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Cleaning pumps remove waste from a dump site at the rate modeled by the function R, given by r of t equals 3 plus 2 times the cosine of the quantity 2 times pi times t divided by 15 with t measure in hours and and R(t) measured in tons per hour. How much waste will the pumping stations remove during the 8 hour period from t = 0 to t = 8? Give 3 decimal places.

Respuesta :

facundo3141592

By integrating the rate, we will see that waste pumped from t = 0 to t = 8 is A = 24.279

How to get the waste pumped in that interval?

We have the function:

R(t) = 3 + 2*cos(2pi*t/15)

This is the rate at which the waste is removed, then the waste that the station pumps between t = 0 and t = 8 is given by:

[tex]A = \int\limits^8_0 {3 + 2*cos(2pi*t/15)} \, dt[/tex]

That integral gives:

[tex]A = \int\limits^8_0 {3 + 2*cos(2pi*t/15)} \, dt \\\\A = 3*(8 - 0) + 2*(15/2pi)*(sin(2pi*8/15) - sin(2pi*0/15))\\\\\\A = 24.279[/tex]

If you want to learn more about integrals, you can read:

https://brainly.com/question/3647553

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