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Re: [Phys-l] quadratic uncertainty



Just realized that I typed over the other root:

1.00 (+0.12 / -0.03) (+0.14 i / -0.14 i)

1.08 (+0.02 / -0.11) (+0.14 i / -0.14 i)

Bob



________________________________________
From: phys-l-bounces@carnot.physics.buffalo.edu [phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of LaMontagne, Bob [RLAMONT@providence.edu]
Sent: Sunday, August 29, 2010 12:02 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] quadratic uncertainty

Hi All,

Just got back from vacation. I have caught up on all the posts on this subject and haven't found any direct response to John's puzzle.

I will venture the following:

1.00 (+0.20 / -0.11) (+0.14 i / -0.14 i)

Bob at PC

________________________________________
From: phys-l-bounces@carnot.physics.buffalo.edu [phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker [jsd@av8n.com]
Sent: Wednesday, August 25, 2010 11:09 PM
To: Forum for Physics Educators
Subject: [Phys-l] quadratic uncertainty

Here's a little puzzle with some seasonal relevance:

We need to find a good value for x
/and for the uncertainty associated with x/
given that:
a x^2 + b x + c = 0 [1]
a = 1 ± .0001
b = -2.08 ± .01
c = 1.08 ± .01

This was mentioned in connection with the annual "sig figs"
donnybrook on the chemistry list. There are a thousand people
on that list, and so far nobody has come up with a solution.
One person came kinda close, but no cigar.

I think it's safe to say that the problem is more interesting
than it might at first appear. The interest-to-difficulty
ratio is pretty good IMHO. After all, it's just a quadratic,
so there's a limit to how hard it can be.

The point of the exercise is to propagate the uncertainty
from the inputs (a,b,c) to the result (x). A lot of people
talk the talk about propagation of uncertainty but have not
much experience actually walking the walk, especially when
it comes to calculations that require more than two or three
steps.

Any method of solution you can think of is fair game.

So ... any takers?

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Forum for Physics Educators
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_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l