Chapter 12.7, Problem 6MRE

To determine

To calculate: The solution of the below indicated variable, also need to state restrictions if any.

  $E{r}^2=k;r$

Answer to Problem 6MRE

Solution for the indicated variable is $r=\sqrt{\frac{k}{E}}$ .

And restrictions are at $k<0$ and $E\le 0$ .

Explanation of Solution

Given information:

Equation $E{r}^2=k$...... $\left(1\right)$

Indicated variable r.

Now get r alone on one side from equation 1.

  $\begin{array}{l}E{r}^2=k\\ r^2=\frac{k}{E}\end{array}$

  $r=\sqrt{\frac{k}{E}}$

The solution of r is meaningful if and only if k and E are positive number and $E\ne 0$ that is $k\ge 0\text{}$ and $E>0$ .

So the restrictions for the indicated variable are at $k<0$ and $E\le 0$ .