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.
−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