5

3 5 ) 3 r'=Ax (J LI 26 d m 1FND '2At A = (-2 (2-...

Question

3 5 ) 3 r'=Ax (J LI 26 d m 1FND '2At A = (-2 (2-

3 5 ) 3 r'=Ax (J LI 26 d m 1 FND '2At A = (-2 (2-



Answers

Solve. $$\frac{\frac{3}{5}}{6 \frac{1}{2}}=\frac{1 \frac{2}{3}}{j}$$

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, so this problem here is provided, and it asks us to justify each one of these steps. And so the first up here, you'll notice that, um, we've got a three. A divide by two and a six divided by five. So to get to this three A by itself it looks like both sides were multiplied by two, which is indeed the case. This gets multiplied by two. That goes away, right? So I'll do this and rest. So if it gets multiplied by two are to this becomes a 12. And this the twos cure cancel. And this is called the Multiplication property of Equality. And then here in order to get that three away here we've divided both sides by three. And that's the same. It's just multiplying here by 1/3. And so you can see that these cancel this becomes a four, and that's what happens here. And this becomes the A. And this is the division Equality Property

Okay to review. Let's first start cancelling out what we can here in the denominator. I have a five to the third and that cancels with the five to the third in the numerator in the numerator have a three squared and I have a three cubed. So that will cancel and leave three in the denominator in the numerator, I have four to the fifth, which will cancel with the Ford of the six and leave a four in the denominator, so we get an answer of one over 12.

Some were multiplying metrics A by matrix I is actually what we call the identity matrix. If you're not familiar with, what's going to happen here? Let's just run through the details. Okay, so the same matrix multiplication we've been doing row one column one. Okay, that should give us a one there. Talk right. Row one column to Okay. One time zero plus two times one. That should give us a two. Okay, what can I way through? But left row two column one, four times one plus three times zero. Br four. And then I lost calculation bottom right, road to column two all the time zero plus three times one. That's just three. Okay, so this matrices are answer 1243 If we haven't already seen it, we should recognize that this his matrix. Okay, Okay, so multiplying a matrix by the identity matrix just returns that same matrix. I can't see matrix equivalent of multiplying numbers by one, for example.


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