December 22nd, and today I do not have much time to film, so I'm not even gonna put a timer. I am going to play around with the script here with you guys, and hopefully show you the best take. This is a scene from Elf, where the store manager is telling Buddy the elf, like, oh, this is a North Pole, and he's like, no, it's not. And then he announces that Santa is coming, and I am playing the manager, and I recorded the lines of Buddy. Oh, wow! Let's see if I remember them. This is the North Pole. Yes, it is. I think I pretty much have the lines. Okay, I need to think about how I am going to approach this. I know what I wanna do. One of them, I am a very kind, patient employer, and like manager, and I wanna make sure that this new employee is feeling welcome and great, because he is great for the job that he has being an elf. Like, he's really good at that, so I wanna make sure to treat him well so that he remains here. And then the other one, I'll do like a more annoyed like, what is this person talking about? Like, I only have this job because it's good money, so let's try the nice one first. The one that's like very accepting, wants to make sure that above all, they feel welcome and they stay in this position. This is the North Pole. Yes, it is. I accidentally played that like a little annoyed. I need to remember, I'm just happy. I am happy, I am happy. Yes, it is. Okay, well, make work your favorite. Work is your new favorite. It is very difficult to stay happy throughout all of that because he is quite annoying. But I think I did a decent job. I'm gonna try it one more time. I think this is my third take of doing it, like, friendly, happy. It's like the smile, smile is my favorite. Oh, time to do the annoyed one. I'm gonna do one final, like mean one.  So one more. I didn't really like that take. I don't know if I liked any of the second version, the mean version at all, but regardless, I'll show you the best take of like the nice version and the best take of the mean version. And I'll see you tomorrow. It's the North Pole. Yes, it is. Yes, it is. Yes, it is. Yes, it is. Why are you smiling like that? I just like to smile, smile is my favorite. Okay, well, work is your new favorite, okay? Make work your favorite. All right, it's time for an announcement. Hi everybody, Santa Claus is coming to town tomorrow at 10 a.m., so. Yes. Oh, okay, so tomorrow at 10 a.m., Santa Claus is gonna be here to take pictures with all of the kids. So save your receipts tomorrow at 10 a.m. Oh, it's the North Pole. No, it's not. Yes, it is. Still, it's not. Yes, it is. No, it isn't. Yes, it is. No, it isn't. Yes, it is. No, it's not. Where's the still? Ah, why are you smiling like that? I just like to smile, smile is my favorite. Okay, well, make work your favorite. Work is your new favorite. Okay. Okay, it's time for an announcement. Okay, everybody, Santa Claus is coming to town tomorrow at 10 a.m., Santa Claus is coming. Yes.  So make sure to save your receipts for 10 a.m. tomorrow.


The southwest rift of Kilauea on Hawaii, there's a vast, fascinating volcanic history sitting here. Layers of rock that were made of pieces that were tossed through the air, glass that froze in the air as it was thrown as molten little bits from the volcano, and then other sorts of layers. Then there's been a great cracking here, probably an inflation from underneath as melted rock is moving underneath that sort of bubbles things up and breaks it. Then an eruption happened at some point, and there was actually a sort of a waterfall of melted rock that was flowing into the crack, and we can see behind me all these places where this stuff has flowed down into the crack. Just a wonderful record of the excitement of the geology at this place.


So what I will do is I will start teaching Laplace law, see Laplace law says if anybody knows what is Laplace law it says pressure is equal to tension twice of tension divided by radius isn't it or we can look at it into tension is equal to pressure into radius. So depending on how we look whether we are looking at the pressure or whether we are looking at the tension that we have to be very clear the equation is in inter relationship. So while we look in respiratory system we are looking into the pressure developed into the alveoli but when we are talking about the cardiovascular system especially the heart and when we are talking about the capillaries then we are talking about the tension developed. In maturation also we are talking about the pressure developed. So respiratory system and maturation we have bothered about the pressure developed and when we are talking about cardiovascular system we have bothered about the tension in the ball. So when we are talking about heart tension in the wall of the ventricle and when we are talking about the vessels tension in the wall of the capillaries or other vessels as in case of aneurysms. So just I will tell you for example in respiratory systems for that I've already made one video Laplace law in respiratory system that you can see after the discussion gets over that in respiratory system we say pressure is equal to twice of tension divided by radius. Why we say so? Because alveoli actually it is in contact with the air and if there is a thin lining of fluid and whenever there is like even contact with air and thin lining of the fluid there develops a surface tension. So here tension is developing because of this difference air and water difference is there. So that causes the tension actually pulls the balls of the alveoli. So if there is a tension tends to pull the ball of the alveoli together it is just like the layer of that on milk what top layer forms whenever it is in contact with this air. So that top layer forms that is because of the pull of the molecules due to the surface tension. So similarly alveoli there is pull on the ball of the alveoli. Now if there is pull on the ball of the alveoli so the diameter of the alveoli is like trying to reduce it is not reducing because everything is being held by the connected tissue okay but it is trying to reduce so what happens that inside the pressure is going to increase okay. So try to understand this here tension is causing development of the pressure inside the alveoli. So when the pressure increases now how much pressure is going to increase depends on the size of the alveoli that's where we are bringing in the radius okay. Now suppose there is a large alveoli and there is a small alveoli now with this formula pressure is equal to twice of tension into radius can anybody tell me pressure is equal to twice tension into radius. Where tension is the same in which of the alveoli pressure will be more a smaller alveoli or larger alveoli? Smaller alveoli and who's radius is less? Who's radius is less? It is the smaller alveoli whose radius is less isn't it? It is the smaller alveoli whose radius is less. So pressure will develop more in the smaller alveoli so suppose there are there are two alveoli side by side and obviously all the alveoli are connected. So suppose there are two alveoli side by side, then tension is almost same in both. But just because of the difference in the radius smaller alveoli is going to develop more pressure and if you know where does the air move, where does the water move, it always moves from high pressure to low pressure. So by that logic what will happen? Air will move from the smaller alveoli because of the higher pressure into the larger alveoli, understanding. So all the smaller alveoli will M2 into larger alveoli because if you see everything is relative, some alveoli will be the smallest, some alveoli little large and then the other will be little larger. So anything which is a smaller, they will slowly slowly empty into the larger alveoli. So what will happen? The lungs will become a big alveolus. They will not have a small small alveoli and which will be very damaging because ultimately the surface area for diffusion of the gases is going to decrease. That is the reason that lungs is having so many small small alveoli that increases the surface area, understanding. So based on the Laplace law, what we are seeing here is surface tension is developing the pressure. See how I am looking at the equation and taking this tension is equal to P into R equation because of the surface tension pressure is developing and because of the surface tension pressure is developing and sorry pressure is equal to 2T by R equation we are seeing, pressure is equal to 2T by R ok. So because of the surface tension pressure is developing and radius is less it is in denominator so pressure will be more ok. Hopefully I have made it clear that how this all smaller alveoli if we see by Laplace law all small alveoli are going to enter into large alveoli. Am I clear? Type S. If I am clear, give me a thumbs up or type S ok. So now this is counteracted by surfactant in our body because if surfactant was not there then only all these alveoli are going to empty into the this larger alveoli. So what surfactant does? We are saying that pressure is more right. So what surfactant does is it decreases more tension, it decreases more tension in the smaller radius. It is like everywhere 8 8 surfactant are there right. So in a smaller radius this 8 surfactant molecules will be more effective in reducing the tension right. So radius is less let me tell radius is less in smaller alveoli and hence tension is also less in a smaller alveoli less in a smaller alveoli due to due to what? Due to surfactant. So same surfactant is able to act better in the smaller alveoli hence the pressure development is same in smaller and larger alveoli. So that is how we look into Laplace law in respiratory system. So please understand tension is developing the pressure. This is the key line. Tension is developing the pressure in the alveoli. Now let us move on to another aspect that is the heart. Very very very important heart it is extremely important because there is concentric hypertrophy and eccentric hypertrophy and how it affects the functioning of the heart, how it increases the tension that is very important because that increases the myocardial oxygen demand and cardiac failure how it helps. So now in heart how we see is that tension developed in the wall of the heart. So we are looking at opposite tension developed in the wall of the heart is equal to pressure and radius. Why we look like this because in heart the muscles contract right when the muscles contract there is a huge development of pressure inside the ventricles. So I told you whenever there is development on the pressure it is like it is pushing the walls. Pressure is going anywhere any container you see what is there molecules are there and what they do they like they like hit on the wall. So that is creating a wall tension similarly when you inflate a balloon what happens if the when the balloon inflates it creates a stretch if you touch it you will feel the tension on the wall of the balloon isn't it. So here pressure is creating the tension on the wall of the ventricle more the pressure more the tension developed on the wall of the ventricle and it is very important concept which is important for oxygen demand oxygen demand okay in the ventricles in the heart. So I will give you an example whenever there is hypertension what happens to overcome the hypertension which is the afterload now the ventricle has to develop more pressure it has to contact more because of which the pressure inside increases then only the blood will overflow so pressure should be more so that the blood overcomes that and moves out. So but who is feeling the weight of this pressure it is the wall of the ventricles who are feeling the weight of the pressure understanding so that is known as wall tension. Now how much tension can it bear how much tension can it bear there is a limit isn't it. So now here comes the concept of thickness so I will give you one extended formula where tension is equal to P R divided by H divided by thickness divided by thickness okay so more the thickness less the tension is developed okay so in simple words in understanding may we see that when the pressure is high tension developed the out of our force will be more so if the wall is thick it will be able to bear that pressure so they they are like the counteracting forces which are acting isn't it and that is what is happening in hypertension what happens that is adaptive concentric hypertrophy is happening so whole this whole muscle hypertrophies there is increase in the thickening of the wall of the ventricle and that helps in bearing the stress which is happening on the wall okay understanding now that is one concept so is that good in hypertension of the concentric hypertrophy happens tension is relieved fine everything is fine but that doesn't happen because after a certain limit heart starts dilating also right so that is that is increasing radius happens and that is because adaptation there is always a limit whenever we talk about physiology there is always a limit to which the body can work to which the adaptation can occur afterwards that the limit is crossed okay and then the maladaptation starts so after that what happens that there is a increase in the radius also because there is some fibrosis going on along with the hypertrophy some fibrosis interstitial fibrosis that you will study in pathology that also happens and there is increase in the radius and then radius increases what happens tension also increases okay so let us quickly and two lines I will tell whenever in respiratory system what we saw tension is developing the pressure and because of this there is movement of the air when we are looking in cardiovascular system how we are looking for the movement of the blood we need pressure development okay you see how I am changing the language in respiratory system tension causes development of the pressure and this will lead to movement of the air if not stopped thankfully surfactant is there which prevents that in heart for the movement of the blood more pressure is developed but this creates tension if this creates wall tension understood have you got it this language is very important that what you are looking looking at in cardiovascular system we talk about wall stress this is wall stress more the wall stress more is the oxygen demand and then high chances of myocardial infarction in concentric hypertrophy or in eccentric hypertrophy whenever there is there is increase in oxygen demand and if it is not met it can lead to myocardial infarction am I clear in cardiovascular in heart if is it clear then please type yes okay harsh was there I think harsh is there or not is coming and going fine no issue so that was about heart now let's come to blood vessels blood vessels what is there same as I told you that in cardiovascular system we have to talk about wall tension so whenever blood is flowing by it is flowing it is due to pressure all the blood vessels have some pressure inside it right so this pressure so suppose this is the vessel right this is the vessel so inside there is pressure what it will do it will it will create a push on the walls right what a wall is very thin what a wall is very thin will it be able to bear this will it be able to bear this yes or no it will break right because it's a push force it will just damage the vessel right it will just damage the vessel and the blood will flow out right now do you know what is the thickness of capillary wall capillary wall it is single cell thick capillary single cell thick then how is it able to bear this pressure how is it able to bear this pressure it should break but that doesn't happen why because capillary diameter is also very less it is its radius is also very less so again you see the equation tension is equal to pr yes very good so the tension is equal to pr divided by thickness right so if thickness is less but its radius is also less so very less tension develops on the walls so that isn't done on the contrary if you see it in the larger vessels in the larger vessels what happens they are having big radius and that is the reason that larger vessels should be thick also so that is the reason that thickness prevents it otherwise if they are of large radius and the pressure you know the pressure is also more then it is going to break the walls of the large arteries so that is why the walls of the large arteries need to be thick so that the tension developed on the walls is less okay so now you understand that even though capillaries are lesser in sorry thickness is less still they are able to withstand the pressure inside the capillaries okay so just because this concept of how we are looking into the equation in respiratory system development of the pressure due to tension in cardiovascular system development of the tension due to pressure understanding okay one example of this is an aneurysm actually in aneurysm what happens so there is weakening of the wall okay it's like wall breaks right so wherever there is weakening because of the pressure what will happen will it be able to be a distress no it will not be able to be a distress and due to this it expands it's like it balloons up in a particular area right so what is happening radius has increased so thickness has decreased and radius has increased so it becomes like a positive feedback thickness has increased due to thickness has decreased due to damage because of that radius has increased it has ballooned up and now the tension developed for the same pressure will be more see see the equation pr divided by thickness thickness decrease tension more radius increase tension more okay so what will happen more tension developed so it is going to damage the wall further if it is damages the wall further then radius is going to increase further so it is kind of a positive feedback right it cannot be stopped and ultimately the vessel ruptures in aneurysm so that is the physiology based on the Laplace law behind the aneurysm okay then coming to maturation where it is you will see the Laplace law again in maturation we have to see in terms of how it is happening in respiration okay because development of the pressure leads to maturation pressure is detected as stretch in maturation for maturation also I have made one video so two Laplace law video already exist on the channel that is Laplace law in respiratory system and Laplace law in maturation both exist so you can have a look in that in cardiovascular system I still need to make and I think after this I can easily make the video on cardiovascular system there I will also talk about in what happens in concentric hypertrophy what happens in eccentric hypertrophy so some components of applied also I will put up so what I was saying in maturation what happens as filling up occurs it is like a balloon right if you fill a balloon with water what will happen it will stretch right so it is a tension which is being developed on the walls okay now so we are looking again pressure is equal to twice of tension divided by radius so that tension starts developing so pressure starts increasing in the urinary bladder okay filling tension increases it's like it becomes taut like this so because of this tautness pressure increases but it is a smooth muscle a smooth muscle has a characteristic of stress relaxation so whenever there is a feeling it relaxes a little bit so it is like that radius is going to increase so even tension is increasing radius is also increasing and hence pressure is not changing but everything is up to a certain limit only right so pressure is not going to change up to a certain limit and that is why that um um this maturation is delayed only starts um after a certain level okay so that was the main applicant respiratory system more authorotical that you will read about it because surfactant is there so it doesn't allow laplace law to operate there but we study like if surfactant was not audio as per a system it exists in this um this um aneurysm as let me know and once again hirsh thank you and i i'm so delighted that my videos are helping students and that was the um concept here that i want to give quality videos to the students and and concept based videos so that they see and they apply the physiology to their learning and not just about writing notes and just getting marks okay thank you thank you hirsh i just wanted to thank you once and any questions are there i will take now have you understood hi simran vasudev have you understood laplace law and i hope that this switching great i like it this topic was selected by you only i think no okay then bye thanks for joining


And by the way everybody's not like that. We're about to move family from one city to another, right? And I talk to the movers, and people know this now. So people are going more and more cash.  I talked to the movers and booked our movers like a month, a month and a half ahead of time and stuff like this. And they're like, it's going back to like 1980s level, right? Treating, commerce, business, right? They were like, oh, okay. If you pay credit card or check, it's this much in tax. But if you pay cash, it's this much and no tax. I'm like cash, right? Cash is king, baby. Saves you money. Keeps money in the pockets of your neighbors. Cash is king.


Today we are heading to Reserva Furnistica Chimborazo. This volcano, Chimborazo, basically, this is the closest place to outer space that you can get on Earth. Holy moly, there's a lot of water around at the moment. Wow. It's like literally just lakes straight on the side of the road. Fellow's saying to go to the side. Okay, wait, stop here. Mama, go home. Hi, I'm Lavi. And I'm Oli. And this is our hero, Bumblebee. Together, we are attempting a Guinness World Record to become the youngest pair to circumnavigate the globe by motorcycle. Join us for season three here in South America. 1,050. 1,050. See, it's a, here we go. We're on our way. Look at this. So Lavi's in the cab. Wow, that's crazy. Look at this. Gracias. What do you think? It's a YouTube channel. Oh my goodness. It's another water. A lot. This. Crazy. Loco, eh? No, no, normal. No, no, no, no. No, no, no, no. There's actually one guy on the motorbike and he's going. He's crazy. Okay, this is a seriously deep bit here. Here we go. It gets seriously, seriously deep just here. I think that car is toast. There's people swimming here on the road. Look, this car is, is it still moving? Oh my God. No, no, he's out. He's out. Oh my God. What is going on here?  The motorcycle would have been completely submerged here. We would have floated away down the river. I've got the front brake on. Hard. Here we go. We're going to tip, we're going to tip. Oh my goodness. Yeah? Okay, you got me? Okay, ready? Okay. Wow.  It was like being on a boat, but in a car.  That's so cool.  Gracias, gracias. Thank you. Gracias. Ciao, ciao. All right. That was a little bit of an interruption. Unexpected interruption. What was going on? What was going on? Unexpected boat ride, hey? Oh man, crazy. Seriously, I'm so thankful for a service because I don't think that we could have made it actually at the end. No, no, no, no. We would have ended up pushing and we would have had, it would have been flooded, totally flooded. That was, that was crazy. Oli is preparing a very nice lunch for us. Oh my God, I'm so excited. So we just went to the supermarket and got ourselves some bread and cheese and add that with the magic ingredient that is Marmite. And I mean, you're in heaven basically.  I'm so excited about this. So of course we just got a slice of cheese. We've got the bread. There's the sandwich, this for you. Yeah, dum, dum, dum. Marmite party. A little bit more water on the road here. Ooh. Wow. Stick me feet up here. Basically got a lake there and it's draining off into the lake down here. So it's just a sideways river on the road. Incredible. Absolutely incredible. Anyway, that one bumblebee could handle on her own. Yes. Oh man, I hope we don't have to take any more trucks. So we're just stopping at a petrol station and we've decided that we are gonna have to disconnect the media mod now and put our rain gear on because we're about to head into the mountains and it looks incredibly dark and yeah, we thought we'd better get ready for it now. Got some sort of queue here. Not sure exactly what's going on. We've just started to go up into the mountains. It looks like a landslide, hey. Wow, they are literally trying to dig it out as we speak. Yeah, I think we really underestimated how difficult it might be to actually travel through here during the rainy season. Jesus. Slowly. We have been told that we can give it a go. There's a river running down the road here as well. We've come off the main road and we're taking this middle road to hope that it's paved all the way. Jungle, baby. So it's getting to like 13 degrees now. We climbed up quite a lot. So this armor is too cold now. So it's time to get back out our coats. So we are good prepared now. We have our fleeces on, our motorbike jackets on, our raincoats on and yeah, this road is so steep and so windy. I think this is the steepest road we have ever driven. It's super crazy. Wow. Hopefully it doesn't get any colder. There's a rain tower. There's a volcano. Yeah. They're at one road, they're at one road. It's the same distance. But this one is the wrong direction. Your camera's dead. So we are nearly at 14,000 feet. It's a really high altitude here. I think it's about 4,000 meters. So the volcano is somewhere over there but it's so cloudy. It's so rainy. We can't see anything. But we are pretty close to the furthest place from the centre of the earth, right here. Pretty much closest we're going to get, eh? We have to continue back on this road and we are about an hour away from where we're going to try and take a room for the night. Right now we've got to get back on this bike and we are going to find our way to somewhere as warm and cozy. I can't believe that we went warm. We had to stop and eat something because we got really sick. Look at my fingers. I'm so cold. I just feel really sick because we went so high up and it's so cold. We went from sea level to like 4,000 meters in a couple of hours. We're both feeling pretty dizzy and wet and cold. I don't mind being wet down at sea level where it's warm and I don't mind being in the mountains but when you combine it together plus the temperature got to three degrees it's ridiculous. My boots are soaking wet because I had to walk in the puddle like in the puddle which was knee deep. We've both got soaking feet. I was expecting this morning a beautiful ride, beautiful views. I have a view of the nice mountain. Nothing. There's nothing. We're nearly at the equator. It's all nice and tropical and warm. We saw alpacas again and you know when you see alpacas you've gone too high. So anyway, we're going down now and we're gonna try and find accommodation as soon as we can. Hopefully within half an hour we'll be in a nice cosy room. So this is the town of Ambato and we've finally arrived. We found a posada, a little hostel, a couple of miles down the road so that should be fine.  Oh my goodness. My socks were for like the last six hours. Soaking wet, freezing cold but we've arrived at Hostal El Gaucho and they have a room for us. It's a little bit expensive here actually. It's like here in town I mean in Ambato. This is one of the cheapest places we could find and it's $25 for the night. Yeah, they actually wanted $30 but I asked for $25 and they said yes. Hey, save $5 here, save $5 there. No harm in trying. Yeah, but the place looks super amazing and we have a secure parking place for Bumblebee as well. So I think we will have a good rest. They have a sign here which says Dusha, hopefully a nice warm shower. Well, it doesn't actually say hot Dusha, it just says Dusha. So we don't know if it's hot but anyway they're just preparing the room for us now and then we can get warm and cozy. Yes, absolutely crazy ride today going from tropical 30 degrees to three degrees high mountain. I cannot believe that. And a bit of a failure because we couldn't really see Chimborazo but anyway, we were there. We were at the highest point in Ecuador pretty much and the furthest place from the Earth's core from the Earth's center and the closest place to outer space. So I mean... I feel like a different person now. Yeah, couldn't really see anything but we were there. Yeah, so that's it from us today. We hope you enjoyed the video. If so, please give us a thumbs up, subscribe to the channel, share the video with your friends and family, comment below. And if you really, really, really like our videos then you can join us on Patreon. The link is in the description below and we will see you next time. Is it hot? It's hot!


But my perceptions are more and more in the maybe mode. It's beginning to come out of my frontal lobes, into my back brain. I'm beginning to more and more perceive things as maybes. Although, of course, the only thing about maybe logic, your critics never noticed that. I put things in maybe terms, and I noticed almost all the really negative criticism I get is by people who assume, because I'm not taking their stand. I must be taking the opposite stand. They have a yes-no logic. I put things in maybe. They assume that means I put it in either yes or no. They can't understand maybe at all. Hi. This is Cheecho again. And we're just going to continue with the section that we're on right now, which is a factoring section. But we're going to do a little diversion and just talk about a certain concept in mathematics that I don't think is taught very well in general. Or it was confusing for me when I was, well, I don't know if I was taught it or it was just assumed that I'm supposed to know this. But it's basically the concept of a let statement or substitution. And in mathematics, again, it's just a language, right? And we can manipulate language any way we want to get an idea across or to make a certain concept easier to understand. And that's what the let statement is really about. Or that's what substitutions can be about, I guess. That's the best way of putting it. What happens is we're given equations for specifically when doing factoring polynomials. We talked about prime factorization, that's series one. But right now we're sort of going off on factoring polynomials. And the reason we're doing this is basically because we want to break down our functions to what they're made out of. Because once we take a function and we break it down into score elements, then we can look at the function and try to figure out what parts of it are common between other functions, right? What are its building blocks, right? That's why we're doing factoring. Now, so far we've been going off on, we've learned the simple trinomial, complex trinomial, difference of squares in GCF, right? And we started talking about the quadratic formula. And the quadratic formula and synthetic division, these two factoring techniques are gonna give us a lot more power because we can go beyond just simple polynomial functions, simple quadratic functions or simple trinomial functions, right? We can start actually factoring or breaking down functions that we can't easily break down into integers and multiplies together, which is the case that's going to be in real life, right? So the quadratic formula and synthetic division are gonna give us a lot more power. And what's gonna happen with this power that we have, we're gonna start going into functions, equations that are way more complicated, right? And what's gonna happen is we're gonna look at these functions, we're gonna encounter functions that may not look like we can do anything with them because they're not the general form that we're used to seeing them in, right? So for example, for the quadratic, we talked about the quadratic formula and the quadratic formula is used for quadratic equations, right? To solve, to break down quadratic equations. And the terminology we've used so far is the following. So so far we've got, basically, we've learned about the quadratic formula and we've done like three examples like this, where the discriminant is graded in zero equal to zero and less than zero, where grade in zero gives you two x-intercepts, equal to zero gives you one x-intercept and when the discriminant is less than zero, you got no x-intercepts, right? Now, the terminology that you're basically gonna encounter is, you know, if you have a quadratic equation like this, a x squared plus b x plus c, you can factor this out as x is equal to negative b plus or minus the square root of b squared minus four, it's the over two a, right? Now, this is true, but for me, this was initially when I learned this was a little confusing because this x and this x are, you know, for this expression, they're the same x, but what happens is you can get functions where it's not a x squared, but the x here is to a higher power, is to the power of four or six or eight and all you need to be able to use the quadratic formula and to use simple trinomial factor and complex trinomial factor is this power to be twice as much as this power, right? Following the properties of a polynomial where the properties of a polynomial that we talked about in series 3A with, you know, video number 89, 90, and 91 where the powers here must be natural numbers, whole numbers, there's an x to the power of zero here, but we avoid that, right? Because anything to the power of zero is just one, right? So as long as the power on the x's is natural and this is natural number and this power is twice as that power the quadratic formula applies. And when I first learned how to use the quadratic formula, this confused me because every now and then we would get an equation where, you know, the questions that I would get is to factor something that wasn't just x squared but x to the power of four, x to the power of six, x to the power of eight. So every now and then you would get equations like this. So you get ax to the power of four plus bx squared plus c. Now what happens in this case? The quadratic formula still applies but it's no longer x that equals this but this becomes x squared because the quadratic formula works for functions for equations that are in this form and this guy is not in this form. So what we have to do is convert this to something that's in this form, right? And knowing our, you know, exponent rules, our radical rules, where we have something like this we can break this down, right? x to the power of four is just x squared to the power of two. So we can break this equation down to the following form. Now if you take a look at this, this says ax squared to the power of two plus bx squared. And what I'm gonna do is gonna put the bx squared in brackets, right? Plus c. Now what we have here is this equation is in this form where the x here is the same as the x squared here, right? And this is where the confusion came with me when I first learned this was because right now if we have this equation in this form, the quadratic formula is not x is equal to this anymore. It's x squared is equal to this. So the quadratic equation changes, it becomes. So it becomes x squared is equal to negative b plus or minus a squared of b squared minus four is c over two a, right? So once you get an equation like this all you have to do is realize that this expression here, this definition isn't what x is equal to. It's not just what this expression here is just not what x is equal to. It's what x represents and x here represents anything which is basically our boxes, right? When I started for the introduction for the quadratic formula, you know I wrote down the equation, one form of the equation where I said we're gonna talk about it further and this is really what we're doing right now. We're sort of expanding on that concept. And I wrote down the general function in the following form. Where I said your quadratic equation you could use for anything written in this form where it's a x to the power of two n plus b x n plus c where n is an element of the natural numbers, right? But it goes beyond this because what happens is you can think about the quadratic equation as b, a box. So what you would have is a box squared plus b box plus c. If you have anything in this form you can write that as, let's shade the sense so it's more clear. So a box squared plus b box plus c is equal. If you wanna factor that it becomes box is equal to the quadratic formula. And remember we talked about this with the difference of squares, a box or a square. I like calling it a box because you can put things in a box, right? So the box represents anything you can put in, right? So anything, so a anything squared plus b anything plus c you can factor out in this form, okay? And this becomes super handy because now what happens is we can factor quadratic or equations like this and this is no longer a quadratic equation or you could write it as a quadratic equation when you rewrite it, right? Now what happens in mathematics when we start doing higher level mathematics we're not gonna use boxes, right? That's just, it's cute and all and it's a great way to introduce the concept but the best way to work with this is not to put boxes here but to put a different letter. So what we could end up doing is saying if let w equal x squared, right? And if we write it that way what we end up having is let's say in here you wanted to factor this guy what you could say is let w equal x squared, right? So if you let w equal x squared and that's the power of a language, right? You can say anything you want as long as you stay consistent with whatever you're saying. So what you can do is break things down even further or condense things that way you can write expressions like this in a form that you can actually understand, right? So as soon as we say let w equal x squared well, x to the power of four if this is x to the power of four x to the power of four is x squared, squared x to the power of two to the power of two, right? But we just said let w equal x squared so we can write this equation as we can write this equation as a w squared plus bw plus c. Now if we do it that way then right away we notice that this is a quadratic equation even though inside of it is embedded another function, right? Because this right now becomes a function w equals x squared. That's the same thing as like saying y is equal to x squared but we're not gonna use y or x because y and x are really generic. We use those terms a lot, those letters a lot to represent a Cartesian coordinate system and unknowns. So what we start doing is we start introducing other letters in the alphabet and you can use any letter you want, right? Preferably not a, b and c because they're already part of the quadratic formula, right? And you wouldn't use x and you generally don't use y because this if you're gonna set it as a function you're gonna set this equal to y or f of x, right? So you're not gonna use y or f of x. You could use k, you could use h, you could use w, you could use z. You can use almost any letter you want to create a new function and that way you can substitute that into an expression that may not look like a quadratic formula and rewrite it so it looks like a quadratic formula and that way you can apply the quadratic formula, right? Which is a lot better than saying x squared is equal to the quadratic formula here because sometimes what you end up having inside the box is a much more complicated function.


I think it's a common misconception that big businesses don't like regulation. But in fact, big businesses do like regulation. They like regulation because you need regulation to act as barriers to entry for other companies, or regulations that help create a standard like the gap accounting standards, or anything that makes it easier for foreign investors to understand the businesses and to invest in our economy. So yes, we do agree that the government intervention is necessary to create these regulations. In fact, big businesses are leading the way pushing for these regulations or for these policies to help create standards that even small businesses would have to follow, and it makes it easier for us just to be efficient in the economy. Another argument for big business is more the increasing lack of government intervention in society. We keep talking about we're going to be cutting the budget, and next year the Republicans are hoping to cut 6 trillion out of the federal budget. So obviously we have to keep rolling back these social programs for our country. And to some extent, people are hoping that these large businesses will step in and fill the void left by the lack of government social programs as they continue to cut the budget. I guess I just wanted to add a more general comment, because it's difficult to argue that this corporate takeover thesis. And I mean, I think about a lot of the examples you're saying, you know, Exxon not paying taxes and things, but I mean, that has to do a lot of things like oil subsidies and all sorts of subsidies that the government offers to Boeing and Lockheed. And I mean, that's a question, yes, that you have to ask the government. And I don't know, I mean, yes, there's lobbying, but I also think a lot of responsibility goes on the government. So you can't necessarily blame the big businesses and for, you know, getting these subsidies, because it also has a purpose to serve, you know, the society here. And also, big businesses, I'm not sure this is really an argument. They don't always make so many profits either. They just have large amounts of capital. A lot do, but not all airlines, for instance. We need them. They don't make a lot of money at all. They're usually, they go through bankruptcy. But the economy needs them and society needs them. So they're necessary. So I just wanted to point out that government intervention there is important. All right, so that's going to be our last question. And I guess I'll ask the judges to take some time to think about, you know, which side you think may have argued stronger case. And like to thank our debaters for researching all semester and presenting these arguments, you guys did a great job. And I think we should all give them a big round of applause. The judges will now move to the chat table. He'll drum or something, yes. Only if you shimmy on the way up. I shimmy unintentionally, actually. Well, as always, I'm always very impressed with the amount of energy and effort both teams have done. I think I've judged these competitions in whole or part five or six times now. And they're always one of the main reasons I love coming back up to you, Mass. Here's how we apply. We felt that the small business team had a good balanced argument and provide a good level of detail. We also appreciated that the multinational pro team did address effectively economies of scale. And that the small cluster approach didn't seem appropriate for certain businesses like telecom and railroads. And we kind of went through some of that. That all said, we all agree that the small business team was more effective in this debate. So congratulations to the small business team. Well, thank you very much to our judges for your questions and your hard work there. And I want to especially congratulate the small business team that won and congratulate all of the debaters for their excellent presentations. So we have some awards to hand out, a certificate for all our debaters. Daniel Brock, Lian King, Angela Lee, Laura Maligno, Thomas Peek, Daniel Schwartz. And last but not least, Luke Sieberg. And we also have for all the debaters and our judges, if we can find them to fit, you guys. This fabulous t-shirt, who was designed by Anastasia, designed this great t-shirt for everybody should look at it. It's kind of a little kind of monopoly board there and says, big business, promoting social welfare, question mark. So we have the right sizes for you all. And I think, where do we have the t-shirts? In the back. So congratulations to everybody. First of all, I want to thank a few people I want to thank. Nicole Dunham, who's done a great job in helping to organize the event. To Kevin Crocker, our undergraduate program director, who did a terrific job helping with the debate. And I want to also thank Jackie Brown-Hazard, who could not be here today because there was a death in her family, but she did a lot of work putting this whole thing together. So let's all thank Jackie as well. So following the debate now, we have our major's, economics major's awards event, end of semester celebration, and barbecue. So please stay for the food and the awards. And enjoy yourselves. Congratulations to everybody.