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.a is the ___The vertical shift, k, is the _____________a = k =

Answer:a is the _amplitude_(Length of the blades)_The vertical shift, k, is the _Mill shaft height_[tex]a = 15\ ft\\\\k = 40\ ft[/tex][tex]y = 15sin(\frac{\pi}{10}t) + 40[/tex]Step-by-step explanation:In this problem the amplitude of the sinusoidal function is given by the length of the blades.[tex]a = 15\ ft[/tex]The mill is 40 feet above the ground, therefore the function must be displaced 40 units up on the y axis. So:[tex]k = 40\ ft[/tex]We know that the blades have an angular velocity w = 3 rotations per minute.One rotation = [tex]2\pi[/tex]1 minute = 60 sec. So:[tex]w = \frac{3(2\pi)}{60}\ rad/s[/tex][tex]w = \frac{\pi}{10}\ rad/s[/tex]Finally:a is the _amplitude_(Length of the blades)_The vertical shift, k, is the _Mill shaft height_[tex]a = 15\ ft\\\\k = 40\ ft[/tex][tex]y = 15sin(\frac{\pi}{10}t) + 40[/tex]