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A surgeon is faced with the problem of grafting an artery. She wishes to minimize the resistance to the resulting flow.
The resistance R to the laminar flow in a pipe L is given by Poiseuille's law: R = L/ r^4
This is where L and r are the length and radius respectively of the pipe. The graft must run from a main artery of radius r_1=0.5 cm to a point 5 cm from the main artery, using a connecting artery of radius r_2=0.46.
Coordinate the problem by assuming that the main artery runs along the x-axis, so the connecting artery needs to run to the point (10,5) and the graft occurs at (x,0).
Answer the following questions in terms of x.
x_{opt} =
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Part 2: In this part we will again be multiplying two functions and calculating the Fourier Transform of the product. The first function is y1(t) = cos(20πt).
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