using-structure-a-semicircle-has-endpoints-2-5-and-28-find-the-arc-length-of-the-semicircle

Name: using structure a semicircle has endpoints 2 5 and 28 find the arc length of the semicircle
Uploaded: 2020-03-09
Duration: 1 min 40 s
Channel: Numerade
Description: USING STRUCTURE A semicircle has endpoints $(-2,-5)$ and $(2,8) .$ Find the arc length of the semicircle.

Question

USING STRUCTURE A semicircle has endpoints $(-2,-5)$ and $(2,8) .$ Find the arc length of the semicircle.

Ali Soave · Accepted Answer

So first we need to find where the center of the circle is. We know that the cheap points that are on the semicircle has a diameter of starting at negative to five and to eight. So the center would be the middle of this diameter of the mid point. So we can use our midpoint formula where we add the exits and tonight by two and add the wives and divide by two. And this becomes our center. This, if we do the calculations, is zero and 6.5. So let&#x27;s put that into our formula for our circle. Radius squared is equal to set of X is gonna put zero minus two. And instead of why, I&#x27;m gonna put 6.5 and then minus eight. So I&#x27;m plugging in this point into this equation squared. So if I do the calculations, I can square root both sides and everything goes underneath. The radical negative two squared becomes 46.5 minus eight is negative. 1.5 y squared. I get 2.25 and then when I square root 6.25 get 2.5. So that&#x27;s my radius. So then using that information about another, she hear my art length is gonna be 100 80 over 360 which is half. And then I want to multiply that times my circumference two times pi times radius to 25. When I do all that, I get about seven points 85

Deep Kaur · Answer

and this question. We have a rectangle mutinous on my circle, a jungle made in Assam musical. Let&#x27;s say this is Oh, so this was be over to that said This is W and this is the Radius, Which is why if we focus on this particular part, we can find out what else is so using by Tigran Tea Room. Um, we also need to write down a few conditions with e. L is less. Stanton and W is less than five based on the left that&#x27;s given for the Radius. So in order to find the constraint will just use of a tag. Renteria, which is going to be l over two squared, equals 45 25 minutes. The whiskered squared on both sides and you will see l equals two 25 minus w school. So this is the equation off the constraint. So said this is the constraint. So now and we have to maximize the area off, you&#x27;re off the rectangle inside that semi circles will say a w o equals W O. And we have to minimize this area and we have eliminated the style here. So what we&#x27;re going to do is we&#x27;re going to eliminate all using this constraint. Equations will say a w Now there is no well when we plug in the value off all their soul say it is to W 25 minus w squirt. In order to find the maximum area we have to put a prime equals zero. So follow We will find out the drilled off dysfunction, uh, a prime. The blue is equal to the dude off the blue is one do 25 minus w squared plus w. And we can say this is half. So how half? 25 minus tore loose squared, minus half the driver do off. The function inside would be negative to w. All right, So this would be do 25 minus w squared. That&#x27;s make this great old half here. And plus, there was a tool so there would be cancelled. Now we would have a negative, too, because there is a negative sign there would have negative to the blue squared 25 minus w squared minus half, and we&#x27;ll plug this equal to zero. It will take this common, and, um and all right, so 25 minus doubly squared. And do Goldman factored out and we will be left with 25 minus to the blue squared equals 20 Ah, either this is equal to zero or this is equal to zero. So we can say 25 minus stewed of loose squared is zero. I&#x27;m from here. We can find out on the value off doubly squared. It&#x27;s just horrifying. Over do or less minus 5/2 will reject. Then you do well, you as both I&#x27;ll and a blue are grew to 10 0 So we&#x27;re going to say the word is five over a route to or it could be five route to over to All right Lent is going to be. I will use a equals w and we&#x27;ll find out the land from that equation and length is going to be to 25 minus doubly squared is going to be too 25 minus 25/2 equals fire. So w is fine root, too. And length is why. Now we have to find out if the area is actually the maximum the absolute maximum at these two points, we&#x27;re going to verify now. In order to do that, we have to find the second Roeder off the area function. So second radio off the area function is going to be the off 2 25 minus of loose squared minus half 25 minus to lose squared, which is going to be do W. You need to just simply fired, so I&#x27;ll just write down. The answer is to W 25 minus terribly squared, minus 3/2 25 minus studio blue squared, minus H W 25. Finest of blue skirt. I know self. We&#x27;ll find it at five. Route to plug in my room if I wrote to for each w there, so do for you. Do 25 minus 25 were two minus 3/2 25 minus 25 minus 85 rue du 25 minus 25/2 minus. Have and the answer would be minus eight. AZ minus eight is less than zero. We can say that this is the absolute maximum because there is no other maximum in the same in trouble. So given the information minus eight, lesson zero, it&#x27;s a negative value. It&#x27;s going to be a maximum, so there is a maximum. However, there is only one maximum in the interval. So we&#x27;ll say in the interval. That&#x27;s why this is going to be the absolute maximum. So w equals five. Ruto over to hell equals for you. Where do our absolute maximum values?

Joseph Lentino · Answer

in this problem. We have a circle. We know that the ark of the circle on the circle. So some mark up here. I&#x27;m not sure how far goes around, but let&#x27;s just draw it like that is going to be three feet. We know that the central angle is going to be my center. The center center angle is going to be 25 degrees were being asked to find the radius of this circle. Well, I know that arc length The arc length is actually equal to the Radius times the radiant measure of the angle. So that&#x27;s sorry. There were radiant. I meant radius. So that&#x27;s our times. Data is equal to the arc length. What do I know? I know the art length is three. I don&#x27;t know my radius, and unfortunately, my angle measure is given in degrees. So I need to convert 25 degrees into radiant measures. I&#x27;m going home all by my pi over 1 80 when I, um multiply that out, I&#x27;m going to get 25 pi over 180 degrees, and that will simplify to five pi over 36. Well, when I multiply both sides by the reciprocal here. I&#x27;m going to get three times 36 divided by five pi That will give me 100. Eat divided by five PI me, uh, in this problem, it&#x27;s in feet so feet and this would be my radius. Well, that&#x27;s great now, but let&#x27;s getting approximation to find out about how big that actually is. When I divide that out, I&#x27;m going to get about 6.8 eight feet as my radius. So either answer would be correct. This would be the precise or exact answer. This would be an approximate answer.

Charles Carter · Answer

is in this problem, Um, were given that we&#x27;re drawing a rectangle with a semi circle. So bear with me on my drawing here, but ah, we have. And we&#x27;re gonna be drawing a rectangle. It&#x27;s something like that. So equation for the semi circle is just a positive eyes of wine for which x squared That&#x27;s wife&#x27;s where the radius was. Five. So it&#x27;s gonna be equal to 25. That&#x27;s our constraining equation. We also know that the area of this rectangle is gonna be people to x times negative x or X plus Nate, no explosive native except zero, but like the length of our base is just gonna be two times X in times line. Okay, So, Arkan, our objective is to maximize our area in our area is equal to two X top spy. Okay, so for this, I&#x27;m going to solve my original equation for why, so that we can plug it into our area function something from why I&#x27;ll get why is equal to the square rear of 25 minus x square? Yeah. Plugging that into my area formula, don&#x27;t have area physical to two acts times a square here of 25 minus X squared. Okay. Somebody used the product rule for this and say you is equal to two acts. Envy is equal to our square root function. Okay, so I need to find a driven. But each of those functions said, d you, it&#x27;s just equal to two and D B. It&#x27;s gonna be equal. Teoh. Negative X over the square root of 25 Money Sex Square? No, just the application of power. Oldest, uh, the inside function is is raised to the 1/2 power. So if we subtract one and move it to the denominator, multiply by the drift of the inside. Good. Ah, on the product. Really? Have you times DV So we have negative two x square over our square It plus B times. Do you tear times a spirit of 25 minus six grand. Okay. And we want to set this derivative equal to zero to find our critical points. Okay, um, so or to solve this, I&#x27;m going to add my negative two x squared term to both sides and then multiple about sides by 25 minus x squared. So I&#x27;m gonna have to Times 25 minus six square equals negative two X square. I&#x27;m not negative cause I added it. But science. Okay, distributing the two. I&#x27;ll have 50 when we go ahead and add the two X squared to both sides of 50 equals four x squared. From there, four X is gonna be equal to the square. 50/4. Uh, I can pull it 25 out. We could pull 25/4 out so I could do five a route to over to. Okay, Let&#x27;s are accidental. You. So now that we have our X value, the width of the rectangle, it&#x27;s gonna be twice that. And so our wits will be fiber to. Okay, then our height. We&#x27;re gonna play this back into our wine function. So five route to over two squared is 50/4, which is 25 ever to. And so why? Because the scary 25 minus 25/2, which is the square root of 25/2, which is gonna be five route torto. Okay, kind of makes sense. And if you maximize the area, we would get something similar to it. A square. Okay, thank you very much.

Aishwarya Krishnakumar · Answer

for problem 38. We&#x27;re off to find the ark length of one part of a circle. So here I have the circle drawn and it asked us to find the ark length of the, um, segment between negative three. So 123 negative. Three and four. So from here, two, four, comma three. So 1234 Come on, three. So this is the segment that we are supposed to find. It&#x27;s all right. So the are Clint formula is us because square root So the inner grow of a to B square root of one plus why Prime squared t x. So to do that, first we&#x27;re gonna solve for y So it be why squared equals 25 minus x squared. Then we have why equals plus or minus I minus. We&#x27;ll be right that clearly plus remind a square root 25 minus x squared. So now we have to take the derivative of this. So the derivative would be why crime equals so we can move it. The two out. So it be negative eggs over the square root of 25 on his squared. So wouldn&#x27;t that we can plug it in to the Art Klink formula. So we have s equals a to be so in this case are a would be from here negative three And there be would be here before And we do this because it&#x27;s on the X axis and we&#x27;re using d X. If we were to use d why we would go from here to here. So negative three, 24 The square root of one plus this derivative squared So that would give us negative x square root of 25 minus x squared and this whole thing squared d x So let&#x27;s simplify this. You have the inner girl of negative 3 to 4 square root Uh, so we can actually d&#x27;oh five over square root of 25 minus x squared DX. So move it up here. Now we can go ahead and actually take the inner girl said, this is a so this is basically five times won over this. So this is actually an identity the into girl of that would be sign of the inverse sine of X over five. So we have five this five times Sign in verse X over five, and this is evaluated between the bounds. Negative three and four. So this gives us five. Sign in verse of you plug in the upper bound before over five, minus the same thing. But you plug in the lower bound and I get a three over five. This gives us an answer of five pie over too.

Finian Lickona · Answer

So for this exercise were given a circle and we&#x27;re told that the radius is 2.5 and the arc length created by our unknown Fada is 15 and we need to solve for this state of value. So we know that our Klink equals radius times data. So that means that 15 equals 2.5 times data. And if we divide away the 2.5 on both sides, we have data equals 15 divided by 2.5, so Seder equals six, okay?

Problem

REASONING EF is an arc on a circle with radius $\…

Problem 27 Hard Difficulty

USING STRUCTURE A semicircle has endpoints $(-2,-5)$ and $(2,8) .$ Find the arc length of the semicircle.

Answer

7.85

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