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Question

ME €ee nal rrlE DerOldcrc OLlr ".4#[Mn erme 4r4TMccA "-8{ Gulld den Laaaa "i={ =ed8-mLhLuECecidettrltdefi FletELarnlnt ertlu4= DetLtd 57 Ik i

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find $\overline{\mathbf{u}}, \operatorname{Re}(\mathbf{u}), \operatorname{Im}(\mathbf{u}),$ and $\|\mathbf{u}\|$. $$\mathbf{u}=(6,1+4 i, 6-2 i)$$

Question asked us to divide and weaken use polynomial long division to do so And our goal a polynomial long division is to multiply something by the six m squared to cancel out our other in terms. So the first term we have to cancel is 18 end to the forest. So what time six m squared gives us 18 end to the fourth, and that would be three three m squared. And when we take our three m squared and multiply it by this minus one, we get minus three. I'm squared. And in order to cancel out our 18 m to the four, it's we have to multiply the green expression by negative one. And when we distribute those negative sign to this three m squared, it becomes positive when we at 42 m squared and now you just bring down our other terms. And now the next time we have to cancel is 66 cute. So how do we go from six m squared to 66 cute and we have to multiply by minus 11 a.m. And when we take minus 11 M and we multiply it by minus one, we get positive 11 m and again to cancel our AR minus 66 cubes. We multiply the blue expression by negative one and both are 66 are 11. EMS will cancel and now we're left with 42 m squared minus seven. How do we go from six m squared so minus 42 m squared and we do that by multiplying by seven. So when we do that, we get 42 m squared seven times minus one gives us minus seven and we have to multiply the red expression by negative one to cancel out our 40 twos. And when we do that and distribute this negative one to the Southern are sevens also can cancel and we're left with the remainder of zero. So that tells us our final answer is three m squared, minus 11 m plus seven

First, we want to arrange his numbers from least two greatest. So we want to imagine our number, line home and look at the negative numbers first, which comes to the farthest left. If we look at the farthest left on the number, line will get negative. 6.11 So let's write them down. Negative 6.11 Then comes negative. 6.1, then negative 6.8 then negative six plank 02 And now we're in their positive numbers. So then, smallest positive number here is 6.3 six and 300 and then 6.0, 76 and seven hundreds. Thank you.

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 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.


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