the blades of a windmill turn on an axis that is 40 feet from the ground. the blades are 15 feet long and…

the blades of a windmill turn on an axis that is 40 feet from the ground. the blades are 15 feet long and complete 3 rotations every minute. write a sine model, y = asin(bt)+k, for the height (in feet) of the end of one blade as a function of time t (in seconds). assume the blade is pointing to the right when t = 0 and that the windmill turns counterclockwise at a constant rate.\na is the \nthe vertical shift, k, is the \na = k =

the blades of a windmill turn on an axis that is 40 feet from the ground. the blades are 15 feet long and complete 3 rotations every minute. write a sine model, y = asin(bt)+k, for the height (in feet) of the end of one blade as a function of time t (in seconds). assume the blade is pointing to the right when t = 0 and that the windmill turns counterclockwise at a constant rate.\na is the \nthe vertical shift, k, is the \na = k =

Answer

Answer:

$a = 15$, $k = 40$

Explanation:

Step1: Determine the amplitude $a$

The amplitude of the sine - wave is the length of the blade. Since the blades are 15 feet long, the amplitude $a$ of the sine function representing the height of the end of the blade is equal to the length of the blade. So $a = 15$.

Step2: Determine the vertical shift $k$

The axis of the wind - mill is 40 feet from the ground. The vertical shift $k$ of the sine function is the height of the axis of rotation of the wind - mill blades from the ground. So $k = 40$.