2013
Mathematics
JAMB
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
Correct Answer: s varies inverely as r2 and t
Explanation
r ∝ 1/√s, r ∝ 1/√t r ∝ 1/√s ..... (1) r ∝ 1/√t ..... (2) Combining (1) and (2), we get r = k/(√s × √t) = k/√(st) This gives √(st) = k/r By taking the square of both sides, we get st = k2/r2 s = k2/r2t
r ∝ 1/√s, r ∝ 1/√t r ∝ 1/√s ..... (1) r ∝ 1/√t ..... (2) Combining (1) and (2), we get r = k/(√s × √t) = k/√(st) This gives √(st) = k/r By taking the square of both sides, we get st = k2/r2 s = k2/r2tTHIS WEEK's
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