Chapter 3.4, Problem 4GP

Solution

The length at which the band provides 13 pounds of resistance.

  $48\text{ inches}$

Given:

The inverse relation that gives the length in terms of resistance is, $L=\frac{8}{3}R+\frac{40}{3}$ .

Concept Used:

• The even inter root of a number is defined for positive values only that are greater than or equal to 0.
• The odd integer root of all real numbers is defined.
• Power of a power property: ${\left(x^a\right)}^b=x^{a\cdot b}$
• The exponent form of the nth root of a number a is given by $\sqrt[n]{a}=a^{\frac{1}{n}}$

Calculation:

In order to find the length at which the band provides 13 pounds of resistance, substitute 13 for R into the inverse function and simplify further as shown below

  $\begin{array}{c}L=\frac{8}{3}R+\frac{40}{3}\\ =\frac{8}{3}\times 13+\frac{40}{3}\\ =\frac{104}{3}+\frac{40}{3}\\ =\frac{104+40}{3}\\ =\frac{144}{3}\\ =48\end{array}$

Therefore, the required length is $48\text{ inches}$ .