+148 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.
+2094 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!
