4. Suppose that a positive integer is written in decimal notation as n = akak–1 … a2a1a0 where 0 ai 9. Prove that n is divisible by 11 if and only if the alternating sum of its digits a0 – ai + … + (–1) kak is divisible by 11.

Michele wanted to measure the height of her school’s flagpole. she placed a mirror on the ground 48 feet from a flagpole, then walked backwards until she was able to see the top of the pole in the mirror. her eyes were 5 feet above the ground and she was 12 feet from the mirror. using similar triangles, find the height of the flagpole to the nearest hundredth of a foot.