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
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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 = \(\frac{8}{v^3}\)
Source: Myschool Past Questions Archive (Record #32461)