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Mth 277
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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Practice Test Question 1 cont
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1. Use double integration to find the center of mass of the region x^2 + y^2 <= 9^2, y >= 0, if the density function is delta(x,y) = 5 * (x^2 + y^2)
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Quick question: Are we supposed to use the delta function as what we integrate? So I have the setup up integral sign from -9 to 9, then another integral sign from 0 to sqrt(81-x^2) and then would it be the 5x^2+5y^2 which is what we are integrating??
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The delta(x,y) function is the density.
If you need to find mass you need to multiply each area increment by the density to find its mass, then sum those mass contributions to form a Riemann sum, then take the limit to get the integral.
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Then dydx. Also, you lost me when you solved for the center of mass of the region mainly with the maximum density and then making the approximation that you did with the less than half to give you 300. This all lead to your answer but it was not very clear how. I am just wondering if this is something I will need to do on the test and I am going to need to see clearly how all those steps are carried out to do so. I am getting a better understanding piece by piece so I thank you for your explanations. It really is helping me learn!
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You appear to be referring to something I posted prevoiusly, but you haven't included that information.
I need to see what I did in order to respond to this question. The general principle is that your questions need to be self-contained. It would quadruple the time it takes to respond to students if I had to search for my previous responses.
I can say that I was probably using an approximation as an indication of a rough answer for comparison with your result.
To find the center of mass about the x axis, for example, you have to find the total torque due about that axis, to the weights of the various regions, then divide this by the total mass.
The torque associated with each area increment is the product of its mass and its distance from the axis. For the torque about the x axis the torque would be y_hat multiplied by the mass contribution of the region.
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