Answer:
A
Step-by-step explanation:
Given p² varies inversely as q then the equation relating them is
p² = [tex]\frac{k}{q}[/tex] ← k is the constant of variation
To find use the condition when q = 6, p = 4 , then
4² = [tex]\frac{k}{6}[/tex]
16 = [tex]\frac{k}{6}[/tex] ( multiply both sides by 6 )
96 = k
p² = [tex]\frac{96}{q}[/tex] ← equation of variation
When p = 12 , then
12² = [tex]\frac{96}{q}[/tex] ( multiply both sides by q )
144q = 96 ( divide both sides by 144 )
q = [tex]\frac{96}{144}[/tex] = [tex]\frac{2}{3}[/tex] → A
