If r varies inversely as the square root of s a... - JAMB Mathematics 2013 Question

(r \propto \frac{1}{\sqrt{s}}, r \propto \frac{1}{\sqrt{t}})

(r \propto \frac{1}{\sqrt{s}}) ..... (1)

(r \propto \frac{1}{\sqrt{t}}) ..... (2)

Combining (1) and (2), we get

(r = \frac{k}{\sqrt{s} \times \sqrt{t}} = \frac{k}{\sqrt{st}})

This gives (\sqrt{st} = \frac{k}{r})

By taking the square of both sides, we get

st = (\frac{k^2}{r^2})

s = (\frac{k^2}{r^{2}t})