ME201 Midterm: ME201 me201mw06q

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Midterm examination: culham, this is a two-hour, closed-book examination, where you are permitted to use: Schaum"s - mathematical handbook of formulas and tables. One 8. 5 in. 11 in. crib sheet. (one side: there are 6 questions to be answered. Read the questions very carefully: clearly state all assumptions, it is your responsibility to write clearly and legibly, reduce all equations to their simplest possible form. ~r(t) = i(2 ln t) j 1 t. ~r(t) = i (et cos t) + j (et sin t) + k (et) when t = 0. Find the dimensions (x, y, z) of a rectangular box of maximum volume that can be contained within a sphere with a diameter of d = 1 m, as shown below. Clearly demonstrate that this is the maximum volume. Note: the diagonal of the box will equal the diameter of the sphere.

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