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4h8 dplL3T Ti-Mp31 4.232 6 "3...

Question

4h8 dplL3T Ti-Mp31 4.232 6 "3

4h8 dplL 3T Ti- Mp 31 4.232 6 "3



Answers

$$e^{-t} \cos 3 t+e^{6 t}-1$$

Okay. So for this problem, the pause transform that we need to solve is eat the power of three. T sign a 60 minus t cute plus aids the tea. Okay, So first we are gonna just call this is gonna be equal to the sort of some of its parts. So that's going to the transport of E to the three. T Sinus 60 a minus. Transform of tea cubes, us transform of e to the T. Okay. And so then, from the table 7.1 that has had to convert all these We get that anything in the former e to the 80 sign a BT is going, Teoh people to be over s minus a squared plus B squared. Thanks. Room for these rules. Anything t to the power of n ends up with the chance form and factorial over ass over and plus one. This is for escritor zero. This is gonna be for s greater than a and then lastly, this e to the A T will be transformed into one over s minus A for s greater than a says we're gonna use to. I saw what we have here and so this e to the three. T sign of 60 then becomes six over s, minus three squared, plus six squared. Then we're gonna get a minus three factorial over. As to the power three plus one. Um, lastly, we get one over s minus one. This is gonna be for our largest A, Which is gonna occur, of course, in this first expression. So this is gonna be for s greater than three. Um, and then this little bit of algebra to simplify it. So we get six over s minus three squared, plus 36 minus three. Factorial ist six over s three plus one. So the fourth power plus one over s minus one, uh, for s greater than three. And this is our final solution.

Yeah please. Hello. So the question is taken from vector valued function and section acceleration given the value of this path is equal to city is given us that is equal to 68 Plus three D sq J plus take your window. Okay. And we need to evaluate the value of speed and acceleration speed for in order to evaluate the speed let us first evaluate the velocity B is equal to eight of change of path. Okay this is a vector quantity. So that will be equal to 16 to why differentiation of 60 with respect to tease 60 plus 16 to J plus three T square in two cases the speed is a square like quantity. So speed from here is equal to square six square plus 60 whole square Plus three D Square Hole Square. So from here the video spirit will be equal to 36 plus 3060 square plus 94. So from here the value of sweet will be called to taking nine common we get three squared four plus 40 square plus T. To the powerful which is the required value street. Put it in the book. I'm sorry. And in after that we need to evaluate the value of acceleration. We know that acceleration is equal to the rate of change of velocity and that is equal to differentiation of six I within spectral T is equal to zero plus differentiation of 16 J. With the spectra, T. Is six G. And thirties differentiation of treaty square. Okay with respect to T is 60 K. So acceleration will be equal to 16 to J Plus T in two. Okay, Which is still required value of acceleration. So hope this clears your doubt and.

Today we are subtracting fractions with unlike basis specifically those involving Paula, no meals that needs to be factored. So these are the two fractions we're dealing with here. And I want to start bye simplifying this. Oh I forgot the negative 30. My apologies. I'm Gonna Simplify it by taking out the 2 1st. This might not go anywhere, but it's a simple thing we can do. So I'm going to do it and then I want factor the bottom Which it can be factored out into plus nine & T -3. Okay And then now we see something cool up top here if we distribute this negative one make this a positive and distribute now you want into the denominator we get negative three and plus T. Which is the same as t minus three which is what we have down here. I'm gonna rewrite that. Just that we don't have any confusion. We have T -3 now up here which means we are only missing this ti plus nine for a common denominator. So we'll do that. We'll multiply both sides by G. Plus nine of the top and bottom rather. Mhm. That now gives me two T. Plus nine plus 18. Sorry over our common denominator O. T. -3 & T. Plus the line. And it does actually look like I did this for no reason. So I'm gonna go ahead and redo it over here. Just really quickly Leave it at two T -30, Adding them together. We get 40 minus 12 over tm minus three. T plus nine. Now we aren't quite done. We're going to take out that four that we see in the numerator. It leaves us with T -3 and the numerator as well as the denominator. Which is great for us because that means we can cancel them out and we're left with four over T. Plus nine. As our answer for this problem.

We know that a squared plus B squared is a plus B I times a minus. B I This is an important concept list in the textbook. So we therefore know that factoring distributing the equation, foiling we have X squared plus negative nine I squared equals 34. Given this, we now know weaken supplies to be X squared, plus negative nine times. Negative one. As you probably know, I scored his negative one. This is a serum listed in the textbook, so we set this equal to 34. Now, we can supervise this to be X squared. Plus nine equals 34. Simple. Find the equation we have X squared equals 25 given excess plus or minus squirt of 25. So axis plus or minus five is gonna be our final answer.


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