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You are not logged in. #1 20101114 04:38:57
Help me do an exercises.Suppose you are climbing a hill whole shape is given by the equation z=1000  0.005x^2  0.01y^2, where x, y and z are mesured in meters, and you are standing at a point with coordinates (60, 40, 966). The positive xaxis points east and the positive yaxis points north. Last edited by seit (20101114 04:39:44) #3 20101114 13:46:21
Re: Help me do an exercises.Hi seit;
Currently, I am the only one in here and there are other questions. I am swamped at the moment.
To be walking south in your system means for the y coordinate to be decreasing and the x coordinate to remain constant. Obviously you are ascending until you get to (60,0). Then what happens?
To walk Northwest means x is decreasing as y is increasing, both at the same rate. So you have this table. Looks like you are descending. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #4 20101114 17:40:10
Re: Help me do an exercises.Hi;
I will try to remember what he told me and do the problem by myself. Taking partials of f(x,y) we get: The vector is: Now dot product g with the unit vector for south [0,1] It is positive you are going uphill as I already showed you with a gradient of .8 Now dot product g with the unit vector for northwest [1/sqrt(2), 1/sqrt(2)]. So you are going downhill with a gradient of .141421 For c) The slope is largest in the direction of the gradient g. The rate ascent is the norm of g, It is positive so that is the steepest ascent. To get the angle with the horizontal you just take the arctan of the norm of g which is 1. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #6 20110112 19:46:34
Re: Help me do an exercises.Hi mano25; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 