prompt list | ground_truth string |
|---|---|
[
{
"content": "Evaluate \\( \\tan(A) \\) where \\( A = \\sum_{k=1}^{17} \\tan^{-1}\\left(\\frac{1}{k^2+k+1}\\right) \\).",
"role": "user"
}
] | \dfrac{17}{19} |
[
{
"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... | $877,783.50 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Assets:
Current Assets:
Cash: $114,000
Inventory: $180,000
Accounts Receivable: $160,000 ($170,000 - $10,000)
Short-term investments: $80,000
Cash surrender value of life insurance contracts: $40,000
Total Current Assets: $574,000
Long-term Assets:
Investments:
Long-term investments: $270,000
Bond sinking fund: $250,0... |
[
{
"content": "In an undirected and weighted graph $G$, if a vertex $v$ is a leaf in all minimum spanning trees (MSTs) of $G$, does $v$ have the same predecessor in all such MSTs? Answer 'yes' or 'no' and 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... | 2.59e8 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... | 1.43e6 kg |
[
{
"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... | 0.613 m |
[
{
"content": "Determine the value of \\( m \\) for which the infinite series \\( \\sum_{n=1}^{\\infty} \\left( \\sqrt[n^m]{2} - 1 \\right) \\) converges.",
"role": "user"
}
] | m > 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... | 7.07 M |
[
{
"content": "For a world record, George Adrian picked 15,832 pounds of apples in 8 hours. Assuming he maintained a constant rate of picking, how many pounds of apples did he pick in 3 hours?",
"role": "user"
}
] | 5937 |
[
{
"content": "Find the degree of the field extension \\([\\mathbb{Q}(i,2^{\\frac{1}{4}}):\\mathbb{Q}(2^{\\frac{1}{4}})]\\).",
"role": "user"
}
] | 2 |
[
{
"content": "Evaluate the limit: $$\\lim_{n \\to \\infty} \\frac{(2^{n+1}+(n+1)^2)(2^{2n+2}+1)}{(2^n+n^2)(2^{2n}+1)}$$",
"role": "user"
}
] | 8 |
[
{
"content": "Suppose $K$ is a finite extension of $\\mathbb{Q}$, and let $p$ be a prime number in $\\mathbb{Q}$. If $p\\mathcal{O}_K = \\mathfrak{P}_1 \\ldots \\mathfrak{P}_n$ is the prime decomposition of $p$ in $\\mathcal{O}_K$, is it true that any prime ideal in $\\mathcal{O}_K$ lying above $p$ is a factor ... | Yes |
[
{
"content": "In a $11\\times11$ grid, calculate the number of non-decreasing grid walks from $(0,0)$ to $(10,10)$ that do not pass through the points $(3,3)$, $(7,2)$, $(3,7)$, or $(7,7)$. The total number of unrestricted paths is $\\binom{20}{10}$. Determine the number of valid paths by subtracting the number... | 60256 |
[
{
"content": "Calculate the volume of a torus using a double integral in Cartesian coordinates.",
"role": "user"
}
] | 2\pi^2 R r^2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 188.9 kg |
[
{
"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... | 87 g/mol |
[
{
"content": "Let \\( \\triangle ABC \\) be a scalene triangle with inradius 1 and exradii \\( r_A, r_B, \\) and \\( r_C \\) such that \\[ 20\\left(r_B^2r_C^2+r_C^2r_A^2+r_A^2r_B^2\\right)=19\\left(r_Ar_Br_C\\right)^2. \\] If \\[ \\tan\\frac{A}{2}+\\tan\\frac{B}{2}+\\tan\\frac{C}{2}=2.019, \\] then the area of ... | 201925 |
[
{
"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... | $507,970.60 |
[
{
"content": "A sequence $(S_n)$ is defined as follows: $S_1 = 1,$ $S_2 = 1,$\n\\[S_n = \\frac{S_{n - 2} \\cdot S_{n - 1}}{S_{n - 2} + S_{n - 1}}\\]for $n > 2.$ Compute $S_{12}.$",
"role": "user"
}
] | \frac{1}{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... | 0.53 s |
[
{
"content": "Prove that the sum \\( \\sum_{i=0}^{5x - 1} 2^{4i} \\equiv 0 \\pmod{11} \\) for any integer \\( x \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Find the smallest integer \\(m_n\\) such that if \\(m_n\\) points are placed inside an equilateral triangle with sides of length 1, at least two points will be at a distance of \\(\\frac{1}{n}\\) or less. What is a possible formula for \\(m_n\\)?",
"role": "user"
}
] | n^2 + 1 |
[
{
"content": "Evaluate the limit: $$\\lim_{c\\to0}\\int_1^\\infty ce^{-x-\\frac{c}{x}}\\mathrm{d}x$$",
"role": "user"
}
] | 0 |
[
{
"content": "Let $A$ and $B$ be $n \\times n$ Hermitian matrices with eigenvalues $\\{\\lambda_{A1},\\ldots,\\lambda_{An}\\}$ and $\\{\\lambda_{B1},\\ldots,\\lambda_{Bn}\\}$, respectively. If $A+B = \\Lambda$ where $\\Lambda$ is a diagonal matrix with diagonal elements $\\{\\lambda_1,\\ldots,\\lambda_n\\}$ and... | \lambda_n |
[
{
"content": "Determine whether the equation \\(5x^2 + 3y^2 - 2z^2 = 0\\) has a non-trivial solution in the 5-adic numbers \\(\\mathbb{Q}_5\\).",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the sum of all integer values of \\(a\\), with \\(|a| \\leq 15\\), such that the inequality \\(\\frac{4x - a - 4}{6x + a - 12} \\leq 0\\) holds for all \\(x\\) in the interval \\([2, 3]\\).",
"role": "user"
}
] | -7 |
[
{
"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... | 0.750 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... | 3815 N/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... | 46.1 kJ |
[
{
"content": "Suppose $H/P$ and $M/P$ are two subgroups of a group $G/P$ such that $(H/P) \\cap (M/P) = \\{P\\}$. Is it true that $H \\cap M = P$?",
"role": "user"
}
] | Yes |
[
{
"content": "Maximize the objective function \\( 24x_1 + 22x_2 + 45x_3 \\) subject to the constraints:\n\\[\\begin{align*}\n2x_1 + x_2 + 3x_3 &\\leq 42, \\\\\n2x_1 + x_2 + 2x_3 &\\leq 40, \\\\\nx_1 + \\frac{1}{2}x_2 + x_3 &\\leq 45, \\\\\nx_1, x_2, x_3 &\\geq 0.\n\\end{align*}\\]\nSolve this problem by inspect... | 882 |
[
{
"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 m/s |
[
{
"content": "Consider the infinite arithmetic sequence $A$ with first term $5$ and common difference $-2$. Now define the infinite sequence $B$ so that the $k^{th}$ term of $B$ is $2$ raised to the $k^{th}$ term of $A$. Find the sum of all of the terms of $B$.",
"role": "user"
}
] | \frac{128}{3} |
[
{
"content": "Determine the order of the zeros of the function \\( f(z) = \\frac{\\sin z}{z} \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Is it possible to isometrically embed the unit sphere $S^m$ into the unit sphere $S^n$ such that the tangent space at a point $p \\in S^m$ matches a given $m$-dimensional subspace $V \\subset T_pS^n$, where $m < n$?",
"role": "user"
}
] | Yes |
[
{
"content": "Is the image of the principal branch of the square root function, which excludes the negative real axis from the complex plane, the same as its pre-image?",
"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... | -$30,086 |
[
{
"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... | 2.691e-11 J |
[
{
"content": "Consider the real $n \\times n$-matrices $A$ and $B$. Determine if $A$ and $B$ can fail to commute given that $e^A = e^B = e^{A+B} = I$. Provide a justification for your answer.",
"role": "user"
}
] | No |
[
{
"content": "Let $a$ and $b$ be positive real numbers such that $a + 2b = 1.$ Find the minimum value of\n\\[\\frac{1}{a} + \\frac{1}{b}.\\]",
"role": "user"
}
] | 3 + 2 \sqrt{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... | Date: June 1, 2016
Account titles and explanation| Debit| Credit|
---|---|---|
Cash| $101,000 ||
Interest expense| $1,500 ||
Premium on Bonds Payable ||$1,000
Bonds Payable ||$100,000
Interest Payable||$1,500 |
[
{
"content": "Let $V$ be a vector space of finite dimension. Determine all linear transformations $T: V \\rightarrow V$ that are nilpotent and have a basis of eigenvectors.",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether a graph $G$ with at least three vertices, where every vertex is the starting point of a Hamilton Path, must contain a Hamilton Circuit. Answer 'yes' or 'no' and 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... | 7.599 kg-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... | 6.34% |
[
{
"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... | (NH_4)_2CrO_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... | 9100 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... | 23.6 |
[
{
"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... | 4NH_3(g) + 5O_2(g) -> 4NO(g) + 6H_2O(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... | 872 m |
[
{
"content": "Determine whether there exists a non-trivial linear functional on \\((C[0,1], ||\\cdot||_2)\\) that does not arise from the inner product on \\(L^2[0,1]\\). Specifically, does there exist an \\(F \\in X^*\\), where \\(X = C[0,1]\\) with the \\(L^2\\) norm, such that there is no \\(g \\in X\\) for ... | Yes |
[
{
"content": "Determine whether there are any local extrema of the function \\( f(x,y) = \\sin(xy) \\) within the domain \\( x \\in (0, \\pi) \\) and \\( y \\in (0, 1) \\).",
"role": "user"
}
] | Yes |
[
{
"content": "Compute the limit \\( \\lim_{n \\to \\infty} P\\left( \\sigma^2 \\in (A_n, B_n) \\right) \\), where \\( A_n = \\frac{(n-1)S_{n}^{2}}{\\chi^{2}_{n-1,\\alpha/2}} \\) and \\( B_n = \\frac{(n-1)S_{n}^{2}}{\\chi^{2}_{n-1,1-\\alpha/2}} \\). Assume \\( X_1, X_2, \\ldots, X_n, \\ldots \\) are i.i.d. rando... | 1 - \alpha |
[
{
"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... | $129.3512 |
[
{
"content": "Is the space $S^2 \\setminus \\{p\\}$, where $p$ is a point on the 2-sphere $S^2$, homeomorphic to the Euclidean plane $\\mathbb{R}^2$? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit \\(\\lim_{(x, y) \\to (0, 0)} e^{\\frac{1}{x^2 + y^2}}\\).",
"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... | 25.91 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... | $806977.47 |
[
{
"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... | 0.25 mi |
[
{
"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... | 11.412g |
[
{
"content": "Find the volume of the solid that lies under the plane $z = x + 5$ and within the cylinder $4x^2 + y^2 = 4$, where $z \\geq 0$. The boundaries are $-1 \\leq x \\leq 1$ and $-2\\sqrt{1-x^2} \\leq y \\leq 2\\sqrt{1-x^2}$. Set up and evaluate the integral to find this volume.",
"role": "user"
}... | 10\pi |
[
{
"content": "Find the minimum value of the expression \\( f(a,b,c) = \\left\\lfloor\\frac{a+b}{c}\\right\\rfloor + \\left\\lfloor\\frac{b+c}{a}\\right\\rfloor + \\left\\lfloor\\frac{c+a}{b}\\right\\rfloor \\) where \\( a, b, c > 0 \\). For what values of \\( a, b, \\) and \\( c \\) is this minimum achieved?",
... | 4 |
[
{
"content": "Evaluate the flux integral \\(\\iint_{S} \\mathbf{F} \\cdot d\\mathbf{S}\\) using the Divergence Theorem, where \\(\\mathbf{F}(x, y, z) = y\\mathbf{j} - z\\mathbf{k}\\) and \\(S\\) is the surface composed of the paraboloid \\(y = x^2 + z^2\\) for \\(0 \\leq y \\leq 1\\) and the disk \\(x^2 + z^2 \... | -\pi |
[
{
"content": "For a positive integer $n$, the ordinary differential equation \\[ y''+\\dfrac{1}{x}y'+\\left(1-\\dfrac{n^2}{x^2}\\right)y=0 \\] has a solution in the form of the Bessel function of order $n$, given by $J_n(x) = x^n \\sum_{k=0}^{\\infty} a_k x^k$. Determine the coefficient $a_1$ by substituting th... | 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... | 12.2518 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... | 37900 |
[
{
"content": "Determine the number of essentially different groups of order 4.",
"role": "user"
}
] | 2 |
[
{
"content": "Find the smallest positive integral solution (x, y, z) to the equation \\( \\frac{1}{x^2} + \\frac{1}{y^2} = \\frac{1}{z^2} \\).",
"role": "user"
}
] | (15, 20, 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... | $92.67 |
[
{
"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... | 2NH3 + ClO- -> N2H4 + Cl- + H2O |
[
{
"content": "Consider the partial differential equation \\( u_{xx} + u_{yy} + \\lambda u = 0 \\) for \\( 0 < x, y < 1 \\) with boundary conditions \\( u(x,0) = u(x,1) = 0 \\) for \\( 0 \\leq x \\leq 1 \\) and \\( u(0,y) = u(1,y) = 0 \\) for \\( 0 \\leq y \\leq 1 \\). Determine which of the following statements... | C |
[
{
"content": "If a Hilbert space operator $T$ has a unique self-adjoint extension, is the extension necessarily the closure of $T$? Answer yes or no and 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... | 1.45 g CuCrO4 |
[
{
"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... | $17.15 |
[
{
"content": "Let $f(x) = \\sin(\\pi x/2)$ for $x \\in \\mathbb{R}$. For $y \\in \\mathbb{R}$, consider the sequence $\\{x_{n}(y)\\}_{n \\geq 0}$ defined by $x_{0}(y) = y$ and $x_{n+1}(y) = f(x_{n}(y))$ for all $n \\geq 0$. Define $g(y) = \\lim_{n \\to \\infty} x_{n}(y)$. Evaluate the integral $\\int_{0}^{3} g(... | 1 |
[
{
"content": "Evaluate the double integral \\( \\iint_D \\frac{1}{\\sqrt{x^2+y^2}}\\,dx\\,dy \\), where \\( D \\) is the region defined by \\( 1 \\le x^2 + y^2 \\le 4 \\). Transform the integral using polar coordinates and find the resulting integral.",
"role": "user"
}
] | 2\pi |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -4.5 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... | 7.90% |
[
{
"content": "Determine all real numbers \\( \\alpha \\) such that for every continuous function \\( f: [0,1] \\to [0,1] \\), there exists a \\( c \\in [0,1] \\) satisfying \\( f(c) = \\alpha \\cdot c \\).",
"role": "user"
}
] | [1, \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... | 45t^2 |
[
{
"content": "Determine all values of \\( \\alpha \\) such that all solutions of the differential equation \\( x^2y'' + \\alpha xy' + 4y = 0 \\) approach zero as \\( x \\to \\infty \\).",
"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... | 0.84 |
[
{
"content": "Calculate the mass of the object enclosed by the surface \\( x^2 + \\frac{y^2}{4} + \\frac{z^2}{9} = 1 \\) where the density is given by \\( \\mu(x,y,z) = e^{\\sqrt{x^2 + \\frac{y^2}{4} + \\frac{z^2}{9}}} \\).",
"role": "user"
}
] | 24\pi(e - 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... | 41.8 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... | 3Ca(OH)_2(aq) + 2H_3PO_4(aq) -> Ca_3(PO_4)_2(s) + 6H_2O(l)
Net ionic equation:
3Ca^2+(aq) + 6OH^-(aq) + 6H^+(aq) + 2PO_4^3-(aq) -> Ca_3(PO_4)_2(s) + 6H_2O(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... | 2.9 pF |
[
{
"content": "Evaluate the integral \\( \\oint_{|z|=2} \\frac{\\cos z}{z^2+1} \\, dz \\) using the residue theorem, given that the integrand has simple poles at \\( z=i \\) and \\( z=-i \\).",
"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... | 2.4 rpm |
[
{
"content": "Provide an example of a finitely generated $R$-module that is torsion-free but not free.",
"role": "user"
}
] | (x, 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... | $30.86 |
[
{
"content": "Determine the minimum number of isoclinic rotations required to transform an arbitrary 2-plane in \\( \\mathbb{R}^4 \\), passing through the origin, into any of the Euclidean orthonormal 2-planes in a standard Cartesian 4D coordinate system.",
"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... | 0.32 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... | |E| = 2100 N/C, downward |
[
{
"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... | $33,494.52 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 23.71 degree Celsius |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to +\\infty} \\left(\\sinh x\\right)^{\\arctan\\frac{1}{x}} \\] without using L'Hôpital's rule.",
"role": "user"
}
] | e |
[
{
"content": "Find all functions \\( f: \\mathbb{R} \\to \\mathbb{R} \\) such that \\[ f(x^2+f(y))=y+(f(x))^2 \\] for all real numbers \\( x \\) and \\( y \\).",
"role": "user"
}
] | f(x) = x |
[
{
"content": "Given that $X$ and $Y$ are standard normal random variables with a bivariate normal distribution, determine the expected value of their product, $E(XY)$, without assuming their independence.",
"role": "user"
}
] | \rho |
[
{
"content": "Find all polynomials $p(x)$ such that $p(p(x)) + p(x) = x^4 + 3x^2 + 3$ for all $x \\in \\mathbb{R}$. Assume $p(x)$ is a quadratic polynomial and determine its coefficients.",
"role": "user"
}
] | x^2 + 1 |
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