A summer camp has 320320 ft of float line with which to rope off three adjacent rectangular areas of a lake for swimming​ lessons, one for each of three levels of swimming ability. A beach forms one side of the swimming areas. Suppose that the width of each area is x feet. Answer parts​ a) and​ b)  ​a) Express the total area of the three swimming areas as a function of x. ​A(x)equals=​(Simplify your​ answer.) ​b) Find the domain of the function.​(Type your answer in interval​ notation.)

Question
Asked Feb 11, 2020
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A summer camp has 320320 ft of float line with which to rope off three adjacent rectangular areas of a lake for swimming​ lessons, one for each of three levels of swimming ability. A beach forms one side of the swimming areas. Suppose that the width of each area is x feet. Answer parts​ a) and​ b)
 
 
​a) Express the total area of the three swimming areas as a function of x.
 
​A(x)equals=
​(Simplify your​ answer.)
 
​b) Find the domain of the function.
​(Type your answer in interval​ notation.)
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Expert Answer

Step 1

Consider the total length of the rope is 320 ft

This rope is used to cover the length of width of rectangle shape swimming area.

Step 2

The rectangle swimming pool are shown in the below figure having one side covered with beach. Consider x ft, y ft be the width and length of each rectangle area.

Trigonometry homework question answer, step 2, image 1

Step 3

The perimeter of the above figure must be equal to 320 ft

Trigonometry homework question answer, step 3, image 1

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Trigonometry