Pre-Calc

A page that is x inches wide and y inches high contains 30 square inches of print. The top and bottom margins are 2 inches deep, and the margins on each side are 2 inches wide.
a. draw a diagram that gives a visul representation of the problem.
b. show that the total area A on the page is A=2x(2x+7)/(x-4)
c. determine the domain of the tion based on the physical constraints of the problem.
d. use a graphing utility to graph the area function and approximate the page size for which the least amount of paper will be used.

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  1. if the page is x by y
    then the printable area = x-4 by y-4

    so (x-4)(y-4) = 30
    xy -4x - 4y + 16 = 30
    xy - 4y = 4x + 14
    y(x-4) = (4x+14)
    y = (4x+14)/(x-4)

    Total area = xy
    = x(4x+14)/(x-4)
    = 2x(2x+7)/(x-4) ---> that would be b)

    c) clearly x> 4

    d) your job with the graphing utility stuff

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