-(18*(1-3*x)).*exp(-3*x.^2-(3*y+1).^2) ... - 6*(1-3*x).^2.*3.*x.*exp(-3*x.^2-(3*y+1).^2) ... - (10*(3/5-81*x.^2)).*exp(-
Posted: Mon Jul 11, 2022 12:46 pm
-(18*(1-3*x)).*exp(-3*x.^2-(3*y+1).^2) ...- 6*(1-3*x).^2.*3.*x.*exp(-3*x.^2-(3*y+1).^2) ...- (10*(3/5-81*x.^2)).*exp(-9*x.^2-5*y.^2) ...+ (20*((3/5)*x-27*x.^3-243*y.^5)).*9.*x.*exp(-9*x.^2-5*y.^2) ...- (1/3*(-18*x-6)).*exp(-(3*x+1).^2-9*y.^2)+2*x;3*(1-3*x).^2.*(-18*y-6).*exp(-3*x.^2-(3*y+1).^2) ...+ 12150*y.^4.*exp(-9*x.^2-5*y.^2) ...+ (20*((3/5)*x-27*x.^3-243*y.^5)).*5.*y.*exp(-9*x.^2-5*y.^2) ...+ 6*y.*exp(-(3*x+1).^2-9*y.^2)+2*y;
Problem #2: There is a stream in the park of Problem #1 above. The stream follows a path given by r(t) = <x(t), y(t)>. One feature about water is that it flows down a path of steepest descent, so that r'(t) = −Vu (x, y). If the river begins at a location r(0) =<-0.04, 0.66> determine the path of the stream along the surface of the park for values of t between 0 and 5, with a stepsize of 0.001. To do that use [0:0.001:5.0] as the second argument of the function ode 45. Note: The Matlab code for the required partial derivatives u, and u, are given by the following two expressions, respectively (which could be produced using Matlab's Symbolic Toolbox, if you have it): - (18*(1-3*x)) .*exp(-3*x.^2-(3*y+1).^2) ... 6* (1-3*x).^2.*3.*x.*exp(-3*x.^2-(3*y+1).^2) (3/5-81*x.^2)).*exp(-9*x.^2-5*y.^2) ... - (10* + (20* ((3/5) *x-27*x.^3-243*y.^5)) . *9.*x.*exp(-9*x.^2-5*y.^2) - (1/3* (-18*x-6)).*exp(- (3*x+1).^2-9*y.^2)+2*x; 3* (1-3*x).^2.* (-18*y-6). *exp(-3*x.^2-(3*y+1).^2) + 12150*y.^4. *exp(-9*x.^2-5*y.^2) + (20* ((3/5) *x-27*x.^3-243*y.^5)). *5.*y.*exp(-9*x.^2-5*y.^2) ... + 6*y. *exp(- (3*x+1).^2-9*y.^2)+2*y; ... (a) What is the height of the river, z, when t = 5? (b) What are the components of the position vector r(5)? Enter the x and y components (in that order) into the answer box below, separated with a comma.
Determine the length of the stream from its source at t = 0, to the end point where t = 5. Note that you will be measuring the length through three dimensions, using x, y, and z.
A straight pipe is run from the end of the stream at t = 5, back to the source of the stream at t = 0. The pipe runs along a straight line from one end to the other. What is the length of the pipe?
For the pipe in Problem #5 above, what is the (positive) difference in height between one end of the pipe and the other?
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Determine the length of the stream from its source at t = 0, to the end point where t = 5. Note that you will be measuring the length through three dimensions, using x, y, and z.
A straight pipe is run from the end of the stream at t = 5, back to the source of the stream at t = 0. The pipe runs along a straight line from one end to the other. What is the length of the pipe?
For the pipe in Problem #5 above, what is the (positive) difference in height between one end of the pipe and the other?