A portion of a roller coaster track is to be built in the shape of a Sinusoid, as shown below. The high point and low point on the track are separated by 50 meters horizontally and 30 meters vertically. The low point is 3 meters below the ground. You have been hired to do the following calculations. a) Determine the particular equation for this Sinusoidal Function by expressing y in terms of x. b) Using the derivative, calculate the slope of the track at x = 10 meters c) Determine the maximum height of this portion of the track using the derivative. d) Using the second derivative of the function in question, show that the track changes concavity half way down this portion. (Note, that this location often called the point of inflection.) e) Find the length of the vertical timber at x = 10 meters. f) Find the length of the horizontal timber at y = 10 meters. Timber supports Ground- Track 50 m- 30 m 3 m