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(3x 3iy) dz; C is the contour in the figure shown below_...

Question

(3x 3iy) dz; C is the contour in the figure shown below_

(3x 3iy) dz; C is the contour in the figure shown below_



Answers

Sketch the region described by the following spherical coordinates in three-dimensional space. $$\rho=\csc \phi$$

So you have these region, you know, he's very cool. Accordance. Very cool. You know, for the dimensional space. It should be up here. The sea picks the Y axis of a point. We're here, miss. Very cold. Gordon. It is described to row. There are and, uh b d sandaled there. Crow is this distance Every project here on the X y plane. I said I will BBC jungle So that we have that to see co ordinate for that point is gonna be grow course The X coordinate will be role sign he course fitter. I wonder why is no so he signed there. Sign off. So course he can physical too. One of our site should have these condition. And then you will reply whenever side by Sign off, Vera or these questions You have She what I'm saying? Off it's a sign of zero. Rove, get that role. Selfie you, sir, has to be smaller down. These with pencil three on the road. Selfie is, uh, the distance. Least us. Do you the C axis. So what this region is saying is that the distance to the C axis gonna be beer down three. So that will give us. Ah, like a ceiling there over these three. But ah, extends, uh, were thrown into the sea. Axe Wilder is actually the Z X. No. Why about this Knows there should be three. So it is these, uh you see their asses, huh? She's, uh this has come his mortar Is the field similar with interior. So my nut seeing there? Well, obviously Cherries.

So here we want to assume the ice strip of our cardboard. So what we end up getting this problem is with the cardboard figure that we have, Oh, and the lines that were given since we're going from A to B. Um and then we have the different bounds that can be written as F of X minus G of X. So the ffx minus G of X, that's where it's founded above by fx and below by G of X. So we're going to bounded by those functions. And then after that, you want to multiply that by the density function, which we're going to call Kiev X. So once that's the case, that's going to be the final function, um and once were given specific values, we'd be able to calculate this more directly.

Very goal coordinates and three dimensional species. Bring on to see the region trained by role in course to three to the point in the three dimensional spacing. It's very good corn units. You have some point here. Um, with this kind of there point to grow. Yeah, he We're always this. These things for the origin row. He is this angle. I'm, uh there is this angle the position on the next plane? Sort of the young. See? She will do Row course three x for me with Rome. Sign you Course. Why? You should want to grow sign sign. You know Onda. Uh well, let me say that Rosie Free were saying that all the points such that the beast to the origin is he won't do three. Our rules are that you are sphere, but all ones were here, but, uh, our key distant the origin So nobody's most fear. So it's fear. Well, how are these? Uh, three. When these, uh, resolve 0.3 geo zero. That morning, the Syrian 30 This one over here would be 003 Yeah, Cartesian coordinates. Cities are last year

So for this problem, we're trying to find the area of all of the black figures that I have drawn below combined on dso kind of an easy way to do this is to find the area of the Red triangle that's missing from all the box figures combined and then subtract up from what the area of an entire rectangle of the shaded figure would be if the triangle was not cut out of it. So to first find the area of the rectangle. The formula for an area of a rectangle is base times height, which in this case would be 20 times 10 um, and then that that area would be 200 then the area of the triangle that's cut out is 1/2 base times height, and that would be 1/2 times. The base of the triangle is 11 and the height of the triangle is given a seven point five, so that would be 11 times 7.5. Divided by two is people to 41.25 so the area is equal to 200 minus 41.25 which is 1 58.75 centimeters squared


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