Verify the conclusion of green's theorem by evaluating both sides of each of the two forms of green's theorem for the field f= 3xi − yj.

take the domains of integration in each case to be the disk r: x^2 + y^2 ≤ a^2 and its bounding circle c: = (acost)i + (asint)j, 0 ≤ t ≤ 2π.

1. the flux is 2. the circulation is ? ?

What is the standard form of -5x^2+2x^4-11+x^3+3x

Suppose you just purchased a digital music player and have put 8 tracks on it. after listening to them you decide that you like 4 of the songs. with the random feature on your player, each of the 8 songs is played once in random order. find the probability that among the first two songs played (a) you like both of them. would this be unusual? (b) you like neither of them. (c) you like exactly one of them. (d) redo () if a song can be replayed before all 8 songs are played.

Eric drove 275 miles in 5 hours. at the same rate how long would it take him to drive 495 miles?