Answer:
see explanation
Step-by-step explanation:
Given
p = kq³
(a)
To find k use the condition when p = 9, q = 3, that is
9 = k × 3³ = 27k ( divide both sides by 27 )
k = [tex]\frac{9}{27}[/tex] = [tex]\frac{1}{3}[/tex]
p = [tex]\frac{1}{3}[/tex] q³ ← equation of variation
(b)
When q = 6, then
p = [tex]\frac{1}{3}[/tex] × 6³ = [tex]\frac{1}{3}[/tex] × 216 = 72
(c)
When q = 1, then
p = [tex]\frac{1}{3}[/tex] × 1³ = [tex]\frac{1}{3}[/tex]
(d)
When p = 576 , then
576 = [tex]\frac{1}{3}[/tex] q³ ( multiply both sides by 3 )
1728 = q³ ( take the cube root of both sides )
q = [tex]\sqrt[3]{1728}[/tex] = 12
