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... | $538,200 |
[
{
"content": "Let the real numbers \\( x \\) and \\( y \\) satisfy the system of equations:\n\\[ \\begin{cases} \nx^{3} - 3x^{2} + 2026x = 2023 \\\\\ny^{3} + 6y^{2} + 2035y = -4053 \n\\end{cases} \\]\nFind \\( x + y \\).",
"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... | 176.4 m |
[
{
"content": "At Annville Junior High School, $30\\%$ of the students in the Math Club are in the Science Club, and $80\\%$ of the students in the Science Club are in the Math Club. There are 15 students in the Science Club. How many students are in the Math Club?",
"role": "user"
}
] | 40 |
[
{
"content": "Let $\\lambda$ be the Lebesgue measure and $\\mu$ be a measure absolutely continuous with respect to $\\lambda$. Suppose for Lebesgue measurable sets $X_n$, $n=1,2,...$, we have $\\lambda(X_n)=1/n$. Determine whether $\\mu(X_n)\\to 0$ as $n\\to \\infty$. Justify your answer.",
"role": "user"
... | No |
[
{
"content": "Given a fifth-degree polynomial \\( f(x) \\) with a leading coefficient of 1, and it satisfies \\( f(n) = 8n \\) for \\( n = 1, 2, \\cdots, 5 \\), find the coefficient of the linear term in \\( f(x) \\).",
"role": "user"
}
] | 282 |
[
{
"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... | Rivera Company
Balance Sheet on December 31, 2020
Current Assets:
Cash $2,750
Short-term investments $3,690
Accounts receivable $1,696
Inventory $1,765
Prepaid Expenses $980
Total current assets $10,881
Long-Term Assets:
Property, plant, and equipment $11,500
Accumulated depreciation -$3,560
Long-term investments $1,300
Total long-term asstes $9,240
Total assets $20,121
LIABILITIES AND STOCKHOLDERS' EQUITY
Current Liabilities:
Accounts payable $1,555
Notes Payable $1,000
Total Current Liabilities: $2,555
Long-Term Liabilities
Mortage payable $2,340
Notes Payable $1,200
Total long-term liabilities $3,540
Total Liabilities $6,095
Owner's equity $14,026
Total liabilities and stockholders' equity $20,121 |
[
{
"content": "Evaluate the limit: \\( \\lim_{x\\to 0} (1 - \\sin x)^{\\cot 2x} \\)",
"role": "user"
}
] | \dfrac{1}{\sqrt{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... | 6.73*10^-6 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... | Down Under Products, Ltd.,
Production Budget
For the Second Quarter
April May June Quarter
Quarter Budgeted units sales 76,000 85,000 116,000 277,000
Add: Desired ending inventory 12,750 17,400 13,950 13,950
Total needs 88,750 102,400 129,950 290,950
Less: Beginning inventory 11,400 12,750 17,400 11,400
Required production in units 77,350 89,650 112,550 279,550 |
[
{
"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... | 0.194 : 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... | 35.22 |
[
{
"content": "Given a convergent series \\(\\sum a_n\\) of positive terms, where \\(\\liminf (na_n) = 0\\), prove or disprove that if \\(\\{a_n\\}\\) is decreasing, then \\(\\lim (na_n) = 0\\).",
"role": "user"
}
] | 0 |
[
{
"content": "Calculate the expected sojourn time for cars that decide to take gas at a station where cars arrive according to a Poisson process with rate \\( \\frac{1}{3} \\). An arriving car finding \\( n \\) cars at the station leaves with probability \\( q_n = \\frac{n}{4} \\) and joins the queue with proba... | \dfrac{384}{71} |
[
{
"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... | 2.36e-13 |
[
{
"content": "Evaluate the double series \\( \\sum^{\\infty}_{n=0} \\sum^{n}_{k=0} \\frac{2^k}{2^n (k+1)(k+2)} \\).",
"role": "user"
}
] | 2 |
[
{
"content": "Determine the intersection \\(\\bigcap_{\\epsilon > 0} S_\\epsilon\\), where \\(S_\\epsilon = \\{ n \\in \\mathbb{N} : \\sin(n) > 1 - \\epsilon \\}\\).",
"role": "user"
}
] | \emptyset |
[
{
"content": "Evaluate the integral \\( \\int_0^{\\infty} e^{-y} y^3 \\, dy \\) using integration by parts and the Gamma function.",
"role": "user"
}
] | 6 |
[
{
"content": "For iid random variables $X_1, X_2 \\sim \\mathcal{N}(\\mu, \\sigma)$, determine the values of $a$ such that $aX_1 + (1-a)X_2$ is independent of $aX_1 - (1-a)X_2$. Provide your answer in terms of $a$.",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Determine whether there exists a vector $y$ such that for any matrix $B$, the inequality \\( \\|By\\| \\geq \\|B\\|\\|y\\| \\) holds.",
"role": "user"
}
] | 0 |
[
{
"content": "Calculate the limit: $$\\lim_{x\\to \\infty} \\left((x+1) \\cos \\left(2\\cos ^{-1}\\left(\\frac{x}{x + 1}\\right) \\left(a - \\frac{1}{2}\\right)\\right) - x\\right)$$ using cosine expansions.",
"role": "user"
}
] | 4a(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... | 32.1 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... | $12,198.02 |
[
{
"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... | 1/8 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.75e5 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... | 5.21% |
[
{
"content": "In a tetrahedron $ABCD$, it is given that $\\angle ADB = \\angle BDC = \\angle CDA = \\frac{\\pi}{3}$, $AD = BD = 3$, and $CD = 2$. Determine the radius of the circumsphere of the tetrahedron $ABCD$. Express your answer in simplest form.",
"role": "user"
}
] | \sqrt{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... | 13.98% |
[
{
"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... | $31,208.77 |
[
{
"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... | 9.27% |
[
{
"content": "Evaluate the limit of the sequence: \\[ L = \\lim_{n\\to\\infty} \\left[\\left(1+\\frac{1}{n}\\right)\\left(1+\\frac{2}{n}\\right)\\left(1+\\frac{3}{n}\\right)\\cdots\\left(1+\\frac{n}{n}\\right)\\right]^\\frac{1}{n} \\]",
"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... | Preferred stock dividends per share:
Year 1: $2.25
Year 2: $3.75
Year 3: $3.00
Year 4: $3.00
Common stock dividends per share:
Year 1: $0.00
Year 2: $0.30
Year 3: $0.88
Year 4: $1.08 |
[
{
"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{\mu_s mg}{cos\theta+\mu_s sin\theta} |
[
{
"content": "Determine the maximum real number \\( k \\) such that for any simple graph \\( G \\) with \\( n \\) vertices (where \\( n \\geq 3 \\)), the inequality \\( x^3 \\geq k y^2 \\) is satisfied, where \\( x \\) is the number of edges and \\( y \\) is the number of triangles in \\( G \\).",
"role": "... | \dfrac{9}{2} |
[
{
"content": "As \\( n \\) approaches infinity, what value does \\( S_n = \\sum_{k = 1}^{2010} \\left( \\cos \\frac{k! \\, \\pi}{2010} \\right)^n \\) approach?",
"role": "user"
}
] | 1944 |
[
{
"content": "In triangle $ABC$, it is given that $\\angle B = 2\\angle C$. Point $D$ is located on side $BC$ such that $AD$ bisects $\\angle BAC$ and $AB = CD$. Determine the measure of $\\angle BAC$. \\(\\boxed{\\text{?}}\\)",
"role": "user"
}
] | 72^\circ |
[
{
"content": "The vertices of a quadrilateral lie on the graph of the function \\( y=\\ln x \\), with x-coordinates being four consecutive positive integers. If the area of the quadrilateral is \\( S=\\ln \\frac{91}{90} \\), find the x-coordinate of the leftmost vertex. Choose from the following options:\n\n(A)... | D |
[
{
"content": "Given the function \\( f(x) = x + \\int_{0}^{1} t(x+t)f(t) \\, dt \\), find the value of \\( \\int_{0}^{1} f(x) \\, dx \\).",
"role": "user"
}
] | \dfrac{42}{23} |
[
{
"content": "Determine whether the following statement is true or false: For any two finite sets $X$ and $Y$, if $\\mu$ is a probability distribution over $Y^X$, and $\\sigma$ is a permutation on $X$, then $\\mu \\circ f_\\sigma^{-1} = \\mu$ for all $\\sigma$, if and only if $\\mu$ is the uniform distribution ... | False |
[
{
"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... | 1.62e-6 C/m^3 |
[
{
"content": "Calculate the limit: $$\\lim_{x\\to\\infty} x^{3/2}\\left(\\sqrt{x+1}+\\sqrt{x-1}-2\\sqrt{x}\\right)$$",
"role": "user"
}
] | -\dfrac{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... | 7.10 m/s |
[
{
"content": "Find all integer pairs \\((m, n)\\) that satisfy the equation: \\[\\sqrt{8+\\sqrt{32+\\sqrt{768}}}=n\\cos\\frac{\\pi}{m}\\]",
"role": "user"
}
] | (24, 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... | 0.19 |
[
{
"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... | 886.62 kJ/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... | C(w,r,q) = wl + vk |
[
{
"content": "Determine the value of \\( \\alpha \\in \\mathbb{R} \\) such that the second derivative of the function \\( f(x) \\) exists at \\( x = 0 \\), where:\n\n\\[\nf(x) =\n\\begin{cases}\ne^{-\frac{1}{x}}, & \\text{if } x > 0 \\\\\n\\sin(x) + \\alpha x^2 - \\log(1+x), & \\text{if } x \\leq 0\n\\end{case... | -\dfrac{1}{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... | $94,565 |
[
{
"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... | 2.75 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... | 12.44 N |
[
{
"content": "Evaluate the contour integral \\( \\int_{\\gamma} \\frac{1}{z^2-1} \\, dz \\), where \\( \\gamma(t) = 2e^{it} \\) for \\( t \\) ranging from \\(-\\pi\\) to \\(\\pi\\).",
"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... | 0.37 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... | 12744.68 |
[
{
"content": "Determine the conic hull of the set \\( T = \\left\\{(x_1,x_2) : (x_1 + 1)^2 + x_2^2 = 4 \\right\\} \\).",
"role": "user"
}
] | \mathbb{R}^2 |
[
{
"content": "Determine the values of \\( \\alpha \\) such that the equation \\( n^{\\frac{1}{\\alpha \\log n}} = 1 \\) holds as \\( n \\to \\infty \\).",
"role": "user"
}
] | \emptyset |
[
{
"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... | displacement |
[
{
"content": "Calculate the sum of the infinite series: \\[ 1 + \\sum_{n=1}^\\infty \\frac{(4n-2)}{3^n} \\]",
"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... | 1.20e+24 |
[
{
"content": "Let $p$ be a prime such that $p \\equiv 3 \\ (\\text{mod} \\ 4)$. Prove that $(\\frac{p-1}{2})! \\equiv (-1)^{t} \\ (\\text{mod} \\ p),$ where $t$ is the number of positive integers less than $\\frac{p}{2}$ that are nonquadratic residues modulo $p$. ",
"role": "user"
}
] | (-1)^t |
[
{
"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... | 16.26 Pa |
[
{
"content": "Let $x, y, z$ be the sides of a triangle such that $x \\neq z$. Determine the range of values for $p$ such that the equation \\( t^2 + 2(x + y + z)t + 3p(xy + yz + zx) = 0 \\) has real roots, given that $x, y, z$ satisfy the triangle inequality.",
"role": "user"
}
] | (-\infty, 1] |
[
{
"content": "Determine whether the following statement is true or false: If $f(x)$ and $g(x)$ are linearly dependent functions, then $\\ln|f(x)|$ and $\\ln|g(x)|$ are also linearly dependent.",
"role": "user"
}
] | B |
[
{
"content": "Is it possible to arrange 2,000,000 regular hexagons, each with an area of 1, in the plane such that the union of their interiors forms a convex polygon with an area of at least 1,900,000?",
"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... | 1.34% |
[
{
"content": "A bookstore is deciding what price it should charge for a certain book. After research, the store finds that if the book's price is $p$ dollars (where $p \\le 40$), then the number of books sold per month is $120-3p$. What price should the store charge to maximize its revenue?",
"role": "user"... | 20 |
[
{
"content": "Suppose that $f$ and $g$ are everywhere continuous but nowhere differentiable functions. Can the composition $f \\circ g$ be differentiable?",
"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... | 22.5 N |
[
{
"content": "Find the volume of the solid in the first octant bounded by the cylinder \\(x^2 + y^2 = 1\\), the plane \\(y = z\\), and the coordinate planes \\(x = 0\\) and \\(z = 0\\).",
"role": "user"
}
] | \dfrac{1}{3} |
[
{
"content": "Circle $A$ has a diameter of 12 inches and circle $B$ has a diameter of 22 inches. What is the ratio of the area of circle $A$ to the area of circle $B$? Express your answer as a common fraction.",
"role": "user"
}
] | \frac{36}{121} |
[
{
"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... | 14.5 hours |
[
{
"content": "Find the expression for \\((g - Pg)(x)\\), where \\(g(x) = x^2\\) and \\(Pg\\) is the orthogonal projection of \\(g\\) onto the closed subspace \\(V\\) of \\(L^2[0,1]\\) such that \\(V^{\\perp} = \\text{span}(f)\\) with \\(f(x) = x\\).",
"role": "user"
}
] | \dfrac{3}{4}x |
[
{
"content": "Given the parabola \\(y^2 = 4x\\) with focus \\((1, 0)\\), consider two circles \\(C_1\\) and \\(C_2\\) that both pass through the focus of the parabola. Circle \\(C_1\\) touches the parabola at point \\(Q\\), and circle \\(C_2\\) touches the parabola at point \\(R\\). The points \\(Q\\) and \\(R\... | 5\sqrt{10} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.2 mL |
[
{
"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... | 7.98 N |
[
{
"content": "There are \\( 4n \\) circles of the same radius on a plane, where \\( n \\) is a positive integer. No two circles are tangent to each other, and each circle intersects with at least three other circles. Let \\( f(n) \\) represent the number of intersection points of these circles. Determine the mi... | 12n |
[
{
"content": "Find a function \\( f(x) \\) such that \\( f''(x) = f(x) \\), \\( f(0) = 0 \\), and \\( f(x) \\to -\\infty \\) as \\( x \\to -\\infty \\).",
"role": "user"
}
] | e^x - e^{-x} |
[
{
"content": "Prove that for any positive integer \\( n \\), the inequality \\( \\sum_{k=1}^{n^3} \\frac{1}{k^{\\frac{2}{3}}} < 3n \\) holds.",
"role": "user"
}
] | 3n |
[
{
"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... | $2,292.00 |
[
{
"content": "Given that $1, x,$ and $x^2$ are solutions of a second-order linear non-homogeneous differential equation on the interval $-1 < x < 1$, determine the general solution involving arbitrary constants. Choose the correct option:\n\n(a) $c_1(1-x) + c_2(x - x^2) +1$\n\n(b) $c_1(x) + c_2 ( x^2) +1$\n\n(c... | 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... | 84.18 |
[
{
"content": "Find \\(\\alpha \\in \\mathbb{R}\\) such that there exists a Lie algebra representation of \\(\\mathfrak{sl}_2 (\\mathbb{R})\\) on \\(C^\\infty(\\mathbb{R})\\) with image equal to \\(\\text{span}_\\mathbb{C} \\{ X , Y , Z_\\alpha \\}\\), where the differential operators are defined as follows:\n\n... | \dfrac{1}{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... | rate = k[A][B]^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... | Add " 1" to the vmlinuz line (before systemctl) or add " systemd.unit=single" (with systemctl) |
[
{
"content": "For the parabola $y = -x^2$, let $a < 0$ and $b > 0$. Define points $P(a, -a^2)$ and $Q(b, -b^2)$. Let $M$ be the midpoint of $PQ$, and $R$ be the point of intersection of the vertical line through $M$ with the parabola. Find the ratio of the area of the region bounded by the parabola and the line... | \dfrac{4}{3} |
[
{
"content": "Solve the equation $xe^{2x}=e^2$ algebraically without using the product logarithm.",
"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... | 1. change in tastes and preferences
2. Decrease in the prices of complementary goods
3. Fall in income levels
4. change in seasons |
[
{
"content": "Evaluate the limit \\( \\lim \\limits_{r \\to \\infty} \\frac {r^C \\int_0^{\\frac{\\pi}{2}} x^r \\sin(x)\\, dx}{\\int_0^{\\frac{\\pi}{2}} x^r \\cos(x)\\, dx} = L \\). Given that \\(C\\in\\mathbb{R}\\) and \\(L>0\\), find the value of \\(\\pi L - C\\).",
"role": "user"
}
] | 3 |
[
{
"content": "Determine whether the following statement is true or false: If a function $f:(a,b)\\to \\Bbb R$ has a limit at every point, then $f$ is bounded.",
"role": "user"
}
] | B |
[
{
"content": "Find all prime numbers \\( p \\) such that the last \\( p \\) digits of \\( p^p \\) form a prime number. It is known that \\( p = 433 \\) satisfies this condition. Are there any other such prime numbers?",
"role": "user"
}
] | 433 |
[
{
"content": "Given the system of equations:\n\\[\\begin{cases}\na + b + c = 1 \\\\\na^2 + b^2 + c^2 = 2 \\\\\na^3 + b^3 + c^3 = 3\n\\end{cases}\\]\nfind the value of \\(a^5 + b^5 + c^5\\).",
"role": "user"
}
] | 6 |
[
{
"content": "Determine \\( \\lim_{t\\to \\infty}\\int_{0}^{\\infty}e^{-tx}\\frac{\\sin x}{x}dx \\).",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -6.06e-12 C |
[
{
"content": "For any complex-valued, nonconstant, and differentiable function $f$, is it possible that \\( \\text{Im} \\int_0^1 f(x) \\, \\mathrm{d}x = \\text{Im} \\int_1^\\infty f(x) \\, \\mathrm{d}x \\)? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine if the function \\( g(x) = \\sum_{n=1}^\\infty \\frac{\\cos(nx^3)}{1+n^5} \\) has a continuous third derivative on \\( \\mathbb{R} \\).",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the number of distinct integral solutions to the equation \\(a \\times b \\times c \\times d = 600\\).",
"role": "user"
}
] | 6400 |
[
{
"content": "In how many ways can 81 be written as the sum of three positive perfect squares if the order of the three perfect squares does not matter?",
"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... | 32 dB |
[
{
"content": "Determine the approximate proportion of line segments with irrational lengths in an n by n lattice as n 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... | -9.95 kW |
[
{
"content": "Calculate the intersection multiplicity of the curves defined by $f(y, x) = y^2 - x^3$ and $g(y, x) = y^3 - x^7$ at the point $(0,0)$. Provide your answer as a single integer.",
"role": "user"
}
] | 9 |
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