Do (0,1) and r+ = (0,[infinity]) have the same cardinality? if so, either give an explicit bijection (and prove that it is a bijection) or provide an injection from (0,1) to (0,[infinity]) and an injection from (0,[infinity]) to (0,1) (so that by cantor-bernstein theorem the two sets will have the same cardinality). if not, then prove that they have different cardinalities

(! ) three cylinders have a height of 8 cm. cylinder 1 has a radius of 1 cm. cylinder 2 has a radius of 2 cm. cylinder 3 has a radius of 3 cm. find the volume of each cylinder

The average number of vehicles waiting in line to enter a parking lot can be modeled by the function f left parenthesis x right x squared over 2 left parenthesis 1 minus x right parenthesis endfraction , where x is a number between 0 and 1 known as the traffic intensity. find the rate of change of the number of vehicles waiting with respect to the traffic intensity for the intensities (a) xequals0.3 and (b) xequals0.6.

When y’all answer can y’all explain too !