Aladder 13 feet long rests against a vertical wall. if the bottom of the ladder slides away from the wall at the rate of 0.5 ft/sec, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 5 feet from the wall? at what rate is the angle between the ladder and the ground changing?

22 points algebra 1//sum and product of rational and irrational numbers. dont have to do all 4 if could much : )) write an example: 1) how the product of two identical irrational numbers can be a rational number. 2) how the product of two different irrational numbers can be a rational number. 3) write a quotient of intergers that is not a real number. 4) is the set of positive irrational numbers closed for the operation of division? if not give a counter example.