Question

If p varies jointly as r and t and inversely as q, then find an equation for p if p=−1 when r=−6, t=−4, and q=3.

What does it mean by "find an equation for p if p......." how are you supposed to find p

Answer 1

Each word in math has its own meaning.

"To vary jointly" means that something is directly proportional (sign ∝) to each variable at a time. Thus we have:

> If p varies jointly as r and t:

$$p∝r\cdot t.$$

> ...and inversely as q:

$$p∝r\cdot t \cdot \frac{1}{q}=\frac{rt}{q}.$$

The word "proportional" means that if you divide the left part of the expression above by its right part, you will get some constant number called a coefficient k, so we can turn our expression to an equation by adding k and changing "∝" for "=" :

$$p=k\cdot \frac{rt}{q}.$$

To find the equation, we need to determine k k. Now just substitute the numbers mentioned in the condition:

$$-1=k\cdot \frac{(-6)\cdot(-4)}{3},$$ $$k=-\frac{1}{8}.$$

And finally, the equation for p:

$$p=-\frac{rt}{8q}.$$