Answer:
z = 27
Step-by-step explanation:
Given that z² is proportional to x³ then the equation relating them is
z² = kx³ ← k is the constant of proportion
To find k use the condition z = 8 when x = 4, thus
8² = k × 4³
64 = 64k ( divide both sides by 64 )
k = 1
z² = x³ ← equation of proportion
When x = 9, then
z² = 9³ = 729 ( take the square root of both sides )
z = [tex]\sqrt{729}[/tex] = 27
