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Math Help - Word Problems - Distance between 2 objects, maximizing area, and more

  1. #1
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    Word Problems - Distance between 2 objects, maximizing area, and more

    I just need help on questions 7, 8, 9, 12, and 13

    For question 7, I keep thinking that the pool area is a square, so wouldn't all sides be equally fenced? Therefore wouldn't the 25M be equally divided by 4 to maximize area?




    Thank-you in advance
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  2. #2
    Senior Member Peritus's Avatar
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    7. square is just a special case of rectangle whose adjacent sides are equal.

    let's denote one of the sides as a and the other as b thus:


    \begin{gathered}<br />
  2\left( {a + b} \right) = 25 \hfill \\<br />
  S = ab = a\left( {\frac{{25}}<br />
{2} - a} \right) \hfill \\ <br />
\end{gathered}

    now let's differentiate S(a):


    \frac{{dS}}<br />
{{da}} = \frac{{25}}<br />
{2} - 2a = 0 \Rightarrow a = \frac{{25}}<br />
{4},b = \frac{{25}}<br />
{4}

    you can differentiate S one more time to make sure that it's maxima.
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  3. #3
    GAMMA Mathematics
    colby2152's Avatar
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    8) Max revenue is when R'(x)=0

    R'(x)=-10x+21

    x=2.1

    Profit at that point is R(21)-C(21) = -5(2.1)^2+21(2.1)-4(2.1)-14 \Rightarrow ???

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