13). An open rectangular box with square ends is to hold 6400 cm^3. It is built at a cost of $ 75/ cm^2 for the base and $25/ cm ^2 for the sides. Find the most economical dimensions.
14). A wall 8 meter high is 3 3/8 meter from a house. Find the shortest ladder which will reach from the ground to the house when leaning over the wall.
15 ). A company has the following schedule of charges : $30 per 1000 for orders of 50 000 or fewer , with the charge per thousand decreased by $ 0.375 for each thousand above 50 000. Find the order that will make the receipts a maximum.
16). Find the minimum distance from the point ( 3 , 4 ) to the parabola
Y^2 = 8x
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- Let R be the region in the first quadrant bounded by the curves y = cos(x) between x = 0 and x= pi/2 a. The volume of the solid obtained by revolving R about