Use green's theorem to find the counterclockwise circulation and outward flux for the field f and curve c. f = (2x + e^x sin y)i - (x + e^x cos y)j c: the right-hand loop of the lemniscate r^2 = cos 2 theta describe the given region using polar coordinates. choose theta-values between -pi and pi. what is the outward flux? (type an integer or a simplified fraction.) what is the counterclockwise circulation? (type an integer or a simplified fraction.)

You drop a rubber ball off the roof of a 50 meter high building onto a paved parking lot. it bounces back up with every bounce, but not quite all the way back up to you. after the first bounce it bounces back only 80 percent of the distance it was dropped from. the pattern continues, meaning after every bounce it comes up to just 80 percent of the previous maximum height. so if before the first bounce the height is 50 meters, what height does the ball reach after the fifth bounce? round your answer to one decimal place and chose the correct response from the choices below:

Problem fathi wants to print out a pdf document that is 48 pages long. to save paper, he decides to print on both sides of each sheet and to print two pages on each side of the sheet. how many sheets of paper will he need?

X/y + 4y/x divided by x/y - 2y/x explain as in depth as you can how you simplfied the fractions. i don't know where to start on this : /