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Andreas93 [3]
3 years ago
6

The time, in seconds, that it takes a pendulum to swing back and forth is modeled by the equation below.

Mathematics
2 answers:
Lorico [155]3 years ago
6 0

46.08 ft

doesn't feel right but if you plug it in it works


2.4pi=2pi(46.08/32)^1/2

Genrish500 [490]3 years ago
3 0

we are given

The time, in seconds, that it takes a pendulum to swing back and forth is modeled by the equation as

f(l)=2\pi \sqrt{\frac{l}{32}  }

where l is the length of the pendulum in feet

We have

f(l)=2.4\pi

so, we can set them equal and then we can solve for l

2.4\pi=2\pi \sqrt{\frac{l}{32}  }

Firstly, we will take square both sides

\left(2.4\pi \right)^2=\left(2\pi \sqrt{\frac{l}{32}}\right)^2

\frac{\pi ^2l}{8}\cdot \:100=5.76\pi ^2\cdot \:100

\frac{25\pi ^2l}{2}=576\pi ^2

\frac{2\cdot \:25\pi ^2l}{2}=2\cdot \:576\pi ^2

25\pi ^2l=1152\pi ^2

\frac{25\pi ^2l}{25\pi ^2}=\frac{1152\pi ^2}{25\pi ^2}

l=\frac{1152}{25}

l=46.08feet

So,

The length of a pendulum that takes 2.4 pi seconds to swing back and forth is 46.08 feet..........Answer

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