If r varies inversely as the square root of s and t, how does s vary with r and t?

Assessment: JAMB UTME - Mathematics - 2013 Subject: General Mathematics

Question 1 Report

s varies inversely as r and t2

s varies inverely as r2 and t

s varies directly as r2 and t2

s varies directly as r and t

Answer Details

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{s t}}

This gives

\sqrt{s t} = \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}

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