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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 2, 2021
 #1
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−12cos(πx/32−7π/8)      the min and max of this is  -12   and  + 12

 

-12 + 30 = 18 ft  min       +12 + 30 = 42 ft    max

 

these will occur at the value of 'x' that makes cos(πx/32−7π/8)    = 1 or  -1

                                                                            this happens at  cos(0) = 1   and  cos (pi) = -1

 

pi (x)/32 - 7pi/8 = 0

x =   28   min                   this will be the min time (because of the -12 multiplier)      8:28 AM

 

pi (x)/32 - 7pi/8 = pi

    x = 60 min                            9:00 AM     for the max

 Mar 2, 2021

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