Calling all math nerds

Discussion in 'General Discussion' started by Sixshot, Nov 1, 2009.

  1. Sixshot

    Sixshot Jeff Goldbluman Group

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    My cousin asked me for help on a math question. I thought I figured it out but my answer seems too simple? Help? It's just algebra, polynomials and such.

    Each of the three dimensions of a cube with sides of length s centimeters is decreased by a whole number of centimeters. The new volume in cubic centimeters is given by V(s) = s^3 - 13s^s + 54s - 72

    a.) Find V(10). This was easy, I just plugged 10 in for s and got 168

    b.) If the new width is s-6 centimeters, then what are the new length and height? I figured they must be the same as the width since it's a cube, so s-6

    c.) Find the volume when s = 10 by multiplying the length, width, and height. I figured plugging 10 in for s in respect to each side (s-6), so 4x4x4 is 64

    Any help or confirmation is appreciated, from one nerd to another.
     
  2. foxfan352

    foxfan352 Well-Known Member

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  3. grimlock1972

    grimlock1972 "No Mas" My Wallet

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    algerbra? gah! burn it with fire!
     
  4. Aernaroth

    Aernaroth <b><font color=blue>I voted for Super_Megatron and Veteran

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    Looks like you're on the right track.

    For b), you could probably find what s actually is, by setting (S-6)^3 = V(S), but your answer for length and height is technically correct.

    For c), looks like you did the right thing as well. You could check your answer by plugging s=10 into your new volume formula though.
     
  5. Dran0n

    Dran0n Junk male

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    I feel I'll get the answer wrong, so I won't bother.
     
  6. aussiehippy

    aussiehippy Au contraire, Blackadder.

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    Dammit, I was all ready to give my opinion when I realised the thread wasn't for Meth Nerds
     
  7. Keiichitron

    Keiichitron Not a physicist, dammit

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    here are my thoughts, assuming this is all that's given.
    a) correct, it's asking you to solve the V(s) formula for 10.
    b) incorrect, the original shape was a cube, each side was reduced by a number, but not the same number (new volume from part a) was 168, which is not a perfect cube). so you need to divide out (s-6) from the V(s) formula. so V(s)=(s-6)(s-something)(s-something)... working on it now
    c) this one is confusing. if s=10, the volume of the cube is 10^3=1000. if they want you to solve V(s) for s=10, you already did that in part a).... is there more to the question?
     
  8. Keiichitron

    Keiichitron Not a physicist, dammit

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    update:
    part b) V(s)=(s-6)(s-4)(s-3)
    so i guess part c) s-6=4 s-4=6 s-3=7 so 4x6x7=168
     
  9. Aernaroth

    Aernaroth <b><font color=blue>I voted for Super_Megatron and Veteran

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    You just bothered.

    I think the insinuation is that each side is reduced by 6, unless its just some really crappy wording. Is there any non-trivial solutions for V(S)=(s-6)^3 ?
     
  10. Keiichitron

    Keiichitron Not a physicist, dammit

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    i think the wording is off, but you can't reduce the three dimensions by the same number and get the original V(s) equation.
     
  11. DeathStorm

    DeathStorm Snoochie Boochies

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    Wait until numbers leave math altogether and are replaced by Greek symbols. I barely made it through non-linear Calculus in college (thank God it was the highest I had to go) and let me tell you, you ain't seen nothing yet.
     
  12. Aernaroth

    Aernaroth <b><font color=blue>I voted for Super_Megatron and Veteran

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    Then I guess your answer is more likely to be the correct one. That's kind of a strange wording though. Maybe this thread should get turned into another one of those "math quiz" threads we had a while back.

    "Do not worry about your difficulties in mathematics, for I assure you mine are greater." - Albert Einstein
     
  13. Keiichitron

    Keiichitron Not a physicist, dammit

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    should've read like this i think:

    A cube has sides S, after reducing each side you get a rectangular prism of volume V(S)=S^3 - 13S^2 +54S - 72.
    a) solve V(S) for S=10.
    b) one side is S-6, what are the other two?
    c) if S=10, find volume by using the height, width, length found in part b.

    i could do math quiz answers, i would stink at coming up with questions.
     
  14. Darkwing48

    Darkwing48 Heroic Decepticon

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    I will approach it as V = len x wid x hgt.
    len = longest side = s
    width = middle length side = s - x
    height = shortest side = s - y

    so V = s(s-x)(s-y) = s( s^2 - s(y+x) + xy ) = s^3 - s^2(x+y) - sxy (Yes sexy)
     
  15. Darkwing48

    Darkwing48 Heroic Decepticon

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    B is a little confusing because on the original equation, How you know which side is reduced.
    If the equation is V(s-6) then...
    V = (s-6)^3 - 13( s-6)^2 + 54(s-6) - 72
    V = (s-6)(s-6)(s-6) - 13(s-6)^2 + 54(s-6) -72
    V = (s-6)(s^2 -12s +36) - 13 (s^2 - 12s +36) +54s - 324 - 72
    V= (s^3 - 12s^2 + 36s - 6s^2 + 72s - 216) - (13s^2 + 156s - 468) + 54s - 396
    V = (s^3 -18s^2 + 108s - 216) - (13s^2 + 156s -468) + 54s - 396
    V = s^3 -(18s^2 + 13s^2) + (108s - 156s) + (468 - 216) + 54s - 396
    V = (s^3 - 5s^2 - 48s + 252) + 54s -396
    V = s^3 - 5s^2 + 6s - 144

    Someone check my answer.
     
  16. Chaos Muffin

    Chaos Muffin Misadventure Veteran

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    head explodes
     
  17. Keiichitron

    Keiichitron Not a physicist, dammit

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    check your signs, you're not carrying some of your negatives through correctly. easier to write it out completely instead of having minus times a whole expression.

    s^3-12s^2+36s-6s^2+72s-216-13s^2+156s-468+54s-324-72
    =
    s^3-12s^2-6s^2-13s^2+36s+72s+156s+54s-216-468-324-72
    =
    s^3-31s^2+318s-648
     
  18. Darkwing48

    Darkwing48 Heroic Decepticon

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    true, I'm better writing this than typing it.
     
  19. red4

    red4 Banned

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    how many sides does a deceptigon have?
     

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