Polynomial functions and calculating dimensions

[euro94]

Maria designed a rectangular storage unit with dimensions 1m by 2m by 4m. By what should he increase each dimension to produce an actual storage that is 9 times the volume of his scale model?

v= (1) (2) (4)
v= 8

v has to be 9 times larger
v= (x+1) (x+2) (x+4)

How do i find the value of x?

 

[genericusrnme]

First thing, do you know what
(x+1) (x+2) (x+4)
should be equal to?

 

[euro94]

Do you do 8^9?

 

[euro94]

So the final volume is 134217728? or do you just do 8*9?

 

[genericusrnme]

Do you do 8^9?

nono, you do not take 8 to the 9th power.
Maria is simply trying to make the storage 9 times the original volume.

or do you just do 8*9?

That is correct but I'm not sure you fully understood where you got the 8*9 from

Regardless, what I meant by

do you know what
(x+1) (x+2) (x+4)
should be equal to?

Was that this is incorrect.

If he wants the model to keep the same scale the ratio of the dimensions must still be 1:2:4

If you use (x+1)(x+2)(x+4), any x you put in there will change that ratio, take x = 1, then you'd get 2:3:5, which is not equivelant to 1:2:4.

How do you suppose we would go about changing the volume whilst keeping that ratio constant?

 

[euro94]

I'm not sure, change the values of (x+1)(x+2)(x+4)

 

[genericusrnme]

I'm not sure, change the values of (x+1)(x+2)(x+4)

That will not retain the scale of the box.

 

[euro94]

expand the function?

 

[genericusrnme]

Which function?

 

[euro94]

expand (x+2)(x+4)(x+1)?

 

[euro94]

or (x+1)(x+2)^2(x+4)^4

 

[euro94]

ohhh or is it 72=(x)(2x)(4x)?

 

[genericusrnme]

ohhh or is it 72=(x)(2x)(4x)?

That is correct but I feel like you're just guessing at this point, do you understand WHY this is?

(x+1)(x+2)^2(x+4)^4

Where did you get this from?

 

[euro94]

Well i tried 72 = (x+4)(x+1)(x+2) and i subbed in 2, and it worked out.