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(iii) . 2 (i): [30 Question pts] pts] 2 Solve 3A: Shoktiply the that Consider the this etv H 8 equation equation equation sin € by Is not it Fetv 1! 8 exact? ...

Question

(iii) . 2 (i): [30 Question pts] pts] 2 Solve 3A: Shoktiply the that Consider the this etv H 8 equation equation equation sin € by Is not it Fetv 1! 8 exact? y

(iii) . 2 (i): [30 Question pts] pts] 2 Solve 3A: Shoktiply the that Consider the this etv H 8 equation equation equation sin € by Is not it Fetv 1! 8 exact? y



Answers

In Problems $1-8$ : (A) Find translation formulas that translate the origin to the indicated point $(h, k)$ (B) Write the equation of the curve for the translated system. (C) Identify the curve. $$(x-3)^{2}=8(y+2) ;(3,-2)$$

In this question we have to solve or given the potential equation that is divide where the X. His. It was too three cause to works let's to sign to the X. And the given condition is Why why why to it was 28. No we can write the situation is the why is it was 23 post two works Let's to sign three x. And multiplied wife PX. Now we integrate yet on both the sides and after integration we can see here we get by the close to three into Signed two works by two and -2 into Signed three x by three. Let's see now we can see we need to find the value of this constancy and for that we are given with the condition that why Bye bye to because to eight it means that If excess by by two then why is it was 28 substitute this value here. So we see we got here it is it was 23 by doing two signed by and minus two Y. Today into sign trip by way too. Wait a while you can see here integration of chinese course so due to the citizen I had to right here of course. So for three years by three. No we substitute the value here. So here we have to write course so this is of course three by way too. And let's see now we can see it value of signed by zero and value of course three by but it is also zero So we got 30 that was too they don't mind a zero. Let's see the value of C. Is eight and now substituting this value. I can say that I get the required solution of this differential equation. That is why is it was true three x 2 signed to works -2 Way three cost 30 X plus eight. This is the of the given question here. Thank you.

All right. So let's write our translation formula. We have ex prime equal X minus h equals X plus eight. In this case we have. Why Prime equaling? Why minus K. And in this case it is why plus three meaning both points are negative. That is the center negative eight negative three. And our translation equation would be ex prime squared over the square root of 12 squared, plus the square root of eight squared and the numerator for that b y crime squared. That's all equal toe one. And this is this set up of an E lips. More specifically, this ellipse is major access is the why orientation and it's minor access is the ex orientation, and that's because the number below the X component of this ellipse is larger.

I'm here. We're, uh you're in the function. There is sign if X plus X squared and were asked to determine whether this is a solution to equation Secondary threw off. Why? That's why it's equal to X squared plus two, which our call equation war. And here there's really not much to do except just take the deal with theirs off our function and plug that into the equation. One that stood it here. So we need first secondary to So we have to take two during their sense the first year. It they're still right, Dex. There's well, the earth of science co sign. They're at their backs squares to x here and then we need one more. Do it after this and that is Theseus Square. Why the X squared? In other words, secondary there fly. They're stereotyped off this on dhe taking do it this term or term uses plus two. And now we just plugged it like this into our equation. This implies that thesis word point. The X square plus y is equal to negative sign X plus two clients are function itself richest sine x us x square. And we have a nice cancellation here and that is equal to X squared plus two. And that and it does agree with the right hand side of our equation. Therefore, dancer is yes, it does satisfy our equation.

Now in this problem, getting were given their function and their function. Name is data That's two times exponential three. T fires exponential of two times t and we asked to determine whether dysfunction is a solution to the fall in the friendship equation, which read Size secondary to Fada When a state of times first to tear through half data plus three times there is vehicle to native two times two special Tootie and which so we sent to take to do it. There's two directors of our function theater here It stood it the first day or two off their own care would be, um, it will be two times three times so six times either three t minus to retire speed to T No, if you're if you're not sure what's going on here simply, I use the exponential do it the other exponential formula. There it off exponential function. It's just itself, but combined with the chain. Or if you have some number here e to eight times t dirty here combined for dissing the changeable and from the changeover, the number eight comes down. Go back to our computation. We have first curative now and the second narrative then would be Just do it there with the first spirit there on that would be six times three riches, 18 times exponential three t My mom stood times two days, four times the institute. And now it's plug this into like this to into our creation here and okay, lets worried it's right down what we're gonna do first, say, the time Steve share out did the tea for three times. Now, the second year it there's here. So we replaced Edward. Thank 18 times E to the three T minus four times e to to t in minus fate of times with Ada is just my function itself times its territory and that were six times e to three t Why? As to time speed to t Finally, my the last term is three times to be two or three t wise to two. Now it's simplified this well, I feel like a turn by turn. We're gonna have exponential and all the terms are exponential, but there will be different powers up on top. Well, the biggest one seems to be inter 60 so it's quite that first, um, I will have 12 either 60 and then next How have e 2 to 5 t which will come from here and that's negative. Negative. So positive. Positive. Six times eat or five T. Now, at this point, you can already see that this is gonna This is not gonna be a solution, because this two terms, we're not gonna go away from this point in time because just collected all possible terms there and then the right hand side, we must have this. But let's just complete this for the sake of completion. And the next highest term is going to be eating before, too. And it looks like the only way that's gonna come from is here and here is real. And there would be so there's one negative sign to a narrator sign three years science, but it's gonna be negative two times e to 40. Now, there's this kind of some cancellation for you through three t term. Let's see. And then plus, I'm gonna have There's six here 18 years or 24 times. There are three times he and e to to t I need you to tea. I have negative for here. Then there were three here. Negative three here on dhe That's gonna be there were 78 or two. Anyway, this is way different thing. Negative. Two times e to To to. Therefore, the answer is that this function theta is not a solution to the given different short bridge.


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