Can someone please help me with this question?
The side view of a roller coster in a hamster's cage is shown below, where h is the vertical height, in mm, of the roller coaster above the bottom of the cage and x is the horizontal distance, in mm, from the start of the roller coaster.
The start of the roller coaster is (0,125), where it is attached to the side of the cage. The maximum height reached by the roller coaster is 250 mm and the roller coaster first reaches the bottom of the cage when x=500. The end of the roller coaster is where it touched the bottom of the cage for the second time.
The highest point of the roller coaster can be modelled by the equation h= Asin(nx) + B, where A, N, and B are real constants.
a) Find the values of A, n and B
b) It is found that the roller coaster is not strong enough to support large hamsters. It is decided that supports are required under each of the 'high points' of the roller coaster. The support is a cuboid of width 50mm. (I can't show the picture but it is a square with a bottom length of 50mm and an upside down parabola on top)
What is the maximum height the cuboid structure can be if its edges touch the arch? Give your answer correct to the nearest millimetre.