Solve for x: 0=3u-7x-9.

Lynbrook West , an apartment complex , has 100 two-bedroom units. The montly profit (in dollars) realized from renting out x apartments is given by the following function.
${\displaystyle P\left(x\right)=-12x^2+2136x-41000}$
To maximize the monthly rental profit , how many units should be rented out?
What is the maximum monthly profit realizable?

Use polar coordinates to find the limit. [Hint: Let ${\displaystyle x=r\cos \text{and}y=r\sin }$ , and note that (x, y) (0, 0) implies r 0.] ${\displaystyle \underset{(x,y)\to (0,0)}{lim}\frac{x^2-y^2}{\sqrt{x^2+y^2}}}$

There are four washing machines in an apartment complex: A, B, C, D. On any given day the probability that these machines break down is as follows:
P(A) = 0.04, P(B) = 0.01, P(C) = 0.06, P(D) = 0.01 .
Assume that the functionality of each machine is independent of that of others. What is the probability that on a given day at least one machine will be working?

Solve for G.S. / P.S. for the following differential equations using separation of variables.
${\displaystyle x^{2}ydy-x{y}^{2}dx+3ydy-2xdx=0}$

Write formulas for the indicated partial derivatives for the multivariable function.
${\displaystyle f(x,y)=7x^2+9xy+4y^3}$
a)${\displaystyle \frac{\partial f}{\partial x}}$
b) $\frac{\partial f}{\partial y}$
c)${\displaystyle \frac{\partial f}{\partial x}{\mid }_{y=9}}$

Describe the procedure for finding critical points of a function in two independent variables.

Prove multivariable function is surjective
The function is ${\displaystyle f:{\mathbb{N}}^2\to \mathbb{N}}$ such that ${\displaystyle f(a,b)=a^b}$