Mathematics 2013 JAMB Past Questions - Question 15: If r varies inversely as the square roots of s and t,how does s vary with r and t?

Correct Answer

D

Explanation

If r varies inversely as the square roots of s and t, we can express this relationship mathematically as:r = k / √(s * t)where k is the constant of variation.To determine how s varies with r and t, we can rearrange the equation to isolate s:√(s * t) = k / rSquaring both sides of the equation, we get:s * t = (k / r)^2Now, let's analyze the relationship between s and r while keeping t constant.If t is held constant, the equation becomes:s = (k / r)^2 / tFrom this equation, we can see that as r increases, s will decrease. This is because as r increases, the denominator (k / r)^2 becomes smaller, resulting in a larger value for s.Similarly, if r decreases, s will increase. This is because as r decreases, the denominator (k / r)^2 becomes larger, resulting in a smaller value for s.Therefore, we can conclude that s varies inversely with r when t is held constant.On the other hand, if we keep r constant and analyze the relationship between s and t, the equation becomes:s = (k / r)^2 / tFrom this equation, we can see that as t increases, s will decrease. This is because as t increases, the denominator t becomes larger, resulting in a smaller value for s.Similarly, if t decreases, s will increase. This is because as t decreases, the denominator t becomes smaller, resulting in a larger value for s.Therefore, we can conclude that s varies inversely with t when r is held constant.