Question

Task 1

Create expressions to represent the dimensions of the pool.

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 polynomial expressions will be used. Your task will be to help Bernard.

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.


A. 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.

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

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

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

Answer 2

If you let:
Width=x
Length = 3*x+3 = 3x+3
Depth=2*length -7 = 2(3x+3)-7 = 6x-1

Answer 3

B) Area of landspace = width*length
C) Volume = length*width*depth
D) obviously depends what you get for (C)

Answer 4

I have to solve for x?

Answer 5

you're aren't explicitly asked to do so, as you do not have sufficient information to do so

Answer 6

you are only asked for expressions

Answer 7

So I don't solve anything?

Answer 8

You said D would be what I got for C

Answer 9

Its only for A that I dont solve?

Answer 10

there's nothing to solve, you are asked to use the variable 'x' to find expressions for area and volume.
I said what you got for D depends what you get for C, not that it's the same

Answer 11

part D requires you to analyse the expression you get for C

Answer 12

For example B right? it asks to determine the polynomial expression to represent the area of land space that the pool will cover so is the answer three? or how do I determine that?

Answer 13

do you understand what a polynomial expression is? :-)

Answer 14

Honestly I dont know

Answer 15

I'll take a shot 3*x+3

Answer 16

Okay, a polynomial expression is one that doesn't have a definite answer, like you don't know what it is, but you can kind of express it

so in this case, we are calling the width 'x' - we have no idea what it actually is, it could be 1m 10 feet, 70 km for all we know...

we then use this expression 'x' as a way of expressing the other dimensions
so we are told that the length is equal to 3 times the width (ie x) + 3
so length =3x+3

Basically a polynomial expression is a function that has a variable (usually 'x') but we don't know what 'x' is, and we use it to express other things

Does that make sense?

Answer 17

Yeah it makes sense I think so the polynomial the length?

Answer 18

How come you excluded the first part and only used =3x+3

Answer 19

I really dont know this Im sorry if im mentally not there

Answer 20

3*x+3 is the same as 3x+3 - i just omitted the times sign

Answer 21

\[\text{Width} = x\]\[\text{Length} = (3 \times x) +3\]\[\text{Depth} = (6 \times x) -1\]
Do you understand those expressions?

Answer 22

Yeah you multiply the variable by the numbers and then you took the number that was apart of the expression and put it on the outside

Answer 23

okay then:
B) Area of land space - which is just the area it takes up (not including depth)
so Area=length x width = (3x+3) * x = ?

C) Volume = area * depth = (3x+3)*x*(6x-1) = ?

you need to work those out, you'll get expressions in 'x'

Answer 24

Like terms?

Answer 25

let's just take it step by step:
part B)

Area= length * width
(3x+3)*x

what does that equal?

Answer 26

6x^2

Answer 27

Naw its 3x^2+3x?

Answer 28

YES! that's part B done!

Answer 29

Right, now part C
Volume = area * depth
(3x^2 +3x) * (6x - 1) = ?

Answer 30

How do I set it up? like terms? or I dont know distributive property

Answer 31

okay so we have:
You get four terms