 Make sure we're live, whoop, should be. Hi everyone, this is Chico. Welcome to our channel and welcome to another live stream. Today is April 24th, 2020 and we're doing another drop in math tutoring session for the 2002 year, 2019, 2020 school year. This is number seven for 2020. I lost count of how many we did in 2019 from the beginning of this year. And this is the second one we're doing in a row. We did one yesterday as well. We did a little bit of mathematics and it was fun. Super fun actually. All these masterings are super fun. If you wanna know who we are, who I am, what I'm doing here, Patreon is where I have, you know, sharing my information. It's a great place to support this project. If you have the funds to support this project or follow this work and or follow this work. Because once you subscribe or follow on Patreon, you'll get notifications as to what we're loading on. So it's a great way to support this project and to follow the work that we're doing. I do upload everything there and share additional information and we will be sharing a lot more information on Patreon. We are live streaming this on Twitch. So if you wanna watch these things live, Twitch is where you wanna be at, okay. It's an amazing platform. We've got a great, great community set up here. So very much do appreciate it greatly, okay. And I do announce when we go live, about 30 minutes usually, half an hour before we go live. Today was 20 minutes before we went live. I overshot my timeline, hello dragons. How's it going? Hope you're doing well. Hello, hello, money man. Money man's in town, how's life? So we do announce this stuff 20 minutes, half an hour beforehand and share other content on Twitter, Gaps, Mayans, VK and Elo. Those are the five platforms that I'm active on. And in terms of announcements anyway, other than Patreon, of course, right. And Discord, so we're trying to decentralize, we're all over the place, which is fantastic. And I do upload these things to YouTube and BitShoot. Almost everything of the process is on BitShoot. Most things on YouTube, unless the sensors really kick into high gear, then we're gonna have to kick down the type of content we share. We've gone through that a couple of times. Mask of Raven, how are you doing? Like your proof thing on our Discord math page. I have to look at it more closely, but it was like, oh, this looks beautiful, right? And we are at times of where there's a little bit of chaos in the world. So, oh, how are you doing? Hey, G. Joe, ciao from Italia. Hello, Italia, how are you doing? So you wanna reduce the pressure on our systems if you are living in a place that there's severe pressure or there might be possibility of emergence, reemergence of certain things happening. So be kind, be careful, go slow. Our pre-COVID economic system was telling people that you gotta go, go, go, go, consume, consume, consume, save, save, save the economy. Post-COVID, I think it's gonna look a little different. I think most of us are thinking about what is important and we should be, okay? Aside from that intro, welcome to the Mastering Gang. Let me take these guys down. I did the intro quickly today. Get into the chat so we don't miss anything. Olive, how are you doing? How's life? Hello, hello. You're at nine PM your time, I think. Nine or 10. I hope it's a good time for you. Hey, you're for Scotland, Scotland worth Coronet. I have an amazing friend, Scottish amazing friend. Tucker is her name, what do you call it? Family name. Scots are an interesting group of people. Loyal, loyal friends, wow, wow, wow, right? Hannah, hey, Chicho, I have a problem. I bought a small charcoal grill. You mentioned this last time, charcoal grill to make grilled meat, but I'm staying with my love partner in her studio apartment during quarantine. The upstairs outdoor rooftop lounge is closed. I don't know where can I grill. Some parks are open. There's an extra area next to her apartment with outdoor concrete tables, but it's next to the sidewalk. Where would be the best place to use my grill and grill meat? I would say, Hannah, if you know a park, a secluded park or something like this, go to a secluded park unless there's fire hazard. So if there's fire hazard, don't go to the parks and do a barbecue, because all you need is a little spark to start chaos. You don't wanna do that, right? Beach is an amazing place. Man, we live in the Pacific Northwest. The number of beaches is amazing. Just, you know, I'm pretty sure you guys can still drive to places. So go to the beach. The beach is an amazing place to do a barbecue. Real homos being, how are you doing? I think it's interesting to see how much our economy depends on frivolous spending, how much of it, insanity, right? And I'm hoping that as soon as we come out of this, and even right now, people don't go back to their addictions, right? Because right now, there's a lot of things closed, right? A lot of things that people were doing that were very destructive to their lives are closed. So one thing you need to be able to break an addiction is distance, is time, right? So right now, there's a lot of people who've had a fair bit of distance, fair bit of time from some of their addictions, destructive addictions, right? And that's the definition of addiction anyway. Passion becomes addiction once you sacrifice everything for one specific passion, then that's an addiction, not good, right? So we'll see what happens. Real homos being, 10 o'clock, it's a good time. Good to see you again, Chico. Hope you're doing well. Doing well, Olive. Thank you very much. Just going ballistic with online stuff, and as you know, I follow a lot of news and everything, right? So I love, I am not bored. I'm waking up very early, very early. Spider-Man, how are you doing? Oh, hello guys. Sorry I'm late. How's it going? Spider-Man, Spider-Man is sometimes late, isn't he? I think so. Does the apartment have a patio? No, good question. Lack of caring. Does the apartment have a patio? And some patios you can't barbecue on too, either. Thank you, Chico. I will pursue the park. No fire hazard right now. It rained last night, yeah, yeah. But sometimes you need a multiple days of rain to reduce the fire hazard, right? I will think about a beach, too, and bring a bucket for water to put out to Char. For sure, for sure. You can't just dig it up and bury it, right? You need, you know, you need to put it out. You need to put it out. Think, Barbara, Chico, I don't know if you remember, but I told you there was a beaver dab. Yeah, yeah, three beavers, you said, right? Near my house. Last night, I saw two of them in the small creek they were inhabiting. They both smacked their tails to let me know I was not welcome, nice. Awesome, beavers, finicky little buggers, aren't they? Well, that's the thing, Chico. I was stating or trying to state a fact. Our economy depends so much on frivolous spending and it doesn't go back after COVID. Then our economy will shrink. Not necessarily, it's gonna grow in different areas. There are businesses, systems, things that are in high demand right now, extremely high demand right now, right? So there are certain things that have collapsed and some of them will never come back again and there is industries that are popping up and people providing services for things that are lacking that people need. We're gonna see a serious shift. This is one of the greatest economic shifts, like one of the huge ones, right? There was a huge transfer of wealth from the bottom to the top with a multi-trillion dollar handout to Wall Street again, right? However, we're also seeing a huge shift, right? There's gonna be a lot of small businesses that go under and the big corporations, some of the bigger ones are gonna consolidate more power. Now it's our choice if we wanna give them that power, because that's the only way they can consolidate, centralize more of it, right? I'm betting that there's gonna be a lot of mini, mini economies popping up everywhere, right? That are doing less bleeding to the centralized institutions. That's my guess, okay? Good afternoon. Catholic traditionals, how are you doing? Martin, lockdown on a pub. I'm drinking down on the side of what I was on, no, brother. Yeah, dang it. Yeah, your situation is different than a lot of other people, right? Like I know people who have gambling addictions, right? But the casinos are closed. They're saving money, right? They don't have, they can't, and man, interacting with them is different, talking with them is different, obviously not in person, but when you're talking with them, interacting with them, their focus is not the casino, right? It's beautiful. They're becoming who they were before their addiction, right? I'm loving the look today. Nice, Spider-Man. Peter is never on time. For some reason, I thought the stream was 1.30. Yesterday's stream was 1.30, and I messed it up too. I was supposed to announce the stream 30 minutes beforehand. I announced it 20 minutes. I went, oh my God, I forgot how to, I forgot to announce it. I forgot to announce it. I know everyone has their theories on life after COVID, but here's mine. Ah, let's read this, real homos being. If this virus returns periodically, just like the flu, then this virus will single-handedly reverse all the progress we made in life expectancy, since it seems to mostly kill the old. Let's think about that. Think about the data. It might be a blip because there is gonna be a certain amount of immunity associated with that as well. You might, you know, there might be, there's gonna be, there is already, and there will be a major numbers-wise, and this is very much math-related, so it's brilliant. We're seeing, we're gonna see a baby boom, right? So there's gonna be a baby boom coming. Okay. The unemployment rate's gonna be the same. Dude, there's so much. Will we see a permanent decline in life expectancy? I think we are already seeing a decline in life expectancy. If you look at the stats for the United States, I'm not sure about Canada because I looked at the United States before, and life expectancy in the United States for at least two or three years was declining, right? So we're gonna see a bigger boom on that, possibly. Okay. I mentioned before I was previously drunk three to six times a week. Haven't had a drink since mid-March. Awesome, dragons. That's really good. By the way, I got some matchup going right now. Okay. It's really good. Matcha is amazing. Tons of antioxidants and minerals and stuff like that. Grats, man. I'm very happy for you, Spiderman says. Yeah, seriously, dragons. Great job, Ding Bover says. Keep it up. I just quit drinking again two days ago. Nice. Hello, friend, I know you can do it. Yeah, for sure. You have a will of iron. The first few months of, and it's a lifestyle, right? It's not just the drinking. It's the lifestyle. Once you stop doing something that had completely taken over your life, now you're sitting there going, what do I do? What do I do? What do I do? The anxiousness, the anxiety, the twitchiness and stuff like that, right? Fill that void. If the streams do it, you're welcome here. Always, always, right? You have a will of iron. Good evening, chichonians, chichonians. Hello, Nate, how are you doing? Hope you're doing well. Good to hear, good to hear indeed. Great to catch another stream. Hello, M1K, what are the two blanks stand for? M, K, if the K was earlier I would say. Thanks, all. Personally, hate drinking at home. Oh, is that what it is? Yeah, it's a dark, dark road you go. We're so happy to have you here, for sure. Yes, very true. There was already a decline, but I just think that the idea of this being periodic thing, like the flu, will be detrimental effects of like. I don't think it's gonna be as bad as it may seem right now, okay? The second wave, if we get a second wave, I think we're gonna get a second wave. Some people are saying it's gonna be way worse than the first wave. Some people are saying there'll be a little bit of herd immunity and stuff happening. But for what I understand, there's mutation versions of this thing and whatnot, we'll see. And by the way, just to let you guys know, how deep are we into this? Boop, let me do this, we're about 15 minutes in. Two things to let you guys know, okay? The COVID math stream where we look at the data at the beginning of the next month, May. I'm thinking about it, but I think what we're gonna do is not look at the data, but talk about the theories of what's going on. And the reason we're doing that is because the technocrats, the mainstream platforms and centralized powers trying to prevent discussion of how people feel about this and everything. So I think it's a good idea to have the platform while we have it available to talk about this, okay? That's one thing. The second thing is for the music livestream tomorrow that we're gonna do tomorrow night, the odds are we're gonna do a sound check tonight with the other people that are on Twitch, okay? So you might get an announcement that we've gone live. I don't know how long it's gonna last, but we're gonna try to do a sound check, make sure we have everything set up for tomorrow night, okay? Just to let you know. So, we'll see. We might just be on for a couple of minutes. It might be five minutes. I don't know, we've never done. And by the way, since there's a lot of you that have been on Twitch for a long time, you know the inner workings of it. So we're gonna be doing, starting here, my partner's gonna do a DJ set to our DJ set, and then we're gonna kick it off to three other people, kick it off to one person, and then they're gonna kick it off to the other, and they're gonna kick it off to the other, right? So it's gonna be like six and a half hour DJ set, right? Now, I'm assuming the best way to do it is we stream and then we just host their stream the way they do it, right? Is that the way we should be doing it? And then we host the next person and then we host the next person, and they're gonna do the same, right? I'm guessing that's the best way to do it because all four are gonna be showing all four streams, right? Just running it past you guys. Chicho, you ever heard of ashwagandha, similar to matcha ashwagandha? No, I've never heard of that. Sounds African from Africa, similar to matcha, but I find it flavorless and easy to consume. Really, I've never heard about it. And I do put honey in this by the way, so it's sweet. Hopefully it doesn't. I saw a study that said that it doesn't seem like it's mutating rapidly, but we'll see. Yeah, there's so many studies out right now. It's hard to make sense of all of it, right? The new antibody tests are showing herd immunity rates are higher than expected. Yeah, I'm seeing that as well, right? So that means our, the fatality rate is lower than what we've been seeing based on if we expect it's been out for a while before we detected it, and there's already herd immunity in there, right? So the numbers we're looking at was based on the official numbers with we're looking at confirmed cases and recovered cases, and we did a few, some ratios, and we had anywhere between five to 10, 15, 12%, there's something fatality rate. So if there is, it's out there already and there's a lot more people that have already got it and showing immunity and stuff like this than kicks down the fatality rate, which is great. One thing it does though, it shows that the infection rate, the R naught value is a lot higher than what was initially being stated, right? So it's way higher than three if it's already within reason, right? So the numbers are very problematic. Oh wow, that sounds interesting. We could have like a little stats stream. Regarding the COVID, oh, regarding looking at the data, the life expectancy and stuff, yeah, for sure we could do, we could do and look at the population distribution, right? So for example, if we're looking at this, population distribution is huge. If you look at a specific country, I don't know what the thing looks like. Let's say this is USA. Let's say this is Nigeria, Nigeria. Let's say this is, where do we have a huge population youth? Huge youth population that's coming up. Iran is one, I think. Iran or it used to be. So USA has a lot of baby boomers. So if this is a zero to let's say 100, you would see, I don't know what it looks like. Let's assume it looks like this, right? Lots of older people, less young people. We're seeing in nine months, we're gonna see a blip of newborns, right? Nigeria has probably like this, right? I looked at the stats. This is 100, this is zero, right? I looked at the stats about 10 years ago for Nigeria and Nigeria's population was 100 million, I think 2000, right? They were expecting the population to be 300 million by 2010, 2100. And 100 years was supposed to be triple, right? Huge, right? And Iran, I believe it has a big youth population and average middle and stuff. If you look at all this, all of these, the population densities, I would love to delve into this stuff. This stuff is fascinating because this stuff really dictates your economy and politics and many things, right? Theory stream sounds incredible. Yeah, Spiderman, I think that's what we're gonna end up doing. Do you know if there's any way to get access to the raw data? Dude, I tried. I looked at, I was trying to consolidate the stuff and we did like three months, four months. I love to play around with it. I have the spreadsheet. I have the spreadsheet for the first 70 days. From January 20th, I think, we went until beginning of April. I haven't entered this, I was staying up with it on a daily basis, but because the data is so problematic, I haven't filled in the data for April yet. So if you look at our Patreon page or let us know, if you do Chicho, COVID-19, COVID-19, you'll see the streams that we did previously. We looked at the data and we graphed them. Okay. If you want, you can post a real homeless being. You can post a question on Discord and one of us will link up the videos. Actually, I do have a COVID-19 playlist on YouTube so you can look at that. Opicham. Opicham, Mathematica. Mathematica, Opicham. I don't know what Opicham is, but Mathematica, it must be Mathematica. Think about Chicho. I'm gonna try and be there tomorrow night and blast it through my speakers. Nice. I have six speakers on one receiver, two stacks of three. Nice. You're gonna love the music, man. You're gonna love it. Hosting is perfect. Okay, hosting is perfect. That would be the best way to do it. Okay, so we host, awesome. So all four people are hosting because the other three are new to Twitch, by the way. I'll give you guys, everyone's, I'll give everybody's Twitch account tomorrow once everything's confirmed. That would work. Yes, I've seen it done before. Okay, cool. Martin, scroll. I should go down. I have four Chicho rewards. I feel rich. Nice. 4,000, 4.7,000 Chicho rewards. So, what's the occasion tomorrow? Just, we're, like, I'm lucky enough to be, to have friends in town and to be around music. And I know a few DJs in Victoria that I've come to and I've gone to a lot of shows and stuff. So I'm lucky enough to have a lot of friends that are DJs and they haven't had the opportunity to play in any venues. I knew some of them that were gonna play. My partner was gonna play at a venue before COVID hit and the venue got canceled, the show got canceled. So everybody's itching to play. So we figured, why not, right? Let's do it. And we might do this on a regular basis. Sharing music is phenomenal, right? And we'll have the playlist as well so you can check out the original tracks and everything, right? We have a two-day DJ stream full of electronic music and dancing. Nice. Well, did I put two days? Six hours, six and a half hours. I hope it's six and a half hours. Great to know, thanks. How advanced of math questions are permissible? High school mathematics, LARC. So if you have math question, let us know. We're sort of not going on math right now talking about everything else. Well, sort of mathematics, I guess. Hopefully you can pop high and say, pop, pop, pop, pop, pop, pop, pop, pop, pop. Okay, I'm gonna scroll down, but there's a sort of analysis is not good. LARC analysis, it depends. What are we analyzing? What's the analysis? COVID playlist. Danite, how are you doing? Welcome, welcome. Given X squared plus P, what does P need to be so that three times three X touches X squared plus P only once, tangent. Three X. Oh, Y equals three X. Yeah. What about any slope like AX? I gotta think about this. Let's draw it out. Check it out. Let's draw it out. When we get any problem, we need to draw it out, right? Let's write the problem down. Mask of Raven has given us the problem, which is fantastic, right? Get to the mathematics. So we got Y is equal to X squared plus P. So our first function, should we use Y? Let's use F of X. F of X is equal to X squared plus P, right? What does P, this dude, right? And that becomes the Y intercept. Have to be, need to be so that three X and we'll call that the new function H of X is equal to three X so that H of X touches this parabola only at one point, right? So check this out. Let's graph this guy. So this guy is a parabola. It follows the form, follows the form F of X is equal to AX minus, I can't call it P. Let's call it M, M squared plus N. And M and N would be the vertex of the parabola. Just subscribe for, hey, Spider-Man. Thank you for the Twitch Prime, so. Analysis is in advanced calculus. Yeah, I wouldn't be able to do it lack of caring. Mask of Raven would know. So our Discord page people would know is proof-based calculus on general real spaces. Yeah. I'm pretty sure Olive, not Olive. Sorry, Olive, I saw your dog, mean papa. Doggy won't pop up to crack me up. What do you call it? Let's go. Discord page, odd make window. Traumatic high school math memories are rushing in. Oh no, take a look at this. This guy is the general form of a parabola, right? Where M is zero, so M is gone, right? And A is one, this guy becomes one, right? So that's what we get. Well, it happens to be if M is zero, right? And this guy is one, then this being your vertex, your vertex is zero and M is your P, zero P. Okay, I should call this P, actually, why not? Okay, so that basically means this parabola is like this. Here, here, here, anywhere along the y-axis, right? This guy is a line, right? I'm in high school at the moment. Just kidding, of course, when I was actually interested in solving problems, not the tu-tu-tu-tu-tu-tu-tu. This guy is a line, right? This guy follows the form H of x is equal to Mx plus B. In this case, this guy follows the form H of x is equal to Mx plus B. In this case, the B is your y-intercept and the M is your slope. So this guy is zero, right? And this guy is three. Now, if you graph this, here, let's do this with a different color pen. Do this with a different color pen. If we graph this, just general equation, this guy here, you would start off at zero, zero and then go up three and then over one, right? So that's this line here. Now, what the question is asking us, we only want this line to touch the parabola at one location, which means it's gotta be tangent to it, right? So if you go like this, this line here, we have to bring it down, bring it down, bring it down, bring it down, bring it down. So it's gonna touch this graph somewhere here, right? That touches it only once. Is that parallel? Oh, that's not parallel. That's horrendous. Let's make sure we make the stink parallel. Make the stink parallel. I'm gonna stand in front gang. I can't do it sideways. Better? A little bit better, right? So, how do we do this, right? We need to find, what was the question? We need to find a point. We need to find a point, right? We need to find a point, we need to find a point. Given that, what does P, oh no, no, we need to find P. So what does P have to be? Oh, the P's gotta be up there. I should have read the question more accurately. So let's modify this. So after you read a question, word problem, draw it, and then read the question again. So make sure you got the question properly. So this is the general thing we had, right? However, this is the line. There is no unknown here. So that is the line. We're not moving the linear line. So I'm gonna erase this and modify our problem so it represents what Mask of Raven was actually asking, right? So I'm gonna erase this, watch this. So Mask of Raven is asking this, if we have this line, X, Y, Y, if we have that line, yeah, let's do it all in green and let's kill this. Because now we understand the mechanism behind this, right? H of X is equal to three X. Let's draw that line. One, two, three, okay, and then one over. So here's our line. So we wanna know what does P have to be for this to touch the graph at one point. So basically we're finding, trying to find the Y intercept of this. And I don't know if it's there or not. This is the unknown, right? Where is this? How do we do this? How do we do this? We're trying to find where they touch. Where they touch only has one solution. Let's think about this. I haven't had a problem like this for a while. I went too far with the Mask of Raven. I thought this was moving as well, right? Ta-ta-ta-ta, discriminant of discriminant, yes. Okay, ta-ta, did I catch it? So how do we do this? How do we do this? So we need to find P. We need to find the vertex of the parabola. The Y part of the vertex for a parabola. We need it to be touching at one location, one solution. So the discriminant has to be zero. That's right. So what you gotta do is just basically solve for the system of equations. Oh, what's your drink? This is matcha, check this out. This is matcha with honey. And I put in, it's got coconut oil in there too. So this is what you're gonna do. You're trying to solve for a system of equations. That's what the question is, right? So this is a solving a system of equations problem. Solve this system of equations. Equations. How do we solve the system of equations? We're trying to find out, when does F of X equal H of X? So first step is, step one, step one, set F of X equal to H of X, right? By the way, I haven't done this type of problem, just so you know, is because I don't have any grade 12 students this year, which really sucks. Because I'm not getting my high level practice problems coming at me. What is matcha is greens. It's like, I think it's got green tea in it and different herbs in there. I'm not absent sure. My partner's the expert in this. So she feeds me this. That's awesome. Super delicious, super good for you. Lots of greens and minerals and antioxidants in there. So we're gonna set F of X equal to H of X. Because that's the function, and that's the function. So we wanna know, when does this equal this? Well, this equals this, when this equals this, right? So now what we do is, we say F of X is X squared plus P, X squared plus P, and H of X is three X, right? So we gotta solve this for P, right? Okay, it's high, called green tea powder. Tea only, is it just tea? Interpsi? It's really good, seriously. Interpsi, if you know it, then you know this drink. So I'm guessing you drink it. Because once you drink matcha, you go, okay, I want this part of my life, right? So how are we gonna solve this? We grab this dookie, bring it over. X squared minus three X plus P is equal to zero. This is a quadratic. All things lead to the quadratic formula, right? All things, like seriously, quadratics is one of the major steps in mathematics that you have to master. Like drink that, just like the Japanese do it, nice. Is it Japanese drink, Martin? Is it from Japan? There's different grades, only ceremonial grade you should drink. Others are like, for like, putting on ice cream, was it? No way. Why won't you just divide the other side by three? Because I want this side to be zero, right? When we're trying to solve an equation, zero is the grand master, right? If this side does not equal zero, then we can't split this up into things multiplied together to give us this, right? So, and we talked about this. If you look up chichu, the power of zero, right? If you have A times B times C times D equal to zero, how could you solve for that? How could, what could A, B and C, A, B, C and D be? Well, at least one of them has to be zero. A equals zero, B equals zero, C equals zero, D is equal to, at least one of them, so all of them could be zero. This can't be said to be true if A times B times C is equal to D. You can't say A has to be D, B has to be D, or C has to be D, it doesn't work. So, that's why we do this. We move everything to one side, right? Now, for us to solve for this, there's three things that can happen here when a parabola and a line are trying to cross, okay? Mask of Raven, X is equal to A to the, where R equals slope of a line, da, da, da, da. You're looking for roots, exactly, right? So, check this out. If you're looking for roots of this, there are three situations when you have a parabola and a line, right? Three things that can happen. You could have, I'm gonna draw them here and then we'll erase them. You could have a parabola and then a line crossing into two places, right? You could have a parabola and a line just touching it in one place, which is the situation we have, right? Or you could have a line where the line doesn't even touch it, right? If you have this situation where you have a parabola crossing a line or try to figure out if a parabola does cross a line, right? Then this is what you have to visualize. So, you go through, you set the first function equal to second function, you bring everything over to one side, set it equal to zero and you're gonna end up with a quadratic, right? Because you have a quadratic and a line. So combine, I'm a line and a quadratic. Combine to give you a quadratic, right? So, what this does, this is really, what's the word called, transposing it or something like this where it's almost equivalent to finding the x-intercepts of a single quadratic because that's what that is, right? These solutions are really, if you wanna think about it, giving you this situation once you combine these two functions. This one would say, oh, the parabola crosses at two points. This one would say, oh, it just touches the x-axis. And this one would say it doesn't touch the x-axis at all. When do we get each one of these situations? When the discriminant and the quadratic formula is either, is, here, let me erase this. We're gonna get the situation if the discriminant, discriminant in this case is greater than zero. Here, if the discriminant is equal to zero. Here, if the discriminant is less than zero. What that means is if the discriminant and the discriminant from the quadratic formula is this, right? B squared minus four AC, right? Because if you remember your quadratic formula, what is your quadratic formula? Your quadratic formula is x is equal to negative B plus or minus square root of B squared minus four AC, right? Square root of B squared minus four AC, all of it divided by two A, right? So, doing a little adjusting, right? And once made a smoothie, da, da, da, da, da, da, da, da. M and P is equal to that. So what we end up having here is the basically driving mechanism for the quadratic formula is the discriminant, this guy here. Because this guy is this guy, and this guy really tells you if you're gonna have one solution, if it disappears, if it's zero, if it's greater than zero, you're gonna have two solutions because you're gonna have negative B plus that divided by two A and negative B minus that divided by two A, or you're gonna have no solutions when the inside of the square root symbol is negative because you can't take the square root of a negative number, right? So, keep this in mind because this is really the mechanism behind solving this thing, right? So I'm gonna erase this. I'm gonna erase this as well, okay? So we wanna solve for this, right? So we don't know what P is, we wanna find out what P is, right? So, but we wanna make sure the discriminant, this guy, X is equal to negative B plus or minus square root of B squared minus four A C over two A, we wanna make sure that this guy here is zero, right? Because if it's zero, then this thing reduces to negative B plus or minus square root of zero over two A, which is equal to negative B over two A. That means that we got this situation where the line is hitting the parabola at only one point, okay? So we're gonna set the discriminant, we're gonna force it to be zero, okay? So we're gonna say this situation, this situation occurs for this when B squared minus four A C is equal to zero. Well, B is negative three squared minus four times A is one and P is P is equal to zero. Nine minus four P is equal to zero. So negative four P is equal to negative nine, divide by negative four. So P is equal to three, oh, not three. I took the square root of it for some reason. Nine over four. I think I did that right anyway. I hope so. Is this right mask of Arabian that would get it? Or did I totally muck it up? Two is the slope of the tangent, which should ring a bell. Does it approach the line, but not touch it? And there is a term for that. I can't remember, is asymptotic to it? Is that what you mean? Sorry, I'm late. Always be making, how are you doing? I was setting up a stream labs, stream labs. The little witches are fun. I'm here, nice. The term for that would be asymptote. And no, it just touches, it just touches. P does equal, yay, we did it right. So that's our answer. P has to be nine over four. So what that means is this guy, if you have the function f of x is equal to, let's write the solution here. f of x is equal to x squared plus nine over four. And if you have h of x is equal to three x, then if you're solving for the system of equations, it means, boop, this. Sorry, it doesn't mean this. It means we're getting this when the y-intercept is nine divided by four is two and a quarter, right? So one, two and a quarter. So that means the vertex of this parabola is gonna be zero and nine over four, two and a quarter, right? Great question, by the way. Great question. I would put this type of question on a grade 11 test, actually. A grade 11 or grade 12, ah, it depends on the grade 11. Ah, okay, sorry. It's been a long time, asymptote. Chico, we were talking about the second part of the question. What's the second part of the question, mask of airmen? Like, what about for any slope AX? For any slope AX, ba, ba, ba, if for, for to touch in one location, so it would be, okay, I'm gonna erase all this. If you, like I can tell you, if this interests you, take a screen capture of it, right? And you can play the video again, take a screen capture. That's one way to take notes when you're, if you're getting tutoring online or education online, you just take screen captures, then you just put those in your notes. Fantastic, right? You can edit out a Chico if you like, just take that, right? So what if this was an A, right? What if this was a A? Which is what I was going for when I laid out the problem initially, right? Mask of airmen, I was modifying, I was moving our line. I thought for some reason there was also variable in there that we need to figure out an unknown, okay? So if there is an A there, then this guy becomes an A. We're just gonna modify this, see where it takes us, right? So this guy becomes AX, right? I'm gonna erase this, I'm gonna erase the rest of this. And we do have to, no, that's legit. We can keep that. Yes, I wasn't awake for your, sorry. Asymptote, I know that word. I've done this guy in the math, not that I have stuff. Asymptote is just, it just approaches as a limit, right? The function just gets closer and closer, but never reaches it. So what we do here, we still want it to touch the parabola of one location. So we still want this. So let's, over here we have to fix this. So this part needs to be fixed. And this part would be, bring this guy over. I should have just erased the three. 2X minus AX plus P is equal to zero. Now we can sub it in again. I think this is the way we should do it. So it's gonna be negative A squared minus four times one times P has to equal zero. So that's just A squared minus four P is equal to zero. So P is equal to negative A squared, negative four. So P has to be A squared over four. Now what does that mean, right? Yeah, this is a cute way of getting one specific derivative. Photoshop, sama hike over GTO for optimum note review. Funny. Sure, it rings about derivatives of the function for the parabola. Drivatives, should we take? Yeah, derivative of the function for the parabola, for sure, right? But could we do it, take the derivative here? No, that would give you the tangent line. Over here, basically we're getting a relationship between P and A. So P has to be A squared over four. We can take the derivative of this. It's gonna get two, well, we still have two. So that gives us a function for a given X value. Yeah, that might do it, let's check it out. Is that what we're talking about? So if we take the derivative of this, we're gonna get two X minus A. Right? So that's any tangent line for the point P of where it crosses, and we set this equal to zero. No, that doesn't work, that doesn't make sense. It doesn't, I don't think so anyway. Is that what we're looking for, masquerade and derivative? That's what I don't understand. We put out a video for it, Olive, did you look at that video? Take a look at that video. I tried my best to explain that calculus stuff. What a derivative is. And there was a lot of people in the chat that were talking about it too. So, and there was some people that commented on this quote. I believe you saw it. How do you use cosine to calculate the side of a right triangle? Sure, let's do, masquerade it. Once you know P is equal to A squared over four, what does X need to be? What does X need to be? Not saying you need derivatives, but it would make the question faster. What does X need to be? Dun, dun, dun, dun, dun, dun, dun, dun, dun, dun. But X can vary. Can it, masquerade it? Oh, I guess you could do this. Like if you're taking the derivative here, right? Two X minus A, this has to be zero. So, two X is equal to A, so X has to be A over two, right? Is that what you mean? Thank you for another interesting problem. Yeah, seriously, masquerade it, thank you. I try to watch it, but I just fall off too fast. Yeah, I saw it, but I'm not smart enough to get it. Plus there's a language, yeah, the language barrier too. And I talk speedy Gonzales style, right? So that's the answer, that's cool. Cool question, question masquerade it. That's super cool. And by the way, what we did here, Olive, take a look at this. This is the function we're trying to solve for, right? So that's the function we're trying to solve for. And we're trying to find when, if you take the derivative, what do you call it? If you, when this parabola really just touches the X axis, right? Where it bounces off the X axis, if we don't even consider any of this, right? Then we find out that P has to be A squared over four. So what we can do is say, okay, then what does X have to be? Take the derivative of this function. Let's assume this is F of X. And this is what we're doing here saying, God, that's a horrendous equal sign, it just drew. Let's do this. What we're saying is F prime of X is two X minus A. If we're saying that, then we're asking, if this is supposed to be, we're trying to force it to bounce off the X axis, right? Then we're setting the tangent to be zero, right? So we're gonna set it equal to zero, zero is equal to two X minus A. And then we solve for X. And what that means is, this X value has to be A over two, and the relationship between A over two, and the relationship between A and P has to be this. It gets a little bit layered, this one. If you plug X is equal to, X equals A over two into that, where P is at, you get the equality holding. That's the way saying it, right? Anyway. Thanks, I enjoy offering fun problems with little twists. Yeah, and good math problems to get the brain flowing and layer as she says layer. Yeah, is to give you a little pause to think about the problem. As you saw, like for me, this wasn't a straight up problem. Oh, solve this, solve this. I had to sort of dig a little deeper and go, okay, what does this really mean? And sometimes I'm off. I go down the wrong road, because as soon as I did it, I had to turn around and ask the person that gave me the problem, hey, did we do it right? We didn't go out and ask for the answer right away. We tried it out, and if he said no, we would have gone, okay, where is the assumption that we made a mistake on, right? What did we think was happening that wasn't happening, right? Which is what I did initially when I read the question. I modified this initially, the line, right? And then read the question again. I went, oh, it was three, right? That's the way you have to approach math problems. So again, anyone in school right now, if you're lucky enough to be in a class that challenges you, that gives you problems where they're not necessarily very difficult technically, they require a little bit of pause before attacking the problem. And if you have someone that can, you know, you can go ask questions off, bounce off ideas on, that's the best way to learn. That's the best way to learn, right? Assuming P is a constant with respect to X. Assuming P is a constant with respect to S, which it is, the value of P is irrelevant since it vanishes under the derivative. Da, da, da. Oh, over here. Is it irrelevant though? Because it still has to be the A connects up to the P. Oh yeah, the driving force would be the A. A is the driving mechanism for this relationship, for this problem, for sure. Yeah, lack of caring, 100% I think. I think I would get it if I just get a bit more patient solving the problem. Yeah, for sure, I'll just enjoy the process. There isn't, like, there's very few things in life that give you the opportunity to sit down and just pause and think about, I don't know if we want to call it abstract but something that's layered like this that is very much connected allows you to take something visual, quantify it, and solve for the visual problem. Like, I don't know anything else that does this. So enjoy them, enjoy, I know it's difficult. It's hard to convince people but once you get into problem solving, it's very meditative. But my main issue is that I don't see it as a big picture stuff. I just learn the formula and put in the numbers and I hate doing that. I want to understand what I'm doing. All of you are not the only one. So my suggestion to you is if whatever you're studying right now, you need to get it done, get the marks for it, do what you need to do but go back to earlier levels of mathematics and try to figure out how to simple stuff works. Like, do you know why an equation line is an equation of a line? Do you know why an equation of a parabola is an equation of a parabola, a quadratic? Just answer some of those questions for you and it'll put everything else into gear. It would be interesting to apply a derivative method to find roots for general cubic functions since the derivative of a cubic is a quadratic. Yeah, I would love it if you would solve for an unknown side of a, oh, right triangle, I knew there was something else. Dude, thank you for bringing it up again. If you show me how, I might go grab my dusty old calculator and do some trick. Dude, we're gonna do it right now. Raise your cue, how are you doing? Let's do some trick, just, and by the way, gang, if I missed a question I said we're gonna do it and I forget about it, put a reminder up. I get lost in the conversation sometimes, sometimes. If you show me, what's the problem? We're gonna do a trick problem right now. When you say it like that, mass sounds truly, it is beautiful, all of it is beautiful. It's freedom, it's one of the tools you need to be able to live as a free human being. Otherwise, you're dependent. Let me see if you have a calculator that's cheating. Okay, that's where the tip, I'll do that. The other is basically about finding tangent stuff, yeah. Yes, calculating makes it easier. So, trigonometry. So we're talking about Sokotoa. So we got, let's call, let's, what do you call that? Let me move this over, we can write the formulas in one side, right? So let's bring our triangle here. A, B, C. Usually, in my part of the world, I use capital letters to represent the angles of a triangle. So this is angle A, capital A, this is angle B, this is angle C. And when I write that, that's 90 degrees, if it's a box, right? The beauty of the question is you get calculus results without necessarily needing calculus in that grade. 11, 12 could do this. And in a triangle, yeah, I've done this before, but we do it again, we do it again. Take a look at this. Here's a triangle. Here's a triangle. Here's a triangle, right? I'm gonna increase this side at this angle. Which side is getting bigger? It's the blue side, right? So I'm gonna decrease this side and the blue side is getting smaller, right? An angle in a triangle controls the opposite side of the triangle, okay? So this guy controls this. So if capital A controls, capital A angle controls this side, I'm gonna call this little a, side little a. That way we have a link between the two. And this guy will control this, that side, oops, little b. Okay, and this side controls that and that side, little c, okay? There are five basic formulas we know for right angle triangles. Two of them, one of them applies to all triangles. Mathematics is indeed beautiful. To paraphrase Galileo, quote, the laws of nature are written by the hand of God in the language of mathematics. Ah, that's a beautiful quote. Catholic traditionalists, quote, the laws of nature are written by the hand of God in the language of mathematics. Formulas we know for triangles, right angle triangles. Well, any triangles, some, some of the angles in a triangle equals 180 degrees, okay? Angles, triangles, I cheat, right shorthand, right? Have fun guys. It's bedtime for me. Stay safe, you all, bye. Bye, Olive, sweet dreams, right? So does anyone know MATLAB? Can I get some help on some code? Code, if yes. I wish I knew MATLAB. It was a time where I tried to study it. Chico, I've got my calculator out. Thank God for solar power calc, calcs because I haven't touched this thing in years. Let's do some trick. Also have a pen, ah, nice, nice. So your first equation is some of the angles in a triangle equal 180 degrees of any triangle. And then we've got Pythagorean theorem. A squared plus B squared equals C squared, right? This squared plus this squared equals this squared, okay? Side links. And then we've got the trig ratios, right? So we've got the trig ratios. And trig ratios are exactly what it says it is. I should write this better so you can read it, right? Trig ratios, trig ratios, and what are ratios? Ask yourself this. What are ratios, okay? What are ratios? We've got sine of an angle is equal to opposite over hypotenuse. Coase of an angle is equal to the adjacent side over the hypotenuse. 10 of an angle is equal to opposite side divided by the adjacent side, right? And what are ratios? Ratios is one thing relative to another thing, right? So when we write down sine of an angle, right? It means pick any angle you want, except a 90 degrees. So either pick A or B. So if you go to A, if you go here, the sine of A for this triangle, sine of an angle, in this case A, it's the opposite side, this guy, which is A divided by the hypotenuse. And this is the hypotenuse, which is C. Okay, now what's sine of B? Sine of B is equal to opposite of B is little B divided by hypotenuse, right? Let's go, coase of B. What's coase of B? Coase of an angle, right? So whenever they say an angle, imagine yourself standing on that angle. We're here. Coase of this angle, here, let's do the blue sticking out. Coase of this angle is adjacent side divided by the hypotenuse. Well, there's two sides adjacent to this angle, right? But this guy already has a name, it's called the hypotenuse, okay? So this guy is gonna be called the adjacent. So, coase of angle B is adjacent over hypotenuse, which is A over C. A over C. Heck, yeah. Sine, cosine tangent, right? Now take a look at this. Hey, sine of A is A over C. Coase of B is A over C. They're the same thing, right? Here's another formula. We're driving another formula right now, by the way. Okay, just for the hell of it, why not, right? Now, take a look at this thing. Before we actually do some number crunching, I want you to appreciate the beauty of a triangle and how some of these things are related. Now, some of the angles in a triangle equal 180 degrees. So, for any triangle, right? This plus this plus this equals 180 degrees, right? Can you effectively define secant and cosecant, or is that out of a... For this one, we can't do that yet. I just type in my calculator. Dang baller, right? So take a look at this. I'm already losing you. I'm already losing you. So hold on, if I'm already losing you, let's do a simple calculation first. Check this out. That's too funny. 35 degrees, right? So, here, let's draw this bigger. Let's do 35 degrees. I'm not gonna do this proof, by the way. Let's skip this, right? I was gonna prove to you that sine A is equal to cose 90 minus A, and this just happens to be B, right? Just know that. That's just where we are, right? No, I got it all right now, hilarious. Take a look at this. Let's do a simple calculation. Funny. Let's say this is 35 degrees, right? The general question you're gonna get regarding trigonometry, the basic stuff that you're gonna get, we found that kid in the class. We already lost him. Here's the question. They're gonna say solve this triangle. Solve this triangle. Now, how many pieces of information do you have in a triangle? You have six pieces of info in a triangle, and they go in pairs, they're related, right? You have three angles, one, two, three, and you have three sides, one, two, three, and an angle is related to the side, right? So these guys are paired up, those guys are paired up, those guys are paired up. So there's relationship between the three and the three, right? But there's six pieces of info in a triangle. Now, to find all the six pieces in the puzzle in this triangle, you need to be told that one of the angles is 90 degrees, and you need to have at least one side, and you can have anything else. Then you can solve for the other six. So you need three pieces of the info for a triangle to find the other three, and one of them has to be a side, and they have to tell you it's a right angle triangle. So they usually tell you it's a right angle triangle, that's one piece of info. So they give you one angle, the main angle, and they can tell you, let's assume they give you this, that's a five, okay? So right now we have one, two, three pieces of info, one of them is the triangle, or one of them is the side, right, and you wanna find the other three pieces. What are the other three pieces? We need to find this side, let's call this C, we need to find this side, let's call this B, and we need to find this angle. What are we gonna call this, big B, theta, W? Anything you want, let's be consistent with this and call this B, okay? So my question is, what do you wanna find first? What do you wanna find first? Do you wanna find B first, C first, or big B first? Do you wanna find little B first or big B first? Which one do you wanna find first thing? I wanna have some matcha, B, little B. Okay, let's find little B. This is what you need to do. Whenever you're given a trig triangle, right angle triangle, when they say solve a right angle triangle, it's the questions that you ask yourself that are the key to solving problems, right? So you ask yourself this, you wanna find this, okay? If you wanna find this, look at the triangle and ask yourself, what information do you have? You're gonna go, okay, you know it's a right angle triangle, you have this side and you have this angle, okay? These are the formulas that you have, right? So you can go by elimination. Let's do this one first. Some of the angles in a triangle equal 180 degrees. Well, you're trying to find this. That really doesn't help you out and you're trying to find this so you can skip this one. The next one is Pythagorean theorem. A squared plus B squared equals C squared. Well, you could call this one A because C is always your hypotenuse, by the way, right? Yeah, perfect. This guy is gonna be what? The big B. Do you wanna find the big B first? We can, right? And by the way, whenever you get this, whenever you get a right angle triangle, here's a shortcut. I always get students that say, oh, we wanna find this. Well, this plus, this plus, this equals 180. So they always go, oh, 90 plus 35, and this is 125, and then you go 180 minus 125, right? And this becomes seven, 10, 50, five, right? So this guy's 55. Here's one place where you can save yourself a little bit of time. If you're dealing with a right angle triangle, it has to be a right angle triangle, then you know this is 90, right? Well, if that's 90, then 180 minus 90 is 90. So if you're dealing with a right angle triangle, you don't have to take it all the way to 180. You know that this plus this is 90. So for you to find this guy, all you gotta do is go 90 minus 35 equals 55. It just saves you a little bit of time, right? That's all, but it's well worth it. Like, you save yourself a little bit of time, right? Okay, so we found big B. We want a little B, but we found big B, that's okay. So this is 55 degrees, okay? Now let's go for this. Now you ask yourself this, okay? Well, this one didn't help us to find little B. This one didn't help us to find, well, it's not gonna help us to find little B because it's gonna be five squared plus B squared equals C squared. Well, we got two unknowns in this. It doesn't work. To solve for one unknown, you need one equation. If to solve for two unknowns, you need two equations. So Pythagorean theorem is gonna work. To solve for this, we needed these two, both of them. So to solve for any side using a Pythagorean theorem, you need two sides. Then you go here, okay, sine theta. So sine of an angle is opposite over hypotenuse. So if you wanna put yourself here, right? Because we have this angle to begin with, right? So if you put yourself here, sine of 35 is opposite over hypotenuse. Well, that doesn't include B, so that's not gonna help us. Let's go here. Cos of 35 is equal to adjacent over hypotenuse. Well, that doesn't help us either because it would be cos of 35 is B over C. That's two unknowns, right? Then you go to 10, you say 10 of 35 is opposite, which is five over B. That's gonna work because that is B only that we have to solve, right? So you're gonna go 10 of 35 is equal to five over B. Cool. Keep in mind, we couldn't do it with these ones. We couldn't isolate B. Yeah, 10 of money is five over B. So what you can do now is you can just punch this in your calculator, it's just a number. 10 of 35, this guy, is just a number. I see everyone just punching in always at the same time. Is that what it comes out to? But I usually just do the cross multiplication right away. B is equal to five over 10 of 35. Do we have confirmation? Is that what it is? I'm gonna punch it in just to make sure. So we're gonna go five divided by 35, 10 of 35, where's my tricks? It's 7.1. Because 10 of 35. Oh, you punched in 10 already, right? So this would be, here, let me do it the long way. So you see what's going on. So we got 10 of 35 is equal to five over B. 10 of 35 was, I think that was 0.7. Yes, you're back, G. Joe. How are you today? Lark, how are you doing? Happy Friday, happy Friday. 35, let me do 10, 10. So 0.7, so 0.700, right? Yeah, is equal to five over B and then cross multiply. So 0.7 B is equal to five and then divide by 0.7. So B is equal to 7.14, I think it was. So five divided by, oops, divided by 0.7. Is 7.14, so this is equal to 7.1, oh, not this one. B is equal to 7.1. B is equal to 7.14. Now, whenever you're doing trigonometry, whenever you're solving for triangles, as soon as you get an answer, you ask yourself, does this make sense? Remember, it's the questions that really are the driving mechanism behind you solving a problem, right? So as soon as you get to here, and in life in general, so questions you ask that are important, Matt, how are you doing? You ask yourself, does it make sense for B to be 7.14? Does it make sense and why? Answer that question then, why? Or anyone else? Why does this, at least it could be a valid answer? And let me ask you this, so to give you an idea, no, because A is equal to five. Well, let's check it out. Let me put it this way. If B was equal to four, would that make sense? Would it make sense for B to be equal to four and C is bigger than A? C has to be bigger than A, yeah? Angle is smaller, 35 degrees, exactly. So take a look at this. If, then it is true. An angle controls the opposite side, 35 is the smallest angle. So five, because it controls that, has to be the smaller side. And we haven't figured this one out yet, but that's the hypotenuse. We're gonna assume it's bigger, right? Then 35, this side has to be smaller than this side because this side is controlled by 55. So whenever you're solving for triangles, you always ask yourself that. Does that number make sense? Or any problem? Whenever you're doing calculations to solve any problem, you ask yourself, does this number make sense? Is that valid? I sometimes fall into the trap where I write down the answer and then I look at it and go, oh, that was ridiculous. Of course that can't be the answer, but does the number doesn't make sense? This number makes sense, right? Because this side had to be bigger than that side because this side is controlled by the angle 55. This side is controlled by the angle 35. And angle 35 controls this side, then this side has to be smaller than that side because that side is controlled by the angle 55. And angle 55 is bigger than angle 35, right? It's a loop, sort of. Then how are you gonna find C? That's the only one left. How are we gonna find C? How are we gonna find C? We can use anything, any of the trick, formulas that have hypotenuse in them. Like we're not gonna use 10 because tangent has opposite and adjacent. We're looking for a hypotenuse. So we already have both angles, right? That we can use for sine and cosine. You never really use the 90 degrees for Sokotoa. And this is referred to as Sokotoa, right? Sokotoa, these guys, right? Sine is equal to opposite divided by hypotenuse. It's just a way to remember the words, right? Cosine is equal to adjacent over hypotenuse or remember the formulas. Tangent is equal to opposite over adjacent. If you wanna remember it that way. For me, I just knew this. I never really go with Sokotoa. I just know sine, when you go to grade 12, you'll find out the sine is really related to the y-axis, right? And cos is, there's more to this, right? So how are we gonna find C? What are we gonna use to find C? We can use cos, we can use sine. What else? We can also use the Pythagorean theorem because we have A and B. Then we can just use Pythagorean theorem to find unit circle, life, yeah. Always be making unit circle. The bigger the angle, the bigger the projected line. Perfect. That's exactly it, right? Understanding journey is more important than the destination. So over here, let's use the Pythagorean theorem. We haven't used it yet. A squared plus B squared equals C squared. Well, C is your hypotenuse. So five squared plus 7.14 squared is equal to C squared. So C squared is equal to, or C, let's write down C and running out of space, right? So what we can do is say, take the square root of both sides. So C is equal to square root of five squared plus 7.14 squared, whatever that comes out to. So 25 plus, I guess, 49 plus squared, how I see a math problem. Yeah, understanding journey is more important than the destination, yeah. It's not as important if you get the right answer is did you do it right, the process? Because you might have had little hiccups along the way, and if you didn't have any hiccups along the way, you got the answer wrong, then your assumption at the beginning or somewhere in the middle through the process was wrong, right? Mask of variance says definitely agree. Yeah, I'm with Martin for sure, 100%, right? Trigonometry. It's powerful, it's brilliant. 8.716, and does it make sense for it to be 8.716? Yeah, because 90 degrees controls this, right? And that's the biggest angle. I would have expected it to be a little bit bigger, but we can do, here I'll do it on my side, just to confirm. That way you are not just guessing at the answer, you'll be able to fix mistakes, yeah. And by the way, one of the things as if, I know there's always been making, for sure does this, I'm pretty sure he does this, any good teacher does and always been making from the interaction with that, it seems to be a very good teacher, right? You always try to get your students to find their own mistakes, right? As soon as you can get a student, if they've made a mistake, don't give them the answer, don't show them right away where they made the mistake. Ask them, where's the mistake? Where did it go wrong? And get them to go through the whole process, right? Quote, and so I continue traveling, hopefully, which is better than to arrive, nice. Yeah, it's like life is a journey, right? Who wants to reach the end? That's a nice ride, man. I don't wanna get off yet. When's this ride end? When's this ride end? No, stop asking the question, right? Enjoy the ride, enjoy the ride. Yeah, ends when it ends, right? Fun problem, trigonometry, trigonometry. I wanna drink more matcha. I wanna grab a seat for a second. Exactly, enjoy the flow, enjoy the flow. The infinity question, when does it end? When does it end? I love Spiderman, chicho. You have early education videos, right? Yeah, and I'm gonna be making more. As soon as I rip some time, I've got some stuff regarding multiplication, just continuation of what we had. I'm going to be adopting with my wife after this craziness is over and I really want him or her to watch some. Oh, dude, no way, awesome, awesome. Congrats on that, by the way. Oh, for that kid is gonna be so lucky. You're gonna teach him mathematics and you got a comic book collection. And oh, dude, your kid is, lucky kid, lucky kid. Oh, that looks delicious, too. Your beverage, yeah. It's super good, creamy, it's crazy. Very nice, very nice. And this is good matcha. They have walnuts and almonds here as a snack. In general, I just pour a bowl for myself and I eat this. I mean, you shouldn't eat this much nuts in a day, but sometimes I do. I try to make this much last. It depends. Sometimes I go through this much in one day, which is too much, right? But sometimes I eat this much. I try to make it last like four, five, six, maybe a week maximum when I'm eating nuts anyway. Sometimes I pop them solo. Sometimes you pop them together. Power food. Also, I think the thing I posted in Discord yesterday is a good example of if you really know how a tool was made, was made, you kind of better understand how it works and you can do more with it. 100% masquerade, I totally agree. That's a great way of putting it. If you know how a tool was made, you can do a lot more with that tool. You know what's weaknesses, you know what's strengths, right? Catholic tradition is congratulation says to Spider-Man, brother, that is wonderful. What a blessing, what a blessing. Thanks so much, you chore. Spider-Man said, I have this all written down and I'm going to try and calculate another problem with different numbers. Nice thing, bud. Good stuff, brother or sister, of course, right? Thank you. That warms my heart. They will be very lucky. Nice. Kind of similar to the recent video you made. Yeah, the recent video I've always been making, put out, it was really good. Just the learning process, what it takes, right? I now realize how messy my note making is. It's basically a code only I can craft. And Dingbao, one of the best ways to improve your learning process is to tighten up the work. Really tighten up the work. If your eye, if you're looking at a page and your eye has to constantly scan all over the place to find the next link, the process of how to do something, you're gonna make mistakes. You don't, you want your eye motion to be as minimal as possible. You want the information to flow, right? It's like speaking, it's like saying a sentence. If you throw words out there random that if you had put them together, it's coherent. If you throw them out in random, it's a puzzle. People have to solve it, right? You don't want a puzzle within a sentence that's supposed to have a meaning. Mathematics is the same way, right? Have a nice flow to everything. The kid is going to be living the good life, good life math and comics. What can go wrong? What can go wrong? Hopefully they don't read some of the evil villains up there and go, oh, they're geniuses. I want to follow in their path. Oh no. Dr. Doom. Awesome, man. Happy for you, Dingmao says. Brother, Ding, okay? Brother, it is. Basically laser vision that only points at what you need, yeah. And aware of the periphery. Aware of what you've done in different parts, right? Mask of Raven. I'm sorry, I missed something. I heard my name. It's just regarding your, I've always been making your previous video that you put out. It was like 16 minutes or something, talking about the learning process, right? It was very good, profound, right? Understand, Chichou, I understand, Chichou. Martin made a comment earlier about knowing how a tool is made. Yeah, Mask of Raven says, it's amazing and related to your video. Chichou agreed, 100%, 100%. All right, fantastic. We're doing nice little math on these math streams. I like it. I'm talking and conversing, right? Super good. I can't wait for the test run tonight. Oh yes, experimental learning is the key. Fun stuff. What do you guys got planned for the weekend? Slowly the recommended quarantines or lockdowns are being lifted. So learning through doing, learning through experience. Yeah, I used to tell people, you need to learn from other people's mistakes because if you only learn from your mistakes, you're not gonna learn very fast, right? Because you only have one life, you're one individual. There are only a certain number of mistakes you can make in your life before it takes you out. But if you learn from other people's mistakes, then there are multiple people's mistakes, multiple people's lives, experimentation you're learning from, and that's what you really learn. Speedy Gonzales style, right? You just suck in the information if you can. I should take a pic of my notes from this and post it in this score. It's a mess. It's actually kind of like for shortening bot. And one thing I do just to let you know, when I work with students, I want to see their work because once I look at their work, I know where the problems lay, right? Where the problems are. So I try to tighten their work on that process. And I sit down with students and if I have the opportunity, I go over their problem solving abilities and I say, hey, listen, why do you have this over here? This belongs over here because it's with this guy. Or why do you have this right under this? This is side work that you should put on the side. So one of the things that I do as someone that tries to help people learn mathematics, I try to explain to kids or to my students how to write the text, right? And one of the examples I use, and my students crack up when I do this, right? And look at their work and if it's really messy, this is what I do, right? You stand in the shoulder of giants, of course, but I very much believe in learning through mistakes. Yeah, mistakes is the key, right? Everything I know was learned that way. Martin, some of it hard lessons, some of it hard lessons. I would argue that the majority of all learning that has ever happened, happened that way. You just erase their work. Do Martin, what a teacher. Yeah, I don't erase it. Yeah, I know how I just erase their work. No, wrong, wrong, wrong. No, I look at their work. Let's say it's a mess. And then I go, I go, listen. Here, I'm gonna write a sentence. You read it to me, right? Oops. What are I writing? Unless you saw me writing every letter in a row, what are I writing? Simmer, how are you doing? Hope your Friday is going well. Damn, I wasn't paying. Oh, oh, you weren't paying attention. You lost it, right? I was also going to ask you something. Oh, I'll always be making masquerade to always be making. It's like anagram, it's like anagram, right? Something about that exact thing. The balance between experiential learning and quickly getting the fundamentals through root learning and what role that has in education. I wrote, I like apples, right? So if I write it like this, it's a mess, no one can read it, right? But I like apples. I like apples, right? So when I see a student that has messy math work, I go, look, if you're messy with your mathematics, it's basically trying to decipher what you did before. Like, if you made a mistake, you gotta look back and try to make sense of that. Forget about it. Tighten up your work. It's a sentence. When you write an equation, x squared plus five x is equal to seven. That's an equation, right? But it's also a sentence in mathematics. This means something, right? So I try to explain to students, people learning mathematics, they're the same thing. They're sentences, tighten up the work. You don't want to write this, that's crazy, right? That's useless. Masquerade is a topic for debate. I pretty much universally reject learning through fundamentals until you are able to learn. I don't know if I would reject it, always be making. I think some fundamentals are, have just become fundamentals, right? It's like basically evolution, right? So some of the stuff, some of the core stuff, some people are innate ability that they're absolute truths to a certain degree, right? Although that is even a real work word. Too busy writing naughty words on your calculator. All good, thanks, buddy. Awesome, awesome, similar. Where's the K? Did I miss the K? Right there. Oh yeah, my writing sucks, by the way. All right. Do as I say, not do as I do, right? Looks like an AV. That's my K. I script. One thing I do that when I work with students, that way they really have to pay attention to what I'm writing for them to follow the work, right? Once they know how to decipher my writing, man, they learn fast. Imagine being so good at math, you write poetry for those with higher knowledge and capacity for understanding. Ding-Bubber, that's what people do. What's the equation? E, oh man, I don't know what it is. E negative pi i is equal to zero, I missed something. Did I miss something? There's one more something in there. X is equal to five plus 53 to the power of a half, minus. Plus or minus, oh, did you solve for this? Quadratic formula? Greetings, seems like I missed something, interesting. But talking about education and learning, yeah. And education and learning is crazy interesting. Oh, negative one. Where's the zero coming? I thought zero was in the equation as well. E to the power of i pi is equal to negative. I thought there was a zero in there too. Oh, you're not absentiary, put question mark. Oh, you have God. Oh yeah, I guess it's minus. Is it minus on this side? That is minus. Minus one is equal to zero. You just bring it over. Smith, thank you very much. Should have done that earlier. Masquerade and chichu, always be making. Experience allows us the tools necessary in order to actually make sense of the fundamentals. Otherwise, they're just abstract symbols on a page. There are a few who can learn that way, but I argue most cannot and do not. It depends on some stuff, right? If you're going into theoretical physics, then you have no choice but to think about the theories, right? So it really depends, always be making in my opinion, because I have students that, and I've worked with students that really like to take their, just imagine the possibilities, right? And that's just theorizing. And they learn the mathematics extremely well. And then I also have had and have students that are more hands-on, and they want to know the intricacies of a specific system of how that applies in the real world. And they learn that very well. So it depends what scale, are the macro, micro, where they want to be, right? It should be plus. Always be making, chichu, and there are times when fundamentals must be learned prior to experience, I agree. For example, it is prudent to learn about how to safely deal with electricity before one starts to wire up high voltage and per circuits, yeah, 100%. Driving a car is an example as well. I mostly, but agreed, you have to drive. You can learn about it, read about it, all you want, but you have to drive to get the experience in, right? I mostly like about mathematics teaching and I'm just wondering, what a purely experiential math journey from nothing to say calculus would look like. Good question, Maske Raven. Always be making, do you know? I think there are people out there who have gone through that. They just visualized the whole thing, chichu. It does, but we'd have to go case by case because I specifically disagree with your theoretical physics example, but it certainly requires a facilitator teacher, for sure. For sure, for majority of humanity. I think there are savants out there that just see it. Have your kids, have your kids lick a battery? Some people like it, but there's levels of it, right? If they like licking a battery, especially nine-volt ones, put it on your tongue, right? I even do it still sometimes, right? It's not a good idea to go put your tongue inside the socket, right? So you have to know that that'll kill you. If n is f of n, if n is odd, n over two, if n is even. Oh, is this a piecewise function? You can't get zero by taking a power of something non-zero. You can't get zero by taking a power of something non-zero. Yeah. What's that experiment? I think just doing experimentally, doing instead of theorizing with one or two, if you wiped out the troops. Dirk, war stuff. We're doing a current events, sort of, I guess, economics stream in a couple of days. We're gonna hypothesize about that then, maybe. It's like learning a new language that has no connection to any others. You wouldn't want to use us to iterate the function, would you? Doom. World War II, it was a huge weight was on Russia. World War II was decided on the Eastern Front. Anyone says otherwise is mistaken. Dude, I know what that function is. I Googled it, tuk, tuk teacher. That's where the facilitator comes in. But a child would be able to make that connection after experience only. Otherwise, you're teaching through fear. Oh, I don't know about that I'll always be making. For sure, we all need teachers. There's no doubt about it. But life can be a teacher, right? And that's experience, I guess. So that's the collapse sequence. It's unproven if the sequence is finite for all starting points. Always be making masquerade. I'll write that down as a philosophy question. Experiential mathematics, it is a real thing. Let us know always be making the math folder or something. Mask of Raven. That function is related to the fact that if you iterate that dude on any natural number, it will go to one. This one. I'm not sure what you mean by iterate. Iterate that number. Iterate, iterate, oh God, I gotta pull out my dictionary. That hasn't been proven. Or is that the one that Ding Bobber says that wrote down, man, is doing math. Curd-doodle, I don't know what that is. I once had an English teacher with a funny high pitch voice. And the first thing he said to his in grade 11 university English was, quote, this is the hardest course you'll ever take. There's a 59% fail rate, end quote. Yeah, I didn't do well, but I passed. Hilarious, that's funny. A racer kill, no. The class sequence, the class sequence, if n is even, half it, if it's not even the multiplied by three, nine, one, oof, his name is Jujube. No, Martin, deloo, zero, zero, five. My booker, how are you doing? My father once said that if you laugh, then the whole world laughs with you. And if you cry, then I'll give you something to cry about you. I hope it was a nice guy, because if it was, I like his sense of humor. If it was, yeah, that cracked me up. 59% sounds like the teacher isn't very good. Yeah, if more than half the class is failing, the teachers will run this. If 25% of the class is failing, you gotta look at what's going on, right? Let's start with any number, then all end in one. For all numbers, we've tried, but we don't know if it's true that it always ends in one. This goes beyond me right now, proof-wise. Oh, we're coming up to the end industry, so I can't explore that right now. He destroyed essays and tore theses apart until you had a deeper understanding of essay writing in English. Good teacher, but I didn't realize it at the time. Dane Bobber, that's good. I had a good English teacher, my best English teacher was when I did geophysics. He was my boss, I gave him my first report, came back, read, it was bloody. He goes, what the hell is this? Just throw it on my desk. I was like, oh my God, he goes, try again. Oh my Jesus. Why can't the government print their own money? Why do the Rothschild, that's politics, brother. That's politics. You're welcome to come talk to us about it when we do politics, economic streams. Dirk, kut dirk, kut dirk, kut dirk one. Okay, and we do talk about that stuff. During math streams, nah, not so much. Oh, we have a, hold on, we got a command. I forgot about our command, check out our command. Check this out, whoop, here's our command. Please, so exclamation mark politics, please keep politics and other heavy top subjects to their respective streams. And we'll be happy to speak about it. And by the way, if you wanna know who I am, go to my blog, okay, and I wrote about politics, economics, and what you wanna talk about. I've been writing about this since 2006, 2007. You'll find my articles online. I used to be on the front page. Hit the front page of dig and read it at the time, okay? Just to let you know, okay? You don't need to preach to the choir. Contribute to the conversation at hand because mathematics will buy you freedom. Shouldn't be grading in the first place. At least in any way like we currently do. Mask of Raven, I totally agree. We shouldn't be grading in the first place. At least in a way we, way, like we currently do. And always be making, put out another video, which he made a very good point, where he said, when you're at work, you don't have your boss grading you. Some places do, but most, I've never had it. Oh, you get a B, chicho, you get a C, or you get an A, chicho. There's no grade, it's just the work you do, right? And collaborations you have. So if we don't grade people, why are we grading? We don't grade people in life. Maybe Wall Street would like to, but forget about that crap. I think he was trying to scare us. I don't know. He once was reading out our grades to us and said we could say no to him, reading it out loud. One kid said no, and he said loudly for himself. And anyways, the whole class laughed. That's your teacher. Too funny, man, no mercy. And it sounds like he was training you guys for life. What to expect outside of university, right? Yay, another command. I now know, ah, nice Spider-Man. Kind of me, but it was funny at the time. For sure, that's bad teaching. Depends, depends. But in general, yeah, you don't wanna do that. Embarrassing people is just going to discourage them. Yeah, but it might light the fire behind other people's asses, right? I don't do that personally. I find a humor in that, but it can destroy people. And you don't wanna do that. He might know English. I don't know, but he doesn't know teaching. I agree with you, 59% of the class is failing. He doesn't know teaching. I regularly fail many students, but it's because they have me for one period a day and every other teacher is traditional. I don't blame them. It's indoctrination, yeah. He was preparing us for university. Good. Grimnor, wow. X plus two, X, is that X supposed to be X squared? X squared plus seven X, five X. Oh yeah, it's this guy, he goes seven. That's the meaning of life, by the way. Grimnor, Grimnor, wow. This is the unified field, the cohesion. Unified field theory. Who needs all four? What do you call it? The thingamajigies, the laws, the nuclear, strong nuclear, weak nuclear, electromagnetic and gravity. We just need X. But I never went to college and dropped out. Oh, that's why your calculator's dusty. Good thing you were wise enough to buy a solar calculator. Is that a double negative? Let's see if we can do it in our heads. What, 21 plus five? Oh no, that's, why do you have positive five in there? Your math writing sort of is a little wacko, but so what is it? 21 times five is 105, right? Negative negative is negative, plus bring it over 75 divided by 21, so 75 over 21. I have a math question. Some old math book defined pi. They're wrong defining it, it's an estimation, very strange, I never, what they're trying to do always be making this estimate pi, right? And I have students that do this, right? Instead of writing down, instead of writing down 3.4, oh sorry, 3.14 dot, dot, dot, they go 22 over seven, is it 22 over seven? I never use it, right? And they say this is pi, it's not pi, they're lying to people, right? This is approximately equal to pi, depending on, what is that equal to? I don't even know how accurate that is. So they're trying to, it's ridiculous, textbooks are brutal. Yeah, it's 3.142, blah, blah, blah, blah, blah. So they use this to approximate pi, and one of the reasons they used to do it is because people didn't have a calculator, right? It's silly. I always find it interesting when folks refer to our system of letter grays as traditional. The assignment of letter grays is actually a modern practice employed for a little more than a couple of hundred years. Yeah, Catholic tradition, this here's a thing. Regarding a lot of things in our societies, you talk to certain people and they always, they go, it's always been like that. And you look at it and you go, always been like that? Like no matter what it is, maybe prohibition, maybe this, it's always been like that. I'm like, always. You mean in your lifetime spent like that? That doesn't, how egocentric, just because in your lifetime spent like that, they say always been like that, so you can't make changes. It's like, what? Crazy. Ding-bubber, are you losing focus again? By the way, ding-bubber, if you like the calculator thing, 8008 plus 8008 equals watch space dandy. Watch space dandy. In the first two minutes, you'll be hooked, right? He goes to a space drive-in that you're gonna love. Okay, space dandy. Split 10 with three. Do you know what pi is exactly in Taylor polynomial form? No, I don't. No. You gotta put dot, dot, dot at the end. Grimner, wow. 10 divided by three is not 0.3333. Stop, it's 0.3333. Dot, dot, dot, repeating. Just want to figure that out. Ch-ch-ch-ch-ch-ch-ch. You're not wrong, it's just modern part of this. Nonsense. Dot, dot, dot, just go on two. Tonight, thank you. Nice. Yeah, watch it, you'll love it. Okay, gang, should we call the stream? No. Let's call the stream gang. People have lost focus. They're losing it. Calculator memes. I guess that would be one of the original calculator memes, right? Swedish math kind of good. My pleasure, ding-bot. Thank you very much, mods. Thank you very much, Mask of Raven, Catholic traditionalist doing the mathematics. Martin, Spider-Man, and everybody that was here. Great conversation, it is weird. I'm going to do more math after the stream. Nice. The chaos of mathematics, the chaos of mathematics. Hayden love, right? Hayden love, mostly love. Gotta love it, gotta love it. Aside from that, gang, let me give you, let you know where we are. Just in case you're here new and do our little closing. Thank you. My pleasure, thank you all. I do enjoy good problems bringing. Order to chaos is the end goal. Haven't done any in so long, no? So thanks for being here, gang. Okay, Patreon, follow us there, support us there. It's the biggest bang for your buck. And it's all open, nothing behind paywalls. So I do share as much as I can. Okay, we are live streaming this on Twitch. You want to follow this work live, Twitch is where you want to be at. Okay, and you can sub, follow on Twitch. And that is also a great way to support this project. I do announce these things on Twitter, Gap, Minds, VK, and Elo. Okay, those are the platforms that I announce things on. So you can follow the work there. All the links will be in the description of this video. I am uploading these videos on YouTube and Bitchute. And we do have YouTube membership available. And YouTube membership is a great way to support this project as well. Okay, aside from that, you know what that is? Flatten the curve, reduce the pressure on your healthcare workers no matter where you are. Some places overwhelmed, some places not. If you're not overwhelmed where you are, it doesn't mean certain places haven't been overwhelmed. Okay, so take care, take care of people. Okay, be kind to people. Aside from that gang, I'll see you guys tomorrow for DJ set. We're gonna do a practice live stream, sort of soundcheck tonight. Hopefully it works. Okay, so we can do our six and a half hour DJ set with four DJs tomorrow. And then we're doing a couple of other live streams the following day. So there's three more live streams coming the next three days. Aside from that, thank you for the sport. Thank you for the love. Thank you for the subs. Thank you for the follows. Bye everyone.