I don't even know where to start

Question

A rancher has 600 feet of fencing to enclose two adjacent rectangular corrals (Assume they are equal)

(a) Write the area A of the corrals as a function of x.
A(x) =

(b) Create a table showing possible values of and the corresponding areas of the corral. (Round your answers to two decimal places.)
x          A
55
60
65
70
75
80
Use the table to estimate the dimensions that will produce the maximum enclosed area. (Round your answers to two decimal places.)
x =
ft (smaller value)
y =
ft (larger value)

(c) Use a graphing utility to graph the area function. Use the graph to approximate the dimensions that will produce the maximum enclosed area. (Round your answers to two decimal places.)
x =
ft (smaller value)
y =
ft (larger value)

(d) Write the area function in standard form to find analytically the dimensions that will produce the maximum area.
A(x) =

Answer 1

1)

 

These rectangles are equal to each other

 

Let the length = x

Let the width = y

 

 

If we draw two equal rectangles adjacent to each other and label the sides, we will see that exactly one side joins the two rectangles.

 

The perimeter will 4x + 2y

 

 

4x + 2y = 600   ------> perimeter

 

2y = 600 - 4x

 

y = 300 - 2x

 

 

Area = 2xy

 

 

Since we want the area in terms of x, substitute the perimeter into the area.

 

A(x) = 2x(300 - 2x)

 

A(x) = 600x - 4x²

 

 

2)

 

Evaluate A(x) for each x value you have here.

 

 

To answer the other questions, use the formula for A(x) we just found as a guide.

 

 

As for graphing utility, use a graphing calculator to plot A(x). 

 

Press Y=.  Type in the function for A(x).  Then press GRAPH.  You will see the graph being constructed.  Press 2ND , TRACE, and hit 4.  Follow the instructions that calculator gives to get your maximum.