Question

You have a steel wire that is 88 inches long. To make a sign holder, you bend the wire x inches from each end to form two right angles. To use the sign holder, you insert each end 4 inches into the ground.

Write a function for the rectangular area A enclosed by the sign holder in terms of x.
A =


(b) Use the table feature of a graphing utility to determine the value of x that maximizes the rectangular area enclosed by the sign holder.
x =

Answer 1

Let's find the function for the rectangular area A enclosed by the sign holder in terms of x:

The rectangular area A is given by:
A = bh, where b = x and h = (88 - 2x - 8) / 2
Substituting b and h into the formula for A:
A = x * (44 - x - 4) / 2

This is the function for the rectangular area A in terms of x.

To find the value of x that maximizes A, we need to use the table feature of a graphing utility:

Create a table with x as the independent variable and A as the dependent variable.
Calculate the value of A for a range of values of x, such as x = 0, 1, 2, 3, ..., 40.
Plot the values of x and A on a coordinate plane.
Find the value of x that corresponds to the maximum value of A on the graph.
The value of x that maximizes the rectangular area enclosed by the sign holder is the x-coordinate of the maximum point on the graph. In this case, it is approximately 20 inches