Question: A student measures five lengths: a = 50 ± 5, b = 30 ± 3, c = 60 ± 2, d = 40 ± 1, e = 5.8 ± 0.3 (all in cm) and calculates the four sums a + b, a + c, a + d, a + e. Assuming the original errors were independent and random, find the uncertainties in her four an-swers. If she has reason to think the original errors were not independent, what would she have to give for her final uncertainties? Assuming the uncertainties are needed with only one significant figure, identify those cages in which the second uncertainty (that in b, c, d, e) can be entirely ignored. If you decide to do the additions in quadrature on a calculator, note that the conversion from rectangular to polar coordinates automatically calculates (√x2 + y2) for given x and y.