conversations listlengths 2 2 | question stringlengths 16 24.8k ⌀ | source stringclasses 10
values | id int64 3 50k ⌀ |
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[
{
"from": "user",
"value": "There are 12 bananas and x apples in the blue basket. The red basket holds half as many fruits as the blue basket. How many fruits are in the red basket?\nIf we know the answer to the above question is 8, what is the value of unknown variable x?"
},
{
"from": "assistant",... | null | tiger_math | 16,478 |
[
{
"from": "user",
"value": "In the sequence $\\{a_n\\}$, $(a_1=1, a_{n+1}=\\frac{a_n}{c\\cdot a_n+1})$ $(c$ is a constant, $n\\in\\mathbb{N^*})$, and $(a_1,a_2,a_5)$ form a geometric sequence with a common ratio not equal to $1$.\n(1) Prove that the sequence $\\{\\frac{1}{a_n}\\}$ is an arithmetic sequence ... | In the sequence $\{a_n\}$, $(a_1=1, a_{n+1}=\frac{a_n}{c\cdot a_n+1})$ $(c$ is a constant, $n\in\mathbb{N^*})$, and $(a_1,a_2,a_5)$ form a geometric sequence with a common ratio not equal to $1$.
(1) Prove that the sequence $\{\frac{1}{a_n}\}$ is an arithmetic sequence and find the value of $c$;
(2) Let $b_n=a_n a_{n+1... | null | null |
[
{
"from": "user",
"value": "What is the difference between the largest possible three-digit positive integer with no repeated digits and the smallest possible three-digit positive integer with no repeated digits?"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the differenc... | What is the difference between the largest possible three-digit positive integer with no repeated digits and the smallest possible three-digit positive integer with no repeated digits? | null | null |
[
{
"from": "user",
"value": "port this code to Fortran:\n```scheme\n(define MRUQueue\n (lambda (n)\n (let ((queue (build-list n identity)))\n (lambda (k)\n (let ((elem (list-ref queue (- k 1))))\n (set! queue (append (take queue (- k 1)) (drop queue k) (list elem)))\n elem))... | null | dolphin | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. A natural number \\( a \\) is increased by 1, and its square is increased by 1001. What is the value of \\( a \\)?"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. The problem says that a natural number \\( a ... | A natural number \( a \) is increased by 1, and its square is increased by 1001. What is the value of \( a \)? | null | null |
[
{
"from": "user",
"value": "A positive integer $n$ is considered to be cubefree if it is not divisible by any cube of a prime number. For example, $1, 2, 3, 5, 6, 7, 10, 11$ are cubefree, while $8, 27, 125$ are not. Can you calculate the total number of such cubefree numbers that exist below the value of $2... | null | null | null |
[
{
"from": "user",
"value": "## problem statement\n\nWrite the equation of the plane passing through point $A$ and perpendicular to the vector $\\overrightarrow{B C}$.\n\n$A(7 ; -5 ; 0)$\n\n$B(8 ; 3 ; -1)$\n\n$C(8 ; 5 ; 1)$"
},
{
"from": "assistant",
"value": "<think>\nOkay, let me try to figure ... | ## problem statement
Write the equation of the plane passing through point $A$ and perpendicular to the vector $\overrightarrow{B C}$.
$A(7 ; -5 ; 0)$
$B(8 ; 3 ; -1)$
$C(8 ; 5 ; 1)$ | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. What is the maximum number of consecutive positive integers that can be added together before the sum exceeds 400?"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. The question is asking for the maximum numbe... | What is the maximum number of consecutive positive integers that can be added together before the sum exceeds 400? | null | null |
[
{
"from": "user",
"value": "Write a JavaScript function to find the first prime number in an array of integers. If no prime number is found, the function should return -1.\n\nHowever, the function should also accept an optional second argument, `k`, which represents the number of prime numbers to be found. ... | null | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Find the sum of the positive integer divisors of \\(2^{2007}\\)."
},
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"from": "assistant",
"value": "<think>\nOkay, so I need to find the sum of the positive integer divisors of \\(2^{2007}\\). Hmm, let me think about how ... | Find the sum of the positive integer divisors of \(2^{2007}\). | null | null |
[
{
"from": "user",
"value": "A ball is thrown straight up into the air with an initial velocity of 30 m/s. Using calculus, find its maximum height and the time it takes to reach that height. Assume that air resistance is negligible."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have th... | null | null | null |
[
{
"from": "user",
"value": "5. Calculate the sum of the expressions $S_{2015}$ and $S_{2016}$ if $S_{2015}=1-2+3-4+5-\\ldots-2014+2015$, and $S_{2016}=1-2+3-4+5-\\ldots-2014+2015-2016$.\n\nProblems worth 10 points:"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to calculate the su... | 5. Calculate the sum of the expressions $S_{2015}$ and $S_{2016}$ if $S_{2015}=1-2+3-4+5-\ldots-2014+2015$, and $S_{2016}=1-2+3-4+5-\ldots-2014+2015-2016$.
Problems worth 10 points: | null | null |
[
{
"from": "user",
"value": "\\section*{Aufgabe 5 - 231045}\n\nErmitteln Sie alle diejenigen Winkelgrößen \\(x\\), für die \\(0^{\\circ} \\leq x \\leq 180^{\\circ} \\quad\\) (1) und\n\n\\[\n\\left(2^{\\sqrt{\\sin x}}-\\sin x\\right) \\cdot \\sin x=1\n\\]\n\ngilt!\n\n"
},
{
"from": "assistant",
"v... | \section*{Aufgabe 5 - 231045}
Ermitteln Sie alle diejenigen Winkelgrößen \(x\), für die \(0^{\circ} \leq x \leq 180^{\circ} \quad\) (1) und
\[
\left(2^{\sqrt{\sin x}}-\sin x\right) \cdot \sin x=1
\]
gilt!
| null | null |
[
{
"from": "user",
"value": "Given the sequence ${a_n}$ where $a_{1}=1, a_{2}=2, a_{n+1}=3a_{n}-2a_{n-1}(n≥2, n∈N^{*})$. Let $b_n=a_{n+1}-a_{n}$.\n(1) Prove that the sequence ${b_n}$ is a geometric sequence.\n(2) Let $c_{n}= \\frac {b_{n}}{(4n^{2}-1)2^{n}}$, find the sum of the first n terms of the sequence ... | Given the sequence ${a_n}$ where $a_{1}=1, a_{2}=2, a_{n+1}=3a_{n}-2a_{n-1}(n≥2, n∈N^{*})$. Let $b_n=a_{n+1}-a_{n}$.
(1) Prove that the sequence ${b_n}$ is a geometric sequence.
(2) Let $c_{n}= \frac {b_{n}}{(4n^{2}-1)2^{n}}$, find the sum of the first n terms of the sequence ${c_n}$, denoted as $S_n$. | null | null |
[
{
"from": "user",
"value": "Example 1 Given real numbers $x, y, z$ satisfy $x+y=5$ and $z^{2}=x y+y-9$.\nThen $x+2 y+3 z=$ $\\qquad$ ."
},
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"value": "<think>\nOkay, let's see. I need to find the value of x + 2y + 3z given that x + y = 5 and z² = xy + y - 9. Hmm, where do I ... | Example 1 Given real numbers $x, y, z$ satisfy $x+y=5$ and $z^{2}=x y+y-9$.
Then $x+2 y+3 z=$ $\qquad$ . | null | null |
[
{
"from": "user",
"value": "6. Rationalize the denominator of $\\frac{6}{\\sqrt[3]{4}+\\sqrt[3]{16}+\\sqrt[3]{64}}$ and simplify."
},
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"from": "assistant",
"value": "<think>\nOkay, so I need to rationalize the denominator of the expression 6 divided by the sum of the cube roots of 4, 16, and 64... | 6. Rationalize the denominator of $\frac{6}{\sqrt[3]{4}+\sqrt[3]{16}+\sqrt[3]{64}}$ and simplify. | null | null |
[
{
"from": "user",
"value": "Let $p(x)=ax^2+bx+c$ and $q(x)=dx^2+ex+f$. If $r(x)=p(q(x))$ and $r'(0)=0$, find $a+b+c+d+e+f$."
},
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"from": "assistant",
"value": "<think>\nAlright, so I have this math problem here that's about quadratic functions and composition. Let me just read it again: We're g... | null | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. How many ten-digit numbers exist in which there are at least two identical digits?"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to figure out how many ten-digit numbers have at least two identical digits. L... | How many ten-digit numbers exist in which there are at least two identical digits? | null | null |
[
{
"from": "user",
"value": "9. In the division equation $\\div 7=12 \\ldots$. , what is the maximum remainder?"
},
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"from": "assistant",
"value": "<think>\nOkay, let's see... I need to figure out the maximum remainder in this division equation where something divided by 7 equals 12 with some re... | 9. In the division equation $\div 7=12 \ldots$. , what is the maximum remainder? | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. If \\(a\\) students are seated on each bench, then 5 students will be left without a seat. If 8 students are seated on each bench, then 4 seats will remain unoccupied. Determine how many benches and how many students there were."
},
... | If \(a\) students are seated on each bench, then 5 students will be left without a seat. If 8 students are seated on each bench, then 4 seats will remain unoccupied. Determine how many benches and how many students there were. | null | null |
[
{
"from": "user",
"value": "You are tasked with implementing a simple command-line application for managing a list of tasks. The application should allow users to add tasks, mark tasks as completed, view all tasks, and delete tasks. The tasks should be stored in memory and should persist for the duration of... | null | null | null |
[
{
"from": "user",
"value": "Given the function $f(x) = \\sqrt{3}\\sin x\\cos x + \\cos^2 x + a$.\n\n(1) Find the smallest positive period of $f(x)$ and the intervals of monotonic decrease. \n(2) If the sum of the maximum and minimum values of $f(x)$ in the interval $\\left[-\\frac{\\pi}{6}, \\frac{\\pi}{3}... | Given the function $f(x) = \sqrt{3}\sin x\cos x + \cos^2 x + a$.
(1) Find the smallest positive period of $f(x)$ and the intervals of monotonic decrease.
(2) If the sum of the maximum and minimum values of $f(x)$ in the interval $\left[-\frac{\pi}{6}, \frac{\pi}{3}\right]$ is $\frac{3}{2}$, find the value of $a$. | null | null |
[
{
"from": "user",
"value": "There are two wooden bars with lengths of 30cm and 50cm, respectively. If you want to make a triangular board without any leftover wood, which of the following lengths of wood can you choose? ( )\nA: 20cm\nB: 30cm\nC: 80cm\nD: 90cm"
},
{
"from": "assistant",
"value":... | There are two wooden bars with lengths of 30cm and 50cm, respectively. If you want to make a triangular board without any leftover wood, which of the following lengths of wood can you choose? ( )
A: 20cm
B: 30cm
C: 80cm
D: 90cm | null | null |
[
{
"from": "user",
"value": "Given vectors $\\overrightarrow{a}=(1,-2), \\overrightarrow{b}=(3,4)$.\n(1) If $(3 \\overrightarrow{a}- \\overrightarrow{b}) \\Vert ( \\overrightarrow{a}+k \\overrightarrow{b})$, find the value of the real number $k$;\n(2) If $\\overrightarrow{a} \\perp (m \\overrightarrow{a}- \\... | Given vectors $\overrightarrow{a}=(1,-2), \overrightarrow{b}=(3,4)$.
(1) If $(3 \overrightarrow{a}- \overrightarrow{b}) \Vert ( \overrightarrow{a}+k \overrightarrow{b})$, find the value of the real number $k$;
(2) If $\overrightarrow{a} \perp (m \overrightarrow{a}- \overrightarrow{b})$, find the value of the real numbe... | null | null |
[
{
"from": "user",
"value": "You are tasked with creating a shell script that simulates a simplified version of the `ddg` command, which is used to search the web using the DuckDuckGo search engine. The script should take a search query as an argument and display the search results in the terminal using the ... | null | codefeedback | null |
[
{
"from": "user",
"value": "5-141 Find all non-zero polynomials $f(x)=a_{0}+a_{1} x+\\cdots+a_{n} x^{n}$ that satisfy the equation $f\\left(x^{2}\\right)=(f(x))^{2}$, where $x$ is a real number."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this problem where I need to find all n... | 5-141 Find all non-zero polynomials $f(x)=a_{0}+a_{1} x+\cdots+a_{n} x^{n}$ that satisfy the equation $f\left(x^{2}\right)=(f(x))^{2}$, where $x$ is a real number. | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. On a plane, 6 lines intersect pairwise, but only three pass through the same point. Find the number of non-overlapping line segments intercepted.\n(A) 24\n(B) 33\n(C) 36\n(D) 21"
},
{
"from": "assistant",
"value": "<think>\... | On a plane, 6 lines intersect pairwise, but only three pass through the same point. Find the number of non-overlapping line segments intercepted.
(A) 24
(B) 33
(C) 36
(D) 21 | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. A dog from point $A$ chased a fox that was 30 meters away from the dog at point $B$. The dog's leap is 2 meters, and the fox's leap is 1 meter. The dog makes 2 leaps while the fox makes 3 leaps. At what distance from point $A$ will the... | A dog from point $A$ chased a fox that was 30 meters away from the dog at point $B$. The dog's leap is 2 meters, and the fox's leap is 1 meter. The dog makes 2 leaps while the fox makes 3 leaps. At what distance from point $A$ will the dog catch the fox? | null | null |
[
{
"from": "user",
"value": "Nick is a runner, and his goal is to complete four laps around a circuit at an average speed of $10$ mph. If he completes the first three laps at a constant speed of only $9$ mph, what speed does he need to maintain in miles per hour on the fourth lap to achieve his goal?"
},
... | Nick is a runner, and his goal is to complete four laps around a circuit at an average speed of $10$ mph. If he completes the first three laps at a constant speed of only $9$ mph, what speed does he need to maintain in miles per hour on the fourth lap to achieve his goal? | null | null |
[
{
"from": "user",
"value": "What is the code to find the index of a specific element in a list?"
},
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"from": "assistant",
"value": "<think>\nOkay, the user is asking for the code to find the index of a specific element in a list. Let me think about how to approach this.\n\nFirst, I remember tha... | null | sharegpt | null |
[
{
"from": "user",
"value": "Curve $C\\_1$: $ρ \\sin θ - 2 = 0$, Curve $C\\_2$: $ρ - 4 \\cos θ = 0$. Determine the positional relationship between curves $C\\_1$ and $C\\_2$ $(\\ \\ \\ \\ )$\nA: Intersect\nB: Tangent\nC: Coincident\nD: Separated"
},
{
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"value": "<think>\nOkay,... | Curve $C\_1$: $ρ \sin θ - 2 = 0$, Curve $C\_2$: $ρ - 4 \cos θ = 0$. Determine the positional relationship between curves $C\_1$ and $C\_2$ $(\ \ \ \ )$
A: Intersect
B: Tangent
C: Coincident
D: Separated | null | null |
[
{
"from": "user",
"value": "一、(50 points) Let $\\triangle A B C$ be inscribed in the unit circle $\\odot O$, and the center $O$ is inside $\\triangle A B C$. If the projections of $O$ onto sides $B C$, $C A$, and $A B$ are points $D$, $E$, and $F$ respectively, find the maximum value of $O D+O E+O F$."
},... | 一、(50 points) Let $\triangle A B C$ be inscribed in the unit circle $\odot O$, and the center $O$ is inside $\triangle A B C$. If the projections of $O$ onto sides $B C$, $C A$, and $A B$ are points $D$, $E$, and $F$ respectively, find the maximum value of $O D+O E+O F$. | null | null |
[
{
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"value": "The American football championship, Super Bowl 50, is happening today at 11:30pm UTC (and you can watch it live online). This challenge was made to celebrate it.\n\nIn an American football game, two teams compete to get the most points, and there are six ways to score these point... | null | null | null |
[
{
"from": "user",
"value": "The coefficient of the $x^3$ term in the expansion of $(1+x)^6$ is ______; the sum of the binomial coefficients in this expansion is ______. (Answer with numbers)"
},
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"from": "assistant",
"value": "<think>\nAlright, so I need to figure out two things here: the coeff... | The coefficient of the $x^3$ term in the expansion of $(1+x)^6$ is ______; the sum of the binomial coefficients in this expansion is ______. (Answer with numbers) | null | null |
[
{
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"value": "In 1960, the Japanese government proposed the \"Income Doubling Plan,\" one of its characteristics was dividing the economy into the private sector and the public sector, and clearly defining the government's responsibility to expand roads, harbors, urban planning, sewers, nation... | In 1960, the Japanese government proposed the "Income Doubling Plan," one of its characteristics was dividing the economy into the private sector and the public sector, and clearly defining the government's responsibility to expand roads, harbors, urban planning, sewers, national housing, and other social capital, as w... | null | null |
[
{
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"value": "How can I implement breadth-first traversal in a specified tree data structure using Python?"
},
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"value": "<think>\nOkay, so I need to implement breadth-first traversal in a tree using Python. I'm a bit new to this, so let me think through how t... | null | null | null |
[
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"from": "user",
"value": "Return your final response within \\boxed{}. Solve the following system of equations for positive numbers:\n\n$$\n\\begin{cases}\nx^{y} = z \\\\\ny^{z} = x \\\\\nz^{x} = y\n\\end{cases}\n$$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to solve this sy... | Solve the following system of equations for positive numbers:
$$
\begin{cases}
x^{y} = z \\
y^{z} = x \\
z^{x} = y
\end{cases}
$$ | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. How many different positive integer solutions are there for the equation \\( x y = 10^{n} \\)?"
},
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"from": "assistant",
"value": "<think>\nOkay, so I need to figure out how many different positive integer solutions there ... | How many different positive integer solutions are there for the equation \( x y = 10^{n} \)? | null | null |
[
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"from": "user",
"value": "I need to write a SPARQL query that retrieves distinct values for a specific variable (?x0) from a given RDF graph. The query should include multiple patterns and constraints, such as retrieving values based on certain properties and their relationships, as well as limiting the n... | null | glaive | null |
[
{
"from": "user",
"value": "You are tasked with implementing a function that processes a dataset using a tree structure and updates the leaf nodes with new values. The tree is represented as a collection of nodes, and each leaf node contains a tensor of distribution parameters. The function iterates through... | null | codefeedback | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. For a given prime \\( p \\), find the number of different sequences of positive integers \\( a_{0}, a_{1}, a_{2}, \\cdots \\) that satisfy\n$$\n\\frac{a_{0}}{a_{1}}+\\frac{a_{0}}{a_{2}}+\\cdots+\\frac{a_{0}}{a_{n}}+\\frac{p}{a_{n+1}}=1... | For a given prime \( p \), find the number of different sequences of positive integers \( a_{0}, a_{1}, a_{2}, \cdots \) that satisfy
$$
\frac{a_{0}}{a_{1}}+\frac{a_{0}}{a_{2}}+\cdots+\frac{a_{0}}{a_{n}}+\frac{p}{a_{n+1}}=1, \quad n=1, 2, \cdots
$$ | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let $M$ be the midpoint of a chord $UV$ of an ellipse, which is parallel to the major axis. Through $M$, two additional chords $AB$ and $CD$ are drawn. Let the intersections of $AC$ and $BD$ with $UV$ be points $P$ and $Q$, respectivel... | Let $M$ be the midpoint of a chord $UV$ of an ellipse, which is parallel to the major axis. Through $M$, two additional chords $AB$ and $CD$ are drawn. Let the intersections of $AC$ and $BD$ with $UV$ be points $P$ and $Q$, respectively. Prove that $M$ is also the midpoint of the segment $PQ$. | null | null |
[
{
"from": "user",
"value": "Given that $O$ is a point in the plane of $\\triangle ABC$, $D$ is the midpoint of side $BC$, and $$2 \\overrightarrow {OA}+ \\overrightarrow {OB}+ \\overrightarrow {OC}= \\overrightarrow {0}$$, then ( )\n\nA: $$\\overrightarrow {AO}= \\overrightarrow {OD}$$\n\nB: $$\\overrigh... | Given that $O$ is a point in the plane of $\triangle ABC$, $D$ is the midpoint of side $BC$, and $$2 \overrightarrow {OA}+ \overrightarrow {OB}+ \overrightarrow {OC}= \overrightarrow {0}$$, then ( )
A: $$\overrightarrow {AO}= \overrightarrow {OD}$$
B: $$\overrightarrow {AO}=2 \overrightarrow {OD}$$
C: $$\overrig... | null | null |
[
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"value": "How can I create a JavaScript program that generates a random number between 0 and 10 and displays a message with the result?"
},
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"from": "assistant",
"value": "<think>\nOkay, I need to create a JavaScript program that generates a random number between 0 and 10 and ... | null | null | null |
[
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"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.All bus tickets in Berland have their numbers. A number consists of n digits (n is even). Only k dec... | 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.All bus tickets in Berland have their numbers. A number consists of n digits (n is even). Only k decimal digits d_1, d_2, ..., d_k can be us... | null | null |
[
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"value": "3. Let $a, b$ be any two distinct positive integers. Then the minimum value of $\\left|a b\\left(a^{4}-b^{4}\\right)\\right|$ is $\\qquad$ .\n\n"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. The problem is asking for the minimum value of |ab(a⁴ - b⁴)|... | 3. Let $a, b$ be any two distinct positive integers. Then the minimum value of $\left|a b\left(a^{4}-b^{4}\right)\right|$ is $\qquad$ .
| null | null |
[
{
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"value": "In an increasing geometric sequence $\\{a_n\\}$, it is known that $a_1+a_n=34$, $a_3 \\cdot a_{n-2}=64$, and the sum of the first $n$ terms is $S_n=42$. Then, $n=$ ()\nA: $3$\nB: $4$\nC: $5$\nD: $6$"
},
{
"from": "assistant",
"value": "<think>\nAlright, let me try to... | In an increasing geometric sequence $\{a_n\}$, it is known that $a_1+a_n=34$, $a_3 \cdot a_{n-2}=64$, and the sum of the first $n$ terms is $S_n=42$. Then, $n=$ ()
A: $3$
B: $4$
C: $5$
D: $6$ | null | null |
[
{
"from": "user",
"value": "Describe a use case of the ternary operator in Python and provide an example code snippet demonstrating its usage. The code must include at least three nested ternary operators and use a user-defined function within the conditionals. Additionally, the code must also utilize list ... | null | sharegpt | null |
[
{
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"value": "Given the function $f(x)=ax^{2}-(a+2)x+\\ln x$, where $a\\in \\mathbb{R}$. \n(I) When $a=1$, find the equation of the tangent line at the point $(1,f(1))$ on the curve $y=f(x)$. \n(II) When $a > 0$, if the minimum value of $f(x)$ in the interval $[1,e]$ is $-2$, find the range ... | Given the function $f(x)=ax^{2}-(a+2)x+\ln x$, where $a\in \mathbb{R}$.
(I) When $a=1$, find the equation of the tangent line at the point $(1,f(1))$ on the curve $y=f(x)$.
(II) When $a > 0$, if the minimum value of $f(x)$ in the interval $[1,e]$ is $-2$, find the range of values for $a$. | null | null |
[
{
"from": "user",
"value": "You are tasked with implementing an interface for a slave IP that is a RISC-V boot RAM of 64-bit locations. The interface should include a method to set the address map after the module's reset, as well as handle fabric read and write requests. The module should also have the abi... | null | glaive | null |
[
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"value": "Return your final response within \\boxed{}. Find an integer whose square root has the sequence 414213462 immediately after the decimal point."
},
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"value": "<think>\nOkay, let's try to figure out this problem. We need to find an integer whose sq... | Find an integer whose square root has the sequence 414213462 immediately after the decimal point. | null | null |
[
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"value": "7.175. $\\lg \\left(x^{3}+8\\right)-0.5 \\lg \\left(x^{2}+4 x+4\\right)=\\lg 7$."
},
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"from": "assistant",
"value": "<think>\nOkay, so I have this logarithmic equation to solve: \\(\\lg \\left(x^{3}+8\\right) - 0.5 \\lg \\left(x^{2}+4x+4\\right) = \\lg 7\\). Hmm, let... | 7.175. $\lg \left(x^{3}+8\right)-0.5 \lg \left(x^{2}+4 x+4\right)=\lg 7$. | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let $\\alpha ,\\ \\beta$ be the distinct positive roots of the equation of $2x=\\tan x$ .\r\n\r\nEvaluate the following definite integral.\r\n\\[\\int_{0}^{1}\\sin \\alpha x\\sin \\beta x\\ dx \\]"
},
{
"from": "assistant",
... | Let $\alpha ,\ \beta$ be the distinct positive roots of the equation of $2x=\tan x$ .
Evaluate the following definite integral.
\[\int_{0}^{1}\sin \alpha x\sin \beta x\ dx \] | null | null |
[
{
"from": "user",
"value": "Three pipes A, B, and C can fill a tank in 10, 15, and 20 hours, respectively. Pipe A is opened for 2 hours, then closed. Pipe B is opened for 3 hours, then closed. If pipe C is then opened, how long will it take to fill the remaining part of the tank?"
},
{
"from": "assi... | null | nvidia_math | 8,948 |
[
{
"from": "user",
"value": "What is the total number of distinct prime factors of \\( 30 \\) when expressed in the form \\( \\mathbb{Z}_n \\) for \\( n \\) being a prime number?"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to figure out the total number of distinct prime factors... | null | automath | 33,458 |
[
{
"from": "user",
"value": "Miss Walter has 50 gold stickers. She also has twice as many silver stickers as gold stickers, and 20 fewer bronze stickers than silver stickers. She wants to give the same number of stickers to each of her 5 students. How many stickers will each student receive?"
},
{
"... | null | null | null |
[
{
"from": "user",
"value": "The value range of the function $$y=\\sin x\\ (\\frac{\\pi}{6} \\leq x \\leq \\frac{\\pi}{2})$$ is ( )\n\nA: \\[-1, 1\\]\n\nB: $$\\left[\\frac{\\sqrt{3}}{2}, 1\\right]$$\n\nC: $$\\left[\\frac{1}{2}, \\frac{\\sqrt{3}}{2}\\right]$$\n\nD: $$\\left[\\frac{1}{2}, 1\\right]$$"
},
... | The value range of the function $$y=\sin x\ (\frac{\pi}{6} \leq x \leq \frac{\pi}{2})$$ is ( )
A: \[-1, 1\]
B: $$\left[\frac{\sqrt{3}}{2}, 1\right]$$
C: $$\left[\frac{1}{2}, \frac{\sqrt{3}}{2}\right]$$
D: $$\left[\frac{1}{2}, 1\right]$$ | null | null |
[
{
"from": "user",
"value": "5. If $a>0, a \\neq 1, F(x)$ is an odd function, then $G(x)=F(x) \\cdot\\left(\\frac{1}{a^{x}-1}+\\frac{1}{2}\\right)$ is\nA. Odd function\nB. Even function\nC. Neither odd nor even function\nD. The odd or even nature depends on the specific value of $a$"
},
{
"from": "as... | 5. If $a>0, a \neq 1, F(x)$ is an odd function, then $G(x)=F(x) \cdot\left(\frac{1}{a^{x}-1}+\frac{1}{2}\right)$ is
A. Odd function
B. Even function
C. Neither odd nor even function
D. The odd or even nature depends on the specific value of $a$ | null | null |
[
{
"from": "user",
"value": "Given the circle $M: (x-1)^2 + (y-1)^2 = 4$, and the line $l: x + y - 6 = 0$. Point $A$ lies on line $l$. If two points $B$ and $C$ exist on circle $M$ such that $\\angle BAC = 60^\\circ$, then find the range of values for the $x$-coordinate of point $A$."
},
{
"from": "a... | Given the circle $M: (x-1)^2 + (y-1)^2 = 4$, and the line $l: x + y - 6 = 0$. Point $A$ lies on line $l$. If two points $B$ and $C$ exist on circle $M$ such that $\angle BAC = 60^\circ$, then find the range of values for the $x$-coordinate of point $A$. | null | null |
[
{
"from": "user",
"value": "Calculate:$(1)\\sqrt{3} \\times \\sqrt{6} + \\sqrt{8}$;$(2)\\frac{2}{\\sqrt{5}-2}$."
},
{
"from": "assistant",
"value": "<think>\nOkay, let me try to solve these two problems. Hmm, starting with the first one: √3 multiplied by √6 plus √8. Alright, let's take it step b... | Calculate:$(1)\sqrt{3} \times \sqrt{6} + \sqrt{8}$;$(2)\frac{2}{\sqrt{5}-2}$. | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Two points $A$ and $B$ move along intersecting lines with constant, but different velocities. Prove that there exists a point $P$ such that at any moment in time, the ratio $AP:BP = k$, where $k$ is the ratio of the velocities."
},
... | Two points $A$ and $B$ move along intersecting lines with constant, but different velocities. Prove that there exists a point $P$ such that at any moment in time, the ratio $AP:BP = k$, where $k$ is the ratio of the velocities. | null | null |
[
{
"from": "user",
"value": "port this code to Rust:\n```mojo\nsub find_restaurants(list1, list2) {\n my %restaurant_map;\n for my $i (0..@$list1-1) {\n $restaurant_map{$list1->[$i]} = $i;\n }\n my $min_sum = Inf;\n my @result;\n for my $j (0..@$list2-1) {\n my $restaurant = $... | null | dolphin | null |
[
{
"from": "user",
"value": "Three classes each choose one out of five scenic spots for a visit. The number of different selections is ( ).\n\nA: $5^3$\nB: $3^5$\nC: $A_5^3$\nD: $C_5^3$"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. The problem is about three classes each choosing... | Three classes each choose one out of five scenic spots for a visit. The number of different selections is ( ).
A: $5^3$
B: $3^5$
C: $A_5^3$
D: $C_5^3$ | null | null |
[
{
"from": "user",
"value": "A cleaning company produces two sanitizer sprays. One spray kills 50% of germs, and another spray kills 25% of germs. However, 5% of the germs they kill are the same ones. What percentage of germs would be left after using both sanitizer sprays together?"
},
{
"from": "as... | null | tiger_lab_math | 9,319 |
[
{
"from": "user",
"value": "The slicing mechanism in Python is universally appreciated, as exemplified by notations like array[5] to directly access the fifth element, array[:5] to retrieve the elements from zero to the fourth, or array[::-1] to reverse an entire array. Despite their apparent simplicity, ea... | null | evolcodegolf | null |
[
{
"from": "user",
"value": "3. In a school, there are fewer than 400 students in the sixth grade, divided into several parallel classes. Six of the parallel classes have the same number of students, and these six classes together have more than 150 students. In the remaining parallel classes in the sixth gr... | 3. In a school, there are fewer than 400 students in the sixth grade, divided into several parallel classes. Six of the parallel classes have the same number of students, and these six classes together have more than 150 students. In the remaining parallel classes in the sixth grade, there are 15% more students in tota... | null | null |
[
{
"from": "user",
"value": "Which of the following operations is correct?\n\nA: $(3x)^{2}=3x^{2}$\n\nB: $(a+2b)^{2}=a^{2}+2ab+4b^{2}$\n\nC: $a^{5}\\div a^{2}=a^{3}(a\\neq 0)$\n\nD: $a\\left(a+1\\right)=a^{2}+1$"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. I have this problem he... | Which of the following operations is correct?
A: $(3x)^{2}=3x^{2}$
B: $(a+2b)^{2}=a^{2}+2ab+4b^{2}$
C: $a^{5}\div a^{2}=a^{3}(a\neq 0)$
D: $a\left(a+1\right)=a^{2}+1$ | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given seven theorems about measuring angles with arcs [1) central angle, 2) inscribed angle, 3) angle formed by a tangent and a chord at the point of tangency, 4) angle formed by two secants intersecting inside the circle, 5) angle for... | Given seven theorems about measuring angles with arcs [1) central angle, 2) inscribed angle, 3) angle formed by a tangent and a chord at the point of tangency, 4) angle formed by two secants intersecting inside the circle, 5) angle formed by a tangent and a secant not passing through the point of tangency, 6) angle for... | null | null |
[
{
"from": "user",
"value": "How does the presence of dark matter affect the gravitational lensing of distant galaxies? Provide a detailed explanation and calculate the expected deviation angles for a galaxy cluster with a known mass and dark matter distribution."
},
{
"from": "assistant",
"value... | How does the presence of dark matter affect the gravitational lensing of distant galaxies? Provide a detailed explanation and calculate the expected deviation angles for a galaxy cluster with a known mass and dark matter distribution. | null | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. The real number sequence \\( \\{a_n\\} \\) satisfies the conditions: \\( a_1 = \\frac{\\sqrt{2}}{2} + 1 \\), \\( a_2 = \\sqrt{2} + 1 \\), and \\( a_{n+1} + a_{n-1} = \\frac{n}{a_n - a_{n-1}} + 2 \\) for \\( n \\geq 2 \\). Determine the... | The real number sequence \( \{a_n\} \) satisfies the conditions: \( a_1 = \frac{\sqrt{2}}{2} + 1 \), \( a_2 = \sqrt{2} + 1 \), and \( a_{n+1} + a_{n-1} = \frac{n}{a_n - a_{n-1}} + 2 \) for \( n \geq 2 \). Determine the general term formula \( a_n = \frac{n}{\sqrt{2}} + 1 \) for \( n \geq 1 \). | null | null |
[
{
"from": "user",
"value": "As a programmer or computer scientist, one might frequently engage with a variety of trees—not the verdant, skyward-reaching type, but rather the elegant and abstract mathematical trees:\n *<- root (also a node)\n /|\\<- edge\n* * *<- inner node\n| / \\\n* * *<- leaf (also a ... | null | evolcodegolf | null |
[
{
"from": "user",
"value": "Explain with a code snippet how to execute an AJAX request in JavaScript and display the response data in a table format on a webpage."
},
{
"from": "assistant",
"value": "<think>\nOkay, I need to explain how to execute an AJAX request in JavaScript and display the re... | null | codefeedback | null |
[
{
"from": "user",
"value": "1. Two ordered pairs $(a, b)$ and $(c, d)$, where $a, b, c, d$ are real numbers, form a basis of the coordinate plane if $a d \\neq b c$. Determine the number of ordered quadruples $(a, b, c, d)$ of integers between 1 and 3 inclusive for which $(a, b)$ and $(c, d)$ form a basis f... | 1. Two ordered pairs $(a, b)$ and $(c, d)$, where $a, b, c, d$ are real numbers, form a basis of the coordinate plane if $a d \neq b c$. Determine the number of ordered quadruples $(a, b, c, d)$ of integers between 1 and 3 inclusive for which $(a, b)$ and $(c, d)$ form a basis for the coordinate plane. | null | null |
[
{
"from": "user",
"value": "Given that $m=3\\int_{0}^{{\\pi}}\\sin xdx$, find the coefficient of $ab^{2}c^{m-3}$ in the expansion of $(a+2b-3c)^{m}$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the coefficient of the term \\( ab^2c^{m-3} \\) in the expansion of \\( (a +... | Given that $m=3\int_{0}^{{\pi}}\sin xdx$, find the coefficient of $ab^{2}c^{m-3}$ in the expansion of $(a+2b-3c)^{m}$. | null | null |
[
{
"from": "user",
"value": "10. Given the vectors $\\boldsymbol{a}=\\left(\\frac{1}{2},-\\frac{\\sqrt{3}}{2}\\right), \\boldsymbol{b}=(\\cos \\alpha, \\sin \\alpha), 0<\\alpha<\\frac{2 \\pi}{3}$.\n(1) Prove that $\\boldsymbol{a}+\\boldsymbol{b}$ is perpendicular to $\\boldsymbol{a}-\\boldsymbol{b}$;\n(2) Le... | 10. Given the vectors $\boldsymbol{a}=\left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right), \boldsymbol{b}=(\cos \alpha, \sin \alpha), 0<\alpha<\frac{2 \pi}{3}$.
(1) Prove that $\boldsymbol{a}+\boldsymbol{b}$ is perpendicular to $\boldsymbol{a}-\boldsymbol{b}$;
(2) Let $\boldsymbol{x}=k \boldsymbol{a}+3 \boldsymbol{b}, \boldsy... | null | null |
[
{
"from": "user",
"value": "Is there a way to merge two given data sets into one contiguous set in Python?"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to figure out how to merge two datasets into one contiguous set in Python. Let's start by understanding what exactly the user i... | null | sharegpt | null |
[
{
"from": "user",
"value": "In a circle of radius 10 cm, an equilateral triangle is inscribed such that the length of each side is a function of the angle formed by the radii to the vertices. Find the value of the angle such that the area of the triangle is half the area of the circle."
},
{
"from":... | null | null | null |
[
{
"from": "user",
"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": "What is the value of $x$ so that $\\frac{8}{x}+6=8$ ?"
},
{
"from": "assistant",
"value": "<think>\nAlright, let's see. I need to find the value of x such that 8 divided by x plus 6 equals 8. Hmm, okay. Let me write that equation down first to visualize it better. So,... | What is the value of $x$ so that $\frac{8}{x}+6=8$ ? | null | null |
[
{
"from": "user",
"value": "37. Use a 22 cm long iron wire to form a rectangle with both length and width being whole centimeters. How many methods are there?"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. The problem is asking me to figure out how many different ways I can form ... | 37. Use a 22 cm long iron wire to form a rectangle with both length and width being whole centimeters. How many methods are there? | null | null |
[
{
"from": "user",
"value": "Given that {an} is an arithmetic sequence, Sn is the sum of its first n terms, and $$S_{11}= \\frac {22π}{3}$$, find the value of tana6 ( ):\nA: $$\\sqrt {3}$$\nB: $$- \\sqrt {3}$$\nC: $$± \\sqrt {3}$$\nD: $$- \\frac { \\sqrt {3}}{3}$$"
},
{
"from": "assistant",
"v... | Given that {an} is an arithmetic sequence, Sn is the sum of its first n terms, and $$S_{11}= \frac {22π}{3}$$, find the value of tana6 ( ):
A: $$\sqrt {3}$$
B: $$- \sqrt {3}$$
C: $$± \sqrt {3}$$
D: $$- \frac { \sqrt {3}}{3}$$ | null | null |
[
{
"from": "user",
"value": "7.3. In a bag for a bingo game, there are 90 barrels with numbers from 1 to 90. What is the minimum number of barrels that need to be drawn at random from the bag to guarantee getting a barrel with a number divisible by 3 or 5 (or both 3 and 5)?"
},
{
"from": "assistant",... | 7.3. In a bag for a bingo game, there are 90 barrels with numbers from 1 to 90. What is the minimum number of barrels that need to be drawn at random from the bag to guarantee getting a barrel with a number divisible by 3 or 5 (or both 3 and 5)? | null | null |
[
{
"from": "user",
"value": "A man is three (3) years older than his wife and four (4) times as old as his son. If the son attains an age of fifteen (15) years after three (3) years, what is the present age of the mother?\nAnswer Choices: (A) 60 years (B) 51 years (C) 48 years (D) 45 years (E) 65 years"
},... | null | tiger_lab_math | 27,379 |
[
{
"from": "user",
"value": "# Task 4.\n\nMasha tightly packed 165 identical balls into the shape of a regular triangular pyramid. How many balls are at the base?"
},
{
"from": "assistant",
"value": "<think>\nOkay, so Masha packed 165 identical balls into a regular triangular pyramid. I need to f... | # Task 4.
Masha tightly packed 165 identical balls into the shape of a regular triangular pyramid. How many balls are at the base? | null | null |
[
{
"from": "user",
"value": "Consider a graph G that has 10 vertices and 15 edges. Determine the number of cut vertices and bridges in the graph G."
},
{
"from": "assistant",
"value": "<think>\nAlright, so I have this problem here about graph theory. It says: Consider a graph G that has 10 vertic... | null | null | null |
[
{
"from": "user",
"value": "In a magical garden, there are 25 exotic trees, of which 7 are bearing blue apples, 10 are bearing red apples, and the rest are bearing golden apples. A mischievous sprite likes to hop from one tree to another. If the sprite randomly picks a tree to rest in, what is the probabili... | null | null | null |
[
{
"from": "user",
"value": "Explore the pattern. Observe the following expressions and verification process: \nWhen $n=2$, there is equation ①: $2\\times \\sqrt{\\frac{2}{3}}=\\sqrt{2+\\frac{2}{3}}$; \nWhen $n=3$, there is equation ②: $3\\times \\sqrt{\\frac{3}{8}}=\\sqrt{3+\\frac{3}{8}}$; \nWhen $n=4$, ... | Explore the pattern. Observe the following expressions and verification process:
When $n=2$, there is equation ①: $2\times \sqrt{\frac{2}{3}}=\sqrt{2+\frac{2}{3}}$;
When $n=3$, there is equation ②: $3\times \sqrt{\frac{3}{8}}=\sqrt{3+\frac{3}{8}}$;
When $n=4$, there is equation ③: $4\times \sqrt{\frac{4}{15}}=\sq... | null | null |
[
{
"from": "user",
"value": "Can anyone provide an example of an R program to calculate the sum of all the elements of a given matrix?"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to figure out how to write an R program that calculates the sum of all the elements in a given matri... | null | null | null |
[
{
"from": "user",
"value": "You are tasked with implementing a data manipulation function for a communication protocol. The function should handle both read and write operations for a specific field within the protocol's data structure.\n\nYou are given a Rust code snippet that defines a field writer for a ... | null | magicoder | null |
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. A parametric graph is given by\n\\begin{align*}\nx &= \\cos t + \\frac{t}{2}, \\\\\ny &= \\sin t.\n\\end{align*}How many times does the graph intersect itself between $x = 1$ and $x = 40$?"
},
{
"from": "assistant",
"value"... | A parametric graph is given by
\begin{align*}
x &= \cos t + \frac{t}{2}, \\
y &= \sin t.
\end{align*}How many times does the graph intersect itself between $x = 1$ and $x = 40$? | null | null |
[
{
"from": "user",
"value": "This text describes a rudimentary encoding algorithm that I recently devised. Although it falters when confronted with texts that contain over 256 distinct characters, it does support Unicode through my Python implementation. The steps to execute the algorithm are as follows:\n\n... | null | evolcodegolf | null |
[
{
"from": "user",
"value": "Let $ f(x)$ be the continuous function at $ 0\\leq x\\leq 1$ such that $ \\int_0^1 x^kf(x)\\ dx\\equal{}0$ for integers $ k\\equal{}0,\\ 1,\\ \\cdots ,\\ n\\minus{}1\\ (n\\geq 1).$\r\n\r\n(1) For all real numbers $ t,$ find the minimum value of $ g(t)\\equal{}\\int_0^1 |x\\minus{... | Let $ f(x)$ be the continuous function at $ 0\leq x\leq 1$ such that $ \int_0^1 x^kf(x)\ dx\equal{}0$ for integers $ k\equal{}0,\ 1,\ \cdots ,\ n\minus{}1\ (n\geq 1).$
(1) For all real numbers $ t,$ find the minimum value of $ g(t)\equal{}\int_0^1 |x\minus{}t|^n\ dx.$
(2) Show the following equation for all real ... | null | null |
[
{
"from": "user",
"value": "Olivia drank 5 glasses of juice on Wednesday and drank three times as many on Thursday. The next day, she decided to cut back, so she only drank 2 glasses of juice for breakfast. How many more glasses of juice in total did Olivia drink on Thursday than Friday?"
},
{
"from... | null | nvidia_math | 48,584 |
[
{
"from": "user",
"value": "Given the universal set as $R$, set $M=\\{x|(x+a)(x-1)\\leqslant 0\\}(a > 0)$, and set $N=\\{x|4x^{2}-4x-3 < 0\\}$.\n(1) If $M\\cup N=\\{x|-2\\leqslant x < \\frac {3}{2}\\}$, find the value of real number $a$;\n(2) If $N\\cup (\\lnot_{R}M)=R$, find the range of values for $a$."
... | Given the universal set as $R$, set $M=\{x|(x+a)(x-1)\leqslant 0\}(a > 0)$, and set $N=\{x|4x^{2}-4x-3 < 0\}$.
(1) If $M\cup N=\{x|-2\leqslant x < \frac {3}{2}\}$, find the value of real number $a$;
(2) If $N\cup (\lnot_{R}M)=R$, find the range of values for $a$. | null | null |
[
{
"from": "user",
"value": "Given that vector $\\overrightarrow{a}$ is a unit vector and vector $\\overrightarrow{b}=(2,2\\sqrt{3})$, if $\\overrightarrow{a}\\perp(2\\overrightarrow{a}+\\overrightarrow{b})$, find the angle between $\\overrightarrow{a}$ and $\\overrightarrow{b}$."
},
{
"from": "assis... | Given that vector $\overrightarrow{a}$ is a unit vector and vector $\overrightarrow{b}=(2,2\sqrt{3})$, if $\overrightarrow{a}\perp(2\overrightarrow{a}+\overrightarrow{b})$, find the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$. | null | null |
[
{
"from": "user",
"value": "Walking at 5/6 of her normal speed, a worker is 12 minutes later than usual in reaching her office. The usual time (in minutes) taken by her to cover the distance between her home and her office is\nAnswer Choices: (A) 36 (B) 42 (C) 48 (D) 54 (E) 60"
},
{
"from": "assista... | null | null | null |
[
{
"from": "user",
"value": "The symmetry center of the function $y= \\frac {1}{3}\\tan (-7x+ \\frac {\\pi}{3})$ is $(\\quad)$\n\nA: $\\left( \\frac {5\\pi}{21},0\\right)$\n\nB: $\\left( \\frac {\\pi}{21},0\\right)$\n\nC: $\\left( \\frac {\\pi}{42},0\\right)$\n\nD: $\\left(0, \\frac { \\sqrt {3}}{3}\\right)$... | The symmetry center of the function $y= \frac {1}{3}\tan (-7x+ \frac {\pi}{3})$ is $(\quad)$
A: $\left( \frac {5\pi}{21},0\right)$
B: $\left( \frac {\pi}{21},0\right)$
C: $\left( \frac {\pi}{42},0\right)$
D: $\left(0, \frac { \sqrt {3}}{3}\right)$ | null | null |
[
{
"from": "user",
"value": "For natural number $n$, define the function $f(n)$ to be the number you get by $f(n)$ adding the digits of the number $n$. For example, $f(16)=7$, $f(f(78))=6$, and $f(f(f(5978)))=2$. \nFind the least natural number $n$ such that $f(f(f(n)))$ is not a one-digit number."
},
{
... | For natural number $n$, define the function $f(n)$ to be the number you get by $f(n)$ adding the digits of the number $n$. For example, $f(16)=7$, $f(f(78))=6$, and $f(f(f(5978)))=2$.
Find the least natural number $n$ such that $f(f(f(n)))$ is not a one-digit number. | null | null |
[
{
"from": "user",
"value": "In my creation, I have developed a novel programming language where pointer arithmetic serves as the foundational mechanism for executing code. Below are illustrative examples demonstrating its capabilities:\n\n(print 0 to 8)\n=9[>1=9-*-1.>-1-1]\n\n(print 1 to 10 with spaces betw... | null | evolcodegolf | null |
[
{
"from": "user",
"value": "In the Cartesian coordinate system, the parametric equation of line $l$ is \n$$\n\\begin{cases} \nx=-5+ \\frac { \\sqrt {2}}{2}t \\\\\ny=-1+ \\frac { \\sqrt {2}}{2}t\n\\end{cases}\n$$\nwhere $t$ is the parameter. Now, taking the origin as the pole and the positive half-axis of $x... | In the Cartesian coordinate system, the parametric equation of line $l$ is
$$
\begin{cases}
x=-5+ \frac { \sqrt {2}}{2}t \\
y=-1+ \frac { \sqrt {2}}{2}t
\end{cases}
$$
where $t$ is the parameter. Now, taking the origin as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is estab... | null | null |
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