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.

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)