Supose you seek a treasure that is buried in the side of a mountain. The mountain range has a sinusoidal vertical cross section. The valley to the left is filled with water to a depth of 50m, and the top of the mountain is 150 m above the water level. You set uup an x-axis at water level and y-axis 200 m to the right of the deepest part of the water. The top of the mountain is at x= 400m.

a. Find a particular equation expressing y for points on the surface of the mountain as function of x.

b. show algebraically that the sinusoid in part a contains the origin ( 0,0)

c. the treasure is located beneath the surface at the point (130,40) . Which would be a shorter way to dog to the treasure, a horizontal tunnel or vertical tunnel? show ure work.