Consider a sample of beams with elliptical cross section. the semi-major axis a and semi-minor axis b are measured and found to have means a¯ and ¯b and standard deviations sa = 0.02¯a and sb = 0.03¯b, respectively. compute the uncertainty in the corresponding beam cross-sectional area a, cross-section perimeter p , and moment of inertia i. that is, compute ua, up , and ui . assume the uncertainty of each term is equal to the standard deviation, i. e., ua = sa and ub = sb. to the extent possible, also report the relative uncertainties ua/a, up /p , and ui/i, simplified as much as possible.