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M(20 poimts] "s (lu TelloInr Aute ~pmntitla...

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M(20 poimts] "s (lu TelloInr Aute ~pmntitla

m (20 poimts] "s (lu TelloInr Aute ~pmntitla



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$m$-Chlorobromobenzene is an isomer ofm-bromochlorobenzene.

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.

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.

In this problem. We asked our ass to find the center of mass of this two dimensional system with the masses. 2 8 to 1 and four in the positions. Negative three negative. 100 And negative one, too. In order to find the center of mass, we first need to calculate the center mass in the ex direction, which we will do by calculating the moment in the UAE direction divided by the total mass. Once you've done that, we will calculate the, um, center of mass in the wind direction. Just calculate the moment in the ex direction of over the center of mess. Okay, So calculating Expert, um, the moment of wise calculating by multiplying the masses by the X coordinates. So we have eight times negative. Three plus one time, zero plus four times negative. One all over. The total mass, which is given by eight plus one is nine plus four gives us 13 doing some arithmetic. We can find out that eight times negative three is negative. 24 0 minus forgives us negative. 28 over 13. Now, to find the center of mass in the UAE direction, we're going to take the moment of X, which is the masses times there. Why Coordinates? So we're going to have eight times negative. One plus one time, zero plus four times two all over the total mass, which is still 13 here. Only two are particularly. Get negative 80 plus h, which gives us zero over 13 for our center of mass. Explore why BAR is given by the coordinate point. Negative 28 over 13 from a zero.

Or got identify the hypothesis in conclusion of this conditional statement. So I pop. This statement is if eight ounces of cereal costs to 99 than 16 ounces of cereal costs 5 98 So hypothesis is after it. But before then, so we have eight ounces of cereal costs 2 99 and then the conclusion is apart after then. So 16 ounces of cereal cost $5.98.


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