The graphs of $u\left(x\right)$ and $v\left(x\right)$ are shown in the following image.

Find the value of $u\left(u\left(9\right)\right)$.

Evaluate the composite function $a\left(b\left(y\right)\right)$ given the following:

$a\left(x\right)=x^2$

$b\left(x\right)=x^2-7$

A certain species of fish in a lake reproduces at a rate that doubles its population every $24\text{ hours}$. The initial population of the fish was $200$. If the population $t$ hours after the initial observation is represented by the function $p\left(t\right)=200\cdot 2^{\frac{t}{24}}$, how long will it take for the fish population to reach $4000$?

Given that ${\log }_{c}a=0.45,{\log }_{c}b=0.65,$ find the value of ${\log }_c\left(a/b\right)$.

Determine the value of $z$ in the equation $3^z=81$.

Determine the value of $z$ that satisfies $\ln 5z+\ln (z+4)=0$.

Find the amplitude and period for the given trigonometric expression below.

$P\left(x\right)=5.7\sin \left(\frac{1}{9}(x-7)\right)$

Is the following trigonometric equation an identity?

$\frac{\cos A}{1+\sin A}=\frac{1-\sin A}{\cos A}$

Evaluate the given expression:

$\cos \left({\cos }^{-1}(-\frac{1}{2})\right)$