Answer:
y = 32
Step-by-step explanation:
Given y is inversely proportional to the cube of x then the equation relating them is
y = [tex]\frac{k}{x^3}[/tex] ← k is the constant of proportionality
To find k use the condition y = 4, x = 2, then
4 = [tex]\frac{k}{2^3}[/tex] = [tex]\frac{k}{8}[/tex] ( multiply both sides by 8 )
32 = k, thus
y = [tex]\frac{32}{x^3}[/tex] ← proportional equation
When x = 1, then
y = [tex]\frac{32}{1^3}[/tex] = [tex]\frac{32}{1}[/tex] = 32
