If w varies inversely as V and U varies directly as w3, Find the relationship between u and v given that u = 1, when v = 2

If w varies inversely as V and U varies directly as w3, Find the relationship between u and v given that u = 1, when v = 2

Answer Details

W $\alpha$ $\frac{1}{v}$u $\alpha$ w3
w = $\frac{k_1}{v}$
u = k2w3
u = k2($\frac{k_1}{v}$)3
= $\frac{k_2{k}_1^2}{v^3}$
k = k2k1k2
u = $\frac{k}{v^3}$
k = uv3
= (1)(2)3
= 8
u = $\frac{8}{v^3}$