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A solurion, when dilurod with $\mathrm{H}_{2} \mathrm{O}$ and boilct, givcs a whire prccipirate. On addition of cxccss N11 Cl/NIIOll, the volume of prccipirate chcercascs lcaying bchind a white gclatinous precipirare. Idcntify the prccipitare which dissolvcs in $\mathrm{N} 1 \mathrm{l}_{1} \mathrm{OH} I / \mathrm{N} \mathrm{I} \mathrm{I}_{4} \mathrm{Cl}$ (a) $7 \mathrm{n}\left[\mathrm{O} 1 \mathrm{l}_{3}\right.$ (b) Al(OII) (c) $\mathrm{M}_{\mathrm{B}}(\mathrm{OH})_{2}$ (d) $\left(\mathrm{ca}(\mathrm{OH})_{2}\right.$

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.

Okay. We won't walk through the process of finding, um, the center of Mass, um, of a given system of point masses. And what I'm gonna do is I'm gonna go ahead and put these in the corn. It plain. So here is the cornet playing and make sure I have enough here, okay? And so the first point mass is at two three. So there is my first point mass. And that point mass is, um, a value of 12 and is at 23 Then I have one at negative one five. And so that point mass is six. And he's that negative. 15 Then I have 1/3 1 at 68 and I believe eight was a here. And that point Mass is four and 1/2 and occurs at 68 And then I have a point mass of 15 at two. Negative too. So there are my four point masses, and, um so just start finding the center of mass. I need the total mass, so we'll just take each of the masses and add them together. And so I get a total of 37.5, Then I want to find the moment about the why axes. So I want how, um, each of these point masses or distributed about the vertical axis, so that's gonna be dependent upon how far they are from the Y axis in the ex direction. So, um, the moment in the Y axis to pin him at the Y axis is each of the point masses times their respective X values. So we take each of the point masses and multiply and by the respective X values. And when we do that, we get a value, uh, 75. Then we're gonna find the moment about the X axis. And so, if I'm looking about at the moment about the X axis, I'm trying to see how these point masses are arranged about this X axis. So that's gonna be dependent upon their why value. And so my take each of the masses and multiplying by the respective why values? Um, because that's gonna be their distance away from the X axis. And then when we do that, we get a total or combined of 72. And so to find the, um X coordinate at the point mass, it is going to be the moment about the Y axis over the total mass. Um, so we get 75 over 37.5, which gives me a two to find. The Y coordinate is the moment about the X axis to buy by the total mass, which is going to give me 72 over 37.5, which becomes 48 over 25. So my center of mass is going to be two comma, 48 over 25. And so let's go ahead and taught him in. And so that means 48 over 25. So it's at two comma, just a little over two would be 50. So it's just a little under two, so right, right there.

Okay, so this is all about National Basketball Association. And each of these variables X, y and Z represents a player who scored the most game points in one game. Um, we had X represents. We had Wilt chamber Mint, Wilt Chamberlain in 1962 scoring quite high. Why being Kobe Bryant 2006 and Z again being Wilt Chamberlain Chamberlain. But in 1962. So even though X and Z are the same person, we have to consider them two different variables because he scored. These are the top scoring individuals who scored the highest points in one game. And so will chamber meant Chamberlain did it twice rate two different years, which, Wow, what an amazing accomplishment. I wish I had that in my lifetime. So we're gonna look at this and see, um, we're going to solve for the number of points that they scored in that one game. So notice my equation to in my equation. Three only has two variables, and they both have X. So I'm gonna use substitution in order to solve this system. So I'm going to solve for why, in this first equation leaving X by itself, Um But what I'm going to dio and I hope I don't confuse you is I am going to move. Why? To the right side and 19 back to the left side just because it's a snake It of why I want it to be a positive y. So when I move wide to the right, Seidemann add y to both sides. Giving me X equals 19 plus y and then moving 19 back to the are not back of, but moving 19 to the left side. I'm in a subtracted, giving me X subtract 19 gives me positive Why now? I could have moved X over and then distributed and then moved the negative one over. This is how I chose to do it. I'll do that for this third equation here again, I'm gonna solve it for Z because I want those same variables Case I am going Teoh, I'll do it the other way. Um, just so you can see both ways this time in a move x to the other side, giving me a negative Z equals 22 Subtract x. This negative c is a negative one Z Now we need to move that naked of one to the other side by dividing, leaving me with a positive Z a negative 22 a positive X. So see, it's the same thing, just two different steps, but giving you the same result. Now I'm gonna go back up to Equation one and plug in what I know is equal toe. Why? Which is X, subtract 19 and plug in what I know is equal to Z, which is naked of 22 plus X now the it's and nine the Y in the Z. Both didn't have a coefficient in front of them, so I have no distributing, so I don't necessarily need those parentheses, so I'm just going to get rid of him now. I'm gonna combine like terms. So on my left side I have one X plus another one X plus another one that's giving me three x total. I have a negative 19 person naked of 22 giving me and negative 41 and then I still have that equal to 2 59 Now, this is a two step equation. I'm gonna add 41 to both sides of the equation. Giving me three x equals how I cannot write Sorry. 300 dividing three by each side, giving me 100. So that means Wilt Chamberlain in 1962 scored 100 points in one game. Wow, by one person. That's quite a bit in basketball. Now let's go back up here to my Why. I know what exes. It's 100. I'm a subtract 19 to give me why. So hundreds subtract 1981 points. So Kobe Bryant in 2006 scored 81 points by himself in one game. And then the last but not least, I'm going to substitute again. 100 in here for X, subtract 22 get 78 points. So then again, Wilt Chamberlain scored the third highest on points in a game with 78 points hold by himself. So that were the three highest, um, points scored by one person. So I'm gonna put him again by, like, an ordered payer X first, no necessary with the points. I'm not going to put my units, then 81 then 78. It's a good sign that it's starting with, um, my largest value and decreasing, because I would think that they would put him in a new order. But there is the interesting fact the top three scoring in individual scoring the players of all time.

Okay, So to start this problem, I'm gonna take my second equation and solve for why? So with that, I'll have y is equal to X minus 19. Then I can take my 30 equation and solve for Z. So Z will be able to x minus 20 chill so I can use thes two things and plug them into my very first equation for my original problem. So with that, I'll have X plus why, which is up here. So X minus 19 and then plus Z but Z is X minus 22 and this is gonna be able to to 59. So with messages combine on my leg terms, I'll have that three acts minus 41 is equal to 2 59 So I had 41 to both sides, so giving me three acts is equal to 300 so x must be 100. So that's the first part of my solution. So now to find, to find why NZ, I can just plug this X ray into these two here. So if I do that, I'll have that why is equal to 100 minus 19? So why be calls 81 and then for Z. So C is equal to 100 minus 22. So Z's equal to 70. So my solutions for this R X equal to 100 why is equal to 81 z a 78?


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