A(x) (8,192) House Figure 1 Figure 2 Tessa has 48 ft of fencing available to construct a fence that will divide her garden into two rectangular sections. Her house forms one side of the garden and a...

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A(x)<br>(8,192)<br>House<br>Figure 1<br>Figure 2<br>Tessa has 48 ft of fencing available to construct a fence that will divide her garden into two rectangular sections. Her house forms one side of the garden and a represents the width, as shown in Figure 1.<br>(a) Express the total area of the two sections as a function of x.<br>A(z) =<br>(b) Find the domain of the function. Write your answer as a compound inequality involving x.<br>Domain of A(z):<br>(c) Using the graph of A(x) shown in Figure 2, determine the dimensions that yield the maximum area.<br>Width:<br>ft<br>Length:<br>ft<br>

Extracted text: A(x) (8,192) House Figure 1 Figure 2 Tessa has 48 ft of fencing available to construct a fence that will divide her garden into two rectangular sections. Her house forms one side of the garden and a represents the width, as shown in Figure 1. (a) Express the total area of the two sections as a function of x. A(z) = (b) Find the domain of the function. Write your answer as a compound inequality involving x. Domain of A(z): (c) Using the graph of A(x) shown in Figure 2, determine the dimensions that yield the maximum area. Width: ft Length: ft

Answered 113 days AfterJun 04, 2022

Answer To: A(x) (8,192) House Figure 1 Figure 2 Tessa has 48 ft of fencing available to construct a fence that...

Ajay answered on Sep 26 2022
67 Votes
Solutions
(a) A(x) can be obtained by knowing the rectangle's perimeter.
As you can see here, the
perimeter of the lawn is:
3x + y = 48
because there are 3 x's and 1 y's, while the total perimeter is 48 ft.
 
Now, to find A(x), we use the are the formula of a rectangle in which:
A(x) = L x W
We know that W = x
 
To get the Length, we can use the perimeter of the lawn:
3x + y = 48
y = 48 -...
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