Set up a Cartesian coordinate system with its origin at the entrance to a tunnel. The mountain rises 350 m above the level of the track and the next valley descends 150 m below the track.
The cross section of the mountain and valley is roughly sinusoidal, with a horizontal distance of
600 m from the top of the mountain to the bottom of the valley.
a. Write a particular equation expressing the vertical displacement y, in meters, from the track
to the surface of the mountain valley as a function of x, in meters, form the tunnel entrance.
b. How long will the tunnel be? How long will the bridge be?
C.
The railway company thinks it might be cheaper to build the line if it is raised by 40 m. The
tunnel will be shorter and the bridge will be longer. Find the new values of x at the
beginning and the end of the tunnel and the bridge. How long will each section be under
these conditions?
All work is shown on my paper