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Answers

Find the value of $m$ so the lines $f(x)=m x+5$ and $g(x)=x$ and the $y$ -axis form a triangle with an area of 10 . [UW]

That six is equal toe. Hi, Dex. Do I did by three X minus seven. And DX actually power for minus one. Divided by five gs minus 15. So he had if we would three X minus seven equals 20 Then access could do seven by three. And if we had access choir minus 40. Questo Jiro access car minus one equal to zero. Then access course to plus minus one on if we could hear five X minus 15 questions zero. Then we get access. Condo Pretty. We have to find Romanoff at by G once and off X. So domain here. Minus infinity. Tu minus one U n yet minus 11 You and yet 17 by three you And yet seven by three be Union Preto in grantee. Is that inquired on said.

So for this problem, we're basically asked to find the difference quotient of this function right here by using our difference quotient formula. And the first part of this is plugging expose age in for X. So I'm going to take this function F of X and plug in X plus H every time I see an X. So that would be X plus H squared -5 times x plus age plus one. That is telling me to subtract all of Quebec's. So I'm going to subtract to this entire function and I'm going to do that by putting the function in parentheses. And then I'm going to divide by each. So for the first part you would have to foil this together by writing X plus H times X plus age. And after you're done boiling you would get X squared Plus two x age plus age squared. Then I'm going to distribute this negative five to both of those terms in the parentheses, so -5 x minus five. Age plus one. And then I'm also going to distribute that negative, the very end to everything in the parentheses, all over age. Now from here, things should start canceling. So it looks like my ex squares are going to cancel. By five exes are going to cancel. Ones will cancel and that leaves me with, I'll put this it's some sort of an order H squared. That's two XH minus five age. All over age. And there's one more thing I can do here because all of these are visible by that age. So I'm gonna go ahead and divide by age. Get rid of an age on each term. That would leave me with H plus two x minus five.

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, age I have four years of full, so I'm just writing the reaction here. Just look at it carefully. I fear so four plus Bs er, two will react to form B A and so forth and at fiesta food plus any edge. We will react to form f e o it 0.2. This is of white PPT. This is of white PPD. So according to the option option B it correct answer for this problem.


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