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Dhlt Eoa tetua ( putala Whot Waat...

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Dhlt Eoa tetua ( putala Whot Waat

Dhlt Eoa tetua ( putala Whot Waat



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Name each alkane.

Okay, so here were given Ah, loss. Transform of t cute Minus t Uh, times e to the power of T plus e to the power of fourty times co Sign of tea says the first thing you can do is just break this up in the three little chunk. So we will evaluate the low cost transform of t cubed. So track that from the transformer tee times e to the power of T now that to the transform for E to the four tee Times Co sign t then to evaluate all of these. We just want to use that table 7.1. Um, that tell us what the u a pause transforms are. So the transform 42 the power end is going to be an factorial. In this case, it's three over s plus and plus one. So again, this case and his three So it's gonna give us two out of four. Okay, then from Atlas attract in this case for the he's out of tee times like t to the power of and we get n factorial of this case is gonna be one over Ah s minus. Whatever each of the team's multiplied by in this case, it's going to be once we get s minus one for the power of and plus once and is what tea is raised to in this case is one us That's just gonna be U to the power of two. And then finally, we'll add that to this last function, which is going to be s minus a being. What he's multiplied by in this e functions has been before over again. That's minus a squares the s minus for it's where 1st 1 um and one being sort of what is multiplied with what to use multiplied by in the coastline function. Um, so if you're looking at table 7.1, that will make sense. And when we violate this will three factorial is going to be a six, and then one factorial is just one. It's worth noting that this is gonna be for s straighter than four. Okay, and then that is our solution

Okay, so we're asked his objective falling. So since one is just in to we need to borrow. So we get to and this is now 11. So 11 minus two is nine. And now, since two is us and eight, we have to borrow. So this is a five, and it turns into a 12 12. Minus eight is for Okay, So now since five minus 85 is less than five minutes borrowed, we get a one here. And in the 15 year 15 a minus eight is seven. And since when is less than seven, we again need to borrow. So this has turned into four. And now we have 11.7, which is for and in four minutes for is zero and two Do not equal to okay.

Okay. Looking at 20 s to the fourth plus 61 sq T plus three s squared T Square. We want to find the factors of this, and we're gonna get to factor by proofing. But first we gotta take out our G c f. And right now I see we have a GCS of s squared. So we're gonna divide each term by F squared. That would leave me with 20 s squared plus 61 s t plus three t squared. Now that I've done that, we're gonna go ahead and bring our s square down to the bottom so that we are ready. Um, to include that with our answer and we don't forget about it. And now I wanna focus on this right here. I want I need four terms. So what I'm gonna do is divide this middle term into two. I do that by 20 times three s 60 and then put the middle term on the bottom. I'm looking for two turns that multiply to give me 60 and combined to give me 61. It made this kind of easy for us. 60 times one is 60 and 60 plus one and 61. So 20 s squared plus 60 s t plus one s t plus a free T square. Now, we got four terms. We're ready to group. We're gonna grew from into choose, and then we'll take out the CIA. My 1st 2 terms have a 20 an s in common, so that's gonna leave me with s plus three t My 2nd 2 terms have, ah, positive t in common. And that's gonna leave me with s plus three two notice my parentheses. Terms are the same. They have to be because they make up one of the factors. The other factor is taking the terms on the outside and combining them into one. So they should be our factors for 20 s to the fourth plus 61 sq T plus three s squared T squared.

In this video, we're gonna go through the answer to question number 19 from chapter 9.3 to rush to find the inverse matrix off F S R E O X, which is a matrix as a function of time given here. First, let's recall that inverse off a product major sees a B is equal to the inverse off B plans by the invested a sharing all of the investors exists. So let's think about how we can write this in a slightly different way. So we kind of want toe, not have to worry about all the u to the t You need to mine it easy to tease. So let's just write the coefficients first 14 and then you see that all the first row almost quite by eating Timmy on the second row E to the minus t you know, 30 points to t so we can turns up by e to the t zeroes ever in the second row zero e to the minus t zero and 3rd 1 00 each of the two teams. Okay, let's call this one a on. Let's call, this one will be, Then we can use this formula to find the total invest. Okay, so first up, let's find inverse off, eh? Let's do it in the usual reduction way. So what we got 111 one minus one. See? You want one? Combine that with the identity. 100010 There. Is there a woman? Okay, we're reducing. Let's subtract the first row from the bottom room. That gives us 00 three minus 101 less. Attract the first road from the second road zero minus 21 Uh, then screw reminds 110 leave in the first row is it is one warning zeros era. Okay, so try it times in the bottom row by 1/3. We got 001 minus 1/3 zero 1/3. Get me. Okay, then this new bomb row, we can subtract that from the 1st 2nd most. So from the first room gonna be 10 because I want one. That one minus one is zero. It's gonna be one minus a bird. Sorry. One minus minus. A bird, which is one plus a bird, which is 4/3 zero minus 00 zero minus 1/3 as much bird. Then subtract the new bottom row from the middle road is your, uh, minus two zero minus one minus minus 30 miles. Off course, a bird which is minus two birds one minus zero is just 10 minus. The third is my herd. Okay, so bottom row stays the same. 001 Mines third, zero third. Let's multiply the middle Robot minds heart to get 010 Ah, my hard times minus 2/3 is 1/3 then one times minus half is mine minus half minus. 1/3 is 16 Then let's do the top road minus this new middle road. Then we're gonna get the matrix on at the identity matrix on the left for the 4/3 minus. Good. This one zero minus 1/2. It's okay. Zero minus minus 1/2. It's 1/2 on minus. 1/3 minus suit is minus 36 Which is my heart. Okay, so this is our inverse off the function called a Now it's fine. In burst off. I actually called bay. So be waas. Eat the tea. 00 zero. It's the minus t zero. Is there? Uh, zero. He said to take the inverse of this. This is really easy. Um, because when you got a non zero elements in the leading diagonal on and it's just the reciprocal off those beating darknet values on the rest is all zero. So eat the minus t 000 e to the T they were zero zero. Eat some honesty. Sorry. He's the mind to t expended in verse off X, which is inverse off. Maybe. Which is? They invest a inverse, which is, if the modesty 00 zero e to the T 000 into my studio tea. That's our invested. Be invested a waas one, huh? Minus off that, But it's hot. Six minds of the zero Third. Then when we we'll find them together, it's question, but we got E to the minus. See, huh? Modesty minus ah, the money's team. Bird eats the tea. Mine's 1/2. It's the mind. Yeah, it's the team. Six. It's the team, but Murray get minus. 1/3 eats the minus Tootie zero on the third eats the mind stated, and that's I invest


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