Amanufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function r(x) = 60x − 0.2x2, where the revenue r(x) is measured in dollars. what is the maximum revenue, and how many units should be manufactured to obtain this maximum?

The inside wheels of a car traveling on a circular path are rotating half as fast as the outside wheels. the front two wheels are six feet apart. what is the number of feet in the path traced by the inside front wheel in one trip around the circle? express your answer in the form "k \pi", where k is an integer.

Evaluate 8j -k+148j−k+14 when j=0.25j=0.25 and k=1k=1.

Amountain climber starts a climb at an elevation of 453 feet above sea level at his first rest stop he has climbed 162 feet and by his second rest stop he has climbed another 207 feet its getting late in the day so the climber starts his way down if the climber desends 285 feet how much does he need to ascend or descend to return to the original starting point