Answer:
x = 12
Step-by-step explanation:
Given x varies as the cube root of y then the equation relating them is
x = k[tex]\sqrt[3]{y}[/tex] ← k is the constant of variation
To find k use the condition x = 6 when y = 8, thus
k = [tex]\frac{x}{\sqrt[3]{y} }[/tex] = [tex]\frac{6}{\sqrt[3]{8} }[/tex] = [tex]\frac{6}{2}[/tex] = 3
x = 3[tex]\sqrt[3]{y}[/tex] ← equation of variation
When y = 64, then
x = 3 × [tex]\sqrt[3]{64}[/tex] = 3 × 4 = 12
