conversations listlengths 2 2 | question stringlengths 16 24.8k ⌀ | source stringclasses 10
values | id int64 3 50k ⌀ |
|---|---|---|---|
[
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"value": "8. (10 points) Let for positive numbers $x, y, z$ the following system of equations holds:\n\n$$\n\\left\\{\\begin{array}{l}\nx^{2}+x y+y^{2}=27 \\\\\ny^{2}+y z+z^{2}=16 \\\\\nz^{2}+x z+x^{2}=43\n\\end{array}\\right.\n$$\n\nFind the value of the expression $x y+y z+x z$."
},
... | 8. (10 points) Let for positive numbers $x, y, z$ the following system of equations holds:
$$
\left\{\begin{array}{l}
x^{2}+x y+y^{2}=27 \\
y^{2}+y z+z^{2}=16 \\
z^{2}+x z+x^{2}=43
\end{array}\right.
$$
Find the value of the expression $x y+y z+x z$. | null | null |
[
{
"from": "user",
"value": "Stretch the x-coordinates of each point on the graph of the function $y=\\sin (x- \\frac {\\pi}{4})$ to twice its original length (the y-coordinates remain unchanged), and then shift it right by $\\frac {\\pi}{6}$ units. The equation of the resulting function graph is\nA: $y=\\si... | Stretch the x-coordinates of each point on the graph of the function $y=\sin (x- \frac {\pi}{4})$ to twice its original length (the y-coordinates remain unchanged), and then shift it right by $\frac {\pi}{6}$ units. The equation of the resulting function graph is
A: $y=\sin ( \frac {x}{2}- \frac {5\pi}{24})$
B: $y=\sin... | null | null |
[
{
"from": "user",
"value": "If the solution set of the inequality $ax^2+bx+a^2-1\\leq0$ with respect to $x$ is $[-1,+\\infty)$, then the values of the real numbers $a$ and $b$ are respectively."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this inequality: \\( ax^2 + bx + a^2 - 1... | If the solution set of the inequality $ax^2+bx+a^2-1\leq0$ with respect to $x$ is $[-1,+\infty)$, then the values of the real numbers $a$ and $b$ are respectively. | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Five buckets, each with a capacity of 15 liters, contain 1, 2, 3, 4, and 5 liters of water, respectively. It is permitted to triple the amount of water in any bucket by pouring water into it from just one of the other buckets (if there... | Five buckets, each with a capacity of 15 liters, contain 1, 2, 3, 4, and 5 liters of water, respectively. It is permitted to triple the amount of water in any bucket by pouring water into it from just one of the other buckets (if there is not enough water to triple the amount, pouring from that bucket is not allowed). ... | null | null |
[
{
"from": "user",
"value": "Let the sum of the first $n$ terms of an arithmetic sequence $\\{a_n\\}$ be $s_n$. If $9s_5+5s_9=90$, then $s_7=$ ( )\nA: $7$\nB: $14$\nC: $21$\nD: $22$"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. The problem says that the sum of the first n term... | Let the sum of the first $n$ terms of an arithmetic sequence $\{a_n\}$ be $s_n$. If $9s_5+5s_9=90$, then $s_7=$ ( )
A: $7$
B: $14$
C: $21$
D: $22$ | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. As shown in the image, 7 small squares form a large square. If the side lengths of these 7 small squares, in increasing order, are $1, 1, 2, 3, 5, 8, 13$, what is the perimeter of this large square?"
},
{
"from": "assistant",
... | As shown in the image, 7 small squares form a large square. If the side lengths of these 7 small squares, in increasing order, are $1, 1, 2, 3, 5, 8, 13$, what is the perimeter of this large square? | null | null |
[
{
"from": "user",
"value": "Subject 4. Determine the numbers $\\overline{a b}$ for which $\\overline{b a}+\\overline{a b}$ and $\\overline{b a}-\\overline{a b}$ are perfect squares."
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. The problem is asking for two-digit numbers, writte... | Subject 4. Determine the numbers $\overline{a b}$ for which $\overline{b a}+\overline{a b}$ and $\overline{b a}-\overline{a b}$ are perfect squares. | null | null |
[
{
"from": "user",
"value": "What is the syntax for filtering a DataFrame using multiple OR conditions in Pandas, while optimizing for time complexity, and also ensuring that the filtering is case-insensitive?"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to figure out how to filt... | null | codefeedback | null |
[
{
"from": "user",
"value": "You are tasked with implementing a User class in Java to manage user information. The class should have a constructor to initialize the user's unique ID, name, and city, as well as a method to retrieve the user's ID.\n\nYour task is to complete the implementation of the User clas... | null | magicoder | null |
[
{
"from": "user",
"value": "Define an even function $f(x)$ on $\\mathbb{R}$, which is increasing on $[0, +\\infty)$, and $f\\left(\\frac{1}{3}\\right)=0$. Then, the solution to the inequality $f(\\log_{\\frac{1}{8}}x) > 0$ is\nA: $\\left(\\frac{1}{2}, 1\\right)$ \nB: $(2, +\\infty)$ \nC: $\\left(0, \\frac... | Define an even function $f(x)$ on $\mathbb{R}$, which is increasing on $[0, +\infty)$, and $f\left(\frac{1}{3}\right)=0$. Then, the solution to the inequality $f(\log_{\frac{1}{8}}x) > 0$ is
A: $\left(\frac{1}{2}, 1\right)$
B: $(2, +\infty)$
C: $\left(0, \frac{1}{2}\right) \cup (2, +\infty)$
D: $\left(\frac{1}{2}... | null | null |
[
{
"from": "user",
"value": "You are given as input a greyscale image. Your task is to find a static or looping pattern in Conway's Game of Life that resembles the input image as closely as possible.\nYour output can be either a still image or a looping animation in some format that can be converted to gif. ... | You are given as input a greyscale image. Your task is to find a static or looping pattern in Conway's Game of Life that resembles the input image as closely as possible.
Your output can be either a still image or a looping animation in some format that can be converted to gif. The output image dimensions should be the... | null | null |
[
{
"from": "user",
"value": "An interior point in a rectangle is connected by line segments to the midpoints of its four sides. Thus four domains (polygons) with the areas $a, b, c$ and $d$ appear (see the figure). Prove that $a + c = b + d$.\n[img]https://1.bp.blogspot.com/-BipDNHELjJI/XzcCa68P3HI/AAAAAAAAM... | An interior point in a rectangle is connected by line segments to the midpoints of its four sides. Thus four domains (polygons) with the areas $a, b, c$ and $d$ appear (see the figure). Prove that $a + c = b + d$.
[img]https://1.bp.blogspot.com/-BipDNHELjJI/XzcCa68P3HI/AAAAAAAAMXY/H2Iqya9VItMLXrRqsdyxHLTXCAZ02nEtgCLcBG... | null | null |
[
{
"from": "user",
"value": "port this code to Groovy:\n```typescript\nfunction canPartitionKSubsets(nums: number[], k: number): boolean {\n const total_sum = nums.reduce((acc, curr) => acc + curr, 0);\n if (total_sum % k !== 0) {\n return false;\n }\n const target = total_sum / k;\n co... | null | dolphin | null |
[
{
"from": "user",
"value": "Let $f:[0,1]\\rightarrow{\\mathbb{R}}$ be a differentiable function, with continuous derivative, and let\n\\[ s_{n}=\\sum_{k=1}^{n}f\\left( \\frac{k}{n}\\right) \\]\nProve that the sequence $(s_{n+1}-s_{n})_{n\\in{\\mathbb{N}}^{\\ast}}$ converges to $\\int_{0}^{1}f(x)\\mathrm{d}... | Let $f:[0,1]\rightarrow{\mathbb{R}}$ be a differentiable function, with continuous derivative, and let
\[ s_{n}=\sum_{k=1}^{n}f\left( \frac{k}{n}\right) \]
Prove that the sequence $(s_{n+1}-s_{n})_{n\in{\mathbb{N}}^{\ast}}$ converges to $\int_{0}^{1}f(x)\mathrm{d}x$. | null | null |
[
{
"from": "user",
"value": " Find the largest $n$ such that the last nonzero digit of $n!$ is $1$.\n"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the largest integer n such that the last nonzero digit of n! (n factorial) is 1. Hmm, interesting problem. Let me try to figu... | Find the largest $n$ such that the last nonzero digit of $n!$ is $1$.
| null | null |
[
{
"from": "user",
"value": "Design a self-replicating program that generates a fractal pattern based on the Fibonacci sequence. The output should dynamically respond to user input by adjusting the scale of the fractal. If the input is a valid Fibonacci number, the program should render the fractal at that s... | null | evolcodegolf | null |
[
{
"from": "user",
"value": "2. In the arithmetic sequence $\\left\\{a_{n}\\right\\}$,\n$$\na_{2}+a_{11}+a_{14}=-6 \\text {. }\n$$\n\nThen the sum of the first 17 terms $\\sum_{i=1}^{17} a_{i}$ is ( ).\n(A) 0\n(B) -34\n(C) 17\n(D) 34"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. ... | 2. In the arithmetic sequence $\left\{a_{n}\right\}$,
$$
a_{2}+a_{11}+a_{14}=-6 \text {. }
$$
Then the sum of the first 17 terms $\sum_{i=1}^{17} a_{i}$ is ( ).
(A) 0
(B) -34
(C) 17
(D) 34 | null | null |
[
{
"from": "user",
"value": "Find all positive integers $n\\geq 1$ such that $n^2+3^n$ is the square of an integer. \r\n\r\n[i]Bulgaria[/i]"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. I need to find all positive integers n (starting from 1) such that n² + 3ⁿ is a perfect square... | Find all positive integers $n\geq 1$ such that $n^2+3^n$ is the square of an integer.
[i]Bulgaria[/i] | null | null |
[
{
"from": "user",
"value": "The number of correct propositions among the proposition \"If $x=5$, then $x^{2}-8x+15=0$\" and its converse, inverse, and contrapositive propositions is \\_\\_\\_\\_\\_\\_."
},
{
"from": "assistant",
"value": "<think>Okay, so I need to figure out how many of the four... | The number of correct propositions among the proposition "If $x=5$, then $x^{2}-8x+15=0$" and its converse, inverse, and contrapositive propositions is \_\_\_\_\_\_. | null | null |
[
{
"from": "user",
"value": "How can I configure Python's logging module to automatically output messages to both stdout and a log file? I want all calls to `logger.warning`, `logger.critical`, and `logger.error` to go to their intended places but also to be copied to stdout. I want to avoid duplicating mess... | null | sharegpt | null |
[
{
"from": "user",
"value": "If the solution of the equation $\\frac{x+m}{x-3}+\\frac{3m}{3-x}=3$ with respect to $x$ is a positive number, then the range of values for $m$ is ()\n\nA: $m \\lt \\frac{9}{2}$\n\nB: $m \\lt \\frac{9}{2}$ and $m\\neq \\frac{3}{2}$\n\nC: $m \\gt -\\frac{9}{4}$\n\nD: $m \\gt -\\fr... | If the solution of the equation $\frac{x+m}{x-3}+\frac{3m}{3-x}=3$ with respect to $x$ is a positive number, then the range of values for $m$ is ()
A: $m \lt \frac{9}{2}$
B: $m \lt \frac{9}{2}$ and $m\neq \frac{3}{2}$
C: $m \gt -\frac{9}{4}$
D: $m \gt -\frac{9}{4}$ and $m\neq -\frac{3}{4}$ | 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.Given a number n. The task is to find the smallest number whose factorial contains at least n traili... | 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.Given a number n. The task is to find the smallest number whose factorial contains at least n trailing zeroes.
Example 1:
Input:
n = 1
Outpu... | null | null |
[
{
"from": "user",
"value": "Given that $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$ of $\\triangle ABC$, respectively. If $a=1$, $b=\\sqrt{2}$, and angle $B$ is the arithmetic mean of angles $A$ and $C$, find the value of $\\sin A$."
},
{
"from": "assistant",
"value": "<t... | Given that $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$ of $\triangle ABC$, respectively. If $a=1$, $b=\sqrt{2}$, and angle $B$ is the arithmetic mean of angles $A$ and $C$, find the value of $\sin A$. | null | null |
[
{
"from": "user",
"value": "18. Given real numbers $x_{1}, x_{2}, \\cdots, x_{10}$ satisfy $\\sum_{i=1}^{10}\\left|x_{i}-1\\right| \\leqslant 4, \\sum_{i=1}^{10}\\left|x_{i}-2\\right| \\leqslant 6$. Find the average $\\bar{x}$ of $x_{1}, x_{2}, \\cdots, x_{10}$."
},
{
"from": "assistant",
"value... | 18. Given real numbers $x_{1}, x_{2}, \cdots, x_{10}$ satisfy $\sum_{i=1}^{10}\left|x_{i}-1\right| \leqslant 4, \sum_{i=1}^{10}\left|x_{i}-2\right| \leqslant 6$. Find the average $\bar{x}$ of $x_{1}, x_{2}, \cdots, x_{10}$. | null | null |
[
{
"from": "user",
"value": "Given the power function $y=({m}^{2}-3){x}^{{m}^{2}+m-3}$ is monotonically decreasing in $(0,+\\infty)$, find the real number $m=\\_\\_\\_\\_\\_\\_$."
},
{
"from": "assistant",
"value": "<think>\nOkay, let me try to figure this problem out. So we have a power function... | Given the power function $y=({m}^{2}-3){x}^{{m}^{2}+m-3}$ is monotonically decreasing in $(0,+\infty)$, find the real number $m=\_\_\_\_\_\_$. | null | null |
[
{
"from": "user",
"value": "The primary function of the RGB (Red Green Blue) color model is to facilitate the sensing, representation, and display of images across various electronic systems, including televisions and computers. Conversely, HSL (Hue Saturation Lightness) serves as an alternative color model... | null | evolcodegolf | null |
[
{
"from": "user",
"value": "The scaling transformation that changes the point (2, 3) into the point (3, 2) is ( )\nA: $$\\begin{cases} \\overset{x'= \\frac {2}{3}x}{y'= \\frac {3}{2}y}\\end{cases}$$\nB: $$\\begin{cases} \\overset{x'= \\frac {3}{2}x}{y'= \\frac {2}{3}y}\\end{cases}$$\nC: $$\\begin{cases}... | The scaling transformation that changes the point (2, 3) into the point (3, 2) is ( )
A: $$\begin{cases} \overset{x'= \frac {2}{3}x}{y'= \frac {3}{2}y}\end{cases}$$
B: $$\begin{cases} \overset{x'= \frac {3}{2}x}{y'= \frac {2}{3}y}\end{cases}$$
C: $$\begin{cases} \overset{x'=y}{y'=x}\end{cases}$$
D: $$\begin{cases}... | null | null |
[
{
"from": "user",
"value": "The slope of the tangent line to the curve $y=\\frac{\\sin x}{\\sin x+\\cos x}-\\frac{1}{2}$ at point $M\\left(\\frac{\\pi }{4},0\\right)$ is ( ).\n\nA: $-\\frac{\\sqrt{2}}{2}$\n\nB: $\\frac{\\sqrt{2}}{2}$\n\nC: $-\\frac{1}{2}$\n\nD: $\\frac{1}{2}$"
},
{
"from": "assistan... | The slope of the tangent line to the curve $y=\frac{\sin x}{\sin x+\cos x}-\frac{1}{2}$ at point $M\left(\frac{\pi }{4},0\right)$ is ( ).
A: $-\frac{\sqrt{2}}{2}$
B: $\frac{\sqrt{2}}{2}$
C: $-\frac{1}{2}$
D: $\frac{1}{2}$ | null | null |
[
{
"from": "user",
"value": "Given that a person's blood pressure follows the function $f(t) = 24\\sin(160\\pi t) + 110$, where $f(t)$ denotes the blood pressure in mmHg, and $t$ is the time in minutes, find the number of heartbeats per minute for this individual."
},
{
"from": "assistant",
"valu... | Given that a person's blood pressure follows the function $f(t) = 24\sin(160\pi t) + 110$, where $f(t)$ denotes the blood pressure in mmHg, and $t$ is the time in minutes, find the number of heartbeats per minute for this individual. | null | null |
[
{
"from": "user",
"value": "B. As shown in Figure 2, in the square $A B C D$ with side length 1, $E$ and $F$ are points on $B C$ and $C D$ respectively, and $\\triangle A E F$ is an equilateral triangle. Then the area of $\\triangle A E F$ is $\\qquad$."
},
{
"from": "assistant",
"value": "<thin... | B. As shown in Figure 2, in the square $A B C D$ with side length 1, $E$ and $F$ are points on $B C$ and $C D$ respectively, and $\triangle A E F$ is an equilateral triangle. Then the area of $\triangle A E F$ is $\qquad$. | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let \\( a_i \\) be real numbers such that \\( \\sum_{i=1}^{\\infty} a_i = 1 \\). Additionally, the sequence satisfies \\( |a_1| > |a_2| > |a_3| > \\ldots \\). Consider \\( f(i) \\) as a bijection of the positive integers onto itself, a... | Let \( a_i \) be real numbers such that \( \sum_{i=1}^{\infty} a_i = 1 \). Additionally, the sequence satisfies \( |a_1| > |a_2| > |a_3| > \ldots \). Consider \( f(i) \) as a bijection of the positive integers onto itself, and it holds that \( |f(i) - i||a_i| \to 0 \) as \( i \to \infty \). Prove or disprove that \( \s... | null | null |
[
{
"from": "user",
"value": "Given that the sum of the coefficients of all terms in the expansion of $({x+\\frac{1}{x}}){(ax+1)^5}$ is $64$, the coefficient of the term containing $x^{3}$ in the expansion is ______."
},
{
"from": "assistant",
"value": "<think>Okay, let's see. The problem is about... | Given that the sum of the coefficients of all terms in the expansion of $({x+\frac{1}{x}}){(ax+1)^5}$ is $64$, the coefficient of the term containing $x^{3}$ in the expansion is ______. | 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.In all schools in Buryatia, in the $1$ class, everyone is told the theory of Fibonacci strings.\n\n\... | 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.In all schools in Buryatia, in the $1$ class, everyone is told the theory of Fibonacci strings.
"A block is a subsegment of a string where ... | null | null |
[
{
"from": "user",
"value": "(10 points) Use the Euclidean algorithm to find the greatest common divisor (GCD) of 459 and 357, and verify it using the method of successive subtraction."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the GCD of 459 and 357 using the Euclidean... | (10 points) Use the Euclidean algorithm to find the greatest common divisor (GCD) of 459 and 357, and verify it using the method of successive subtraction. | null | null |
[
{
"from": "user",
"value": "Among the numbers $2^{-75}$, $3^{-50}$, $5^{-25}$, $80^{-12.5}$, the largest one is ( )\nA: $2^{-75}$\nB: $3^{-50}$\nC: $5^{-25}$\nD: $80^{-12.5}$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to figure out which of these numbers is the largest: 2^{-7... | Among the numbers $2^{-75}$, $3^{-50}$, $5^{-25}$, $80^{-12.5}$, the largest one is ( )
A: $2^{-75}$
B: $3^{-50}$
C: $5^{-25}$
D: $80^{-12.5}$ | null | null |
[
{
"from": "user",
"value": "If $|a| = 5$, $|b| = 3$, then the number of possible values for $a \\cdot b$ is ( ).\n\nA: 1\nB: 2\nC: 3\nD: 4"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to figure out how many possible values the dot product a · b can take if the magnitudes of vect... | If $|a| = 5$, $|b| = 3$, then the number of possible values for $a \cdot b$ is ( ).
A: 1
B: 2
C: 3
D: 4 | null | null |
[
{
"from": "user",
"value": "There are three boxes of stones. Each hour, Sisyphus moves a stones from one box to another. For each transfer of a stone, he receives from Zeus a number of coins equal to the number of stones in the box from which the stone is drawn minus the number of stones in the recipient bo... | There are three boxes of stones. Each hour, Sisyphus moves a stones from one box to another. For each transfer of a stone, he receives from Zeus a number of coins equal to the number of stones in the box from which the stone is drawn minus the number of stones in the recipient box, with the stone Sisyphus just carried ... | null | null |
[
{
"from": "user",
"value": "Which of the following terms is of the same type as $3x^{2}y$?\n\nA: $2xy^{2}$\n\nB: $3xy$\n\nC: $-yx^{2}$\n\nD: $3xyz$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this problem here asking me which of the given terms is the same type as 3x²y. The opt... | Which of the following terms is of the same type as $3x^{2}y$?
A: $2xy^{2}$
B: $3xy$
C: $-yx^{2}$
D: $3xyz$ | null | null |
[
{
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"value": "32. $[\\mathbf{1 7}]$ Let $f(x)=x^{2}-2$, and let $f^{n}$ denote the function $f$ applied $n$ times. Compute the remainder when $f^{24}(18)$ is divided by 89 ."
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. The problem is about applying a function mult... | 32. $[\mathbf{1 7}]$ Let $f(x)=x^{2}-2$, and let $f^{n}$ denote the function $f$ applied $n$ times. Compute the remainder when $f^{24}(18)$ is divided by 89 . | null | null |
[
{
"from": "user",
"value": "The value range of the real number $a$ for which the function $f(x) = (x - a)e^x$ has no extreme points in the interval $(2, 3)$ is ( )\n\nA: $(-\\infty, 3] \\cup [4, +\\infty)$ \nB: $[3, 4]$ \nC: $(-\\infty, 3]$ \nD: $[4, +\\infty)$"
},
{
"from": "assistant",
"va... | The value range of the real number $a$ for which the function $f(x) = (x - a)e^x$ has no extreme points in the interval $(2, 3)$ is ( )
A: $(-\infty, 3] \cup [4, +\infty)$
B: $[3, 4]$
C: $(-\infty, 3]$
D: $[4, +\infty)$ | null | null |
[
{
"from": "user",
"value": "4. On each side of a right-angled triangle, a semicircle is drawn with that side as a diameter. The areas of the three semicircles are $x^{2}, 3 x$ and 180 where $x^{2}$ and $3 x$ are both less than 180 . What is the area of the smallest semicircle?"
},
{
"from": "assista... | 4. On each side of a right-angled triangle, a semicircle is drawn with that side as a diameter. The areas of the three semicircles are $x^{2}, 3 x$ and 180 where $x^{2}$ and $3 x$ are both less than 180 . What is the area of the smallest semicircle? | null | null |
[
{
"from": "user",
"value": "The display has a row of 4 parallel holes, each of which can display 0 or 1. If each time it displays two of the holes, but two adjacent holes cannot be displayed at the same time, the total number of signals that the display can show is ______."
},
{
"from": "assistant",... | The display has a row of 4 parallel holes, each of which can display 0 or 1. If each time it displays two of the holes, but two adjacent holes cannot be displayed at the same time, the total number of signals that the display can show is ______. | null | null |
[
{
"from": "user",
"value": "How can I build an AI powered web crawler?"
},
{
"from": "assistant",
"value": "<think>\nOkay, I need to figure out how to build an AI-powered web crawler. Let's start by breaking down what a web crawler does. From what I know, a web crawler automatically navigates th... | null | sharegpt | null |
[
{
"from": "user",
"value": "Given $α=60^{\\circ}$, if point $P(a,b)$ $(a > 0,b > 0)$ is on the terminal side of $α$, then the eccentricity of the hyperbola $\\frac{x^{2}}{a^{2}} - \\frac{y^{2}}{b^{2}}=1$ is\n\nA: $2$\n\nB: $\\frac{2 \\sqrt{3}}{3}$\n\nC: $\\sqrt{3}$\n\nD: $\\frac{\\sqrt{3}}{2}$"
},
{
... | Given $α=60^{\circ}$, if point $P(a,b)$ $(a > 0,b > 0)$ is on the terminal side of $α$, then the eccentricity of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}}=1$ is
A: $2$
B: $\frac{2 \sqrt{3}}{3}$
C: $\sqrt{3}$
D: $\frac{\sqrt{3}}{2}$ | null | null |
[
{
"from": "user",
"value": "The solution to the fractional equation $\\frac{3}{{x+1}}-\\frac{2}{{x-1}}=0$ is ______."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this equation here: 3 over (x + 1) minus 2 over (x - 1) equals zero. Hmm, I need to solve for x. Alright, let me thin... | The solution to the fractional equation $\frac{3}{{x+1}}-\frac{2}{{x-1}}=0$ is ______. | null | null |
[
{
"from": "user",
"value": "Given the universal set $U=\\mathbb{R}$, set $A=\\{x|x^{2}-x-2=0\\}$, and set $B=\\{y|y=x+3,x\\in A\\}$, find $A\\cup B=$ _____."
},
{
"from": "assistant",
"value": "<think>\nOkay, let me try to figure out this problem step by step. So, we have the universal set U as ... | Given the universal set $U=\mathbb{R}$, set $A=\{x|x^{2}-x-2=0\}$, and set $B=\{y|y=x+3,x\in A\}$, find $A\cup B=$ _____. | null | null |
[
{
"from": "user",
"value": "You are tasked with creating a function to calculate the minimum number of wins required for a team to achieve a certain level of success in a sports tournament. The success level is determined by a given threshold value `n`. The team's win and loss records are represented by var... | null | codefeedback | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Simplify the fraction by rationalizing the denominator: $$\\frac{4}{\\sqrt{108}+2\\sqrt{12}+2\\sqrt{27}}.$$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to simplify the fraction 4 divided by (sqrt(108) plus... | Simplify the fraction by rationalizing the denominator: $$\frac{4}{\sqrt{108}+2\sqrt{12}+2\sqrt{27}}.$$ | null | null |
[
{
"from": "user",
"value": "Given that the elements in set $A$ satisfy $2x+a \\gt 0$, $a\\in R$, if $1\\notin A$ and $2\\in A$, then the range of values for $a$ is ____."
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. The problem says that set A consists of elements x such that 2x... | Given that the elements in set $A$ satisfy $2x+a \gt 0$, $a\in R$, if $1\notin A$ and $2\in A$, then the range of values for $a$ is ____. | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given the sequence \\( \\left\\{a_{n}\\right\\} \\) defined by:\n\\[ a_{0}=2, \\quad a_{1}=3, \\quad a_{2}=6 \\]\nand for \\( n \\geq 3 \\), the recurrence relation:\n\\[ a_{n}=(n+4) a_{n-1}-4 n a_{n-2}+(4 n-8) a_{n-3}, \\]\nfind the g... | Given the sequence \( \left\{a_{n}\right\} \) defined by:
\[ a_{0}=2, \quad a_{1}=3, \quad a_{2}=6 \]
and for \( n \geq 3 \), the recurrence relation:
\[ a_{n}=(n+4) a_{n-1}-4 n a_{n-2}+(4 n-8) a_{n-3}, \]
find the general term of the sequence \( \left\{a_{n}\right\} \). | null | null |
[
{
"from": "user",
"value": "93 Choose two different numbers from $\\{19,20,21, \\cdots, 91,92,93\\}$, so that their sum is even. The total number of ways to do this is $\\qquad$."
},
{
"from": "assistant",
"value": "<think>\nOkay, let me try to figure out this problem. So, we need to choose two ... | 93 Choose two different numbers from $\{19,20,21, \cdots, 91,92,93\}$, so that their sum is even. The total number of ways to do this is $\qquad$. | null | null |
[
{
"from": "user",
"value": "You are tasked with implementing a class that represents a version control system. The class should have a property `has_changes` that can be set to `True` or `False` to indicate whether there are pending changes in the system. Additionally, the class should have a method `commit... | null | magicoder | null |
[
{
"from": "user",
"value": "After completing the study of the content related to ellipses and hyperbolas in the textbook, Xiaoming raised a new question: What is the trajectory of the points on the plane whose product of distances to two fixed points is a constant? What properties does it have? The teacher ... | After completing the study of the content related to ellipses and hyperbolas in the textbook, Xiaoming raised a new question: What is the trajectory of the points on the plane whose product of distances to two fixed points is a constant? What properties does it have? The teacher highly praised his spirit of exploration... | null | null |
[
{
"from": "user",
"value": "You are tasked with creating a register file module in Verilog. The module should have inputs for clock signal, reset signal, load signal, input data, source A, source B, and destination. It should also have outputs for register A and register B.\n\nThe register file should have ... | null | null | null |
[
{
"from": "user",
"value": "Given the parabola $y^{2}=4x$ whose directrix intersects with the hyperbola $\\frac {x^{2}}{a^{2}}- \\frac {y^{2}}{b^{2}}=1$ ($a > 0,b > 0$) at points $A$ and $B$, and point $F$ is the focus of the parabola. If $\\triangle FAB$ is a right-angled triangle, then the range of the ec... | Given the parabola $y^{2}=4x$ whose directrix intersects with the hyperbola $\frac {x^{2}}{a^{2}}- \frac {y^{2}}{b^{2}}=1$ ($a > 0,b > 0$) at points $A$ and $B$, and point $F$ is the focus of the parabola. If $\triangle FAB$ is a right-angled triangle, then the range of the eccentricity of the hyperbola is \_\_\_\_\_\_... | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. There are 900 three-digit numbers $(100, 101, \\cdots, 999)$. Each number is printed on a card; some of these numbers, when seen upside-down, still appear as three-digit numbers. For example, when 198 is seen upside-down, it still appe... | There are 900 three-digit numbers $(100, 101, \cdots, 999)$. Each number is printed on a card; some of these numbers, when seen upside-down, still appear as three-digit numbers. For example, when 198 is seen upside-down, it still appears as a valid three-digit number. Therefore, at most $\qquad$ cards can be omitted fr... | null | null |
[
{
"from": "user",
"value": "Given a hyperbola $\\frac{x^{2}}{a^{2}} - \\frac{y^{2}}{b^{2}} = 1$ (where $a > 0, b > 0$), let $F_1$ and $F_2$ be its left and right foci, respectively. Suppose there exists a point $P$ on the right branch of the hyperbola such that $|PF_2| = |F_1F_2|$, and the distance from $F_... | Given a hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ (where $a > 0, b > 0$), let $F_1$ and $F_2$ be its left and right foci, respectively. Suppose there exists a point $P$ on the right branch of the hyperbola such that $|PF_2| = |F_1F_2|$, and the distance from $F_2$ to the line $PF_1$ is equal to the leng... | null | null |
[
{
"from": "user",
"value": "The zero point of the function $$f(x)=2^{x}- \\frac {2}{x}-a$$ is within the interval $(1, 2)$. Then, the range of the real number $a$ is \\_\\_\\_\\_\\_\\_."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this problem here: I need to find the range of t... | The zero point of the function $$f(x)=2^{x}- \frac {2}{x}-a$$ is within the interval $(1, 2)$. Then, the range of the real number $a$ is \_\_\_\_\_\_. | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Nine polygons with an area of 1 each are placed inside a square with an area of 5. Prove that some two of them have a common area of at least \\(1 / 9\\)."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to pro... | Nine polygons with an area of 1 each are placed inside a square with an area of 5. Prove that some two of them have a common area of at least \(1 / 9\). | null | null |
[
{
"from": "user",
"value": "Given two sequences $\\{a_n\\}$ and $\\{b_n\\}$ are both arithmetic sequences, and $a_1=15$, $b_1=35$, $a_2+b_2=60$, then $a_{36}+b_{36}=$ ______."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this problem here with two arithmetic sequences, {a_n} and ... | Given two sequences $\{a_n\}$ and $\{b_n\}$ are both arithmetic sequences, and $a_1=15$, $b_1=35$, $a_2+b_2=60$, then $a_{36}+b_{36}=$ ______. | null | null |
[
{
"from": "user",
"value": "You are tasked with implementing a settlements API for a financial platform. The API should provide methods for retrieving settlements based on certain criteria. You are given an interface `ISettlementsApi` with two methods: `GetAllSettlements` and `GetSingleSettlement`. The `Get... | null | null | null |
[
{
"from": "user",
"value": "Solve the equations:\n1. $x(x-2)=x-2$;\n2. $x^{2}-6x+5=0$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to solve these two equations. Let me start with the first one: x(x - 2) = x - 2. Hmm, let's see. Maybe I should expand the left side first. If I di... | Solve the equations:
1. $x(x-2)=x-2$;
2. $x^{2}-6x+5=0$. | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. On a birch tree, there were white and black crows – a total of 50. There were definitely white crows, but the number of black crows was not less than the number of white crows. On an oak tree, there were also white and black crows, and... | On a birch tree, there were white and black crows – a total of 50. There were definitely white crows, but the number of black crows was not less than the number of white crows. On an oak tree, there were also white and black crows, and there were a total of 50 crows. On the oak tree, the number of black crows was also ... | null | null |
[
{
"from": "user",
"value": "Given that $a$ and $b$ are the roots of the equation $x^{2}-3x-5=0$, then the value of the expression $\\frac{1}{a}+\\frac{1}{b}$ is ____."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the value of 1/a + 1/b where a and b are the roots of the q... | Given that $a$ and $b$ are the roots of the equation $x^{2}-3x-5=0$, then the value of the expression $\frac{1}{a}+\frac{1}{b}$ is ____. | null | null |
[
{
"from": "user",
"value": "Problem 5. The numbers $a, b$, and $c$ satisfy the equation $\\sqrt{a}=\\sqrt{b}+\\sqrt{c}$. Find $a$, if $b=52-30 \\sqrt{3}$ and $c=a-2$."
},
{
"from": "assistant",
"value": "<think>\nOkay, let me try to figure out this problem. The equation given is √a = √b + √c, an... | Problem 5. The numbers $a, b$, and $c$ satisfy the equation $\sqrt{a}=\sqrt{b}+\sqrt{c}$. Find $a$, if $b=52-30 \sqrt{3}$ and $c=a-2$. | null | null |
[
{
"from": "user",
"value": "How can I create a Python program that prints out the first 20 numbers of the Fibonacci sequence?"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to create a Python program that prints the first 20 numbers of the Fibonacci sequence. Let me think about ho... | null | glaive | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. If $\\overline{\\mathrm{ab}} \\times 65 = \\overline{48 \\mathrm{ab}}$, then $\\overline{\\mathrm{ab}} =$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to solve this equation where a two-digit number, writte... | If $\overline{\mathrm{ab}} \times 65 = \overline{48 \mathrm{ab}}$, then $\overline{\mathrm{ab}} =$ | null | null |
[
{
"from": "user",
"value": "### Legendary Pac-Man Challenge\n\nIn an unprecedented milestone, a gamer achieved the longest continuous run in the classic arcade game Pac-Man, surpassing all previous records without losing a single life. This is the moment Pac-Man navigates through the infamous maze at its pe... | null | evolcodegolf | null |
[
{
"from": "user",
"value": "8. Given the hyperbola $x^{2}-y^{2}=t(t>0)$ with its right focus at $F$, any line passing through $F$ intersects the right branch of the hyperbola at points $M$ and $N$. The perpendicular bisector of $M N$ intersects the $x$-axis at point $P$. When $t$ is a positive real number n... | 8. Given the hyperbola $x^{2}-y^{2}=t(t>0)$ with its right focus at $F$, any line passing through $F$ intersects the right branch of the hyperbola at points $M$ and $N$. The perpendicular bisector of $M N$ intersects the $x$-axis at point $P$. When $t$ is a positive real number not equal to zero, $\frac{|F P|}{|M N|}=$... | null | null |
[
{
"from": "user",
"value": "In how many ways can we form three teams of four players each from a group of $12$ participants?"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this problem: \"In how many ways can we form three teams of four players each from a group of 12 participants... | In how many ways can we form three teams of four players each from a group of $12$ participants? | null | null |
[
{
"from": "user",
"value": "Let \\( n \\geq 2 \\) be some fixed positive integer and suppose that \\( a_{1}, a_{2}, \\ldots, a_{n} \\) are positive real numbers satisfying \\( a_{1}+a_{2}+\\cdots+a_{n}=2^{n}-1 \\).\n\nFind the minimum possible value of\n\n\\[\n\\frac{a_{1}}{1}+\\frac{a_{2}}{1+a_{1}}+\\frac{... | Let \( n \geq 2 \) be some fixed positive integer and suppose that \( a_{1}, a_{2}, \ldots, a_{n} \) are positive real numbers satisfying \( a_{1}+a_{2}+\cdots+a_{n}=2^{n}-1 \).
Find the minimum possible value of
\[
\frac{a_{1}}{1}+\frac{a_{2}}{1+a_{1}}+\frac{a_{3}}{1+a_{1}+a_{2}}+\cdots+\frac{a_{n}}{1+a_{1}+a_{2}+\c... | null | null |
[
{
"from": "user",
"value": "Given a complex number $z=3+4i$ (where $i$ is the imaginary unit), find $|z|$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the modulus of the complex number z = 3 + 4i. Hmm, modulus... I remember that the modulus of a complex number is like i... | Given a complex number $z=3+4i$ (where $i$ is the imaginary unit), find $|z|$. | null | null |
[
{
"from": "user",
"value": "Consider an $8 \\times 8$ chessboard, on which we place some bishops in the 64 squares. Two bishops are said to attack each other if they lie on a common diagonal.\n\n(a) Prove that we can place 14 bishops in such a way that no two attack each other.\n\n(b) Prove that we cannot d... | Consider an $8 \times 8$ chessboard, on which we place some bishops in the 64 squares. Two bishops are said to attack each other if they lie on a common diagonal.
(a) Prove that we can place 14 bishops in such a way that no two attack each other.
(b) Prove that we cannot do so with 15 bishops. | null | null |
[
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Given a vector of N positive integers and an integer X. The task is to find the frequency of X in vector.\n \nExample 1: \nInput:\nN = 5\nvec... | Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Given a vector of N positive integers and an integer X. The task is to find the frequency of X in vector.
Example 1:
Input:
N = 5
vector = {1, 1, 1, 1, 1}
X = 1
Output:
5
Explan... | null | null |
[
{
"from": "user",
"value": "(2012•Jiangxi) Let the sequences $\\{a_n\\}$ and $\\{b_n\\}$ both be arithmetic sequences. If $a_1+b_1=7$, $a_3+b_3=21$, then $a_5+b_5=\\ ?$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this problem here where there are two arithmetic sequences, {a_n}... | (2012•Jiangxi) Let the sequences $\{a_n\}$ and $\{b_n\}$ both be arithmetic sequences. If $a_1+b_1=7$, $a_3+b_3=21$, then $a_5+b_5=\ ?$ | null | null |
[
{
"from": "user",
"value": "Has anyone experienced a situation where they initially used Python for a project, but due to performance issues, had to switch to another language? We are considering using Python for larger projects and would like to understand if there have been instances where Python's speed ... | null | sharegpt | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. 144. Find the triangle with the smallest possible perimeter, given the following information:\n\na) Two vertices $A$ and $B$ of the triangle and a line $l$ on which the third vertex lies;\nb) A vertex $A$ and two lines $l$ and $m$ on w... | 144. Find the triangle with the smallest possible perimeter, given the following information:
a) Two vertices $A$ and $B$ of the triangle and a line $l$ on which the third vertex lies;
b) A vertex $A$ and two lines $l$ and $m$ on which the vertices $B$ and $C$ lie;
c) Three lines $l$, $m$, $n$ on which the vertices $A... | null | null |
[
{
"from": "user",
"value": "11. Given $(3 x+1)^{5}=a x^{5}+b x^{4}+c x^{3}+d x^{2}+e x+f$, then $a-b+c-d+e-f=$ $\\qquad$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this problem here: Given that (3x + 1)^5 is expanded into the form ax^5 + bx^4 + cx^3 + dx^2 + ex + f, I need to ... | 11. Given $(3 x+1)^{5}=a x^{5}+b x^{4}+c x^{3}+d x^{2}+e x+f$, then $a-b+c-d+e-f=$ $\qquad$ | null | null |
[
{
"from": "user",
"value": "Given a sphere $O$ with radius $R$, points $A$, $B$, and $C$ are on the surface of sphere $O$. The distance from the center of the sphere $O$ to the plane $ABC$ is $\\frac{1}{2}R$. It is given that $AB=AC=2$ and $\\angle BAC=120^{\\circ}$. Find the surface area of sphere $O$.\nA:... | Given a sphere $O$ with radius $R$, points $A$, $B$, and $C$ are on the surface of sphere $O$. The distance from the center of the sphere $O$ to the plane $ABC$ is $\frac{1}{2}R$. It is given that $AB=AC=2$ and $\angle BAC=120^{\circ}$. Find the surface area of sphere $O$.
A: $\frac{16}{9}\pi$
B: $\frac{16}{3}\pi$
C: $... | null | null |
[
{
"from": "user",
"value": "The coordinates of the focus of the parabola $y=x^{2}$ are __________."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the coordinates of the focus of the parabola given by the equation y = x². Hmm, let's start by recalling what a parabola is and... | The coordinates of the focus of the parabola $y=x^{2}$ are __________. | null | null |
[
{
"from": "user",
"value": "In $\\triangle XYZ$, medians $\\overline{YM}$ and $\\overline{ZN}$ intersect at centroid $G$. If $YM = 21$, $ZN = 28$, and $YG = 7$, find the length of side $\\overline{XZ}$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the length of side XZ i... | null | nvidia_math | 35,601 |
[
{
"from": "user",
"value": "7.034. $\\lg \\left(3^{x}-2^{4-x}\\right)=2+0.25 \\lg 16-0.5 x \\lg 4$."
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. I need to solve this logarithmic equation: lg(3^x - 2^{4 - x}) = 2 + 0.25 lg 16 - 0.5x lg 4. Hmm, logarithms can be tricky, but maybe... | 7.034. $\lg \left(3^{x}-2^{4-x}\right)=2+0.25 \lg 16-0.5 x \lg 4$. | null | null |
[
{
"from": "user",
"value": "Given $f(x+1)=f(x-1)$ and $f(x)=f(-x+2)$, the equation $f(x)=0$ has exactly one root in the interval $[0,1]$, which is $\\frac{1}{2}$. Then, the number of roots of $f(x)=0$ in the interval $[0,2014]$ is ( ).\n\nA: $1006$\n\nB: $1007$\n\nC: $2013$\n\nD: $2014$"
},
{
"from"... | Given $f(x+1)=f(x-1)$ and $f(x)=f(-x+2)$, the equation $f(x)=0$ has exactly one root in the interval $[0,1]$, which is $\frac{1}{2}$. Then, the number of roots of $f(x)=0$ in the interval $[0,2014]$ is ( ).
A: $1006$
B: $1007$
C: $2013$
D: $2014$ | null | null |
[
{
"from": "user",
"value": "7. Given that the domain of $f(x)$ is symmetric about the origin, $f(x)=g(x)+h(x)$, where $g(x)$ is an odd function, $h(x)$ is an even function, then $g(x)=$ $\\qquad$ (express $g(x)$ in terms of $f(x)$)"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to... | 7. Given that the domain of $f(x)$ is symmetric about the origin, $f(x)=g(x)+h(x)$, where $g(x)$ is an odd function, $h(x)$ is an even function, then $g(x)=$ $\qquad$ (express $g(x)$ in terms of $f(x)$) | null | null |
[
{
"from": "user",
"value": "4. Let $H$ be a point on the plane of $\\triangle A B C$, and let $a, b, c, h$ represent the vectors $O A, O B, O C, O H$ respectively. If $\\boldsymbol{a} \\cdot \\boldsymbol{b}+\\boldsymbol{c} \\cdot \\boldsymbol{h}=\\boldsymbol{b} \\cdot \\boldsymbol{c}+\\boldsymbol{a} \\cdot ... | 4. Let $H$ be a point on the plane of $\triangle A B C$, and let $a, b, c, h$ represent the vectors $O A, O B, O C, O H$ respectively. If $\boldsymbol{a} \cdot \boldsymbol{b}+\boldsymbol{c} \cdot \boldsymbol{h}=\boldsymbol{b} \cdot \boldsymbol{c}+\boldsymbol{a} \cdot \boldsymbol{h}=\boldsymbol{c} \cdot \boldsymbol{a}+\... | null | null |
[
{
"from": "user",
"value": "You are tasked with creating a word ladder solver using the Compressed Sparse Graph Routines (`scipy.sparse.csgraph`) in Python. A word ladder is a word game in which players find paths between words by switching one letter at a time, with the goal of finding the shortest path be... | null | glaive | null |
[
{
"from": "user",
"value": "If the proposition \"There exists an $x \\in \\mathbb{R}$ such that $x^{2}+(a-1)x+1 \\leqslant 0$\" is false, then the range of the real number $a$ is $\\_\\_\\_\\_\\_\\_$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the range of the real num... | If the proposition "There exists an $x \in \mathbb{R}$ such that $x^{2}+(a-1)x+1 \leqslant 0$" is false, then the range of the real number $a$ is $\_\_\_\_\_\_$. | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. In the Cartesian coordinate system \\( XOY \\), given two points \\( M(-1,2) \\) and \\( N(1,4) \\), point \\( P \\) moves on the \\( X \\) axis. When the angle \\( \\angle MPN \\) is maximized, what is the \\( x \\)-coordinate of poin... | In the Cartesian coordinate system \( XOY \), given two points \( M(-1,2) \) and \( N(1,4) \), point \( P \) moves on the \( X \) axis. When the angle \( \angle MPN \) is maximized, what is the \( x \)-coordinate of point \( P \)? | null | null |
[
{
"from": "user",
"value": "I have an algorithm that outputs all prime numbers from 1 to 'n'. Can you help me make some adjustments to improve its performance? I understand that increasing the time or space complexity is acceptable in some cases, but it's not recommended to always do so. Please provide a mu... | null | sharegpt | null |
[
{
"from": "user",
"value": "Given sets $A=\\{x \\,|\\, |x-2|<1\\}$ and $B=\\{x \\,|\\, (x-1)(x-4)<0\\}$, which of the following statements is correct?\n\nA: $A \\cap B = \\emptyset$\n\nB: $A \\cup B = \\mathbb{R}$\n\nC: $A \\subseteq B$\n\nD: $B \\subseteq A$"
},
{
"from": "assistant",
"value": ... | Given sets $A=\{x \,|\, |x-2|<1\}$ and $B=\{x \,|\, (x-1)(x-4)<0\}$, which of the following statements is correct?
A: $A \cap B = \emptyset$
B: $A \cup B = \mathbb{R}$
C: $A \subseteq B$
D: $B \subseteq A$ | null | null |
[
{
"from": "user",
"value": "Three, (50 points) Given a positive integer $n$. Find $\\sum_{k=1}^{n}\\left[\\frac{n}{2^{k}}-\\frac{1}{2}\\right]$, where $[x]$ denotes the greatest integer not exceeding the real number $x$.\n\n---\n\nPlease note that the format and line breaks have been preserved as requested.... | Three, (50 points) Given a positive integer $n$. Find $\sum_{k=1}^{n}\left[\frac{n}{2^{k}}-\frac{1}{2}\right]$, where $[x]$ denotes the greatest integer not exceeding the real number $x$.
---
Please note that the format and line breaks have been preserved as requested. | null | null |
[
{
"from": "user",
"value": "A restaurant offers meals where each customer can choose 4 different dishes, consisting of 2 meat dishes and 2 vegetable dishes, from the options provided by the restaurant. Currently, the restaurant has prepared 5 different meat dishes. To ensure that each customer has more than... | A restaurant offers meals where each customer can choose 4 different dishes, consisting of 2 meat dishes and 2 vegetable dishes, from the options provided by the restaurant. Currently, the restaurant has prepared 5 different meat dishes. To ensure that each customer has more than 200 different choices, the restaurant n... | null | null |
[
{
"from": "user",
"value": "You are tasked with implementing a filtering feature for a web application that allows users to filter items based on tags and groups. You are provided with a TypeScript class `Filter` that represents the filtering criteria. The class has two properties: `selectedTags`, an array ... | null | magicoder | null |
[
{
"from": "user",
"value": "In $\\triangle ABC$, $A=60^{\\circ}$, $b=1$, and $S_{\\triangle ABC}= \\sqrt{3}$. Find the value of $\\dfrac{c}{\\sin C}$.\n\nA: $\\dfrac{8 \\sqrt{3}}{81}$\n\nB: $\\dfrac{2 \\sqrt{39}}{3}$\n\nC: $\\dfrac{26 \\sqrt{3}}{3}$\n\nD: $2 \\sqrt{7}$"
},
{
"from": "assistant",
... | In $\triangle ABC$, $A=60^{\circ}$, $b=1$, and $S_{\triangle ABC}= \sqrt{3}$. Find the value of $\dfrac{c}{\sin C}$.
A: $\dfrac{8 \sqrt{3}}{81}$
B: $\dfrac{2 \sqrt{39}}{3}$
C: $\dfrac{26 \sqrt{3}}{3}$
D: $2 \sqrt{7}$ | null | null |
[
{
"from": "user",
"value": "Given points $P_{1}(1,3)$, $P_{2}(4,-6)$, and point $P$ is on the line $P_{1}P_{2}$, and $\\overrightarrow{P_{1}P}=2\\overrightarrow{PP_{2}}$, then the coordinates of point $P$ are ______."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the coord... | Given points $P_{1}(1,3)$, $P_{2}(4,-6)$, and point $P$ is on the line $P_{1}P_{2}$, and $\overrightarrow{P_{1}P}=2\overrightarrow{PP_{2}}$, then the coordinates of point $P$ are ______. | 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.Problem\n\nThere is a dial-type padlock. This Nanjing lock has five dials and an enter button.\n\nRo... | 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.Problem
There is a dial-type padlock. This Nanjing lock has five dials and an enter button.
Rotate the five dials to create a five-digit i... | null | null |
[
{
"from": "user",
"value": "2. (6 points) Find the pattern and fill in the number: $1 、 4 、 3 、 8 、 5 、 12 、 7 、$"
},
{
"from": "assistant",
"value": "<think>\nAlright, let's tackle this sequence problem. The given numbers are 1, 4, 3, 8, 5, 12, 7, and we need to figure out the next number. Hmm,... | 2. (6 points) Find the pattern and fill in the number: $1 、 4 、 3 、 8 、 5 、 12 、 7 、$ | null | null |
[
{
"from": "user",
"value": "You are tasked with creating a program that analyzes the frequency of words in a given text file and returns the top N most frequently occurring words. Your program should ignore common English stop words (e.g., \"the\", \"and\", \"of\") and should be case-insensitive (i.e., \"Th... | null | codefeedback | null |
[
{
"from": "user",
"value": "A line passing through the focus of the parabola $y^2=4x$ at an angle of $\\frac{\\pi}{4}$ intersects the parabola at points P and Q. If O is the origin, then the area of $\\triangle POQ$ is ______."
},
{
"from": "assistant",
"value": "<think>\nOkay, let me try to fig... | A line passing through the focus of the parabola $y^2=4x$ at an angle of $\frac{\pi}{4}$ intersects the parabola at points P and Q. If O is the origin, then the area of $\triangle POQ$ is ______. | null | null |
[
{
"from": "user",
"value": "What is the value of \\(\\arctan(1)\\) in radians?"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to figure out the value of arctan(1) in radians. Hmm, arctan is the inverse of the tangent function, right? So arctan(1) should give me the angle whose tan... | null | automath | 12,766 |
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