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Math Help - Rectangle formula help please

  1. #1
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    Rectangle formula help please

    A rectangle is placed under the parabolic arch given by
    f(x) = 27
    3
    x2 by using a point (x, y) on the parabola, as shown in the figure.
    Write a formula for the function
    A(x) that gives the area of the
    rectangle as a function of the
    x-coordinate of the point chosen.
    a.
    f(x) = 6(27 3x2)
    b .
    f(x) = 27x 3x3

    c .
    f(x) = 54x 6x3

    d . f(x) = 162x 6x3

    Algebra is my weakness. Please help.
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  2. #2
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    Here's the pic in a different format
    Attached Thumbnails Attached Thumbnails Rectangle formula help please-rectangle.jpg  
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by wvmcanelly@cableone.net View Post
    A rectangle is placed under the parabolic arch given by
    f(x) = 27
    3
    x2 by using a point (x, y) on the parabola, as shown in the figure.
    Write a formula for the function
    A(x) that gives the area of the
    rectangle as a function of the
    x-coordinate of the point chosen.
    a.
    f(x) = 6(27 3x2)
    b .
    f(x) = 27x 3x3

    c .
    f(x) = 54x 6x3

    d . f(x) = 162x 6x3

    Algebra is my weakness. Please help.
    see the diagram below.

    the width of the rectangle is 2x.
    the height of the rectangle is y, which is given by y = f(x) = 27 - 3x^2

    the area is given by width * height

    so A(x) = 2x(27 - 3x^2) = 54x - 6x^3
    Attached Thumbnails Attached Thumbnails Rectangle formula help please-parabola.gif  
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  4. #4
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    thanks, the explanation is very helpful and easy to understand. I appreciate it.
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