Respuesta :
we are given
The 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 feet
We 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
The length of a pendulum that takes 2.4 pi seconds to swing back and forth is 46.08 feet if the time, in seconds, that it takes a pendulum to swing back and forth is modeled by the equation is f(l)=2pi√l/32
What is a function?
It is defined as a special type of relationship and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have an expression that modeled the time, in seconds, that it takes a pendulum to swing back and forth:
[tex]\rm f(l) = 2\pi\sqrt{\frac{l}{32} }[/tex]
When f(l) = 2.4π, put this value in the above expression:
[tex]\rm2.4\pi = 2\pi\sqrt{\frac{l}{32} }[/tex]
Squaring both sides:
[tex]\rm(2.4\pi)^2 = (2\pi\sqrt{\frac{l}{32} })^2[/tex]
[tex]\rm5.76\pi^2 = 4\pi^2\frac{l}{32} }[/tex]
l = 46.08 feet
Thus, the length of a pendulum that takes 2.4 pi seconds to swing back and forth is 46.08 feet if the time, in seconds, that it takes a pendulum to swing back and forth is modeled by the equation is f(l)=2pi√l/32
Learn more about the function here:
brainly.com/question/5245372
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