If r varies inversely as the square root of s and t, how does s vary with r and t?
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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: 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})
There is an explanation video available below.