prompt list | ground_truth string |
|---|---|
[
{
"content": "Calculate \\(\\lim_{n \\to \\infty}{\\frac{1^1+2^2+3^3+\\cdots+n^n}{n^n}}.\\) Provide a rigorous proof of this limit.",
"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... | 3.05 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... | 6.43mol |
[
{
"content": "In triangle $ABC,$ $\\sin A = \\frac{3}{5}$ and $\\cos B = \\frac{5}{13}.$ Find $\\cos C.$",
"role": "user"
}
] | \frac{16}{65} |
[
{
"content": "Determine whether the series \\( 1 - \\frac{1}{2^\\alpha} + \\frac{1}{3} - \\frac{1}{4^\\alpha} + \\frac{1}{5} + \\cdots \\) converges or diverges based on the value of \\( \\alpha \\).",
"role": "user"
}
] | \alpha = 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... | 1256.53 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... | 0.72 s |
[
{
"content": "Calculate \\( E(W^2(3) - W(3)W(1)) \\) using the Ito calculus method.",
"role": "user"
}
] | 2 |
[
{
"content": "Suppose the quadratic polynomial \\(p(x) = ax^2 + bx + c\\) has positive coefficients \\(a, b, c\\) in arithmetic progression in that order. If \\(p(x) = 0\\) has integer roots \\(\\alpha\\) and \\(\\beta\\), find the value of \\(\\alpha + \\beta + \\alpha \\beta\\).",
"role": "user"
}
] | 7 |
[
{
"content": "Is the Lebesgue measure of the boundary of a bounded Lipschitz domain in \\(\\mathbb{R}^n\\) zero?",
"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... | Meadows: $5,000, Leef: $15,000 |
[
{
"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... | Dehydrogenation of alkanes and dehydration of alcohols, and other elimination reactions as well as thermal cracking. |
[
{
"content": "Let \\( p_{1}, p_{2}, \\ldots, p_{97} \\) be prime numbers (not necessarily distinct). Determine the greatest integer value of the expression:\n\n\\[ \\sum_{i=1}^{97} \\frac{p_{i}}{p_{i}^{2}+1} = \\frac{p_{1}}{p_{1}^{2}+1} + \\frac{p_{2}}{p_{2}^{2}+1} + \\ldots + \\frac{p_{97}}{p_{97}^{2}+1} \\]",... | 38 |
[
{
"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... | 0.0605 or 6.05% |
[
{
"content": "Evaluate the line integral \\( \\oint\\limits_{C} xy^2dx +x^2ydy+z^3dz \\), where \\( C \\) is the curve of intersection of the plane \\( x+y+z=1 \\) and the cylinder \\( x^2 +y^2=4 \\), oriented counterclockwise when viewed from above.",
"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... | Intelligence |
[
{
"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... | 37.63 |
[
{
"content": "Suppose $R$ is a gcd domain and satisfies the condition that for all $a, b \\in R$, if $\\gcd(a, b) = 1$, then $\\langle a \\rangle + \\langle b \\rangle = R$. Does this condition imply that $R$ is a Bézout domain?",
"role": "user"
}
] | Yes |
[
{
"content": "Find the value of $a$ such that the graphs of $y = a^x$ and $y = x$ intersect at a point where their second derivatives are also equal.",
"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... | $17,088.28 |
[
{
"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... | 1.4e-9 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... | 18334.71 |
[
{
"content": "Determine whether the following statement is true or false: For any positive integer $k$, the integral of $|\\chi_{[k,\\infty)}(x) - 1|$ over the real line is finite.",
"role": "user"
}
] | B |
[
{
"content": "Determine the radius of convergence of the power series \\( \\sum_{n=1}^\\infty 2^{n^2} \\, x^{n!} \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Determine which of the following conditions is necessary and sufficient for the set $F$, defined as above, to be a field:\n\n(a) $R$ is a commutative ring but not an integral domain\n(b) $R$ is an integral domain but not a commutative ring\n(c) $R$ is a commutative integral domain\n(d) None of the... | 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... | $1,615,112.07 |
[
{
"content": "Evaluate the sum \\( \\sum_{n=-\\infty}^{\\infty} \\text{sinc}(\\pi(2t-n)) \\).",
"role": "user"
}
] | 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.0278 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... | 3612.5 |
[
{
"content": "Does a convex polynomial on \\(\\mathbb{R}^n\\) that is bounded from below always attain its minimum value at some point?",
"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... | 3.35 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... | 37.3 m/s |
[
{
"content": "Determine the radius of convergence of the series \\(\\sum_{n=1}^\\infty b_nz^n\\), where \\(b_n\\) is the number of pairs of integers \\((x,y)\\) such that \\(x^2+y^2<{n^2+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... | 350 s |
[
{
"content": "Given that \\( \\int_0^1 f(x) \\, dx = 0 \\) and \\(-1 \\leq f(x) \\leq 1\\), find the maximum value of \\( \\int_0^1 [f(x)]^3 \\, dx \\).",
"role": "user"
}
] | \dfrac{1}{4} |
[
{
"content": "Determine whether the following statement is true or false: If \\( R[x] \\) is a unique factorization domain (UFD), then \\( R \\) is a UFD.",
"role": "user"
}
] | 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... | $930 |
[
{
"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... | 0.25 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... | \theta-\alpha \approx \frac{v_{S',S}}{c}\sin{\theta} |
[
{
"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... | 4x=y^2+K |
[
{
"content": "From a point \\(P=(3,4)\\), perpendiculars \\(PQ\\) and \\(PR\\) are drawn to the line \\(3x+4y-7=0\\) and a variable line \\(y-1=m(x-7)\\) respectively. Find the maximum area of \\(\\triangle PQR\\).",
"role": "user"
}
] | 9 |
[
{
"content": "Evaluate the sum \\( \\sum_{k=80}^{167} \\frac{1}{\\sin k^\\circ \\sin (k+1)^\\circ} \\).",
"role": "user"
}
] | 280 |
[
{
"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... | 0.80 L |
[
{
"content": "Given the equation \\(140x^{0.75}y^{0.25} = 213,415\\), find the rate of change of \\(x\\) with respect to \\(y\\) when \\(x = 3000\\) and \\(y = 200\\).",
"role": "user"
}
] | -5 |
[
{
"content": "Determine the number of different symmetric matrices $A \\in \\mathbb{R}^{3\\times 3}$ that satisfy the following conditions:\n- Both $[1,2,2]^T$ and $[2,1,-2]^T$ are eigenvectors of $A$.\n- $A$ has three distinct eigenvalues.\n- There exists an integer $n > 1$ such that $A^n = A$. \n\nHow many su... | 6 |
[
{
"content": "Determine the smallest positive integer \\( k \\) such that \\( k^{2018} + 2018 \\) is a prime number.",
"role": "user"
}
] | 3 |
[
{
"content": "If the subsequences $x_{2n}$ and $x_{3n}$ of a sequence $x_n$ both converge to the same limit, does the sequence $x_n$ necessarily converge? Justify your answer.",
"role": "user"
}
] | No |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Horizontal Analysis
Westwind Corporation
Comparative Income Statement
For the Years Ended December 31, 2016 and 2015
Increase or (Decrease)
Amount Percentage
2016 ... |
[
{
"content": "Calculate the limit: \\[ \\lim_{x \\to 0^+} (\\sin x)^x \\] without using L'Hôpital's rule. Use the fact that \\( a^b = e^{b \\ln a} \\) and the approximation \\( \\sin(x) \\sim x \\) as \\( x \\to 0 \\) to find the limit.",
"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... | 3.30e-32 M |
[
{
"content": "Let $f:[a,b]\\to \\mathbb{R}$ be a function that is continuous on $[a,b]$ and differentiable on $(a,b)$. Suppose there exists $c\\in (a,b)$ such that $f'(c)=0$, $f'(x)<0$ for all $x\\in (a,c)$, and $f'(x)>0$ for all $x\\in (c,b)$. Determine whether it is true that $f$ is strictly decreasing on $[a... | True |
[
{
"content": "Given the equations \\(a+b+c=-3\\) and \\(a^3+b^3+c^3-20(a+3)(b+3)(c+3)=2013\\), where \\(a, b, c\\) are integers and \\(a \\le b \\le c\\), find the value of \\(3a+b+2c\\).",
"role": "user"
}
] | -14 |
[
{
"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... | 1.2275 |
[
{
"content": "True or false? If the gradient and Hessian of a function $f$ and its second-order Taylor polynomial $p$ are equal at the point $(-2,1)$, does this imply that $(-2,1)$ is a saddle point of $f$?",
"role": "user"
}
] | B |
[
{
"content": "Evaluate the integral: $$\\int\\limits_{-\\infty}^{\\infty}x^4e^{-\\frac{1}{2}x^2}\\;\\mathrm{d}x$$",
"role": "user"
}
] | 3\sqrt{2\pi} |
[
{
"content": "How many positive integers less than or equal to 100 have a prime factor that is greater than 4?",
"role": "user"
}
] | 80 |
[
{
"content": "Find the residue of \\( \\frac{(z+1)^3}{(z-2)^2} \\) at \\( z=2 \\).",
"role": "user"
}
] | 27 |
[
{
"content": "The sequence 1, 2, 4, 5, 10, 11, 22, 23, 46, 47, $\\dots$ is formed as follows:\n\n$\\bullet$ Start with the number 1.\n\n$\\bullet$ Add one to get 2.\n\n$\\bullet$ Double that to get 4.\n\n$\\bullet$ Add one to get 5.\n\n$\\bullet$ Double that to get 10, and so on.\n\nWe repeat the steps of \"add... | 49 |
[
{
"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... | $17,500 |
[
{
"content": "Suppose $f$ and $g$ are continuous functions on $(0,\\infty)$ such that $\\lim_{x\\to\\infty}|f(x)-g(x)|=0$. If $f$ is uniformly continuous on $(0,\\infty)$, is $g$ also uniformly continuous on $(0,\\infty)$? Answer \"Yes\" or \"No\" and justify your answer.",
"role": "user"
}
] | No |
[
{
"content": "Evaluate the limit: $$\\lim_{n \\to \\infty} \\int_{0}^{1}\\frac{n\\cos(x)}{1+n^2x^{3/2}}\\, dx.$$",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether the following statement is true or false: If \\( \\lim\\limits_{n\\to\\infty}a(n)=0 \\) and \\( \\lim\\limits_{n\\to\\infty}a(n)b(n)=1 \\), then \\( \\lim\\limits_{n\\to\\infty}|b(n)|=\\infty \\).",
"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... | 11.744 |
[
{
"content": "Among the following five integers, determine which one is the largest:\n\n(A) \\(2009^{2010}\\);\n\n(B) \\(20092010^{2}\\);\n\n(C) \\(2010^{2009}\\);\n\n(D) \\(3^{\\left(3^{a^{3}}\\right)}\\);\n\n(E) \\(2^{10} + 4^{10} + \\cdots + 2010^{10}\\).",
"role": "user"
}
] | D |
[
{
"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... | $822,640 |
[
{
"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... | $287,500 |
[
{
"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... | $62,200 |
[
{
"content": "Given the function \\( f : \\mathbb{R} \\to \\mathbb{R} \\) with the properties:\n\n- \\( f(1) = 1 \\)\n- \\( f(x+y) = f(x) + f(y) \\) for all \\( x, y \\in \\mathbb{R} \\)\n- \\( f\\left(\\frac{1}{x}\\right) = \\frac{f(x)}{x^2} \\) for all \\( x \\in \\mathbb{R} \\setminus \\{0\\} \\)\n\nFind \\(... | 2021 |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\rightarrow\\infty} \\frac{\\sqrt{2^n+n^2}-\\sqrt{2^n+1}}{2^{n/2}}$$ without using derivatives or integrals.",
"role": "user"
}
] | 0 |
[
{
"content": "Let $A$ and $B$ be sets such that $|A| = 8$ and $|B| = 5$. Find the number of functions $f: A \\rightarrow B$ such that no element in $B$ has exactly 3 pre-images from $A$. In other words, for all $b \\in B$, $|\\{ a \\in A \\mid f(a) = b \\} | \\neq 3$. Determine the total number of such function... | 154305 |
[
{
"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 = \sqrt{\frac{GM}{r}} |
[
{
"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... | 1.7915 W |
[
{
"content": "Determine the degree of the field extension \\(\\mathbb{Q} \\left( \\zeta_{14} + \\zeta_{14}^9 + \\zeta_{14}^{11} \\right)\\) over \\(\\mathbb{Q}\\), where \\(\\zeta_{14}\\) is a 14th primitive root of unity.",
"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... | 68.79 grams |
[
{
"content": "For positive integers $N$ and $k$, define $N$ to be $k$-nice if there exists a positive integer $a$ such that $a^{k}$ has exactly $N$ positive divisors. Find the number of positive integers less than $1000$ that are neither $7$-nice nor $8$-nice.",
"role": "user"
}
] | 749 |
[
{
"content": "Let \\[f(x) =\n\\begin{cases}\nx^2+2 &\\text{if } x<n, \\\\\n2x+5 &\\text{if }x\\ge{n}.\n\\end{cases}\n\\]If the graph $y=f(x)$ is continuous, find the sum of all possible values of $n$.",
"role": "user"
}
] | 2 |
[
{
"content": "Alice is given the numbers $2$, $3$, $5$, $7$, and $9.$ She must choose a pair of these digits, with the digits being different, to form a two-digit number. How many of the numbers she can construct will be divisible by $3$?",
"role": "user"
}
] | 6 |
[
{
"content": "Determine whether the inclusion \\(\\mathfrak{i}^n \\subseteq \\mathfrak{i}\\) can be an equality for some positive integer \\(n\\) if \\(\\mathfrak{i}\\) is an ideal of a commutative ring with 1 that is not the whole ring.",
"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... | 28N |
[
{
"content": "Given a periodic function $f(x)$ with period $t$ such that $f(2x+3) + f(2x+7) = 2$ for all $x \\in \\mathbb{R}$, find the smallest possible value of $t$. \\(t\\) is the period of the function.",
"role": "user"
}
] | 8 |
[
{
"content": "A country has 1985 airports. From each airport, a plane takes off and lands at the farthest airport from its origin. Is it possible for all 1985 planes to land at only 50 specific airports, given that the ground is a plane, flights are in straight lines, and the distance between any two airports i... | Yes |
[
{
"content": "Evaluate the integral \\( \\int_{C}\\frac{|z|e^{z}}{z^{2}}dz \\), where \\( C \\) is the circumference of the circle of radius 2 centered at the origin.",
"role": "user"
}
] | 4\pi i |
[
{
"content": "Determine whether the following statement is true or false: There cannot exist topologies \\(\\tau, \\tau^{'}\\) on an infinite set \\(X\\) such that the product topology for \\((X,\\tau)\\) and \\((X,\\tau^{'})\\) coincides with the cofinite topology on \\(X\\times X\\).",
"role": "user"
}
... | A |
[
{
"content": "Find the limit of the sequence \\(a_n = \\log(n^3 - 3n^2) - \\log(en^3 + 2n + 7)\\) as \\(n\\) approaches infinity.",
"role": "user"
}
] | -1 |
[
{
"content": "Find the largest positive constant \\( c \\) such that \\[ c \\leq \\frac{\\sup_{t\\in [0,1]} |x+ty| }{|x|+|y|} \\] for all real numbers \\( x \\) and \\( y \\).",
"role": "user"
}
] | \dfrac{1}{3} |
[
{
"content": "Given the polynomial \\(p(x) = ax^3 + bx^2 + cx + d\\) with the condition \\(|p(x)| \\leq 1\\) for all \\(|x| \\leq 1\\), determine the maximum value of \\(|a| + |b| + |c| + |d|\\).",
"role": "user"
}
] | 7 |
[
{
"content": "Find the greatest integer that divides $p^8 - 1$ for every prime number $p > 7$. Express your answer as an integer.",
"role": "user"
}
] | 480 |
[
{
"content": "Evaluate the integral for $N > 0$:\n$$ \\frac{\\exp\\left(-\\frac N2\\right)}{2\\pi N} \\iint \\exp\\left(-\\left( \\frac {x^2-2xy-2Ny+2y^2}{2N}\\right)\\right) \\,dx\\,dy $$",
"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... | Kramer Company
Balance Sheet
As of December 31, 2014
Assets
Current Assets:
Cash $1,200
Accounts Receivable $700
Inventories $2,000
Total Current Assets $3,900
Non-Current Assets:
Equipment $8,000
Total Non-Current Assets $8,000
Total Assets $11,900
Liabilities
Current Liabilities:
Accounts Payable $1,400
Total Cur... |
[
{
"content": "Triangle $ABC$ is a right triangle with legs $AB$ and $AC$. Points $X$ and $Y$ lie on legs $AB$ and $AC$, respectively, so that $AX:XB = AY:YC = 1:2$. If $BY = 16$ units, and $CX = 28$ units, what is the length of hypotenuse $BC$? Express your answer in simplest radical form.",
"role": "user"
... | 6\sqrt{26} |
[
{
"content": "Evaluate whether the integral \\( \\int_0^\\infty \\sum_{n=0}^{\\infty} \\frac{x^n}{2^{(n+1)^s x^{n+1}} + 1} \\, dx \\) is equal to the Riemann zeta function \\( \\zeta(s+1) \\) for all \\( s \\ge 1 \\). Here, \\( \\zeta(s) = \\sum_{n=0}^{\\infty} \\frac{1}{(n+1)^s} \\) is the zeta function define... | \zeta(s+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... | Rate = 3.19e-4 [NH4+][NO2-] |
[
{
"content": "Let \\(a \\leq b < c\\) be the lengths of the sides of a right triangle. Determine the maximum constant \\(M\\) such that \\(\\frac{1}{a}+\\frac{1}{b}+\\frac{1}{c} \\geq \\frac{M}{a+b+c}\\).",
"role": "user"
}
] | 5 + 3\sqrt{2} |
[
{
"content": "Find the limit of the sequence defined by the recurrence relation \\( a_{n+1} = \\frac{a_n + n a_{n-1}}{n+1} \\) with initial conditions \\( a_0 = 0 \\) and \\( a_1 = 1 \\).",
"role": "user"
}
] | \ln 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... | $3,636 |
[
{
"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_2]_{eq} = 0.081~M
[I_2]_{eq} = 0.081~M
[HI]_{eq} = 0.638~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... | -288 J |
[
{
"content": "Evaluate the infinite series: \\[ \\sum\\limits_{n=1}^\\infty \\frac{n^2}{3^n}. \\]",
"role": "user"
}
] | \dfrac{3}{2} |
[
{
"content": "Determine the correct vector potential $f$ for the vector field $F = (x + 2y)i + (3y + 2z)j + (x^2 − 4z)k$, which satisfies $\\nabla \\times f = F$. Which option represents a valid vector potential?\n\nA) $(yz + 3z^2 − xy)i + (4xyz)j$\nB) $(2xy − z/2)i + (x^3 − 2yz)j$\nC) $(z^3/3 + 2(x^2)y)i + (xy... | D |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\to\\infty}\\frac{\\sum_{k=1}^{n} (-1)^{k+1}\\frac{1}{2k-1}}{\\sum_{k=1}^{n} \\frac{1}{2k}} \\]",
"role": "user"
}
] | 0 |
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