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.

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

BlancoGringo Nov 1, 2018

edited by
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Nov 1, 2018

edited by Guest Nov 1, 2018

edited by Guest Nov 1, 2018

edited by Guest Nov 1, 2018

edited by Guest Nov 1, 2018

#1**+2 **

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

E_{max} = E_{min} ( M + 1) / (1 - M)

CPhill Nov 1, 2018

#2**+1 **

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

BlancoGringo Nov 1, 2018

#4**0 **

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

BlancoGringo Nov 1, 2018

#5**+2 **

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

#6**+1 **

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.

BlancoGringo Nov 1, 2018