![$\sqrt[2]{2}$](http://latex.artofproblemsolving.com/1/8/6/1869ac018fb72a26a12ab14499cbf1b1c13b4a10.png)
,![$\sqrt[3]{3}$](http://latex.artofproblemsolving.com/1/7/a/17a6bb5dc11696b8650b6d3a11e770f861f4c326.png)
,![$\sqrt[5]{5}$](http://latex.artofproblemsolving.com/a/b/9/ab90f2d42dc24065e2a64988fe76f22eb9359799.png)
.
,
,
,
Point 
is chosen on the circle with radius 
is chosen on the circle with radius 
is chosen on the circle with radius 
Find (in terms of 
be a continuous and bounded function such that![\[x\int_{x}^{x+1}f(t)\, \text{d}t=\int_{0}^{x}f(t)\, \text{d}t,\quad\text{for any}\ x\in\mathbb{R}.\]](http://latex.artofproblemsolving.com/3/6/c/36cafc551e8173e7873db9731a4e3c3fad9efbf8.png)
is a constant function.
is increasing for all 
.
![\[
f(x) = \sqrt{1 - x^a}, \quad a \geq 0
\]](http://latex.artofproblemsolving.com/e/f/1/ef14689f1894683256f9a0155037788366496929.png)
![\( x \in [0,1] \)](http://latex.artofproblemsolving.com/7/6/d/76d950c78d04a107e9fcb49b26ab353531c93b92.png)
.
,
be a continuous and bijective function, such that 
[list=a]
and 
for any 
.
Y by akpi2, PikaPika999
Hi, I wanted to ask everyone, before the written competition, each state had to do their chant. What chant did you and your team make xd!
Im in WV and I think we did the least cringe chant, and it goes like this:
(After one person says something, the other person following waits ~2 seconds, and then says their line)
P1: Hi
P2: Hi
P3: Hi
P4: Bye
Lol if you were at the national competition you prob remember.
Im in WV and I think we did the least cringe chant, and it goes like this:
(After one person says something, the other person following waits ~2 seconds, and then says their line)
P1: Hi
P2: Hi
P3: Hi
P4: Bye
Lol if you were at the national competition you prob remember.
This post has been edited 1 time. Last edited by ilovebender, May 12, 2022, 1:09 AM
