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
jamb 2013mathematics

The correct answer is B. s varies inverely as r2 and t

If r varies inversely as the square root of s and t, then we can write the relationship as \(r = \frac{k}{\sqrt{st}}\), where k is the constant of variation.

Solving for s, we get \(s = \frac{k^2}{r^2t}\). This shows that s varies inversely as \(r^2\) and t.

Therefore, the correct answer is B. s varies inversely as r^2 and t.

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