Chapter 9, Problem 9CR

a

To determine

To find:The mean value of the proportion between the given values.

Answer to Problem 9CR

The mean value is $\frac{3}{2}$

Explanation of Solution

Given information:

The extreme numbers are given as follows:

  $a=\frac{1}{4}$ and $b=9$

Formula Used:Mean of the proportion $(m)=\sqrt{ab}$

where

“ a ” is the first extreme number of the proportion

“ b ” is the second extreme number of the proportion.

Calculation :

We know that for any two numbers, the mean proportional is the square root of the product of those terms. Hence, we say

  $\begin{array}{l}m=\sqrt{ab}\\ m=\sqrt{9\times \frac{1}{4}}=\sqrt{\frac{9}{4}}\\ m=\frac{3}{2}\end{array}$

b

To determine

To find:The value of “ y ” in the given equation i.e. $\frac{5}{5-y}=\frac{10}{y-10}$

Answer to Problem 9CR

There is no solution for the given equation

Explanation of Solution

Given information:The given equation is as follows

  $\frac{5}{5-y}=\frac{10}{y-10}$

Calculation :

We simplify the given equation by cross multiplying the denominators. We get

  $5y-50=50-10y$ , where $y\ne 5,10$

Hence, we get

  $y=10$

But this is not an acceptable solution, because for cross multiplying the denominators we assumed that

  $y\ne 5,10$

Hence, there is no solution for the given equation