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Math Help - Express the area as a function

  1. #1
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    Express the area as a function

    A rectangle has perimeter 20m. Express the area of the rectangle as a function of the length of one of its sides.

    A(L) = ??

    Thanks for the help.
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  2. #2
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    The perimeter of the rectangle is 2l + 2w = 20

    so w = 10 - l.


    The area of the rectangle is A = lw

    A = l(10 - l)

    A = 10l - l^2.
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  3. #3
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    Thank you so much, I understand that one now. But now I am again stuck on one more questions.

    Express the surface area of the a cube as a function of the its volume.

    Step 1. v = a * h

    Step 2. surface area of cube = 6a^2

    Step 3. answer: a = v/h

    Step 4. surface area of cube = 6(v/h)^2

    A(v) = 6(v/h)^2

    Am I correct?
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  4. #4
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    Hello, hydride!

    Express the surface area of the a cube as a function of the its volume.

    Let s = side of the cube.

    Then its volume is: . V \:=\:s^3 \quad\Rightarrow\quad s \:=\:\sqrt[3]{V}


    The surface area is six times the area of a face: . A \:=\:6s^2

    Therefore: . A \;=\;6\left(\sqrt[3]{V}\right)^2 \;=\;6V^{\frac{2}{3}}
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  5. #5
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    Thanks!
    I was close, but I understand now.
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