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Question

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Answers

$$ \frac{w^{2}-3 w+6}{w-5}+\frac{9-w^{2}}{w-5} $$$$ \frac{2 z^{2}-3 z+6}{z^{2}-1}-\frac{z^{2}-5 z+9}{z^{2}-1} $$

The question is, who solved the falling linear equation by love? Last transformation. So DeLeon Eric question is that dash less omega or the prudish equals to desert minus omega and said dash minus omega dash equals to certain minus omega. Give one Zen X zero. Is it close to one on omega eg zero is equal to zero. So after thing these two equations we came to the conclusion that is that dash less omega dash will be equipped to lose their death minus omega dash as both are equal to is at minus omega minus. So taking omega Omega dash to the leper inside we get we will make our dash It was through zero that is a major national polls to zero by two which we considered at sea or the points and and we know that make we are given with omega zero equals zero that is seem will be put zero therefore omega value with me zero So now to find the exact value taken Ah, the question Zack Dash equals 20 to minus zero that is zero dash equals two. They're now applying villa plus toe Both the science we get love plus off the dash equals to love plus off zag. So applying the formula love blasts off. Who said that would be s Who said s minus Zack back zero. It was too love plus off. That would be there s nose then at zero we are given when one supporting this value Yes, Zag s minus one will be able to use their Yes, not taking this is their desks. So the left hand side we get s minus one. Is there SS Homan equals to one. Therefore zag s would bakeware toe one number one s minus one Now applying the love plus and worse zero p would be equals to erase to the party as we know that love plus in worse off one upon s minus A is the close toe heiress to the party Unity Salah Plus in verse off one upon s minus one would be a quarto. Here is to the party. So this is the final answer for this question. So

For this program, we first assume that the solution to this so the W has a policy Ray six expansion. With this assumption, we can ride out the Garrett tears off taboo eso we packing these three functions into the OD deaf in society close to submission K from two to infinity que times k minus one a que ext became minus to plus summation K from one to infinity three k a k extricate minus que because it zero to infinity a que extricate so we can collect, um, the same or their terms. So, for example, a constant we have to a two front miners a zero and we know this constant has to be zero. It gives us a two week close to ah, why have of a zero in the linear in your term, we have six a three miners twice off a one equals zero. It gives us a three close to minus 1/3 off a zero so we can stop here for a little off for a while because we have some initial conditions. So the initial condition directly gives us what's easier. And what's a one so easy are requested to and they won t close to zero. With this initial conditions, a two will be one. A three will be zero. Okay, so, um, this rewrite this left inside in the following way. So we have with splitter first term into twice off a two plus six a three x cross summation que from four to infinity K times K minus one. A k x two became minus two in the full of second term. Should be three a one x plus the rest and for last term is minus a zero minus a one x minus. Submission que From two to infinity A k Xscape. Um, so we collect the same terms and by shifting the index for this so we can shift the index for this particular term. So the new index would be K for all the summation k from two to infinity. So the starting point is decreasing by two. That means everything inside will increased by two. So as we make this shifting, we are able to merge off the summations into one. So the summation will be K start off run two to Infante, e K plus two times, Cape Cross one. Hey sub k plus two crossed, three K K minus a k Times extricate. And we already discussed the 1st 2 terms and that this turn gives us a recursive relation. Eight. Case plus two equals to one miner's three K over K plus two times K plus one face up cape. Okay, so we know that a zero because two to a one you close to zero and a two week cost. One a three course zero and for a four before if we bragging K Coast to to into this recursive relational before he caused to why number 12 A to minors six. A two now gives us minus five off 12 A. To So before you cause a four ecos toe minus five over tough a five equals zero because a five equals or something times a three a six equals Teoh. So when Katie cost before, we have 30 on the denominator and the miners 11 times a for So we have a six. He caused toe 11/72. Okay, so that means the first of non zero terms for this function, w will be two plus x square miners five or 12 extra fourth power plus 11/72 x 36

In the given question we are told to find the imaginary part of the complex number, zinc. Right? So we have a few options which are given us one by two I times Zd plus Z bar. The second option is one by two times Z minus Z bar. The third option is one by two times that plus Z. Bar. And the fourth option is one by two I times Z minus Z. Bar. So we need to choose and choose an answer from any of these four options. So in the options we can see that we have Z and Z bar. Right? So if we consider these at the complex numbers, letters of the form expressed by Y, then then that burger is denoting the conjugate of the complex numbers said, which is given by X minus I will. Right? So the imaginary part of zen is white, right? It is why? So what we need to find is to find which relation given these options, give us the answer as white. So what we're going to do is to take the first option and we can see that in each options we have that plus that bar. Or that is that minors that bar. So let's find what is that? Plus that bar. Right? So the place that bar is expressed by white plus X minus iy. Which is equal to two X. So here when we add that injured bar we have we are eliminating the uh imaginary part of the complex numbers. Right? So what about that minors at bar? We will have expressed I write minus express minus X plus I. Y. And this would give us plus two. I. Right to I to a Y would be the result of that bitterness. That bad. So the imaginary part of that is given by Y. So in order to take wife from this, what we need to do is to multiply one by two, right? So when we multiply one by two i on both sides of the abo equation, we will have one by two I times that minus that bar is equal to Y, which is the required imaginary part of the complex numbers. It. So this is given as the option one by two, I times that minus the bar is the option D. So D is the correct answer. So I hope you understood the method. Thank you.

In this problem, we were asked to find the center of mass of the two dimensional system with masses 2 34 to 1 in six in the positions. Negative too negative. Three 55755100 and negative 30 In order to do this, we'll need to calculate both this center of mass in the extraction, which is given by the moment of why, over the total mass and then the center of mass in the UAE direction, which is given by the moment of action over to the trouble of mass First calculating X bar, the moment of wise given by each of the masses. Times there X coordinates allotted together so we can find that by three times negative too, plus four times five plus to turn someone plus 1 10 1 zero plus six times negative three all over the total mass is going to be three plus for someone close to his nine plus one is 10. Post six gives you 16. So doing some arithmetic we get three times a year to is negative. Six plus 20 is 14 plus 14 is 28 poses zero post negative 18 is going to give you 10 over 16 or 1.6 now to find the center mass in the wind direction, we're going to find Calculate the moment of X, which is given by the masses times there y components. So we have three times negative. One negative, three plus four times fine, but two times one plus one time zero was six times zero all over the total mess, which is still 16 now doing our athletic three times three makes nines with negative nine plus 20 which is this 11 plus two gives his 13 and both of these terms to goto zeros. We get 13 over 16. So are finally answer is export y bar it wa ce 10 over 16 comma 13 over 16.


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