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3D AssignmentComplete the tableName of ObjectRectangularCylindricalSphericaly =Xr =5Sphere (centered at the origin radius 2)...

Question

3D AssignmentComplete the tableName of ObjectRectangularCylindricalSphericaly =Xr =5Sphere (centered at the origin radius 2)

3D Assignment Complete the table Name of Object Rectangular Cylindrical Spherical y =X r =5 Sphere (centered at the origin radius 2)



Answers

Sketch the set (described in cylindrical coordinates).
$$ r=2, \quad z=3 $$

So we're gonna be converting from rectangular to both cylindrical and spherical. Um So we're gonna be having X squared plus y squared plus b squared. Um equaling 25. And we know that if we did cylindrical this would be r squared plus Z squared equals 25. But if we do um satirical, you know this whole thing is going to be row squared. So row would equal five. Then we can also look at other options such as um well consider um for ex crib for X cred Weisberg, this one would be a little bit more clear with regards to rectangular unlike the or the cylindrical unlike the previous one because that can be turned into our square and then this would be left as is however if we wanted to convert it to um empirical, we'd want to keep in mind that there's going to be this X squared, y squared Z squared. So we might be able to get in terms of row feta and feet

Spirit called X squared plus y squared equals three Z. Square. So um this is rho squared sine squared fee, coastline squared data plus rho squared sine squared fee signed squirt data equals three rose squared. So sine squared feet. So divide the roads squares out. Then from these two over your factor out. Sign squared fee and you get co sine squared data plus sine squared data. And that equals to three. Cosine squared fee. Because I? M squared plus sine squared. That's your favorite identity. It's equal to one. So now I have sine squared fee Equals three Coastline Square fee. Just wanna Take the square root of both sides. So sign fee equals plus or -23 coastline fee. Okay so I'm going to divide by coastline fee and I get signed fee over cosine fi equals plus and minus the square root of three. So that's the tangent of fee equals plus or minus the square to three. Sofia's fiver three for the positive square root and then for the negative square root 25 or three because remember fee has to be Between zero and Pi. So here's the picture, 60° done this way and then rotate that all the way around the circle. And then took by over three so 120°. And that give you the other half of the cone

In this question even see equal squared on the three times x squared plus y square here in a spherical coordinate disease. Every coach to the times that goes on number five and under working. So I will have the tree now x squared. It would be in the spherical coordinate X Graco jet Oppose squared times The signs scrammed of five times Go size square on the tee. Time for the White Square. Gather boughs Where Time, Cy Square and the five time size Gramma Tita. And it was signified. We should get it. Will you go to this grassroots off the three. Now I can factor that foursquare and sigh Square five outside inside handed cosas square teeter plus size square, Tita. But it's not just want equal to one and therefore should get in the bro. Ghost five Every coated a square root under three wells. Wear size grab, Tita. And from here we go again In the book, go side five equal. Judah Now score with three temps, bro. Times signed a five on here. Notice. Done because five in the interval. Vagenas soldier by and I found a sigh Fund of five. Maybe, uh, quite the ICO Ju zero now for this only can remove the square with Onda square There were cancelled and then again, this time of five. Now and now I'm divide both side by this quantity on wounded by everything here by the pro Comes goes under five donation camp Iko Judah one equal Jenna Skurdal a three and then this one. You have the dungeon under five. It means not a dungeon under five equals one underscored about three on decent implies that the five most ico Judah Uganda wanted the three. So most in Cochin buyout up, uh, six and just give me the answer here.

So we're gonna be converting from rectangular to both cylindrical and spherical. Um So we're gonna be having X squared plus y squared plus b squared. Um equaling 25. And we know that if we did cylindrical this would be r squared plus Z squared equals 25. But if we do um satirical, you know this whole thing is going to be row squared. So row would equal five. Then we can also look at other options such as um well consider um for ex crib for X cred Weisberg, this one would be a little bit more clear with regards to rectangular unlike the or the cylindrical unlike the previous one because that can be turned into our square and then this would be left as is however if we wanted to convert it to um empirical, we'd want to keep in mind that there's going to be this X squared, y squared Z squared. So we might be able to get in terms of row feta and feet


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