MATH SOLVE

4 months ago

Q:
# The time, in seconds, that it takes a pendulum to swing back and forth is modeled by the equation below.f(l)=2pi√l/32 where l is the length of the pendulum in feetWhat is the length of a pendulum that takes 2.4 pi seconds to swing back and forth?Thank you!!

Accepted Solution

A:

we are givenThe time, in seconds, that it takes a pendulum to swing back and forth is modeled by the equation as[tex]f(l)=2\pi \sqrt{\frac{l}{32} }[/tex]where l is the length of the pendulum in feetWe have [tex]f(l)=2.4\pi[/tex]so, we can set them equal and then we can solve for l[tex]2.4\pi=2\pi \sqrt{\frac{l}{32} }[/tex]Firstly, we will take square both sides [tex]\left(2.4\pi \right)^2=\left(2\pi \sqrt{\frac{l}{32}}\right)^2[/tex][tex]\frac{\pi ^2l}{8}\cdot \:100=5.76\pi ^2\cdot \:100[/tex][tex]\frac{25\pi ^2l}{2}=576\pi ^2[/tex][tex]\frac{2\cdot \:25\pi ^2l}{2}=2\cdot \:576\pi ^2[/tex][tex]25\pi ^2l=1152\pi ^2[/tex][tex]\frac{25\pi ^2l}{25\pi ^2}=\frac{1152\pi ^2}{25\pi ^2}[/tex][tex]l=\frac{1152}{25}[/tex][tex]l=46.08feet[/tex]So, The length of a pendulum that takes 2.4 pi seconds to swing back and forth is 46.08 feet..........Answer