conversations listlengths 2 2 | question stringlengths 16 24.8k ⌀ | source stringclasses 10
values | id int64 3 50k ⌀ |
|---|---|---|---|
[
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"from": "user",
"value": "Given that the sequence $\\{a_n\\}$ is an arithmetic sequence, and $a_2+a_3=1$, $a_{10}+a_{11}=9$, then $a_5+a_6=$ ?\n\nA: $4$\n\nB: $5$\n\nC: $6$\n\nD: $7$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to solve this arithmetic sequence problem. Let me... | Given that the sequence $\{a_n\}$ is an arithmetic sequence, and $a_2+a_3=1$, $a_{10}+a_{11}=9$, then $a_5+a_6=$ ?
A: $4$
B: $5$
C: $6$
D: $7$ | null | null |
[
{
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"value": "3. Consider the arbitrary triangle $\\triangle A B C, N$ the midpoint of $[A C], E$ the symmetric point of $B$ with respect to $N$ and $P$ the symmetric point of $C$ with respect to $B$. If the line $P E$ intersects the sides $[A B]$ and $[A C]$ at points $M$, respectively $F$, c... | 3. Consider the arbitrary triangle $\triangle A B C, N$ the midpoint of $[A C], E$ the symmetric point of $B$ with respect to $N$ and $P$ the symmetric point of $C$ with respect to $B$. If the line $P E$ intersects the sides $[A B]$ and $[A C]$ at points $M$, respectively $F$, calculate the ratio $\frac{F M}{M P}$.
Pr... | null | null |
[
{
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"value": "6.010. $\\frac{1}{x^{3}+2}-\\frac{1}{x^{3}+3}=\\frac{1}{12}$."
},
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"value": "<think>\nOkay, so I need to solve the equation \\(\\frac{1}{x^{3}+2} - \\frac{1}{x^{3}+3} = \\frac{1}{12}\\). Hmm, let me see. First, maybe I can simplify the left side ... | 6.010. $\frac{1}{x^{3}+2}-\frac{1}{x^{3}+3}=\frac{1}{12}$. | null | null |
[
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"value": "5. Line $l$ lies on plane $\\alpha$, line $m$ is parallel to plane $\\alpha$, and is skew to line $l$. A moving point $P$ is on plane $\\alpha$, and is equidistant from lines $l$ and $m$. Then the locus of point $P$ is ( ).\n(A) Line\n(B) Ellipse\n(C) Parabola\n(D) Hyperbola"
}... | 5. Line $l$ lies on plane $\alpha$, line $m$ is parallel to plane $\alpha$, and is skew to line $l$. A moving point $P$ is on plane $\alpha$, and is equidistant from lines $l$ and $m$. Then the locus of point $P$ is ( ).
(A) Line
(B) Ellipse
(C) Parabola
(D) Hyperbola | null | null |
[
{
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"value": "Instructions: Given the Target and Argument texts detect the stance that the argument has towards the topic. There are three types of stances \"in favor\", \"against\", and \"neutral\". \nInput: Topic: Republika Srpska secession from Bosnia and Herzegovina\n Argument: Republika S... | null | null | null |
[
{
"from": "user",
"value": "Given the sets $A=\\\\left\\\\{ x\\\\left| 2{{x}^{2}}-x-3 < 0 \\\\right. \\\\right\\\\}$ and $B=\\\\left\\\\{ x\\\\left| y=\\\\lg \\\\tfrac{1-x}{x+3} \\\\right. \\\\right\\\\}$, find the probability that a real number $x$ chosen randomly from the interval $(-3,3)$ belongs to $(A\... | Given the sets $A=\\left\\{ x\\left| 2{{x}^{2}}-x-3 < 0 \\right. \\right\\}$ and $B=\\left\\{ x\\left| y=\\lg \\tfrac{1-x}{x+3} \\right. \\right\\}$, find the probability that a real number $x$ chosen randomly from the interval $(-3,3)$ belongs to $(A\\bigcap B)$. | null | null |
[
{
"from": "user",
"value": "2. Given are sets $A, B$, and $C$ such that:\n\n- $A \\cup B \\cup C=\\{1,2,3, \\ldots, 100\\}$;\n- $A$ is the set of all natural numbers not greater than 100 that are divisible by 2;\n- $B$ is the set of all natural numbers not greater than 100 that are divisible by 3;\n- $B \\c... | 2. Given are sets $A, B$, and $C$ such that:
- $A \cup B \cup C=\{1,2,3, \ldots, 100\}$;
- $A$ is the set of all natural numbers not greater than 100 that are divisible by 2;
- $B$ is the set of all natural numbers not greater than 100 that are divisible by 3;
- $B \cap C$ is the set of all natural numbers not greater... | null | null |
[
{
"from": "user",
"value": "In the sequence $\\{a_n\\}$, for $n \\geq 2$, $a_n = \\frac{2S_n^2}{2S_n - 1}$ and $a_1 = 1$,\n(1) Find the general formula for the $n$-th term of the sequence $\\{a_n\\}$;\n(2) Calculate the sum of the first $n$ terms of the sequence $\\{a_n\\}$, denoted as $S_n$."
},
{
... | In the sequence $\{a_n\}$, for $n \geq 2$, $a_n = \frac{2S_n^2}{2S_n - 1}$ and $a_1 = 1$,
(1) Find the general formula for the $n$-th term of the sequence $\{a_n\}$;
(2) Calculate the sum of the first $n$ terms of the sequence $\{a_n\}$, denoted as $S_n$. | null | null |
[
{
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"value": "Chris’s internet bill is $45 per month for 100 GB and $0.25 for every 1 GB over. His bill for this month is $65. How many GB over was Chris charged for on this bill?"
},
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"value": "<think>\nOkay, so Chris has this internet bill that's normally $4... | null | tiger_lab_math | 14,280 |
[
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"value": "In the complex plane, the point corresponding to the complex number $\\frac {i}{1+i}$ is located in ( )\nA: The first quadrant\nB: The second quadrant\nC: The third quadrant\nD: The fourth quadrant"
},
{
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"value": "<think>\nOkay, let's see. I need... | In the complex plane, the point corresponding to the complex number $\frac {i}{1+i}$ is located in ( )
A: The first quadrant
B: The second quadrant
C: The third quadrant
D: The fourth quadrant | null | null |
[
{
"from": "user",
"value": "Let $O$ be the center of the base $\\triangle ABC$ of the regular tetrahedron $P-ABC$. A moving plane through $O$ intersects the three lateral edges or their extensions of $P-ABC$ at points $Q, R, S$, respectively. Then the sum $\\frac{1}{PQ} + \\frac{1}{PR} + \\frac{1}{PS}$ (\n(... | Let $O$ be the center of the base $\triangle ABC$ of the regular tetrahedron $P-ABC$. A moving plane through $O$ intersects the three lateral edges or their extensions of $P-ABC$ at points $Q, R, S$, respectively. Then the sum $\frac{1}{PQ} + \frac{1}{PR} + \frac{1}{PS}$ (
(A) has a maximum value but no minimum value
(... | null | null |
[
{
"from": "user",
"value": "A fruit distributor purchased 10 boxes each of two types of fruits, $A$ and $B$, and distributed them to Store A and Store B for sale (in whole boxes). The expected profit per box of fruit at Store A and Store B is shown in the table below:\n\n| | $A$ Fruit / Box | $B$ F... | A fruit distributor purchased 10 boxes each of two types of fruits, $A$ and $B$, and distributed them to Store A and Store B for sale (in whole boxes). The expected profit per box of fruit at Store A and Store B is shown in the table below:
| | $A$ Fruit / Box | $B$ Fruit / Box |
|----------|-----------------... | null | null |
[
{
"from": "user",
"value": "Pretend to be Rose Otoribashi, praising one of his subordinates."
},
{
"from": "assistant",
"value": "**(Clears throat, adopting a stern yet proud tone, as Rose Otoribashi from the series \"God of High School\")**\n\n\"Ah, **(pauses for a brief moment)**... Min, I mus... | null | null | null |
[
{
"from": "user",
"value": "7. From $1,2, \\cdots, 1995$, what is the maximum number of numbers that can be selected such that none of the selected numbers is 19 times another?"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to figure out the maximum number of numbers I can select ... | 7. From $1,2, \cdots, 1995$, what is the maximum number of numbers that can be selected such that none of the selected numbers is 19 times another? | null | null |
[
{
"from": "user",
"value": "\n\nThe arithmetic mean of ten different natural numbers is 15. Find the greatest possible value of the greatest of these numbers."
},
{
"from":... | 
The arithmetic mean of ten different natural numbers is 15. Find the greatest possible value of the greatest of these numbers. | null | null |
[
{
"from": "user",
"value": "You are given a 2D array of integers. Your task is to implement a function that rotates the array 90 degrees clockwise.\n\nFor example, given the following 2D array:\n```\n2 3\n4 5 6\n```\nThe function should rotate it 90 degrees clockwise to produce:\n```\n4 2\n5 3\n6\n```\n\nYo... | null | magicoder | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Bored in an infinitely long class, Evan jots down a fraction whose numerator and denominator are both $70$ -character strings, as follows:\n\\[ r = \\frac{loooloolloolloololllloloollollolllloollloloolooololooolololooooollllol}\n{loloo... | Bored in an infinitely long class, Evan jots down a fraction whose numerator and denominator are both $70$ -character strings, as follows:
\[ r = \frac{loooloolloolloololllloloollollolllloollloloolooololooolololooooollllol}
{lolooloolollollolloooooloooloololloolllooollololoooollllooolollloloool}. \]
If $o=2013$ and ... | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. A fair six-sided die is thrown 10 times. What is the probability that the faces 1, 2, 3, 4, 5, and 6 will appear exactly 2, 3, 1, 1, 1, and 2 times, respectively (event A)?"
},
{
"from": "assistant",
"value": "<think>\nOkay... | A fair six-sided die is thrown 10 times. What is the probability that the faces 1, 2, 3, 4, 5, and 6 will appear exactly 2, 3, 1, 1, 1, and 2 times, respectively (event A)? | null | null |
[
{
"from": "user",
"value": "Determine all prime numbers $p$ for which there exists a unique $a$ in $\\{1, \\ldots, p\\}$ such that $a^{3}-3 a+1$ is divisible by $p$.\n\n---\n\nThe translation maintains the original formatting and structure of the source text."
},
{
"from": "assistant",
"value": ... | Determine all prime numbers $p$ for which there exists a unique $a$ in $\{1, \ldots, p\}$ such that $a^{3}-3 a+1$ is divisible by $p$.
---
The translation maintains the original formatting and structure of the source text. | null | null |
[
{
"from": "user",
"value": "How can I transform a Numpy array of size (128 x 128) into a (64 x 64) array by averaging each 2x2 non-overlapping blocks in the original array?"
},
{
"from": "assistant",
"value": "Transforming a Numpy array by Downsampling through Averaging\n========================... | null | null | null |
[
{
"from": "user",
"value": "Figure 0 consists of a square with side length 18 . For each integer $n \\geq 0$, Figure $n+1$ consists of Figure $n$ with the addition of two new squares constructed on each of the squares that were added in Figure $n$. The side length of the squares added in Figure $n+1$ is $\\... | Figure 0 consists of a square with side length 18 . For each integer $n \geq 0$, Figure $n+1$ consists of Figure $n$ with the addition of two new squares constructed on each of the squares that were added in Figure $n$. The side length of the squares added in Figure $n+1$ is $\frac{2}{3}$ of the side length of the smal... | null | null |
[
{
"from": "user",
"value": "Design a more intricate variant of the previously mentioned challenge that resembles a crossword puzzle! In this version, each grid square may contain either one or two characters, but with an additional stipulation that requires words formed in both horizontal and vertical orien... | null | null | null |
[
{
"from": "user",
"value": "Find the smallest prime $p$ such that the digits of $p$ (in base 10) add up to a prime number greater than $10$."
},
{
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"value": "<think>\nOkay, so I need to find the smallest prime number p where the sum of its digits (in base 10) is also a prime ... | Find the smallest prime $p$ such that the digits of $p$ (in base 10) add up to a prime number greater than $10$. | null | null |
[
{
"from": "user",
"value": "Generate a list of 30 distinct prime numbers between 10 and 500, avoiding any prime numbers that are 1 mod 4 (i.e., when you divide the number by 4, the remainder should not be 1). Your function/method should be able to handle boundary cases as well, such as when there are fewer ... | null | codefeedback | null |
[
{
"from": "user",
"value": "I have a string and I want to generate another string that contains only the unique characters from the original string. How can I achieve this using Python?"
},
{
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"value": "<think>\nOkay, let's see. The user wants to take a string and create anot... | null | glaive | null |
[
{
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"value": "G5.4 In figure $3, \\triangle A B C$ is a right-angled triangle and $B H \\perp A C$. If $A B=15, H C=16$ and the area of $\\triangle A B C$ is $S$, find the value of $S$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this geometry problem here. Let me... | G5.4 In figure $3, \triangle A B C$ is a right-angled triangle and $B H \perp A C$. If $A B=15, H C=16$ and the area of $\triangle A B C$ is $S$, find the value of $S$. | null | null |
[
{
"from": "user",
"value": "How many positive common divisors do $10^{100}$ and $10^{121}+10^{813}+10$ have?"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find how many positive common divisors 10^100 and 10^121 + 10^813 + 10 have. Hmm, let's start by recalling that the number... | How many positive common divisors do $10^{100}$ and $10^{121}+10^{813}+10$ have? | null | null |
[
{
"from": "user",
"value": "George bought some food for his trip: a bottle of juice, a sandwich, and a bottle of milk. The sandwich was for x, and the juice was two times more expensive. The bottle of milk cost was 75% of the total cost of the sandwich and juice. How much did George pay for his food?\nIf we... | null | tiger_math | 28,380 |
[
{
"from": "user",
"value": "In the arithmetic sequence $\\{a_n\\}$, the first term $a_1=0$, and the common difference $d\\neq 0$. If $a_k=a_1+a_2+a_3+\\ldots+a_7$, then $k=$ （ ） \n A． 22 B． 23 C． 24 D． 25"
},
{
"from": "assistant",
"value": "<think>\nAlright, so I have this problem here about... | In the arithmetic sequence $\{a_n\}$, the first term $a_1=0$, and the common difference $d\neq 0$. If $a_k=a_1+a_2+a_3+\ldots+a_7$, then $k=$ （ ）
A． 22 B． 23 C． 24 D． 25 | null | null |
[
{
"from": "user",
"value": "(1) $x(x-1)-3(x-1)=0$; \n(2) $x^{2}+2x-1=0$."
},
{
"from": "assistant",
"value": "<think>\nAlright, let's tackle these two equations one by one. I need to solve both of them, right? Let me start with the first one: \\( x(x - 1) - 3(x - 1) = 0 \\). Hmm, okay. Let me t... | (1) $x(x-1)-3(x-1)=0$;
(2) $x^{2}+2x-1=0$. | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. We have filled an $n \\times n$ table with 1s and -1s in such a way that for any two different rows, the numbers in the corresponding positions match as many times as they differ. Show that the sum of the numbers written in the table i... | We have filled an $n \times n$ table with 1s and -1s in such a way that for any two different rows, the numbers in the corresponding positions match as many times as they differ. Show that the sum of the numbers written in the table is not greater than $n^{3 / 2}$. | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. For given integer $n \\geq 3$ , set $S =\\{p_1, p_2, \\cdots, p_m\\}$ consists of permutations $p_i$ of $(1, 2, \\cdots, n)$ . Suppose that among every three distinct numbers in $\\{1, 2, \\cdots, n\\}$ , one of these number doe... | For given integer $n \geq 3$ , set $S =\{p_1, p_2, \cdots, p_m\}$ consists of permutations $p_i$ of $(1, 2, \cdots, n)$ . Suppose that among every three distinct numbers in $\{1, 2, \cdots, n\}$ , one of these number does not lie in between the other two numbers in every permutations $p_i$ ( $1 \leq i \leq m$ ... | null | null |
[
{
"from": "user",
"value": "(OIM 1983)\n\nFind all functions $f: \\mathbb{R}_{+}^{*} \\rightarrow \\mathbb{R}_{+}^{*}$ such that, for all $x, y>0, f(y f(x))=x f(y)$ and $\\lim _{x \\rightarrow+\\infty} f(x)=0$."
},
{
"from": "assistant",
"value": "<think>\nOkay, let's try to tackle this function... | (OIM 1983)
Find all functions $f: \mathbb{R}_{+}^{*} \rightarrow \mathbb{R}_{+}^{*}$ such that, for all $x, y>0, f(y f(x))=x f(y)$ and $\lim _{x \rightarrow+\infty} f(x)=0$. | null | null |
[
{
"from": "user",
"value": "How can I refactor the given JavaScript code snippet to implement the ternary operator, chained or nested ternary operators? I want to handle multiple conditions and integrate error handling. \n\n```javascript\nlet y = 20;\n\nif (y < 0) {\n y = y - 15;\n} else if (y > 30) {\n y... | null | sharegpt | null |
[
{
"from": "user",
"value": "7.104. $\\frac{\\lg x^{2}}{\\lg (6 x-5)}=1$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to solve the equation (lg x²) / (lg (6x - 5)) = 1. Hmm, let me start by recalling what lg means. I think lg is logarithm base 10, right? So log base 10 of x squa... | 7.104. $\frac{\lg x^{2}}{\lg (6 x-5)}=1$. | null | null |
[
{
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"value": "You are tasked with creating a function that takes an object and generates a URL for the image detail using the Django Rest Framework. The function should take the object's slug and use it to construct the URL with the specified version.\n\nWrite a Python function called get_imag... | null | glaive | null |
[
{
"from": "user",
"value": "Louie sells Dodge, Hyundai, and Kia vehicles, and his company has 400 vehicles for sale on the store's parking lot. Half of the vehicles on the lot are Dodge, and there are half as many Hyundai vehicles on the lot as there are Dodge vehicles. How many Kia vehicles are on the lo... | null | tiger_lab_math | 26,309 |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. What is the largest factor of $130000$ that does not contain the digit $0$ or $5$ ?"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the largest factor of 130,000 that doesn't have any digits 0 or ... | What is the largest factor of $130000$ that does not contain the digit $0$ or $5$ ? | null | null |
[
{
"from": "user",
"value": "How can I efficiently and accurately determine the datatype of a given input parameter in Python?"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to figure out how to determine the datatype of a given input parameter in Python. Hmm, I remember that Pytho... | null | glaive | null |
[
{
"from": "user",
"value": "Create a function to calculate the sum of squares of each element in a given tuple and append the results to a specific list. The function should handle tuples containing zero and negative numbers, and return an error message if the tuple is empty. The function should also handle... | null | codefeedback | null |
[
{
"from": "user",
"value": "The increasing interval of the function $y=3x-x^3$ is ( )\nA: $(1, +\\infty)$\nB: $(-\\infty, -1)$ and $(1, +\\infty)$\nC: $(-1, 1)$\nD: $(-\\infty, -1) \\cup (1, +\\infty)$"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. I need to find the increasing i... | The increasing interval of the function $y=3x-x^3$ is ( )
A: $(1, +\infty)$
B: $(-\infty, -1)$ and $(1, +\infty)$
C: $(-1, 1)$
D: $(-\infty, -1) \cup (1, +\infty)$ | null | null |
[
{
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"value": "10. Given that $a$ and $b$ are real numbers, the system of inequalities about $x$\n$$\n\\left\\{\\begin{array}{l}\n20 x+a>0, \\\\\n15 x-b \\leqslant 0\n\\end{array}\\right.\n$$\n\nhas only the integer solutions $2, 3, 4$. Then the maximum value of $ab$ is . $\\qquad$"
},
{
... | 10. Given that $a$ and $b$ are real numbers, the system of inequalities about $x$
$$
\left\{\begin{array}{l}
20 x+a>0, \\
15 x-b \leqslant 0
\end{array}\right.
$$
has only the integer solutions $2, 3, 4$. Then the maximum value of $ab$ is . $\qquad$ | null | null |
[
{
"from": "user",
"value": "Q:Here is a review left by a customer on a product. Would you say he was satisfied or dissatisfied? Title: More please! Review: 1st, I want to say that i love the music of this cd. next, i want to hear more from the singer, Amleset Solomon. she sounds so good. I know a lot of fat... | null | null | null |
[
{
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"value": "You are tasked with implementing a payment processing system for a mobile application. The system should support various payment methods and operations. You are given a list of possible payment operations as shown below:\n\n```swift\nenum PaymentOperation {\n case createCardTo... | null | codefeedback | null |
[
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"value": "12. The smallest positive period of the function $f(x)=\\cos ^{3} x-\\sin ^{2} x$ is"
},
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"value": "<think>\nOkay, let's see. The problem is asking for the smallest positive period of the function f(x) = cos³x - sin²x. Hmm, periods. So, trigonome... | 12. The smallest positive period of the function $f(x)=\cos ^{3} x-\sin ^{2} x$ is | null | null |
[
{
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"value": "11 Prime numbers $p$, $q$, $r$ satisfy $p+q=r$, and $(r-p)(q-p)-27 p$ is a perfect square, then all triples $(p, q, r)=$ $\\qquad$ ."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find all triples of prime numbers (p, q, r) such that p + q = r, and t... | 11 Prime numbers $p$, $q$, $r$ satisfy $p+q=r$, and $(r-p)(q-p)-27 p$ is a perfect square, then all triples $(p, q, r)=$ $\qquad$ . | null | null |
[
{
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"value": "A class consists of 26 students with two students sitting on each desk. Suddenly, the students decide to change seats, such that every two students that were previously sitting together are now apart. Find the maximum value of positive integer $N$ such that, regardless of the stu... | A class consists of 26 students with two students sitting on each desk. Suddenly, the students decide to change seats, such that every two students that were previously sitting together are now apart. Find the maximum value of positive integer $N$ such that, regardless of the students' sitting positions, at the end the... | null | null |
[
{
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"value": "Quest for Uniqueness \nYour mission is to devise a function that accepts a positive integer m (greater than 0) as input through standard input, command-line arguments, or function parameters and returns a list. The conditions are as follows:\n\n1. The list must only consist of i... | null | evolcodegolf | null |
[
{
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"value": "The graph of the function $y=2011+\\log_a(x+2012)$ ($a>0$, $a\\neq1$) always passes through a fixed point."
},
{
"from": "assistant",
"value": "<think>\nAlright, let's tackle this problem. So, the question is about the graph of the function y = 2011 + log_a(x + 2012),... | The graph of the function $y=2011+\log_a(x+2012)$ ($a>0$, $a\neq1$) always passes through a fixed point. | null | null |
[
{
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"value": "Return your final response within \\boxed{}. Given a convex quadrilateral ABCD, prove that if the perimeters of triangles ABC, BCD, CDA, and DAB are equal, then ABCD is a rectangle."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to prove that if a conve... | Given a convex quadrilateral ABCD, prove that if the perimeters of triangles ABC, BCD, CDA, and DAB are equal, then ABCD is a rectangle. | null | null |
[
{
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"value": "Return your final response within \\boxed{}. Adam is playing Minesweeper on a $9\\times9$ grid of squares, where exactly $\\frac13$ (or 27) of the squares are mines (generated uniformly at random over all such boards). Every time he clicks on a square, it is either a mine, in... | Adam is playing Minesweeper on a $9\times9$ grid of squares, where exactly $\frac13$ (or 27) of the squares are mines (generated uniformly at random over all such boards). Every time he clicks on a square, it is either a mine, in which case he loses, or it shows a number saying how many of the (up to eight) adjacen... | null | null |
[
{
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"value": "A sequence $\\{a\\_n\\}$ satisfies $a\\_1=1$, $\\sqrt{\\frac{1}{a\\_n^2}+2}=\\frac{1}{a\\_{n+1}} (n\\in\\mathbb{N}^*)$, and $b\\_n=\\frac{1}{a\\_n^2\\cdot 2^n}$. Determine the sum of the first $n$ terms of the sequence $\\{b\\_n\\}$, denoted as $S\\_n=$ \\_\\_\\_\\_\\_\\_."
},
... | A sequence $\{a\_n\}$ satisfies $a\_1=1$, $\sqrt{\frac{1}{a\_n^2}+2}=\frac{1}{a\_{n+1}} (n\in\mathbb{N}^*)$, and $b\_n=\frac{1}{a\_n^2\cdot 2^n}$. Determine the sum of the first $n$ terms of the sequence $\{b\_n\}$, denoted as $S\_n=$ \_\_\_\_\_\_. | null | null |
[
{
"from": "user",
"value": "How can I create a migration to add a 'Country' model to the 'venues' app in Django?"
},
{
"from": "assistant",
"value": "<think>\nOkay, I need to create a migration to add a 'Country' model to the 'venues' app in Django. Let me think through the steps. \n\nFirst, I r... | null | sharegpt | null |
[
{
"from": "user",
"value": "Where in a house can you find toilet paper?\nA: grocery store\nB: cabinet\nC: bathroom\nD: kitchen\nE: rest area"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's tackle this question step by step. The question is asking where in a house you can find toilet pa... | Where in a house can you find toilet paper?
A: grocery store
B: cabinet
C: bathroom
D: kitchen
E: rest area | null | null |
[
{
"from": "user",
"value": "9. Given $x>0, y>0$, and $\\frac{1}{2 x+y}+\\frac{1}{y+1}=1$. Then the minimum value of $x+2 y$ is $\\qquad$ ."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the minimum value of \\( x + 2y \\) given that \\( x > 0 \\), \\( y > 0 \\), and the eq... | 9. Given $x>0, y>0$, and $\frac{1}{2 x+y}+\frac{1}{y+1}=1$. Then the minimum value of $x+2 y$ is $\qquad$ . | null | null |
[
{
"from": "user",
"value": "Given a text-based representation of a fractal shape using a limited set of characters, along with a scaling factor that is an even number greater than 2, expand each character into a defined pattern that corresponds to its original structure, resizing it to fit within the specif... | null | evolcodegolf | null |
[
{
"from": "user",
"value": "Given $f(x)=\\sin ^{2}x+ \\sqrt {3}\\sin x\\cos x- \\frac {1}{2}(x\\in \\mathbb{R})$.\n(1) Find the minimum positive period and the range of the function $f(x)$;\n(2) In $\\triangle ABC$, let the angles $A$, $B$, $C$ correspond to the sides $a$, $b$, $c$ respectively, with $A$ be... | Given $f(x)=\sin ^{2}x+ \sqrt {3}\sin x\cos x- \frac {1}{2}(x\in \mathbb{R})$.
(1) Find the minimum positive period and the range of the function $f(x)$;
(2) In $\triangle ABC$, let the angles $A$, $B$, $C$ correspond to the sides $a$, $b$, $c$ respectively, with $A$ being an acute angle, $a=2 \sqrt {3}$, $c=4$. If $f(... | null | null |
[
{
"from": "user",
"value": "In $\\triangle ABC$, $\\sin A + \\cos A = \\sqrt{2}$, and $\\sqrt{3} \\cos A = -\\sqrt{2} \\cos (\\pi - B)$, find the three internal angles of $\\triangle ABC$."
},
{
"from": "assistant",
"value": "<think>\nAlright, let's tackle this triangle problem. Okay, so we have... | In $\triangle ABC$, $\sin A + \cos A = \sqrt{2}$, and $\sqrt{3} \cos A = -\sqrt{2} \cos (\pi - B)$, find the three internal angles of $\triangle ABC$. | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. The value of \\((\\sqrt{25}-\\sqrt{9})^{2}\\) is:\n(A) 26\n(B) 16\n(C) 34\n(D) 8\n(E) 4"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this math problem here: the value of (√25 - √9) squared, with options A t... | The value of \((\sqrt{25}-\sqrt{9})^{2}\) is:
(A) 26
(B) 16
(C) 34
(D) 8
(E) 4 | null | null |
[
{
"from": "user",
"value": "2. For a finite set of points $M$ in the plane, it has the property: for any two points $A, B$ in $M$, there must exist a third point $C \\in M$ such that $\\triangle A B C$ is an equilateral triangle. Find the maximum value of $|M|$."
},
{
"from": "assistant",
"value... | 2. For a finite set of points $M$ in the plane, it has the property: for any two points $A, B$ in $M$, there must exist a third point $C \in M$ such that $\triangle A B C$ is an equilateral triangle. Find the maximum value of $|M|$. | null | null |
[
{
"from": "user",
"value": "Given vectors $\\overrightarrow{a}=(1,2)$, $\\overrightarrow{b}=(0,1)$, $\\overrightarrow{c}=(-2,k)$, if $(\\overrightarrow{a}+2\\overrightarrow{b}) \\parallel \\overrightarrow{c}$, then $k=$ ( )\nA: $(-8)$\nB: $(-\\frac{1}{2})$\nC: $(\\frac{1}{2})$\nD: $(8)$"
},
{
"fro... | Given vectors $\overrightarrow{a}=(1,2)$, $\overrightarrow{b}=(0,1)$, $\overrightarrow{c}=(-2,k)$, if $(\overrightarrow{a}+2\overrightarrow{b}) \parallel \overrightarrow{c}$, then $k=$ ( )
A: $(-8)$
B: $(-\frac{1}{2})$
C: $(\frac{1}{2})$
D: $(8)$ | null | null |
[
{
"from": "user",
"value": "Background\nAlice and Bob play a game called construct a binary word. To play the game, you fix a length n >= 0, a set G of length-n binary words called the goal set, and a length-n string t containing the letters A and B, called the turn order. The game lasts for n turns, and on... | Background
Alice and Bob play a game called construct a binary word. To play the game, you fix a length n >= 0, a set G of length-n binary words called the goal set, and a length-n string t containing the letters A and B, called the turn order. The game lasts for n turns, and on turn i, the player defined by t[i] selec... | null | null |
[
{
"from": "user",
"value": "Given the functions $f(x) = 3\\sin(\\omega x)$ ($\\omega > 0$) and $g(x) = 2\\cos(2x + \\varphi) + 1$, their graphs have the exact same axis of symmetry. If $x \\in \\mathbb{R}$, then the range of $f(x)$ is \\_\\_\\_\\_\\_\\_\\_\\_."
},
{
"from": "assistant",
"value":... | Given the functions $f(x) = 3\sin(\omega x)$ ($\omega > 0$) and $g(x) = 2\cos(2x + \varphi) + 1$, their graphs have the exact same axis of symmetry. If $x \in \mathbb{R}$, then the range of $f(x)$ is \_\_\_\_\_\_\_\_. | null | null |
[
{
"from": "user",
"value": "Introduction \nThe Travelling Salesman Problem (TSP) is a well-known challenge, where the objective is to determine the minimum Hamiltonian cycle given a list of N cities. The goal is to identify the shortest route that visits each city and returns to the starting point. However... | null | evolcodegolf | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. 288 points are placed inside a square ABCD of side 1. Show that one can draw a set S of lines of length 1 parallel to AB, joining AD and BC, and additional lines parallel to AD, joining each of the 288 points to a line in S, so that th... | 288 points are placed inside a square ABCD of side 1. Show that one can draw a set S of lines of length 1 parallel to AB, joining AD and BC, and additional lines parallel to AD, joining each of the 288 points to a line in S, so that the total length of all the lines is less than 24. Is there a stronger result? | null | null |
[
{
"from": "user",
"value": "Given two circles $x^2+y^2-4x-3=0$ and $x^2+y^2-4y-3=0$, and their intersection points are A and B, then the length of segment AB is \\_\\_\\_\\_\\_\\_."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this problem with two circles, and I need to find the... | Given two circles $x^2+y^2-4x-3=0$ and $x^2+y^2-4y-3=0$, and their intersection points are A and B, then the length of segment AB is \_\_\_\_\_\_. | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Determine the maximum value of $m$ , such that the inequality\n\n\\[ (a^2+4(b^2+c^2))(b^2+4(a^2+c^2))(c^2+4(a^2+b^2)) \\ge m \\]\n\nholds for every $a,b,c \\in \\mathbb{R} \\setminus \\{0\\}$ with $\\left|\\frac{1}{a}\\right|+\\lef... | Determine the maximum value of $m$ , such that the inequality
\[ (a^2+4(b^2+c^2))(b^2+4(a^2+c^2))(c^2+4(a^2+b^2)) \ge m \]
holds for every $a,b,c \in \mathbb{R} \setminus \{0\}$ with $\left|\frac{1}{a}\right|+\left|\frac{1}{b}\right|+\left|\frac{1}{c}\right|\le 3$ .
When does equality occur? | null | null |
[
{
"from": "user",
"value": "Given vectors $\\overrightarrow{a}$ with magnitude $|\\overrightarrow{a}|=2$ and $\\overrightarrow{b}$ with magnitude $|\\overrightarrow{b}|=1$, the angle between $\\overrightarrow{a}$ and $\\overrightarrow{b}$ is $60^{\\circ}$. If $\\overrightarrow{a}$ is perpendicular to $(\\ov... | Given vectors $\overrightarrow{a}$ with magnitude $|\overrightarrow{a}|=2$ and $\overrightarrow{b}$ with magnitude $|\overrightarrow{b}|=1$, the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is $60^{\circ}$. If $\overrightarrow{a}$ is perpendicular to $(\overrightarrow{a}+\lambda\overrightarrow{b})$, find... | null | null |
[
{
"from": "user",
"value": "In a triangle, $a>b>c$, and $a=2(b-c)$. Let the projection of side $c$ onto side $a$ be denoted by $p$, and show that $4 c+8 p=3 a .-\\mathbf{H}$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this geometry problem here. Let me read it again to make sur... | In a triangle, $a>b>c$, and $a=2(b-c)$. Let the projection of side $c$ onto side $a$ be denoted by $p$, and show that $4 c+8 p=3 a .-\mathbf{H}$ | null | null |
[
{
"from": "user",
"value": "How can an AI extract the domain name from an email address using JavaScript?"
},
{
"from": "assistant",
"value": "Extracting the domain name from an email address in JavaScript can be accomplished through various methods, including regular expressions (regex) or simp... | null | null | null |
[
{
"from": "user",
"value": "Write a code that iterates over the provided list of dictionaries and prints the value of \"name\" in each dictionary. Additionally, print the length of each name. If a dictionary does not contain the key \"name\", print \"Name not found\".\n\nThe time complexity of your solution... | null | codefeedback | null |
[
{
"from": "user",
"value": "The arithmetic sequence $\\\\{a\\_n\\\\}$ has a first term $a\\_1=1$, and a common difference $d\\\\neq 0$. If $a\\_1$, $a\\_2$, and $a\\_5$ form a geometric sequence, what is the value of $d$?\n\nA: $3$\nB: $-2$\nC: $2$\nD: $±2$"
},
{
"from": "assistant",
"value": "<... | The arithmetic sequence $\\{a\_n\\}$ has a first term $a\_1=1$, and a common difference $d\\neq 0$. If $a\_1$, $a\_2$, and $a\_5$ form a geometric sequence, what is the value of $d$?
A: $3$
B: $-2$
C: $2$
D: $±2$ | null | null |
[
{
"from": "user",
"value": "1. Solve the equation $2 x^{2}-3 x=2 x \\sqrt{x^{2}-3 x}+1$ in $\\mathbb{R}$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this equation to solve: 2x² - 3x = 2x√(x² - 3x) + 1. Hmm, that looks a bit complicated, but let me try to break it down step by ... | 1. Solve the equation $2 x^{2}-3 x=2 x \sqrt{x^{2}-3 x}+1$ in $\mathbb{R}$. | null | null |
[
{
"from": "user",
"value": "Given $\\sin\\left(\\frac{\\pi}{3} + \\alpha\\right) = \\frac{1}{3}$, then $\\cos\\left(\\frac{5\\pi}{6} + \\alpha\\right) =$ ( )\n\nA: $\\frac{1}{3}$\n\nB: $-\\frac{1}{3}$\n\nC: $\\frac{2\\sqrt{2}}{3}$\n\nD: $-\\frac{2\\sqrt{2}}{3}$"
},
{
"from": "assistant",
"value... | Given $\sin\left(\frac{\pi}{3} + \alpha\right) = \frac{1}{3}$, then $\cos\left(\frac{5\pi}{6} + \alpha\right) =$ ( )
A: $\frac{1}{3}$
B: $-\frac{1}{3}$
C: $\frac{2\sqrt{2}}{3}$
D: $-\frac{2\sqrt{2}}{3}$ | null | null |
[
{
"from": "user",
"value": "Given $m-2n=7$, find the value of the polynomial $2023-2m+4n$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to solve this problem where I'm given that m minus 2n equals 7, and I have to find the value of the polynomial 2023 minus 2m plus 4n. Hmm, let ... | Given $m-2n=7$, find the value of the polynomial $2023-2m+4n$. | null | null |
[
{
"from": "user",
"value": "A four-sided cone has each of its vertices painted with a different color, and the two endpoints of each edge have different colors. If there are only $4$ colors available, how many different painting methods are there in total?\nA: $48$\nB: $72$\nC: $96$\nD: $108$"
},
{
... | A four-sided cone has each of its vertices painted with a different color, and the two endpoints of each edge have different colors. If there are only $4$ colors available, how many different painting methods are there in total?
A: $48$
B: $72$
C: $96$
D: $108$ | null | null |
[
{
"from": "user",
"value": "Given the question: As you go farther from the nucleus of an atom, the electron levels have more and more energy. Lonnie works in a lab. He is studying atoms and discovers that the electrons that are farther away from the nucleus are moving less. or more?\nThe answer is:"
},
... | null | null | null |
[
{
"from": "user",
"value": "Circles of radius $3$ and $6$ are externally tangent to each other and are internally tangent to a circle of radius $9$. The circle of radius $9$ has a chord that is a common external tangent of the other two circles. Find the square of the length of this chord.\n\n[asy] pointpen... | Circles of radius $3$ and $6$ are externally tangent to each other and are internally tangent to a circle of radius $9$. The circle of radius $9$ has a chord that is a common external tangent of the other two circles. Find the square of the length of this chord.
[asy] pointpen = black; pathpen = black + linewidth(0.7)... | null | null |
[
{
"from": "user",
"value": "Example 5. For what values of $B$ and $C$ is the line $\\frac{x-3}{1}=\\frac{y-2}{B}=$ $=\\frac{z+2}{C}$ perpendicular to the plane $3 x-2 y+5 z=0$?"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to figure out for what values of B and C the given line i... | Example 5. For what values of $B$ and $C$ is the line $\frac{x-3}{1}=\frac{y-2}{B}=$ $=\frac{z+2}{C}$ perpendicular to the plane $3 x-2 y+5 z=0$? | null | null |
[
{
"from": "user",
"value": "<p>How can I execute the following query in Python?</p>\n\n```sql\nselect field11, field12\nfrom Table_1 t1\nleft outer join Table_2 t2 ON t2.tbl1_id = t1.tbl1_id\nwhere t2.tbl2_id is null\n```\n\nI have these Python classes defined:\n\n```python\nclass Table1(Base):\n ....\n\n... | null | glaive | 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.We have been given N balloons, each with a number of coins associated with it. On bursting a balloon... | 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.We have been given N balloons, each with a number of coins associated with it. On bursting a balloon i, the number of coins gained is equal ... | null | null |
[
{
"from": "user",
"value": "You are tasked with creating a script in TCL that automates the interactive input for a command-line tool. The script must handle various prompts and provide default values as needed. The script should also check for specific questions and validate the input provided. The script ... | null | glaive | null |
[
{
"from": "user",
"value": "Let f(z)=z^3-7z^2+10z-6, g(z)= z^4+6z^3+11z^2+6z. Solve for a if f(a)g(-a)=f(1).g(-1)"
},
{
"from": "assistant",
"value": "<think>\nAlright, let's see. I need to solve for \"a\" in the equation f(a)g(-a) = f(1)g(-1). The functions f(z) and g(z) are given as polynomial... | null | nvidia_math | 35,458 |
[
{
"from": "user",
"value": "Can you provide a program in Kotlin that takes an integer array and returns the largest value within the array?"
},
{
"from": "assistant",
"value": "<think>\nOkay, I need to write a Kotlin program that takes an integer array and returns the largest value. Let's think ... | null | glaive | null |
[
{
"from": "user",
"value": "Observing the chords connected between $n$ points on a circle, it is found that 2 points can connect 1 chord, 3 points can connect 3 chords, 4 points can connect 6 chords, 5 points can connect 10 chords, and 6 points can connect 15 chords. Please explore the pattern, and determin... | Observing the chords connected between $n$ points on a circle, it is found that 2 points can connect 1 chord, 3 points can connect 3 chords, 4 points can connect 6 chords, 5 points can connect 10 chords, and 6 points can connect 15 chords. Please explore the pattern, and determine how many chords can be connected if th... | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. \nIn triangle \\(ABC\\), \\(\\angle A = 60^\\circ\\). Points \\(M\\) and \\(N\\) are on sides \\(AB\\) and \\(AC\\) respectively, such that the circumcenter of triangle \\(ABC\\) bisects segment \\(MN\\). Find the ratio \\(AN:MB\\)."
... |
In triangle \(ABC\), \(\angle A = 60^\circ\). Points \(M\) and \(N\) are on sides \(AB\) and \(AC\) respectively, such that the circumcenter of triangle \(ABC\) bisects segment \(MN\). Find the ratio \(AN:MB\). | null | null |
[
{
"from": "user",
"value": "You are given a code snippet that seems to be incomplete. Your task is to complete the code by implementing a function that calculates the sum of all even numbers in a given array.\n\nYou need to implement the function `sumOfEvenNumbers` that takes an array of integers as input a... | null | magicoder | null |
[
{
"from": "user",
"value": "You are working on a software development project and need to follow a specific Git workflow when interacting with the GitHub repository. Your task is to create a feature branch for active development, add new development on the feature branch, update your feature branch with the... | null | glaive | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Find the remainder when \\( 1021^{1022} \\) is divided by 1023."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the remainder when 1021 raised to the power of 1022 is divided by 1023. Hmm, let's start ... | Find the remainder when \( 1021^{1022} \) is divided by 1023. | null | null |
[
{
"from": "user",
"value": "# 7. Problem 7\n\nFind the number of natural numbers not exceeding 2016 and coprime with it. Recall that two integers are called coprime if they do not have common natural divisors other than one."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find h... | # 7. Problem 7
Find the number of natural numbers not exceeding 2016 and coprime with it. Recall that two integers are called coprime if they do not have common natural divisors other than one. | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. \nSolve the following equation and provide its root. If the equation has multiple roots, provide their product.\n\n\\[ \\sqrt{2 x^{2} + 8 x + 1} - x = 3 \\]"
},
{
"from": "assistant",
"value": "<think>\nOkay, let me try to ... |
Solve the following equation and provide its root. If the equation has multiple roots, provide their product.
\[ \sqrt{2 x^{2} + 8 x + 1} - x = 3 \] | null | null |
[
{
"from": "user",
"value": "Formulate a structured query language command to extract the distinct designations of clients from the 'Orders' table, who have registered transactions on the specific calendar day of '2020-06-25'. Additionally, amend the query to only include clients who have made a cumulative t... | null | codefeedback | null |
[
{
"from": "user",
"value": "You are tasked with implementing a class that manages genres for a media application. The class should provide functionality to add, remove, and retrieve genres, as well as wrap genre-related actions in a graphical user interface (GUI).\n\nYour task is to implement the `GenreMana... | null | magicoder | null |
[
{
"from": "user",
"value": "$5 \\cdot 120$ A certain meeting was attended by $12 k$ people, each of whom greeted exactly $3 k+6$ others. For any two people, the number of people who greeted both of them is the same. How many people attended the meeting?"
},
{
"from": "assistant",
"value": "<thin... | $5 \cdot 120$ A certain meeting was attended by $12 k$ people, each of whom greeted exactly $3 k+6$ others. For any two people, the number of people who greeted both of them is the same. How many people attended the meeting? | null | null |
[
{
"from": "user",
"value": "Arrange three identical red balls and three identical black balls in a row, and then number them from left to right as 1, 2, 3, 4, 5, 6. The number of arrangements where the sum of the numbers of the red balls is less than the sum of the numbers of the black balls is ( )\nA: 10\... | Arrange three identical red balls and three identical black balls in a row, and then number them from left to right as 1, 2, 3, 4, 5, 6. The number of arrangements where the sum of the numbers of the red balls is less than the sum of the numbers of the black balls is ( )
A: 10
B: 11
C: 15
D: 18 | null | null |
[
{
"from": "user",
"value": "If the vectors $\\overrightarrow{a}=(-4,3)$ and $\\overrightarrow{b}=(1,3)$, then the coordinates of the projection vector of $\\overrightarrow{a}$ in the direction of $\\overrightarrow{b}$ are ______."
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. I n... | If the vectors $\overrightarrow{a}=(-4,3)$ and $\overrightarrow{b}=(1,3)$, then the coordinates of the projection vector of $\overrightarrow{a}$ in the direction of $\overrightarrow{b}$ are ______. | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. I am twice as old as you were when I was as old as you are now. When you are as old as I am now, the sum of our ages will be 140 years. How old are you, and how old am I?"
},
{
"from": "assistant",
"value": "<think>\nOkay, ... | I am twice as old as you were when I was as old as you are now. When you are as old as I am now, the sum of our ages will be 140 years. How old are you, and how old am I? | null | null |
[
{
"from": "user",
"value": "$$\n\\begin{array}{l}\n\\text { 6. Let } a \\in \\mathbf{R}^{+}, \\\\\nA=\\left\\{(x, y) \\left\\lvert\\,(x-1)^{2}+(y-2)^{2} \\leqslant \\frac{4}{5}\\right.\\right\\} \\\\\n\\text { and } B=\\{(x, y)|| x-1|+2| y-2 \\mid \\leqslant a\\}\n\\end{array}\n$$\n\nare point sets in the p... | $$
\begin{array}{l}
\text { 6. Let } a \in \mathbf{R}^{+}, \\
A=\left\{(x, y) \left\lvert\,(x-1)^{2}+(y-2)^{2} \leqslant \frac{4}{5}\right.\right\} \\
\text { and } B=\{(x, y)|| x-1|+2| y-2 \mid \leqslant a\}
\end{array}
$$
are point sets in the plane $x O y$. Then $A \subseteq B$ if
(A) $a \geqslant 2$
(B) $a \geqsla... | null | null |
[
{
"from": "user",
"value": "6. $\\overline{a b}$ and $\\overline{b a}$ represent two-digit integers, then the number of $\\overline{a b}$ that satisfy the equation $(a+b) x^{2}-\\overline{a b} x+\\overline{b a}=0$ with both roots being integers is ( ).\n(A)0\n(B) 2\n(C) 4\n(D) 6"
},
{
"from": "assis... | 6. $\overline{a b}$ and $\overline{b a}$ represent two-digit integers, then the number of $\overline{a b}$ that satisfy the equation $(a+b) x^{2}-\overline{a b} x+\overline{b a}=0$ with both roots being integers is ( ).
(A)0
(B) 2
(C) 4
(D) 6 | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. \nGiven \\( x > 0 \\), \\( y > 0 \\), and the following system of equations:\n\\[\n\\left\\{\n\\begin{array}{l}\n\\cos^2(\\pi x) + 2 \\sin(\\pi y) = 1, \\\\\n\\sin(\\pi x) + \\sin(\\pi y) = 0, \\\\\nx^2 - y^2 = 12\n\\end{array}\n\\righ... |
Given \( x > 0 \), \( y > 0 \), and the following system of equations:
\[
\left\{
\begin{array}{l}
\cos^2(\pi x) + 2 \sin(\pi y) = 1, \\
\sin(\pi x) + \sin(\pi y) = 0, \\
x^2 - y^2 = 12
\end{array}
\right.
\]
Find the ordered pair \((x, y) = \qquad\). | null | null |
Subsets and Splits
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