If r varies inversely as the square root of..

Question 1 Report

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

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 = $\frac{k^{2}}{r^{2} t}$

View Answer