12. An open rectangular box has one side of its base 4 feet long and is to have

Question

12. An open rectangular box has one side of its base 4 feet long and is to have a volume of 200 cubic feet. Find the dimensions for which the amount of material needed to construct the box is as small as possible. 13. A particle is moving on a straight line. The velocity of the particle for 0sis 30 is shown in the table below for the selected values of 12 15 18 21 24 27 30 7.5 10.1 12 13 13.5 14.1 14 13.9 13 12.2 t(sec.)03 69 vt) (m/sec) a) Using the midpoints of five subintervals of equal length, find the approximate value ot jv(i)dr. b) During what intervals of time is the acceleration negative?

Explanation / Answer

12 . Volume = l w h

      200 = 4 wh

      w h = 50

      w = 50/h

     S = 2 *4*w +2*4*h +2*w*h = 8w + 8h + 2wh

     S = (400/h) +8h + 100

     S ' = -(400/h2) +8

    S ' =0

     h2 =50

    h = 5 sqrt 2

    w = 50/5 sqrt 2 = 5 sqrt 2 ft

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