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conversations list | question string | source string | id int64 | full_text string |
|---|---|---|---|---|
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Find [the decimal form of] the largest prime divisor of $100111011_6$.\n"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the largest prime divisor of the number 100111011 in base 6, converted to decima... | Find [the decimal form of] the largest prime divisor of $100111011_6$.
| null | null | user Return your final response within \boxed{}. Find [the decimal form of] the largest prime divisor of $100111011_6$.
assistant <think>
Okay, so I need to find the largest prime divisor of the number 100111011 in base 6, converted to decimal form. Hmm, let me start by understanding the steps involved here. First, I ... |
[
{
"from": "user",
"value": "The maximum value of the function $f(x)=\\frac{4}{{x-3}}+x(x＜3)$ is ( ).\n\nA: $-4$\n\nB: $1$\n\nC: $5$\n\nD: $-1$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the maximum value of the function f(x) = 4/(x - 3) + x, but only for x less than 3.... | The maximum value of the function $f(x)=\frac{4}{{x-3}}+x(x＜3)$ is ( ).
A: $-4$
B: $1$
C: $5$
D: $-1$ | null | null | user The maximum value of the function $f(x)=\frac{4}{{x-3}}+x(x＜3)$ is ( ).
A: $-4$
B: $1$
C: $5$
D: $-1$ assistant <think>
Okay, so I need to find the maximum value of the function f(x) = 4/(x - 3) + x, but only for x less than 3. The options given are A: -4, B:1, C:5, D:-1. Hmm, let me think step by step.
First... |
[
{
"from": "user",
"value": "5. The length of the diagonal $AC$ of the rhombus $ABCD$ with an acute angle at vertex $A$ is 12. Points $M$ and $N$ on sides $DA$ and $DC$ are the bases of the heights of the rhombus dropped from vertex $B$. The height $BM$ intersects the diagonal $AC$ at point $P$ such that $AP... | 5. The length of the diagonal $AC$ of the rhombus $ABCD$ with an acute angle at vertex $A$ is 12. Points $M$ and $N$ on sides $DA$ and $DC$ are the bases of the heights of the rhombus dropped from vertex $B$. The height $BM$ intersects the diagonal $AC$ at point $P$ such that $AP: PC = 2: 3$. Find the length of the seg... | null | null | user 5. The length of the diagonal $AC$ of the rhombus $ABCD$ with an acute angle at vertex $A$ is 12. Points $M$ and $N$ on sides $DA$ and $DC$ are the bases of the heights of the rhombus dropped from vertex $B$. The height $BM$ intersects the diagonal $AC$ at point $P$ such that $AP: PC = 2: 3$. Find the length of th... |
[
{
"from": "user",
"value": "Given the function $f(x) = ax^2 + (b-3)x + 3$, where $x \\in [2a-3, 4-a]$ is an even function, find the value of $a+b$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the value of a + b given that the function f(x) = ax² + (b - 3)x + 3 is an eve... | Given the function $f(x) = ax^2 + (b-3)x + 3$, where $x \in [2a-3, 4-a]$ is an even function, find the value of $a+b$. | null | null | user Given the function $f(x) = ax^2 + (b-3)x + 3$, where $x \in [2a-3, 4-a]$ is an even function, find the value of $a+b$. assistant <think>
Okay, so I need to find the value of a + b given that the function f(x) = ax² + (b - 3)x + 3 is an even function on the interval [2a - 3, 4 - a]. Hmm, let me recall what an even ... |
[
{
"from": "user",
"value": "If the function $f(x) = (x+a)^3$ holds true for any $x \\in \\mathbb{R}$ such that $f(1+x) = -f(1-x)$, find the value of $f(2) + f(-2)$."
},
{
"from": "assistant",
"value": "<think>\nOkay, so I have this problem here: the function f(x) = (x + a)^3 satisfies the equati... | If the function $f(x) = (x+a)^3$ holds true for any $x \in \mathbb{R}$ such that $f(1+x) = -f(1-x)$, find the value of $f(2) + f(-2)$. | null | null | user If the function $f(x) = (x+a)^3$ holds true for any $x \in \mathbb{R}$ such that $f(1+x) = -f(1-x)$, find the value of $f(2) + f(-2)$. assistant <think>
Okay, so I have this problem here: the function f(x) = (x + a)^3 satisfies the equation f(1 + x) = -f(1 - x) for all real numbers x. I need to find the value of f... |
[
{
"from": "user",
"value": "Given that the radius of circle $\\odot O$ is 6, and the distance between point $A$ and the center $O$ is 5, then the position relationship between point $A$ and circle $\\odot O$ is ( ).\n\nA: Point $A$ is outside circle $\\odot O$\n\nB: Point $A$ is inside circle $\\odot O$\n\n... | Given that the radius of circle $\odot O$ is 6, and the distance between point $A$ and the center $O$ is 5, then the position relationship between point $A$ and circle $\odot O$ is ( ).
A: Point $A$ is outside circle $\odot O$
B: Point $A$ is inside circle $\odot O$
C: Point $A$ is not inside circle $\odot O$
D: Po... | null | null | user Given that the radius of circle $\odot O$ is 6, and the distance between point $A$ and the center $O$ is 5, then the position relationship between point $A$ and circle $\odot O$ is ( ).
A: Point $A$ is outside circle $\odot O$
B: Point $A$ is inside circle $\odot O$
C: Point $A$ is not inside circle $\odot O$
... |
[
{
"from": "user",
"value": "Given that in acute triangle $\\triangle ABC$, the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and $(b+c)(\\sin B+\\sin C)=a\\sin A+3b\\sin C$. \n$(1)$ Find angle $A$; \n$(2)$ Find the minimum value of $\\frac{1}{\\tan B}+\\frac{1}{\\tan C}$."
... | Given that in acute triangle $\triangle ABC$, the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and $(b+c)(\sin B+\sin C)=a\sin A+3b\sin C$.
$(1)$ Find angle $A$;
$(2)$ Find the minimum value of $\frac{1}{\tan B}+\frac{1}{\tan C}$. | null | null | user Given that in acute triangle $\triangle ABC$, the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and $(b+c)(\sin B+\sin C)=a\sin A+3b\sin C$.
$(1)$ Find angle $A$;
$(2)$ Find the minimum value of $\frac{1}{\tan B}+\frac{1}{\tan C}$. assistant <think>
Okay, let's see. I have this pr... |
[
{
"from": "user",
"value": "Out of the 120 people who attended the party, 1/3 are men while x% are women. The rest are children. How many children attended the party?\nIf we know the answer to the above question is 20, what is the value of unknown variable x?"
},
{
"from": "assistant",
"value": ... | null | tiger_math | 28,288 | user Out of the 120 people who attended the party, 1/3 are men while x% are women. The rest are children. How many children attended the party?
If we know the answer to the above question is 20, what is the value of unknown variable x? assistant <think>
Okay, let's see. The problem says there are 120 people at a party.... |
[{"from":"user","value":"For an integer $n \\ge 3$ we consider a circle with $n$ points on it.\nWe p(...TRUNCATED) | "For an integer $n \\ge 3$ we consider a circle with $n$ points on it.\nWe place a positive integer (...TRUNCATED) | null | null | "user For an integer $n \\ge 3$ we consider a circle with $n$ points on it.\nWe place a positive int(...TRUNCATED) |
[{"from":"user","value":"Define a function $f(x)$ on $R$ such that $f(-x) = f(x)$, and for any disti(...TRUNCATED) | "Define a function $f(x)$ on $R$ such that $f(-x) = f(x)$, and for any distinct real numbers $x_{1}$(...TRUNCATED) | null | null | "user Define a function $f(x)$ on $R$ such that $f(-x) = f(x)$, and for any distinct real numbers $x(...TRUNCATED) |
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