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MetheMeraiat =4TateiaTafIAtIAhahFatan CatemninolnardLen neaealltettae=...

Question

MetheMeraiat =4TateiaTafIAtIAhahFatan CatemninolnardLen neaealltettae=

Methe Meraiat =4TateiaTafIAtIAhah Fatan Catemninolnard Len neaeallte ttae=



Answers

$\begin{array}{|c|c|c|c|c|}\hline m_{i} & {12} & {6} & {4.5} & {15} \\ \hline\left(x_{i}, y_{i}\right) & {(2,3)} & {(-1,5)} & {(6,8)} & {(2,-2)} \\ \hline\end{array}$

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.

To find these two matrices together. Here. First thing we need to do is check the dimensions will work. Okay? First matrix we've got is two rows three columns. That's a two by three. The second matrix is a three row one column matrix. These inner two dimensions have to match which they do. That means is a resulting matrix will be dimension the outer dimensions. Okay, So we're gonna have to buy one. Matrix is our answer just two spots here. Okay, we'll fill in the first spot. This is gonna be row one. Column one. Okay, so everything in row one thinks everything in column one negative one times six plus zero times negative four plus seven. Thanks one. Okay, this should give us negative six plus zero plus seven. That should give us a one in that first little spot right there. Okay, The second guy this is gonna be row two column one. Okay, so we're gonna take everything in row two times that same column right there. So three times six less negative five that was negative for plus two times one spent 18 plus 20 plus two should give us 40. Okay? So one in the first row, 40 in the second round, and that is the result of this modification.

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.

As we know that, as we know that under root burk is equal to and is equal to reflective index is equal to reflective index, which is demands. And lace. Richard diamonds and diamonds and Elise went pretty so diamonds and so diamonds and will be equal to am not L not he not option D is the correct answer for this problem. I hope you understand the solution.


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