1-Crouton wants to build a path from his house on one side of a river that is 100ft wide to his friend Preston’s house, who lives on the other side of the river and downstream 1000ft (see picture). It will cost $4/ft to build the road over land, and it will cost $6/ft to build a bridge across the river. How long should the road (length labeled x) and the bridge (length labeled y) be in order to minimize Crouton’s cost of building the path? How much will the total path cost? (Round your answers to two decimal places.)
2-A waffle cone (see picture) with diameter 4 inches and height 6 inches is filled with melted ice cream that is dripping out the bottom so that the radius of the surface of the ice cream is decreasing at a rate of 0.2 in/min. At what rate is the volume of the melted ice cream changing when the ice cream is 2 inches deep? Volume of a cone is 13 2ℎ
13πr2h. (Hint: Similar triangles will help with this problem.)
You must do this problem using related rates methods in order to receive a score of 2!