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Point) Find Mz , My; and 2,y) for the laminas of uniform density p bounded by the graphs of the equation_ y = 2} y = 4Express your answer in term of pMI My...

Question

Point) Find Mz , My; and 2,y) for the laminas of uniform density p bounded by the graphs of the equation_ y = 2} y = 4Express your answer in term of pMI My

point) Find Mz , My; and 2,y) for the laminas of uniform density p bounded by the graphs of the equation_ y = 2} y = 4 Express your answer in term of p MI My



Answers

Find $M_{x}, M_{y},$ and $(\overline{x}, \overline{y})$ for the laminas of uniform density $\boldsymbol{\rho}$ bounded by the graphs of the equations.
$y=-x^{2}+4 x+2, y=x+2$

Giving the equation we have Y. Y. To be equal to minus X. Quick Platz four S last two then why? To be called two X plus two. This is the equation which is bounded by luminous of uniform density. So the first is to find the mass mm. So um is going to be equal to Tomorrow which is the density from 0 to 3 of this situation. So I first have my next X squared plus four X. Last two minus The 2nd equation. X. Last two. Oh dear. It's so if you simplify so you can face simplify what you have in the brackets thing you take the integral of that. And this is going to give us minus room is cube divided by three Bloods three X squared divided by sue. The interval from 0 to 3. The lower ends. Embargoes desserts. I have nine route. He read it by two. So if I want to find em ex my M. X. It's going to be equal to you. You your integer from 0 to 3. My equations. I have minus X Squared. Bloods four eggs last two Plus X. Plus two, divided by two times minus X. Grade. Last four X. The last two minus eggs. Last two. The eggs. So let's simplify so I still have my rule. So how real my integer from 0-3. If I simplify this then this is going to give me X minus X. Grade. Last five X. So this but Bloods full then I have minus X squared here plus three X. The ace. You can still go ahead and simplify this too. Oh expand. If I expand I have roots Divided by two. Main. Seger from 0 to 3. So expand what you have in the buckets. And this gives me X. To the powerful minus eight eggs. Keep glad loving X squared plus 12 X. The X. Okay name this is going to be equal to. So let's see this is going to be equal to no rule divided by two. Let's find anti girl using son. Move. You could apply the son who here. And if I play this some rude thing, I have eggs to the power five Divided by five. Then my second one is going to give me too eggs to the powerful less loving s. Keep To the power three last six eggs Squared from 0 to 3. Hello lou interlagos deserves so you substitute for three. And this gives you 99. No Divided by five that is full of em. So why buy. So it is means that my wife is going to be equal to M. X. Divided by um which is M ASIS 99 divided by five room divided by this. I have two Divided by nine. So this council that this goose is one year then loving the So I have Loving Times two is 22 divided by five. Then let's so for mm way M. Y. is going to be a room interior from 0 to 3 as well. I have my ex my questions expect let's four. It's last two minus X plus two the S. And this is going to give me My rule insignia from 0 to 3. Let's forget this. And that will give us three X. Then these goods are we? So I have minus X. Times this. So I have minus s cube thing less three X. Squared the X. And this gives me you this is being tv -X. to the power four divided by four plus sq From 0 to 1. Simplify this. And I have from 0 to 3. This is three. The interval is from 0 to 3 deserve it to me. And this will give you 20's survey divided by for rule so eggs bear eggs. Burr is going to vehicle. So M. Y divided by and M Y. Is 20 serving divided by four. Rule divided by AM mm his name. You want to so I have to divided by night. Yeah. So don't forget these councils that to here 1 2 here too. nine here 19 here three. So I'm reducing to the lowest fraction. So I have three divided by it soon. This implies that's my eggs back. Why buy? It's going to be equal to three divided by two 22 divided by five. Which is our final results?

An application of insulin gration since I don't remains centers of muds and centuries. So yeah, I want to find a moment along the X. Y exits in the same choice at all. So we have the lumina bounded by the guts of equation X. To be called to four minutes ways. Great Same x equal to zero so we can find the muds there. Mm to be go to to peru you see you guys are ready to to of four minus wife's grade do I? Which is going to be full to to row two for why minus Y. Kiev divided by three. That's true too. two and this is going to give us 32 32 rue divided by to me. So if I'm looking for the movement along why then this is going to be equal to two integral from 0 to 2 04 minutes twice. Quake Divided by two times for my next white squared no way. And this is going to be equal so you can multiply expand face, expand what you have in the pockets saying you play the integration using the sum rule to do that. So I have rules 16 Y mine It's It's divided by three YQ Blood's whites. The par five divided by five. The interval is from 0 to 2. And this is going to give me 256 rue divided by 15. Okay, so M. X. So X. I can find this strange X. Bar which is M Y divided by M. And this is going to be 25 six roof divided by 15 And I have three divided by 32 rue, which is going to be equal to. So I have this Listen to the last five This and that then 32 goes here eight. So this gives me it's divided by five, but by symmetry, by symmetry from the equation giving you realize that M. X. And Our Wiper its go to zero. So this implies us a century S Y bar. It's going to be equal to is divided by five zero.

An application of insulin gration since I don't remains centers of muds and centuries. So yeah, I want to find a moment along the Xy exits in the same choice at all. So we have the lumina bounded by the guts of equation X. To be called to four minutes ways. Great. Same x equal to zero. So we can find the mods there. Mm to be go to to peru You see you guys are ready to to of four minus wife's grade do I? Which is going to be full to to row two for way minus Y. Kiev divided by three. That's true too. two. And this is going to give us 32 32 rue divided by to me. So if I'm looking for the movement along why then this is going to be equal to To my integral from 0 to 2 oh four minutes. Twice. Quake Divided by two times for my next white squared the way and this is going to be equal so you can multiply expand face, expand what you have in the pockets saying you play the integration using the some room to do that. So I have rule 16 Y mine. It's It's divided by three YQ Blood's whites. The par five divided by five. The interval is from 0 to 2. And this is going to give me 256 row divided by 15. Okay, so M. X. So X. I can find this strange X. Bar which is M. Y divided by M. And this is going to be 25 six roof divided by 15. And I have three divided by 32 rue which is going to be equal to. So I have this Listen to the last five This and that then 32 goes here eight. So this gives me it's divided by five but by symmetry by symmetry from the equation giving you realize that M. X and Our Wiper it's go to zero. So this implies us a century S. Y. Bar it's going to be equal to is divided by five zero.

An application of insulin gration since I don't remains centers of muds and centuries. So yeah, I want to find a moment along the Xy exits in the same choice at all. So we have the lumina bounded by the guts of equation X. To be called to four minutes ways. Great. Same x equal to zero. So we can find the mods there. Mm to be go to to peru You see you guys are ready to to of four minus wife's grade do I? Which is going to be full to to row two for way minus Y. Kiev divided by three. That's true too. two. And this is going to give us 32 32 rue divided by to me. So if I'm looking for the movement along why then this is going to be equal to To my integral from 0 to 2 oh four minutes. Twice. Quake Divided by two times for my next white squared the way and this is going to be equal so you can multiply expand face, expand what you have in the pockets saying you play the integration using the some room to do that. So I have rule 16 Y mine. It's It's divided by three YQ Blood's whites. The par five divided by five. The interval is from 0 to 2. And this is going to give me 256 row divided by 15. Okay, so M. X. So X. I can find this strange X. Bar which is M. Y divided by M. And this is going to be 25 six roof divided by 15. And I have three divided by 32 rue which is going to be equal to. So I have this Listen to the last five This and that then 32 goes here eight. So this gives me it's divided by five but by symmetry by symmetry from the equation giving you realize that M. X and Our Wiper it's go to zero. So this implies us a century S. Y. Bar it's going to be equal to is divided by five zero.


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