Question

A house is built on a property with the house 600 feet from where the driveway needs to meet the road. The ground is level, but due to a small pond on one side of the property and some apple trees they don’t want to cut down on the other side, the path for the driveway is in the shape of a sine curve, with the sides having the equations f ( x ) = 25 + 10 sin ⁡ ( x 100 ) and g ( x ) = 10 + 10 sin ⁡ ( x 100 ) , with the dimensions in feet. You need to pave this driveway with concrete with a depth of 4 inches. How much concrete will you need, how wide is the driveway, and how long is this driveway along the curve (i.e., not the 600 feet straight distance)?

Answer 1