MATH 115-018 QUIZ 11 / 7 Apr 2005 Name: h r 1. (3 points) A stained glass window is to be made in the shape shown to the right, with a rectangular section surmounted by a semi-circular top. If P ft of border material are available, what should the dimensions of the window be to maximize its area? (You may assume that P > 2. The circumference of a circle is C = 2?r.) 2. (2 points) Suppose that the velocity of an orange-and-chartreuse-clothed math professor gradually in- creases in the course of a class period, and is given (in meters/second) by v(t) = 2et2 (where t is in hours). Use a Riemann sum with ąt = 0:5 hr to estimate the total distance travelled by the professor during an hour and a half class period. 321 2 1 ?1 3. (3 points) Find the average value of the function shown to the right, for the domain shown. The arc in the flgure is a semi-circle. Be sure it is clear how you obtain your answer. quiz11.dvi
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