find-the-coordinates-of-the-centroids-of-the-given-figures-each-region-is-covered-by-a-thin-flat-p-6

Name: find the coordinates of the centroids of the given figures each region is covered by a thin flat p 6
Uploaded: 2019-07-10
Duration: 8 min 16 s
Channel: Numerade
Description: Find the coordinates of the centroids of the given figures. Each region is covered by a thin, flat plate. The region bounded by $y=2(x+1), y=3 x+2,$ and $y=8$

Question

Find the coordinates of the centroids of the given figures. Each region is covered by a thin, flat plate. The region bounded by $y=2(x+1), y=3 x+2,$ and $y=8$

Amy Jiang · Accepted Answer

okay, were given this graph right here is why X cubed minus six X in this graph right here is equal to ex Murder Street X squared is equal to white. Let&#x27;s find our intersection points because we&#x27;re asked defined area of this petition. Be tree. Okay. What&#x27;s it from equal to each other yet? It&#x27;s minus three x squared. Is it X cubed? Minus six x. Okay, now moving them all to one side. We&#x27;re gonna x cubed. Minus four plus three X squared minus six X minus eight people is out. How can we find a route based on this? We already know two of them. One of them think that one and the other one is two. So let&#x27;s go with exes. X minus two and long Divide and find our other two words. Okay, we get X our X squared over here. So this is execute minus two X squared. Jack, this We get five x squared here when it&#x27;s X X. Okay? Yeah, doing it. That so? This is no. Five x by the X squared minus 10 x To check this, we get four x minus eight. Annan plus four get four x minus a projecting this. We get so Okay, so our new equation is X minus two times X squared. Housewife, ex plus four. And we can factor that because we know one&#x27;s negative one. That&#x27;s experts one. And was this expose for I believe, with strike our expanded, it&#x27;ll get X squared plus four x x plus for yeah, that Dubai. Okay, so our roots are excessive. Multitude. I&#x27;m here in section 4 30 is exiting good to negative one in negative for But it&#x27;s point over here that we didn&#x27;t know was negative for all right. Now working with this, let&#x27;s take the in a row from Negative Forge. Negative one of the top graph, which is excused. Money six X, uh, checked our bottom bath, which is three x R eight minus three. Explode the X plus in a girl from negative. One, 222 overtop craft, which is It&#x27;s minus three X squared minus our bottom graphic X cubed minus X x. Your ex. Well, yeah, actually, from looking at this now, they gave us the points for roots. I should have known that this was a major for okay. Anyways, simplifying this a bit. What? Yeah, plus the exquisite minus six X when it&#x27;s eight. The X plus in a girl from Bigger one. You too. Um, I&#x27;m gonna execute minus three x squared plus six x Those eight. The external instinct in a growing list. Well, that&#x27;s just Hey, I&#x27;m an extra before or for Phyllis three X Tuned off. Three assists. Executed minutes six x squared over two inches. Three X squared minus h x. You violated that. Make one good for plus negative X for over floor minus X cubed minus four plus three x when it&#x27;s when it&#x27;s our cost paychecks. So they&#x27;re the same thing, which is, uh, you&#x27;re signed, but different. Evaluated at two and negative. Hey, I&#x27;m running over here. Your ex For what? That&#x27;s execute minus three x squared when it&#x27;s aged. Excesses, Evaluated ads. You got a four and good one, but the opposite signs evaluated at negative one and two getting up again. They have one yet one over four minus one one is three plus thanks minus evaluation and negative for we get Make it four to Power of four. Does that give me 256 but it by 4 64 Plus I think the four to her straight. Just English 64 minus 34 To show you get 48 minus plus eight times for religious with 32. Okay, now a valuation. Uh, too. You get two to the par four, which is 16 over four. Yeah, the water by four. So I got confused, okay before, But this is a negative science. It&#x27;s gonna to part three, which gives me negative eight plus 2 +5252 witches before times three, which is 12 us two times a day, but 16 and evaluation. And make it one for this is Linus. You have one over four plus one minus Berta plus three X. So it&#x27;s three when it speaks. Okay, now, combining these that&#x27;s seen its combined a constant. So we have negative one minus three and plus eight minus 64 plus 64 plus 48 minus 32. Hottest over here. Minus four minus state plus 12 plus 16 minus one. What is three plus state? We get 40 and then our fractions are 1/4 over 14 which is gives me 1/2. So our area is actually what a 0.5

Amy Jiang · Answer

Okay, so we have a blue graph, which is why it&#x27;s equal to three excluded Plus eight X plus nine and this red graph, which is three y. Did you go to expose 24? Let&#x27;s evaluate with respect to mm, probably with respect to X would be good, but I need this point over here. Have a serial quickly graft us out in my draft. Infatuated. Three. Why we go to expose 24. And why is he for June 3 X squared plus eight x plus 24. Um, did it did it right. The X squared was eight. Experts story for why you 23 x squared plus eight x one in three Worry. It&#x27;s weird to give me a second here. Intimacy problem. And in the book, this is problem 40. Oh, I see what my problem is. I did close to four and instead of close line. Okay, so our points 22nd points are bigger. Two points right here. It&#x27;s negative. Two points for two. Okay, so we have from negative 2.42 two minute of several points. 14 of our top graph, which is next over three plus 24 What if i three, which is eight minus three X squared, minus eight x minus nine D x and that gives me Let&#x27;s Siege and we simplify a bit. What&#x27;s negative. Eight plus one over three that use me. Negative. Seven to over three. Seven times three looks to use me. Negative. 23 over three. So we get the integral from the two points for two. She had negative 0.14 Uh, eights, Linus 30 we can simplify it too. So what&#x27;s it&#x27;s minus nine using ahead of one and in minus 23 over three X minus three x squared. It&#x27;s interesting how all of the values that negative. Okay, evaluating that we get negative. X When is 23 over six x squared and minus. X cube are three cancels from negative 0.142 negative to ports for two. Okay, so it&#x27;s plug in the ghetto. So we have negative times, Negro. It&#x27;s for 14 Mmm. Yes. Minus 23 over six times in a four foot change. Her to minus negative. Put 14 to 53 Well, can&#x27;t. It gives me 0.67610667 minus minus, minus two points for two minus 23 over six times. You know, two points for two to power to minus two negative. Two points for 2 to 53 It is me. Minus 5.857045333 Okay, so now, adding these together with Quincy all 67610667 This gives me approximately 5.92

Amrita Bhasin · Answer

Okay, so graphing are two regions. It&#x27;s the first step. So we have Well, your equation like this three y equals X was 24. And then we have our parable equation through X squared plus X plus nine. That looks like this. Okay, we have 200 section points. As you can clearly see, this over here is the shaded region are intersection points are negative. 2.418 comma, 7.194 And I would highly recommend using a calculated to find the intersection points do second trace and then intersection points because this is really difficult to do by hand. Okay, we&#x27;ve got the two intersection points. Now we know that when we&#x27;re finding the area, we&#x27;re doing Juve Xmas off our backs. So using our intersection points Negative. 2.418 and negative 0.138 after back G of X minus After backs. So 1/3 ax plus eight minus three x squared. Minus eight x minus nine de axe. Integrating negative X cubed minus 23 over six X squared. Minus acts from the bounds of negative 2.4182 Negative. 0.138 Applying them fundamental theorem. A calculus. You should end up with 5.9 to 5

David Marsella · Answer

So here we have the region to find by the parabola X equals Y squared minus four and the line y equals X over three. We want to find the area of this region Eso first, we&#x27;re just gonna examine it, decide whether we&#x27;re gonna do this disrespect to extra why our equations haven&#x27;t been given to us in any specific order. Uh, but if we do, our vertical and horizontal Sinovel wind test will find that if we do this with respect to X, we will need to regions one here and one here. However, if we do it with respect toe, why we can perform it with a single region, Uh, and therefore only one integral. So this looks like initially this looks like this is going to be the simpler way to do it. So that&#x27;s how we&#x27;re gonna do it. Which means we did our line in terms of why so X equals three. Why? And we know that our general form, in terms of life, our area is gonna be the integral from a to B of f of why minus g of y do I. We have our two equations already. Uh, the on our horizontal line. The right end of our line touches X equals three y. So that&#x27;s gonna be our f of why and the left side, the most negative side of our line or end of our line. It&#x27;s our problem. So a parabola is gonna be our G avoid. Now we need to find our A and B, which are going to be these points here. So we&#x27;re gonna have to calculate those. So we set them eagle to each other. We have three y equals y squared minus four, which rearranges into y squared minus three. Why minus four equals zero, which factors into y plus one time is why minus four equals zero. So we have a why of negative one and four. So our boundary points for this are gonna be here at negative one and here head for so ever and B so we can fill in our integral. So we have the integral from negative one, 24 of three. Why minus why squared minus four de y. We can distribute that negative to get a simple polynomial, and we&#x27;ll end up with four plus three y minus y squared de y. This makes Thean a derivative, very straightforward. With the power rule we get for why plus three y squared over two minus. Why cubed over three from negative 1 to 4. Now we can perform our substitution ins. We end up with 16 plus 24 minus 64/3 minus negative for plus three halves, plus 1/3 after combining. All of these are area comes out to 125 over six and there it is. You&#x27;re done.

Linh Vu · Answer

So this is the graph. I&#x27;m the on tree functions and we&#x27;re from the graph. We see that intersection here goes under gone, uh, zero and Jew The second point Him? We don&#x27;t know yet. So let&#x27;s What you find is one. And the last one is very clear. That and upon trees, they&#x27;re Oh, so let&#x27;s try to find this intersection here. And it&#x27;s B agenda far minus x square and with the ex crab Bliss Joseph, With them it go. And now we will have we bring everything. One side&#x27;s always again. The Jew ANC square on. I would try to bring the X on one side and the number on the other side. So we have the two x square We could you two so x square court you won so angsty. Could you bless? A man is one so grey and this problem here will be one and three. So now we will try to spin this into grow into the £2. The first part will be here one here and the second branch will be the 2nd 1 hand will be here and we do too up. Damn! So the total area echo Joe the first indica goes from 0 to 1 and it&#x27;s between Duh this girl. Yeah, And this one here. So we have Onda excrement. You is a both that we have the X Square plus to minus the job. Less angst, the angst and for the father&#x27;s on is from the green one and fund a bubble one with the hangers from 1 to 3. And we see that this one here is above this one. So we will have far minus thanks Square minus Juba&#x27;s angst Andi act. And isn&#x27;t his fund up? Burba one. And now we will have a go Jew. And to cover room near to one. Thanks, Crab bliss. Thanks, Ana de act. And I found a second wouldn&#x27;t have from 1 to 3 minus next square. Bless angst. Blessed you do your ex and we get it on the equal to export Treaty of Arbitrary Plus X Square on with you evaluated from 0 to 1. Plus, there&#x27;s only three months expert to develop a tree plus X squared it. Damn it! You just you angst evaluated under one and three. So it we compute this one. Which again? The answer. We co Jew you and that&#x27;s the final Funda. Toto, I uh

Problem

Find the coordinates of the centroids of the give…

Problem 17 Easy Difficulty

Find the coordinates of the centroids of the given figures. Each region is covered by a thin, flat plate. The region bounded by $y=2(x+1), y=3 x+2,$ and $y=8$

Answer

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