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
Guest
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