Question

Find the mean proportional for each of the following:

(iii) $17.5,0.007$

Answer 1

Calculate the mean proportional:

If $y$ is the mean proportional between $a$ and $b$, then $a:y::y:b$.

Let $x$ be the required mean proportional.

Then, for the numbers $17.5,0.007$, the equivalent proportional expression is $17.5:x::x:0.007$.

$$\begin{gathered} \Rightarrow 17.5:x=x:0.007(Changingtheproportionalitysigntoequalsign) \\ \Rightarrow \frac{{\displaystyle 17.5}}{x}=\frac{x}{{\displaystyle 0.007}} \\ \Rightarrow 17.5·0.007=x·x(Crossmultiplyingbothsides) \\ \Rightarrow 0.1225=x^2 \\ \therefore \pm 0.35=x(Takingsquarerootonbothsides) \end{gathered}$$

As $-0.35$ does not lie between the given two numbers, therefore, the mean proportional is $0.35$.

Final Answer: The mean proportional is $0.35$.