5

51} 8 1 4 H 8 { 33 # 8 L 1 H J 8 H 1 0 1 8 8 8 8...

Question

51} 8 1 4 H 8 { 33 # 8 L 1 H J 8 H 1 0 1 8 8 8 8

51} 8 1 4 H 8 { 33 # 8 L 1 H J 8 H 1 0 1 8 8 8 8



Answers

$h-f, h f,$ and $h / f$ if $h=\left\{(-4,13),(-1,7),(0,5),\left(\frac{5}{2}, 0\right),(3,-5)\right\},$ and $f=\{(-4,-7),(-2,-5),(0,-3),(3,0),(5,2),(9,6)\}$

You're going to be subtracting these fractions. Ah We're going to start by trying to find the number, The lowest number that can be divided by 8, 5, 2 and 10. And that number will be 40. So we will make all of our denominators 40. So we have to look at what we multiply by each of our denominators In order to get 40. And in the case of eight we take eight times five to get 40. So therefore we need to take five times 5 to give us our new numerator of 25. five times 8 is 40 two times a gives us 16, two times 20 is 40 three times 20, gives us 60 10 times four is 40 And 11 times four gives us 44. So um when we subtract a negative will really be adding. So we can think of us as having a plus here, the negative 25 plus 16. Well give us -9 over 40 And then 60 -44 will give us 16. So the negative 9 -16 Gives us -25 Over 40. Now we're not quite done yet, Because both 25 and 40 Can divide by five, so our answer further simplifies into negative 5/8.

So in this problem, we're given this matrix and were asked to use the matrix capability of a graphing utility to find the determinant. So I went to Desmond's dot com, went up here to math tools, matrix calculator, and got this matrix calculator here. So in our new matrix and our matrix is a four by four. So four rose and four columns. Now the entries one minus one, C A A and four and two and six zero my S four and then to zero two and six and then zero two, eight zero. Okay, where's my matrix now? Just do D E T right here to get the determinant determinant of a yes, Negative,

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.

This question gives us a sequence and assets to determine a formula. As we can see, the first term is negative three and then each term after this is equivalent to negative 2/3 times the term that was previously. Therefore, it's negative three times negative 2/3 because that's what it was times the term times the previous term to the power and minus one.


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