prompt list | ground_truth string |
|---|---|
[
{
"content": "Given a state machine with the following pathway and cost matrices: \\( \\text{Pathway matrix} = \\begin{pmatrix} 0 & 1 \\\\ 0 & 1 \\end{pmatrix} \\), \\( \\text{Cost matrix} = \\begin{pmatrix} 0 & 0 \\\\ 0 & 5 \\end{pmatrix} \\). If the starting state is 0 and \\( t = 1000 \\), calculate the tota... | 4995 |
[
{
"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... | 1.08e-3 /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... | The acid and base are carbonic acid and bicarbonate. The concentration of bicarbonate is 0.2 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... | 144.7 V |
[
{
"content": "Let $S$ be the set of $3 \\times 3$ matrices $\\rm A$ with integer entries such that $\\rm AA^{\\top} = I_3$. Determine the cardinality of the set $S$. What is $|S|$?",
"role": "user"
}
] | 48 |
[
{
"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... | $136,986.30 |
[
{
"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... | 378 K |
[
{
"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... | 5.3e+25 |
[
{
"content": "A 5-inch by 7-inch picture is placed on a rectangular piece of red paper such that a 0.5-inch wide red border is seen along each side of the picture. What is the area of the visible red border, in square inches?",
"role": "user"
}
] | 13 |
[
{
"content": "Let $f$ be a function mapping $\\mathbb{R}^n$ to $\\mathbb{R}$. If $f$ is Riemann integrable over a set $S$, does $f$ remain Riemann integrable if a subset $Q \\subset S$ is removed? Provide a justification for your answer.",
"role": "user"
}
] | No |
[
{
"content": "Find the centroid coordinates $(\\bar{x}, \\bar{y})$ of the plane region bounded by the curves $x^2 - y^2 = 4$.",
"role": "user"
}
] | (0, 0) |
[
{
"content": "Determine the interval of convergence for the power series: $$\\sum_{n=1}^{\\infty }(-1)^nx^{2n+1}\\frac{1\\cdot 3\\cdot 5\\cdot ...\\cdot (2n-1)}{n!\\cdot 2^{n}}$$",
"role": "user"
}
] | [-1, 1] |
[
{
"content": "For the space \\((l^2,\\|\\cdot\\|_2)\\), consider a bounded linear functional \\(\\Phi\\) and the sequence \\(e_n=(0,0,...,1,0,...)\\). Determine the smallest value of \\(p \\geq 1\\) for which the series \\(\\sum_{n=1}^\\infty |b_n|^p\\) converges, where \\(b_n=\\Phi(e_n)\\). What is the optimal... | 2 |
[
{
"content": "Below is a portion of the graph of a function, $y=f(x)$:\n\n[asy]\nimport graph; size(8cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-3.25,xmax=5.25,ymin=-3.25,ymax=4.25;\n\npen cqcqcq=rgb(0.75,0.75,0.75);\n\n/*grid*/ pen gs=linewidth(0.7)+cqcqcq+... | 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... | 2.016 rad/s^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... | 0.4m |
[
{
"content": "Find the minimum value of the expression:\n\\[\n\\begin{aligned}\nA & =\\sqrt{\\left(1264-z_{1}-\\cdots-z_{n}\\right)^{2}+x_{n}^{2}+y_{n}^{2}}+ \\\\\n& \\sqrt{z_{n}^{2}+x_{n-1}^{2}+y_{n-1}^{2}}+\\cdots+\\sqrt{z_{2}^{2}+x_{1}^{2}+y_{1}^{2}}+ \\\\\n& \\sqrt{z_{1}^{2}+\\left(948-x_{1}-\\cdots-x_{n}\\... | 1975 |
[
{
"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... | $189,555.68 |
[
{
"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_0n |
[
{
"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... | 2.497m |
[
{
"content": "Determine which of the two functions, \\( f(n) = \\frac{\\log n}{\\sqrt{\\log n}} \\) or \\( g(n) = \\sqrt{\\frac{n}{\\log n}} \\), grows asymptotically faster as \\( n \\to \\infty \\).",
"role": "user"
}
] | g(n) |
[
{
"content": "Let $G$ be a finite simple undirected graph. Suppose there exist subgraphs $G_1, G_2, \\dots, G_n$ of $G$, such that $G_i \\cong K_5$ or $K_{3,3}$, $E(G_i) \\cap E(G_j) = \\emptyset$ and $|V(G_i) \\cap V(G_j)| \\leq 3$, for $i \\neq j$. Is it true that the genus of $G$ is greater than or equal to ... | Yes |
[
{
"content": "The function $f$ defined by $f(x)= \\frac{ax+b}{cx+d}$, where $a$,$b$,$c$ and $d$ are nonzero real numbers, has the properties $f(19)=19$, $f(97)=97$ and $f(f(x))=x$ for all values except $\\frac{-d}{c}$. Find the unique number that is not in the range of $f$.",
"role": "user"
}
] | 58 |
[
{
"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... | f = \frac{1}{2\pi}\sqrt{\frac{\rho g}{\rho' H}} |
[
{
"content": "Determine if the following integral correctly represents the area of the region resulting from the intersection of the polar curves \\( r_1(\\theta)=2(1+\\cos\\theta) \\) and \\( r_2(\\theta)=2(1-\\cos\\theta) \\):\n\\[ 2A= \\int_{-\\frac{\\pi}{2}}^{\\frac{\\pi}{2}} [r_2(\\theta)]^2 \\, d\\theta +... | 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... | 6.578e-5 T 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... | -1.84e-5 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... | 59.7 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... | 2.77 |
[
{
"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... | $2,570,000 |
[
{
"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... | 1.02% |
[
{
"content": "Evaluate the double integral \\( \\iint_D \\frac{\\sqrt{x+y}}{\\sqrt{x-2y}}~dA \\) where \\( D \\) is the region in \\( \\mathbb{R}^2 \\) enclosed by the lines \\( y = \\frac{x}{2} \\), \\( y = 0 \\), and \\( x+y = 1 \\). Use the change of variables \\( u = x+y \\) and \\( v = x-2y \\). Calculate ... | \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... | 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... | 256 m |
[
{
"content": "Determine whether a $3 \\times 3$ rotation matrix can be expressed as a linear combination of fewer than nine constant basis matrices, where each basis matrix is a $3 \\times 3$ matrix and the scalar weights vary for different rotation matrices.",
"role": "user"
}
] | No |
[
{
"content": "Suppose $F_m = 2^{2^m} + 1$ is a prime number for $m \\geq 1$. Determine whether it must be true that $\\frac{F_m + 1}{2}$ is divisible by 3, i.e., $3 \\mid \\frac{F_m + 1}{2}$.",
"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... | -$3.10 |
[
{
"content": "There exists a scalar $c$ so that\n\\[\\mathbf{i} \\times (\\mathbf{v} \\times \\mathbf{i}) + \\mathbf{j} \\times (\\mathbf{v} \\times \\mathbf{j}) + \\mathbf{k} \\times (\\mathbf{v} \\times \\mathbf{k}) = c \\mathbf{v}\\]for all vectors $\\mathbf{v}.$ Find $c.$",
"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... | 3.92e+03 N m |
[
{
"content": "Determine whether the subspace of $[0,1]^\\mathbb{N}$, consisting of monotone (not necessarily strictly) real sequences with values in $[0,1]$ and equipped with the product topology, is connected.",
"role": "user"
}
] | Connected |
[
{
"content": "Determine the number of solutions for the system of equations: \\( x^2 + y^3 = 29 \\) and \\( \\log_3 x \\cdot \\log_2 y = 1 \\), where \\( x, y \\in \\mathbb{R} \\).",
"role": "user"
}
] | 2 |
[
{
"content": "Determine the largest value of \\( X \\) such that for any 25 real numbers \\( a_1, a_2, \\ldots, a_{25} \\) whose sum is an integer, there exists at least one number \\( a_i \\) for which \\( \\left|a_i - \\frac{1}{2}\\right| \\geq X \\). Round your answer to the nearest hundredth.",
"role": ... | 0.02 |
[
{
"content": "What is the largest positive integer $r$ such that there are infinitely many elliptic curves over the rationals with rank at least $r$?",
"role": "user"
}
] | 19 |
[
{
"content": "Given that the function \\( f:[0,\\infty)\\to[0,\\infty) \\) is absolutely continuous and \\( \\limsup_{x\\to\\infty}\\int_x^{x+h}f'(y)dy = 0 \\) for all \\( h>0 \\), determine whether the limit \\( \\lim_{x\\to\\infty}\\int_x^{x+h}f'(y)dy \\) exists and equals zero for all \\( h>0 \\).",
"rol... | 0 |
[
{
"content": "Let $\\mathbf{u}$ and $\\mathbf{v}$ be vectors such that $\\|\\mathbf{u}\\| = \\|\\mathbf{v}\\| = 2$ and $\\mathbf{u} \\cdot \\mathbf{v} = -1.$ If $\\theta$ is the angle between the vectors $\\mathbf{u} + \\mathbf{v}$ and $2 \\mathbf{u} - \\mathbf{v},$ then find $\\cos \\theta.$",
"role": "us... | \frac{1}{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... | 5094 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... | 582 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... | 993.77 |
[
{
"content": "Real numbers $x$ and $y$ satisfy the equation $x^2 + y^2 = 10x - 6y - 34$. What is $x+y$?",
"role": "user"
}
] | 2 |
[
{
"content": "Find the limit of the sequence \\(a_n = \\left[\\frac{(n+1)(n+2)\\cdots(n+n)}{n^n}\\right]^{1/n}\\) using Cauchy's second limit theorem.",
"role": "user"
}
] | \dfrac{4}{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... | 1.61e9 J |
[
{
"content": "Determine the value of the p-adic limit: \\[ \\lim_{n \\to \\infty} p^{p^n} \\] Is it 0 or 1?",
"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... | 2.767 |
[
{
"content": "Three noncollinear points and a line $\\ell$ are given in the plane. Suppose no two of the points lie on a line parallel to $\\ell$ (or $\\ell$ itself). There are exactly $n$ lines $m$ perpendicular to $\\ell$ with the following property: the three circles with centers at the given points and tang... | 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... | 138.73 g/mol |
[
{
"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. Derive the total revenue function, which is the product of quantity and the inverse demand function.
2. Derive the marginal revenue function by differentiating total revenue with respect to quantity.
3. Derive the marginal cost function by differentiating the total cost with respect to quantity.
4. Set marginal revenue equal to marginal cost and solve for the profit-maximizing quantity. |
[
{
"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... | 6360 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... | 80 g |
[
{
"content": "Consider a random variable \\( X \\) with probability density function \\( f(x) = \\frac{k(p)}{x^p} \\) for \\( x > 1 \\), where \\( p > 0 \\) and \\( k(p) \\) is a positive constant. Determine the set of values for \\( p \\) such that the variance of \\( X \\) is finite, but the fourth moment doe... | (3, 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... | 17.04% |
[
{
"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... | 1.84 m |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n \\to \\infty}\\int_{0}^{\\infty}\\frac{\\cos^{n}(x)}{\\sqrt{1 + \\pi/2 + x^{2}}}\\,\\dd x \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the integral: $$\\int_{-2}^2\\left(x^3\\cos\\frac{x}{2}+\\frac{1}{2}\\right)\\sqrt{4-x^2}\\ dx$$",
"role": "user"
}
] | \pi |
[
{
"content": "In an isosceles triangle \\( ABC \\) with base \\( BC \\), a point \\( K \\) is marked on the extension of side \\( AC \\) beyond point \\( C \\). A circle is inscribed in triangle \\( ABK \\) with center at point \\( I \\). Another circle is drawn through points \\( B \\) and \\( I \\), touching ... | 90^\circ |
[
{
"content": "Given the function \\( f(x,y) = \\frac{1}{1-xy} \\), find the value of \\( \\frac{\\partial ^8 f}{\\partial x^4\\partial y^4}(0,0) \\).",
"role": "user"
}
] | 576 |
[
{
"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... | 2.25 m/s |
[
{
"content": "Determine algebraically the point of intersection between the functions $x$ and $\\log_3(17-x^3)$ without graphing the equation $x=\\log_3(17-x^3)$. Provide the solution as a coordinate pair $(x, y)$. ",
"role": "user"
}
] | (2, 2) |
[
{
"content": "Determine the number of permutations \\( \\alpha \\in S_9 \\) such that \\( \\alpha \\omega \\alpha^{-1} = \\gamma \\), where \\( \\omega = (13624)(587)(9) \\) and \\( \\gamma = (15862)(394)(7) \\).",
"role": "user"
}
] | 15 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.407 cm^3 |
[
{
"content": "Determine the total number of possible game situations in Connect Four on a $7 \\times 6$ grid, considering that discs must be stacked on top of each other.",
"role": "user"
}
] | 127^7 |
[
{
"content": "Determine the value of \\( t \\) for which the integral \\( \\int_{0}^{\\infty} \\left( \\frac{x+1}{3x^2-t} - \\frac{t}{2x+1} \\right) \\, dx \\) converges.",
"role": "user"
}
] | \dfrac{2}{3} |
[
{
"content": "Given a Poisson distribution with parameter \\( \\lambda \\), where \\( \\lambda \\) is a random variable with probability density function \\( f(\\lambda) = e^{-\\lambda} \\), find the expectation of the random variable. The Poisson distribution is given by:\n\\[ p(x, \\lambda) = e^{-\\lambda} \\... | 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... | -1.40e+9 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... | $77,184.65 |
[
{
"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... | 16.19 |
[
{
"content": "Solve the equation \\( \\arccos(x) + \\arcsin(x^2 - x + 1) = \\frac{\\pi}{2} \\) for \\( x \\in [-1,1] \\).",
"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... | $520 |
[
{
"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... | 450 nm |
[
{
"content": "How many functions $h$ from $\\mathbb{N} \\cup \\{0\\}$ to $\\{0, 1\\}$ exist such that there is a natural number $k$ for which $h(i) = f(i)$ for all $i \\geq k$, given a function $f$ from $\\mathbb{N} \\cup \\{0\\}$ to $\\{0, 1\\}$?",
"role": "user"
}
] | \aleph_0 |
[
{
"content": "Compute the Riemann-Stieltjes integral \\( \\int_{-1}^{1} \\cos x \\ \\mathsf{d}g(x) \\), where \\( g(x) = -\\mathsf{1}_{[-1,0]}(x) + 3 \\cdot \\mathsf{1}_{(0,1]}(x) \\).",
"role": "user"
}
] | 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... | 188.46 |
[
{
"content": "A right triangle has an area of 120 square units, and a leg length of 24 units. What is the perimeter of the triangle, in units?",
"role": "user"
}
] | 60 |
[
{
"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... | $346,000 |
[
{
"content": "Can there exist two nonisomorphic number fields with the same degree, the same discriminant, and the same simple Galois group for their splitting field?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the value of $b$ ($b \\neq a$) such that the causal linear shift-invariant system described by the difference equation \\( y(n) - ay(n-1) = x(n) - bx(n-1) \\) is an allpass system, meaning the magnitude of its frequency response is constant, independent of frequency.",
"role": "user"... | \dfrac{1}{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... | $85,661.62 |
[
{
"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... | 0.368 kg |
[
{
"content": "Given a positive integer $n$, let $P(n)$ be the product of the non-zero digits of $n$ (if $n$ is a one-digit number, $P(n)$ is $n$ itself). Let $S = P(1) + P(2) + P(3) + \\ldots + P(999)$. Determine the largest prime factor of $S$. \\( \\boxed{?} \\)",
"role": "user"
}
] | 103 |
[
{
"content": "Find the minimum value of the function \\( f(x, y) = 6\\left(x^{2} + y^{2}\\right)(x + y) - 4\\left(x^{2} + xy + y^{2}\\right) - 3(x + y) + 5 \\) in the region \\( D = \\{(x, y) \\mid x > 0, y > 0\\} \\).",
"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... | Date Purchases Cost of Goods Sold Ending Inventory
May 7 161 units x $10 = $1,610 161 units x $10 = $1,610
June 1 83 units x $10 = $830 78 units x $10 = $780
July 28 96 units x $13 = $1,248 78 units x $10 + 96 units x $13 = $780 + $1,248 = $2,028
August 27 78 units x $10 + 50 units x $13 = $780 + $650 = $1,430 46 units x $13 = $598
Total $2,858 $2,260 $598 |
[
{
"content": "Given the sets \\( M = \\{ (x, y) \\mid 3x^2 + 4y^2 - 6mx + 3m^2 - 12 = 0 \\} \\) and \\( N = \\{ (x, y) \\mid 2y^2 - 12x + 9 = 0 \\} \\), determine the range of \\( m \\) such that \\( M \\cap N \\neq \\emptyset \\). Choose the correct option:\n\nA. \\( m \\geq -\\frac{5}{4} \\)\nB. \\( -\\frac{5... | C |
[
{
"content": "Let $a, b, c, p$ be rational numbers, with $p$ not being a perfect cube. If $a + b p^{1/3} + c p^{2/3} = 0$, prove that $a = b = c = 0$.",
"role": "user"
}
] | a = b = c = 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... | 0.0337 m/s^2 |
[
{
"content": "Determine whether the function \\( f(t) = \\int_0^t \\sin(t\\sqrt{1+x^2}) \\, dx \\) has a local minimum at \\( t = 0 \\).",
"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... | 2367.53 N |
[
{
"content": "Determine the total number of ordered pairs \\((x, y)\\) of non-negative integers that satisfy the equation:\n\\[ x!y! = x! + y! + 2 \\]",
"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... | 82.62 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... | 2.61 years |
[
{
"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... | 3267.26 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... | 18 kg/m^3 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.