Froject Design a larger roller coaster meeting the specifications below and prepare a neat and complete project report as specified by the Project Report Guidelines located on the lab website. The due date will be specified by your TA. Suppose you are asked to build a roller coaster with an overall horizontal displacement of 600 feet. The coaster should ascend along a straight line y = fl(:c) of slope 2.5 for the first 30ft horizontally. We continue along three cubics, fo(z) = az + bz + cx + d, f3(z) = ex' + f2? + gz + h, and f4(z) = iz + jz? + kz + [ for 150ft each. In addition, the coaster should be 210ft above the ground at the 120ft mark, reach a bottom of 37.5ft above the ground at the 270ft mark, and reach a peak 97.5ft above the ground at the 390ft mark. Finally, the coaster should start a soft landing 45ft above the ground along a cubic f5(z) = mz + na? + oz + p for the last 120ft. Your task is to: 1. Write a system of 16 equations in 16 unknowns such that your track is both continuous and smooth. Make sure to include your equations in your report and you must explain the reasoning for your equations in your report. 2. Solve the equations in (1) with SageMath to find the values a-p. 3. Define and plot a piecewise-defined function, F(m), for your roller coaster. Include the equation for your completed piecewise-defined function (with all values a-p plugged in) as well as the graph of your roller coaster. 4. Find the maximum height of your roller coaster and the mark where it occurred