A1. (a) In Fig 1, an island is at 2 miles distance in north of a shoreline. A tourist is staying at a villa on the shore that is 3

miles west of the island. The tourist is planning a trip from the villa to the island. Knowing that the tourist runs in a straight line at a rate of 5 mph and swims in a straight line at a rate of 2 mph. How far should the tourist run before swimming to minimize the time it takes to reach the island? (b) A machine component is to be manufactured from a material with density 2.7 g/cm3and with a shape defined by rotating the function f(x)= V1+ x about the positive x axis, with x=0 corresponding to one end of the component. If the component is 3cm long, and solid, calculate it's mass

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