Question

If r varies directly as p and inversely as q2, and r = 27 when p =3 and q = 2, find r when p = 2 and q= 3

Answer 1

Answer:

k = 36 and r = 8

Step-by-step explanation:

Given that r varies directly as p and inversely as q² then the equation relating them is

r = $\frac{kp}{q^2}$ ← k is the constant of variation

To find k use the condition r = 27 when p  3 and q = 2, thus

27 = $\frac{3k}{4}$ ( multiply both sides by 4 )

108 = 3k ( divide both sides by 3 )

k = 36

r = $\frac{36p}{q^2}$ ← equation of variation

When p = 2 and q = 3, then

r = $\frac{36(2)}{3^2}$ = $\frac{72}{9}$ = 8