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# seems easy...but can't grasp

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Solve for Emax. I have the answer cause of the back of the book and have read the directions/samples in the book, but for the life of me I can't figure out how the process to get there. Even tried to change equation to a= (b-c)/(b+c) to hopefully make more sense and it didn't work.

\(M = (Emax-Emin)/(Emax+Emin)\)

Nov 1, 2018
edited by Guest  Nov 1, 2018
edited by Guest  Nov 1, 2018
edited by Guest  Nov 1, 2018

#1
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OK....let's use your  example  and solve for  "b"

So  we have

M  = ( b - c)  / ( b + c)     multiply both sides by  ( b + c)

M ( b + c)  = b - c         distribute the M on the left

Mb + Mc  =  b  - c      subtract b, and Mc from both sides

Mb - b   =   - Mc -  c       multiply both sides by - 1

b - Mb  = Mc + c        factor both sides

b( 1 - M)  =  c ( M + 1)      divide both sides by (1 - M)

b  =  c ( M + 1) / ( 1 - M)

So......back-substituting, we have

Emax  =  Emin ( M + 1) / (1 - M)

Nov 1, 2018
#2
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I had got to this point-  Mb + Mc  =  b  - c      subtract b, and Mc from both sides

Mb - b   =   - Mc -  c       multiply both sides by - 1 <---- Was skipping this part

was getting M = c(1-m)/(m+1)

When that didn't work I started racking my brain and then overlooking these steps and was becoming a brain drain cycle.

b - Mb  = Mc + c        factor both sides

b( 1 - M)  =  c ( M + 1)      divide both sides by (1 - M)

Thanks! Rereading a couple times to get this to stick

Nov 1, 2018
#3
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OK, BG..   glad to help......I hope it makes some sense  !!!!

CPhill  Nov 1, 2018
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Big issue I just realized my brain was having, and maybe you could explain this to me...Why when you get to

Mb + Mc  =  b  - c      subtract b, and Mc from both sides

Why can't I just add "c" to the the left and be done?

Mb + Mc + c = b

Nov 1, 2018
edited by BlancoGringo  Nov 1, 2018
#5
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Remember that we want to isolate  "b"

So....taking it from here

Mb + Mc  =  b - c

We want all the terms involving "b"  on on side of the equation and everything else on the other side

So....the way to do this is to subtract b from both sides  and subtract Mc from both sides

And we have

Mb - b  =   -Mc - c         which we can write as

Mb - b  =  (-1) (Mc + c)       multiply both sides by -1

(-1) (Mb - b)  =  (-1)(-1)(Mc + c)

-Mb + b  =  Mc + c

b - Mb   =  Mc + c        factor out the b on the left  and the c on the right

b ( 1 - M)   = c ( M + 1)      divide both sides by  (1 - M)

b  =   c(M + 1)  / ( 1 - M)

And  b  is isolated.....

CPhill  Nov 1, 2018
edited by CPhill  Nov 1, 2018
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Facepalm...im overlooking Mb in that. I got a brain that calculates numbers like it's owned by Texas Instruments...but introduce a letter and it messes with my brains algorithms.

Nov 1, 2018
#7
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HAHAHA!!!!....I know what you mean...."abstract" letters used to give me trouble, too  [ and sometimes still do ]....but...the more you work with them, the better you will get....

CPhill  Nov 1, 2018