Chapter 10.4, Problem 10P

You decide to install a rope swing at the bend in the river. The time t in seconds for the rope swing to make one swing is given by $2\sqrt{\frac{1}{3.3}}$

where I is the length of the rope swing in feet. If one swing takes 3.5 seconds, how long is the rope stving? Round your answer to the nearest tenth of a foot.

To determine

To find: that how long is rope swing when one swing takes $3.5$ seconds.

Answer to Problem 10P

The rope swing $l=10.10$ when one swing takes $3.5$ seconds.

Explanation of Solution

Given information:

The function is $t=2\sqrt{\frac{l}{3.3}}$ .

Calculation: to find the solution, first substitute and then simplify,

  $\begin{array}{l}t=2\sqrt{\frac{l}{3.3}}\\ 3.5=2\sqrt{\frac{l}{3.3}}\text{ [substitute]}\\ 1.75=\sqrt{\frac{l}{3.3}}\text{ [divide]}\\ \frac{l}{3.3}=3.06\text{ [square]}\\ l=10.10\text{ [multiply]}\end{array}$

Thus, The rope swing $l=10.10$ when one swing takes $3.5$ seconds.