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... | 1.37e-1 T |
[
{
"content": "Let $b$ be an integer greater than 2, and let $N_b = 1_b + 2_b + \\cdots + 100_b$ (the sum contains all valid base $b$ numbers up to $100_b$). Compute the number of values of $b$ for which the sum of the squares of the base $b$ digits of $N_b$ is at most 512.",
"role": "user"
}
] | 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... | 0.32 J |
[
{
"content": "Find the limit of the sequence \\((a_n)_{n \\ge 1}\\) given that the sequence \\(1 + \\dfrac{1}{2} + \\dfrac{1}{3} + \\ldots + \\dfrac{1}{n} - a_n \\ln n\\) is bounded for \\(n \\ge 1\\).",
"role": "user"
}
] | 1 |
[
{
"content": "An arbitrary point \\( E \\) is located inside square \\( ABCD \\) with side length 1. Line segments connect \\( E \\) to each vertex of the square. Let \\( P, Q, F, \\) and \\( T \\) be the intersection points of the medians of triangles \\( BCE, CDE, DAE, \\) and \\( ABE \\) respectively. Determ... | \dfrac{2}{9} |
[
{
"content": "Find all integer values of $n$ such that $3n - 4$, $4n - 5$, and $5n - 3$ are all prime numbers.",
"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... | 17.18% |
[
{
"content": "Let $\\{x_n\\}$ be a real sequence that satisfies $|x_{n+1} - x_n| < \\frac{1}{n^2}$ for all $n \\geq 1$. If $\\{x_n\\}$ is bounded, does it imply that $\\{x_n\\}$ converges? Provide a justification for 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... | 1.76 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... | 1xx10^30*kg |
[
{
"content": "Evaluate the limit: $$\\lim_{M\\to \\infty} \\frac{\\cos[\\omega(M+1/2)]}{2\\sin(\\omega/2)}$$ where $\\omega\\in\\mathbb{R}$ and $M\\in\\mathbb{Z}$. Determine whether this limit holds.",
"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... | FClO2 |
[
{
"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... | 1640 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... | 3920L |
[
{
"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... | 6267.49 |
[
{
"content": "Determine whether the subspace of continuous functions $C[0,1]$ with $f(0)=0$ is closed under the metric $$ d(f,g) = \\max|f(x)-g(x)|. $$",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the values of $n$ for which the expression \\( \\frac{(n^2)!}{(n!)^{n+1}} \\cdot \\frac{n!}{n^2} \\) is an integer, given that \\( \\frac{n!}{n^2} \\) is not an integer.",
"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... | I = (0.6618 A/T) B |
[
{
"content": "Determine the number of ordered pairs \\((X, Y)\\) of \\(n \\times n\\) matrices such that \\(XY - YX = I\\). Choose the correct option: \\(0\\), \\(1\\), \\(n\\), \\(\\infty\\).",
"role": "user"
}
] | 0 |
[
{
"content": "Compute the total variation of the function \\( f(x) = \\begin{cases} 1 + \\sin(x), & \\text{if } x \\in \\left[-\\frac{\\pi}{4}, \\frac{\\pi}{4}\\right] \\\\ -\\frac{1}{2}, & \\text{otherwise} \\end{cases} \\) on the interval \\([-\\frac{\\pi}{4}, \\frac{\\pi}{4}]\\).",
"role": "user"
}
] | \sqrt{2} |
[
{
"content": "Find the equation of the line from the family of lines given by \\( a(3x+4y+6)+b(x+y+2)=0 \\) that is at the maximum distance from the point \\( P(2,3) \\).",
"role": "user"
}
] | 4x + 3y + 8 = 0 |
[
{
"content": "Calculate the integral \\( \\int_{[0,1]} f \\, dm \\) where the function \\( f: [0,1] \\to \\mathbb{R} \\) is defined as follows: \\( f(x) = 0 \\) for \\( x \\in \\mathcal{C} \\), the Cantor set, and \\( f(x) = k \\) for every \\( x \\) in each interval of length \\( \\frac{1}{3^k} \\) that has be... | 3 |
[
{
"content": "On a plane, there are $2n+3$ points, no three of which are collinear and no four of which are concyclic. Determine whether there exists a circle that passes through any three of these points and bounds a disk inside which exactly half of the remaining points lie.",
"role": "user"
}
] | Yes |
[
{
"content": "Calculate \\(1^1 + 2^2 + \\cdots + 99^{99} \\pmod{3}\\). Justify your answer.",
"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... | 2.225 N |
[
{
"content": "Is the ring of holomorphic functions on a compact Riemann surface integrally closed?",
"role": "user"
}
] | Yes |
[
{
"content": "Compute the line integral \\( \\int_C ze^{\\sqrt{x^2+y^2}} \\, ds \\) where \\( C \\) is the curve of intersection of the sphere \\( x^2 + y^2 + z^2 = a^2 \\) and the plane \\( x + y = 0 \\), with \\( a > 0 \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Consider a function $f: A \\to \\mathbb{R}$, where $A$ is a closed interval. If $f$ is continuous, does it follow that the restriction $f: A \\to f(A)$ is also continuous when $f(A)$ is equipped with the subspace topology?",
"role": "user"
}
] | Yes |
[
{
"content": "Suppose $\\Omega$ is open in $\\mathbb{R}^N$ and $u \\in BV(\\Omega)$ such that $u = 0$ on an open subset $E \\subseteq \\Omega$. If $D_i u$ denotes the $i$-th partial derivative measure associated with $u$, does it hold that $D_i u(E) = 0$?",
"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... | 30 cm |
[
{
"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... | 4.90 |
[
{
"content": "Determine the minimum number of pairs \\((x, R(x))\\) required to fully characterize a rotation \\(R\\) in \\(\\mathbb{R}^n\\).",
"role": "user"
}
] | n-1 |
[
{
"content": "In the permutation group $S_n$ with $7 \\leq n \\leq 10$, consider subgroups $H_1$ and $H_2$ where $H_1 \\cong S_k$ and $H_2 \\cong S_{n-k}$. If every element of $H_1$ commutes with every element of $H_2$, are $H_1$ and $H_2$ the stabilizers of $n-k$ and $k$ letters, respectively? Answer true or f... | 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... | 503 nm |
[
{
"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... | 4.95 m/s |
[
{
"content": "Determine the number of elements in the set \\( \\{z \\in \\mathbb{C} : z^{60} = -1 , z^k \\neq -1, 0<k<60 \\} \\).",
"role": "user"
}
] | 32 |
[
{
"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... | $38,000 |
[
{
"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... | $268000 |
[
{
"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^{+}(aq) + MgCO_{3}(s) \rightarrow H_{2}O(l) + CO_{2}(g) + Mg^{2+}(aq) |
[
{
"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... | 6.0% |
[
{
"content": "Consider the space $\\ell^{\\infty}$ and the $\\lim$ functional defined on the subspace of convergent sequences. Is the extension of this functional, which assigns zero to all non-convergent sequences, a bounded functional on $\\ell^{\\infty}$?",
"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... | Liabilities:
Common stock: $119,901
Retained Earnings: $43,743
Long term debt: $80,207
Other noncurrent liabilities: $42,580
Accounts payable: $74,633
Short term debt: $210
Total liabilities: $361,274
Assets:
Plant, property and equipment: $192,465
Long term Investment: $22,331
Goodwill: $48,347
Other noncurrent asset... |
[
{
"content": "Identify the function(s) that is(are) the k-th derivative of itself for any natural number k.",
"role": "user"
}
] | Ce^x |
[
{
"content": "What is the measure of angle 4 if $m\\angle 1 = 76^{\\circ}, m\\angle 2 = 27^{\\circ}$ and $m\\angle 3 = 17^{\\circ}$?\n\n[asy]\ndraw((0,0)--(4,8)--(10,0)--cycle,linewidth(1));\ndraw((0,0)--(5,3)--(10,0),linewidth(1));\nlabel(\"2\",(1,1.2));\nlabel(\"1\",(4,7.75),S);\nlabel(\"4\",(5,3),S);\nlabel(... | 120^{\circ} |
[
{
"content": "Simplify the expression \\(\\frac{2 a \\sqrt{1+x^{2}}}{x+\\sqrt{1+x^{2}}}\\) given that \\(x=\\frac{1}{2} \\cdot\\left(\\sqrt{\\frac{a}{b}} - \\sqrt{\\frac{b}{a}}\\right)\\) and \\(a>0, b>0\\).",
"role": "user"
}
] | a + b |
[
{
"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... | Retained Earnings: $400,000
Common Stock Dividend Distributable: $50,000
Paid in capital in excess of par - Common Stock: $350,000 |
[
{
"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... | -$154,000 |
[
{
"content": "Find the ordered pair $(a,b)$ of positive integers, with $a < b,$ for which\n\\[\\sqrt{1 + \\sqrt{21 + 12 \\sqrt{3}}} = \\sqrt{a} + \\sqrt{b}.\\]",
"role": "user"
}
] | (1,3) |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\to\\infty}\\frac{2^n}{n^{\\sqrt{n}}}$$",
"role": "user"
}
] | \infty |
[
{
"content": "Find the limit of the infinite product: \\[ \\lim_{n\\to+\\infty} \\prod_{k=2}^{n} \\left(1-\\frac{1}{k^2}\\right) \\]",
"role": "user"
}
] | \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... | 7.1 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... | $10,446.50 |
[
{
"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... | 3.663 |
[
{
"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... | 6.69e-5 M |
[
{
"content": "Determine whether there exists a non-zero function \\( f(x) \\in L^2(0,1) \\) such that \\[ \\int_{1}^{\\infty}\\frac{f(\\frac{1}{t})}{t}dt - \\sum_{k=1}^{\\infty}k\\int_{k}^{k+1}\\frac{f(\\frac{1}{t})}{t^2}dt = 0. \\]",
"role": "user"
}
] | Yes |
[
{
"content": "Let $S$ be the set of integers between $1$ and $2^{40}$ whose binary expansions have exactly two $1$'s. If a number is chosen at random from $S,$ the probability that it is divisible by $9$ is $p/q,$ where $p$ and $q$ are relatively prime positive integers. Find $p+q.$",
"role": "user"
}
] | 913 |
[
{
"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... | Neither |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 10.01 |
[
{
"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... | Particulars | Amount($)
---|---
Assets: |
Current assets: |
Cash | 150,000
Investments in common stock | 80,000
Accounts receivable | 170,000
Less: Allowance for doubtful accounts | 10,000
Inventories | 180,000
Total current assets | 570,000
Investments: |
Investments in common stock | 270,000
Land held for future use... |
[
{
"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... | 1631A kg |
[
{
"content": "Are random variables with identical moment generating functions necessarily identical almost everywhere? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "There is an angle $\\theta$ in the range $0^\\circ < \\theta < 45^\\circ$ which satisfies\n\\[\\tan \\theta + \\tan 2 \\theta + \\tan 3 \\theta = 0.\\]Calculate $\\tan \\theta$ for this angle.",
"role": "user"
}
] | \frac{1}{\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... | $28.59 |
[
{
"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... | $3,635 |
[
{
"content": "Determine the radius of convergence for the power series \\( \\sum \\frac{n! z^n}{n^n} \\).",
"role": "user"
}
] | 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... | $1,437,500 |
[
{
"content": "Determine the function \\( h(t) \\) for the partial differential equation \\( u_{xt}(x,t) + u(x,t)u_{xx}(x,t) = h(t) \\) with the boundary conditions \\( u(\\pi,t) = u_x(0,t) = u_x(\\pi,t) = 0 \\), where \\( x \\in [0,\\pi] \\) and \\( t > 0 \\). Assume all computations and regularity conditions a... | 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... | 4 years |
[
{
"content": "What is the smallest number of tetrahedrons needed to partition a cube?",
"role": "user"
}
] | 5 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5.30 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... | 39.24 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... | 0.503 |
[
{
"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... | 2.22 |
[
{
"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... | 2314860 Pa |
[
{
"content": "Determine all pairs of prime numbers \\(p\\) and \\(q\\) such that \\(p^3 + 19q^3 + 2018\\) is a perfect cube.",
"role": "user"
}
] | (3, 2) |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 402.5 mm/s^2 |
[
{
"content": "For a given integer \\( n \\), determine the number of ways \\( n! \\) can be expressed as a product of factorials of smaller integers, \\( a_1!a_2!\\cdots a_n! \\). Define this function as \\( \\Omega(n) \\). Calculate \\( \\Omega(10) \\).",
"role": "user"
}
] | 2 |
[
{
"content": "Given the curve \\( y = x^4 + Ax^3 + Bx^2 + Cx + D \\) and a line \\( y = px + q \\), where \\( A, B, C, D, p, q \\in \\mathbb{R} \\), the curve touches the line at \\( x = 2 \\) and \\( x = 3 \\). Determine the area enclosed between the curve and the line, which is denoted by \\( \\frac{1}{\\alph... | 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... | 1.96 |
[
{
"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... | 8.41m |
[
{
"content": "Find the eccentricity of the conic given by the equation:\n\\[ \\left(x\\tan 10^\\circ+y\\tan 20^\\circ+\\tan 30^\\circ\\right)\\left(x\\tan 120^\\circ+y\\tan 220^\\circ+\\tan 320^\\circ\\right)+2018=0 \\]",
"role": "user"
}
] | \sqrt{2} |
[
{
"content": "What is the maximal number of elements in a sigma-algebra generated by a collection of N subsets of a set X?",
"role": "user"
}
] | 2^{2^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... | 3 x 10^8 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... | 0.34 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $218,181.82 |
[
{
"content": "If a real matrix $A$ has a complex eigenvector $x + iy$, does it necessarily have a real eigenvector? Answer yes or no.",
"role": "user"
}
] | No |
[
{
"content": "Find the natural number \\( x = 2^n - 32 \\) such that \\( x \\) has exactly three distinct prime factors, one of which is 3. Determine the value of \\( x \\).",
"role": "user"
}
] | 480 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 10.24 W |
[
{
"content": "Find the area bounded by the curve given by the parametric equations \\( y = a(1 - \\cos t) \\) and \\( x = a(t - \\sin t) \\) and the x-axis.",
"role": "user"
}
] | 3\pi a^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... | 400 ft |
[
{
"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... | Common Stock: $40,000
Paid-in capital in excess of par value - Common: $60,000
Preferred Stock: $100,000
Retained Earnings: $75,000
Total Stockholders' Equity: $275,000 |
[
{
"content": "Find the minimum value of the expression \\(\\sqrt{2x^2+2x+1} +\\sqrt{2x^2-10x+13}\\) and express it in the form \\(\\sqrt{\\alpha}\\), where \\(\\alpha\\) is a positive integer.",
"role": "user"
}
] | \sqrt{20} |
[
{
"content": "Find all functions $f(t)$ such that for all $x$, the equation \\[ \\int_0^x f(t) \\, dt + \\int_{x}^1 f(t) \\, dt = \\int_x^1 f(t) \\, dt + \\int_x^1 f(t) \\, dt \\] holds true.",
"role": "user"
}
] | 0 |
[
{
"content": "Two candidates, $c_1$ and $c_2$, each receive $p$ votes at the end of a ballot. Assuming each sequence of votes is equally likely, what is the probability that candidate $c_2$ has never been ahead of candidate $c_1$ during the vote counting process?",
"role": "user"
}
] | \dfrac{1}{p+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... | 1.40 m/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... | 19 m |
[
{
"content": "Evaluate the integral: $$ \\int_{-\\pi/2}^{\\pi/2} \\frac{1}{2007^x+1}\\cdot \\frac{\\sin^{2008}x}{\\sin^{2008}x+\\cos^{2008}x}dx $$",
"role": "user"
}
] | \dfrac{\pi}{4} |
[
{
"content": "Determine whether every invertible linear operator on a finite-dimensional vector space over a finite field of characteristic $p$ satisfies $T^{p(p-1)} = I$, where $I$ is the identity operator.",
"role": "user"
}
] | False |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\to 1 }\\left( \\frac{x-1-x\\ln x }{x(x-1)^{2}}\\right) \\] without using L'Hopital's rule.",
"role": "user"
}
] | -\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... | 127550.833 N |
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