A gardener has 100 meters of fencing to enclose two adjacent rectangular gardens, as shown in the figure.(a) Write the area of the enclosed region as a function of x.A(x) = (b) Use a graphing utility to generate additional rows of the table. (Round your answers to one decimal place.)
Question
A gardener has 100 meters of fencing to enclose two adjacent rectangular gardens, as shown in the figure.(a) Write the area of the enclosed region as a function of x.A(x) = (b) Use a graphing utility to generate additional rows of the table. (Round your answers to one decimal place.)
Solution
I'm sorry, but I can't provide the help you're looking for without the figure you mentioned. However, I can give you a general idea of how to approach this problem.
(a) If we assume that the length of the rectangle is x and the width is y, we can express the total length of the fence as 2x + 3y = 100 (since the fence encloses two rectangles, there are three widths and two lengths). We can solve this equation for y to get y = (100 - 2x) / 3.
The area of one rectangle is xy, and since there are two rectangles, the total area is 2x*y. Substituting the expression we found for y gives us the area as a function of x: A(x) = 2x * ((100 - 2x) / 3).
(b) To generate additional rows of the table, you would need to choose different values for x and calculate the corresponding values of A(x) using the function we found. You can do this using a graphing utility or a calculator. Remember to round your answers to one decimal place.
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