Use Nath Editor to enter formulas and mathematical expressions. Problem Your car has no cup holder, so you must place your filled coffee cup on the passenger Seat beside you when you start out in the morning. Bitter experience has taught you that the cup is least stable - and most prone to spill - when it is completely full, but becomes more stable as you drink the coffee and thereby lower its level in the cup. The picture on the left shows a coffee cup partially filled with coffee. We will assume th at it is the most stable when the centroid of the cup-plus-coffee is lowest. Assume that the centroid of the cup-plus-coffee is represented by the function of the depth y (in cm) of the coffee in the cup: +n. [cp2 - at + if + 0. [dl e 10' + 'Zy Calculate the optimal depth y of the coffee in your cup. (HINT: the centroid function is lowest when to the nearest whole number. Include the sketch of the centroid function where U S y S H fu) : 0.) Round your answer ) and verify your solution graphically. Example: if [cl :2, then Ol Grading This posting will be graded out of 100 points. Ifyou receive an uns may receive help from your classmates or look at their postings to see where you went wrong. You may continue working on this posting until the last day of the current module. atisfactory grade. you may rework and repost the problem, You Smith en or author