Consider the region r bounded by curves y=ax^2+3, y=0, x=0, and x=3, for a ≥minus1. let s 1 and s 2 be solids generated when r is revolved about the x- and y-axes, respectively.
a. find v 1 and v 2, the volumes of s 1 and s 2, as functions of a.
b. are there values of agreater than or =minus1 for which v 1(a)= v 2(a)?

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.)