"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... | 0.53 |
[
{
"content": "Given a positive integer $n$ where $n \\geq 2$, determine the minimum number $m$ such that from the set of numbers $1, 2, \\ldots, 3n$, there exist four distinct numbers $a, b, c, d$ among the selected $m$ numbers satisfying $a = b + c + d$. Find the minimum value of $m$. \\(\\boxed{\\text{your an... | 2n + 2 |
[
{
"content": "Consider an unending sequence of independent trials, where each trial is equally likely to result in any of the outcomes 1, 2, or 3. Given that the outcome of the first trial is 1, and outcome 3 is the last of the three outcomes to occur, find the conditional probability that the outcome of the se... | \dfrac{1}{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... | 2.9 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... | 14 g |
[
{
"content": "Evaluate the contour integral \\( \\oint_C \\frac{dz}{z-2} \\) around the circle \\( |z-2| = 4 \\).",
"role": "user"
}
] | 2\pi i |
[
{
"content": "Given \\((2x^2+3x+4)^{10}=\\sum_{r=0}^{20}a_rx^r\\), find the value of \\(\\frac{a_7}{a_{13}}\\).",
"role": "user"
}
] | 8 |
[
{
"content": "Find the number of ordered triples $(x,y,z)$ of real numbers such that\n\\[x^4 + y^4 + z^4 - 4xyz = -1.\\]",
"role": "user"
}
] | 4 |
[
{
"content": "Identify the imaginary part of the analytic function $f(z)$ given that $\\Re(f'(z)) = 2\\Im(z)$ and $f(1+i) = 2$. Choose the correct option from the following:\n\n(1) $-2xy$\n(2) $x^2-y^2$\n(3) $2xy$\n(4) $y^2-x^2$",
"role": "user"
}
] | D |
[
{
"content": "Express the integral \\( f(x) = \\int_0^{2\\pi} e^{x \\sin \\theta} \\, \\text{d}\\theta \\) in terms of common functions.",
"role": "user"
}
] | 2\pi I_0(x) |
[
{
"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... | Functionalism |
[
{
"content": "Evaluate the contour integral \\( \\oint_{|z|=1} \\frac{1}{2z - \\sinh(z)} \\, dz \\) using the residue theorem.",
"role": "user"
}
] | 2\pi i |
[
{
"content": "Find the sum of the values of $x$ such that $\\cos^{3}3x+\\cos^{3}5x= 8\\cos^{3}4x\\cos^{3}x$, where $x$ is measured in degrees and $100 ^\\circ < x < 200^\\circ$.",
"role": "user"
}
] | 906 |
[
{
"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... | 46.26 amu |
[
{
"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... | 58,781.25 units |
[
{
"content": "Find the sum a + b + c for the ordered triplet (a, b, c) of real numbers that maximizes the expression \\((1 - x)(2 - y)(3 - z)(x + \\frac{y}{2} + \\frac{z}{3})\\) under the conditions \\(x < 1\\), \\(y < 2\\), \\(z < 3\\), and \\(x + \\frac{y}{2} + \\frac{z}{3} > 0\\).",
"role": "user"
}
] | \dfrac{3}{2} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.111 g |
[
{
"content": "Find the largest possible integer \\( n \\) such that in a grid of size \\( 100 \\times n \\), where each row contains a permutation of the numbers \\( 1, 2, \\ldots, 100 \\), no two rows can have the same permutation after any number of operations. An operation consists of choosing a row and swap... | 2^{99} |
[
{
"content": "Solve the following system of equations for \\(x\\) and \\(y\\):\n\\[\n\\begin{align*}\n & 2x^2 - 5xy - 5y^2 + x + 10y - 35 = 0, \\\\\n & x^3 + 5xy^2 + 42 = 0.\n\\end{align*}\n\\]",
"role": "user"
}
] | (-3, 1) |
[
{
"content": "Let \\( K/\\mathbb{Q} \\) be a cubic number field that is Galois with class number 1. Thus, \\( \\text{Gal}(K/\\mathbb{Q}) \\) is a cyclic cubic group, and \\( \\mathcal{O}_K \\) is a principal ideal domain (PID). Let \\( p \\) be a rational prime that does not divide the discriminant of \\( K \\)... | 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... | 120000 rpm |
[
{
"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... | 1.22e-10 m/s^2 |
[
{
"content": "Find the value of \\( \\lim_{x\\rightarrow {0}^{+}}\\sum_{n=1}^{\\infty}{(-1)}^{n-1}\\frac{1}{n!{x}^{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... | Stockholders' Equity:
8% Preferred Stock, $100 par, 10,000 shares authorized, 4,000 shares issued: $400,000
Common Stock, $3 par, 600,000 shares authorized, 300,000 shares issued, 285,000 outstanding: $900,000
Paid in capital in excess of par-preferred: $25,000
Paid in capital in excess of par-common: $380,000
Paid in ... |
[
{
"content": "Compute the limit: \\[ \\lim\\limits_{n\\rightarrow\\infty} \\int_{\\mathbb{R}^n_+}g \\left( \\frac{x_1+ \\cdots +x_n}{n} \\right)f(x_1,\\ldots,x_n) \\, dx_1\\cdots dx_n \\] where $\\xi_1,\\xi_2,\\ldots,\\xi_n$ are independent Exp($1$) random variables with joint density $f(x_1,\\ldots,x_n) = e^{-... | g(1) |
[
{
"content": "Find $q(x)$ if the graph of $\\frac{x^3-2x^2-5x+3}{q(x)}$ has vertical asymptotes at $2$ and $-2$, no horizontal asymptote, and $q(3) = 15$.",
"role": "user"
}
] | 3x^2 - 12 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | The concentration of B at equilibrium is sqrt(2K) |
[
{
"content": "Determine whether a group with an uncountable number of elements can have a countable number of distinct subgroups. Answer with 'Yes' or 'No'.",
"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... | 1053.6 |
[
{
"content": "Evaluate the integral \\( \\int^{4}_{0}\\int_{0}^{\\sqrt{4x-x^2}}\\sqrt{x^2+y^2}\\, \\text{dy dx} \\).",
"role": "user"
}
] | \dfrac{128}{9} |
[
{
"content": "One of Euler's conjectures was disproved in the 1960s by three American mathematicians when they showed there was a positive integer such that $133^5+110^5+84^5+27^5=n^{5}$. Find the value of $n$.",
"role": "user"
}
] | 144 |
[
{
"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... | \( -pE\hat{y} \) |
[
{
"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... | generativity |
[
{
"content": "Find the value of \\(x\\) that satisfies the equation: \\((x^2+100)^2=(x^3-100)^3\\).",
"role": "user"
}
] | 5 |
[
{
"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... | 16.25 m/s |
[
{
"content": "In a right triangle $\\triangle ABC$ with a right angle at $A$, the angle bisectors $BD$ and $CE$ of angles $\\angle ABC$ and $\\angle ACB$ intersect the opposite sides at points $D$ and $E$, respectively. Given that $AE=8$ and $AD=9$, determine the perimeter of $\\triangle ABC$. \\(\\boxed{\\text... | 72 |
[
{
"content": "Find a primitive root modulo $11^2$. Provide your answer as a single integer.",
"role": "user"
}
] | 2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $6,000, $11,000, $3,700, and $13,300 |
[
{
"content": "Given two similar matrices A and B, where A is symmetric and non-negative, determine if there exists a matrix P that is not orthogonal and a matrix B that is not symmetric such that A = PBP^{-1}.",
"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... | 29.61 degrees Celsius |
[
{
"content": "On a plane, two vectors \\(\\overrightarrow{OA}\\) and \\(\\overrightarrow{OB}\\) satisfy \\(|\\overrightarrow{OA}| = a\\) and \\(|\\overrightarrow{OB}| = b\\), with \\(a^2 + b^2 = 4\\) and \\(\\overrightarrow{OA} \\cdot \\overrightarrow{OB} = 0\\). Given the vector \\(\\overrightarrow{OC} = \\lam... | 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... | Privacy |
[
{
"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... | 10.99% |
[
{
"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... | [NO] = 0.060 M, [Cl2] = 0.030 M, [NOCl] = 2.94 M |
[
{
"content": "In Terence Tao's Analysis I, a number \\(x\\) is defined as eventually \\(\\epsilon\\)-close to a sequence \\((a_n)\\) if there exists an \\(N\\) such that for all \\(n \\geq N\\), \\(d(x, a_n) < \\epsilon\\). A number \\(x\\) is continually \\(\\epsilon\\)-adherent to \\((a_n)\\) if it is \\(\\ep... | 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... | 540,540.54 |
[
{
"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... | 150 rev/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... | 1.18 * 10^-3 g/L |
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