prompt list | ground_truth string |
|---|---|
[
{
"content": "Determine whether the maximum value of the function \\( f_k = (x-1)\\,e^{(x-1)^k-x^k} \\) decreases as \\( k \\) increases.",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit: $$\\lim_{(x,y,z) \\to (0,0,0)} \\frac{x^2y^2z^2}{(x^2+y^2+z^2)^2}$$",
"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... | V=mv^2/2e |
[
{
"content": "Use the method of Lagrange multipliers to find the maximum value of the function \\( f(x,y,z) = 25x^{\\frac{2}{5}}y^{\\frac{1}{5}}z^{\\frac{1}{5}} \\) subject to the constraint \\( 24000 = 80x + 12y + 10z \\).",
"role": "user"
}
] | 2310 |
[
{
"content": "Calculate the Gaussian curvature $K$ for the set $S = \\{(x,y) \\in \\mathbb{R}^2 \\mid x^2 + y^2 < 1\\}$, given that the first fundamental form is $ds^2 = \\frac{4}{(1-x^2-y^2)^2}(dx^2 + dy^2)$. The coefficients of the first fundamental form are $E = G = \\frac{4}{(1-x^2-y^2)^2}$ and $F = 0$. Exp... | -1 |
[
{
"content": "Determine the values of $T$ for which the differential equation $x''(t) = -x(t)$ has non-unique solutions given the boundary conditions $x(0) = a_1$ and $x(T) = a_2$.",
"role": "user"
}
] | T = n\pi |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 12.6 |
[
{
"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... | $39,010 |
[
{
"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... | 8160689693 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... | 108.3 N/m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | co-dependent relationship |
[
{
"content": "Find the sum of the series \\( \\sum_{n=2}^{\\infty} \\frac{\\binom{n}{2}}{4^n} \\) using generating functions.",
"role": "user"
}
] | \dfrac{4}{27} |
[
{
"content": "Find all functions \\( g : \\mathbb{R} \\to \\mathbb{R} \\) that satisfy the functional equation: \\[ x(g(x+y)-g(x))=y(g(x+y)-g(y)) \\; \\forall x , y \\in \\mathbb{R}. \\]",
"role": "user"
}
] | g(x) = ax + 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... | 2.14e-7 m^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... | $692,000 |
[
{
"content": "In an isosceles triangle \\(ABC\\) with \\(AB = BC\\), the altitude \\(AF\\) intersects the altitude \\(BD\\) at point \\(O\\), such that \\(\\frac{BO}{OD} = h\\). Determine the ratio in which the angle bisector \\(AE\\) divides the altitude \\(BD\\).",
"role": "user"
}
] | \sqrt{h + 2} |
[
{
"content": "What is the minimal Hamming distance of the concatenated word $R$, where $R$ is formed by concatenating a word $M$ of size $n^2$ bits (organized into an $n \\times n$ matrix with $n > 3$) and the encoded main diagonal $B$ using a Hamming code with a minimal distance of 3, given that $M$ is unencod... | 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... | 24.2 kg |
[
{
"content": "Let \\((X_i)_{i=1}^{20}\\sim N_6(\\mu,\\Sigma)\\). Determine the distribution of the quadratic form \\((X_1-\\mu)^T\\Sigma^{-1}(X_1-\\mu)\\).",
"role": "user"
}
] | \chi^2_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... | K_2SO_3(aq)+2HNO_3(aq) o 2KNO_3(s)+SO_2(g)+H_2O(l) |
[
{
"content": "A triangle has side lengths 7, 8, and 9. There are exactly two lines that simultaneously bisect the perimeter and area of the triangle. Let $\\theta$ be the acute angle between these two lines. Find $\\tan \\theta.$\n\n[asy]\nunitsize(0.5 cm);\n\npair A, B, C, P, Q, R, S, X;\n\nB = (0,0);\nC = ... | 3 \sqrt{5} + 2 \sqrt{10} |
[
{
"content": "For a unit octahedron defined by \\(O^2 = \\{(x,y,z): |x|+|y|+|z|=1\\}\\), consider the set \\(L(r) = \\{(x,y,z) \\in O^2: P(x,y,z)=r\\}\\), where \\(P(x,y,z)\\) is the sum of the positive coordinates of \\((x,y,z)\\). Given \\(r \\in (0,1)\\), determine the length of \\(L(r)\\). Are these lengths... | 3\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... | 11.2 |
[
{
"content": "Is the space of simple predictable processes, topologized by uniform convergence, metrizable?",
"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... | 3.636 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... | 24,200,000 |
[
{
"content": "Let $K$ be an algebraically closed field and $n$ be an integer. Let $M$ be a maximal ideal of the polynomial ring $K[X_1,...,X_n]$. The quotient ring $K[X_1,...,X_n]/M$ is a field and isomorphic to $K$. Does there exist an isomorphism of fields $\\sigma: K[X_1,...,X_n]/M \\to K$ such that for all ... | 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... | 11.46% |
[
{
"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... | 51184.9g |
[
{
"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... | 7.95% |
[
{
"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... | 1.0 |
[
{
"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... | Equivalent Units:
Materials: 150,000
Conversion Costs: 140,000
Unit Costs:
Materials: $1.60
Conversion Costs: $0.75
Total: $2.35 |
[
{
"content": "Let $\\mathbf{P}$ be the matrix for projecting onto the vector $\\begin{pmatrix} 4 \\\\ -7 \\end{pmatrix}.$ Find $\\det \\mathbf{P}.$",
"role": "user"
}
] | 0 |
[
{
"content": "Let \\( f(x) = [n + p \\sin x] \\), where \\( x \\in (0, \\pi) \\), \\( n \\in \\mathbb{Z} \\), \\( p \\) is a prime number, and \\([x]\\) represents the greatest integer less than or equal to \\(x\\). Find the number of points at which \\( f(x) \\) is not differentiable. Choose the correct answer... | D |
[
{
"content": "Given the function \\( f(x) = \\sin x + \\cos x \\), you are allowed to write the derivative of any previously written function, as well as the sum and product of any two previously written functions. This process can be repeated multiple times. Determine the constant \\( c \\) such that a functio... | 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... | 6.545% |
[
{
"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... | 0.778 mL |
[
{
"content": "Compute the derivative \\( f'(e^{i 2\\pi/3}) \\) for the function \\( f(z) = z^{1/4} \\), where the branch is defined in \\( \\mathbb{C} - (\\infty,0] \\) and satisfies \\( f(1) = -i \\).",
"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... | 60.13 g |
[
{
"content": "Find the remainder when \\(5^{5^{5^{5^{5^{5^5}}}}}\\) is divided by 125.",
"role": "user"
}
] | 0 |
[
{
"content": "Derive the expressions for the dual 1-forms $θ_1, θ_2, θ_3$ in terms of $dx, dy, dz$ given the cylindrical frame field $E_1, E_2, E_3$, without using the cylindrical equations.",
"role": "user"
}
] | \theta_1 = \frac{x \, dx + y \, dy}{\sqrt{x^2 + y^2}}, \quad \theta_2 = \frac{-y \, dx + x \, dy}{\sqrt{x^2 + y^2}}, \quad \theta_3 = dz |
[
{
"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... | 52.07 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... | 8165 |
[
{
"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... | 3.88% |
[
{
"content": "Given the function \\( g = \\sqrt{1+\\dot{x}^2} \\), where \\( \\dot{x} \\) is a function of time, simplify the Euler-Lagrange equation:\n\\[ \\frac{\\partial g}{\\partial x} - \\frac{d}{dt} \\left[ \\frac{\\partial g}{\\partial \\dot{x}} \\right] = 0 \\]\nto show that \\( \\ddot{x} = 0 \\).",
... | \ddot{x} = 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... | 3Fe_3O_4 + 8Al -> 4Al_2O_3 + 9Fe |
[
{
"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... | 2.24cm |
[
{
"content": "Let $\\Omega$ be a bounded domain in $\\mathbb{R}^N$, $N\\geq 2$. Let $u\\in W^{1,p}(\\Omega)$, the class of all measurable functions $u:\\Omega\\to\\mathbb{R}$ such that \\( \\|u\\|_{W^{1,p}(\\Omega)}:=\\|u\\|_{L^p(\\Omega)}+\\|\\nabla u\\|_{L^p(\\Omega)}<\\infty. \\) Let $1<q<p^*=\\frac{Np}{N-p}... | No |
[
{
"content": "Determine whether every completely metrizable normed vector space is a Banach space. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Let $f: \\mathbb{R} \\to \\mathbb{R}$ be a function such that $$(f \\circ f \\circ f)(x) = (f \\circ f)(x) + x$$ for every $x \\in \\mathbb{R}$. Compute $f(0)$. \\( \\boxed{} \\)",
"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... | $62.69 |
[
{
"content": "Determine if the property (*) is preserved for metrics that are Lipschitz equivalent to $d_1$.",
"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... | 68 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... | 10000 |
[
{
"content": "Evaluate \\( \\Delta z \\) along the path \\( y = x^2 \\) from the point \\((0,0)\\) to \\((1,1)\\). Given the differential \\( dz = xydx + xydy \\), find the change in \\( z \\) as you move from \\((0,0)\\) to \\((1,1)\\) along the path \\( y = x^2 \\).",
"role": "user"
}
] | \dfrac{13}{20} |
[
{
"content": "Assume $f,g\\colon [0,1]\\to [0,1]$ are continuous functions such that $g(0)<f(0)$ and $g(1)>f(1)$. Determine if there exists a smallest $t\\in(0,1)$ such that $g(t)\\geq f(t)$. 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... | 357 g Cu2S |
[
{
"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... | 10.0 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... | 4.74e-3 ohm |
[
{
"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... | $27,500 |
[
{
"content": "Determine the number of elements of order 10 in the symmetric group $S_{10}$. Provide your answer as a single integer.",
"role": "user"
}
] | 514080 |
[
{
"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... | 21.4 atm |
[
{
"content": "Does the Hilbert cube have the fixed point property for continuous functions?",
"role": "user"
}
] | Yes |
[
{
"content": "Compute $\\sin 600^\\circ$.",
"role": "user"
}
] | -\frac{\sqrt{3}}{2} |
[
{
"content": "A company has $n$ workers. The company is creating subdivisions and distributes the workers among these subdivisions. Each subdivision must have an odd number of workers, and the intersection of workers from any two subdivisions must be even, including the possibility of being zero. What is the ma... | 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... | 17.45 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | E=\frac{3kqd^2}{r^4} |
[
{
"content": "Determine whether $\\aleph_0^{\\aleph_0} = 2^{\\aleph_0}$ or $\\aleph_0^{\\aleph_0} > 2^{\\aleph_0}$. Justify your answer.",
"role": "user"
}
] | \aleph_0^{\aleph_0} = 2^{\aleph_0} |
[
{
"content": "In a discrete random walk starting at $x=0$ with equal probabilities of moving left or right, what is the probability that the particle will visit every point in the interval $[-n,n]$ infinitely many times?",
"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... | 2WO3 + 2H+ + 2e- --> W2O5 + H2O |
[
{
"content": "Consider the affine surface $X \\subset \\mathbb{C}^3$ defined by $z = x^a y^b$, where $(x, y, z)$ are coordinates on $\\mathbb{C}^3$. On this surface, the divisor $D = \\{z = 0\\} = a \\cdot \\{x = 0\\} + b \\cdot \\{y = 0\\}$. Given the map $\\phi: \\mathbb{C}^3 \\to \\mathbb{C}^3$, $(x, y, z) \... | pD |
[
{
"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... | liver failure |
[
{
"content": "Determine whether the statement \"Every saddle point is an isolated critical point\" is true or false.",
"role": "user"
}
] | B |
[
{
"content": "Determine the largest real number \\(\\alpha\\) such that for any positive integers \\(m\\) and \\(n\\) with \\(\\frac{m}{n} < \\sqrt{7}\\), the inequality \\(\\frac{\\alpha}{n^{2}} \\leq 7 - \\frac{m^{2}}{n^{2}}\\) holds.",
"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... | 3.27 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... | 8.33 s |
[
{
"content": "Minimize the expression \\( \\sqrt{2x^2+2x+1} + \\sqrt{2x^2-10x+13} \\) subject to the constraint \\( y = x \\).",
"role": "user"
}
] | 2\sqrt{5} |
[
{
"content": "Evaluate the limit \\( \\lim_{(x, y)\\to (0,0)}\\frac{y^3}{x^4+\\sin^2y} \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Consider a holomorphic homeomorphism $f: U \\rightarrow U$ of the unit disc $U$. Must $f$ extend to a continuous map $f: \\overline{U} \\rightarrow \\overline{U}$? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Consider the function $f: \\mathbb{R^2} \\rightarrow \\mathbb{R}$ defined by\n$$f(x, y) = \\begin{cases} \\dfrac{xy}{x^2 + y}, & x^{2} \\neq -y\\\\ 0, & x^2 = y \\end{cases} $$\nDetermine which of the following properties holds at the point $(0, 0)$:\n\nA) The directional derivative does not exist... | D |
[
{
"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... | 166.5 |
[
{
"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... | $O(n\operatorname{log} \operatorname{log} n)$ |
[
{
"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... | $42.68 |
[
{
"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... | 80867 N/m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | {eq}s = 3.49\times10^2 (\frac{r_b}{r_a}) \ m{/eq} |
[
{
"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... | 700.9635 km/h |
[
{
"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... | sequential research method |
[
{
"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... | R_T = \frac{(R_2 + \frac{R_4 * R_5}{R_4+R_5}) * R_3}{R_2 + \frac{R_4 * R_5}{R_4+R_5} + R_3} + R_1 |
[
{
"content": "Let $E = \\{e_1, \\ldots, e_n\\}$ and $F = \\{f_1, \\ldots, f_n\\}$ be two orthonormal bases of a vector space $V$. Is the transfer matrix $[Id]_F^E$, which represents the identity transformation from basis $E$ to basis $F$, an orthogonal matrix? Justify your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Given the equations of two lines:\n\\[ n(m-1)x + m(n-1)y = amn \\]\nand\n\\[ mx + ny = amn \\]\nwhere \\( m \\) and \\( n \\) are real constants satisfying \\( 0 < m < n < 1 \\), determine the condition under which these two lines intersect. Show that this condition implies \\( x + y = 0 \\).",
... | x + y = 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... | 66.67 |
[
{
"content": "Construct an uncountable set $X \\subset \\mathbb{R}_{\\geq 0}$ such that for all distinct $a, b \\in X$, $a + b \\not\\in X$. Provide an example of such a set.",
"role": "user"
}
] | [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... | MgCO3 |
[
{
"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... | 14710000 |
[
{
"content": "Given that $f(x)$ is continuous and \\( \\int_0^{x^2} f(t) \\, dt = x + \\sin\\left(\\frac{\\pi}{2}x\\right) \\), find the value of $f(1)$. \\( \\boxed{?} \\)",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Find the maximum value of the function \\( f(r,t) = r^{2n} - 2r^n \\cos(nt) + 1 \\) over the domain \\((r,t) \\in [0,1] \\times [0,2\\pi]\\), where \\( n \\) is an integer.",
"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... | $2,393,290 |
[
{
"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... | 0.0916 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... | 55 A |
[
{
"content": "Calculate the curl of the radial unit vector \\( e_r = (\\sin\\theta \\cos\\phi)i + (\\sin\\theta \\sin\\phi)j + (\\cos\\theta)k \\) in spherical coordinates.",
"role": "user"
}
] | 0 |
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