Solve the following mathematical problems:

if $\frac{a}{q-r}=\frac{b}{r-p}=\frac{c}{p-q}$ then show that, a+b+c=pa+qb+rc

Solve the following mathematical problems:

The profit of a company is given in taka by p= $3x^2-35x+50$, where x is the amount in Taka spent on advertising. For what values of x does the company make a profit?

Solve the following mathematical problems:

An amount of tk 7,200 is spent to cover the floor of a room by carpet. An amount of tk 576 would be saved if the breadth were 3 meters less. What is the breadth of the room?

Solve the following mathematical problems:

Find the three digit prime number whose sum of the digit is 11 and each digit representing a prime number. Justify your answer.

Solve the following mathematical problems:

prove that a cyclic parallelogram must be a rectangle .

Solve the following mathematical problems:

After travelling 108km, a cyclist observed that he would have required 3 hours less if he could have traveled at a speed 3 km/hr more. At what speed did he travel?