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Queetlot CornplutlonMocng anolhor quosbon Wil [email protected] INa Fusponsa Queston 16Let j6,Y)Thenl 8,(,0-2,01,410A48 0B -[60 OC81 00 No correci AnswerUotnalo Jarulliet Ine4aM...

Question

Queetlot CornplutlonMocng anolhor quosbon Wil [email protected] INa Fusponsa Queston 16Let j6,Y)Thenl 8,(,0-2,01,410A48 0B -[60 OC81 00 No correci AnswerUotnalo Jarulliet Ine4aMaelhleen,

Queetlot Cornplutlon Mocng anolhor quosbon Wil [email protected] INa Fusponsa Queston 16 Let j6,Y) Thenl 8,(,0-2,01,41 0A48 0B -[60 OC81 00 No correci Answer Uotnalo Jarulliet Ine4aMaelhleen,



Answers

$$\left(-4 y^{2}-3 y+8\right)-\left(2 y^{2}-6 y-2\right)$$

Okay, given 16 y squared minus 34 Y plus 18. Um, the first thing we want to do is take a g c f out. You'll notice they're all even. And, um, the G c f in this case is gonna be too. So when I divide all of this bite to it gets me to eight y squared, minus 17. Why? Plus nine. And that'll get our numbers more manageable. Now, I want to remind you that you'll tend to forget that g c f so I would encourage you to go ahead and write it down where you're gonna write your final answer at this point from here. We need to replace that middle term. So we're gonna do eight times nine, which gives us 72. And then we got negative 17 on the bottom, which is what we're gonna replace. Looking for two numbers that multiply to give me 72 combined to give me negative 17. So I'm thinking nine and eight is 72. If you make them both negative, there's still somebody, too. And they combined to give me negative 17. So now just focusing on this quadratic I got eight y squared minus nine. Why? Minus eight? Why? Plus nine. Now going from here. We're gonna group our 1st 2 and we're gonna group our last two together, and we're gonna take out the G C A. So from my first group, they both have a Y in common. So if I factor that out, I'm left with eight. Why? Minus nine for my second group. Be careful. You always gotta take that sign with you. So I've got a negative, and the only other thing they have in common is and that is a warning. So I got negative one, which is gonna leave me with eight y minus nine. So going back, our original factor of two is now gonna be, um, multiplied by eight. Why? Minus nine. And then we're also going to take our two terms on the outside and put them together as a factor Is what so two times eight y minus nine times of want minus one will give us our original quadratic of 16 y squared minus 34 Y plus 18

Were asked to solve this differential equation right here. Right on. And the general solution is given by the sum of the homogeneous plus the particular solution. So let's figure out the homogeneous first. So the homogeneous from the function that satisfies the homogeneous equation satisfies this. So we have to solve this right here. So the characteristic equations is this. And so this factors is our plus three times are plus two. And so we get the roots are 16 minus three, nor is equal to minus two, huh? And so this gives us that there function. Y h is a key to the minus three t plus B eats the minus duty. Hey. All right, so now let's find the particular solution. Okay, so we've got a polynomial here and we know how to deal with this. We can use the method of undetermined coefficients so the particular solution will be given by Cem. Well, this is of order to this pole. No meal. So I have to try a polynomial of order to the quadratic. So we try something like this, we plug it in, and then we gonna solve for Lambda to Lambda One and Lambda zero. Okay, so let me get some space here, all right? So why Key is given by plumb the two t squared plus Lambda won t plus lambda notes we want to solve for these coefficients right here. Okay, so six times, Let's Okay, so let's just go ahead and differentiate thes So we get the following. Hey, so now I want to plug this in, right? So here's how I like to do it. They actually figure out what these individual terms are, and then add them up. And then five Landa p prime. So that's 10 lander to tea was five under one, then Lambda P Double prime was to number two. Okay, you add these all up, you get that this left hand side is equal to six London to t squared, plus just group the terms to get so that we can use, um, comparison. You know, compare a coefficients more easily. Okay? And so this has to be equal to 18 t squared. Right? Okay, Okay. So to under two plus five. Lambda one close six. Lambda zero. It's the two right here. Okay. So comparing coefficients. We get these equations right here. All right, And so this gives us that lander to 0 to 3. Okay. And then now feed this into the second equation. We get the 30 plus six. Lambda one is a zero, which gives us that Lambda One is equal to minus five. No, Feed this into this equation and we get six. Lambda North is equal to Well, so this is, um, minus of minus six plus 25. So that's 19. So Lamda note. Okay, so let me write the results down here. So we said that. Ah, number 20 for three. Lambda one, Zeke to minus five. Plan Do not seek to 19 by six. Okay. And so this will give us completely what the particular solution is. And so the particular solution is given by three T squared. Plus will three t squared minus five T plus 19 by six. The homogeneous function was given by a E to the minus three tea plus B e to the minus two tea. And so therefore, the general solution, which is what we're asked to find, is given by this, and we are done

I can write the given expression eyes taking success common. So I get three by minus two multiplication. Why square minus five? Why, I just displayed the middle term as minus five y plus y minus five. Bye four Wise square. And here it is T d y squared minus two y plus three by minus two. Going forward and solving it For that I get the value Add so dislocated carefully I can I devaluate six Multiplication three by minus two by four y squared multiplication. Why? Why? Minus five plus one? Why in minus pipe I just take some value is common in numerator as village denominator and on solving it further I get the evaluate so just look at it carefully. Six months application three by minus two by four Wide square multiplication Y plus one Bye bye Plus one multiplication Why minus five by three by minus two Canceling the same term this term this term on disturbed, disturbed get canceled this term Get to end this term This time get three and this tangle toe so on solving it further I get the final values three multiplication Why minus five Bye two y squared as our answer

So here's an order of operations problem off the side. I'm going to write penned ass P. But I m and G next to each other in A and s because if you remember, multiplication and division go in order from left, right? And so do addition and subtraction. Another thing to remember is that this fraction bar acts like a grouping symbol. So what that means is we're going to do everything on the top. First, we'll do everything on the bottom second, and then once we finally have an answer on the top of the bottom, then we'll divide those. So if I look on the top and I followed penned as I scan through, I look for parentheses and I see parentheses. So the first thing that I'm going to do is eight minus six. And so what that's going to give me is six times eight minus six, which is two squared, divided by now at the same time. What I also want to do is because I know my top in my bottom are separate. I'm gonna scan through the bottom and I'm gonna look for parentheses. I don't see any Look for exponents. I don't see any, Never looked for multiplication and division. And so the first thing I see is 12 but a bit too. So at the same time, I'm gonna dio 10 plus 12 divided by two, which is six plus four. So on the top I scan through again. I had parentheses, but only have one item inside. So Ravana exponents this exponent of two is on Lea attached to the two. So two squared is going to be four. So six times, four over on the bottom. I'm gonna go in order cause I have his addition. 10 plus six is 16 and then plus for so no, the top again. I've got six times four, which is 24 divided by 16 plus for just 20. And so now if I reduce my answer to reduce my answer, I would divide top and bottom by their common factor. So the first time I think of is four. And so I would get 6/5. So my answer is six pits. I could also write that as one 1/5


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