Question

MEDAL AWARDED FOR HELP (Polynomials)
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 polynomial expressions will be used.

To fit the dimensions of the various land spaces, he realizes that 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 than twice the length.

Task 1
Create expressions to represent the dimensions of the pool

Answer 1

I have this - Width = W, L = 3W + 3, D = 7 – 2L

Is that correct

Answer 2

I'm realllllly desperate. This is only one of more questions on this and I need help. If someone helps me out they can have my kik or something

Answer 3

Also next question is : 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.

Answer 4

Yes that is correct

Answer 5

Thank you @Matthew071 can you continue helping? :)))))

Answer 6

Sure :)

Answer 7

What is your next question

Answer 8

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.

Answer 9

Didnt you just already do that? First I think its just asking is just create a variable for width. A variable can be any letter or symbol. So what you did was create Width=W and W is the variable of width. Now in terms of width means just put the equations as in terms of width. So as you did L=3W or Length is 3 times the width plus 3.

Answer 10

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

I'm sorry i copied the wrong one

Answer 11

Its ok now lemme see

Answer 12

Ok so we assume the pool is a rectangle so all we need to know is that Area=LeangthxWidth

Answer 13

So now we just plug in that formula where Area=(W)(3W+3)

Answer 14

Then we just simplify the equation where Area=3W^2+3W

Answer 15

And that will be all

Answer 16

I see. Thank you. More questions coming. I don't know how to thank you more than just a medal. Any ideas?

Answer 17

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

also heres another one

Answer 18

Keep the questions coming

Answer 19

Ok now you know that Area=3W^2+3W now all you have to do is Plug into the formula for Volume. V=LWH or V=(Area)(D), Having said that we just plug in the variables and we have V=(3W^2+3W)(7-2L)

Answer 20

Oh by the way I forgot to mention on the first part of the problem, since Depth is in terms of L we have to make it in terms of W

Answer 21

So would it be 6w -4

Answer 22

My Bad


Just a simple fix

D=7-2(3W)
D=7-6W
V=(3W^2+3W)(7-6W)


Now do the FOIL method and you get

Volume=-18w^3-3W^2+21W

Answer 23

My bad again

Answer 24

Volume=(3W^2+3W)(1-6W)

Answer 25

you were correct on one part of the depth equation except for one part

Answer 26

Okay thank you. You're a godsend. Hold on i'm looking at the assignment

Answer 27

Ok and your welcome

Answer 28

4. Classify the volume polynomial by degree and number of terms.

It is a trinomial correct?

Answer 29

Indeed and the degree is the term with the highest power in the equation so what is the highest power?

Answer 30

So we know the highest power is cubed so what does that tell you?

Answer 31

As in \[x^3+x^2+x\]

the degree is 3 because the highest power is the degree

Answer 32

Catch my drift?

Answer 33

I undestand. its a 3rd degree trinomial

Answer 34

CORRECTAMUNDO!!!

Answer 35

:D

Answer 36

Next i have to draw a diagram and i dont think you can help me with that, so thank you so much for your help. i wanna thank you more than just a medal.... How can I?

Answer 37

Anything really :)

Answer 38

Cool, I'll kik you. Thank you friend

Answer 39

No problamo