If w varies inversely as \(\frac{uv}{u + v}\) and w = 8 when
u = 2 and v = 6, find a relationship between u, v, w.
A
uvw = 16(u + v)
B
16uv = 3w(u + v)
C
uvw = 12(u + v)
D
12uvw = u + v
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
W \(\alpha\) \(\frac{\frac{1}{uv}}{u + v}\)
∴ w = \(\frac{\frac{k}{uv}}{u + v}\)
= \(\frac{k(u + v)}{uv}\)
w = \(\frac{k(u + v)}{uv}\)
w = 8, u = 2 and v = 6
8 = \(\frac{k(2 + 6)}{2(6)}\)
= \(\frac{k(8)}{12}\)
k = 12
i.e 12 ( u + v) = uwv
Source: WAEC / JAMB / NECO Classroom Archive (Record #60713)