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I didn't really know on the forum to put this, it isn't really homework or coursework, but it is a very small part of a project I am doing for uni, so essentially it could be worth marks so here it is, anyway...
Im rubbish at combining errors and was wondering if someone could just guide me on this sepcific issues... I am trying to get the error in a pythagorean distance, i.e the error in...
Distance =(x2 + y2 + z2)1/2
Now I have all the errors of x, y and z respectively. My problem is that I don't think I am combining the error corrrectly, see section3...
So what I am doing is to say...
1. x*x, y*y and z*z are all combinations of errors, for all of which I have been using...
z = axy
where a=1, x=x, y=x, such that...
E(x2) = 2x3(E(x))2
which is the same for the error in y2, and the same for the error in z2.
2. next I say, find the error in x*x + y*y + z*z, for which I use...
z = ax + by + cz where a=b=c=1
where the error is...
(E(z))2 = a2(E(x))2 + b2(E(y))2 + c2(E(z))2
I work all this through and get a value for the error in x*x + y*y + z*z, then...
3. error in distance = (x*x + y*y + z*z)1/2, for which I use...
z = axb where a=1, b=0.5
this uses the formula E(z)/z = bE(x)/x
So I rearrange all this, calculate the individual errors, but I get a number that is just plain wrong.
So, in summery of how I do it...
1 - Work out the error in
----a = x*x
----b = y*y
----c = z*z
2 - work out the error in...
----d = a + b + c
3 - work out the error in...
----e = d1/2
Is this a correct way of going about it ?
Thank you!
Homework Statement
Im rubbish at combining errors and was wondering if someone could just guide me on this sepcific issues... I am trying to get the error in a pythagorean distance, i.e the error in...
Distance =(x2 + y2 + z2)1/2
Now I have all the errors of x, y and z respectively. My problem is that I don't think I am combining the error corrrectly, see section3...
The Attempt at a Solution
So what I am doing is to say...
1. x*x, y*y and z*z are all combinations of errors, for all of which I have been using...
z = axy
where a=1, x=x, y=x, such that...
E(x2) = 2x3(E(x))2
which is the same for the error in y2, and the same for the error in z2.
2. next I say, find the error in x*x + y*y + z*z, for which I use...
z = ax + by + cz where a=b=c=1
where the error is...
(E(z))2 = a2(E(x))2 + b2(E(y))2 + c2(E(z))2
I work all this through and get a value for the error in x*x + y*y + z*z, then...
3. error in distance = (x*x + y*y + z*z)1/2, for which I use...
z = axb where a=1, b=0.5
this uses the formula E(z)/z = bE(x)/x
So I rearrange all this, calculate the individual errors, but I get a number that is just plain wrong.
So, in summery of how I do it...
1 - Work out the error in
----a = x*x
----b = y*y
----c = z*z
2 - work out the error in...
----d = a + b + c
3 - work out the error in...
----e = d1/2
Is this a correct way of going about it ?
Thank you!