for-the-following-exercises-compute-the-center-of-mass-overlinex-rhosqrtx-text-for-x-in14

Question

For the following exercises, compute the center of mass $\overline{x} .$
$$
ho=\sqrt{x} 	ext { for } x \in(1,4)
$$

Amy Jiang · Accepted Answer

Okay, so X bar is just in a row from 1 to 4 of X times piece. That&#x27;s X three over to the X over in a girl from 1 to 4 of this team, which is extra one over to the ex. What do we get from here? Well, that simplifies order in a road with comes to over five extra five over, too. About later at four and one over to over three extra three or two evaluated at four At one we get, This is equal to see We have been three over five times for five older, too, but it&#x27;s once a drive over to all over 14 3 over two minus one times three. Open to excuse me three times 31 over 5 a.m. Seven. This becomes 93 over 35.

Amy Jiang · Answer

Okay, So, given that P is equal to one for ex Canadian, the end negative. 123 Okay. No, that GM is equal to P T X and X far is equal to the integral of it. 123 of this, Ext Eme Over. Actually, it is. You play. Stop that T X T X over in a government. 123 P. T X Plugging in what we know, we know P is equal to one. So we have explore easy culture in Rome in 123 of x t x over integral part of one degree of this the X does that give me that Just X squared over two over X, evaluated at negative a positive three And they want to excuse me nine over to minus one. Squared over to over three and one, it&#x27;s plus one. And to simplify support before, which is just

Mauricio Araiza Canizales · Answer

So we went to calculate the center of mass off a search in La Mina knowing that its density is equal to one and we want to do so in the interval. Negative. 123 Sorry. Off ex native from negative. 123 So we want to find X with a lineup of it. And we know that this particular coordinate this interview, my ass, it&#x27;s gonna be equal to the moment with respect to the Y axis divided by the total mass of de la manana. So let&#x27;s find out this trick wanted his first. So the total must&#x27;ve de la Mina is defined as robe Sorry as integral from a TV of Rome Thames FX. The ex says we&#x27;re not given any information about F effects. We must assume that it&#x27;s it is equal to one. Genesis will have the integral from native 123 off one Sorry of Roe the ex we know row with the consent over here. So we&#x27;ll have just row times the integral from native 123 the ex This just gonna be grow temps exit violated from native 123 And in this case is gonna be for a row. Now let&#x27;s find a moment with respect to y axis. In this case, the moment would respect to the Y axis. It&#x27;s gonna be the integral sorry road. Tim&#x27;s an integral from a TV off Ex Temps ffx DX, which in this case can be re written as the ISRO Terms of integral from native 123 affects the X. We know that the inter roll effects it&#x27;s just gonna be excess quarter. You&#x27;re right. I&#x27;d like to violated from native 123 which is road divided by two times nine minus one, which is just equal to for a row. And if we plunk all of these two ballots over here, we found out that for row, but by four row sickle to one. Therefore the center of mess, he said X equal to one

Vikash Ranjan · Answer

in the post room. Send it off, Maas. Its bark off on and well, it won&#x27;t be. Wait and answer You less is given by formal. Are we stayed? Exploit. It was traditional. It will be X in tow. Royals dears. A bond in division off it will be Royals. India&#x27;s That&#x27;s what The question We have expired equals digression off it&#x27;s in books. A squad digs from bone Didn&#x27;t dual integration Esquire. The X is equal. Do the person of the well experience a bond. You&#x27;re going division. It is about me. So after indicating we are men as equals, it&#x27;s far for a pawn four limited X cube on three limit didn&#x27;t do well. So we have this final little guys in a bar for upon four minus zero. It want Why help our tree mind by three. Manage Ito, This is Eagle Do in a bar for upon four into three by l u. This is eagle do three upon for So we have the ex baht as tree of 14 is a dancer for the one problem

Vikash Ranjan · Answer

center Mass. It&#x27;s bar, often internally to be with Rolex is given by this formula on Dhe were in the question we have. It&#x27;s funny. Quells indeed. Eljero don&#x27;t do excuse about ex debts upon in Diggle, You do good about X d eggs. So this can be so already using this formula. It is I late on DDE the started because it becomes X in the box minus you. Don&#x27;t don&#x27;t do one into the vortex, dears. Bon. You know Max is the guns. Excuse me, but it&#x27;s mine. Issued about X. You don&#x27;t do a ban. Even products did I do This becomes so do the power to minus Q tip our two minus deal minus your bar. Jiro A bomb? You, the bar do mine asking about judo. This is equal. Do you, Barto Mar plus one of our own. You Barbu minus one. This is our ex. But this is an answer to the given problem

Vikash Ranjan · Answer

it&#x27;s Jim. We&#x27;ll find the center of mass expire often end family to be. But Rex is given by this formula. And according to this formula, we have this X bar. He was indeed I want to be X in the l A X dx. Born in division one Toe E one into Helen X X. This is our first interview ever. Visit our second and Diga Let it be. I do understand. I want the faster fall you&#x27;ll recall reading. I won. So I want you guys and the next intellect a scar upon to minors in Eagle off one of our necks in tow. Excess choir upon. Dude. Yes, this is equal. Do weapon do. It&#x27;s a spot at an X minus. Get off! It&#x27;s on to the X is equal to one of us. Do it. Just bought at an X minus on a bunch of drugs. Squad upon two one. Does he? This is the limit. No, we have this as when I want to. Yes. Quiet, Ellen in minus 11 Fool! E squad, Mine ass. What about due into one squad in the melon? One minus. But upon fold and new ones. This is equal when about two years fired into one of minors. Here, spot upon food minus this Ellen one becomes Jiro This father for this becomes hero that we have master. So this is equal. Do? Yes. Far upon to minus your squad on full glass. 114 So we have you think about us? Yes, Squire. Upon four plus one About four. This is how I want now for I do we have. This is our I do. This is equal. Do integral oneto e one into l A x d x equal do cracks in tow. It&#x27;s my last one about ex Indo X. The X people do X in the next minus. It&#x27;s so while Doofy is our desire, our limits. So we have e l A n e minus e minus one Ln one minus one. This is Gino. So we have e minus e last one. This is equal to one. Therefore we got I do as one tends. We can say that I went about I do eat because yes. What? Upon four plus one upon for a bone one with people do yes. Fired upon four plus one upon. For this is our answer. Do the given problem

Problem

For the following exercises, compute the center o…

Problem 268 Hard Difficulty

For the following exercises, compute the center of mass $\overline{x} .$
$$
\rho=\sqrt{x} \text { for } x \in(1,4)
$$

Answer

$\overline{x}=\frac{93}{35}$

Related Courses

Calculus

Related Topics

Discussion

Top Calculus 2 / BC Educators

Grace H.

Catherine R.

Michael J.

Joseph L.

Calculus 2 / BC Courses

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 6

Video Transcript

Gilbert Strang

Calculus

Grace H.

Catherine R.

Michael J.

Joseph L.

Integration Review - Intro

Definite vs Indefinite

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$\overline{x}=\frac{93}{35}$

Calculus

Grace H.

Catherine R.

Michael J.

Joseph L.

Integration Review - Intro

Definite vs Indefinite

Gilbert StrangCalculus

Grace H.

Catherine R.

Michael J.

Joseph L.

Gilbert Strang

Calculus