conversations listlengths 2 2 | question stringlengths 16 24.8k ⌀ | source stringclasses 10
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"value": "5. For any positive integer $k$, let $f_{1}(k)$ be the sum of the squares of the digits of $k$, and for $n \\geqslant 2, f_{n}(k)=$ $f_{1}\\left(f_{n-1}(k)\\right)$. Then $f_{2006}(2006)=$ $\\qquad$"
},
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"value": "<think>\nOkay, so I need to figu... | 5. For any positive integer $k$, let $f_{1}(k)$ be the sum of the squares of the digits of $k$, and for $n \geqslant 2, f_{n}(k)=$ $f_{1}\left(f_{n-1}(k)\right)$. Then $f_{2006}(2006)=$ $\qquad$ | null | null |
[
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"value": "Your task is to sort an array containing the strings \"quarter\", \"dime\", \"nickel\", and \"penny\" any number of times in no specific order and arrange them so that they adhere to this sequence: quarter dime nickel penny (in other words, greatest to least monetary value), whil... | null | null | null |
[
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"value": "Given the following properties of a fluid system: \n\n- Density differential \\(\\Delta \\rho = 500 \\, \\text{kg/m}^3\\)\n- Density of the surrounding fluid \\(\\rho = 1000 \\, \\text{kg/m}^3\\)\n- Dynamic viscosity \\(\\mu = 0.001 \\, \\text{Pa-s}\\)\n- Gravitational accelerati... | null | automath | 26,957 |
[
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"value": "9.1. It is known that $a^{2}+b=b^{2}+c=c^{2}+a$. What values can the expression\n\n$$\na\\left(a^{2}-b^{2}\\right)+b\\left(b^{2}-c^{2}\\right)+c\\left(c^{2}-a^{2}\\right) ?\n$$\n\ntake?"
},
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"value": "<think>\nOkay, let's see. The problem says th... | 9.1. It is known that $a^{2}+b=b^{2}+c=c^{2}+a$. What values can the expression
$$
a\left(a^{2}-b^{2}\right)+b\left(b^{2}-c^{2}\right)+c\left(c^{2}-a^{2}\right) ?
$$
take? | null | null |
[
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"value": "Return your final response within \\boxed{}. Consider a $1 \\times 1$ grid of squares. Let $A, B, C, D$ be the vertices of this square, and let $E$ be the midpoint of segment $CD$. Furthermore, let $F$ be the point on segment $BC$ satisfying $BF = 2CF$, and let $P$ be the interse... | Consider a $1 \times 1$ grid of squares. Let $A, B, C, D$ be the vertices of this square, and let $E$ be the midpoint of segment $CD$. Furthermore, let $F$ be the point on segment $BC$ satisfying $BF = 2CF$, and let $P$ be the intersection of lines $AF$ and $BE$. Find $\frac{AP}{PF}$. | null | null |
[
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"value": "How can I generate a class definition in HTML to create an alert box with a custom message using JavaScript?"
},
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"value": "<think>\nOkay, the user is asking how to generate a class definition in HTML to create an alert box with a custom message ... | null | null | null |
[
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"value": "Given that the line $l$ intersects the ellipse $\\frac{x^2}{16} + \\frac{y^2}{12} = 1$ at points $A$ and $B$, with the midpoint of $AB$ being $M(2, 1)$, determine the equation of line $l$."
},
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"value": "<think>\nOkay, so I need to find the equat... | Given that the line $l$ intersects the ellipse $\frac{x^2}{16} + \frac{y^2}{12} = 1$ at points $A$ and $B$, with the midpoint of $AB$ being $M(2, 1)$, determine the equation of line $l$. | null | null |
[
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"value": "Let $p_1 = b^3 + 3^b + b \\cdot 3^{(b+1)/2}$ and $p_2 = b^3 + 3^b - b \\cdot 3^{(b+1)/2}$. If $1 \\le b \\le 125$, how many integral values of $b$ are there such that $p_1 + p_2$ is a perfect square?"
},
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"value": "<think>\nAlright, so I have thi... | null | null | null |
[
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"value": "In $\\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively. It is known that $(b-2a)\\cos C+c\\cos B=0$. \n$(1)$ Find $C$; \n$(2)$ If $c= \\sqrt{7}$ and $b=3a$, find the area of $\\triangle ABC$."
},
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... | In $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively. It is known that $(b-2a)\cos C+c\cos B=0$.
$(1)$ Find $C$;
$(2)$ If $c= \sqrt{7}$ and $b=3a$, find the area of $\triangle ABC$. | null | null |
[
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"value": "Problem 5.2. Several people were seated around a round table such that the distances between adjacent people are the same. One of them was given a sign with the number 1, and then everyone was given signs with numbers 2, 3, and so on, in a clockwise direction.\n\nThe person with ... | Problem 5.2. Several people were seated around a round table such that the distances between adjacent people are the same. One of them was given a sign with the number 1, and then everyone was given signs with numbers 2, 3, and so on, in a clockwise direction.
The person with the sign numbered 31 noticed that the dist... | null | null |
[
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"value": "Given the universal set $U=\\mathbb{R}$, set $A=\\{x\\mid -1 1\\}$, find $A\\cap(\\neg_{U}B)=(\\ \\ \\ )$.\n\nA: $(-1,1)$\nB: $(-1,1]$\nC: $[1,3)$\nD: $(1,3)$"
},
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"value": "<think>\nOkay, so I need to find the intersection of set A and the comp... | Given the universal set $U=\mathbb{R}$, set $A=\{x\mid -1 1\}$, find $A\cap(\neg_{U}B)=(\ \ \ )$.
A: $(-1,1)$
B: $(-1,1]$
C: $[1,3)$
D: $(1,3)$ | null | null |
[
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"value": "8.15 If $2^{a}+2^{b}=3^{c}+3^{d}$, then the number of negative integers among $a, b, c, d$ is\n(A) 4.\n(B) 3.\n(C) 2.\n(D) 1.\n(E) 0.\n(14th American High School Mathematics Examination, 1963)"
},
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"value": "<think>\nOkay, so I need to solve this... | 8.15 If $2^{a}+2^{b}=3^{c}+3^{d}$, then the number of negative integers among $a, b, c, d$ is
(A) 4.
(B) 3.
(C) 2.
(D) 1.
(E) 0.
(14th American High School Mathematics Examination, 1963) | null | null |
[
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"value": "How do I declare a pointer for the first element in a list of a struct like this:\n```\nsection .bss\nstruc agenda\n name resb 10\n number resd 10\n type resw 10\nendstruc\n```"
},
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"value": "<think>\nOkay, let's see. The user wan... | null | sharegpt | null |
[
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"value": "In a modified card game that involves unique combinations of suits and ranks, a specific ranking is established based on a series of non-standard rules. The ranking is as follows:\n\n- Suits are ranked in the order: Hearts < Diamonds < Clubs < Spades.\n- Within each suit, ranks a... | null | evolcodegolf | null |
[
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"value": "3. Given a 2015-digit number divisible by 9. Let the sum of its digits be $\\boldsymbol{a}$, the sum of the digits of $\\boldsymbol{a}$ be $\\boldsymbol{b}$, and the sum of the digits of $\\boldsymbol{b}$ be $\\boldsymbol{c}$. Find the number $\\boldsymbol{c}$. (14 points)."
},... | 3. Given a 2015-digit number divisible by 9. Let the sum of its digits be $\boldsymbol{a}$, the sum of the digits of $\boldsymbol{a}$ be $\boldsymbol{b}$, and the sum of the digits of $\boldsymbol{b}$ be $\boldsymbol{c}$. Find the number $\boldsymbol{c}$. (14 points). | null | null |
[
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"value": "On the table there are $k \\ge 3$ heaps of $1, 2, \\dots , k$ stones. In the first step, we choose any three of the heaps, merge them into a single new heap, and remove $1$ stone from this new heap. Thereafter, in the $i$-th step ($i \\ge 2$) we merge some three heaps containing ... | On the table there are $k \ge 3$ heaps of $1, 2, \dots , k$ stones. In the first step, we choose any three of the heaps, merge them into a single new heap, and remove $1$ stone from this new heap. Thereafter, in the $i$-th step ($i \ge 2$) we merge some three heaps containing more than $i$ stones in total and remove $i... | null | null |
[
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"value": "## Task 14/81\n\nIn a plane, let equilateral triangles $D_{i}$ with side lengths $a_{i}=2 i-1, i=1 ; 2 ; 3 ; \\ldots$ be arranged along a line $g$ such that the \"right\" vertex of triangle $D_{k}$ coincides with the \"left\" vertex of triangle $D_{k+1}$ and that the third vertic... | ## Task 14/81
In a plane, let equilateral triangles $D_{i}$ with side lengths $a_{i}=2 i-1, i=1 ; 2 ; 3 ; \ldots$ be arranged along a line $g$ such that the "right" vertex of triangle $D_{k}$ coincides with the "left" vertex of triangle $D_{k+1}$ and that the third vertices all lie in the same half-plane generated by ... | null | null |
[
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"value": "In the three-dimensional Cartesian coordinate system, the points for which the distance from the origin is not greater than $5$ are:\n\nA: $(1,1,1)$\n\nB: $(1,2,2)$\n\nC: $(2,-3,5)$\n\nD: $(3,0,4)$"
},
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"value": "<think>\nOkay, so I need to figur... | In the three-dimensional Cartesian coordinate system, the points for which the distance from the origin is not greater than $5$ are:
A: $(1,1,1)$
B: $(1,2,2)$
C: $(2,-3,5)$
D: $(3,0,4)$ | null | null |
[
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"value": "(5 points) Given lines $a$, $b$, $c$, and plane $\\alpha$, which of the following conditions makes $a \\parallel b$ true?\n\nA: $a \\parallel \\alpha$ and $b \\parallel \\alpha$ \nB: $a \\perp c$ and $b \\perp c$ \nC: $a \\parallel c$ and $b \\parallel c$ \nD: $a \\parallel \\... | (5 points) Given lines $a$, $b$, $c$, and plane $\alpha$, which of the following conditions makes $a \parallel b$ true?
A: $a \parallel \alpha$ and $b \parallel \alpha$
B: $a \perp c$ and $b \perp c$
C: $a \parallel c$ and $b \parallel c$
D: $a \parallel \alpha$ and $b \perp c$ | null | null |
[
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"value": "If the focus of the hyperbola $C$ lies on the $x$-axis and the asymptotes are $y=±\\frac{\\sqrt{5}}{2}x$, then the eccentricity of $C$ is ____."
},
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"value": "<think>\nOkay, let's see. I need to find the eccentricity of a hyperbola C whose focus ... | If the focus of the hyperbola $C$ lies on the $x$-axis and the asymptotes are $y=±\frac{\sqrt{5}}{2}x$, then the eccentricity of $C$ is ____. | null | null |
[
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"value": "Given the function $f(x) = x^2 - 2ax + 1$ is increasing on the interval $[1, +\\infty)$, then the range of the real number $a$ is."
},
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"value": "<think>\nOkay, so I have this problem here: Given the function f(x) = x² - 2a x + 1 is increasing on... | Given the function $f(x) = x^2 - 2ax + 1$ is increasing on the interval $[1, +\infty)$, then the range of the real number $a$ is. | null | null |
[
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"value": "Consider a graph with 6 vertices, labeled $A$, $B$, $C$, $D$, $E$, and $F$, and 9 edges. Determine if it has a perfect matching, and if so, find one."
},
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"value": "<think>\nOkay, so I need to figure out if a graph with 6 vertices (A, B, C, D, E,... | null | tiger_lab_math | 8,214 |
[
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"value": "Return your final response within \\boxed{}. On a chessboard of size $8 \\times 8$, $k$ rooks and $k$ knights are placed so that no piece is attacking any other piece. What is the maximum possible value of $k$ for which this is possible?"
},
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"va... | On a chessboard of size $8 \times 8$, $k$ rooks and $k$ knights are placed so that no piece is attacking any other piece. What is the maximum possible value of $k$ for which this is possible? | null | null |
[
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"value": "2. Given the lengths of the three altitudes of $\\triangle A B C$ are $\\frac{2}{n+6} 、 \\frac{1}{3 n+12} 、 \\frac{1}{8-2 n}$. Then the range of values for $n$ is"
},
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"value": "<think>\nOkay, let me try to figure out this problem. So, we have a ... | 2. Given the lengths of the three altitudes of $\triangle A B C$ are $\frac{2}{n+6} 、 \frac{1}{3 n+12} 、 \frac{1}{8-2 n}$. Then the range of values for $n$ is | null | null |
[
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"value": "7. Given a sequence of natural numbers $a_{n}$, the terms of which satisfy\n\nthe relations $a_{n+1}=k \\cdot \\frac{a_{n}}{a_{n-1}}$ (for $n \\geq 2$). All terms of the sequence are integers. It is known that $a_{1}=1$, and $a_{2018}=2020$. Find the smallest natural $k$ for whic... | 7. Given a sequence of natural numbers $a_{n}$, the terms of which satisfy
the relations $a_{n+1}=k \cdot \frac{a_{n}}{a_{n-1}}$ (for $n \geq 2$). All terms of the sequence are integers. It is known that $a_{1}=1$, and $a_{2018}=2020$. Find the smallest natural $k$ for which this is possible. | null | null |
[
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"value": "What is the length of the optimal Golomb ruler with 4 ticks?"
},
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"value": "<think>\nAlright, so I need to figure out the length of the optimal Golomb ruler with 4 ticks. Hmm, okay. I remember that a Golomb ruler is a ruler where all the marks ar... | null | null | null |
[
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"value": "Given the function $f(x)=\\frac{{x}^{2}-ax}{{e}^{x}}$, where $a\\in R$. \n$(1)$ If $a=2$, find the monotonic interval of $f(x)$; \n$(2)$ If $a=1$, and $x_{1}$, $x_{2}$ are two real roots of the equation $f(x)=\\frac{lnx+1}{{e}^{x}}$, prove that $x_{1}+x_{2} \\gt 2$."
},
{
... | Given the function $f(x)=\frac{{x}^{2}-ax}{{e}^{x}}$, where $a\in R$.
$(1)$ If $a=2$, find the monotonic interval of $f(x)$;
$(2)$ If $a=1$, and $x_{1}$, $x_{2}$ are two real roots of the equation $f(x)=\frac{lnx+1}{{e}^{x}}$, prove that $x_{1}+x_{2} \gt 2$. | null | null |
[
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"value": "The condition \"$x^{2} > 2012$\" is a __________ of \"$x^{2} > 2011$\".\nA: Sufficient but not necessary condition\nB: Necessary but not sufficient condition\nC: Necessary and sufficient condition\nD: Neither sufficient nor necessary condition"
},
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... | The condition "$x^{2} > 2012$" is a __________ of "$x^{2} > 2011$".
A: Sufficient but not necessary condition
B: Necessary but not sufficient condition
C: Necessary and sufficient condition
D: Neither sufficient nor necessary condition | null | null |
[
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"value": "I am trying to create a form in my web application using Struts and JSP. The form should have a hidden field for courseInstanceID, fileID, and pageNumber, a textarea for comments, and a submit button. Additionally, I want to have a hyperlink that will redirect to a repository pag... | null | glaive | null |
[
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"value": "Let the function $f(x)$ have domain $D$. If there exists a non-zero real number $l$ such that for any $x \\in M$ (where $M \\subseteq D$), we have $x+l \\in D$ and $f(x+l) \\ge f(x)$, then $f(x)$ is called an $l$-increment function on $M$. If the function $f(x) = x^2$ with domain... | Let the function $f(x)$ have domain $D$. If there exists a non-zero real number $l$ such that for any $x \in M$ (where $M \subseteq D$), we have $x+l \in D$ and $f(x+l) \ge f(x)$, then $f(x)$ is called an $l$-increment function on $M$. If the function $f(x) = x^2$ with domain $[-1, +\infty)$ is an $m$-increment functio... | null | null |
[
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"value": "You are tasked with implementing a resolution manager for a client-server application. The resolution manager is responsible for building a resolver map, which contains a list of resolvers used to handle different types of data. Each resolver is a class that implements a specific... | null | codefeedback | null |
[
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"value": "We shall soon have a new logo & site design, let us use this last breath of the simple times and golf this ASCII version of the speech bubble beta logo, ensuring that the final output contains no spaces between the lines while preserving the original formatting and structure:\n+-... | null | evolcodegolf | null |
[
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"value": "13. Find the largest real number $x$ such that $\\sqrt[3]{x}+\\sqrt[3]{4-x}=1$."
},
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"value": "<think>\nOkay, so I need to find the largest real number x such that the cube root of x plus the cube root of (4 minus x) equals 1. Hmm, let me think a... | 13. Find the largest real number $x$ such that $\sqrt[3]{x}+\sqrt[3]{4-x}=1$. | null | null |
[
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"value": "4. Let $D$, $E$, and $F$ be points on the sides $BC$, $AB$, and $AC$ of $\\triangle ABC$, respectively, such that $AE = AF$, $BE = BD$, and $CF = CD$. Given that $AB \\cdot AC = 2BD \\cdot DC$, $AB = 12$, and $AC = 5$. Then the inradius $r$ of $\\triangle ABC$ is $\\qquad$"
},
... | 4. Let $D$, $E$, and $F$ be points on the sides $BC$, $AB$, and $AC$ of $\triangle ABC$, respectively, such that $AE = AF$, $BE = BD$, and $CF = CD$. Given that $AB \cdot AC = 2BD \cdot DC$, $AB = 12$, and $AC = 5$. Then the inradius $r$ of $\triangle ABC$ is $\qquad$ | null | null |
[
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"value": "The base and one of the legs of an isosceles triangle are the two roots of the equation $x^{2}-7x+10=0$. Find the perimeter of this triangle."
},
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"value": "<think>\nOkay, let's see. The problem says that the base and one of the legs of an isosce... | The base and one of the legs of an isosceles triangle are the two roots of the equation $x^{2}-7x+10=0$. Find the perimeter of this triangle. | null | null |
[
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"value": "Return your final response within \\boxed{}. The ticket price for the stadium was 25 rubles. After reducing the ticket prices, the number of spectators at the stadium increased by 50%, and the revenue from ticket sales increased by 14%. What is the new ticket price for the stadiu... | The ticket price for the stadium was 25 rubles. After reducing the ticket prices, the number of spectators at the stadium increased by 50%, and the revenue from ticket sales increased by 14%. What is the new ticket price for the stadium after the price reduction? | null | null |
[
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"value": "23. A natural number is divided by $3, 5, 7, 11, 13$, respectively, the sum of the quotients is 185, and the sum of the remainders is 8 (if divisible, the remainder is recorded as 0), this natural number is $\\qquad$ ."
},
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"value": "<think>\nOka... | 23. A natural number is divided by $3, 5, 7, 11, 13$, respectively, the sum of the quotients is 185, and the sum of the remainders is 8 (if divisible, the remainder is recorded as 0), this natural number is $\qquad$ . | null | null |
[
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"value": "1. In the diagram, $B D$ and $A E$ intersect at $C$ and $A B=B C$. Also, $\\angle A B C=40^{\\circ}$ and $\\angle D C E=x^{\\circ}$. What is the value of $x$ ?"
},
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"value": "<think>\nOkay, let's try to figure out this geometry problem step by st... | 1. In the diagram, $B D$ and $A E$ intersect at $C$ and $A B=B C$. Also, $\angle A B C=40^{\circ}$ and $\angle D C E=x^{\circ}$. What is the value of $x$ ? | null | null |
[
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"value": "7. (10 points) Calculate: $(1000+15+314) \\times(201+360+110)+(1000-201-360-110) \\times(15+314)$ $=$ . $\\qquad$"
},
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"value": "<think>\nOkay, let me try to figure out this problem. So, the question is to calculate this big expression: (1000 + 1... | 7. (10 points) Calculate: $(1000+15+314) \times(201+360+110)+(1000-201-360-110) \times(15+314)$ $=$ . $\qquad$ | null | null |
[
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"value": "Find the value of $h$ such that the following equation in base $h$ is true: $$\\begin{array}{c@{}c@{}c@{}c@{}c} &&6&4&5&3_h\\\\ &+&7&5&1&2_h\\\\ \\cline{2-6} &1&6&1&6&6_h.\\\\ \\end{array}$$"
},
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"value": "<think>\nOkay, so I need to find the val... | null | tiger_math | 4,539 |
[
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"value": "Given the function $f(x) = \\log_{a}x$ ($a > 0$, $a \\neq 1$) defined on the interval $[2, 4]$, the difference between its maximum and minimum values is $2$. Find the value of $a$."
},
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"value": "<think>\nOkay, let me try to solve this problem. S... | Given the function $f(x) = \log_{a}x$ ($a > 0$, $a \neq 1$) defined on the interval $[2, 4]$, the difference between its maximum and minimum values is $2$. Find the value of $a$. | null | null |
[
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"value": "Given the polar coordinate equation of curve $C\\_1$ as $ρ=2\\cos θ$, and the parametric equations of curve $C\\_2$ as $ \\begin{cases} x=-\\frac {4}{5}t \\\\ y=-2+ \\frac {3}{5}t\\end{cases}$ (where $t$ is a parameter).\n(1) Determine the positional relationship between $C\\_1$ ... | Given the polar coordinate equation of curve $C\_1$ as $ρ=2\cos θ$, and the parametric equations of curve $C\_2$ as $ \begin{cases} x=-\frac {4}{5}t \\ y=-2+ \frac {3}{5}t\end{cases}$ (where $t$ is a parameter).
(1) Determine the positional relationship between $C\_1$ and $C\_2$;
(2) Let $M$ be a moving point on $C\_1$... | null | null |
[
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"value": "13. Person A departs from location A to location B, while persons B and C depart from location B to location A. After person A has traveled 50 kilometers, persons B and C start from location B simultaneously. As a result, person A meets person B at location C, and person A meets ... | 13. Person A departs from location A to location B, while persons B and C depart from location B to location A. After person A has traveled 50 kilometers, persons B and C start from location B simultaneously. As a result, person A meets person B at location C, and person A meets person C at location D. It is known that... | null | null |
[
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"value": "Given vectors $\\overrightarrow{a} = (1, 2)$, $\\overrightarrow{b} = (x, -2)$, and $\\overrightarrow{a}$ is perpendicular to ($\\overrightarrow{a} - \\overrightarrow{b}$), find the real number $x$."
},
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"value": "<think>\nOkay, so I need to find ... | Given vectors $\overrightarrow{a} = (1, 2)$, $\overrightarrow{b} = (x, -2)$, and $\overrightarrow{a}$ is perpendicular to ($\overrightarrow{a} - \overrightarrow{b}$), find the real number $x$. | null | null |
[
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"value": "Given a point on the parabola $y^{2}=6x$ is twice the distance from the focus as it is from the $y$-axis, then the $x$-coordinate of this point is ______."
},
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"value": "<think>\nOkay, so I have this problem here: Given a point on the parabola y²... | Given a point on the parabola $y^{2}=6x$ is twice the distance from the focus as it is from the $y$-axis, then the $x$-coordinate of this point is ______. | null | null |
[
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"value": "Translate the proposition \"∃a∈R, a²+1<2a\" into its negation (fill in true or false)"
},
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"value": "<think>\nAlright, so I need to figure out the negation of the proposition \"There exists a real number a such that a squared plus 1 is less than ... | Translate the proposition "∃a∈R, a²+1<2a" into its negation (fill in true or false) | null | null |
[
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"value": "## Task B-2.3.\n\nThere are 8 steps to the top of the staircase. In how many ways can we reach the top if we can climb by one step or by two steps?"
},
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"value": "<think>\nOkay, so the problem is about figuring out how many different ways there a... | ## Task B-2.3.
There are 8 steps to the top of the staircase. In how many ways can we reach the top if we can climb by one step or by two steps? | null | null |
[
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"value": "In how many ways can we form three teams of four players each from a group of $12$ participants?"
},
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"value": "<think>\nOkay, so I have this problem here: \"In how many ways can we form three teams of four players each from a group of 12 partici... | In how many ways can we form three teams of four players each from a group of $12$ participants? | null | null |
[
{
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"value": "Given the functions $f(x) = |x+3|$ and $g(x) = m-2|x-11|$, if $2f(x) \\geq g(x+4)$ always holds, the maximum value of the real number $m$ is $t$ \n(1) Find the real number $t$ \n(2) Given that the real numbers $x$, $y$, $z$ satisfy $2x^2+3y^2+6z^2=a$ ($a>0$), and the maximum va... | Given the functions $f(x) = |x+3|$ and $g(x) = m-2|x-11|$, if $2f(x) \geq g(x+4)$ always holds, the maximum value of the real number $m$ is $t$
(1) Find the real number $t$
(2) Given that the real numbers $x$, $y$, $z$ satisfy $2x^2+3y^2+6z^2=a$ ($a>0$), and the maximum value of $x+y+z$ is $\frac{t}{20}$, find the ... | null | null |
[
{
"from": "user",
"value": "The roots of the cubic equation $x^3+x^2-2x-1=0$ cannot possibly be in the interval:\nA: $(-2, -1)$\nB: $(-1, 0)$\nC: $(0, 1)$\nD: $(1, 2)$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to figure out which interval cannot possibly contain any roots of ... | The roots of the cubic equation $x^3+x^2-2x-1=0$ cannot possibly be in the interval:
A: $(-2, -1)$
B: $(-1, 0)$
C: $(0, 1)$
D: $(1, 2)$ | null | null |
[
{
"from": "user",
"value": "Let $ f(x)\\equal{}5x^{13}\\plus{}13x^5\\plus{}9ax$. Find the least positive integer $ a$ such that $ 65$ divides $ f(x)$ for every integer $ x$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the least positive integer a such that the function ... | Let $ f(x)\equal{}5x^{13}\plus{}13x^5\plus{}9ax$. Find the least positive integer $ a$ such that $ 65$ divides $ f(x)$ for every integer $ x$. | null | null |
[
{
"from": "user",
"value": "10.2 Can the digits in the 30-digit number $11 \\ldots 122 \\ldots 233 \\ldots 3$ (which contains 10 ones, 10 twos, and 10 threes) be rearranged to form a square of a natural number?"
},
{
"from": "assistant",
"value": "<think>\nAlright, so I need to figure out if the... | 10.2 Can the digits in the 30-digit number $11 \ldots 122 \ldots 233 \ldots 3$ (which contains 10 ones, 10 twos, and 10 threes) be rearranged to form a square of a natural number? | null | null |
[
{
"from": "user",
"value": "Construct a function in R programming language that illustrates a histogram visualization of a presented numerical data collection. The function should also calculate and display the mean and standard deviation on the histogram. The data collection can contain up to 1 million ent... | null | codefeedback | null |
[
{
"from": "user",
"value": "Mia has 4 times as many shells as David. Ava has 20 more shells than Mia. Alice has x% the number of shells Ava has. If David has 15 shells, what the total number of conch shells they all have?\nIf we know the answer to the above question is 195, what is the value of unknown vari... | null | tiger_math | 28,595 |
[
{
"from": "user",
"value": "2. If real numbers $x, y$ satisfy\n$$\n\\begin{array}{l}\n\\frac{x}{2^{10}+5^{3}}+\\frac{y}{2^{10}+6^{3}}=1, \\\\\n\\frac{x}{3^{10}+5^{3}}+\\frac{y}{3^{10}+6^{3}}=1,\n\\end{array}\n$$\n\nthen $x+y=$ $\\qquad$ (the result should be written in the form of a power)."
},
{
"f... | 2. If real numbers $x, y$ satisfy
$$
\begin{array}{l}
\frac{x}{2^{10}+5^{3}}+\frac{y}{2^{10}+6^{3}}=1, \\
\frac{x}{3^{10}+5^{3}}+\frac{y}{3^{10}+6^{3}}=1,
\end{array}
$$
then $x+y=$ $\qquad$ (the result should be written in the form of a power). | null | null |
[
{
"from": "user",
"value": "13. Given the curve $x y^{2}=1(y>0)$, the slope $k$ of the tangent line at point $\\left(x_{0}, y_{0}\\right)$ on the curve is $k=-\\frac{1}{2 \\sqrt{x_{0}^{3}}}$. A line parallel to the $y$-axis is drawn through point $P_{1}(1,0)$, intersecting the curve at $Q_{1}$. A tangent li... | 13. Given the curve $x y^{2}=1(y>0)$, the slope $k$ of the tangent line at point $\left(x_{0}, y_{0}\right)$ on the curve is $k=-\frac{1}{2 \sqrt{x_{0}^{3}}}$. A line parallel to the $y$-axis is drawn through point $P_{1}(1,0)$, intersecting the curve at $Q_{1}$. A tangent line is drawn through $Q_{1}$, intersecting th... | null | null |
[
{
"from": "user",
"value": "Given the function $f(x)= \\begin{cases} x+2,(x\\leqslant -1) \\\\ x^{2},(-1 < x < 2) \\\\ 2x,(x\\geqslant 2)\\\\ \\end{cases}$.\n\n1. Find the values of $f(-3)$, $f(4)$, and $f(f(-2))$.\n2. If $f(m)=8$, find the value of $m$."
},
{
"from": "assistant",
"value": "<thi... | Given the function $f(x)= \begin{cases} x+2,(x\leqslant -1) \\ x^{2},(-1 < x < 2) \\ 2x,(x\geqslant 2)\\ \end{cases}$.
1. Find the values of $f(-3)$, $f(4)$, and $f(f(-2))$.
2. If $f(m)=8$, find the value of $m$. | null | null |
[
{
"from": "user",
"value": "Let $m$ be a real number, and $f(x) = m - \\frac{2}{2^{x}+1}$ ($x \\in \\mathbb{R}$).\n\n(1) If the function $f(x)$ is an odd function, find the value of $m$.\n\n(2) Prove by definition that for any $m$, $f(x)$ is a monotonically increasing function on $\\mathbb{R}$.\n\n(3) If th... | Let $m$ be a real number, and $f(x) = m - \frac{2}{2^{x}+1}$ ($x \in \mathbb{R}$).
(1) If the function $f(x)$ is an odd function, find the value of $m$.
(2) Prove by definition that for any $m$, $f(x)$ is a monotonically increasing function on $\mathbb{R}$.
(3) If the function $f(x)$ is an odd function, and the ineq... | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. The integers \\( a \\) and \\( b \\) are such that the quadratic polynomials \\( x^2 + ax + b \\) and \\( x^2 + bx + 1100 \\) have a common root, which is a prime number. Find \\( a \\). List all possible values."
},
{
"from": ... | The integers \( a \) and \( b \) are such that the quadratic polynomials \( x^2 + ax + b \) and \( x^2 + bx + 1100 \) have a common root, which is a prime number. Find \( a \). List all possible values. | null | null |
[
{
"from": "user",
"value": "23. Container A contains 2 liters of sulfuric acid solution with a concentration of $30 \\%$, and container B contains 3 liters of sulfuric acid solution with a concentration of $10 \\%$. Now, sulfuric acid solutions with concentrations of $6 \\%$ and $22 \\%$ are being added to ... | 23. Container A contains 2 liters of sulfuric acid solution with a concentration of $30 \%$, and container B contains 3 liters of sulfuric acid solution with a concentration of $10 \%$. Now, sulfuric acid solutions with concentrations of $6 \%$ and $22 \%$ are being added to containers A and B, respectively, at rates o... | null | null |
[
{
"from": "user",
"value": "Let $\\alpha$ and $\\beta$ be the roots of $x^2 + px + 2 = 0,$ and let $\\gamma$ and $\\delta$ be the roots of $x^2 + qx + 3 = 0.$ Express\n\\[(\\alpha - \\gamma)(\\beta - \\gamma)(\\alpha + \\delta)(\\beta + \\delta)\\]in terms of $p$ and $q.$"
},
{
"from": "assistant",... | null | tiger_math | 19,718 |
[
{
"from": "user",
"value": "2. Let $n$ be a positive integer, and satisfy $n^{5}=438427732293$, then $n=$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find a positive integer n such that n^5 equals 438,427,732,293. Hmm, fifth roots can be a bit tricky, but maybe I can figure ... | 2. Let $n$ be a positive integer, and satisfy $n^{5}=438427732293$, then $n=$ | null | null |
[
{
"from": "user",
"value": "Given sets $A=\\{x|0 \\lt x \\lt 9\\}$ and $B=\\{x|m+1\\leqslant x\\leqslant 2m-1\\}$. \n$(1)$ When $m=5$, find $A\\cap B$; \n$(2)$ If $A\\cap B=B$, find the range of real numbers $m$."
},
{
"from": "assistant",
"value": "<think>\nOkay, let me try to solve this prob... | Given sets $A=\{x|0 \lt x \lt 9\}$ and $B=\{x|m+1\leqslant x\leqslant 2m-1\}$.
$(1)$ When $m=5$, find $A\cap B$;
$(2)$ If $A\cap B=B$, find the range of real numbers $m$. | null | null |
[
{
"from": "user",
"value": "How can I implement a Java function that compares two numbers and prints out the larger one?"
},
{
"from": "assistant",
"value": "<think>\nOkay, I need to create a Java function that compares two numbers and prints the larger one. Let me think about how to approach th... | null | sharegpt | null |
[
{
"from": "user",
"value": "Calculate the value of the function \\\\(f(x)=2x^{5}-3x^{3}+5x^{2}-4\\\\) at \\\\(x=2\\\\) using the Qin Jiushao algorithm, where \\\\(v\\_{3}=\\\\) \\_\\_\\_\\_\\_\\_. (Note: In the function \\\\(f(x)=a\\_{n}x^{n}+a\\_{n-1}x^{n-1}+…+a\\_{1}x+a\\_{0}\\\\), the Qin Jiushao algorit... | Calculate the value of the function \\(f(x)=2x^{5}-3x^{3}+5x^{2}-4\\) at \\(x=2\\) using the Qin Jiushao algorithm, where \\(v\_{3}=\\) \_\_\_\_\_\_. (Note: In the function \\(f(x)=a\_{n}x^{n}+a\_{n-1}x^{n-1}+…+a\_{1}x+a\_{0}\\), the Qin Jiushao algorithm is defined as \\( \\begin{cases} \\overset{v\_{0}=a\_{n}}{v\_{k}... | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let \\(ABCD\\) be a parallelogram. Assume that there is a point \\(P\\) inside the parallelogram that lies on the central perpendicular of \\(AB\\) and that \\(\\angle PBA = \\angle ADP\\).\n\nShow that \\(\\angle CPD = 2 \\angle BAP\\... | Let \(ABCD\) be a parallelogram. Assume that there is a point \(P\) inside the parallelogram that lies on the central perpendicular of \(AB\) and that \(\angle PBA = \angle ADP\).
Show that \(\angle CPD = 2 \angle BAP\) holds. | null | null |
[
{
"from": "user",
"value": "Given \\\\( \\overrightarrow{a}=(3,4) \\\\) and \\\\( \\overrightarrow{b}=(-8,6) \\\\), the vector \\\\( \\overrightarrow{a} \\\\) and \\\\( \\overrightarrow{b} \\\\) are\nA: Parallel to each other\nB: Perpendicular to each other\nC: The angle between them is \\\\(30^{\\circ}\\\\... | Given \\( \overrightarrow{a}=(3,4) \\) and \\( \overrightarrow{b}=(-8,6) \\), the vector \\( \overrightarrow{a} \\) and \\( \overrightarrow{b} \\) are
A: Parallel to each other
B: Perpendicular to each other
C: The angle between them is \\(30^{\circ}\\)
D: The angle between them is \\(60^{\circ}\\) | null | null |
[
{
"from": "user",
"value": "For the function $f(x)$ defined as in the original question, find the number of values of $x$ that satisfy the equation $f(f(x)) = x$."
},
{
"from": "assistant",
"value": "<think>\nAlright, so I need to figure out how many values of x satisfy the equation f(f(x)) = x ... | null | tiger_math | 33,388 |
[
{
"from": "user",
"value": "Simplify $$\\sqrt {a^{ \\frac {1}{2}} \\sqrt {a^{ \\frac {1}{2}} \\sqrt {a}}}$$\n\nOptions:\n\nA: $$a^{ \\frac {1}{4}}$$\n\nB: $$a^{ \\frac {1}{3}}$$\n\nC: $$a^{ \\frac {1}{2}}$$\n\nD: a"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to simplify this ne... | Simplify $$\sqrt {a^{ \frac {1}{2}} \sqrt {a^{ \frac {1}{2}} \sqrt {a}}}$$
Options:
A: $$a^{ \frac {1}{4}}$$
B: $$a^{ \frac {1}{3}}$$
C: $$a^{ \frac {1}{2}}$$
D: a | null | null |
[
{
"from": "user",
"value": "The school is preparing to purchase prizes for a \"Chinese ancient poetry\" recitation competition. It is known that purchasing $3$ type A prizes and $2$ type B prizes from the central market costs a total of $120$ yuan; purchasing $5$ type A prizes and $4$ type B prizes costs a ... | The school is preparing to purchase prizes for a "Chinese ancient poetry" recitation competition. It is known that purchasing $3$ type A prizes and $2$ type B prizes from the central market costs a total of $120$ yuan; purchasing $5$ type A prizes and $4$ type B prizes costs a total of $210$ yuan.
$(1)$ Find the unit... | null | null |
[
{
"from": "user",
"value": "Given an input of a pair of nonnegative integers describing a chamfered mover in a grid, output a representation of the accessible cells the mover can reach. \n\nA chamfered mover operates by a distinctive pattern, moving a combination of m steps in one direction and n steps diag... | null | null | null |
[
{
"from": "user",
"value": "$$\n\\begin{array}{l}\n\\text { 20. Let } 135^{\\circ}<\\alpha<180^{\\circ} \\text {, and } \\\\\nP\\left(\\cos \\alpha, \\cos ^{2} \\alpha\\right), Q\\left(\\cot \\alpha, \\cot ^{2} \\alpha\\right), \\\\\nR\\left(\\sin \\alpha, \\sin ^{2} \\alpha\\right), S\\left(\\tan \\alpha, ... | $$
\begin{array}{l}
\text { 20. Let } 135^{\circ}<\alpha<180^{\circ} \text {, and } \\
P\left(\cos \alpha, \cos ^{2} \alpha\right), Q\left(\cot \alpha, \cot ^{2} \alpha\right), \\
R\left(\sin \alpha, \sin ^{2} \alpha\right), S\left(\tan \alpha, \tan ^{2} \alpha\right)
\end{array}
$$
be the four vertices of a trapezoid... | null | null |
[
{
"from": "user",
"value": "What is the derivative of the function \\( y = x^{\\sin(x)^{\\tan(x)}} \\) with respect to \\( x \\)?"
},
{
"from": "assistant",
"value": "<think>\nOkay, I need to find the derivative of the function \\( y = x^{\\sin(x)^{\\tan(x)}} \\) with respect to \\( x \\). Hmm, ... | null | null | null |
[
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N numbers written on a blackboard. \n\nIn one operation, Chef can:\nChoose any 3 integers ... | Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N numbers written on a blackboard.
In one operation, Chef can:
Choose any 3 integers A, B, and C written on the blackboard.
Era... | null | null |
[
{
"from": "user",
"value": "The function $f(x)$ is an odd function. When $x > 0$, $f(x) = x^3 - \\cos x$. When $x < 0$, the expression for $f(x)$ is ( )\n\nA: $x^3 + \\cos x$\n\nB: $-x^3 + \\cos x$\n\nC: $-x^3 - \\cos x$\n\nD: $x^3 - \\cos x$"
},
{
"from": "assistant",
"value": "<think>\nOkay, l... | The function $f(x)$ is an odd function. When $x > 0$, $f(x) = x^3 - \cos x$. When $x < 0$, the expression for $f(x)$ is ( )
A: $x^3 + \cos x$
B: $-x^3 + \cos x$
C: $-x^3 - \cos x$
D: $x^3 - \cos x$ | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. A convex quadrilateral \\(ABCD\\) is given such that \\(\\angle BAD = 2 \\angle BCD\\) and \\(AB = AD\\). Let \\(P\\) be a point such that \\(ABCP\\) forms a parallelogram. Prove that \\(CP = DP\\)."
},
{
"from": "assistant",
... | A convex quadrilateral \(ABCD\) is given such that \(\angle BAD = 2 \angle BCD\) and \(AB = AD\). Let \(P\) be a point such that \(ABCP\) forms a parallelogram. Prove that \(CP = DP\). | null | null |
[
{
"from": "user",
"value": "convert this code from Mojo to Erlang:\n```mojo\nsub singleNumber(nums as List of Int) returns Int\n var ones = 0\n var twos = 0\n for n in nums do\n ones = (ones XOR n) AND (NOT twos)\n twos = (twos XOR n) AND (NOT ones)\n end\n return ones\nend\n```... | null | dolphin | null |
[
{
"from": "user",
"value": "Let $(x-1)^{21} = a + a_1x + a_2x^2 + \\ldots + a_{21}x^{21}$, then find the value of $a_{10} + a_{11}$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this problem here: given the expansion of (x - 1)^21, which is written as a + a₁x + a₂x² + ... + a₂₁x... | Let $(x-1)^{21} = a + a_1x + a_2x^2 + \ldots + a_{21}x^{21}$, then find the value of $a_{10} + a_{11}$. | null | null |
[
{
"from": "user",
"value": "2. For the quadratic function $y=a x^{2}+b x(a b \\neq 0)$, when $x$ takes $x_{1}, x_{2}\\left(x_{1} \\neq x_{2}\\right)$, the function values are equal. Then, when $x$ takes $x_{1}+x_{2}$, the function value is"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I... | 2. For the quadratic function $y=a x^{2}+b x(a b \neq 0)$, when $x$ takes $x_{1}, x_{2}\left(x_{1} \neq x_{2}\right)$, the function values are equal. Then, when $x$ takes $x_{1}+x_{2}$, the function value is | null | null |
[
{
"from": "user",
"value": "1. Divide the set of positive even numbers $\\{2,4, \\cdots\\}$ into groups in ascending order, with the $n$-th group containing $3 n-2$ numbers:\n$$\n\\{2\\},\\{4,6,8,10\\},\\{12,14, \\cdots, 24\\}, \\cdots \\text {. }\n$$\n\nThen 2018 is in the group. $\\qquad$"
},
{
"f... | 1. Divide the set of positive even numbers $\{2,4, \cdots\}$ into groups in ascending order, with the $n$-th group containing $3 n-2$ numbers:
$$
\{2\},\{4,6,8,10\},\{12,14, \cdots, 24\}, \cdots \text {. }
$$
Then 2018 is in the group. $\qquad$ | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given that the sides \\( a, b, c \\) of triangle \\( \\triangle ABC \\) form a geometric sequence, with \\( \\angle A, \\angle B, \\angle C \\) being the angles opposite to sides \\( a, b, c \\) respectively, determine the range of \\(... | Given that the sides \( a, b, c \) of triangle \( \triangle ABC \) form a geometric sequence, with \( \angle A, \angle B, \angle C \) being the angles opposite to sides \( a, b, c \) respectively, determine the range of \( \sin B + \cos B \).
A. \(\left[\frac{1}{2}, 1+\frac{\sqrt{3}}{2}\right]\)
B. \((1, \sqrt{2}]\)
... | null | null |
[
{
"from": "user",
"value": "$\\left[\\begin{array}{l}{[\\text { Identical Transformations }]} \\\\ {[\\text { Factorization }]}\\end{array}\\right]$\n\nFor different numbers $a$ and $b$, it is known that $\\frac{a}{b}+a=\\frac{b}{a}+b$. Find $\\frac{1}{a}+\\frac{1}{b}$."
},
{
"from": "assistant",
... | $\left[\begin{array}{l}{[\text { Identical Transformations }]} \\ {[\text { Factorization }]}\end{array}\right]$
For different numbers $a$ and $b$, it is known that $\frac{a}{b}+a=\frac{b}{a}+b$. Find $\frac{1}{a}+\frac{1}{b}$. | null | null |
[
{
"from": "user",
"value": "A machine can operate at various speeds, and the number of defective items it produces per hour varies with the speed of operation. Let $x$ represent the speed (in revolutions per second), and $y$ represent the number of defective items produced per hour. Now, we have observed 4 ... | A machine can operate at various speeds, and the number of defective items it produces per hour varies with the speed of operation. Let $x$ represent the speed (in revolutions per second), and $y$ represent the number of defective items produced per hour. Now, we have observed 4 sets of values for $(x, y)$: $(8, 5)$, $... | null | null |
[
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Jon Marius shouted too much at the recent Justin Bieber concert, and now needs to go to the doctor b... | Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Jon Marius shouted too much at the recent Justin Bieber concert, and now needs to go to the doctor because of his sore throat. The doctor’s ... | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. In the first month, there is one pair of mature rabbits. Each month, they give birth to 3 male and 2 female rabbits. The female rabbits mature in one month and then start giving birth to 3 male and 2 female rabbits each month. How many... | In the first month, there is one pair of mature rabbits. Each month, they give birth to 3 male and 2 female rabbits. The female rabbits mature in one month and then start giving birth to 3 male and 2 female rabbits each month. How many rabbits are there after the $n$-th month ($n \in \mathbf{Z}_{+}$)? | null | null |
[
{
"from": "user",
"value": "I am trying to create a program that converts an image to HTML, but I am having trouble with the implementation. I need to create a form with two panels - InputPanel and OutputPanel. The InputPanel should contain an image selection button, a convert image button, and input parame... | null | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. \nLet\n\n$$\nS=C_{k+1}^{1} S_{k}(n)+C_{k+1}^{3} S_{k-2}(n)+\\ldots\n$$\n\nwhere the last term in this sum is $C_{k+1}^{k+1} S_{0}(n)$ for even $k$ and $C_{k+1}^{k} S_{1}(n)$ for odd $k$. Prove that $S=\\frac{(n+1)^{k+1}+n^{k+1}-1}{2}$.... |
Let
$$
S=C_{k+1}^{1} S_{k}(n)+C_{k+1}^{3} S_{k-2}(n)+\ldots
$$
where the last term in this sum is $C_{k+1}^{k+1} S_{0}(n)$ for even $k$ and $C_{k+1}^{k} S_{1}(n)$ for odd $k$. Prove that $S=\frac{(n+1)^{k+1}+n^{k+1}-1}{2}$. | null | null |
[
{
"from": "user",
"value": "Given that the sequence $\\{a\\_n\\}$ is an arithmetic sequence with a common difference of $-2$, and $a\\_3=a\\_2+a\\_5$.\n(I) Find the general term formula of the sequence $\\{a\\_n\\}$.\n(II) Find the maximum value of the sum of the first $n$ terms of the sequence, denoted as ... | Given that the sequence $\{a\_n\}$ is an arithmetic sequence with a common difference of $-2$, and $a\_3=a\_2+a\_5$.
(I) Find the general term formula of the sequence $\{a\_n\}$.
(II) Find the maximum value of the sum of the first $n$ terms of the sequence, denoted as $S\_n$. | null | null |
[
{
"from": "user",
"value": "Devise a method that alternates the provided sequence of characters into its equivalent hexadecimal notation and print out the result. Handle all possible edge cases, including but not limited to non-alphanumeric characters, long strings, and null values. Then create a second met... | null | null | null |
[
{
"from": "user",
"value": "11. Let the line $y=k x+b$ intersect the curve $y=x^{3}-x$ at three distinct points $A, B, C$, and $|A B|=|B C|=2$. Then the value of $k$ is"
},
{
"from": "assistant",
"value": "<think>\nOkay, let me try to figure out this problem step by step. So, the problem says th... | 11. Let the line $y=k x+b$ intersect the curve $y=x^{3}-x$ at three distinct points $A, B, C$, and $|A B|=|B C|=2$. Then the value of $k$ is | null | null |
[
{
"from": "user",
"value": "2. $s_{1}=4, s_{2}=2 \\rightarrow a_{2}=3^{4} \\cdot 5^{2}=2025$\n\nProblem 4 Answer: $P(A)=\\frac{3}{4}$"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. I need to figure out how the given problem connects to the answer provided. The example given is wh... | 2. $s_{1}=4, s_{2}=2 \rightarrow a_{2}=3^{4} \cdot 5^{2}=2025$
Problem 4 Answer: $P(A)=\frac{3}{4}$ | null | null |
[
{
"from": "user",
"value": "Given a triangular pyramid $(P-ABC)$ that is inscribed in a sphere $(O)$, with $PA=PB=PC=2$, the sum of the areas of the three side faces of the triangular pyramid $(P-ABC)$ is at its maximum. What is the surface area of the sphere $(O)$?"
},
{
"from": "assistant",
"v... | Given a triangular pyramid $(P-ABC)$ that is inscribed in a sphere $(O)$, with $PA=PB=PC=2$, the sum of the areas of the three side faces of the triangular pyramid $(P-ABC)$ is at its maximum. What is the surface area of the sphere $(O)$? | null | null |
[
{
"from": "user",
"value": "Enumerate the initial ten non-negative integers and illustrate their correlation in a table which shows each integer exponentiated to both the 3rd and 4th degree. Additionally, provide a short explanation comparing the growth rate of cubes vs. 4th powers for these integers. Valid... | null | null | null |
[
{
"from": "user",
"value": "$2 \\cdot 126$ The number of roots of the equation $2 \\sqrt{x-3}+6=x$ is\n(A) 3.\n(B) 2.\n(C) 1.\n(D) No real roots.\n(2nd China Tianjin \"Chinese Youth Cup\" Mathematics Invitational, 1988)"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. I need to sol... | $2 \cdot 126$ The number of roots of the equation $2 \sqrt{x-3}+6=x$ is
(A) 3.
(B) 2.
(C) 1.
(D) No real roots.
(2nd China Tianjin "Chinese Youth Cup" Mathematics Invitational, 1988) | null | null |
[
{
"from": "user",
"value": "The coefficient of the $x^2$ term in the expansion of $(1+x)^6(1-x)$ is ___."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the coefficient of the x² term in the expansion of (1 + x)⁶ multiplied by (1 - x). Hmm, let's see. I remember that when y... | The coefficient of the $x^2$ term in the expansion of $(1+x)^6(1-x)$ is ___. | null | null |
[
{
"from": "user",
"value": "You are tasked with creating a script to automate the transfer of files between two Google Cloud instances using the `gcloud compute scp` command. The script should take two arguments: the name of the file to be transferred and the destination directory on the second instance. Th... | null | magicoder | null |
[
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You will receive 3 points for solving this problem.\n\nManao is designing the genetic code for a new... | Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You will receive 3 points for solving this problem.
Manao is designing the genetic code for a new type of algae to efficiently produce fuel... | null | null |
[
{
"from": "user",
"value": "Based on a chat message \nThe Challenge \nGiven an input number \\$n > 9\\$, first construct its reverse while ensuring that leading zeros are disregarded. Next, identify and compile a comprehensive list of all prime factors exclusive to the number and its reverse, which share ... | null | null | null |
[
{
"from": "user",
"value": "9.26 In a tournament, 16 chess players are participating. Determine the number of different first-round schedules (schedules are considered different if they differ in the participants of at least one game; the color of the pieces and the board number are not taken into account).... | 9.26 In a tournament, 16 chess players are participating. Determine the number of different first-round schedules (schedules are considered different if they differ in the participants of at least one game; the color of the pieces and the board number are not taken into account). | null | null |
[
{
"from": "user",
"value": "Let $ T \\equal{} \\int_0^{\\ln2} \\frac {2e^{3x} \\plus{} e^{2x} \\minus{} 1} {e^{3x} \\plus{} e^{2x} \\minus{} e^x \\plus{} 1}dx$. Evaluate $ e^T$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to evaluate e raised to the power of T, where T is this ... | Let $ T \equal{} \int_0^{\ln2} \frac {2e^{3x} \plus{} e^{2x} \minus{} 1} {e^{3x} \plus{} e^{2x} \minus{} e^x \plus{} 1}dx$. Evaluate $ e^T$. | null | null |
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