Answer:
h(t) = 36sin(1440x)+ 40
Step-by-step explanation:
Given the information:
- highest point: 76 inches=>
- lowest point: 4 inches =>
- 4 revolutions per second => period: [tex]\frac{1}{4}[/tex] per second = [tex]\frac{360}{\frac{1}{4} } =1440[/tex]
y = a sin (bx+c) + k for different values of a, b, and c
=> Amplitude (a) = (highest point - lowest point) / 2 = 36
=> asymptom (k) = (highest point - lowest point) / 2 = 40
=> model for the height of the rope in inches as a function of time in seconds given that the rope starts at its lowest point is:
h(t) = 36sin(1440x)+ 40
Hope it will find you well.
