If r varies inversely as the square root of s and t, how does s vary with r and t?
A. s varies inversely as r and t2 B. s varies inverely as r2 and t C. s varies directly as r2 and t2 D. s varies directly as r and t
Correct Answer: B
Explanation
\(r \propto \frac{1}{\sqrt{s}}, r \propto \frac{1}{\sqrt{t}}\) \(r \propto \frac{1}{\sqrt{s}}\) ..... (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 = \(\frac{k^2}{r^{2}t}\)
