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

A.

u = \(\frac{8}{v^3}\)

B.

v = \(\frac{8}{u^2v^3}\)

C.

u = 8v3

D.

v = 8u2

Correct answer is A

W \(\alpha\) \(\frac{1}{v}\)u \(\alpha\) w3

w = \(\frac{k1}{v}\)

u = k2w3

u = k2(\(\frac{k1}{v}\))3

= \(\frac{k_2k_1^2}{v^3}\)

k = k2k1k2

u = \(\frac{k}{v^3}\)

k = uv3

= (1)(2)3

= 8

u = \(\frac{8}{v^3}\)