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Homework Help: Polynomial functions and calculating dimensions

  1. Mar 5, 2012 #1
    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?
     
  2. jcsd
  3. Mar 5, 2012 #2
    First thing, do you know what
    (x+1) (x+2) (x+4)
    should be equal to?
     
  4. Mar 5, 2012 #3
    Do you do 8^9?
     
  5. Mar 5, 2012 #4
    So the final volume is 134217728? or do you just do 8*9?
     
  6. Mar 5, 2012 #5
    nono, you do not take 8 to the 9th power.
    Maria is simply trying to make the storage 9 times the original volume.

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

    Regardless, what I meant by
    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?
     
  7. Mar 5, 2012 #6
    I'm not sure, change the values of (x+1)(x+2)(x+4)
     
  8. Mar 5, 2012 #7
    That will not retain the scale of the box.
     
  9. Mar 5, 2012 #8
    expand the function?
     
  10. Mar 5, 2012 #9
    Which function?
     
  11. Mar 5, 2012 #10
    expand (x+2)(x+4)(x+1)?
     
  12. Mar 5, 2012 #11
    or (x+1)(x+2)^2(x+4)^4
     
  13. Mar 5, 2012 #12
    ohhh or is it 72=(x)(2x)(4x)?
     
  14. Mar 5, 2012 #13
    That is correct but I feel like you're just guessing at this point, do you understand WHY this is?

    Where did you get this from?
     
  15. Mar 5, 2012 #14
    Well i tried 72 = (x+4)(x+1)(x+2) and i subbed in 2, and it worked out.
     
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