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Vesna [10]
3 years ago
5

Help 6 · (10 + 2) + (10 − 2)

Mathematics
2 answers:
ivann1987 [24]3 years ago
7 0

Answer:

4

Step-by-step explanation:

10+2=12

10-2=8

8-12=4

LuckyWell [14K]3 years ago
3 0
6 · (10 + 2) + (10 − 2) = 80
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You have D dollars to buy fence to enclose a rectangular plot of land (see figure at right). The fence for the top and bottom co
alex41 [277]

The perimeter of the rectangular plot of land is given by the expression below

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\begin{gathered} D=4(2x)+3(2y) \\ \Rightarrow D=8x+6y \\ D\rightarrow\text{ constant} \end{gathered}

Furthermore, the area of the enclosed land is given by

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Substituting into the equation for the area,

\begin{gathered} A=(\frac{D-6y}{8})y \\ \Rightarrow A=\frac{D}{8}y-\frac{3}{4}y^2 \end{gathered}

To find the maximum possible area, solve A'(y)=0, as shown below

\begin{gathered} A^{\prime}(y)=0 \\ \Rightarrow\frac{D}{8}-\frac{3}{2}y=0 \\ \Rightarrow\frac{3}{2}y=\frac{D}{8} \\ \Rightarrow y=\frac{D}{12} \end{gathered}

Therefore, the corresponding value of x is

\begin{gathered} y=\frac{D}{12} \\ \Rightarrow x=\frac{D-6(\frac{D}{12})}{8}=\frac{D-\frac{D}{2}}{8}=\frac{D}{16} \end{gathered}<h2>Thus, the dimensions of the fence that maximize the area are x=D/16 and y=D/12.</h2><h2>As for the used money,</h2>\begin{gathered} top,bottom:\frac{8D}{16}=\frac{D}{2} \\ Sides:\frac{6D}{12}=\frac{D}{2} \end{gathered}<h2>Half the money was used for the top and the bottom, while the other half was used for the sides.</h2>

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1 year ago
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