prompt list | ground_truth string |
|---|---|
[
{
"content": "Determine the number of intersections between the graphs of the functions \\( y = x^2 - 3x + 1 \\) and \\( y = -\\cos x \\) within the interval \\([0, 2\\pi]\\) without graphing.",
"role": "user"
}
] | 2 |
[
{
"content": "Given a compact metric space $(X,d_X)$ and another metric space $(Y,d)$, where the metric capacity of $(Y,d)$ is at least that of $(X,d_X)$, i.e., \\( \\kappa_X(\\epsilon) \\leq \\kappa_Y(\\epsilon) \\) for all \\( \\epsilon \\in (0,1] \\), does there necessarily exist a continuous injection of $(... | 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... | 21.97 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... | 55.48% |
[
{
"content": "Sam decides to start a rumor. Sam tells the rumor to her three friends. Each of Sam's three friends then tells the rumor to three friends who have not heard the rumor. This continues for five total cycles. Sam telling her three friends was the first cycle. How many people, not including Sam, will ... | 363 |
[
{
"content": "Calculate the difference in the value of the integral \\( \\int _{|z|=1} \\frac{1}{z}dz \\) when the curve is traversed in a clockwise direction versus a counter-clockwise direction.",
"role": "user"
}
] | -4\pi i |
[
{
"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... | 0.22 m |
[
{
"content": "Given that $\\cos x - 4 \\sin x = 1,$ find all possible values of $\\sin x + 4 \\cos x.$",
"role": "user"
}
] | -4 |
[
{
"content": "Let $X$ be a real Banach space and $f:X\\to\\mathbb{R}$ be a continuous linear function. Suppose $(r_n)$ is a sequence of real numbers converging to some $r>0$. Define the sets $$H=\\{x\\in X:f(x)=r\\},$$ $$H_n=\\{x\\in X:f(x)=r_n\\}.$$ Prove or disprove: For any $z\\in H$, $d(z,H_n)\\to 0$ as $n ... | 0 |
[
{
"content": "Let \\( f \\) be the function defined for all \\((x,y)\\) as follows: \\[ f(x,y)= \\begin{cases} \\frac{xy(x^2-y^2)}{x^2+y^2}, &\\text{if }(x,y)\\ne(0,0)\\\\ 0, &\\text{if }(x,y)=(0,0) \\end{cases} \\] Determine the value of \\( \\frac{\\partial^2 f}{\\partial x \\partial y} \\) at \\((0,0)\\).",
... | 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... | $86,450 |
[
{
"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 resistance of A is 6.0 ohms, and the resistance of B is 3.0 ohms. |
[
{
"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... | 1.350 m |
[
{
"content": "Evaluate the line integral of the vector field \\( \\mathbf{F}(x,y) = x^2y^2 \\mathbf{\\hat{i}} + x^3y \\mathbf{\\hat{j}} \\) over the square with vertices (0,0), (1,0), (1,1), (0,1) in the counterclockwise direction. Calculate the integral by hand.",
"role": "user"
}
] | \dfrac{1}{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... | 2 J |
[
{
"content": "In triangle $ABC,$ $\\angle B = 30^\\circ,$ $AB = 150,$ and $AC = 50 \\sqrt{3}.$ Find the sum of all possible values of $BC.$",
"role": "user"
}
] | 150 \sqrt{3} |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n \\to \\infty} \\frac{n^{\\lg\\lg n}}{(3/2)^n} \\]",
"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... | -2237 J |
[
{
"content": "Given an integer lattice $\\mathcal{L}(B) = \\sum_{i=1}^n x_i B_i$ where $x_i \\in \\mathbb{Z}$ and $B = [b_1, b_2, ..., b_n]$ is a basis, determine whether a point $t \\in \\mathbb{R}^n$ that lies within the span of the lattice vectors is inside the fundamental parallelepiped of the lattice. Can ... | Yes |
[
{
"content": "Find the eigenvalues of the matrix $A = (p_{ij})$ where $\\sum_{i=1}^3 p_{ij} = 1$ for all $j = 1, 2, 3$. Assume $A$ is a $3 \\times 3$ matrix.",
"role": "user"
}
] | 1 |
[
{
"content": "Given a set \\( L = (1, 2, \\ldots, n) \\) where \\( n \\) is odd, and two functions defined as \\( f(L) = (3, 4, \\ldots, n, 1, 2) \\) and \\( g(L) = (3, 4, \\ldots, n, 2, 1) \\), is it possible to achieve any permutation of \\( L \\) through combinations of \\( f \\) and \\( g \\)?",
"role":... | 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... | -3.56e12 |
[
{
"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... | 1.36 m |
[
{
"content": "Evaluate the contour integral \\( \\int_{\\gamma}\\frac{\\mathrm{d}z}{z} \\) where \\( \\gamma \\) is a closed curve consisting of a circle centered at the origin traced counterclockwise and a square centered at the origin traced clockwise.",
"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... | $7,129,000 |
[
{
"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... | 10.80 |
[
{
"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... | 2.0e1 kJ/mol |
[
{
"content": "Evaluate the limit: $$\\displaystyle\\lim_{x\\to0}\\frac {(\\tan(x)-x)^2} {(\\ln(x+1)-x)^3} $$",
"role": "user"
}
] | -\dfrac{8}{9} |
[
{
"content": "Evaluate the limit: $$ \\lim_{t\\to 1^-} (1-t) \\sum_{n=0}^\\infty \\frac{t^n}{1+t^n} $$",
"role": "user"
}
] | \ln 2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 13.8 m/s |
[
{
"content": "The partial fraction decomposition of\n\\[\\frac{x^2 - 19}{x^3 - 2x^2 - 5x + 6}\\]is\n\\[\\frac{A}{x - 1} + \\frac{B}{x + 2} + \\frac{C}{x - 3}.\\]Find the product $ABC.$",
"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... | 80.00 g |
[
{
"content": "Consider two compactifications $(C_1, \\iota_1)$ and $(C_2, \\iota_2)$ of a locally compact Hausdorff space $X$, where $\\iota_1$ and $\\iota_2$ are topological embeddings with dense images. Determine whether a continuous map $\\pi : C_1 \\to C_2$ such that $\\pi \\circ \\iota_1 = \\iota_2$ must m... | Yes |
[
{
"content": "Determine the minimum layer width required for universal approximation in deep feedforward networks with ReLU activation function, given that the input dimension is $\\nu$. Provide your answer in terms of $\\nu$.",
"role": "user"
}
] | \nu + 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... | 295.73 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... | May 3: Received a bill from the law firm of Davenport Associates for $6,300, payable upon receipt, for bond consulting fees.
May 11: The Board of Directors declared a cash dividend of $7 per share for shareholders of record on May 13th, payable on May 17th. |
[
{
"content": "Evaluate the integral \\( \\int_{1}^{2}\\sqrt[3]{\\frac{2-x}{x^7}}\\,dx \\).",
"role": "user"
}
] | \dfrac{3}{8} |
[
{
"content": "What is the smallest positive four-digit integer equivalent to 6 mod 7?",
"role": "user"
}
] | 1000 |
[
{
"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... | 0.55 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... | implicit cost |
[
{
"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... | 0.0438 N m |
[
{
"content": "Find the expression for the optimal value of \\(\\alpha\\) in the capacitor charging equation to maximize the slope of the voltage curve at time \\(T\\).",
"role": "user"
}
] | \dfrac{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... | Fit the data to a quadratic equation of the form y(x)=Ax^2+Bx+C. The acceleration will be A/2. |
[
{
"content": "Consider a function \\( f: \\Bbb R\\rightarrow \\Bbb R \\) defined by \\[ f(x)=\\int_0^x f(t) ~\\mathrm dt. \\] Find the value of \\( f(\\ln(5)) \\).",
"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... | 34,500 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.62 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... | $8166.185 |
[
{
"content": "Find the expected value of the integral \\( \\int_0^t B(s)^2 \\, ds \\), where \\( B(s) \\) is a standard Brownian motion.",
"role": "user"
}
] | \dfrac{t^2}{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... | 13.0 |
[
{
"content": "Find the number of positive integers \\( n \\) not greater than 2021 that satisfy the condition:\n\\[ \\left(\\lfloor \\sqrt{n} \\rfloor^2 + 1\\right) \\mid \\left(n^2 + 1\\right). \\]",
"role": "user"
}
] | 46 |
[
{
"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... | 1.28 kJ/mol |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\rightarrow\\infty} \\left(\\frac{\\ln 2}{2}+\\frac{\\ln 3}{3}+\\cdots + \\frac{\\ln n}{n} \\right)^{\\frac{1}{n}}$$",
"role": "user"
}
] | 1 |
[
{
"content": "Let $V$ be a vector space with $\\dim(V)=n$. If a linear operator $T: V \\rightarrow V$ has $n-2$ distinct eigenvalues, determine the maximum possible dimension of $\\ker(T)$. \\( \\text{Express your answer as a single number.} \\)",
"role": "user"
}
] | 3 |
[
{
"content": "Is a real, symmetric, and positive semidefinite matrix with all eigenvalues equal to 1 necessarily the identity matrix?",
"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... | $6,158.08 |
[
{
"content": "Calculate the 2022nd derivative of the function \\( f(x) = x^{2019} \\cos(x) \\) at \\( x = 0 \\).",
"role": "user"
}
] | 0 |
[
{
"content": "In a doctor's clinic, patients arrive at an average rate of 10 per hour. The consultation time per patient is exponentially distributed with an average of 6 minutes per patient. The doctor does not admit any patient if at any time 10 patients are waiting. Calculate the expected number of patients ... | \dfrac{55}{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... | C2 |
[
{
"content": "Consider the space $K(X)$ of all non-empty compact subsets of a metrizable space $X$, equipped with the topology from the Hausdorff metric. Suppose $K_n \\in K(X)$ is a sequence such that $K_1 \\supseteq K_2 \\supseteq \\ldots$. Show that $\\lim\\limits_{n \\to \\infty} K_n = \\bigcap\\limits_{n=1... | E_{\frac{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... | 4.42e-8 C |
[
{
"content": "Compute the limit: $$ \\lim_{x\\to\\infty} \\left( \\frac{x^2+x+1}{3x^2+2x+1} \\right) ^{\\left( \\frac{3x^2+x}{x-2} \\right)} $$",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the integral \\( \\int_{-\\infty}^{\\infty} xe^{-2\\lambda |x|} \\, dx \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n \\to \\infty} \\frac{(2^n)!}{2^{n!}} \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Find the median of the random variable $Y = e^Z$, where $Z$ is a standard normal distribution ($Z \\sim N(0,1)$).",
"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... | 5.52% |
[
{
"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... | $1,001,605 |
[
{
"content": "Determine the number of solutions to the congruence equation \\(x^2 \\equiv -1211 \\pmod{2020}\\).",
"role": "user"
}
] | 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... | 257.60 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... | humanistic approaches |
[
{
"content": "Determine whether the following statement is true or false: If a sequence of independent and identically distributed random variables $X_n$ converges almost surely, then it converges to a constant.",
"role": "user"
}
] | True |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 105300 |
[
{
"content": "Find the value of \\( r \\), where \\( r > \\frac{1}{2} \\), such that two non-vertical normal lines from the point \\((r, 0)\\) to the parabola \\(x = y^2\\) intersect perpendicularly. One of these normal lines is the x-axis. The derivative of the parabola is \\(\\frac{dy}{dx} = \\frac{1}{2\\sqrt... | \dfrac{3}{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... | 354.27 kW |
[
{
"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... | 0.1337 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... | 18m |
[
{
"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... | 1369.773 kJ |
[
{
"content": "In a random graph with $n$ nodes, where each node is connected to $k$ randomly chosen nodes, determine the probability that the graph is connected if $k = \\frac{\\log n + c}{n}$, where $c$ is a constant that tends to 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... | 35 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... | $1,698,500.00 |
[
{
"content": "Let $X$ be a topological manifold and let $\\{Y_i : Y_i\\subset X\\}$ be a finite family of pairwise disjoint submanifolds of $X$. If the union $\\bigcup_i Y_i$ is an open submanifold in $X$, does this imply that there is at least one $Y_i$ which is an open submanifold in $X$? Answer yes or no.",
... | 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... | 19.32 Units |
[
{
"content": "Determine whether a subset of real numbers with a non-empty interior always has a boundary with non-zero measure. Provide a justification for your answer.",
"role": "user"
}
] | No |
[
{
"content": "Consider a sequence \\((x_1, x_2, \\ldots)\\) generated by sampling uniformly and independently from the integers \\(\\{0, 1, 2, \\ldots, 9\\}\\). From this sequence, construct the real number \\(x = 0.\\overline{x_1x_2x_3\\ldots}\\). What is the probability that \\(x\\) is a rational number?",
... | 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... | 14.75% |
[
{
"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... | 81.55 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... | 1.55e-36 |
[
{
"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... | \(x'=\sqrt{\frac{b}{n_0^2(1+\alpha y)^2-b}}\) |
[
{
"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... | 6.2e6 m/s |
[
{
"content": "Find the radius of convergence for the power series \\( \\sum a_n x^n \\) given that \\( \\lim\\sup |a_n| \\) is a finite, positive number.",
"role": "user"
}
] | 1 |
[
{
"content": "Let $A$ be a Lebesgue measurable subset of $\\mathbb{R}$ with $m(A) < \\infty$, where $m$ denotes the Lebesgue measure. Given $\\epsilon > 0$, does there exist an open set $G$ and a closed set $F$ such that $F \\subset A \\subset G$ and $m(G - F) < \\epsilon$?",
"role": "user"
}
] | Yes |
[
{
"content": "Given a function $f: \\mathbb{R} \\to \\mathbb{R}$ defined as $f(x) = 4x$ for rational numbers $x$ and $f(x) = x + 6$ for irrational numbers $x$, let $E = \\{x \\in \\mathbb{R} \\mid f \\text{ is continuous at } x\\}$. Determine all the limit points of the set $E$. Provide your answer as a set of ... | \emptyset |
[
{
"content": "Calculate the value of the double summation \\( \\sum\\sum_{1\\leq i<j\\leq 100} (\\alpha_i\\alpha_j)^5 \\), where \\( \\alpha_1, \\alpha_2, \\dots, \\alpha_{100} \\) are the 100th roots of unity.",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the values of $p$ for which the limit \\( \\lim_{n \\to \\infty} \\left( 1 + \\frac{1}{n^p} \\right)^{n^p} \\) equals $e$.",
"role": "user"
}
] | p > 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... | 0.0066 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... | 4.47 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... | Balance Sheet on December 31, 2015
ASSETS
Current Assets
Cash $5,000
Accounts receivable $28,500
Office supplies $7,178
Total Current Assets $40,678
Long-Term Assets
Land $43,000
Vehicles $199,000
Less: Accumulated depreciation $(40,994)
Total Long-Term Assets $201,006
Total assets $241,684
LIABILITIES
Current Liabilities
Accounts payable $9,000
Interest payable $14,000
Total Current Assets $23,000
Long-Term Liabilities
Notes Payable $43,000
Total Long-Term Liabilities $43,000
OWNER'S EQUITY
Capital Account $175,684
Total owner's equity $175,684
Total liabilities and equity $241,684 |
[
{
"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... | 6.45e5 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... | 5.25e5 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... | $30,260 |
[
{
"content": "Given that \\((1+(2/3)x)^n \\cdot (3+nx)^2 = 9+84x+\\dotsb\\), find the value of \\( n \\).",
"role": "user"
}
] | 7 |
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