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Math Help - Function problems

  1. #1
    Newbie Twilight's Avatar
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    Function problems

    I have 2 word problems that I am having trouble with:

    The surface area of a cylindrical can of radius r and height h is
    2pi r squared + 2pi r h. If the can is twice as high as the diameter of its top, express its suface areqa S as a function of r.

    and:

    A rectanular region of 6000 square feet is to be fenced in on three sides with fencing that costs $3.75 per foot and on the fourth side with fencing that costs $2.00 per foot.

    a. Express the cost of the as a function a function of the length x of the fourth side.

    b. Find the domain of the function.

    Any help would be greatly appreciated.
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  2. #2
    MHF Contributor
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    The surface area of a cylindrical can of radius r and height h is
    2pi r squared + 2pi r h. If the can is twice as high as the diameter of its top, express its suface areqa S as a function of r.


    The diameter of the top (and of the bottom too) is 2r
    So the h will be 2(diameter) = 2(2r) = 4r
    Then,
    A = 2pi(r^2) +2pi(r)(4r)
    A = 2pi(r^2) +8pi(r^2)
    A = 10pi(r^2)

    In function form,
    A(r) = 10pi*r^2 --------------------------answer


    A rectanular region of 6000 square feet is to be fenced in on three sides with fencing that costs $3.75 per foot and on the fourth side with fencing that costs $2.00 per foot.

    a. Express the cost of the as a function a function of the length x of the fourth side.

    The function of the what?
    The perimeter fence?

    Okay.

    Let x = length of the rectangle
    And y = width of the rectangle

    x*y = 6000
    So,
    y = 6000/x

    Cost of perimeter fence, C = (x +2y)(3.75) +x(2.00)
    C(x) = (x +2(6000/x))(3.75) +2x
    C(x) = 3.75x +45,000/x +2x
    C(x) = 5.75x +(45,000/x) -----------------answer.


    b. Find the domain of the function.

    Domain is what will give C(x) positive real value.
    So, domain is from just after zero up to infinity. Or x > 0 ----answer.
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