The function f(x)=2x^{3}-33x^{2}+168x+9 has one local minimum and one local

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.] ${\displaystyle \underset{(x,y)\to (0,0)}{lim}\frac{x^2-y^2}{\sqrt{x^2+y^2}}}$

Select the correct answer:
Which statement best describes the zeros of the function ${\displaystyle h\left(x\right)=(x-6)(x^2+8x+16)}$?
A. The function has two distinct real zeros
B. The function has three distinct real zeros.
C. The function has one real and two complex zeros.
D. The function has three complex zeros.

Evaluate the algebraic expressions for the given values of the variables.
${\displaystyle {(x-y)}^2,x=5\text{ and }y=-3}$

Solve using separation of variables:
$y^{\prime }-xy+y=2y$

Engineering statistics, i need solutions in 15 minutes please. MCQ/Engineering company has a task of checking compressive strength for 100 concrete cubes. The results revealed that 85 cubes passed the compressive strength test successfully and 15 cubes failed in the test. If 10 cubes are selected at random to be inspected by the company, determine the probability that the 8 cubes will pass the test and 2 cubes will fail in the test by using the Combinatorial Analysis. A-0.6553 B-0.2919 C-0.3415 D-0.4522 E-0.1156

1) A group of preschooters has 63 boys and 27 girl. What is the ratio of boys to all children?