If w varies inversely as uru+r u r u + r and is equal to 8 when u = 2 and r = 6, find a relationship between u, v, w.

If w varies inversely as $\frac{ur}{u+r}$ and is equal to 8 when u = 2 and r = 6, find a relationship between u, v, w.

Answer Details

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 = $\frac{k(2+6)}{2\left(6\right)}$
= $\frac{k\left(8\right)}{12}$
k = 12