Variations problem question

Question

Suppose y varies inversely as the cube of x, if x is reduced to 1/2 of its original value, what happens to y?

Answer 1

y = k/x³

 

x → x/2 ⇒

 

y' = k/(x/2)³ = 8k/x³ = 8y ⇒

 

y increases by a factor of 8 if x drops to x/2.