Question on: JAMB Mathematics - 2013
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
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Correct Option: B
(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})
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