Hi everybody, it's Jamie Nutter from Culture That Works and our new company called WorkXO here in Washington DC and you are watching Six Degrees of Association with Sarah, Rob and Andrew. And welcome to another episode of Six Degrees of Association. You came back and we couldn't be happier. We are the only online TV show that's dedicated to association success. Once again, I'd like to welcome our lovely panel for today, we've got Rob Barnes from Uptify and also Andrew McCullum from Fitness Australia. Thank you Sarah. Great. So just to set the scene for everyone who's only joining us for the first time, each episode of this TV show contains feature stories, regular segments and everything needed to bring associations into the 21st century. So first of all, I'd just like to go through some feedback from our last or our first episode. Feedback. We are open to feedback. Just some questions really, just on some of the things that we actually spoke about, really regarding the main area of topics. So Rachel M, she said she loved the show. What are your actual thoughts on member levels? So we're talking gold, silver, bronze. Wow. I want two minutes. I kind of feel like membership levels is the old school. But I guess look at the end of the day, how you package it is going to be based on how you, what you know about your own industry or profession. You know, I think mostly associations membership offering needs to reflect the way their actual industry or professions sell their products and services into the community. Okay. I'll take a slightly different view Rob, wouldn't be the first time, but I tend to think, you know, if you have categories of whether it's gold, silver, bronze level one, two or three, you're at risk of categorizing and really pigeonholing your members into certain categories.  I think, you know, in building flexibility into a model is desirable. And I think by doing that, allowing that, the member really decides what they want to get out of the association. Yeah, that's a good point. That's a good point. People are used to choosing their own adventure in the 21st century. You can do it just about anywhere else, associations have to learn to adapt to that. I love the iPhone model, isn't it really? Yeah. Everyone buys the same product out of the box, a week later, no two are the same. Different apps, different background, different wallpapers. And I think, you know, membership should aspire to deliver on that sort of flexibility for association. So there you are, Rachel Ems. You need the iPhone model of the membership. And from Darren H. So last time we actually spoke about the Uber versus taxis situation that happened. I see what comes down from you. So do you have any ideas on how they could have done it better? My first thing is that I can't believe that taxis didn't see, the taxi councils didn't see this coming. For them to be in a situation where they felt like their monopoly was going to last forever and not see that the entire world around them has changed, that's where the fail happened. Yeah. I couldn't agree more, I mean Uber came into Australia three, four years ago possibly and still they're saying, you know, pretending this isn't happening, they're, you know, making arguments about passenger safety and so forth. But, you know, I mean, one thing I think, and not necessarily the taxi councils, but I look at cab charge in Australia, I mean, cab charge or a multi-million dollar organization have made tremendous profits over the last three years. Why not invest some of that profit back into making a payment gateway, replicating some of the payment methods that makes Uber so successful? You know, that to me is where not the taxi council itself, but, you know, the role of the taxi council is to introduce and to encourage this sort of development for its members. So, yeah, I think they, there are a lot of fails to use your term that we could, that could have been done a lot better here. But for Darren's benefit, I think the key lesson here for associations is you need to be paying attention to what is outside your association. The world has changed dramatically. It's a bit like the, you know, there's a great story online about the necktie association for people who's made and sold neckties, who all of a sudden looked around their boardroom table and realized that no one was wearing a necktie. No one had paid attention to the fact that the times that moved on were not in old England anymore. You just get so into it, don't you? That's exactly right. So, that's really the lesson for most associations is paying attention to what's going on in society and how it's impacting what you guys are doing. Great. So, that's what I mean for a future segment. I think necktie association. Thanks for that one. We need to pick that one up. Yeah. Good work. Anyway, moving on. So, also we had some very attentive people in the first episode, it seems. So, Andrew, did you get bikes for your bell or bell for your bikes? I think my intent was to get a bell for my bike and I can say that they are suitably attached now. Thank you for our very attentive viewers as well for picking that up. Anytime you want me to bring anything like that up, just let me know. More than happy to do it. Bikes for our bells. You're going to leave fast for the next episode. There's an episode titled, I'm sure, Bikes for our Bells. At least, you know, we're not editing too heavily. So, now we get to the fun part, my most favourite part of the actual show.  So, we have our two panellists. Talk about some association that they've even given a thumbs up or a thumbs down to in the past few weeks. So, let's start with you, Rob. Who does your thumbs up go to? Well, thanks. So, as is probably expected, I've not chosen an association for my thumbs up. This is awkward. I know. You're on top of the episode content, aren't you, Rob? I've got the run sheet here. I'm cool. But there's a really great book that some people that I know quite well, I tend to call them friends. Andrew, if that's okay. Sure. Jamie Nutter and Maddie Grant have written a book. It was released late last year. And it's called When Millennials Takeover. And I think that it's the first time I've actually seen and read a book that talks about this subject, you know, this generational kind of subject in a way that's a user guide. And while it's not directly aimed at associations as such, there's so much in here that impacts associations. Okay. And the way it's been written is a real user guide that I think association executives could get a great deal out of. So they talk about what I love about society is like the ridiculously optimistic future of business. And associations are in business. They're in business to turn their surpluses into effort and value for their members. And the impact of the workforce being dominated by millennials is right now is starting to have a material effect. So the book itself identifies what Jamie and Maddie call I guess they're these values that define what the future of business is. Digital, clear, fluid and fast. Okay. And when I think about that as a mantra, as, you know, I'd love to know a 21st century association that says, you know what, we need a new constitution. And the constitution is about digital, clear, fluid and fast. Imagine a business plan that talks about how will we be digital, clear, fluid and fast in the 21st century. And it's relationship to the people who are going to be working in our association. So big thumbs up to Jamie, Jamie Nodder and Maddie Grant for this book. It's a real user guide for how we can do better. It has a great impact on association management. I feel so, yes, it's a little bit off script. It's not an association, but it's for association. So I'm running with it.  Thumbs down. Everybody else I've ever seen present about generations. So. Oh, jeez. It is. I've seen, look, I've seen some good presentations about the impact of the generations, but I'm kind of tired of seeing the same chart saying, hey, this is what baby boomers are. And this is what Gen X is. And this is what I just don't think people relate to that. They don't often see themselves as that person and like being typecast if you like. And I do feel like, I know millennials, Gen Y's or whatever that are not, they don't behave and don't have those kind of traits that they're being sort of labelled with. So if there's anything that we could do better as associations is perhaps stop trying to do this demographic research and anything that just labels people. I think people are, I don't know. You get tired of it.  And we as associations need to be able to cater for the way people see us, not us make decisions on how people, you know, should be defined by us anyway. So I'm just a little, you know, I'd love to see some different work and in contrast to the way Jamie Nodder and Maddie Grant wrote in their book, that's the sort of presentation that I think associations need to be seeing, not some of these charts. So thumbs down for some of the generational presentations that I've seen being presented to associations. Any comments on that guys, feel free to hashtag 6DA and let us know. Or even if you read the book or even heard of the book, that would be great as well. Over to you, Andrew. Once again, I'll try and keep this brief, unlike my fellow panellists here. I've got to give a wrap. Museums Australia and then New Zealand Equivalent, I'll do my best museums, Eotaroa. Not bad. Thank you. These two bodies are combining resources to host the Joint Museums Australasia Conference for the first time in May this year. Early indications are that they're going to almost triple the delegate numbers they have traditionally got for their respective conferences. By combining the two, they're obviously delivering a fantastic outcome for their members. The members are voting with their feet and pursuing a joint opportunity, which is delivering great outcomes for them this year. They don't have to attract some international interest too, I'd imagine. I'd imagine so, yeah. And obviously with a greater presence than would previously for two different conferences. Fantastic account. So thumbs up to those museums Australia and I won't try the New Zealand Equivalent for a second time. I'll rest on my laurels the first time. Again, a bit of a thumbs down. I read with interest, Association of Forums 2015 Board Survey. Interesting, one finding in there, 42% of boards take part in some sort of board performance evaluation or, you know, critical assessment of their effectiveness as a board. And this staggered me. 42% less than half of boards in Australia are actually undertaking some form of board review. Now, I mean if I'm a board member, my expectation is that the staff working for the organisation I'm a representative of, I want all of them having some form of regular evaluation, regular feedback from a manager. And the fact that only less than half of boards are getting that sort of participating what's a pretty basic fundamental exercise in performance enhancement. To me it's a really disappointing. I'm surprised you're surprised. You're surprised, I'm surprised. I didn't say I was surprised. Perhaps disappointed is where I'm going to. I think that board self-reflection, board self-evaluation, you and I both know how hard it is to, and it's often driven by the executive team, right? It's like, well, we have to be evaluated. We want everybody, it's a culture of reflection and feedback and the like. Performance enhancement. And the board members are saying, well, I just volunteer for this. I don't need performance reviews in my voluntary role as well as in my sort of work role. So I'm not surprised by it. Yes, maybe disheartened that feedback and self-reflection on these things aren't part of board culture, particularly when you have AICD providing training which has a lot of this embedded in it now. And AICD training is almost compulsory for board members these days. And it's a big part of it. So it's certainly worthy of a thumbs down. I agree, I agree. That's definitely. Okay, now we get into the next part which is the lunchtime special. This week we're actually going to be talking about associations and competitions. So I'm going to hand it over to Andrew and Rob for the next four minutes to talk about the topic. Do associations do competition well? Sarah said four minutes. Four minutes. Have I ever spoken for four minutes? Several times. Just many times over. I think this is an interesting tone to me. You know, I see it a lot.  You're our members. Why are you, why would you go somewhere else? And I think it's almost something, there's a feeling that some associations, they almost, they feel they should have an immunity from competition in a commercial space. Unless there is a very specific competition that's in place. So you see, at some stage, there's a historical split. You know, at some point that there's been a professional college or something and there's been a massive disagreement between two segments and it's actually split into two different associations. So there's inherent competition in that, which has its own troubles. But I get where you're coming from. Like that concept of, well, we are the professional society for X. Nobody else is going to do business in this space because why would anybody else want to try? But that's not the point, is it? No. And it's all nice. It's one side is competition with another association and another professional body. And then there's competition in that commercial space of, well, we're going to invest for our members. We're going to deliver a commercial outcome for our members. That's going to deliver revenue for the association, deliver benefits for our members. And that level also, there's sort of that, you know, it's almost an implied obligation that the member has to, well, because our association's delivering this on this business proposition, we should support it. There's a lot. And the association sometimes feels that. I agree. I think there's less, there's not enough attention paid to what the sector or just what the business environment is that surrounds that profession or that industry. So where if you're a trade association and your members are large corporates, you know, in whatever sector it might be, the association itself may not be paying enough attention to where else those companies are getting value? Where are they getting value in terms of their legal services and industrial relations advice? Where else are they getting? Because that's what they're competing with. They're not seeing that. Or if they're, if our associations continue to do the oh, well, was me kind of, well, we're just a not-for-profit or we're just a, we can't deliver that. Well, that's bollocks, I think, in the 21st century. There are plenty of opportunities. Competitions and inevitability, it simply doesn't go away. Just ask the Taxi Council, right? You wasn't paying enough attention to the fact that, yeah, and I think the challenge is, and perhaps harking back to what Jamie Norder and Maddie Grant are talking about is there is no such thing as not competition for millennials who are making decisions these days, right? I mean, right now, I would hazard a guess that you could set up a new membership organisation, regardless of whether it's not-for-profit or a membership-based organisation from your mobile phone in less time than it takes to have a board meeting and probably have more followers, more members, maybe willing to pay things. Like, in less than a day, you could do that and you could do it from a device you can hold in your hand. Our associations are running constitutional organisations that have been around for however long. It's just crazy. It's a board meeting we're having a discusser at the next board meeting in two months' time. Even the concept- It's not a conducive to commercially viable, successful organisations, is it? The concept, I think, Geoff DeCarnia talks about this a little bit about when he talks about the principles of sort of governance into the future or governing for the loss of control, he calls it. And it's this concept that eight people, 12 people, 19 people, elected, appointed, to sit around a table can make decisions that are in the best interests of 20, 30,000 members. Did they never met? Who they never met? It's crazy in the 21st century because the internet allows those 20,000 members to talk amongst themselves from their phones any time they're like without any reference to the association whatsoever. That's where the competition is happening and it is rarely on the agenda of most boards and associations. It's like the old selling point of an association where we offer networking opportunities. You know, Facebook offers networking opportunities too but you don't necessarily need to join you to get that sort of benefit, is it? Okay, my turn. Sorry guys, time's up. Thank you for that. So we say they don't do it well? No. Okay. I think they can do it a lot better. Okay, we're almost at the end of the 22 minute mark. So now the next section is where we talk about associations and there really is an association for everything. Today we're going to be spotlighting the Association for Pet Obesity Prevention. Over to you, Andrew. Thank you and I love this segment and this segment's about highlighting these great associations. It's certainly trying to and you know, I love the fact there is an association for everything and we're certainly endorsing these organizations that we mentioned. But yes, the Association for Pet Obesity Prevention or APOP as I've turned them, they were founded in 2005, headquartered in North Carolina and have a membership made up of very dedicated veterinarians, animal health practitioners of various levels and they're dedicated, committed to making the lives of dogs, cats, all other domestic pets healthier and more vital. But there is a serious side to APOP as well and that is that they are also promoting parallel weight loss between pets and pet owners. So we don't want an unhealthy dog nor do we want an unhealthy owner of that unhealthy dog, clearly. So to the good people of APOP, proud to salute you this week. The fine work you're doing on behalf of dogs, cats and their unhealthy owners everywhere and we appreciate you being a part of this segment. Good job. I love that. That's great. APOP. I love it. It's just great how they blend in animals with their owners. It's been a while since I've heard an association founded in 2005. So it's so recent. So that's great. Yeah. Crazy. Love to hear from someone at APOP. Yeah. Sounds good. Okay, guys, we're now at the two-minute warning, sorry. So this is a part where we actually take your feedback, pose it to our panel, talk about anything that's come through our Twitter feed as well, which is hashtag 6DA. So first of all, from TimD98, great show, guys. Any plans for any guest speakers in the future? Yes. Absolutely. As soon as one accepts our many invitations, I think. It returns our calls. One of the two. Well, I think one of the plans for the show was always to be at some of the key association events and take the show on the road. And thanks to the help of the guys that ran back conferencing, we're going to be able to do that. And so when we're there, we've got access to some of the people that we'd love to have. And yes, invitations are out there. We'd love to have some panelists come on and join us and do their stuff live. Great. And we're open to ideas or anyone who you think maybe is doing really, really well in this space and feel free to let us know and we can make contact with them and make it happen because that's what we do, right? Yeah, that's it. We make it happen. Make it happen. So Nelson for five, six love the shirts. So great work on the shirts, guys. Yeah. I think they look really good. I can't take any credit on the shirts. No, no. I think that's all. So yeah, anything. I think we need to get some other things around here just to... There's definitely some adornment. Yeah. It's a bit plain at the moment in Chattel. It's okay. We're growing into it. We're growing into it. I think the response so far to the merch has been good. Yep. We'll have merch tents set up in no time. Some of that. We could be very commercially astute and dare I say it, do we do competition well with the merchandising division very soon. So... Perfect. So guys, closing comments. Yeah. So I feel like we've created a great opportunity to be able to showcase some of the great work associations doing in a way that's not just the blog post and it's going to be a little bit more engaging. Absolutely. People feeding back, giving us some story ideas. Andrew's done some great work investigating some of the feature articles and some of the associations from around the world. We definitely want it to take that. The next opportunity is to build that community around the show. So when we launched the online community at AssociationSuccess.org, as many people getting involved in that is really going to bring the show to life. Excellent. Yeah, I'm with you. It's constantly surprising to me just how big the association sector is both here in Australia and overseas of course. So, you know, there's so many great stories out there. There's so many things with great topics to talk about. So really looking forward to exploring them further in future episodes. Should be great. Okay, that brings us to the end. Thank you everyone for joining. Remember to log on and go to hashtag 6DA to share your comments and your feedback and anything else that you really want to share. We'll take anything right now. And also head online to the online community association success.org to share even more feedback with us and to watch other episodes. Remember guys, that too much agreement kills a chat and we'll see you next time.


Hello friends, my name is Saurabh Deshmukh, working as an assistant professor in Department of Mechanical Engineering, Volchian Institute of Technology, Solapur. In this video, we are going to perform the static structural analysis of a cantilever beam using APDL, the learning outcome. After the end of this session, the learner will be able to perform analysis of cantilever beam using link 180 element. So we have opened the APDL window here. So first of all, we will need to choose the preferences. Just click on the preference, the new tab will open. So we are going to perform the structural analysis here. So click on that and just click on OK. So after that, click on the pre-processor. Then we need to select the element type. So click on the element type, then add, edit, delete option. You will find here. So click on that element, then click on the add. We are going to choose the link element here. So click on the link and 3D finest range 180 link you will find here. So just click on the OK. Now close this window. Now the real constants. But we are using here ansys 2021 version. So the real constants for the link 180 elements are not supported for the latest version of ansys. So you will find it here. Just click on the real constant, add here. Just click on the link 180 and just click on the OK. You will find the real constant for the link 180 element type are no longer supported here. So we need to create the link here. So first of all that, we will use the material properties. So click on the material property. Just click here on the material models. Then for the structural linear elastic, we are going to select the structural seal. So it will be isotropic. So the Young's modulus for the structural seal is 2E5, 2 into 10 raise to 5. That is Newton per mm square and the Poisson's ratio is 0.3. So click on the OK. You will find here the material is here, we have created a material. So just click on the close button. Now go to the modeling. Create key points. Now we are going to use the key points in the active coordinate system. Just click on the active coordinate system. There is no need to give the key point number. The answers by default take it in the sequence that is 1, 2, 3, 4. So there is no need to assign the values here. And you will find three sections here for x, y, z location in active coordinate system. So first is of x coordinate, second is of y coordinate and third is of z coordinate. So by default, if we click on the apply button, it will be taken as 0. So obviously the first element we are going to take at origin. So we will directly apply here. Then for the second element, it is at 300 mm. So just click, just right here, 300 mm, apply. And the third key point will be at 700 mm away from the origin. So it will be taken as a 700, apply. And the fourth key point is at 1000 mm away from the origin. So it will be 1000. Okay, just click on the apply and close it. You'll find the four key points are formed here. We have created four key points. Now we are going to create the lines. So click on the lines, a line and straight line. Click on the first key point to second. The first line is formed. The second to third and third to fourth. Just click on the OK button. Now we need to create the links here. So go to the sections. You will find option link because we can't give the real constant. That is area for the beams here. So click on the link, then add. We need to create three links here for three different step bars. We have studied in the previous problems, okay, previous video. So the first link, just give the, for the first step bar, give the one ID here. So click on the OK, then click on one and you will find here section data that is link area. Okay, so the first area of the link is 300 mm square. So click on the OK. Then we need to add another element. I just click on the add. Now we need to give the different ID name here. So we will click here, we will write here two, okay, then two again and the area of the second beam is 200 mm square. Just click on OK and then for third link, we need to give here three, okay, then three and the area of the third beam is 90 mm square. So we have written here 90 in the box of link area. So click on the OK here. We have created three links for three different bars. Now we need to mesh these lines here. Before that, we need to apply the area, okay, so go to the mesh attributes, then click on the lines, picked lines, then select the first line, click on the OK. You'll find here the material number, okay, the material is uniform for all the beams. So we'll keep it as one, then link 180, we are going to perform the analysis using link 180. There is no problem. Just we need to here select the element section, okay. The first section is of 300 mm square, mm square area. The second section is of 200 mm square area and third section is of 90 mm square area. So the first line is of 300 mm square. So just click and click on the up line, okay. Then select the second line, just click on the OK here. Then we need to select here second element, okay, element section of 200 mm square cross-sectional area. Just click and apply, then select the third line to apply the 90 mm square section here, okay, and then click on third, just click on the OK. So we have applied different areas for the different lines. Now we have applied the area. Now we need to mesh these lines, okay. Just click on the mesh tools, you'll find here a dialog box. Now we will divide these lines into one element, okay, because we are going to find the nodal values. So at first node, second node, third node and fourth node. So we need to mesh these lines or discretize these lines into one element. So just you'll find here line section. So select on the set, click all the three lines, click on OK. You'll find either we can give the length, edge, element, edge length or number of element division. So we will divide the lines into one element. So we will click here and apply here one, then click on OK. Then again go to the mesh tool. Just click here on the mesh button, select all three lines to machine it and OK. So we have meshed the lines here. Now we are going to apply the boundary conditions, okay. So the loads, define loads, apply, you'll find a structure here, structural, then displacement, okay. So we can choose here either key points or not because the key points are only nodes here for the elements, okay. So though we will select on the key points here, we are going to fix this support, okay. So click on the key point here, click on the OK. The new dialog box will get open and here we will find the degrees of freedom to be constrained. So we are going to constraint all degrees of freedom. So click on the all and click OK. So you will find here we have constrained this key point here or node here. So now we will apply here the force of 50 kilo Newton as we have discussed in earlier video. So click on the force oblique moment, on the key point, just select key point, then click on the OK. You'll find the direction of force or momentum, okay. So in f of x, f of y and f of z, we are going to apply in the direction of x axis. So we'll keep it as f of x and then 50 kilo Newton that is 50 into 10 raise to 3, okay. So click on the OK. So we have applied here a force of 50 kilo Newton. So we are going to now solve this problem, go to the solution, solve, you'll find two option current load step and from load step files. So we can give the different load step in a PDL but for this problem we have we have chosen only one load step. So just click on the current load step, click on OK. The solution is done here, close the dialog box. Now we will see the results here, the deformation, okay. So go to the list results, we are going to we are going to calculate the nodal values, okay. So click on the nodal solutions, then degrees of freedom solution. Obviously we have applied the force in x direction. So we are going to find the calculate or find the x component of displacement, okay. So we have selected it and click on OK. So you'll find it here the first displacement is 0 because we have constrained it for the second node it is 0.25 mm for the second for the third node it is 0.75 mm and for the third node it is 1.5033 mm. So these are we have calculated these values analytically in previous video you can check the link in the description and you will also find the maximum deformation value. So it is occurring at node 4 and its value is 1.5 mm, okay. I hope you have understood how to perform the structural analysis using APDL. These are the references, thank you.


Hey y'all, welcome to what Chelsea eats. This evening, I want to make two smoothies for breakfast in the morning because I have an early morning and I don't think I'm gonna have time to make anything for me and my husband, so I'm gonna make smoothie. So what I have here is about a cup and a half of blueberries that I had mixed with some homemade yogurt that I made and if you want the coconut yogurt recipe that I have, I'll link it below. So I'm just gonna put this in the blender because I didn't finish it. I've got deglic dates, and I'm just gonna use two of these and I have some unsweetened almond milk organic, and I have one packet of flat-leaf parsley, and this is going to be our breakfast for the morning. So I've added some washed flat-leaf parsley to the blender. That's the first thing I'm adding to the blender. Next, I've got the blueberries and yogurt that was left over in the refrigerator. You can leave the yogurt out. I'm just adding it because I don't want it to go bad. Go bad. Plus it's going to make the smoothie taste a little creamier. I added two large frozen bananas. Next, I added two deglic jake dates. If you have medjool dates, just use one because deglic jake dates are much smaller than a medjool date, or you can leave it out. It just depends on how sweet you want your smoothie to be here. It's because it's good for building the blood. So if you have anemia, it would be good to add parsley to your smoothies. Plus it gives you a different taste to the smoothies. Okay, I'm going to measure two cups of almond milk. And usually I make my milk. There are recipes on my channel with almond milk, hemp seed milk, so you can go through the recipe section and find that, but I'm measuring it just because I didn't want to not put enough. And I also wanted to just measure this out so that I can give you the exact ingredients for this recipe. Because lots of people can wing their smoothies, but a lot of people they need the exact ingredients. So next I'm just going to blend this until it's smooth and I'm going to store it overnight. And I'll show you how I do that in just a second. So here's the smoothie all nice and blended, blended smooth. And it's probably going to be about three cups per smoothie. Actually, yes, this is about five and a half cups. So just about three cups each. Okay, so what I'm going to do is take these two mason jars and I'm going to fill them up with the smoothie as much as possible almost. Probably two and a half cups each. And I'm storing them in mason jars just in case because I think my husband actually has meetings tomorrow. So he might take this in his lunch bag and drink it either on the way to work or when he gets to the office. And sometimes in the mornings, I go to the park and to walk. When I'm done walking, I like to have my breakfast. So there you have it. Those are two yummy smoothies that are good for the gut, good for building your blood and giving you a good amount of energy to last you throughout the morning. All right, if you like this video, please give it a thumbs up, share it with a friend. Don't forget to subscribe. And until next time, y'all, talk to you soon. Take care.


Hello and welcome to another session on jumps of geometry Now in this theorem, it's given that the external bisectors of any two angles of a triangle Concurrent with the internal bisector of the third angle so Points to be noted here First of all, they're saying external bisectors of any two angles of a triangle Let's try and understand what's external bisector is first of all. So let's say this is a triangle and If I produce one of the sides So a b c is a triangle and let's say I produce this bc side to D then if I draw this line which is Let's say cm Now if these two angles are equal, then we say that cm is the external angle bisector of ad now We can have, you know Multiple external angles at a point actually. So if I produce let's say a c Like that. So this could also be the external angle, isn't it? So let's say this is theta This is theta. So hence multiple external angles are possible For a triangle, okay now so once we have understood this what is an external back bisector Now we need to understand what x circle is. So let's understand what an x circle is So many of you would have come across the concept of in circle But let's understand what x circle is. So first of all, we have to have our triangle. So let me draw a triangle So this is a triangle and now I let's say this triangle is a bc and I extend Right bc and extend Let's say b a like that. Now guys The circle which is tangent to all the three sides which three sides B a extended, let's say this is d bc extended Let's say e and the side ac. So it would appear to be something like that Okay, so this circle which will be formed which is Tangent to all the three sides Yeah, so one ac and the other two b a extended and bc extended will be called as x circle and the center of this circle, let's say the center is over here wherein, let's say if you drop a perpendicular on a b like that and Like that on the three sides. Let's say like that. So these you know the center this o is the x center What is it x? Center, okay, and the circle this one here will be called x circle So you can imagine if this is one x circle, there could be you know couple of more in fact two more So if I draw this draw that and here is another circle like that So this one will be another one and let's say if you produce this and produce that So there will be another one like that Okay, so there could be three x circles and x centers possible and the one which is let's say inscribed within the Triangle will be called be in circle and the center of this will be called in Center so I hope you now understood the concept of x circle and in circle, right? Now let us explore the given theorem. It says the external bisectors of any two angles of a triangle, okay? So in the given picture if you see closely a bc is the triangle So let me highlight the triangle a bc is the given triangle, okay? and You can see I a or z a z b if you can notice this z a Z b Right, so basically a b is being produced and x c and x b So bc is being produced in both sides and Y c and y a so a b ac is produced on both sides. So if you see You have external angles z a So this z a bc this one is an external angle, isn't it this angle is an external angle and it's bisector I see I be so this line here is the bisector Okay off this external angle similarly I a See this one is an external bisector of Angle b c y a angle b c y a So you can take your time and see b c y a so these are the external bisectors and The question our theorem says the external bisectors of any two angles of a triangle are concurrent With the internal bisector of the third angle. So these are the two external bisectors. I a b and I a c are the two external bisectors and we have to prove that a I a a I a is the internal bisector of angle B a c a I a is bisector of Angle B a C Right, this is what the theorem is suggesting similarly if you take these two external bisectors then B Angle the bicep internal bisector of B that is this line B. I B Also pass through I B or you have to prove that if you join B. I B B and I B then it is the Internal bisector or bisector of internal angle B and likewise the other side this one So these are the two external bisectors and Right, so I hope you understood the theorem. Okay, so now let's look at the proof so I a B I a B is the External Or sorry not external is the bisector. I a B is the bisector of Angle I a B C Sorry not I a Z a Z a Z a B C Z a B C Okay, so I a B is the bisector of angle Z a B C and I A C I a C is the bisector of Angle Z sorry why a Why a C B Correct. Look closely. You will get it now. That means I a is equidistant equidistant from From which two sides B Z a and B C Why why is that because we know that if Because angle bisector is nothing but the locus of Points which are equidistant from the two sides and we have seen this in the previous session So hence if this is an angle and if you trace the trace the locus of all the points which are equidistant from both the Sides then you will get the angle bisector. So this will be angle bisector. This is what we have learned, isn't it? So I a is equidistant from B Z a and B C similarly I a is equidistant equidistant from BC and and Why a C because if you see this point I a is lying on the angle bisector this angle bisector then I a must be equidistant from both from both DC as well as Why a C is it now from these two we can say I a I a is equi equidistant from Which two sides B Z a as well as why a C? correct I a is equidistant from B Z a and why a C or I a is equidistant equidistant from I can say a Z a a a Z a and a Why a isn't it because if you see B Z a is nothing but extended a Z a or Extended a B is B Z a and extended a C is a why a okay now from this We can say What what can we say about it so hence? So I a is equidistant from B Z a And why a C or I a is equidistant from a Z a and A why a now what is this if you see clearly that means I a must I a must lie on the bisector of angle Z a a Why a isn't it because if a point is equidistant again the same theorem if a point is equidistant from two intersecting lines Right two intersecting lines. They are equal as this is equal to this then this point will lie on the angle bisector why? because if you take these two triangle, let's say P Q R and S in these two triangles these two if you see these two triangles what happens? So this side or let's say this side is what this side This is 90 degrees and this side is common. That means these two triangles are congruent and hence This angles would be equal. Okay, so hence we prove that I a must lie I a must lie on the bisector of angle Z a A why a and what is it? It is nothing but I a lies on bisector I a lies on bisector of angle B a C hence Proved right that means all the three bisectors two external bisectors External angle bisector and one internal third angle internal bisector all are Concurrent so this is a very interesting theorem


Hi everybody, I'd like to speak today about Unicraft or how to cut your cloud computing costs by half. So the private and public cloud have been huge success stories and for good cause. On the positive side, they're very easy to use. They provide great scalability so you can grow your business very easily with them. And they provide a multitude of services. For instance, Amazon claims that they have over 200 fully-featured services. But everything's not perfect and on the downside, the virtual machines that are being run on the cloud tend to be extremely bloated. They're on most for all of the time even though they're not needed most of the time. And all of this is of course bad for the environment. So we need to cut down on the fact that's being run on public clouds and we do this in two ways. We need to first deep load our VMs and we also need to stop idle VMs from running all the time. The problem has two parts. The first one is to do with size. So if you look at your virtual machine that you deploy on the cloud, it's made out of multiple components. Of course your application and this is the bit that you actually care to run. But underneath there's a lot of unused components that are being run and all of those orange parts are wasted resources that are costing you money. The second part of the problem has to do with time. When you deploy your virtual machine it immediately starts running even though it may be idle. At some point in time some client request traffic comes in and it becomes active. Once it's done dealing with those active requests, it goes idle again and then the cycle repeats. The problem is once again all these idle orange parts are costing you money and those are wasted resources. So one way we can deal with this is through specialization and by achieving high efficiency. And in the virtualization space, specialized virtual machines are essentially what we call unikernals and I'll explain a little bit more about what unikernals are in a moment. So the goal we have is first we want these to be easy to build and run. In the past there's been a lot of unikernal projects that were efficient but had to be hand built all the time and would take months of expert work to run a single application. There should be easy or no application porting. We shouldn't require modifications to the actual application. And the third one is of course that they should perform well.  They can start and stop very quickly and have good migration times. There's been even some papers showing that these can boot in as little as a few milliseconds, which is not far from what a process takes to actually start. They have very low memory footprint so you can imagine running real world applications such as Nginx with a few megabytes of RAM or less. You can have high density because they would quickly, because they consume little memory, you can fit thousands of such virtual machines on a single x86 server. They can have high performance so you can have as many as 300,000 requests per second on an Nginx server. And of course they have as a side-to-side security features like a small trusted compute base and so forth. So let me just show you what a unikern actually is in one slide. Imagine all you want to do is run a web server. Normally what you do is you take a general purpose OS and distributions such as Linux and Ubuntu. And on it you're going to have third-party libraries and you're only going to do a few of those to run the web server, but you get all of them. There's OS libraries, same deal, not everything is needed by the web server and then out of the kernel you don't need all the functionality of the kernel but you get all of it anyways. In fact what we'd like to do is by some sort of magic be able to take those colored squares and build a custom operating system and software stack for that web server. And that's essentially what a unikernel is. But it takes lots of development time. In the past we had to manually sort of build this unikernel from scratch for each single application. So the question is how do we transparently build efficient and posix compliant unikernels such that we can get the efficiency without having to spend a lot of expert time porting applications. So we have two design principles with Unikraft. The first one is that we wanted a fully modular kernel that would make it really easy to pick and choose components we want and we don't want for particular applications. And the second one is that we wanted to provide high performance specialized APIs to get even better performance. So on the modular kernel, one question would be why not just use Linux and configure it. And to answer this question we put together a dependency graph for the major subcomponents of Linux. And if you see a line between two such components it means there is a dependency and the blue numbers above them is how many dependencies there are. And it becomes pretty clear that it's kind of hard to take out one of these components. It requires a lot of engineering effort. So Unikraft is built from scratch to be fully modular. Could we do it with existing Unikernel projects? The problem is that most of them require significant expert work as I mentioned to build for each application. They're often non posix compliant so you cannot just run standard applications. And the Unikernels themselves the kernel part is still monolithic it's just smaller but it's not necessarily easy to plug and play components in and out. Unikraft is built from scratch with some boron. The second design principle had to do with specialized APIs and here's a little example to show you what I mean. Imagine you have an application and obviously compiles against some sort of libc in this case glibc and under that it needs to do some networking so it uses sockets. The network stack is underneath and eventually you get to some high performance API. In Unikraft you could bypass all of that and go straight to UDP and I'll talk a bit more about that later. So this is the generic Unikraft application you have sorry architecture you have the application on top. And under that you have the libc layer so far we support muscle and new lib. Under that you have what's called the poses compatibility layer it's a bunch of different libraries such that you can run standard applications on Unikraft. And under that you have the core of Unikraft and all the black boxes are the actual specialized APIs. So for instance this red box shows my previous example where if you want to do high performance networking you would plug you could bypass all the posix socket stuff and plug directly into UK NetDev. Same thing if you're trying to do file systems if you know all you want to do is retrieve some files for a very simple web server you could design your own custom file system to go even faster and I'll show an example of that later. You can have different memory allocators in Unikraft so far we support different about five of them because different applications perform differently when using different memory allocators. So let's go to the first goal which is things should be easy to build and run. So nothing to show you that let me just show you a little video we have a tool called craft that wraps around Unikraft. And the easiest thing you can do is say craft up and you choose an application in this case engine X and you give a name for the actual virtual machine that's going to get built. And that single command is going to fetch all the sources that it needs to build including the engine X sources. And once it's done building it's going to actually launch the virtual machine in this case it's on KVM and there you go it's up and running. And just to make sure it is working properly we get the IP address and we're going to download a simple web page there is. Let's try it once again. And a third time and then you can see that it's actually up and running so with a single command you've now built a custom stack for engine X and are now running it. So the second goal is that we should be able to run applications without having to port them or it should be easy. So for this we have two approaches to essentially POSIX compatibility. The first one we call auto porting and in this case we assume we have access to the sources like or engine X or redis or a skewered light. And what we do is we build them with the native application the native build system. But against muscle. And then we link the resulting object files into Unicraft. We have our own ported version of muscle. And then of course muscle requires Cisco so we have a Cisco shim layer. And under that we have our own implementation of Cisco's that go to the different Unicraft kernel libraries. We also have a mode called binary compatibility. This is for the case where we have no access to sources. So instead we take an unmodified L compiled under Linux. And we have a library that is essentially an elf reader and loader. And then we trap the actual Cisco's and redirect them to the Cisco shim layer. So it all boils down to Cisco support. Essentially this little box under here. So regarding Cisco support there was a paper. So far we support about 146 Cisco's but to put this in context there was a paper back in 2016. That was did an analysis of how many Cisco's are actually needed to run useful applications. Linux has in the order 350 Cisco's which is quite a bit. But as it turns out you don't need all of these to run applications. So to take a little point in that study space if you have in the range of 145 as is the case with Unicraft right now. You could run in the order of 50% of the applications. Of course it matters which of the Cisco's you actually support not just any 145. So to get a little bit more precise we did our own study in Unicraft. And we took the top 30 Debian popcorn applications the most popular ones. And we here have a plot where in the x-axis we have all the applications. And then the y-axis we show how much system call support we have in Unicraft for each of the applications. And the takeaway message is that it's mostly green. We mostly support all of them and with a bit more work we would support the remaining ones. But are all the Cisco's that are we did the analysis for really really needed. The reason we asked this question is because from working with Unicraft over time we noticed that sometimes when we didn't have any Cisco support for an application that was using it in the source code the application would still run fine. So we started to dig a little bit more as to why that was. And the intuition is that you have a lot of snippets of code in applications and this is from Redis that is resilient to the lack of an actual Cisco. So in this case the Cisco is get our limit. And if the call is not there if it fails then Redis defaults to a same value. And there's a lot of this in application code. So it turns out that maybe you don't need all the Cisco's that are in the source code to actually properly run the application. So to dig into this a little bit more we started putting together a tool that basically is its Linux based and dynamic. And it starts splitting an application Cisco's into you know which Cisco's are in the source code which Cisco's are in the static binary. But then it doesn't have that dynamic analysis that tells you yes this Cisco is acquired meaning if you don't have it the application will not run. It will tell you which are working if you stop them meaning if you return you know sis you return I don't have the Cisco which of the Cisco's will still make the application run even if you don't have them. And then we have another category we call faked which means we return a success value, but we don't do any work. And we see if that also allows the application to run or not. And the analysis is based on an application's own test suites and benchmarks. So here's the results. This is an analysis of five applications but the results are similar for other application for more applications as well we have Redis engine X men cash T as good light and they just proxy here. And on the y axis we have the number of system calls that are used or needed. And as I mentioned, the legend is the categories I spoke about before. Just to give you a point in the space I'm not going to go over all of this. If you take engine X and if you look at the actual static binary, you think you would need in the order of 110 system calls. And actually the picture is not as bad as that because if you run the full test suite of engine X, it turns out that you need about 50 or so Cisco's that's the pink or violet part. And but there's several Cisco's that you don't even need and many that you can actually stop or fake and the application will run the entire suite of engine X programs correctly. In fact, you don't need to support everything that is in the sort of an application source code. Finally, on the last category, we want to obtain great performance, of course. And one of the questions is this auto porting sacrifice performance. So to answer this question, we compared a manual port that we did of SQLite on Unicraft and compare it to the auto porting version. And to do the measurement, we do we measure the time it takes to do 60,000 insertions. And as a baseline, we take Linux, which it takes about one second. We compared against the manual port on new live, which is also about one second just slightly worse than Linux. And against muscle also the manual port. The most interesting bar though is this one, which is the auto porting bar. And in this case, you can see that we don't take a hit from the reporting. And so this is good news. So now let me show you a few performance graphs. So the first one is image sizes versus other projects. In the X axis, we have Unicraft first and then we have a number of other Unicernel projects, but also Linux and Lupine Lupine being a Unicernel based on Linux. And on the Y axis, we have image size and megabytes for a few different applications, a low world application, but then also engine X rays and SQLite. And you can see here that Unicraft comes here at the bottom where the very basic image just a low world is a couple of 100 kilobytes and the actual other applications are a few megabytes in size. Unicraft boot times. We support different VMMs. So we have Kimo, Kimo with an interface, Kimo micro VM, and then a few more specialized VMMs such as solo five and firecracker from Amazon. And we measure the total boot time. We also split the measurement between the actual VMM and how long the Unicraft guest takes to boot. And you can see here that the worst case scenario with Kimo is about 40 milliseconds where most of the time is spent on the VMM. If we add a network interface, then the time goes up slightly. If we use micro VM, which is a faster version of Kimo, then it goes significantly down to nine milliseconds, although you can still see that this is dominated by the VMM. And then the fastest times you get are with solo five and firecracker, just a few milliseconds. What about memory requirements? Again, we're comparing against other projects and Linux. Same applications as before. And you can see that Unicraft, when running the actual applications only means a few megabytes, at most, in this case, two to seven megabytes, depending on the application. Okay, so some performance numbers to do with engine X throughput now. Again, against the number of different projects against Linux as well. And we are measuring throughput in thousands of requests per second on the Y axis. And you can see Linux as a baseline Linux KVM, we have about 100,000 requests per second. Linux native, so non-virtualized, is about 175,000 and Unicraft is all the way up here with almost 300,000 requests per second. Red is performance, same setup as before. And we measure how long it takes to do gets and sets. And I'm not going to really go over this, but basically you can see that Unicraft is basically at the performance of Linux native. Boot times with different allocators. I mentioned that one of the things you can specialize for in Unicraft is different memory allocators. We support five different ones and there's an API that allows you to add more. And you can see that the actual boot time varies with the actual memory allocator. The standard one called binary body takes about three milliseconds, but we even built a custom boot allocator that is really, really simple. It's just meant to go fast. If you do that, then you can go in less than a millisecond boot in less than a millisecond. Throughput is also affected by memory allocators. So we did a test where we use four different memory allocators for Redis for gets and sets. And you can see that there's a significant variation between tiny alloc, which is a simple memory allocator and meme alloc for Microsoft. So it really does matter which memory allocator you're using. Now, just a little brief thing about specialized APIs. As an example, we targeted the file system area. In this case, we're trying to do a simple web server that does, that serves static files. And for this, we custom design a file system that is based on a hash. It can quickly retrieve files. That file system is called SHFS. And so in this graph, we show how many cycles it takes to retrieve a file when it's there and when it's not there. On the left-hand side is Unicraft. On the right-hand side is Linux. So Linux VFS, you can see it takes in the order of 4,000 cycles when the file is not there and 2,600 when it is. We also disable mitigations because this affects performance. So you get 3,200 for the null file and about 2,000 for when a file is there. As a baseline, we use Unicraft without specialization. It's using our standard VFS core and you already get some gains compared to Linux. But you get the most gains, of course, when we use SHFS. And then you get really low times of about 300 cycles. We also took Unicraft to the cloud.  There you can see some instances running. So for this test, we took two large instances at first. And on one, we put a standard Nginx Debian image with Linux. And on the other one, we put the same Nginx version but on Unicraft. And we did a throughput test and we got about two times the throughput. We also took then a, we kept it one large instance. And then we compared against the medium instance. On the large one, we put Linux and on the medium one Unicraft. And we got about the same performance. So this means that it's 50% more efficient. Of course, we wanted to see if this translated to any money gains. So we looked at our bill on the Amazon EC2 console. And you can see here that we basically had 50% savings by using Unicraft in this scenario. So we'd like to go toward seamless integration and deployment. And to do this, we are integrating into a few major frameworks. The first one is Kubernetes. We have this almost working, but it's not public yet. Where we basically can directly plug into Kubernetes. You use the standard Qubectl commands, the standard dashboard. But underneath we're actually creating and running Unicraft Unicranos. For monitoring, we have now support for Prometheus and Unicraft. So you can use your standard Prometheus dashboards to monitor the statistics and the runtime of Unicraft. And we're in the process of integrating Unicraft into virtual studio code so you can do your development of applications and so forth. And the building of Unicranos directly from the... As I probably failed to mention so far, Unicraft is an open source project under the umbrella of the Linux Foundation and the ZEM project. So if you want to go check it out, you can go to www.unicraft.org. And you'll find lots of information, documentation, upcoming events and so forth. Just to show you a little graph of GitHub star growth for Unicraft. We've been doing fairly well in the past few months, but we are always, always happy to receive more support. So please go check us out. If you want to know all the gory details, there was a Eurosis best paper award given to Unicraft in this year. So please go check it out. If you really know, really want to see the analysis of how Unicraft works. And just to conclude, we think high performance POSIX Unicranos are now a reality. And as I mentioned, please go check out our websites. Please go try it out. Give us feedback about what works, what doesn't work. And if you'd like to contribute, we would be more than happy to have your contributions. And on that note, thank you so much for your attention and I'd be happy to take any questions.


Hello and welcome to the session. In this session we discussed the following question that says construct a triangle ADC in which AD equal to 6 cm, BC equal to 7 cm and CA equal to 6.5 cm, find a point P equidistant from B and C and also equidistant from AD and BC. Let us consider some useful method to be used in the construction. Locals of a point equidistant. The straight line is the given. Let's proceed with the solution now, ADC in which AD is 6 cm, BC is 7 cm and CA is 6.5 cm. In the next step, we have 6 cm and in the next step, we have 6.5 cm. At this point of intersection of the two arcs, we point next step, we join the triangle ADC in which AD is of measure 6.5 cm and BC is of measure 7 cm. ADC is the required triangle ADC. Let's suppose to find a point P which is equidistant from the points B and C equidistant from the sides AD and BC. Equidistant from two given points is the right point P which is equidistant from the points B and C would be the right by sector of BC. That is the line joining the points B and C. The right by sector side BC, by sector of the side BC would be equidistant from the points B and C. Next we know that the locals of the points equidistant lines would be the by sector of the angles between the given intersecting straight lines point P which would be equidistant from the sides AD and BC also. So we will draw the angle by sector formed between the straight lines AD and BC, angle by sector, angle by sector of the angle ADC. Now as you can see that the right by sector of the side BC and the angle by sector of angle ADC intersect at also from the points B and BC. That point I should hope you have understood the solution of this question.


What's good, George Boar Ross back again with another video. So I'm going to check out 10 WWE gimmick matches that should never see the light of day. Not all the time does WWE come up with a interesting gimmick match that actually works and actually has people wanting to see more of it. Sometimes they come up with gimmick matches that are just completely nonsensical and should never ever see the light of day. We're going to check out some of those instances where those gimmick matches just have never been created. Appreciate all of the support. Let's get right into this one. There have been some iconic match types throughout WWE history from the Hell in a Cell match to the TLC match. These matches are incredibly popular with fans and I so beloved that WWE even turned these match types into their own pay-per-view beginning in 2009. Nevertheless, there are also some match types that are truly awful and the majority of the fan base hoped they never returned. These match types usually insult the viewer's intelligence and have less than sell a track record when it comes to producing great matches. Join us now as WrestleMania looks at 10 WWE gimmick matches that should never ever see the light of day. Be sure to subscribe and hit that notification bell for daily wrestling videos and follow us on Facebook for exclusive lists. Also check out our new channel, WrestleMania Shorts. Number 10, The Stairs Match. A 2014 TLC pay-per-view was rebranded for one year only as tables, ladders, chairs and stairs. The Stairs addition into the pay-per-view name was added because one match on the pay-per-view card would be the first time ever, Stairs Match. Yeah, sounds incredible. The Big Show collided with Eric Rowan in the match and to put it politely, it wasn't good. They'd never been desired from fans to see a match dedicated to Stairs, mainly because they are a common feature of most matches and even throwing an opponent into them doesn't usually result in a DQ. Big Show and Rowan did the best they could with the bizarre stipulation but the match failed to meet WWE's expectations. They clearly expected the stipulation to take off but this was the first and only Stairs match in WWE history that's extremely unlikely that the match type will ever return again. No more. Number 9, The Swamp Fight. When the COVID-19 pandemic shook the world, WWE were forced to change the way they conducted their business. Due to no fans being in attendance for Raw Smackdown and their pay-per-view events, they would introduce fans to cinematic matches. Some of these cinematic matches were better than others. Notably, the Boneyard match between Taker and Stiles was acclaimed by many but some matches just fell short. The 2020 Horror Show Extreme Rules event was headlined by Bray Wyatt vs Braun Strowman. This wouldn't be a standard 1v1 match up as it would be the first time ever Swamp Fight. While some fans praised WWE for doing something new, a lot of fans believed that this match type didn't warrant a main event position on the pay-per-view. The match itself was shot like a movie and it featured cameos from Alexa Bliss and the Wyatt Family member version of Strowman. It failed to connect like other cinematic matches and hopefully WWE will never revisit the unique match speculation ever again. Number 8, The Eye for an Eye Match. Speaking of the 2020, this match was so f***ing infuriating. Talented wrestlers like Seth, Enrae, should not be just subjected to doing dumb, nonsensical, makes no absolute sense whether you type it and put it on paper or actually put it into motion. Someone should have said, hey, this ain't it. An eye for an eye match where your opponent has to take out your eye for them to win.  Money horror show at Extreme Rules, The Swamp Fight wasn't the only gimmick that debuted on the show. Arch rivals Rey Mysterion said Rollins competed in an eye for an eye match. This match could be won when the eye of an opponent was extracted. Yeah, literally. This was a rather sinister match for a PG product and WWE actually used prosthetics to make it seem like Mysterious Eye was actually removed. Mysterion Rollins had tremendous chemistry in the ring but the stipulation was just too much and a standard Street Fighter steel cage match would have sufficed that it's highly probable that the eye for an eye match remains retired but you never know. One day, WWE could decide to book the sequel to one of the most infamous matches of the modern era.  The Kiss My Ass Match type has been used a number of times throughout WWE history. Perhaps the most notable time it was used was back in 1999 at the Summer Slam pay-per-view. The Rock took on Billy Gunn but the match type added very little to the match itself. The match has even been used in the PG era as two former world champions in Seamus and Dolph Ziggler competed in the match type at the 2015 Extreme Rules pay-per-view. This match didn't work for a PG audience and the WWE were evidently reluctant to follow through on the stipulation of a wrestler kissing another wrestler behind. The problem with the match is that it creates a booking problem as someone is always going to look insanely weak and embarrassed so it's best to avoid the match all costs. Number 6, Zombie Lumberjack Match. A lot of these are pandemic matches, bro. I get it and I appreciate WWE for trying something different but you a zombie lumberjack match, bro. I get used trying to promote for the movie with I think Batista was in the movie. I think I ain't enough actually seeing that movie. It wasn't that bad but bro what are we doing? This is just so bad. It's so bad. Oh my god. To promote the army of the dead Netflix movie, WWE did something special for their 2021 WrestleMania backlash pay-per-view. They would have Damian Priest and the Miz compete in a zombie lumberjack match. The match would be a standard lumberjack match but on the outside of the ring instead of wrestlers there would be actual zombies. This match received insanely negative reviews from fans as well as critics such as Dave Meltzer, one of the stars of the movie Batista even told fans to stop tweeting him about the match.      Dave was like why you tweet me? Why you tweet me?  That was, I'm good man. I'm good.  Match and informed them to tweet Vince McMahon if they didn't like it. It's unlikely that the match will ever be brought back. However they reportedly paid a healthy sum to promote the movie in this manner and with the army of dead two planned it wouldn't be out of the question that we see a second installment of the zombie lumberjack match. Number five, blindfold match. On the surface a blindfold match is an exciting concept. Two wrestlers where their vision removed can in theory create a hilarious matchup. However when it becomes obvious after seeing one of the two of these matches in WWE that the wrestlers could clearly see out of the blindfolds the magic is lost. The concept doesn't work if everyone is aware of the secret behind the match and WWE have been reserved in using the match type over the past decade but that doesn't mean that they won't ever bring it back. If the match type is ever brought back it needs to be tweaked or a modern day WWE audience isn't going to like what they're seeing. Number four, the kennel from hell match. On the unforgiving pay-per-view in 1999 saw WWE debut their most infamous match ever.  This match saw a steel cage getting closed by a hell in a cell and that ringside was supposedly savage dogs ready to tear the wrestlers apart. The match was a total disaster as the dogs themselves began to defecate and mate on the outside of the ring and this sinister matchup quickly turned into one of the funniest matchups ever. During an interview with inside the ropes Al Snow would discuss the dreaded match and this is what he had to say. The match will never return to WWE but to even know it may one day show up in the WWE video game installment. Number three, pole matches. The whole match that every wrestling company including WWE have failed to master is its matches involving an object on a pole. Whether the match be a kendo stick or a contract on a pole match they are usually massive let downs. One of the problems with the match is that they can be rather anticlimactic as there is a lot of stalling and wrestlers don't have weapons as they would in a TLC match to provide exciting spots. WTW's use of the pole match is also a big reason where the match is universally hated as Vince Russo has a habit of using the match in the most unusual ways possible. Nevertheless, WWE have struggled to master the match and even when they use the match type on pay-per-view in 2017 for Bayley's match with Alexa Bliss the match was so bad that it almost completely destroyed Bayley's entire character and persona. Number two, chairs match. In 2009 for their inaugural TLC pay-per-view, WWE would debut the chairs match. The rules of the chairs match stated that the steel chairs are the only legal weapon in the match and due to WWE being a PG product this limited what wrestlers could do as chair shots to the head was strictly prohibited. The first chairs match would be between Batista and the Undertaker and the match was incredibly awkward as a concept just didn't work. There have been several chairs matches over the past decade and the majority of them have been terrible. The concept simply didn't translate well and nobody was ever crying out for a gimmick specific match relating to a steel chair. And number one, the Punjabi prison match. The Punjabi prison is one of the most unique structures in WWE history but the match type itself has resulted in some downright awful pay-per-view matches. The concept was first used in 2006 and the Punjabi prison features two bamboo cages and the first wrestler to escape the two cages wins the match. The match type is confusing but it also lacks a sense of brutality that was needed for a match type of this nature. Additionally, one of the major flaws in the match was that it was notoriously hard for fans and attendants to see what was going on meaning that all three of the Punjabi prison matches have been met with a lukewarm response. The last time they used the concept was back in 2017 and the match was heavily panned by fans so it would be nonsensical for them to bring back the match type. All three of the Punjabi prison matches have been linked to the great Kali in some way and with Kali being out of the WWE for a number of years hopefully the Punjabi prison match remains retired for good but they have it folks. My number one pick still would be that eye-for-eye match because that's just, you know, sneering in right quote-unquote almost lost his eye. It was a fake eyeball. It was just awful. And then close second would probably be, it's either that one or you could choose the zombie one, the zombie lumberjacks. That's just, all right, that's turn off your TV inducing bad.  So comment down below. Let me know what other gimmick matches do you feel like should never be seen on WWE television ever again and would you replace the number one spot even though the Punjabi prison matches they've never been good or what not the concept and how it looks looks cool but in execution it usually doesn't work that way. So that's why I would rearrange some of these matches to be number one whether it's the eye-for-eye match or the zombie lumberjack match. They would probably be number one on my list or equally as bad but I appreciate all of them support world 250k and I'm still here to speak to you to present ship of the world. Appreciate y'all kicking me. See y'all next one. Peace.


So it's useful to remember that while we can always attempt trial and error factorizations, there are some special products that are easy to factor. And if you recognize when you have a special product, it's much easier to factor. For example, if we expand A plus B squared, we find the product is A squared plus 2AB plus B squared. And this gives us a very specific form. Notice that this product is the sum of two perfect squares plus twice the product of the square roots. And so if we ever run into any expression that is the sum of two perfect squares plus twice the product of the square roots, we know that it's the square of a binomial. Well, the first thing to check is to see whether we have the square of a binomial. So is 4x squared plus 9y squared plus 12xy the square of a binomial. So remember the square of a binomial has a very specific form. And so we want to see if our expression has the same form. And so we might notice that 4x squared is the square of 2x. 9y squared is the square of 3y and 12xy is 2 times the product of the square roots, 2x and 3y. And so we have the square of a binomial and that's going to factor as A plus B squared, 2x plus 3y squared. So let's try to factor. Now in the real universe math problems drop out of the sky with instructions on how to solve them. Oh wait, they don't. So we do need to check. Let's see if we can use this new fangled tool of the square of a binomial. And so remember we require that we have the sum of two perfect squares and twice the product of the square roots. So well this 25x squared looks like it might be a perfect square so let's see if it is. And it is in fact the square of 5x. We have these other two terms. 10x doesn't look like it's a perfect square but maybe 1 is and so we find. And so 1 is 1 squared, a perfect square. And now for the check, the remaining term, 10x, that needs to be 2 times the product of the square roots, 5x and 1. And so we should check it. And it is. So we have the square of a binomial and it's going to factor as a plus b squared. 5x plus 1 squared. How about something like this? Well to begin with remember that when we find the square of a binomial we have a bunch of added terms. So we might want to rewrite this as 18x squared plus minus 24x plus 8. A useful thing to begin with is to always start by removing any common factors. And we see here that all of these terms are even so they all have a factor of 2. So let's remove that common factor and now let's see what we have. So we notice that 9x squared is a perfect square. Minus 12x doesn't look like it'll be a perfect square, but 4 has possibilities. And then minus 12x, well that's 2 times the square roots, 3x and 2. Oh wait, that's not true. However, all is not lost. Remember that every real number has 2 square roots, 1 positive and 1 negative. So if we use 4 as minus 2 squared and change our other square root here, then minus 12x is 2 times the product of the square roots, 3x and minus 2. And so this is the square of a binomial. And that means we can factor, it's the square of the sum of the square roots, 3x and minus 2. So let's try to factor 4x squared minus 20x plus 9. And so we notice that 4x squared is a perfect square. 9 is a perfect square. And minus 20x is 2 times the product of the square roots.  And so minus 20x is 2 times the product of the square roots.  And not quite. Remember when you write equals, you are guaranteeing left-hand side and right-hand side are identical. And minus 20x is not 2 times 2x times minus 3, which means that this is not the square of a binomial. If it factors, we'll need to use trial and error. And the important thing to remember here is that we can always attempt trial and error factorization. And sometimes we have to.


So we had to check out WWE most insulting chance in history now It's good to know that the crowds will be coming back this year in a couple months I believe you guys were saying sometime in July the crowds will be allowed to come back So I'm looking forward to that It's gonna make these shows a whole lot better in my opinion because there's gonna be actual fans there to voice their opinion on certain things that's happening in the ring other than the Virtual fans that we have right now in the Thunderdome. So I'm looking forward to that And I just want to check out some nostalgia Crowd chance because it if you guys don't know WWE fans can be very vocal in Certain cities in certain areas and they will let you know how they feel in the ring like any wrestling in the ring They'll let you know if they like you they'll let you know if they hate you and they'll let you know if they Want you off like off their TV out the ring. Don't want you to wrestle anymore That's what makes WWE fans sometimes great and sometimes toxic But we're gonna check this out appreciate all the love and support roll to 40k. We're almost there and let's do this The FU champ Not to change the channel champ ECW man Yo, them fans was hardcore for real for real Funny thing is the Miz we didn't win that WrestleMania to he won that at WrestleMania and retain the championship Oh Yeah, I remember this this is when Samoa Joe had got busted open Legit and there was blood everywhere.  Come on, bro.  They really should have embraced it led Jason Jordan getting to that heel character because no one cared about Jason Jordan, bro They shouldn't have never split him up with Chad I think he was with Chad Gable in American out for they shouldn't have never split that tag team up, but hey Hey, what do I know? This is appropriate action appropriate chance because he's a heel at this point This is the heel rock Hollywood rock Oh This was such at this point chopper was the best heel in WWE at this point his few with Johnny Gargano, bro He was literally Just despicable to the point when the crowd is chanting FU on live television, bro Like that's how good of a heel he was bro at this point No one was a better heel than chapel, bro hands down This was a fantastic Yeah, this was the night after he beat the Undertaker and we all thought he retired the Undertaker He didn't say anything and I actually liked this because I thought for a second They were teasing him to become heel. I think this was the moment He should have became hill comment down below if you agree with me after he beat the Undertaker that next night on Monday night Raw that was nuclear heat the heat that he should be getting as a heel But he was still technically a face Cuz at the end of this whole little segment all he said This is my yard walked out the ring crowd is giving him nothing But hate for like 15 minutes down there just hate and in the next week it comes out as a face still I was like, bro They had the opportunity to turn him heel if he would have just been like man screw the fans I'ma do whatever I want to I retired the Undertaker, bro You have a star instantly because now everyone wants to see him get his ass beat bro But hey, we got the room and we got now so I a man The timing could have been a little bit better But we got what we we've deserved for a long time a actual heel character that we want to see lose for the right reasons And I love that they knew everyone just wanted to see Stephanie get beat up Everyone wanted to see that man, and I like the fact that I think that was the WrestleMania Ronda and The was it was it that WrestleMania? We're running down. I'm trying to think I'm getting old because I remember there was a WrestleMania Ronda got into the ring with the rock. It was like a little quick segment That was the situation, but I know she ended up having an actual match Like that like I want to say maybe the next year It was one of the better matches like it was our actual first in-ring debut at WrestleMania And I think that was the WrestleMania when she tapped out Stephanie man, so I could be wrong coming down below. Let me know. I don't know you guys will correct me if I'm wrong here But I'm thinking I'm just getting old man. Just getting old Do y'all remember that phase when Roman had contacts, oh my god He had contacts that blue eyes are the cringe.  Yes, leave John.  I want y'all to understand that was accidental He was not trying to actually crack John Cena's nose, but he broke his nose like you could it was brutal He was a heel at this point stuff only was a major heel at this point and he became For the time being a mega face, especially in this promo because people were just like, thank you, bro You're into John Cena. He's out of here. Thank you so much, bro This is great man, this is where I can't wait for the crowds to come back man It's gonna be amazing just to have some fans live fans more than what NXT has behind the little plexiglass Like actual rows and rows of fans. It's gonna be cool. I'm not even a lot to you The fans that go to Monday night raw. I think they're just gonna go just so they can see some live wrestling I hope that People that's booking that show when it does happen. They put on a good show for them They entertain them not like they've been doing for the past few months on Television with no fans and live attendants They need to entertain these people that are paying a hard-earned money to come to these shows because if they keep putting on the same Bull crap that they've been putting on Monday night raw in front of a live crowd I want that live crowd to let them know how much this sucks the show sucks and we want our money back I want them to do this on live television so they can get their act together and put on some better shows So that way more people will be interested in watching But I appreciate y'all and all the love and support man Roads of 40k appreciate y'all kicking in with me and I'll see y'all next week. Peace