the variable j varies jointly as the square of h and as the cube root of a, and it varies inversely as s. What happens to j when h is doubled, a is multiplied by 8, and s is multiplied by 4?

Question

the variable j varies jointly as the square of h and as the cube root of a, and it varies inversely as s.  What happens to j when h is doubled, a is multiplied by 8, and s is multiplied by 4?

Reiny · Accepted Answer

j = k(h^2)(a^(1/3)/s

when h is doubled , a multiplied by 8, s multiplied by 4

j₂ = k (4h^2)(2a^(1/3)/(4s)

j₂ / j = [ k (4h^2)(2a^(1/3)/(4s) ] / [k(h^2)(a^(1/3)/s]
= 4(2)/2 = 2

the value of j will double