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 = [tex]\frac{kp}{q^2}[/tex] ← k is the constant of variation
To find k use the condition r = 27 when p 3 and q = 2, thus
27 = [tex]\frac{3k}{4}[/tex] ( multiply both sides by 4 )
108 = 3k ( divide both sides by 3 )
k = 36
r = [tex]\frac{36p}{q^2}[/tex] ← equation of variation
When p = 2 and q = 3, then
r = [tex]\frac{36(2)}{3^2}[/tex] = [tex]\frac{72}{9}[/tex] = 8
