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Find the coordinates of the centroids of the given figures. Each region is covered by a thin, flat plate. A highway marking pylon has the shape of a frustum of a cone. Find its centroid if the radii of its bases are $5.00 \mathrm{cm}$ and $20.0 \mathrm{cm}$ and the height between bases is $60.0 \mathrm{cm}$.

Calculus 2 / BC

Chapter 26

Applications of Integration

Section 4

Centroids

Campbell University

Baylor University

University of Michigan - Ann Arbor

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she's a coon. Um, readies are night is so if you want to place these in day X Y c, it's places 12 year so cool on Duh. Oh, it's, uh, upside down. So hungry base, He's want up. So we have here on high. I'd each on these descends Here is our are I want the friend this central eat this enjoyed so Kobe's one x y and see, uh, by symmetry evals the rotations around Thera in cylindrical coordinates the armory six people to the average. Why? Which you cannot be serious. We need to find What is that? A little reserve Risch. See, I see. So that should be able to recall the surface. Yes. Way would only be considering the lateral surface without the base so really being around this surface of, uh so these c bar would be control no one over the area office. Yeah, and then dangerous over is we'll see. Ah, there's the soon when this is a differential. Where you undying? Uh, well, these region can be described. Um, us. Well X is equal to our course dinner. Why? You should go to our scientific. You'll be up here. Ah, so I see the bill are you know that Ah, for C equals age. The well, it's called these, uh, he's, uh we're not there. So the distance or not, she people too, are not this us. Berries are not so so that Well, uh, all right, this is the line is gonna be a line that has ah, well, see, divided by age times are not because, Well, that he's, uh, home. And that should be are so that what would you plug in C equals tool, which you get the h castles with the age and then our is gonna be able to or not. But we wanted to write C in terms of peace, but that c is gonna people toe there divided by are not ah, them's h So, uh, So they see Cordant. The surface is gonna be Are we are not Does each and so Aled these differential Verria inferential area. I was gonna be go to our there are cross probably. Car supplier comes the Are you there? So these is Victor, is did it that more? That is determinant of this matrix. My J. Okay, These victory there is that determine So here we have a very British. It's so the components with respect. So for ex, you would have people fix that's gonna be minus are saying saying of fear for why our course funding for, uh, see you the it's you on the directive. With respect to, um you are being, uh So our clothes are sign or filler run for K is gonna be h Well, they are Not that these these victor, um is gonna have I component is gonna be are temps age or are not him schools? No. So the sleeves up again, j reminders that claims that So plus, are those age or age we are not We are not, uh, them's sign off their dance g for the cake component would be Are so minus are so I squared. Uh huh. So we r squared, Um, when the entire square closes. Quote on that for the came component sort of these, these Victor is gonna have. So you have. Well, my these would be that a square soul. Uh uh. He should be that we would expect to are so there should be in order. So these comes out like our So when we're computing these These were here. Should be the addicts of the component with respect to our So they had these X with respect water privy. Just co sign off There they will see just time. So that is correct there and then that is clear with the where are not well Davis Square. On that time, schools squared. But for these comes with same square What sine squared and then for daddy would be just Ah, well, this is one So plus r squared on the middle. Easy is one. So it would be began factory are are screwed wolf each. We are not square glass one. So that is the differential. Are is the normal victories not? No Until when we're doing that. When were interpreting, See? Integrating Oh, sees you are them's age over are not We'll be interviewing that this from being these from the differential Are EMC squared off age? Well, they're not plus one. The are the fear. Ah, so well are those from zero up to age No. Two are not Eichler not Montero's all the way around 30 to buy. So these would be well the drill. We're gonna be young. This will be just constant so each over are not times Discworld off age We are not squared. Plus one Dana would have the injury go y squared er which is are you thirds to the, uh all that evolution between are not a zero. So are not cube hurts. And in that times interval from zero to buy Oh, fairer. Which movies is to buy? Um, sure that these would be Oh, well, we can to simplify things you can right is fraction. So you just square Yes, are not squared Well, they are not squirt so that if you have the square it on that this is equal to this choir it on top off the and then these comes up are not so these This whole thing would be age times the square root h squared plus are not squared over So are not dance or not. Terms are not from Dana are not just their power. Get out of my three. Them stood by uh so the's councils to close their so this vehicle to to buy terms age times are not have to square it off age square plus iron not squared hurts So you have done and then. Well, these which is that, but the area the there no would be just, uh, doing these. We don't see. So the area kind of equal leader from Syria to buy, I promise you two are not of these. Oh, we are. That was this quaint little mm. We are not squared. Was one the are deep there. So that is the area. And then we'll be drilling off our PR. He's, uh, r squared house. So Well, that way, today s we can pull this out on being evaluate the interval so that it would be square it off age, squirt. Well, that fraction is he going to each square Plus are not squared but are not squared. Have been, huh? Dot Times are not squared Hopes. Something that times angel from Syria to five. If there are you see by so that these it's gonna be ableto the H squared. Plus are not squared from Dean over are not Times are not squared hubs. That was to buy ah that these councils on battles councils. So it would be by Thames my ironwork square root off age square. Blessed are not squared. So that is there the area. Lundeen. Well, we need to divide these baby area. So the overage body for C with people too. These number to buy? Yeah, times each. That is. They're not Times the square root are not square plus age squared parents. Uh, well, that divide my knees by stems are not screwed for each square Plus are not squared. Uh, but this number she wanted that number 21 when dividing fractions is the same us These multiplied by that divided by dismal reply like that. So that becomes to buy a judge are not It's quite rude from Dean. You know, my for me by are not Does this square root So, uh, very nice. This is clothes. What's council are not councils, my casuals. So that should be ableto to age third's. So that really average value for C. But, um, one thing to note is that Ah, well, that is replays. The cone, like with the base, went up. So my first see you would be you have, um, to age thirds. But would they with the bay some top? Well, bay sometimes. So that we for corn with base on So which are usually you draw a cone with the race on the bottom. So if you wanted to see what is there others see for this case? You? Me too. I think these values We got hatch from the so so struck each from bad value. Let me have better so to third's which you did that to be rich third's. So if the basis on the bottom would be H thirds, no cases to each hurts.

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