# All Questions

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### Help understanding proof on Jensen's Inequality

I need help understanding the proof for Jensen's inequality in "Real and Complex Analysis" by Rudin. 3.3 Theorem (Jensen's Inequality) Let $\mu$ be a positive measure on a $\sigma$-algebra ...
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### Collision between moving circular discs

I am trying to figure out how to detect collision between two moving circular discs that move along a pretedermined path with a known speed. Example: Circular disk A moves along the path AB with ...
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### Express the number $4$ and $5$ and $6$ and $7$ and $8$

Express the number $4$ and $5$ and $6$ and $7$ and $8$ with trigonometric identities or series or equations. example: Express the number $1$, $$cos^2 x + sin^2 x=1$$ Express the number $2$, ...
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### Special case on counting in a string of 7 letters

I have the following question: Suppose $S_7$ is the set of all strings of length seven that can be formed with the letters $A, B, C, D, E, F$ and $G$ when repetitions are allowed. How many strings ...
### What is the maximum amount of solutions to $f(x+1)f(x)= ax^2+bx+c$.
$f(x)$ is going to be in the form $mx+h$ thus, $(mx+m+h)(mx+h) = ax^2+bx+c$. With basic algebra $m= \pm \sqrt{a}$. Also $(m+h)(h)=c$. I would guess that because $(m+h)h=c$ has two solutions max if $m$ ...
What is the central vertex for a cyclic graph $C_n$? and for complete graph $K_n$? The eccentricity is the same for all vertices!