
How do I find A/B to complete the partial fraction? I can't use s = 0 o.o Did I make a mistake?
Posted 13 December 2012 - 03:24 PM
Kingroy: ( 4:40 PM - 02/10/14)
u can't own black people
Kingroy: ( 4:40 PM - 02/10/14) #ThanksLincoln
Posted 13 December 2012 - 03:28 PM
Kingroy: ( 4:40 PM - 02/10/14)
u can't own black people
Kingroy: ( 4:40 PM - 02/10/14) #ThanksLincoln
Posted 27 December 2012 - 08:17 PM
Edited by Waker, 27 December 2012 - 08:33 PM.
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Posted 24 January 2013 - 11:31 AM
. Given the general function F = c x^a y^b , where x ,y are variables and a, b, c are constants, derive the following general expression for the relative error:
sF / F = sqrt[ (a sx / x)^2 + ( b sy / y )^2 ]
s = little sigma
any help would be nice
Edited by MotherHugging Lexaeus, 24 January 2013 - 12:05 PM.
“Sorrow can be alleviated by good sleep, a bath and a glass of wine.” - Saint Thomas Aquinas
Posted 24 January 2013 - 12:27 PM
Assuming little sigma is a function, but that... isn't helping me comprehend anything that's going on here. Sigma means a lot of different things in different contexts, and the only one I've ever studied is the Number Theory context, where s(n) is the sum of divisors of n, but that definitely is not what's being used here.
Kingroy: ( 4:40 PM - 02/10/14)
u can't own black people
Kingroy: ( 4:40 PM - 02/10/14) #ThanksLincoln
Posted 24 January 2013 - 12:54 PM
Error stuff
Error Analysis
Gathering quantitative data requires the use of instruments. The resulting measurements will necessarily have errors due to the instrument’s inherent precision, the operator’s technique of measurement, and the randomness of the sample’s dimensions. Basic statistics allows for an accurate representation of the sampled data, due to these variances.
Precision
An instrument’s precision is taken to be the smallest possible measurement that is designated on the device. For example, a meterstick has a precision of 0.1 cm. Each measuring device has its own precision, which then determines the number of significant figures with which to record the data. The estimated error e is then often recognized to be half of the instrument’s precision used to measure the observable.
Accuracy
If a standard value (xstand) is known, an accuracy comparison with an observed value (xobs) can be found: [ (xstand - xobs) / xstand ] x 100%
0 % would represent the best accuracy, but does not imply the absence of errors. Accuracy is reported as negative when the observed value is larger than the standard value.
If a standard value is not known, it is possible to compare 2 observed values against one another. This can occur when comparing 2 differing methods of calculating the same quantity:
(xobs1 - xobs2) / [ (xobs1 + xobs2) / 2 ] x 100%
In this case the denominator is found from the average of the 2 observed values, so that neither value is treated as a standard (both are treated with equal weight).
Mean
The mean, or average of a set of similar measurements is simply found by the sum of all data divided by the sample number N: x = S xi / N
Standard Deviation
The standard deviation then determines the variance of the sample data with respect to the mean: sx = sqrt [ S ( xi – x)2 / (N-1) ]
Standard deviation is an example of an absolute error and has the same units as the sample data. It provides a confidence interval with regard to future measurements, or a standard value. Statistically, the following expectations are noteworthy:
1s = 68 % 2s = 95 % 3s = 99.7 %
The relative error can then be found according to sx / x, and is often expressed as a percentage by multiplying by 100. This relative error then gives a reasonable expectation of the desired accuracy for the experiment.
Propagated Error
Consider a physical quantity F that depends on several observables F ( x1 , x2 , x3, …xn ).
If the standard deviation of each observable is known, then the propagated error (total error) can be found, and generally depends on all observable errors according to:
sF = sqrt { [ s1 ( ¶F / ¶x1 ) ]2 + [ s2 ( ¶F / ¶x2 ) ]2 + . . . + [ sn ( ¶F / ¶xn ) ]2 }
¶F represents the partial differentiation with respect to each variable x. If standard deviations are not known for all of the individual variables x (for example, s1 since perhaps only 1 measurement was performed) , then estimated error values (e) may be substituted.
The total relative error can then be found according to sF / F, multiplied by 100 for a percentage value.
Typical Propagated Error Functions
The function F = x + y where x ,y are variables yields sF = sqrt [ ( sx )2 + ( sy )2 ]
The function F = c xa yb where x ,y are variables and a, b, c are constants yields
sF / F = sqrt [ (a sx / x)2 + ( b sy / y )2 ]
¶ = partial differential
s = little sigma
Edited by MotherHugging Lexaeus, 24 January 2013 - 12:56 PM.
“Sorrow can be alleviated by good sleep, a bath and a glass of wine.” - Saint Thomas Aquinas
Posted 24 January 2013 - 01:36 PM
Alright, cool. I'll write out steps for you.
sF = sqrt( (sx*ac xa-1yb)2 + (sy*bc xayb-1)2 )
AND
F = sqrt( (cxayb)2 )
since that simplifies to what you started with. Inverse functions. :D
So:
sF/F = sqrt( [ (sx*ac xa-1yb)/(cxayb) ]2 + [ (sy*bc xayb-1)/(cxayb) ]2 )
sF/F = sqrt( (a*sx/x)2 + (b*sy/y)2 )
since c and yb cancel in the first, and the x exponents combine to give x in the denominator. Same for the second term, except the xa cancels and a y gets left in the denominator.
Kingroy: ( 4:40 PM - 02/10/14)
u can't own black people
Kingroy: ( 4:40 PM - 02/10/14) #ThanksLincoln
Posted 24 January 2013 - 08:50 PM
Let xi be the number of books in box i, with i ∈ [1,6] ⊆ ℕ.
Then i=1∑6 xi = 43, by assumption.
We proceed by contradiction.
Suppose that xi ≤ 7 for all i ∈ [1,6].
Then we see that i=1∑6 xi ≤ 7 * 6 = 42.
By our assumptions, this sum is exactly 43, which lies outside the above range.
This is a contradiction.
Therefore, for some i ∈ [1,6], we have that xi > 7, or that xi ≥ 8 □
But, really, you can do this proof in much less time with as much clarity. You know. How you did it. >.>
Kingroy: ( 4:40 PM - 02/10/14)
u can't own black people
Kingroy: ( 4:40 PM - 02/10/14) #ThanksLincoln
Posted 02 February 2013 - 06:13 PM
...V HAS COME TO...
Posted 02 February 2013 - 07:18 PM
Set up a system of equations. :0
You want:
a*[1,2] + b*[3,h] = [k,2]
which becomes:
a + 3b = k
2a + hb = 2
First, do the cases a = 0, b = 0, and a=b=0, so that you can divide by b later.
a=0
3b = k
hb = 2
By assumption, b =/= 0 (implies k =/= 0), so
h = 2/b
k = 3b
b = k/3
h = 6/k
b=0
a = k
2a = 2
a = 1
k = 1
h can be any number (in the stated range?)
a=0,b=0 doesn't work.
now for both non-zero, it gets interesting.
k = a+3b => a = k - 3b
h = (2a - 2)/b
h = (2k - 6b - 2)/b
= blahblahblah
not my homework you can figure out the rest I guess.
Kingroy: ( 4:40 PM - 02/10/14)
u can't own black people
Kingroy: ( 4:40 PM - 02/10/14) #ThanksLincoln
Posted 07 February 2013 - 02:02 AM
What might be pretty bad is I took differtional equations and super aced it and i can't remember any of it. Well, hopefully messing around with this will refresh my mind.
“Sorrow can be alleviated by good sleep, a bath and a glass of wine.” - Saint Thomas Aquinas