If r varies inversely as the square root of s and t, how does s vary with r and t?
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Correct Answer: Option 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 = \(\frac{k^2}{r^{2}t}\)
\(r \propto \frac{1}{\sqrt{s}}, r \propto \frac{1}{\sqrt{t}}\)
\(r \propto \frac{1}{\sqrt{s}}\) ..... (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 = \(\frac{k^2}{r^{2}t}\)