Let S be the unit sphere with outward orientation N and B denote the unit ball, that is the inside of the unit sphere. Let F(x, y,z) = ^xi + ^yj + ^zk. Compute the following: (i) ∫∫S (F. N)dA
(ii) ∫∫B div(F)dV
(iii) What did you notice? Compare this to Green's Theorem.

Multiply −2x(6x^4−7x^2+x−5) express the answer in standard form. enter your answer in the box.

Dean and karlene get paid to write songs. dean is paid a one-time fee of $20 plus $80 per day. karlene is paid a one-time fee of $25 plus $100 per day. write an expression to represent how much a producer will pay to hire both to work the same number of days on a song.

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.)