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A series of locks manages the water height along a water source used to produce energy. As the locks are opened and closed, the water height between two consecutive locks fluctuates.

The height of the water at point B located between two locks is observed. Water height measurements are made every 10 minutes beginning at 8:00 a.m.

It is determined that the height of the water at B can be modeled by the function f(x)=−12cos(πx/32−7π/8)+30 , where the height of water is measured in feet and x is measured in minutes.

What is the maximum and minimum water height at B, and when do these heights first occur?

 

The first minimum water height of _____ feet occurs at _____ a.m. The first maximum water height of _____ feet occurs at _____ a.m.

 Mar 20, 2020
 #1
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The wave goes from 13   to  -13

Max height: 13 + 24 = 37ft

Minimum height: -13 + 24 = 11 ft

 

Here is the work:

 

The minimum height will be when the cos fxn = 1  

So when cos (?) is -1 (0 degrees)

Therefore, (pi)x/60 - 5pi/12 = 0

 

 

That will get us x=25.

 

The maximum height will be when -13 ( cos ( pix/60 - 5pi/12) = 13

There are two ways to write this. Go with whatever is easiest for you.

Second way: cos ( pi x / 60 - 5pi/12)   = -1      pi x/60 - 5pi/12 =   pi      

 

Both will get you  x = 85 minutes =  9: 25

 

Hope this helped!

 Mar 20, 2020

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