Woilo University KIOT Numerical Methods Group Assignment for ADD Students (20 %) 1. An engineer involved in construction requires 4800, 5800 and 5700m of sand, fine gravel, and coarse gravel, respectively, for a building project. There are three pits from which these materials can be obtained. The composition of these pits is Sand % Pit 1 Pit 2 52 20 Pit 3 25 Fine gravel % Coarse gravel% 30 18 50 30 20 55 How many cubic meters must be hauled from each pit in order to meet the engineer's needs? (Solve by using Crout's method). 2. The following systems of equations is designed to determine the concentrations (the c's in g/m3) in a series of coupled reactors as a function of the amount of mass input to each reactor (right-hand sides in g/day) - (17c1-2c-3c, = -25 -5c,-21c, 2c = 2 5c1 +5c2-22c3 = -3 Solve this system using the Gauss-Seidel method to a stopping tolerance of 5%. 3. The population of a certain town is given below. Year: Population: (in thousands) 1931 40.62 1941 1951 1961 1971 60.80 71.95 103.56 132.68 Estimate the population in the years 1976 and 2003. Also find the rate of growth of population in 1991. 4. In some determination of the volume v of carbondioxide dissolved in a given volume of water at different temperatures 6, the following pairs of values were obtained v 6 2 600 10 500 26 61 400 350 obtain by the method of least squares, a relation of the form v = a + be. 5. The velocity v (km/min) of a moped which starts from rest, is given at fixed intervals of time t (min) as follows: t: 2 4 6 8 10 12 14 16 18 20 V: 10 18 25 29 32 20 11 5 2 0 Estimate approximately the distance covered in twenty minutes. N.B:- Maximum No. of Students in a Group is 6. - Submission date is at Final Exam Date.