b x must be greater than 0 feet but no more than 10.04 feet.
Practice makes perfect
a The pool and the decking together form a rectangle.
The width of this rectangle is (12+x), and its length is (24+x) feet. Recall that the area of a rectangle is the product of its width and length.
A=(12+x)(24+x)Let's write and simplify an inequality representing that the total area cannot exceed 750 square feet.
We can use a calculator to sketch the graph of the quadratic function corresponding to this inequality.
We begin by pushing the Y= button and typing the equation in the first row.
To see the graph you will need to adjust the window.
Push WINDOW, change the settings, and push GRAPH.
Let's copy the graph from the calculator screen.
Since x represents a distance, only positive values are meaningful.
The solution of the inequality is the set of values of x for which the graph is not above the horizontal axis.
b From the graph of Part A we see that the possible widths of the deck has an upper bound. To find this bound, we either use a calculator or solve a quadratic equation.
x^2+36x-462=0
Let's follow the graphical approach and use calculator to find the x-intercept of the graph.
From the screen with your graph push 2nd and TRACE and choose zero from the menu.
The calculator will prompt you to choose a left and right bound and to provide the calculator with a best guess of where the zero might be.
The result we got gives an upper bound for the possible values of x satisfying the inequality of Part A.
We can combine this with the constraint that x must be positive to write the solution set to the inequality.
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