math question #2?

Question

P varies joinly as h and v^2. When h=7 and v=2, P=140. Find P when h is 12 and v is 5.

Answer 1

This means that for any three p, h, v:

p/(h * v^2)

... is the same value. So:

p1 / (h1 * v1^2) = p2 / (h2 * v2^2)

140 / (7 * 2^2) = P / (12 * 5^2)
140 / (7 * 4) = P/(12 * 25)
140/28 = P/300
5 = P/300
1,500 = P

When h=12 and v=5, P=1,500.

Answer 2

P varies jointly with h and v^2 means that P varies directly with both v and h. The formula is;
p1/(h1*v1^2) =p2/(h2*v2^2)
therefore 140/(7*2^2) = P/(12*5^2)
140/28 = P/300
P = 1500