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  3. q 3. the total mass of a variable density rod is g

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

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Question

Advance Math

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

m=

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

L = the total length of the rod. The following datahave 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

?, 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 thecompeting species model

de?ned by

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

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

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