Question 3 - Minimize Cost / 10 marks A 50 km stretch of highway runs west to east Bamyan Sumara between two towns, Bamyan and Sumara. There are two new housing developments south of these two towns. Jamrin is located 30 km south of Bamyan and Zimrin is located 40km south of Sumara. The local government is planning to connect a road from each of the new settlements (Jamrin & Zimrin) to a common point on the existing highway. Find the point on the existing Jamrin highway to make the connection to minimize the total length of the new roads. Zimrin Question 4 - Motion of a Marble / 10 marks The position function of a marble moving along a track is s(t) = _ (5 - -1 13) 7 for t = 10 a) Find the marble's velocity and acceleration function. b) When does the marble return to its starting position, s(0)? c) At what time(s) is the marble at rest? d) During what intervals are s(t), v(t), and a(t) positive and when are they negative? Summarize it in a chart (similar to what is shown in the next question). 2 Question 5 - Sketch a Graph / 10 marks 3) Sketch (plot) the graphs of position, velocity, and acceleration of a particle (for 0