Question

Is This Right?

Answer 1

At times, it is necessary to make plans even when all of the facts are not there. Bernard is currently facing such a dilemma. Bernard is asked to create a swimming pool and deck design for a new series of model homes currently being designed. Each home will have varying pool sizes depending on the lot size; however, there will be some similarities, so polynomials expressions will be used. Your task will be to help Bernard.

To fit the dimensions of the various land spaces, he realizes the length of the pool has to be three times the size of the width, plus 3, and the depth has to be 7 less twice of the length.


Task 1
Create expressions to represent the dimensions of the pool.

Create a variable to represent the width of the pool. Determine the expressions to represent length and the depth in terms of the width variable.

Length = 3w + 3
Depth = 2l – 7
Width = 1/3 l-1

Determine the polynomial expression to represent the area of land space that the pool will cover.

Surface Area of Rectangular Prism = 2(wh+lw+lh)

2(((1/3 l-1)∙(2l-7) )+((3w+3)∙(1/3 l-1) )+

Using the area and the depth expressions, determine the polynomial expression that is used to represent the volume.

The volume of a rectangular prism is length times width times height.
(3w+3)∙(2l-7)∙(1/3 l-1)

Classify the volume polynomial by degree and number of terms.

I simplified the volume and it came out to…

〖21l〗^2 w+13lw+〖2l〗^2+21w-13l+21

This is a third degree polynomial.

Answer 2

My answers are there as well. >v<