5

67G4496 m49...

Question

67G4496 m49

67 G4 4 9 6 m 49



Answers

Find each sum or difference. Write in simplest form. $$ 8 \frac{1}{6}+14 \frac{5}{6} $$

Yes. This this problem illustrates a special product of Binah meals. Yes, we have six M plus I time six in minus time. And whenever you have by no meals that are of the form A plus B times a minus bi. Our final answer will be a square minus B square. So if a is six m a squared is 36 m square and it be is 55 squared is 25. So final answer here is 36 m squared minus 25. Thank you very much.

And this problem we're being asked to multitrack multiply a try no meal by a binomial. I'm gonna do this using the distributive property. So I'm gonna take the first term in my try No meal, which is m squared, and I have to multiply that to my vinyl meal and minus four. Then I'm gonna take the second term in the tri no meal, which is positive to him. And I also need to multiply it by the binomial and minus four. And I'm gonna take the last term the China meal minus nine. And I'm also gonna multiply that by the binomial and minus four. Now we just have to go ahead and distribute well m squared times m is m to the third and M squared times. Negative floor is negative for M squared. Now we multiply two m times m which is positive to m squared and then we have to m times negative four, which is negative eight AM Lastly, we're gonna multiply a negative nine times m, which is negative night em and negative nine times negative. Four is positive 36. And now we just have to combine our life terms. So if You know, this are like terms are already next to each other, that I'm squares, they're together, and the M terms are together. So I'm gonna bring down that first term and to the third. Then we combine negative for M squared plus two squared, which is negative to m squared. Now we combined. Negative, Adam minus nine. Um, which is negative. 17. And that last term doesn't have a life term, so we just bring down. So now with sounds are finally

Today we are solving or rather subtracting fractions with Unlike denominators specifically involving fractions with Paulino meals in the denominator. So in this case these are the two fractions I'm giving to work with. I want to start by factoring and notice right away this is a polynomial, that's a difference of two squares. So I can factor it as 12 M over M plus six and minus six. That then shows me that in order to have a common denominator, I'm only missing an at minus six from over here. So I'm going to multiply the top and bottom by end minus six, Distributing out the six gives me 6 um minus 36 Over are now common denominator of M-plus six times M minus six. Now that we have a common denominator, I can simply subtract enumerators six M minus 12. M. Is negative six M minus 36 over our common denominator. Yeah, I do notice too that I can take a negative six out of the top here, which gives me Native six times M-plus six over this common denominator, which then makes it so I can cancel out my M plus six is, and I'm left with negative six over m minus six as my final answer to this problem.

So here we have the free body diagram for each of the two masses. We can apply Newton's second law in the Y direction for the first mass. And here uh in part at least for part a uh the elevators moving upward at a constant velocity, constant velocity means that we're in translational equilibrium. This can be set to zero and we can say that the N. T. S. Of one minus mm someone G minus Tees up to would be equal to zero. And so tease of one. It would simply be equal to M. Sub one G plus T. Sub two. Applying Newton's second law in the Y direction for the second mass. Here again we have translational equilibrium. So this will be set to zero and we have that here T sub two equals M. Sub two G. We can of course substitute one into the other and we have that. Then T. Sub one was equaling two. M. Sub one. Key Plus M. Sub two G. Of course T someone would then be equal two G. multiplied by m someone Plus M. Sub two. For part A. We can then solve This would be equal to 9.81 m/s squared. This would then be multiplied by 2.0 plus 4.0 units of kg. This is going to give us then 58.9 Newton's. And so for part B. Now we have an acceleration so for part B we're going to do the exact same thing. However, now we have an acceleration we don't have translational equilibrium. So here we have to say tease of one minus M someone G minus T Sub two is going to be equal to one times A. The acceleration of the system of course then T someone Is going to be equal to M. Sub one, multiplied by a plus G plus teams of two. Some of forces we'll be needing that Some of forces in the Y direction would be equal to than the mass sub two times the accelerations in the Y direction. Of course here is simply uh the acceleration of the system. So we consider county. So two -M Sub two G would be equal to mm to a T sub two is then found to be equal to M sub two multiplied by a plus G. We can substitute one into the other. T sub one than equals M sub one A plus G Plus M Sub two A plus G. And this is simply equaling piece of one. Oh Equalling then M sub one Plus M. Sub two multiplied by A plus G. And at this point we can actually solve. So here Tisa one would then be equal to 2.0 Plus 4.0 units of kg, multiplied by 3.0 plus 9.81 units of meters per second squared. And so teachers have one is found to be equal to 76.9 Newton's. That is the end of the solution. Thank you for watching.


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