Q 3. The total mass of a variable density rod is given by m= where m...

Q 3. The total mass of a variable density rod is given by

m=

where m = mass, ρx= density, Ac(x) = cross-sectional area, x = distance along the rod, and

L = the total length of the rod. The following data have been measured for a 20m length rod.

Determine the mass in grams to the best possible accuracy.

x,m	0		2	4	6	8	10	12	14	16	18	20
ρ, g/cm²		4.00	3.98	3.95	3.89	3.80	3.74	3.6	3.55	3.41	3.37	3.30
Ac, cm²	100		102	103	106	110	114	120	130	133	1142	150

Q 4.With the aid of fourth order Runge-Kutta method, solve the competing species model

deﬁned by

where the populations and are measured in thousands and t in years. Use a step size of

0.2 for 0 ≤ t ≤ 2 and plot the trajectories of the populations with Matlab or GNU Octave.

Expert Solution

Colby Messinger answered 2 years ago

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