As you ride a ferris wheel, your distance from the ground varies sinusoidally with time. when the last passenger boards the ferris wheel and the ride starts moving, let your position be modeled by the diagram provided. let t be the number of seconds that have elapsed since you began moving. it takes you 5 seconds to reach the top of the wheel (38 feet above the ground) and 20 seconds to make a complete revolution. the diameter of the wheel is 30 feet.
a) what is the lowest you go as the ferris wheel turns?
b) why is this number always greater than 0?
c) predict your height above the ground when t = 3, t = 8, t = 15, and t = 19.

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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