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Thread: 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.

    $\displaystyle A(L) = ??$

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

    so $\displaystyle w = 10 - l$.


    The area of the rectangle is $\displaystyle A = lw$

    $\displaystyle A = l(10 - l)$

    $\displaystyle A = 10l - l^2$.
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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. $\displaystyle v = a * h$

    Step 2. surface area of cube = $\displaystyle 6a^2$

    Step 3. answer: $\displaystyle a = v/h$

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

    $\displaystyle A(v) = 6(v/h)^2$

    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 $\displaystyle s$ = side of the cube.

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


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

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