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Off-Topic Discussion => General Discussion => Topic started by: Killer Whale on December 31, 2009, 01:18:14 am

Title: Quick maths question
Post by: Killer Whale on December 31, 2009, 01:18:14 am: I don't know how to do this, does someone else?(if in fact it's possible, which I don't believe it's not)

What is m in terms of d (m=?d?) when
d=(m^3+147m^2+1052m)/300+1
Title: Re: Quick maths question
Post by: Spicious on December 31, 2009, 09:01:14 am: It's possible to solve any cubic exactly. See http://en.wikipedia.org/wiki/Cubic_function#General_formula_of_roots. The solutions all seem to be horrible messes in this case though.
Title: Re: Quick maths question
Post by: watsisname on December 31, 2009, 10:25:25 am: ~~Is this problem stated correctly? I'd think there would be a variable in the denominator, too. <_<~~ Nevermind, I'm just dumb. D:

Also, ^{superscripts!} :P
Title: Re: Quick maths question
Post by: Ghostavo on December 31, 2009, 11:47:13 am: Yay (http://www.wolframalpha.com/input/?i=++d%3D%28m%5E3%2B147m%5E2%2B1052m%29%2F300%2B1).
Title: Re: Quick maths question
Post by: Killer Whale on December 31, 2009, 09:11:06 pm: according to Yay. (http://www.wolframalpha.com/input/?i=++d%3D(m^3%2B147m^2%2B1052m)%2F300%2B1)

for d=(m^3+147m^2+1052m)/300+1
if m = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
d = 5, 10, 16.02, 23.08, 31.2, 40.4, , 50.7, 62.12, 74.68, 88.4

for m = -(2 sqrt(3) sqrt(151875 d^2-186350625 d-1017411019)-1350 d+828225)^(1/3)/3^(2/3)-6151/(3^(1/3) (2 sqrt(3) sqrt(151875 d^2-186350625 d-1017411019)-1350 d+828225)^(1/3))-49
if d = 5, 10, 16.02, 23.08, 31.2, 40.4, 50.7, 62.12, 74.68, 88.4
m = ERROR, ERROR, ERROR, ERROR, ERROR, ERROR, ERROR, ERROR, ERROR, ERROR
if anything under ~1232.44 is used as d, you get an error because you can't sqrt negatives. (using Excel, cause my calculator can only fit in the first half)

@wiki, In mathematics, a cubic function is a function of the form f(x)=ax³+bx²+cx+d, where a is nonzero. a Does equal zero.
Title: Re: Quick maths question
Post by: Spicious on January 01, 2010, 01:02:55 am: I think you may find a=1/300, b=147/300, c=1052/300 and d=1-d. http://en.wikipedia.org/wiki/Cubic_function#The_nature_of_the_roots may also be of interest. For any value of d there will be either 1 or 3 solutions that are real.
Title: Re: Quick maths question
Post by: Killer Whale on January 01, 2010, 03:21:19 am: Quote from: Killer Whale on December 31, 2009, 09:11:06 pm
@wiki, In mathematics, a cubic function is a function of the form f(x)=ax³+bx²+cx+d, where a is nonzero. a Does equal zero.
:mad: a isn't zero!! a is one!!
Title: Re: Quick maths question
Post by: Scotty on January 01, 2010, 03:30:17 pm: Quote
I think you may find a=1/300, b=147/300, c=1052/300 and d=1-d

Doesn't that mean that d = 1/2?
Title: Re: Quick maths question
Post by: Spicious on January 01, 2010, 05:52:44 pm: It looks that way but the left one refers to the value of the constant term of the cubic and the right one is the variable of the equation.