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 feet what is the length of a pendulum that takes 2.4 pi seconds to swing back and forth?

46.08 ft

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

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

we are given

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

where l is the length of the pendulum in feet

We have

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

Firstly, we will take square both sides

So,

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

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

center= (-2,0)

radius= sqrt2/2

step-by-step explanation: