56. a rectangular frame of uniform depth for a shadow box is to be made from a 36-in. piece of wood.

36 in.

a. write a function to represent the display area in terms of x.

b. what dimensions should be used to maximize the display area?

c. what is the maximum area?

Answer and explanation:

Given : A rectangular frame of uniform depth for a shadow box is to be made from a 36-in. piece of wood.

To find :

a) Write a function to represent the display area in terms of x.

The perimeter of the box is 36 inches.

Let x and y be the length and width of the box.

So,

....(1)

The area of the box is

Substitute y from (1),

The function in terms of x,

b. What dimensions should be used to maximize the display area?

As A is a quadratic function with a negative leading coefficient.

The vertex is the maximum point on the function.

So, the x-coordinate of the vertex is the value of x that will maximize the area.

Here, a=-1 and b=18

Substitute in (1),

The dimension 9 in. by 9 in. should be used maximize the display area.

c) What is the maximum area?

Substitute the value of x in the area,

The maximum area is 81 square inches.

step-by-step explanation:

mean or average is 40.6

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