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Math Help - Page Design

  1. #1
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    Page Design

    A page with dimensions of (17/2) inches by 11 inches has a border of uniform width x surrounding the printed matter of the page.

    (a) Write a formula for the area A of the printed part of the page as a function of the width x of the border.

    (b) Give the domain and range of the area A.

    (c) Find the area of the printed page for borders of widths 1 inch, 1.2 inches and 1.5 inches.

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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by magentarita View Post
    A page with dimensions of (17/2) inches by 11 inches has a border of uniform width x surrounding the printed matter of the page.

    (a) Write a formula for the area A of the printed part of the page as a function of the width x of the border.

    (b) Give the domain and range of the area A.

    (c) Find the area of the printed page for borders of widths 1 inch, 1.2 inches and 1.5 inches.
    Area of paper = 11\left(\frac{17}{2}\right)=\frac{187}{2} \ \ in^2

    Area of the printed part = A(x)=\left(\frac{17}{2}-2x\right)\left(11-2x\right)=\frac{187}{2}-39x+4x^2

    Area of the printed part cannot exceed area of the paper, so

    4x^2-39x+\frac{187}{2}<\frac{187}{2}

    Domain of Area A = \left\{0<x<\frac{39}{4}\right\}

    Range of Area A = \left\{0<A(x)<\frac{187}{2}\right\}

    For part (c), just substitute these values in A(x).
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  3. #3
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    ok...........

    Quote Originally Posted by masters View Post
    Area of paper = 11\left(\frac{17}{2}\right)=\frac{187}{2} \ \ in^2

    Area of the printed part = A(x)=\left(\frac{17}{2}-2x\right)\left(11-2x\right)=\frac{187}{2}-39x+4x^2

    Area of the printed part cannot exceed area of the paper, so

    4x^2-39x+\frac{187}{2}<\frac{187}{2}

    Domain of Area A = \left\{0<x<\frac{39}{4}\right\}

    Range of Area A = \left\{0<A(x)<\frac{187}{2}\right\}

    For part (c), just substitute these values in A(x).
    As always, I thank you for your great help.
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