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Student Support Forum: 'Plotting non-linear values and solving' topicStudent Support Forum > General > "Plotting non-linear values and solving"

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Author Comment/Response
sk597653
10/20/12 4:47pm

In Response To 'Re: Re: Re: Plotting non-linear values and solv...'
---------
OK, here's what support helped with:
Define C-
c = 0.000011501

Define b and y1-
b = 1 + k c + k x/(2 s)
k x
1 + 0.000011501 k + ---
2 s

y1 = (Sqrt[ (b - (b^2 - 2 k^2 c x/s))])/(2 k c)

2
k x 0.000023002 k x k x 2
43474.5 Sqrt[1 + 0.000011501 k + --- + ---------------- - (1 + 0.000011501 k + ---) ]
2 s s 2 s
-------------------------------------------------------------------------------------
k

***we are calling this equation y1, but it actually is set equal to the y values from my list of data. How does the FindFit or Solve function know to set the y values, if we are calling it y1 and never define it as the y values in the coordinates? Similarly, at this point my x in the equation below is showing blue, this denotes that x has not been defined a value, so again does the FindFit or Solve function know to assign the coordinate {x,y} values once data has been defined?***

Define data-
data = {{0.0, 0.0}, {0.0000079, 0.357}, {0.0000119,
0.400}, {0.0000158, 0.514}, {0.0000198, 0.565}, {0.0000208,
0.748}, {0.0000248, 0.754}, {0.0000277, 0.880}, {0.0000329,
0.896}, {0.0000365, 0.937}, {0.0000395, 0.927}, {0.0000456,
0.992}, {0.0000484, 0.949}, {0.0000527, 0.995}, {0.0000589,
1.03}, {0.0000599, 1.02}, {0.0000654, 1.07}, {0.0000739,
1.05}, {0.0000735, 0.995}, {0.0000782, 0.951}, {0.0000793,
0.946}, {0.0000831, 0.985}, {0.0000900, 0.996}, {0.0000971,
1.01}, {0.0000962, 1.02}}

Out- -6
{{0., 0.}, {7.9 10 , 0.357}, {0.0000119, 0.4}, {0.0000158, 0.514}, {0.0000198, 0.565}, {0.0000208, 0.748}, {0.0000248, 0.754}, {0.0000277, 0.88}, {0.0000329, 0.896},

{0.0000365, 0.937}, {0.0000395, 0.927}, {0.0000456, 0.992}, {0.0000484, 0.949}, {0.0000527, 0.995}, {0.0000589, 1.03}, {0.0000599, 1.02}, {0.0000654, 1.07},

{0.0000739, 1.05}, {0.0000735, 0.995}, {0.0000782, 0.951}, {0.0000793, 0.946}, {0.0000831, 0.985}, {0.00009, 0.996}, {0.0000971, 1.01}, {0.0000962, 1.02}}

Finally try to FindFit-
FindFit[data, y1, {k, s}, x]

Out- error message, not real numbers and
-6
FindFit[{{0., 0.}, {7.9 10 , 0.357}, {0.0000119, 0.4}, {0.0000158, 0.514}, {0.0000198, 0.565}, {0.0000208, 0.748}, {0.0000248, 0.754}, {0.0000277, 0.88},

{0.0000329, 0.896}, {0.0000365, 0.937}, {0.0000395, 0.927}, {0.0000456, 0.992}, {0.0000484, 0.949}, {0.0000527, 0.995}, {0.0000589, 1.03}, {0.0000599, 1.02},

{0.0000654, 1.07}, {0.0000739, 1.05}, {0.0000735, 0.995}, {0.0000782, 0.951}, {0.0000793, 0.946}, {0.0000831, 0.985}, {0.00009, 0.996}, {0.0000971, 1.01},

2
k x 0.000023002 k x k x 2
43474.5 Sqrt[1 + 0.000011501 k + --- + ---------------- - (1 + 0.000011501 k + ---) ]
2 s s 2 s
{0.0000962, 1.02}}, -------------------------------------------------------------------------------------, {k, s}, x]
k

***Now, I am not fully convinced that y and x in the equation are using the coordinate values in the calculation.

Furthermore, when I picked the second coordinates, 0.0000079=x and plugged it into the equation, using 2900000 as k and 0.94 as s, I was able to calculate a value close to 0.1. If I am able to do it by hand, why isn't the program able to?

Do you think that the fact the equation is defined as y1 could be an issue, and that my x is blue? I'm really suspicious that the equation is not calculating with the coordinate {x,y} from data. How can I be sure that it is?

OY! Thank you for your help :) k probably ranges from 10^4 --> 10^7 while s would probably range from 0.5-2.0



Attachment: Samantha2.Reply (4).nb, URL: ,

Subject (listing for 'Plotting non-linear values and solving')
Author Date Posted
Plotting non-linear values and solving sk597653 10/17/12 3:05pm
Re: Plotting non-linear values and solving Bill Simpson 10/17/12 11:22pm
Re: Re: Plotting non-linear values and solving sk597653 10/18/12 12:57pm
Re: Re: Re: Plotting non-linear values and solv... Bill Simpson 10/18/12 3:47pm
Re: Re: Re: Re: Plotting non-linear values and ... sk597653 10/20/12 4:47pm
Re: Re: Re: Re: Re: Plotting non-linear values ... Bill Simpson 10/22/12 02:06am
Re: Re: Re: Re: Re: Re: Plotting non-linear val... sk597653 10/23/12 10:40am
Re: Re: Re: Re: Re: Re: Re: Plotting non-linear... Bill Simpson 10/23/12 11:57pm
Re: Re: Re: Re: Re: Re: Re: Re: Plotting non-li... sk597653 10/26/12 4:22pm
Re: Re: Re: Re: Re: Re: Re: Re: Re: Plotting no... Bill Simpson 10/26/12 9:53pm
Re: Re: Re: Re: Re: Re: Plotting non-linear val... sk597653 10/23/12 11:09am
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