Algebra

A community college campus plans to construct a rectangular parking lot on land bordered on one side by a highway. There are 640 feet of fencing available to fend the other three sides. Let x represent the length of each of the two parallel sides of fencing.
a) Express the length of the remaining side to be fenced in terms of x. b) What are the restrictions on x? c) Determine the function A that represents the area of the parking lot in terms of x. d) Determine the values of x that will give an area between 30,000 and 40,000 square feet. e) What dimensions will give a maximum area, and what will this area be?

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  1. a)
    Total: 640 feet
    Two short sides: 2x
    long side 640-2x
    b)
    Since long side must be positive, we have 640-2x≥0
    c)
    Area = short side * long side
    A(x)=x(640-2x)
    d)
    find x such that
    30000≤A(x)≤40000
    Make a table that gives x and A(x),
    Hint:
    A(50)=27000 <30000
    A(86)=40248 >40000

    e)
    If you have done calculus, find A'(x) and equate to zero.
    If you have not, then complete squares of A(x):
    A(x)=ax²+bx+c
    -2x²+640x
    where a=-2, b=640, c=0
    The maximum occurs at x=-b/2a

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