5

2 8 0 { Vi qi F 1 1 8 1 2 2 8 5 M 2 ~ ria [ 2 2 0 8 6...

Question

2 8 0 { Vi qi F 1 1 8 1 2 2 8 5 M 2 ~ ria [ 2 2 0 8 6

2 8 0 { Vi qi F 1 1 8 1 2 2 8 5 M 2 ~ ria [ 2 2 0 8 6



Answers

$$\left|\begin{array}{cccc} 1 & -1 & 8 & 4 \\ 2 & 6 & 0 & -4 \\ 2 & 0 & 2 & 6 \\ 0 & 2 & 8 & 0 \end{array}\right|$$

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.

In the problem farm so far The ghost unease It iss I mean for one indeed. His barber minus two It What is over is less bs. It is by minus two years left No way! Have to find pretty bad ABC ladies Hillis 14 a minus two is less. Five less is less One do so after solving this is the have equals my history be was do one thing This country minus three over age blessed one class is yes. Is this fire minus two is last Fine. So this is equal to minus three over days. Plus one. A glass case minus one Last do for is my Well, it's fine. Let's do this. Fire this can. Regan has minus three over. Class is minus one over ish minus one. Police fire plus two plus two is minus one with less. Teoh wholeness Booth. The leftist waas. We have this sequence to is left off this so the young them Yes industry need the bar dynasty less about team cost two d glass even about sign to be

Today we are adding fractions with uncommon denominators in this case specifically uncommon denominators with polynomial. Now the two fractions we are adding in this problem are right here. Unfortunately we do have S as our variable. I will do my best to distinguish between n E S s and fives that might pop up. Okay, so the first step in adding any fractions is to get a common denominator. You do that with polynomial is by factoring So in this case we will factor mhm into s minus aid. So it's going to be plus four & S -2. And then over here it's going to be s. It looks like two and 5 and it will be plus five and minus two. Okay, now we need to find our L C D or at least common denominator. We find that by taking every binomial we see in the denominator and writing at once, in this case we see it S plus four. We see an s. Plus five Or an S -2. Excuse Me. And we see an S plus five. Yeah. Now we see another S -2. But since we already wrote it once, we don't need to write it again and this is our at least common denominator. The next step is now we need to put these fractions into their equivalent common denominator forms. We do that by multiplying them by the binomial. That's missing. In the case of the two S. We are missing an S plus five. So we multiply both the top and bottom by an S plus five. In the case of the four, we are missing an S plus four. So we multiply the top and bottom by an S plus four. Yes. No, we simplify it out. Don't do that by distributing. So we'll distribute the two S and we'll distribute the form to S times S is to S squared To s. Times five is plus 10 S. And that'll be over the LCD, Not just right. LCD to save some time. That's going to be plus four times five is 20. There I go again. Always with us, variable four times s is for S Times four is Plus six teen. Now that is also over the LCD and since they are sharing a denominator, we can simply add living marine hours. Okay, When we add them out here, we're gonna get to S squared for S plus 10 S. Is 14 S and plus 16 at the end here. And that's going to be over our at least common denominator of S plus four S minus two and S plus five. Thus this fraction down here in the corner, is our answer to this problem.

Hi. Today we're computing the inverse lack last transform of the function Negative eight s squared minus five s plus three, all divided by it's plus one times s squared minus three s plus two. Now, the first thing we do here is we perform a partial fractions to composition. First, the fact it factor the denominator f minus one. So that's minus two. This means that the interior of the lack last trance the universe transformed here could be written us something of s plus one plus something over s minus one plus something over ass minus two. Playing an s equals negative one into this equation. Ignoring the fact is that would give you an infinity in this case here gives us that a number which we can plug into here will find its equal to two. Plugging s equal to one into this equation and ignoring the term s minus one gives us zero, which is what the confusion here is. And playing an s equal to and ignoring this denominated term gives us the number negative three. Therefore, this is the part of fractions to composition, and we can take the inverse transform off each term quite simply to get the result that the inverse transformers x two e to the negative T minus three each the Tootie.


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