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Let x be the triangulation of the klein bottle shown . so xwould have 18 2-simpices.a)compute the homology groups and their dimensions using maplesoftware or by han...

Question

Let x be the triangulation of the klein bottle shown . so xwould have 18 2-simpices.a)compute the homology groups and their dimensions using maplesoftware or by hand (though i wouldn't recommend it). what are thedimensions of h0(x),

let x be the triangulation of the klein bottle shown . so x would have 18 2-simpices. a)compute the homology groups and their dimensions using maple software or by hand (though i wouldn't recommend it). what are the dimensions of h0(x),



Answers

A graphing calculator is recommended.

Find the dimensions that give the largest area for the rectangle shown in the figure. Its base is on the x-axis and its other two vertices are above the x-axis, lying on the parabola
y = k ? x2, k = 8.
(Round your answers to two decimal places.)
height



width



In discussions have given their if omega is the region under the car, why if he calls to under route X squared minus a Squire and the limits are accessible to a two X equals two route to a then we need to sketch omega and then we need to find the area of omega and locate the central there's a horse all discussion. This catch of the omega is shown below so this is a sketch for the omega and the limits are a two on the road to a so we need to find this area scheduled area so let's see how to find the idea the expression to culture. The area is given by a recalls to integration a two on the road to a and the function is under route access choir minus is choir dx We know that the integration of under texas clemency is quality actually calls to one upon to X underwrote access square minus a Squire minus half a square log X plus under route extra square minus a Squire. And the limits are E to route to a Now what are the limits? So we get area? Hey recalls to 1.2 he's choir into on the road to minus log under rule two plus one So this is the final value for the area. Now let's see how to calculate this android we can write Expert into a equals two. Integration mm to route to a X into underwrote Access choir -1ire dx no to follow this integration consider X is choir minus it is critical to you therefore by the differentiation we can right two weeks dx recalls to do you hands ex D. S will be calls to do you upon to No when we substitute X equals two way in excess clemency is critical to you so we get U equals to zero and when we substitute X equals two on the road to A so we get U equals to a Squire. So based on these values the above integration becomes expert into a recalls to integration zero to a Squire. Underwrote to you do you account to the silver calls to one up on three U to the power three x 2 upon three x 2. And the limits are 0 to a square and expert in the way will be close to A cube upon three So when we substitute the value of area finally we get asked about it. The calls to to A upon three into underwrote too minus log Under a 2-plus 1. Now let's calculate by bar the expression for the Viber into a will be calls to integration A to route to a one upon to into X squared minus a Squire. Yeah So this will be equals two 1.2 and two X cube upon three miners integration of a square Yes will be called to a square X. And the limits are E two route to a no society or the limits so we get 1.2 22 a cube upon three minus route to Thank you minus 1.2 A Cube by three -Aq. When your father Albert finally, we get Viber into a recalls to a cube upon three and two to minus road to. And the value of fiber will be called to one upon a into A Cube about three In 2 to -2, substitute the value of area. So finally we get why are the calls to two minus route to A upon three and two due to minus log Route two Plus 1 hands X. Bar and by bar represents the central of the region. This is Viber and this is expert. I hope you understood the solution. Thank you.

In this problem here for U. C s toe. Approximate the mass off the cob. Lemina, that is Z equals toe into the power minus X squared minus y square, which lies about the region and used by X Square plus y squared equals to nine India X y plane such that the density function is delta or X y zed. Because toe under road X squared plus y square, the mass of the problem in a sigma density delta is given by AM is equals to double integral sigma direct RTs named this s number one here DS is equals to another would call x or call y whole square plus call X or calls a whole square plus one. Now consider the curve. Lemina that has given that equals toe into the power minus X square minus y square have differentiate the function partially with respect to X and y girls said our collegues equals toe curl our collegues into the power minus X squared minus vice square. Now differentiating this into the power minus X square minus vice square call over. Collegues minus X squared minus phi square. We got minus two eggs into the power minus X Square minus y square Now, Carl zero. Or call y people's toe. Call over Carl Y U to the power minus X squared. Minus five square. It was to you, to the bar minus X squared minus five square. Call over. Carl Y minus X squared minus y squared equals toe minus two. Why? It took power minus X squared minus vice square. Therefore D s is equals to under rude minus two X e to the power minus X squared minus white square, Full square, plus minus two eggs into the power minus X squared minus white square, full square plus one. I was simply think this we got DS equals toe under rule for you to the power minus two X squared minus vice Where? X Square plus Vice Square plus one. Now put the values off Delta and DS in number one equation. We got em Musicals too. Double integration Sigma under rude X squared plus y square Melilla under do or into the power minus two X square minus y square Medical X squared plus y squared plus one dx dy lie now substitute X is equals toe. Are Kasai in Tita? And why is equals tow our scientific data therefore X square plus why square is equal to our square and d X de vie is equals. Tow r D r d theta The limits are zero less than equal toe are less than equal to +30 less than equal toe Rita less than equal toe five before the mass off the Lemina is Emma's equals toe double Integral Sigma under Rule X Square plus vice Square. MaliVai under rule for you to the par minus toe X Square minus y square X squared plus y squared plus one DX dy vie is equals toe double integral 0 to 2 pi and 0 to 3 on the roof are square on the rue for E to the power minus two are square R squared, plus one R D R D Theater. We'll get double integral 0 to 2 pi. 0 to 3 are square under rude. Four are square into the power minus two are square plus one. The R D theta now use maple to evaluate the above integral. The input and out food will be double integral. 0 to 2 pi 0 to 3 are square on a rude four are square into the bar. Minus two are square plus one de are de Tita. Now at 10 digits, this will be 57.89 57512 Therefore, the mass off the cuff Lemina that is Z equals toe to the power minus X Square minus Y square will be 57.89 5751 so there's a solution.

In discussion. It has given that if omega is the region between the curve. Why if equals two. Cause hyperbolic X. And the X axis from X is equal to zero. Two. Access equals to one. Then we need to find the area of the omega and centered of your mother. Let's see how this all this question. The expression for the area can be written as A vehicles to integration. Act physicals to zero To Act Physicals to one. Why D. X. So we can write it as Integration. We go to one cause hyperbolic X. D. X. We know that the integration of cost hyperbolic X. D. x equals two. Sine hyperbolic X. Therefore the area will be calls to sine hyperbolic X. And the limits are 0 to 1. When we suggested the limits we get Sine Hyperbolic 1 -1 sine hyperbolic zero. And this will be calls to he squared minus one upon TUI. So this is the area. Now let's find this android. The value of X. Bar into a Can Britain us integration 0- one. X. Into cause hyperbolic X. Dx by the integration we can right X saying hyperbolic X minus because hyperbolic X. 0 to 1. And when we substitute the limits we can write Sine Hyperbolic 1-. Cause Hyperbolic one Plus 1. And this will be calls to E -1 upon E. Therefore the value of X. Bar will be called to E -1 upon E upon hey and this will be calls to E -1 upon E. Upon He Square -1 upon to we therefore the value of X. Bar will be called to two upon E plus one. Similarly we can find the value of my bar and we can write Why Bar into He recalls to integration 0- one. One by two. Cause hyperbolic Squire X. D. X. By the integration we can right one by four. Sine hyperbolic X. Cause hyperbolic X plus X. And the limits are 0- one. No substitute the limits we get one by four. Sine hyperbolic one. Cause Hyperbolic one Plus 1. And this will be equals two. It was the powerful plus four E Squire minus one upon 16. 8 of the power to to find the value of my bar. We can divide this expression by A. This will be calls to it to the powerful plus four E squared minus Fun upon 16 E Squire upon A. So this will be calls to why bar if he calls to each of the power for plus for E Squire minus one upon 16 E Squire upon He Square -1. A pawn to E. This will be calls to He to the power four plus four e sq -1 upon eight E. Into E squared minus fun. Therefore, this ain't Roid will be close to two upon E plus one. Coma eight of the power four plus four E square minus one upon eight E E squared minus one. This is the final answer. I hope you understood the solution. Thank you.

So here are question is given find the dimensions that give me a lot of this area for the rectangle sean individual. So before only it is said that a graphing calculator is recommended. Right? So we will see we were just calculated by ourselves. If it does not work then we can go ahead with the graphing calculator. So now it is said that its base is on the X axis right? And its other two advertises are above the excess excess, right? Lying on the parable Ebola by equals two k minus x squared. It's ok. Is equal to eight and we are asked to round off around your answers to two decimal places. All right, So we need to find the hide as well as David. Okay, so we are given with the values of the uh you can say the equation of a parabola. Right? So can we find the area? Yes, we can find the area so legislate here first. So the equation of area becomes two X into eight minus eight X eight minus x squared. So we are given with Y equals two k minus X squared. And k is given to us is eight. And here the advertises the coordinates are X. And Y. So can we say this? This land, this land, one, Land is, this is eggs. Uh And this is X again. So can we write this? Is adding both the values. We will just get this value as two words. So we are finding the area for the two expert. Now we need to find the area 40 rectangle Red Lodge's Syria. We need to find. So how can we find this? We we will just uh we will just uh see if we found out the value of X. Then we can easily find the area. So let us see how it is possible. So, if we differentiate this equation like Right. so for maximum area, for maximum media, whether wherever maximum area is concerned, we are just differentiating the equation. If we are given with the equation of Parabolas cities, D A V I D X with respect to X. Yes, so it will be simply 16 minus. This is six X squared, right? So yep. Yeah, yeah, so your maximum area is actually differentiation of area equals to zero. We just do like this. So it becomes X is squared equals 2, 16, that is mhm 16 are gone six, you can see. So it will be X equals two. Plus miners wrote over eight by three. So we got the value plus minus, I wrote over a biking. So for we will find a secondary motive chances. So uh for secondary radio, yeah, we will just confirm that this is the value of X or not. Right, so here it is uh D squared a by D X. Square. That will give us please 16 differentiation of 16 0 and it will be minus 12 X. So this will be Mhm. So we can find here let let we will just put the value X. X equals two, wrote over eight by three. Yeah great. It will be again the square, anybody in the square will be court. This will be minus 12. Route over eight by three. That is less than zero. Their food we can say dad Road over eight by three is the maximum value. Yeah. Uh huh. Yes. So here the value of X becomes what this is coordinate. So access actually road eight by three year. Okay, so it is it will be minus X minus Y. Right, so this will be minus route over eight batteries. So that makes plus minus values of X. Alright, so now the way to become we can right here with the word we have calculated with us two weeks. So two weeks becomes to route over eight by trees. That will give us yeah, we will just find it that you go home. Yeah. Eight by three gives us Yeah, that's mhm. 3.27 up to two decimal places we need to find. So your height becomes so it will be eight minus X squared S Y is given to us. So it is eight minus wrote over eight by three square. That will give us eight minus eight by three. It will be 16 by three. So that will give us 16 by three will be five point to retake. So this is an answer as weight 3.73 point 27 and hired as 5.33


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