The ratio 216:x is equivalent to the ratio x^{2}:216. What is the value of x?

Which of the values satisfies this inequality ${\displaystyle 2x-10<-4}$
(a) 2
(b) 3
(c) 4
(d) 5

Determine whether the sequence converges or diverges
${\displaystyle a_n={(1+\frac{k}{n})}^n}$

Absolute maxima and minima Determine the location and value of the absolute extreme value of ƒ on the given interval, if they exist.
${\displaystyle f\left(x\right)=x^{\frac{1}{3}}(x+4)on[-27,27]}$

Evaluate.
$\frac{4}{5x{y}^3}+\frac{2x}{15y^2}$

Simplify $$\sqrt{3}(7+5\sqrt{5})$$.

The number of units N of a finished product produced by a particular automobile company where x units of labor and y units of capital are used is approximated by ${\displaystyle N=50x^{\frac{1}{2}}{y}^{\frac{1}{2}}}$
Estimate how many units will be produced using 256 units of labour and 144 units of capital.

Suppose that $x$, $y$, $z$, $\nu$, $N$, $g$ are some postitive parameters and $A$, $B$ and $C$ are variables that belong to $(0,+\mathrm{\infty })$. I want to identify one or all of the feasible points taht solve the following system of inequalities with respect to $A$, $B$ and $C$
$$\begin{gathered} xA-\nu gB-NgC>0 \\ -\nu gA+yB-NgC>0 \\ -\nu gA-\nu gB+zC>0 \end{gathered}$$