Question

Find the mass of the plate D bounded by the given lines if the surface density of the plate p(x,y)[g/cm^2] is the known function:
p(x,y)=(2x+5y)/(x^2+y^2),
and the plate D is bounded by the following lines;
x^2+y^2=9; x^2+y^2=16; x=0; y=0 (x>0, y>0)
Make a sketch, show the plate configuration and present your answer with the corresponding dimension assuming that spatial variables x and y are in cms.

Answer 1

Okay, Do you have a clue what the plate currently looks like?

Answer 2

No what I wrote was all that was given

Answer 3

Okay, Give me a sec to work this out.

Answer 4

Okay, are you still there. I think I got it.

Answer 5

yep sure am

Answer 6

Okay, so your desired mass M would be:

Answer 7

You would be integrating only a section of the bounded area

Answer 8

Does that help?

Answer 9

Yes but where did the boundary conditions of 3 and 4 come from?

Answer 10

Okay, if you sketch the circle, one being with a radius of 3 and the other of a radius of 4.

Answer 11

x^2+y^2=9; x^2+y^2=16; first circle has a radius of 3 and the second a radius of 4

Answer 12

Yes sorry just saw that as its taken from the given lines

Answer 13

and since you only have all positive values, you would be integrating only up to to pi/2

Answer 14

first quadrant of the circle correct?

Answer 15

Right

Answer 16

That's what this states x=0; y=0 (x>0, y>0)

Answer 17

x greater than zero and y greater than zero

Answer 18

Man, I didnt see that but its so obvious when you explain it. Thanks for that!
So my sketch is just the 2 circles shown and then the area inbetween the circles is what we are finding. What the question asking when it says "with the corresponding dimension"?

Answer 19

Yes, there are 2 circles, and it is between these two circles.

Answer 20

Nice! got that bit, what about the last bit of the question when it refers to the "dimension"?