When driving to church one Sunday my wife Amy held a cutting board perfectly horizontally with a sliced apple on it. When I went around a flat curve too quickly the apple slice began to slide off the plate so I had to slow down. We found that the fastest we could go around the turn was at a speed of just 8.75 m/s. Any faster and the apple slice would begin to slide. Assuming the radius of the road's curve is 45.0 m determine the following: 

a) What is the coefficient of static friction between the apple slice and the cutting board? 

b) My wife, knowing her physics, decided to hold the cutting board at an angle, thus allowing us to take the turn at a higher speed. Explain how this enabled us to take the turn at a higher speed. 

c) If Amy inclined the cutting board at an angle of 35.0 relative to the horizontal what speed would we need to be at for the apple slice to stay in place with no friction force between the apple slice and the cutting board?

d) Assuming the coefficient of static friction