for-the-following-exercises-compute-the-center-of-mass-overlinex-rholn-x-text-for-x-in1-e

Question

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

Vikash Ranjan · Accepted 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

Amy Jiang · Answer

Okay, so we&#x27;re asked to computer center of masculine. That p is equal. D&#x27;oh Thanks. U us. Thanks. Eat it. And in effect, okay. For ex contained in barrel to one. That&#x27;s this X bar acquitted in the world from 01 of X times are a P which is therefore X four plus export heated in the X the X over to interval from Joe&#x27;s one of this p which is excuse us Ex Agent X X is a popular you enjoy solving this yourself You get X four is equal to extra five over five. My speeds in the complex explained It&#x27;s too exposed to over Mexico are four before my speech and little x X plus one Both the valet at once is all this gives me 11 You minus 25 over five e all over by You wanted space over or eat. Okay. It simplifies to for over five times 11 e minus 25 over five e minus eight

Mauricio Araiza Canizales · Answer

in the following problem. We want to point center of Mass, Given that the density of the function wrote is equal to X give plus X temps e to the negative X on the inter on the domain X in between 01 And since we&#x27;re not giving any information about effects, we can assume that this is just one. So to find the center of mass, we&#x27;ll have the following formula. The moment would respect to the Y axis divided by the total mass of salami. So let&#x27;s first find the moment with respect to the Y axis. This is to finance the integral from A to B of grow effects. Kim&#x27;s Ex Temps FX DX. Usually you will pull this drove out of the out of the integral since it is a constant term, however, since Roe Barry&#x27;s with X when it included Inside the square the integral story. So if we sifted through her bounce in their ballots for Roe and if effects will have the integral from Syria to one effect stems X cube plus X times E to the negative x the ex, the moment would respect to the Y axis is just then the integral from church one now. Well, we will distribute this X over here off extra the fourth plus X squared times e to native X The ex This first integral is release it to compute, which is just next to the five divided by five. The 2nd 1 requires a graphing calculator or some for program, and if you do so, you&#x27;ll find out that it is X Square. Tim&#x27;s either the new T X minus two X temps, either the negative X minus to eat of the negative X evaluated from 0 to 1. Now let&#x27;s substitute this. This valley is for a moment would respect to the y axis. So this 1st 1 is just one of her five minus eight of the negative one minus two times Eve did in 81 minus two times Eater Negative one minus zero 00 Native to then the moment of inertia. Sorry. The moment with respect to the Y axis just becomes one of her five minus five e to native one plus two, which in this case is just one 11 over five Sorry, minus five e overeat, which is just 11 over E minus 25 divided by five e so I&#x27;m actually going to use in the white word. So now let&#x27;s calculate the total mass of the La Mina just given by the Integral from a TV off ro effects temps ffx DX. We&#x27;ll have the integral from church one of excuse plus X times, either the negative x t x Again This first interval is released to compute. We&#x27;ll have extra bit fourth divided by four minus. So the second, Integral will look out will require again the use if it graphing calculators. Computers, software This is equivalent. The interview is gonna be negative x times either the negative x minus either the negative Becks validated from Syria to one. Now let&#x27;s substitute the battles for for this mess. So we&#x27;ll have one over four minus either the native one wait to see the negative one plus one. This simplifies to five over, four minus to eat. Rescinding native one. She&#x27;s just five over four, minus two over either the negative one, which is just then five e minus eight, divided by four e. This is a total mess of Philomena. So now let&#x27;s substitute this back into our first a question. So we&#x27;ll have 11 times E minus 25 divided by five e divided by five e minus eight. Divided by four e with Justin Simplifies to four, divided by five times, 11 temps, Times 11 E minus 25 Divided by five e minus eight This is the solution to this question.

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

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

Problem

For the following exercises, compute the center o…

Problem 269 Hard Difficulty

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

Answer

$\frac{1}{4} e^{2}+\frac{1}{4}$

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$\frac{1}{4} e^{2}+\frac{1}{4}$

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Calculus