The time, in seconds, that it takes a pendulum to swing back and forth is modeled by the equation below. , where l is the length of the pendulum in feet What is the length of a pendulum that takes seconds to swing back and forth?
F(l)=2\pi \sqrt{\frac{l}{32}} where l is the length of the pendulum in feet
what is the length of a pendulum that takes 2.4\pi seconds to swing back and forth ?
A)1.72 ft
B)3.05 ft
C)38.40
D)46.08

Question

mathstudent55 · Answer

$F\left(l\right)=2\pi \sqrt{\frac{l}{32}}$

$F(l) = 2.4\pi$

Set the two right sides equal and solve for $l$.

anonymous · Answer

still dont understand

mathstudent55 · Answer

Let's call the time t.
Your equation then is

$t =2\pi \sqrt{\frac{l}{32}}$

You are asked to find the length, $l$, for a given time of $2.4\pi $ seconds.

Since you equation is solved for $t$, time, let $t$ be $2.4\pi $, and solve for $l$.

$2.4\pi =2\pi \sqrt{\frac{l}{32}}$

mathstudent55 · Answer

You need to solve the last equation above for $l$.

mathstudent55 · Answer

Start by switching sides to get $l$ on the left side:

$2\pi \sqrt{\frac{l}{32}}= 2.4\pi $

The next step is to divide both sides by $2\pi$.

anonymous · Answer

let me try

anonymous · Answer

the answer would be d 46.08  right

mathstudent55 · Answer

Correct

mathstudent55 · Answer

$2\pi \sqrt{\frac{l}{32}}= 2.4\pi$

$\dfrac{\cancel{2\pi}}{\cancel{2 \pi}} \sqrt{\frac{l}{32}}= \dfrac{1.2~\cancel{2.4\pi}}{\cancel{2 \pi}}$

$\sqrt{\frac{l}{32}}= 1.2$

$(\sqrt{\frac{l}{32}})^2= (1.2)^2$

$\dfrac{l}{32} = 1.44$

$l = 46.08$