Chapter 46, Problem 68A

To determine

To solve for the unknown value in the given equation.

Answer to Problem 68A

  $H=\pm 2.885$.

Explanation of Solution

Given information:

The given equation is $\frac{6.08}{3H^2-12}=\frac{5.87}{12.53}$.

Calculation:

We have been given the equation as $\frac{6.08}{3H^2-12}=\frac{5.87}{12.53}$.

We will perform some basic mathematical operation to solve the given equation as below.

  $\frac{6.08}{3H^2-12}=\frac{5.87}{12.53}$

  $\Rightarrow 5.87(3H^2-12)=6.08\times 12.53\left\{\text{Cross multiply}\right\}$

  $\Rightarrow 17.61H^2-70.44=76.1824$

  $\Rightarrow 17.61H^2-70.44+70.44=76.1824+70.44\{\text{Adding 70}\text{.44 on both sides}}$

  $\Rightarrow 17.61H^2=146.6224\left\{\text{Simplify}\right\}$

  $\Rightarrow \frac{17.61}{17.61}{H}^2=\frac{146.6224}{17.61}\left\{\text{Dividing}\text{by}17.61\text{on}\text{both}\text{sides}\right\}$

  $\Rightarrow H^2=8.326$

  $\Rightarrow H=\pm \sqrt{8.326}$

  $\Rightarrow H=\pm 2.885$

  $\text{Check:}$

  $\frac{6.08}{3H^2-12}=\frac{5.87}{12.53}$

  $\frac{6.08}{3{(\pm 2.885)}^2-12}=\frac{5.87}{12.53}$

  $\frac{6.08}{3\times 8.326-12}=\frac{5.87}{12.53}$

  $\frac{6.08}{12.987}=\frac{5.87}{12.53}$

  $\frac{5.87}{12.53}=\frac{5.87}{12.53}$

Hence, solution of the equation will be given by-

  $H=\pm 2.885$.