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Hello guys, first post here.
I am trying to solve a tricky equation for a friend's business and have got so far with the problem.
The problem as given to me is as follows: Make S the subject of:
S = ( C+(CJ-C)+R+(RJ-R)+( L(S+Q+U+K)) ) ((SJ-S)+U+((CJ-C) (SJ-S)))
Tidying this up
S = (C + R + (CJ-C) + (RJ-R) + L(S+Q+U+K)) - (U + (SJ-S) + ((CJ-C) - (SJ-S)))
This is where I start to stuggle and my Maths A - level starts to betray me - getting rid of the brackets. I think a muinus outside the bracket changes the signs inside? So:
S = (C + R + CJ - C + RJ - R + LS + LQ + LU + LK) - (U + SJ - S + CJ - C - SJ + S)
S = C + R + CJ - C + RJ - R + LS + LQ+ LU + LK - U - SJ + S -CJ +C +SJ -S
Simplifying (+C removes -C and +R removes - R, -S removes +S?)
S = CJ + RJ + LS + LQ + LU + LK - U - SJ -CJ + C + SJ
SJs also cancel so
S = CJ + RJ + LS + LQ + LU + LK - U - CJ + C
S / LS = CJ + RJ + LQ + LU + LK - U - CJ + C
The question is - am I right so far, and how do I finish this and make S the subject. Any Maths genius able to help me?
Many Thanks
Ben
Last edited by benmilesbc (2007-05-11 03:37:42)
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You're right so far, apart from the very last step. Instead of dividing by LS, you take it away.
You had:
S = CJ + RJ + LS + LQ + LU + LK - U - CJ + C
Cancel the CJs and subtract LS:
S - LS = RJ + LQ + LU + LK - U + C
Factorise the left side:
S(1-L) = RJ + LQ + LU + LK - U + C
Divide by (1-L):
S = (RJ + LQ + LU + LK - U + C)/(1-L)
Done!
Why did the vector cross the road?
It wanted to be normal.
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Thanks for that but urg, the problem is a lot more complicated than i Thought, and I had screwed up previously making the above totally wrong lol. Ill post it in its total:
S = (C+V+R+T+A) (Q+U+K)
But
A = (L(S+Q+U) (S+Q+U))
V = (CJ-C)
T = (RJ-R)
Q = (SJ-S)
K = (CJ-C) (SJ-S)
So
S = ( C+V+R+T+A ) (Q+U+K)
S = ( C+(CJ-C)+R+(RJ-R)+ (L(S+Q+U) (S+Q+U)) ) ((SJ-S)+U+((CJ-C) (SJ-S)))
S = ( C+(CJ-C)+R+(RJ-R)+ (L(S+(SJ-S)+U) (S+(SJ-S)+U))) ((SJ-S)+U+((CJ-C) (SJ-S)))
Tidying this up:
S = ( C+ R+(CJ-C)+(RJ-R)+ (L(S+(SJ-S)+U) (S+(SJ-S)+U))) (U+(SJ-S)+ ((CJ-C) (SJ-S)))
Removing Brackets ( outside the brackets changes the signs inside)
S = ( C+ R+CJ-C+RJ-R+(LS+L(SJ-S)+LU) (S+SJ-S+U))) (U+SJ-S+CJ-CSJ+S)
S = ( C+ R+CJ-C+RJ-R+(LS+LSJ-LS+LU) S-(SJ-S)-U)) (U+SJ-S+CJ-CSJ+S)
S = ( C+ R+CJ-C+RJ-R+LS+LSJ-LS+LU S-SJ+S-U) (U+SJ-S+CJ-CSJ+S)
S = C+ R+CJ-C+RJ-R+LS+LSJ-LS+LU S-SJ+S-U U-SJ+S-CJ+C+SJ-S
Simplify This ( i think this is maybe where i screwed up if not before)
S = RJ+LSJ+LU-SJ-2U+C
Subtract LSJ and add SJ to each side
S LSJ+SJ = RJ+LU-2U+C
Factorise the left side
S( LJ+J) = RJ+LU-2U+C
Divide by ( LJ+J)
S = (RJ+LU-2U+C) / ( LJ+J)
Trouble is, it nowhere near works when using actual figures, so my equation must be wrong
Any help would be much appreciated!
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You're very nearly right. The mistake is when you factorised, just before the end.
S - LSJ + SJ = S(1 - LJ + J). You just forgot to put that 1 in there.
Following that through gives you a final equation of S = (RJ+LU-2U+C) / (1LJ+J).
Why did the vector cross the road?
It wanted to be normal.
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