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*expires 2/18*) Fit the points by means of a quadratic function , using the least square method. First, do this step by step, as we did in class; then, use the built-in`Maple`command, described in the notes. Check that the two solutions agree. - 8.
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*expires 2/18*) Fit the set of points

with a line, using the least square method we used in class. You will see that this is not a good fit. Think of a better way to do the fit and use`Maple`to do it. Explain in your solution why you think your better way is better. - 9.
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*expires 2/18*) In this problem we will estimate the charge of the electron: If an electron of energy is thrown into a magnetic field , perpendicular to its velocity, its trajectory will be deflected into a circular trajectory of radius . The relation between these three quantities is:

where and are, respectively, the charge and the mass of the electron, and is the speed of light. The rest mass of the electron is defined as , and is about equal to Joules. In our experimental set-up the energy of the emitted electrons is set to be .

Use`read`to make`Maple`load and execute the commands in the file`electron_data.txt`, which is located in the`Worksheets`directory of the`mat331`account. This defines a list called`electron`. Each element of the list is a pair of the form , and these quantities are expressed in Teslas and meters. Use least square fitting to determine the best value for . [*Hint: Notice that the right hand side of (1) is just a constant--calculate it once and for all and give it a name. Then (1) is a very easy equation, which is linear in the unknown parameter . To verify your solution:*Coulomb].

Physical constants courtesy of N.I.S.T. - 10.
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*expires 2/18*) Prove relation (1), knowing the following physical facts: In relativistic dynamics Newton's law is replaced by

(2)

(3)