Propagating the error through a multi-variable function three variables are measured to be a = 12 . 3 ± 0 . 4, b = 5 . 6 ± 0 . 8 and c = 89 . 0 ± 0 . 2. calculate the mean and uncertainties in z when it b and c z = a − b , via (iii) the relations: z = a − b a + b , 2 × is related to a , z = a + b , (ii) z = ab c , (v) z = arcsin b a , (vi) z = a × b (vii) z = ln ( abc ) , (viii) z = exp ( abc ) , z = a + tan b c , (x) z = 10 abc