Let R be the region in the first quadrant bounded by the graph of y=x, the vertical line x = 9, and the x-axis, as shown in the figure. a) Write, then evaluate (show all of your work), an integral expression that gives the volume of the solid generated when R is rotated about the x-axis.
b) Write, then evaluate (show all of your work), an integral expression that gives the volume of the solid generated when R is rotated about the vertical line x = 9.

At the olympic games, many events have several rounds of competition. one of these events is the men's 100-meter backstroke. the upper dot plot shows the times (in seconds) of the top 8 finishers in the final round of the 2012 olympics. the lower dot plot shows the times of the same 8 swimmers, but in the semifinal round. which pieces of information can be gathered from these dot plots? (remember that lower swim times are faster.) choose all answers that apply: a: the swimmers had faster times on average in the final round. b: the times in the final round vary noticeably more than the times in the semifinal round. c: none of the above.

Factor the polynomial, if possible. if the polynomial cannot be factored, write prime. 9n^3 + 27n^2 – 25n – 75

Atotal of 766 tickets were sold for the school play. they were either adult tickets or student tickets. there were 66 more student tickets sold than adult tickets. how many adult tickets were sold?