On a chessboard compute the expected number of plays it takes a knight, starting in one of the four corners of the chessboard, to return to its initial position if we assume that at each play it is equally likely to choose any of its legal moves. (no other pieces are on the board.)

Technicians have installed a center pivot, circular irrigator for a farm that covers 25 acres. a.) how long is the irrigation boom (in feet) from the center pivot to its farthest extent? b.) if the irrigation boom makes 4 full revolutions in a day, how many miles does the end of the boom travel in 5 days?