Solving non-rational expressions on 49G?



#8

Hi.. Anyone knows how to solve these kinds of expressions on a HP49:?

((40000*A+4000)/exp(A))=5000

Looks very simple, but just get the words:
"Not reducible to a rational expression"


#9

I wouldn't even know how to solve this by hand but the numeric solver [RS][7] gives the following answer straight away A=2.863E-2

You can also use ROOT which gives the same answer with a guess of 0. But a different answer with a guess of 2. So I don't know...


Arnaud

Edited: 16 June 2008, 10:01 a.m.


#10

Quote:
I wouldn't even know how to solve this by hand

Neither would I, but I have researched and have found the exact result is

x = -W(-e^(-1/10)/8) - 1/10 or

x = 0.028630541938, to 12 places.

where W(x) is [link:http://en.wikipedia.org/wiki/Lambert's_W_function]Lambert's W function[/link]. Please take a look at the general solution formula in example 1. I think this matches the numeric result you have found.

Programs to compute the W function on the HP-33S and some other HP calculators can be found

here.

Regards,

Gerson.


#11

Welcome back here, Gerson! (And congrats for your solution).
Regards

Jean-Michel.

#12

Nice link. Spot on. Time to get back to do a bit of maths...

#13

Quote:
I wouldn't even know how to solve this by hand ...


That<'s what we have calculators for :)

I have just found out, thx to the numeric solver as you told me.

Thanks

#14

Equation to solve, using the HP-49:

((40000*A+4000)/exp(A))=5000

which simplifies to

40*A - 5*exp(A) + 4 = 0

whose derivative is

40 - 5*exp(A)

Solving that for zero yields A = ln(8) ~= 2.079441542.

This is the inflection point for the initial guess that determines which solution the HP-15C gives, but not on the HP-49G.

Quote:
the numeric solver [RS][7] gives the following answer straight away A=2.863E-2

You can also use ROOT which gives the same answer with a guess of 0. But a different answer with a guess of 2.


The "different" (but still valid) answer is 3.30455610804.

My difficutly was figuring out how to copy 'n' paste the expression into the "NUM.SLV" form after symbolic solution "S.SLV" failed. I finally saved it to a variable and loaded that using "CHOOSE".

(Sigh.) Once again, I would have had my answers so much faster with an ancient HP-34C or HP-15C, despite the vast difference in computational speed.

-- KS


Edited: 17 June 2008, 1:56 a.m.


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