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(b) Find L-1{F} ifs -1F(s) = s2 _ 8s + 25...

Question

(b) Find L-1{F} ifs -1F(s) = s2 _ 8s + 25

(b) Find L-1{F} if s -1 F(s) = s2 _ 8s + 25



Answers

Let $S_{m}=\frac{1}{2^{2}-1}+\frac{1}{4^{2}-1}+\ldots+\frac{1}{(2 n)^{2}-1}$, then value of $S_{25}$ is (a) $25 / 54$ (b) $25 / 53$ (c) $25 / 51$ (d) $1 / 2$

In this example. We're trying to solve the equation for B, which means we're trying to find the value of B that would make the equation true. To get beat by itself, I would follow D C B A, which stands for distribute combined balance. Answer. So the first thing I'm gonna see if I could do is distributive property, and I'm distributing 3/4 and to. So if I were to multiply 3/4 by 24 you can actually do that off to the side. So 3/4 tens 24/1 four, divided by four is 1 24 divided by 46 and so that would give me 18 minus 3/4 times. Negative eight would get me four. Divided by four is 18 Divided by four is to get me negative. Six. Okay, that if I were to distribute my 22 times five b is 10 b plus two times one is too, so I would have can be plus two. Next. I would see if there's any, like, terms that I can combine 18 and 6 ft or not like terms 10 b into or not like terms. Next I would balance and I would begin by balancing my variables, followed by my numbers, if necessary. So to balance my variables, I even need to bring the negative six b term over to the right where the positive 10 b term over to the left. And to do this I can only use addition or subtraction, so I'm gonna choose toe add six b since negative six p plus six p will be zero, but also because when I added on the other side, the result will be positive and I try to do that as often as possible. So this would get me 18 equals 16 B plus two. Now, I need to balance my numbers 16 and two. But to do this, I'm gonna use reverse penned ass. So I begin by subtracting two from both sides which will get me 16 equals 16 b. And then my final step would be to divide both sides by 16 which means my solution would be B equals one

In this example we're trying to solve for the value of A That would make the equation true, since there was variables on both sides. I like to follow the acronym D. C. B A in order to get the variable isolated. And so that means first, I'm gonna look to see if I could distribute and right here I can distribute. It's important to note that the thing that's being distributed is a negative, for if it helps, you could do keep change opposite to show that. So the eight a term is just gonna drop down when you redistribute a negative four to a negative five A. That's gonna be positive. 28. And when we distribute a negative four again, it's being distributed to a negative to. If it helps, you could do keep change opposite. Negative four times negative two would be positive. Eight. Equal sign comes straight down, and on the right hand side we have 12 day. Next, we're gonna look to see if we can combine like terms from the left side of the equation. I can combine a and 28 to get 28 a bring down the plus eight and equals 12 8. Now I'm ready to balance, and I'm gonna first balance my variables followed by my numbers. So to balance my variables, I either need to bring my 12 a term over to this side on my 28 a term over to this side. And when I do that, my only options are to add or subtract. Now, Typically, I would subtract 12 a because subtracting 12 a from 28 a would result in a positive. But I just don't like how that would leave a zero on this side, and that could be confusing to people sometimes. So in this instance, I'm actually going to subtract 28 day and then whatever I do on one side, I have to go in the other. Now, the reason this is gonna work is because 28 a minus 28 a will be zero, and so it's gonna cancel it out on the left side and put it on the right side. And again, the result is going to be negative. 16 a. But this is one of the few times where I'm okay with it being a negative, because if I had done it, the other way, I would have had a zero over here. Next. I'm going to divide both sides by negative 16. And so my solution would be a equals. I see the Fraction eight over negative 16 which would simplify to negative one. There was my solution.

We're being asked to find a someone and D for an arithmetic sequence where Ace of 12 is 24 a some 25 is equal to 50. Well, because we know the 12 term is 24 we know the 25th term is 50. We would have to add our common difference 13 times to get from 24 the 50. So, in other words, if we start with 24 and we add our common difference 13 times so plus 13 d, we should get to our 25th term, which is equal to 50. So now we just need to solve this equation. So we're going to subtract 24 from both sides and 50 minus 24 is 26. So we have 13 d is equal to 26. Then we divide by 13 and 26. Divided by 13 is to start comin differences, too. So now we can find a someone. So to find a someone, we're gonna use our formula to find the M term. So we have a seven is equal to a serve one plus and minus one times D, and we're going to use the fact that the 12 term is 24 which means that a seven will be 24 equals. We don't know ace of one. Plus we know and his 12. We have 12 minus one times D, which is two. And now we just solved race of one. Well, 12 minus one is 11. 11 times two is 22. We're gonna 24 is you go the ace of one post 22. And now we subtract 22 from both sides of the equation and 24 minus 22 is two. And now we found a sore.

Hey guys, in this primary, 2016 to the X is equal to four. And that five to the experts Y is equal to 6. 25. They were asked to solve for the value of y. First things first, let's solve for the value of X by taking log base 16 of both of these signs. Log base is king of please. If you do, a lot of these 16 of 16 to the X is equal to log base 16 of four. The right the left hand side simplifies to X and the right hand side. You could rewrite as log base 16 to the 16 to the minus one half power. Because if you take 16 to these are one half power. Because if you take the square root of 16, you get four. We basically rewrote for 16 to 1 have power, and that makes X equivalent to one half. Now, if you now, uh, doing the same steps if you take a log base five, uh, five X plus y and you take log base 56 25. We know that 6 25 is equal to five to the fourth power, so log base 56 25 is going to be equal. Four Log base 55 up to the X plus y equals X plus y. We know that X is one half So one half plus y is equal to four. And from here this is simple algebra. We get that y is equal to U 7/2. Now the answer choice that corresponds to 7/2 is answer choice C.


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