 Hi everyone, this is Chichou. Welcome to my channel and welcome to another live stream. Today, today is December 8th, 2020 And we're doing a drop in math tutoring session number 65. Let's do a little mathematics open discussion. So almost anything goes except politics and If there's math, math supersedes everything else, right? So we'll do mathematics and there's we can do a little bit of physics and stuff as well we've done a few of these before and the routine is basically You know, we do a little salutations and whatnot and slowly as people come in if they have questions math questions We try to deal with them. Hopefully we can help out if I can't help out There's sometimes a lot of times there's people in the chat that their math is a little bit more powerful than mine so they are always willing to lend a hand and Aside from that while we wait for notifications to go out on discord and Twitch to let you know what this is all about I am on patreon patreon.com forward slash chichou CHY CHO If you want to support this work, if you want to follow this work If you want to know what this work is about which is all layered on mathematics Over here Patreon is a great place To follow the work and support this work I don't put anything in my on-paywalls everything's great or comments share and share a like and If you do follow the work for a while, and if you do think that this work Deserves your support again patreon is a fantastic way to make sure that we continue to do what it is that we are doing We are live streaming on twitch twitch.tv forward slash chicholive CHY CHO If you want to participate in the chat and the chat's gonna pop up here as people start rolling in Twitch is where you want to be at and for those of you who've been supporting this work on twitch Liking following sharing Commenting dropping in with your math questions and whatnot and other live streams have been doing Thank you very much for your support and as always mods. Thank you for taking care of business and being here I do announce these live streams 30 minutes before we go live on parlor Hello minds VK gap and Twitter part of our decentralization and we do share additional content on those platforms as well Including our discord page twitch sent out awesome elder. God. How are you doing and any time you want you can come to our chat come to our twitch page and in the chat if you type in exclamation mark social all the links will be there including our discord page link, which is sort of here We've got 650 plus people I guess now on discord and Continue to grow so speak turned out to be a fantastic forum where people we have a whole bunch of different folders That people talk about different things some are more active than others Some people only participate in certain folders and whatnot and I personally a few other people I know we scan everything, which is fantastic slick. Mick. How are you doing? Oh boy? Have I got some math for you is differentiation appropriate for these streams or not? We can do What do you call it? polynomial I don't know my Taking derivatives rules of all the other ones and whatnot. I haven't Haven't explored that far down or refreshed myself that far down yet but the concept of Calculus just Introductory calculus really taking the derivative what it means and stuff like that slick mick. We can do I've refreshed myself to a level where I'm comfortable talking about it and Explaining what the derivative is what the slope is sending it equal to zero finding the inflection points and blah blah blah blah blah blah And it's fantastic super fun. Nikki. How are you doing? Hola? Hola? Hope you're doing well Three more on discord and it's six six six. Oh, maybe we should freeze it there No one else allowed until someone drops out Oh, and how are you doing? Hitchhiker. What a good stream to catch. Awesome. Yeah math streams. I love these streams man, really it's just Just exploration right and challenging yourself and keeps me on my toes Because a whole bunch of different types of questions that come my way some stuff I don't know and I end up learning a lot through these live streams, right? And it makes me feel good making myself available for at least at least four hours a month to at least two sessions a month So far, this is our second session this month and we'll probably do another one this month Actually, it's holidays. So people might might not be up for doing mathematics. I am always so maybe we'll do Some math doing holidays as well, but we're doing anywhere between two to four math sessions a month, which is Phenomenal, I think it's awesome And as I've said before the more people speak the language of mathematics the better our society will be, right? So I hope More people will come litter in the language of mathematics Slick me. I'll save it for next stream because I've got loads of polynomials for you to hilarious like like Polynomials, polynomials are fun really who doesn't like smooth functions without any breaks and points and asymptotes All right, polynomials is just like a roller coaster. You're going for a nice rod up and down All right, sometimes just straight up sometimes straight down Sometimes you're just on a flat surface. Sometimes you're at a point right For live streams We don't have any visuals which we do today when we're just doing open discussions We do upload those streams the audio of it to soundcloud.com forward slash chicho CHYCHO as podcast and they should be available on your favorite podcasting platform including Spotify and iTunes so you can follow the work there and This is mathematics. We're going to be uploading this both to bit shoot and YouTube and if you want to support this work on those platforms you can subscribe you can like you can share you can comment You can definitely turn on notifications on bit shoot. You're guaranteed to get them on YouTube. I don't know I don't get I Rarely get notifications from YouTube from the channels off subscribe to on YouTube anymore, right? The ones I'm subscribed to on bit shoot I get notifications on there and I'm watching more Content on bit shoot now that I am on YouTube Mainly because I watch a lot of political stuff The lecture stuff. They're still abundant on YouTube. I hope that The lecture stuff will become more abundant on bit shoot and other Sites as well And if you're on YouTube another way you can support this work is you can join The channel membership and there's a button there and for those of you who join YouTube membership Thank you very much for your support. Oh and off topic I've got crazy amounts of uni deadlines lately, but I'm getting through the Assange video slowly But surely the more education the better now bring on the math. Also, the the Assange videos are fantastic Are they not the interviews and the discussions and the? The the perspective that they give you Regarding our society and keep in mind those videos were from like ten years ago, right? If not well ten years, let's say Plus and minus minus I believe right so ten years ago, right? Oh plus and minus ten years ago and those discussions that in those 12 videos that they had between the different people that came on to Julian Assange's Show are Ridiculously relevant to our societies right now, right? Nikki Hickey easy question. Hopefully what counts as calculus calculus is the introduction of time into mathematics Let me take these guys down, right? So So Nikki take a look at this Let's do Let's do blue today. No, let's do brown today. I got different color. So let's assume we got the following function, right? So here's a following function Here's a following polynomial function, right? You got your x you got your y which we'll call f of x right Us graphing this thing us finding the x-intercept the y-intercept finding out what degree it is and all that jazz is Pre-calculus they call it for me for me really the distinction is very moot to say the least, right? But calculus is the introduction of time into this equation. So basically what happens is Let's assume your x is your time. You're looking at this function and Asking yourself what happens to you if you're Let's say riding on this function What happens to this function as you move along this function, right? That's calculus and once you start asking yourself that Certain features regarding this function pop up, right? One of the first ones is the slope at a given point, right? So for example You're this guy you've come around here and you're riding this wave You can ask yourself, what's the slope? What's the gradient? of this function at a given point, right? So if this is regarding speed, let's assume this was time and this was speed then What's the slope here? What's the slope here? Right and over here at this point at this point at this point at this point What you find out is if you take the derivative if you try to find the slope at This point this point this point and this point you're gonna find out the slope is zero and What that allows you to do if you remember the power of zero is this like there's problems with zero and there's a Power of zero that really allows us to do the mathematics or take mathematics to the level that we are right now, right? The power of zero is this A times B times C times D is equal to zero I've mentioned as a gazillion times you guys probably already know this but I always do this, okay? How do you multiply four things four two or more things to give you zero at least one of them has to be zero, right? So you can set as soon as you get this you get you can set a is equal to zero B is equal to zero C is equal to zero D is equal to zero you can't do this with any other number Power of zero right now keep this in mind, right? That's just straight up mathematics Keep this in mind. That's the power of zero Now take a look at this thing if this is a function f of x and it is the way I've drawn it, right? If you take the droid of this function Which is you define it as this, right? F prime of x is the droid of this function Okay, now this function right now the way I've drip drawn it is degree one two three four five So this is here. Let me write this here Well, let's assume that's f of x Let me write it here f of x is this let's assume. This is f of x is equal to Two x to the power five plus four x cubed plus two x and let's assume This is negative one minus one. So you're why I intercept this negative one, right? So let's assume that's the equation of this function, right? We I don't think it is but let's assume that's what it is, right? Then if you take the derivative of this function You would get The derivative equal to 10 x to the power four plus 12 x squared plus two Okay, that would be the derivative of this function and if this is Factorable and it would be because that's really just a quadratic, right? If this is factorable that means you can break this up into things Multiply it together to give you zero and it'd be four of them, right? Let's assume there'll be four of them, okay? Then what you can do you can apply this to it. So you could say each one of these Can be zero this could be zero this could be zero this could be zero and This could be zero and what is that going to give you that? If you solve for that is going to give you these points the x part of these points Right and there's four of them, right? And then what you can do as soon as you get the x value of it whatever the x value is It's a number. You can take this number Plop it back down into the original function Boop and find F of This number and it'll give you the y value and what's the y value the y value is this point So now you know exactly where the bumps occur when the uppercurve when the down occurs You know exactly where those points are That is considered to be calculus because you're analyzing this function You're taking the derivative looking at the slope and the slope of anything slope Oops slope slope of a function Is equal to rate of Change and What is the one absolute we have in life? The one absolute in life is change Right. It's not death in taxes death in taxes or change, right? Novelty our world Looks for novelty novelties introduce introduction of something new and it's the change Right. So change the rate of change is really Though you can think about it as the beginning of calculus And again for me, I don't draw that boundary to me. It's all mathematics, right? It's just something else you can do and Free a song free a song free a song, right? That's our all bot reminding us. Here's the mic by the way, right? Slick is math wizard the graph of the cubic function cuts the x-axis and x is equal to negative 3 and X is equal to 2 and y is equal to verify Is that what this one is? No, this one. What is that a question? We want to do we want to do that question We could do it. Sure. And I knew how are you doing? Welcome to another live stream. Should I erase this? I Hope that's clear. Let's see what slick mix is the graph of a cubic function cuts the x-axis at darling darling and Y is equal to this verify. Oh, so we want to do this. Let's do it. Sure. Let me erase this. Okay Let's do a question that's like make Sephora Nikki. I hope that's clear. Is that okay? Yeah, that's a guy might read it properly without trying to do multiple things at the same time Nikki I should have before erasing this I should have asked you is that clear sort of where They make the distinction If you have any questions about it Let us know I'm gonna write down this question actually the graph of a cubic function so cubic function Cubic Function Cuts the x-axis has x-intercepts has X ints equal to negative three and two negative three and two and Y at and y-intercept and Y int is equal to six or negative six negative six and y-intercept is equal to negative six Verify that f of x verify F of x is equal to I like small case f. I'm gonna make my f prettier That's Verify that f of x is X cube plus 2x squared x cube plus 2x squared Minus 5x minus 6 minus 5x minus 6 That's the question The stock market is much much simpler the stock market is much much simpler. It's not actually you can you get the stock market Is on the base level? It's really simple, right? Really, it's ridiculous is simple our minds. We're human beings that are Wired to find the pattern recognition But if you want to verify those patterns, you got to run the calculus You got to look at the calculus right the rate of change, right? So you can run the mathematics in different models to make predictions and hopefully place the right bet, right? So mathematics allows you to Game the system really so take a look at this thing now. You don't even need this this part They could give you this and say cubic function has x intercepts of negative three and two and a y Intercept of negative seven six find the function, right? But in this case, they're saying verify that this is the function, but you don't need that They could just say find the function. Okay, I have no clue how to do this one So I'm sorry if you if you this turns into a much more. No, it's not really it's not a complex Well, it's great 11 great 12 question odd make. How you doing? Oh, hey, Chicho. I'm amazed. I've seen three streams in a row. Nice odd make. You just missed my little Hokey-Pokey introduction to what calculus is You could have corrected me on some mistakes. I did. Oh, yeah stock market math is super hard Yeah, it could be super hard. All right on the base ridiculously easy We're hard wired to look for patterns if you want to Profit from it on a guaranteed basis almost guaranteed basis or give you an advantage You can run the mathematics or run the calculus through it and that gives you a huge advantage over anybody else Okay, super nostalgic scene you for Of calculus though super nostalgic seeing you for calculus though seeing you seen off calculus Okay, let's take a look at this thing. Look We got a function. It's a cubic function, right? So there's a couple of ways you can think about it. So let's think about it this way If it's a cubic function, then you're gonna have f of x is equal to a x You can call this BX and whatnot, but they've already given it to us, right? So let me write it out this way. I'm gonna write it out really complicated, but it's not complicated, right? Jim Simmons with the disagree Jim Simmons, I know the name a BX plus C Dx plus ABC D e a BC D e F X plus ABC D F G F G. I gotta say my alphabet in a row. Otherwise, I don't know what's there, right? So if it's a cubic function, then you're gonna have possibly three factors You don't necessarily need to Because of the way this question is laid out, I'm assuming all the factors are gonna be real number set, right? See you do calculus typing Typing is hard calculus is just a very fun time is what I mean. Oh, yeah, yeah fun It is fun. If you understand it, you can it's very meditative by the way You can take a look at a function and just break it down and graph it find special points, right? So right now remember these Are the X intercepts for a function and there's could be some kind of multiple to the function, right? Right now. They've already told us this They've already told us that the X intercept. It's got two X intercept now We don't know we can't confirm that it only has two X intercept But we're it has these two X intercepts for sure, right? Now they've told us this do we have enough information to be able to do this I'm gonna lay it out and then we'll see what we have, right? So they're telling us f of X is Equal to a and one of the X intercepts is X is equal to negative three So if I write down, I'm gonna write it like this. This isn't legit terminology, but it's visually you understand what it means, right? X is equal to negative three. You got X is Equal to oh, sorry X is equal to yeah negative three and X is equal to two and we don't know what this one is f of f X plus G okay, and that's not the same f of X is this here. Let me Rewrite this so you don't get confused I'm trying to lay it out in a way G H let's call the G H G H. Okay. I'm trying to sort of explain it More than do it right now, right? So this isn't legit, but what we do is we bring this guy over and we bring this guy over and then we can place it in So f of X is equal to a X plus three X minus two and we've got another factor here G times X plus H Okay Okay, so far it cuts the y-axis at Z. Oh it cost a Zero on well when I put down Y intercept of negative six That's the point zero and negative six, right? So what we could do right now is This when it says it cuts the y-axis at zero negative six. That's what that means Right slick, Mike. I think you you've missed a zero I didn't miss the zero if I say y intercept is negative six It's implied that X is zero because the only way you can cut the x-axis at negative six Then the y and then the X has to be zero So if I say y int is equal to negative six, then that means zero and negative six Okay What are differentials in calculus you're finding the slope of a function That's really it Is that clear slick, Mike, I hope so Now what they've done as well, they've given us a point so we can plug in this point in this function, right? Zero for X and negative six for Y Okay, perfect. My myself. No, it's not a mistake. It's a misconception A lot of people have a hard time like for example when I say X X intercept of negative three What's the coordinates that I'm giving you slick, Mike? Rick your airmark. No, it's it's it's you're just learning this, right? So if I say X intercept of negative three and two, what are these points? What are these points slick, Mike? Let us know Before I continue by the way my snacks bacon Cooked up a whole bunch of bacon. I hope you know if you're there veggies out there. You're okay with this Exactly racer negative three and zero and two and zero right The maple syrup We're actually kills by the way. How you doing? These are maple bacon They're already dipped in maple as Canadians like maple syrup and everything Sorry, why is also zero on X intercept and X always zero on the wine stuff exactly, right? So They've given us a point this Because we know that's the wine to set which gives us zero and negative six Good job. Thanks. Perhaps we get so what we could do is just plug that in for X and Y in this function Okay, let me erase this and let's do it and we're just playing right now. Let's see what it gives us So the Y is negative six. That's your f of X, right? So negative six is equal to a X is zero zero plus three zero minus two G times zero is zero plus H Okay cool Now what we can do is just multiply this out. You're gonna get negative six is equal to That's gonna be three a times three times negative two times H Which so negative six is equal to a H times negative six divided by negative six. So a times H is equal to one Okay Does that work? I Hope that's clear. So a times H is equal to one. So we've got two unknowns here a and H What are we gonna do? Well, we haven't figured out the other factor yet Right, we don't know the G and we don't know the H and we don't know the a we know these guys All right, so keep this in mind. I'm running out of room a little bit. Unfortunately. I'm going a little bit to I The not theoretical but Experimental with this. I'm playing around with this a little bit too much directly solving this. Okay So take a look at this thing. They want us to verify that this function The cubic function has this information is this guy. Well, what we can do is if We sub in X is equal to negative three. What should f of X be now? Keep this in mind We might not continue this. This is just an Aside to a certain degree, right? If they just want us to verify that We have a half day today because there was testing. So I am here to hang out Earlier than normally will awesome grand now for us, but I really don't even know if we could find the other factor for this because They didn't give us the other X intercept, right? And we needed another point So going down this route if they didn't give us this verified that this is the function We probably wouldn't come out be able to come up with a function because we don't have another point on the graph We would need the other point on the graph But for us to verify that this is the function, all we got to do is this take a look What's y going to be equal to? If we sub in negative three For this function you guys have already answered it. What's f of negative three going to be? What should f of negative three be? All right, and on that note, what should f of two be? Right, and if you want to verify that the X intercept is negative six What do we need to do? What do we plug in for the X value to find out what the Y intercept is? Ask you, what are we doing? Just got back from work. Hello everyone. Hello. Hello. I mess read the question It also cuts at exit. Oh, yeah, we would need the other X intercept by the way We need the other X intercept as soon as I got down to here. I'm going wait a second We're missing one bit of information, right? If it also cuts at the X is equal to negative one then Check this out This would be This would be X equals negative one so X plus one and this would be zero plus one and this would be one right, so one so one so a is equal to one and Free a science free a science free a science, right? Right I'm just gonna make clean this up a little bit one So this would be a times negative six divided by negative six so a is equal to one cool What does this a value mean the a value is this guy here the number in front of the X cubed right The number in front of the X cubed Free a science and part of science indeed So let me ask you this if f of negative three What would f of negative three equal? What is this side equal? It has to equal zero if it's a Factor of this now we can by the way now we can continue with this because we got the other bit of information and Negative one right but just to answer this question and then I'm going to erase this line And we're going to continue with the train of thought right it should be zero Right, so all we got to do is confirm that when we plug in X is equal to negative three here It's going to equal zero so what we can do is go negative three cubed Plus two times negative three squared minus five times negative three minus six negative three cubed is negative 27 Oh, that's what you were punching in Graham. Awesome. Thank you negative three squared is nine nine times two is 18 negative three times five, but it's negative is going to be plus 15 minus six and if you add all those up That's going to be negative 33 and that's going to be Positive 33. So it's equal to zero So this whole thing is going to be equal to zero So we just confirmed that X is equal to negative three is an x-intercept and you're going to get the same thing for two All right, you're going to get that equal to zero and if you plug in X is equal to zero because that's what it's telling you if you find f of zero Well, that's going to be zero because zero cubed is zero zero squared is zero times two zero five times zero zero So it's going to be negative six. So we just confirmed that as well. And if you want to confirm X is equal to negative one f of negative one you plug it all in that's also going to be zero Okay, that confirms it, but let's drive the equation like the way I said, we don't even need this guy, right? So I'm going to erase this Let's take this out So once we want to drive it, we got the a is equal to one. So all we have to do is go back to here We just take it back to here Right and plug in a is equal to one foil this whole thing out. We're going to end up with that All right, so let's do it So this is going to be f of x is Is equal to We're is equal to one times x plus three times x minus two times x plus one Now the one is just one. You don't care about that doesn't do anything foil this baby out All right. So this is going to be x plus three That's going to be x squared Plus x minus 2x minus 2 Combine those guys you get negative x and then foil this guy in or expand this guy in so that's going to be x cubed minus x squared minus 2x plus 3x squared Minus 3x minus 6 Combine your like terms you got x squared that guy and that guy combined because plus 2x squared This guy and this guy combined you get minus 5x minus 6. Is that the same as that? It is indeed and That's it. You just confirmed it, right? Now that's okay Straight up and this would be like great 11 Math in my part of world some other parts of the world. This is like grade 8 The graph of g of x intersects f of x above cool. We've got two functions. We've got layered Right, let f of x equal g of x and solve the resulting Equation to find the coordinates where g of x cuts f of x part 2. Okay. Awesome. The graph of g of x and it makes sense Okay, maple leaf It is not verified with coefficients Is that for part two of the question? Is that what you're punching at? No, you're doing this part You're doing this a I wonder where you're doing ABC because you're trying to find ABC. Oh, that's what you're trying to do g of x They they have to give us g of x right Equation resulting to find the coordinates where you yeah, you need g of x slick Mac. Otherwise, we don't know Right, so watch this. I'm gonna erase all this. I'm gonna keep this guy up here. Okay, so this was part one P1 and that's gonna do let's do p2 Okay, this is big brain stream. I don't know. I Don't know if I would call it big brain stream. I would call it just math stream Hopefully we don't get smooth brain So check this out part two says this you got a function g of x G of x which is equal to negative 2x minus 6 and they're asking you When does this function cross this function? When does g of x hit f of x, right? So for now for us to get a visual Let's graph it and you'll you'll get a feel for what this looks like, right? So Let's do a little graph. I'm gonna give myself a little bit of room Let's graph g of x first g of x the y-intercept is negative 6 and the slope is negative 2, right? So you're gonna go 1 2 3 4 5 6 That's the y-intercept and the slope is negative 2 which is negative 2 over 1 so you go 1 2 down and 1 over Here's g of x. Okay, this is g of x Let's graph f of x Okay Let's graph f of x the x-intercept of negative 3 2 and negative 1 right so negative 3 Now I don't know where that is right now, but I'm gonna go negative 3 is here negative 3 2 and negative 1 and The y-intercept of negative 6 wait a second they cross at negative 6 same location cool Okay Am I doing homework? I don't know if I'm doing homework. Hopefully it's not the slick mix homework Hopefully it's trying to understand how this works, right? and The coefficient the way you graph cubic functions or polynomial functions higher degree or any polynomial function if the number in front of the leading coefficient is positive and the Highest degree the degree the highest exponent is odd then the function opens like this So this thing is gonna go like this like this like this and This is f of x So how many places is this function going to cross most likely one Two three we already know this one We already know that it crosses at x is equal to negative 6 because the y-intercept is both x is equal to negative 6 Right, so what we're talking about is this? They cross here So this is gonna have an x and a y point they cross here Which is 0 and negative 6 and they cross here, which is going to be x2 and y2. It's a different point Right. Hopefully this isn't too small. It looks pretty small on my on my screen No, no not my homework. Just wanted to better understand What sample problems I've attempted before but get trapped somewhere or another yeah, which is fine And you know what even if it's your homework, that's fine We're doing it right now, which means you're gonna learn it, right? Because there's no way we can do your whole homework. It's not gonna work Right at some point you're gonna have to write a test and there's layers, right? If you don't understand this you won't understand future stuff coming up So consider it like I said, it's a drop-in math tutoring session, right? It's a class Right where we're talking about mathematics. I'm gonna show you how to do certain things If there's a problem you have you'll ask me and we do it, right? It's about learning not about Getting somebody else to do your work for your copying, right? So take a look at this thing. We're looking for these three points. We already got this one The y-intercept here was negative six the wine step here was negative six so we know where they cross each other 12 hours stream from my test, please Now take a look at this thing. How are we gonna find this point and we're gonna find this point and Finding where they cross means this at this point This x and this y this point Exists both on this function and on this function, right? Obviously here's Geovax here is f of x That point is on both functions, right? So what we're doing here here. Let me do this in red So you see the difference. Hopefully this will come out That's f of x, right? Red and brown pretty much the same color So at this point This x is the same as this x is the same as that x and this y is the same as this y because Geovax is really y is the same of same as f of x, right? So what we can do is Say hey where they cross Their x's are the same and their y's are the same. So all we need to do is say set Geovax equal to f of x f of x we want to find out when Geovax hits f of x they cross each other if we solve the both equations We can reach the point coordinate points, right? We set them equal to each other I Usually tell my students we're doing when we're doing this if you call this y1 and y2 You're setting y1 equal to y2 not this y equal to that y but this function equal to that function So all we're going to do now is set negative 2x minus 6 is equal to x cube plus 2x squared minus 5x Minus 6 yeah, we'll take this off We already know what we're talking about right give ourselves a little bit more Minus 6 so all we're going to do now is solve This x equation, right? So whenever you have x's to different powers You want to bring everything to one side and set it equal to zero so I'm going to grab this do I can bring it over right So when you bring it over at the side flips so this becomes plus 2x Plus 6 right and what I do when I bring them over I line them up according to which ones we're going to mix them with Right they can combine like terms this side is zero Right this side becomes x cubed plus 2x squared Minus 3x and negative 6 and 6 is zero is equal to what's left on this side zero Cool, we don't even need synthetic division anymore Now what do you need to do? You need to factor this because you're trying to solve this equation How do you solve this equation? This is difficult to solve if you're not aware of should we say it again How do you multiply a times b times c times d is equal to zero? How do you figure out what a b c and d are? The only way that's possible is if at least one of them is equal to zero right? Maple leaf, how are you doing? Maple leaf bacon Maple bacon is a great snack I don't know on the healthy side. I don't think so but good protein, good fat How do we factor this? Because that's what we need to do. We've taken a function That is Something plus something plus something is equal to zero Something plus something plus something is equal to zero And we want to factor this into things multiply together to give us zero we want to factor this into This times this times this is equal to zero The reason we want to do that Is because we can as soon as you have things multiplied together give you zero you can set each one equal to zero So you can go this is equal to zero or this is equal to zero or that is equal to zero and I do not eat bacon maple leaf zest We divide every term X cubed no You factor it. Don't divide every term by x cubed Okay, what you're going to do is factor this thing. How do you factor this thing? How do you factor this thing? What's the easiest way to factor this thing? Factoring means First type of factor and you always look for always always always GCF is there a GCF here? Thank you for the follows by the way gang Okay, is there a GCF in this function? If there is what is the GCF in this function? What is the GCF in this function? And GCF means greatest common factor Right What do they what does this term and this term and this term have in common? It's the x right so take out an x from all of them x out of x cubed x out of 2x squared x out of 3x if you take an x out what do you got left? What do you multiply x by to give you x cubed x squared? What do you multiply x by to give you 2x squared? 2x what do you multiply x by to give you negative 3x negative 3 cool So we already got one of these guys we already got this guy All right perfect Then what do we do? Maple leaf Good, right, then what do we do? Now you got to factor this how do you factor this? Well This x in front stays now. You're looking for two numbers that multiply to give you negative three add to give you two Because when you do that you can factor this now x x Three times negative one gives you negative three three plus negative one gives you two Plus three minus one look at this We've got three things multiplied to get it to give us zero How do we solve this? We solve it by Setting each one equal to zero so x can equal zero x plus three can equal zero and x minus one can equal zero This means x is equal to negative three and x is equal to one These are x's Right When x is equal to zero this function crosses this function Well, we can't just write down the x because if you're on a Cartesian coordinate system x and y You need both an x and a y Right, so what you do is sub and zero for x in g of x or f of x to find out what the y associated with it is All my x's live in texas Right if you're gonna do that you can do it in both functions doesn't make a difference You're going to get the same value check this out g of zero is going to be negative six f of zero is going to be negative six so the point where they cross is zero negative six Right if you set in zero for x this disappears So g of zero is negative six if you put a zero for x here these disappear. So you get negative six Gx as much as gx is much easier for zero is ridiculously easy. Anyway, all the x's disappear, right? How about negative three? Let's do it here Not f of negative three. Let's do g of negative three because it's way easier g of negative three Is going to be negative two times negative three minus six, right? Well So that's going to be six minus six. So that's going to be zero What? Oh, look the other point is negative three and zero. So it's right here That's the other point All right, if you plug in x is equal to negative three right You're going to get the same answer you're going to get y is equal to zero Cool. Well, take a look at that thing. We already knew when x is negative three That's going to be zero because it's an x-intercept very cool Yeah, to find a y-intercept for the new function For the new function that we found let's try one g of one g of one Is going to be negative two times one minus six Which is going to be negative eight. So the point is one and negative eight. So this point here My graph isn't very accurate. That was a one one and negative eight This point here was negative three and zero You just found the three places where this function crosses this function and you can check this Sub and x is equal to one for f of x, right? So f of one One cube does one Plus two times one squared is going to be two Minus five times one is five minus six So that's going to be three minus five is negative two minus six is negative eight. We've got the same answer, right? Same answer same answer That's our first point. That's our second point. That's our third point where oh, you don't even see the bottom guy Hey, come on stick those are my Painters tape holding down the bottom there you go right I hope that makes sense It's a good question. This thing comes up in grade 11 in my part world, too Slick mick, what grade are you in and which part of the world are you from? we're I want to find out what grade you're in that you're getting these types of questions What grade are you in and where bacon bacon and maple bacon Oh This is gonna focus. I don't know Vegetarians are gonna freak if they see this Crafter, how are you doing? Well, they probably won't Hope you're doing well fun Very powerful That's in my part of the world for sure In canada They teach this in if you're lucky you get it in grade 10 Okay, if you have a good teacher Most students will encounter this in grade 11 However, in some parts of the world you're going to encounter this in grade eight Okay, I'm pretty sure in russia. They're seeing this in grade seven or eight In grade eight the latest Okay In iran they're getting this in grade eight Okay Still trying to understand the wonders of thermodynamics or thermodynamics crazy difficult Thermodynamics I found I found My perception Of thermodynamics heat and water flow I found those to be the most difficult for me to comprehend in physics anyway Flow you can like fluid dynamics. So thermal dynamics and fluid dynamics fluid dynamics you could sort of associate it to Uh electricity right and electricity magnetism is is not that bad. It's Conceptually it's It's understandable because we see it all the time But I found thermodynamics and hydrodynamic uh Yeah, water difficult and they are difficult. They're very chaotic water is anywhere It's interesting powerful I'm going to erase this Ground the three hardest classes I ever had for my physics degree classical mechanics physical optics and thermal physics So tough out of control out of control All right, I was okay with classical mechanics Uh optics is difficult as well optics. I found Yeah, it was the flips and the it was a lot of geometry and optics And thermal physics thermodynamics difficult. Luckily, it's only the beginning of thermodynamics. It's going to get harder I like modern physics. What do you mean with modern physics? classical mechanics gram that's just are we talking about classical mechanics like projectiles and stuff And what's modern physics? What do you consider modern physics to be? Salute gang. I hope you guys have good snacks and good drinks tea When you're doing work, it's nice to have math work. It's nice to have little snacks here and there It doesn't have to be bacon. Hopefully it's healthier snacks that you have Classical mechanics modern physics is like relativity Uh, derivation of speed of light physics from the last 100 years or so. Okay So you're going to yeah, relatively derivations of the speed of light. Okay But the classical mechanics projectiles projectiles are found to be some of the easiest Apparently we'll be getting one of our hardest classes next semester Controls and systems. Oh, what are you in crafter? This sounds like an engineering class. Yeah Are you are you in like hydrogeology or something? I've taken hydrogeology classes are super cool But you said you were oh thermodynamics What are you in what what I mean engineer? Yeah, sounds like engineering Chico, you might think so, but this was junior level college mechanics Lots of gradients and Taylor see Taylor series. Whoa I've done Taylor series back in the day, but I don't remember it I would have to do some serious reveal on that stuff Taylor series really I seriously would have to look that up 48 transforms and stuff that stuff was super cool, man Super cool. You're like, well, how does this work? You do it and it works and you're like, how does this work and Trying to get the how and why is it was very difficult. It was more do Do Arash, how are you doing? Welcome. Welcome. Oh, yeah, four year transform Laplacian, etc. Yeah, yeah grandma with you Uh Laurange math. Yeah, I found that stuff difficult as well. I did just because conceptually I Really didn't understand what was going on back then. Anyway, I haven't looked at it since so That's what we're doing right now. Yeah, I crafter you get a lot of that stuff in engineering Um, and I've for me. I've taken some of those classes as well It's so Cool, actually is very difficult to relate that hardcore math to real world very difficult I agree with you ground and unfortunately our education system doesn't even try to relate it Not even at the university level, right? It was It was more like just do it's like, what am I doing? Oh, just do it It runs a filter through it and you get this out of it Okay What is this some kind of magic wand? When I was taking it at some point I'll get back into it and look at it, but We'll do that as a meditative meditative project, I guess It's quite uh, it's quite a difference with high school math very difference with the high school math Very different uncle sweetheart. How are you doing? Very complicated so many factors so many factors like everyone's everyone's toning in Giving their comments. We all had a bad time It's just symbols on the blackboard And the and the symbols they say oh, this is this this is lambda. This is lambda Here's lambda. It's the wavelength of Some kind of function Well, what is that function? Oh, it's a function that you run through with this lambda and you change the lambda You get different filters on what? Now I understand it more even though I don't know it I understand Why aspect of more? Even though I don't know the how of it anymore back then I knew how to do it, but I didn't know the why of it Weird, eh? When they teach it to you they show you how to do it, but you don't know why you're doing it as you get older Right You understand why some of these things exist, but you no longer know how to do it or I don't anyway Graham I took a class in college called Mathematical methods of physical sciences the professor of time classes Classes daughter ended up being one of my students. Oh, no way. Super cool, man. Super cool Super cool and free a science free a science free a science Gotta do gotta do gotta do Fun what else should we do gang? What else should we do? Everyone's pretty chill right now Fun now we could talk about whatever if you guys want to talk just and we are basically talking about Crazy, let's talk about light light. Oh my god light Light is a trigonometry really Laugh, I love the free a song is what haha Force gender reassignment and optics. Oh god optics Optics optics. I have a theory. What's your theory? What's your theory uncle sweetheart That light rays do not travel in straight lines Ah Light rays do bend. That's one thing. We know they are curved Right salute to you as well reassignment Obeying the laws of the Fibonacci sequence. You think they bend according to laws of Fibonacci sequence. How so? And negative and a positive and negative and a positive meaning They crisscross each other meaning they crisscross each other. So Fibonacci sequence. By the way light does bend that was From Einstein's theory of relativity, right? You get that optic effect, right? So if you have a huge body Right, so let's say there's a huge body Of something and we're the observer here, right? We're standing here and uh You get the lens effect. I think it's called the lens effect, right? If you get another body here, right? If light is traveling from this and is going through this body Or past this body the light bends to come to us Light bends to come to us bends here and then go straight, right? So light does bend but the Fibonacci sequence. Let's check this out Uh, meaning they crisscross otherwise the intensity of light will dissipate over space Light 10 bends around masses proportional to set mass. Yeah, now bend the other way Crossing each other bend the other way crossing each other Like this one bend the other way How so? The diamond shape are bigger far away Up Bend the other way like this like that And Fibonacci sequence is this again. Uh, well not zero but zero one one two three five Eight 13 21 etc, right I wish I could show you some pics posted on our discord That's a curve Oh, so what do you need the diamond shapes are bigger far away less intense up Then bend the line down Crossing the other bend the line down Bend the line down So like this Post in discord. Yeah post in discord. It's like a net Think of this chicho rays coming out of the source. Yes now many Many any many in 3d sphere. Oh So you're saying this stuff is going Oh like a Like this And then here as well, of course, right Why why do you think that is that's that's the case the diamonds close to the source very tiny Concentrated intense. Yes. This is why we aren't burnt Or blinded by the sun imagine the earth Where the second sphere is Here. Oh, so you're saying if this was the earth The reason the earth doesn't get burned is because the rays are Recreating to a certain degree, right And why light loses intensity over space? Well, one of the reasons we're not burn is because of the magnetic field, right Listen, okay, let's check it out. This is why this is why what is it and why light loses intensity over Solar Panels. Yeah Get better at an angle and not flat Do they No prize in coming no prize in coming rocks. It kills the rays don't hit the earth at 90 degrees or straight They're coming in at angles In every direction Okay, but it's not not because of the magnetic field Right If they did a solar panel Would max efficiently flat not a 30 degree angle is uh, I don't know that is solar or solar panels Um, efficiently at 90 degrees. So you're saying this, right? So let's assume this is a solar panel Right, here's a solar panel right So this is the front of the solar panel and if the light is shining I was assuming that this the rays Would be from the sun would be coming in hitting directly and you would get the most out of it But you're saying that because they do this It's actually more efficient to bend the solar panel to be a 30 degrees Right, I'm going to draw the same thing So you want this angle my 30 degrees sucks, but Uh 30 degrees so maybe 30 degrees here. Let me read keep on reading Not a 30 degree angle. It's a less efficient flat Okay, and the most they can get is like only 40 efficiency out of a panel if the panels were cone shape Yeah, the cone shape. I know it would pick up rays from every direction not straight Cheecho remember curved rays both directions Oh, yeah, that's right. Not a Direct hit the panel angle angle. So you're going like this And both directions like that cool You may want to review how solar panels work mechanically. Yes. So that's what you're saying. Okay, cool I don't know. I don't know the inner workings of solar solar panels But I know the tube shape ones are more efficient So they can make cylindrical solar panels and they become more efficient, but I haven't learned I don't know the reason why you're saying that's the reason why and it's three-dimensional So it's not just that they're going like this. They're also coming in This way and this way So that's the reason that way you're saying it, right? It has to do with how the light travels from the sun Curve rays in every direction. Fibonacci law. Where's the Fibonacci law coming to place? This is why the source is a small globe Bright, so why where's the Fibonacci coming to this? Where's the Fibonacci coming to this? Fibonacci is a curve Is it not is it a curve? Gram is Fibonacci a curve? It's a spiral. It's a spiral. Yeah, it's not a curve. Yeah, it's a spiral Right, you can make the golden we've we've got a video on that the Fibonacci sequence in the golden spiral, right? So you're saying The rays curve As like this, right? So let me see if I can make this we have we have a couple of videos out there We generate the golden spiral, right? If you do chicho here, I'll link it up for you guys Okay, so you know what we're talking about here The far away globe the far away globe Link it to us in our discord page brother Let's see if this is going to focus. Let's make sure it will go focus Okay, let me find you the The videos we did and we did this a while ago There we go, there's one and there's the other and so here's these guys Here's me on the ground on a tennis court drawing the using the Fibonacci numbers to create the golden rectangle, okay And here is the way my friend who's an artist Generates the golden ratio rectangle Going from the outside in using the angles. I generated using the The Fibonacci sequence Oops, come on. Where is this? That's the first video and this is the second or the second link has the first video and those Is the next one not intense though the big The far away is very big not intense though. Okay also mirrors Do you do you have a link? Yeah? I just linked it up brother those rays never stop curling over space possibly Possibly I'm not well versed enough to know regarding that so It is Like anything is possible. The one thing I do know is we know very little like really Graham To sweetheart. So the most important question. How could you prove this? Ah, very good Graham is asking a very good question. How do you prove this? Right? Cause a like for this Is this my blue? We'll use the blue like that I Really the solar panels. I'm not well versed in right but as far as I know spherical or A cylindrical solar panel is more efficient than a flat swirl panel, right? So just because that is the case that's not proof enough that the light rays bend like this How do you prove it? That is the key and then how do you repeat that proof? That's the scientific method, right? You come up with a hypothesis you take measurements, right? You do your calculation as you do your thing and You hypothesize what could be and then you do your measurements. You measure that you see that thing happening Can it be repeated? Does it stand the test of rigor? We can write an actionable hypothesis. Yeah Graham is very good at that by the way Going through the steps required To be able to Come up with the conclusion, right? My immediate thought is that you could design a series of solar panels in various shapes Measure their efficiency and go from there. Yeah That would be my approach as well have and The different curves would be it right and I'm pretty sure this data must be available, right? The solar panels have been around for how long now how many decades now There must have been experiments done to try to Optimize solar panels, right? So if you could get access to that data And figure out which curvature because it doesn't have to be just like this it could be The solar panels could be like this or like this, right? So which one's more efficient? What's the cause of divergence in a laser beam? Graham, do you know what the cause of the divergence in a laser beam is? Or anybody else? Do you guys know what the cause of the divergence in a laser beam is? I'm not even curved rays I don't even know what divergence and laser beam really means Right, what is divergence and like In what respect? Yeah, like what is what is divergence? Hello Gina. How are you doing? Hello? Are you saying there's internal divergence and cylindrical panels? I'm not saying anything, but I think uncle sweetheart is possibly saying or refraction refraction at least Okay, the further away the bigger the dot The bigger the dot the further away. Why would it get bigger? Okay, the further away the bigger the dot over space. It's curving Now is is is it light that's curving or Is light following the curvature of spacetime? Like those red laser beams Lights, I don't know. I didn't really play it around with laser beams too much. That's the kicker, right? I'm not very good at the laser stuff Also dollar I think the the thing with laser beam is you have to condense the the light to be able to project the laser beam Otherwise light disperses, right? Is that what you're talking about? It's diffusing through space almost like a flashlight if you Took just a section of that. I would have to look at drawings for me to Comprehend what's going on bacon maple bacon? Gran and the diffusion rate is according to the chemical makeup of the air Yeah, hard without illustration Uncle sweetheart Do an illustration posting our discord page I'm pretty sure that people are interested in that. I am curious You should stay more focused in a vacuum and Free a saunch free a saunch free a saunch in a vacuum Is really the true speed of light the the projection of light, right? So it's not going through some kind of Graham there's an experiment you can do where you shine a laser distance meter through a Glass container with different densities of liquid which causes a later laser Distance meter to read different values. Yeah All right, depending on what the medium is that light is traveling and it travels Actually the speed of light is absolute so It it refracts Felix, how are you doing? Hey chichou. I had a lesson on differentials today So this stream is well timed awesome differentiation Differentiation did you guys do polynomials? No, Felix The speed of light is absolute only in a vacuum. It moves of different speeds and different mediums. Okay. Thank you for a correction graph right So speed of light absolute in a specific medium, right? Or in a vacuum. Well, it would be It would be The same speed for a given material, right There's a learning math help to earn make a lot of money Look, I can't guarantee you that learning math will help you to Earn and make a lot of money But I can guarantee you this it will not hurt Right, so it is an asset that you can accumulate knowledge that you accumulate that will never Make you earn less money it will definitely It can definitely help you make more money and make you allow you to make more informed decisions On your finances See is absolute anywhere. Just atmosphere refracts light. So it runs biggest path Longest shortest path shortest path Learning math is a good investment in yourself indeed. It's the most valuable asset you can accumulate Uh, you can acquire to help you make more money There's no doubt about it. And if you're only interested in making money The best thing you can do is learn mathematics. Like there's Nothing else comes close really like That would be it How do I know when I am done with a math topic and I'm ready to move on to another? In our education system, they like to put a break between The different topics, right? But that's not the way it is, right? Think of mathematics as a language When are you done learning about adjectives so you can move on to pronouns so you can move on to Verbs Are you ever done learning about adjective pronouns and verbs? Are you ever done learning about how to Put a sentence together like just imagine writing a sentence, right? That says exactly what you want to say, right? So let's assume you have this I like apples I like apples All right Are you done with that sentence? Is that the only way you can say that sentence? No, it's not You can say apples. I like Apples I like When you learn to say I like apples Were you done with the language of mathematics or like with the language of english? Were you done? in Knowing how to say I like apples or Are you better for it? Do you have more power at disposal knowing that you could say it this way apples? I like right Obviously the answer is now you know more Mathematics is the same way and you know, they teach you how to deal with Plus and minus and then they teach you how to deal with Multiplication and division and then they teach you how to move around an equal sign But if you understood mathematics, you would know that Adding subtracting multiplying dividing all of these is just adding right what And as soon as you learn about the equal sign they say initially they say These are equations you're solving right initially they say these are equations And then you find out they're not really equations. They're functions Right They're functions And what are these functions? Well equations Are just functions For a given y or x value. What and then what are these functions? These are models Models models of what things that are going on our everyday lives, right? And it's just a continuous and how do you manipulate these? Wow right Manipulate manipulate blah blah blah right and just continues continues continues Okay, so I don't know if you're ever done with mathematics. It's just A tool at your disposal That you can use is a language we have to analyze the world around us. Are we ever done with english? No, we just use english We were learning about felix. We're learning about finding the minimum or maximum turning point of a polynomial graph Using differentiation example find the gradient formula For a graph and making it equal to zero the turning point. Awesome. We just talked about this earlier And and the stream I'm not really interested in making money at all My overall life plan is to work a humble manual labor trade job in a rural area to be And in nature as much as possible sure felix you can do that But you can use and this is something we all need to do, right? We need to have some kind of nested investment Now you can invest in your knowledge. You can invest in your house. You can invest in your community You can invest in your family, right? You can invest in your farm. You can invest in your home. You can invest in many things but You need to invest you can't just live day to day. You have to know about the past Be in the present and think about the future Right now if you have mathematics You can sort of and this is just because of our current geopolitical economic system You can use mathematics to make sure that you're going to be stable over an extended period of time Just do your calculus and figure out what it is that you're going to need what your expenses are going to be and stuff like this So mathematics can help you on that front irrelevant if you just want to work on a farm Be self-sufficient and stuff like this or you want to go rule the world Right? ground Learning is always happening. It doesn't start or stop. There's always more to learn. I agree with chicho our school system needlessly Compartmental compartmentalizes things in a way that is harmful. I feel yeah, and that is exactly How I feel about it like when I work with my students when I teach and you guys must have noticed this When we do in these sessions, I don't necessarily just stick with adding and subtracting I jump all around this thing because it's all relevant Right? It's all very important and it applies everywhere I like to earn money enough money Felix says to buy a Plot of land with fertile soil build my own house homestead and live off the land until the end of my day is awesome, Felix But you need to have a safety net right Which country do you live in? Is healthcare covered if it's not covered you have to have a certain amount of money put aside To deal with potential problems that you might encounter with your health. Okay, or Things that might go wrong with the house you live in pipe blows, right? If a pipe blows you need to Bring in specialists to fix the pipe, right? Maybe a water main. Maybe a gas pipe or whatever it is, right? You need To hire someone to come and deal with your thing, right? You have to have a nest egg on the side So if you know mathematics, you can probably build up your nest egg a lot faster Because the mathematics will allow you to be able to understand the different types of investments that you can make in our current geopolitical economic system to build up your nest egg to Have that safety net, right? Continue investing yourself indeed and investing yourself and family and community Is the best investment really you can make right Your name is difficult it in this Bxj very interesting. Thank you. My pleasure I'll live bar This is my type of asmr educational discussion fun Win win win Hey, what is your level of math? pick Dean oh success I teach mainly high school mathematics My level of mathematics my education is like on my degree in jude I majored in geophysics with a minor in mathematics And I worked as a geophysicist for about 10 years. I'm about to eat a giant slab of fish. Nice I'm eating bacon bacon Bacon maple bacon on poppin maple bacon. Mmm. It's very good. Actually. It's super delicious. Look at that Is that going to be our thumbnail? Is that going to be our thumbnail? Yep Maybe Felix I live in the uk and luckily Health care is covered here. I found a self-sufficient commune in Wales that I'd like to live in For a few years once I finish leave college awesome. Felix You're acquiring experiences And one other thing that you're doing is you're building connections Great investment Graham also distinct school subjects are largely in an illusion indeed Indeed like let's take that to heart game Distinct school subjects are largely in illusion There's math and physics. There's history in math. There's writing in history There's everything and everything else indeed You have to have a holistic approach to education period and to life period, right? Pick d06 cool. I have a phd in math and fractal analysis for my part. Awesome. Cool. Cool. Cool. What's this? What's this? Pick them. That's great. Graham says that's great to pick them Stick around we may need to ask some questions Microtwist, what are you eating bacon? Maple bacon very delicious bacon maple bacon Super fun. Felix. Have you seen the new season of attack and tight? What I seen When was this new season released the first episode came out? What I didn't notice dude. Thank you. Okay. We're ending the stream Attack on Titan is out They have a new animation studio and it's absolutely stunning dude. Felix. You just made my day I'm gonna make Right a little note to myself attack on Titan. What the hell? Attack on Titan man. It's long overdue. What the hell? What's taking them so long? Bring it up. Bring it out Super cool. Thank you very much Felix appreciate it Anyway, I can drop a link in here. You can't drop a link in here. You got to go to our discord page Go here And we have a math folder All right, and I don't know if we have a physics. We've got a science folder All right, so you can drop the links there. I have illustrations on my Pine puncher. Cool. Link it up in our discord page, man In the math folder, okay, Felix no problem. Dude. Thank you Attack on Titan gang if you guys haven't seen attack on Titan and Warning given it's pretty intense It's super super fantastic Super fantastic super fantastic What a great animated series. I even like the movie man. The movie was fun, too Now but the tv the the animated series this is season four. Is it not Felix? I think it's season four Yeah, I believe so and Free a song free a song free a song I'll send some of the attack on Titan fan art I drew yesterday to the discord. I spent three hours on my back kills, but it was worth it Nice. I'd love to take a look at it. Hell. Yeah attack on Titan was is a fantastic There's amazing anime out there gang and and by the way Felix we haven't If you're gonna link it up You can link it up both in the anime folder and the comic book folder if you want because Attack on Titan has a graphic novel like I don't know how long it's been going for All right, you can link them up in both Uh Fantastic, man. I'm so looking forward to watching it and it's going to be released once a week Hey, I wish they did it one in one shot. I do a whole marathon on it. Wait you watch anime Dude, yeah, I watched a lot of anime. I love anime Anime is amazing Sage you do what's your favorite anime? What you can't say. There's so much amazing anime out there all right More of a general question. I feel it is very difficult to live life without a strict routine Otherwise I get too distracted or too involved with something and can't get enough done What are your thoughts on this? Um, I think some people need the discipline. Some people can do multitasking. Some people can do chaotic work Uh, I think it's really personal and whatever works for you works for you Banana Stein hey, hey, hey for me Obviously, you know, I set my schedule I have discipline You know, we've been streaming for three plus years now, I guess and I've only had to cancel one stream Right, so I set up my schedules and I do boom boom boom So I I don't mind the discipline times But I also do a lot of chaotic work, right and I also love multitasking And sometimes it it seems like I'm not getting a lot done from my perspective. I know anyway, I know for I get a lot done. I'm sure I'm creating a lot of work But what happens is I'm working on five or five project on one shot And it takes a while for one of them to be done But when one is done, the other ones go boom boom boom. They're all done, right? So that's my preferred way of doing it. My favorite anime. Anime is Noriko Shippuden. Ah, nice mind I love cowboy people of Samurai Champloo space dandy. It's all the same studio. Those ones studio Ghibli is amazing attack on titans fantastic My hero academia more recent is amazing Star Blazers, dude, I just did a marathon the first three seasons of Star Blazers from the 1978 series Um Like a few months ago. I did a marathon on them. I love anime Under sweetheart left a link on your discord chicho coffee sig It's my it's my bacon. Ha ha you're doing coffee cigarettes Very philosophical channel. I wish You all the best Thank you very much. I'm just a chicho Vegan hunter god and thank you for popping in. I'm glad you're liking the stream Felix, I just linked up my sketch in the animation channel. Let's go. Awesome. Felix. Thank you As long as we are sowing seeds of your funeral Future self. I think it is productive indeed. Cowboy Peepop and Samurai Champloo are awesome indeed and there's soundtracks Whoa, whoa, whoa What soundtracks and samurai champloo? I give full credit to for introducing me to nujabas, right and nujabas Rest in peace one of the greatest music producers of all time, right? Unfortunately, he passed away way before his time Banana stein I usually have a general plan for what I need to Wait, where'd it go? What I need to need to be done for the week and I just do whatever I feel like at the moment I've tried to follow a strict schedule, but never works out for me. Yeah, everybody different, right? Cool. Leo. How you doing? Chicho, I don't know if I am catching the tail end or not But just letting you know my package arrived today right on can't wait to treasure this dm Turner book forever Awesome, right on brother. I'm so happy you got there. I have a great read through it, man. There's a lot there There is a lot there a lot to process a lot to process and by the way gang if you guys don't want to know what's going on we did as a appreciation of the people who've been here on On our live streams and watching my videos on youtube and stuff like this Like I've been doing this for like 15 years right uploading videos and sharing content But I've been on twitch for like three years right and as an appreciation for all the help and all the all the interaction We did a one thousandth youtube upload video That was our 400th plus twitch live stream where we auctioned off stuff and people using their channel points Of winning things and we auctioned up comic books that I published in the 1990s jam That I made in the last couple of years two three years a honey local unpasteurized honey that we get in my area and two dm Turner books Okay And they're available for free online and those are treasures Okay, and one of them went to kulia like one hunter my favorite was Kyoto animation by But they burned down tt Kyoto Oh, I don't what Kyoto animation What did Kyoto animation produce But I understand but I'm four months ahead From my class in physics and advanced mathematics So my way of doing it seems to work. Awesome. And if it works for you, that's the key, right? sage cage I love nurutu because I was watching it when it aired and I was in high school. Ha ha nice pick it in you ha You who have the soul of a teacher. Did you like assassination classroom? I don't think I've seen assassination classroom Assassination classroom. I don't think I've seen it I've seen some high school What was that called? Where they turn into zombies The kids that was super good Vegan hunter god laugh out loud the way you read my name. It's like you find that mesmerizing bizarre Hashtag mission accomplished Also xbj or bxj. Have you heard of the anime psycho mob 100 yeah interesting anime stuff Yeah, I don't know. I can't remember. I've seen psycho mob You know what? I might have it's a while ago. Is it not? I think I might have seen it. I can't remember right now Mr. Beers, can you explain your point system? What are the purchases auctions? It's just channel points if you click on the bottom In in chat if you click on the little face of a bearded person giving a sticking out of stung That's me with little infinity symbol right if you click on that there's points on there and we held an auction Where people Bid it on things that I was showing and the highest bidder One and then they redeemed their points Oh my god door assassination classroom the ending still oh dude link this up I don't I haven't seen assassination classroom. I gotta I gotta see this Graham chichol for your information my package arrived to nice graham and graham ended up getting three things I think graham got honey Strawberry and crab apple is that what you got graham? Felix could you explain the methods for completing the square? I've always found it confusing completing square. Sure. Let's do it Let's do completing squares speedy ones out of style Tt is a cry face. They created a silent voice You would love it. I'm pretty deep and looks at people's morality That vegan haunted god link it up on our discord and I'll take a look at it Chicho Coolio, holy cow. Just realized this dm. Turner book was published in september 1994 That's the year and month. I was born. Oh, dude Check this out. Complete the square All right, complete the square. I got a video out there if you do chicho complete the square You'll find it. Right. I got a few videos out there. Right. So chicho will complete the square chicho completing The square let me show you the main one or I don't know if there is a main one There's a whole bunch of ones. Yeah, check this out. Here's the full-on asmr version one that I put out Okay That's that's a big smile on my face Here's this one. Okay. Take a look at this. I'm about to go through it with you speedy gonzala style, right My mob psycho 100 is made by the creator of one punch man is amazing. So good But are very comedic driven and highly enjoyable. Awesome I I'm mad. I don't know if I've seen it or it's something that I've seen in previews the comic book previews Mob psych is a kid that's dressed up in a black suit, right? Like or black outfit. Is that mob psycho 100? Take a look at completing square completing square is to be able to express a quadratic function in a form where you can read it in Graphic, right? So if you have a quadratic function a x squared plus b x plus c What you want to do is rewrite this rewrite In the form of f of x is equal to a x minus p squared plus q Right? Yeah, black outfit and mob. So yeah, that's the one. I've seen it, but I haven't seen the animation Sounds like it. Yeah. Yeah. Yeah. Yeah. I've seen the graphic novels for it But I haven't delved into it yet. If you can brother Ashway link this up in our discord page under animation and I'll remember to Grab it Have a look through it So the reason we want to do this is because this and plus and minus If this number in front is negative, you know, the parabola opens down if it's positive, you know, the parabola opens up This is the axis of symmetry and this is the vertex the p and q are the vertex Vertex and it's the opposite sign of side of p P and q are the vertex, right? So for example, this is the way you do it, right? f of x Is equal to negative two actually negative three x squared plus 18 x Plus two, right? Let's say we want to graph this thing Now this thing is difficult to graph because it's not in a form that we can just read it and get the vertex and graph everything Right? We can factor it find the x intercepts take the average of the x intercepts, right? If there are x intercepts and then that's your axis of symmetry plug it back into the equation Find the y part of vertex and then grab it that way. Well, there's a better way to do it. It's an algorithm, right? You go like this put brackets around the x squared and x term Make sure you take the coefficient in front of the x squared out of the bracket because you want the x squared to be solo, right? Posted an image and short description of assassination classroom in your discord So you remember to check it out later. Awesome. Thank you very much. Cool. Okay So you want to take the negative three out of the brackets, right? So if you take that out, you got x squared here But because the x term is inside the bracket you have to compensate for that And the way you compensate for that is you take whatever was here and divide it by whatever you took out of the bracket, right? So you divide this by negative three So that becomes negative six x plus two, right? Because you're asking yourself What do you multiply negative three by to give you positive 18? Well, you multiply it by negative six All right, the next step is take the coefficient in front of the x term Divide it by two and you're always in this step always dividing it by two if you can simplify You simplify this becomes negative three Circle it the reason you're going to circle it is because you're going to reference it Circle it square it you get nine circle this because you're going to use that as well Right, so I when I'm doing mathematics in general I like to highlight things that I'm going to use in different parts of my algorithm solution, right? Now what you do is You add and subtract this number inside the brackets Six x plus nine minus nine plus two some people say well while you're adding a subtracting was that's equal to zero That's exactly why we're adding a subtracting because you can't just take a number and randomly add it to a function Without changing the function, right? You don't want to change the function You just want to take this function, which is in this form and rework it massage it To write it in this form so you can just read it And graph it, right? That's why you can only add zero to a function without changing it and Nine minus nine is zero, right? This part is called completing the square. That's what this whole thing is called This is called completing the square completing The Square Right Why is it called completing the square because we're going to make a perfect square out of this thing? Okay, and free massage free massage free massage Right now what we're going to do is This part we're going to factor This guy we're going to take out of the bracket When you take this guy out of the bracket anything in front of the bracket is standing guard And whatever comes out of the bracket has to multiply this so you multiply this by negative three Negative nine times negative three is positive 27 plus 27. Okay In this part you ask yourself What are what are two numbers that multiply to give you nine and have to give you negative six? You don't even have to think about it because it's this guy right here That's the reason we circled it negative three times negative three gives you nine negative three Plus negative three gives you negative six, right? Okay So this becomes negative three x minus three Times x minus three. Well, that's just x minus three squared Two plus 27 is 29 cool We just completed the square we took an expression that was in this form and rewrote it in this form We took this and rewrote it like this now we can graph it. Let's graph it What does this tell us? This tells us that the vertex Is the opposite sign of negative three three and 29 Right What a pro does it does it in his head while looking at the camera instead of the board I'm actually looking at the screen. So I know where things are All right What things Is magic Matha magic, right? So three and 29 one two three and let's say 29 is here, right? Three and 29 What's the y-intercept of this function? Well the y-intercept you can graph from here, right? If you set x is equal to zero this disappears this disappears and it's two So the y-intercept is two How how to do it for quadratic forms and Then So here's the y-intercept is two the axis of symmetry Axis of symmetry is x is equal to three That's the line where the parabola is symmetrical, right if You do this hopefully this year is just as far away this year Well, if this is two if this is zero and two and the axis of symmetry is three What's the mirror point of this point? Well, if the axis of symmetry is three, there's a three there and a three there So this point becomes six and two Right So now you can graph it Because this thing opened down because it was negative, right The only other thing left is to find your x-intercepts Right and the x-intercepts are easy to find. I have to go go read, but I really like the content I'll definitely be back. Awesome. Mr. Buris Buris Thank you for popping in and thanks for coming back later Right, so if you want to find the x-intercept boink boink Well on the x-intercept the y is zero. We know that right Also, all we got to do is set f of x the y equal to zero and isolate the x Okay, zero is equal to negative three x minus three squared plus 29 here. Let's do this here Bring the 29 over so negative 29 is equal to negative three x minus three squared divide by negative three So you get 29 over three is equal to x minus three squared Right and then square root both sides squared of 29 over three is plus and minus the square root of 29 over three is equal to x minus three So your x-intercept is going to be bring it down here The x-intercepts are going to be three plus and minus squared of 29 over three Hey, what's the three? Does the three ring a bell? The three is your axis of symmetry right The three is your axis of symmetry So the distance here and the distance here is here's three Right, and if you go three plus the square root of 29 over three, which is just a number Right three plus the square root of 29 over three It's just a distance you're traveling from here to here And if you go three minus the square root of 29 over three, that's just the distance that you're traveling here, right? So this point Is three plus the square root of 29 over three and zero and this point is Three minus the square root of 29 over three and zero this point right there That's how you do complain square and that's why it is so powerful It takes something that you couldn't read And converts it to something that you can read That you just read it off and you just do it Right powerful important Right, I hope that helped I hope that helped And that was Felix Gang let's call the string Okay, thank you for being here great discussions Fantastic a little bit of mathematics a little bit of philosophy a little bit of light bending around objects and going all over the place cool cool cool and A little bit discussion about education and every now and then Free as such free as such free as such All right, thanks for the explanation my pleasure Felix. I hope it helps and check out the video I linked up It should help. I I hope okay because I go through it slower and Show you with the variables and we go through the whole thing and graph it and slower, right? So you you'll see what it how it plays out gang aside from that I am on patreon Vegan hunter god chicho. Do you mind sparing two minute extra and give me a quick overview of how to rearrange Different symbols pretty pretty. Yeah, for sure. Let's do it Adios chicho in chat make sure to watch the new season Of tac on Titan watch this moving around just isolating a variable, right? So look Isolating a variable. You're just doing algebra my pleasure My pleasure It would mean a lot to me a lot of people teach order of operations But I'm stuck at rearranging rearranging look they teach you bed mass right bed mass bed mass Right, they all say bed mass bed mass bed mass through your brackets exponents division multiplication and addition of subtraction Division multiplication addition subtraction have the same way, right? But bed mass is for simplifying. It's not for solving when you're isolating variables. You're solving Okay, when you're simplifying you go this way Simplify when you're solving you go this way Right you you take care of addition subtraction first division multiplication and then exponents and then brackets Right, so it's the reverse order So whenever you're solving search for something you're solving for an equation. You're trying to again Isolate a variable. So for example, what if I gave this to you? x minus b square c is equal to y w over q divided by z Here we'll add this here to plus is equal to k What do you want to solve for let's say you want to solve for x solve for x Right, it means you got to get x by itself Cool. Let's do it. I always learn it as Pete paid as parentheses. Yeah, there's different ways they teach it, right? In my part of world, I call it bed mass. So we want to solve for x That means here. I'm going to put this here so we don't lose the flow right solve for x solve for x Right That means you want to get this by itself if you want to get this by itself You want to undo everything that is being done to it and this is an equal side, right? Well, first thing we've got to do is do the addition subtractions first now Remember this subtraction is inside the bracket. You can't hit this up yet, right? So on this side of the equation you got to get rid of this guy first because that's an addition so if we're going to Get rid of the addition you grab this doohickey and bring it over which means really minus y w over q Which means it becomes minus y w over q and whenever you're solving for equations Line up Please excuse my dear and Sally My dear and Sally What you want to do? Did she taught you pen pen mass? What you want to do is line up your equal sign, right? So if I had enough room here, I would write my equal sign here But we don't so I'm going to write the equal sign here, right? And on this side, we got k minus y w over q on this side. We got c x minus b squared over z So do we have any more addition subtraction outside of the bracket because the brackets over here we don't Because we already got these guys on this side. We want to get x by itself. That's what solving is, right? So what are we going to take care of next division multiplication? Okay, let's take care of the division multiplication The x is inside the bracket. It's being squared. So that's an exponent So you've got to take care of division multiplication outside of this That's a c and a z, right? Well, how do you get rid of the c you get rid of the c the c is multiplying this you do the opposite of multiplication you divide so you multiply this By something over c the something is a z because the z here is on the bottom Is dividing the x. So how do you get rid of the z? You multiply it by z z So what happens here c kill c z kill z. Well, if you do something on one side, you got to do to the other side That's what an equal sign means, right? So you multiply this whole side by z and c z over c Okay So z over c z over c z kill z c kill c So right now we got x minus b squared is equal to k minus y w over q times z over c cool We still need to get to the x. How are we going to get to the x? Unsweetheart a wavelength or y. Okay. I'm going to do this before I read that Well, we we took care of addition subtractions. We took care of multiplication division. That's being done to the x Now what we've got to do is Exponents so we've got to rid of we've got to get rid of squared How do you get rid of squared you get rid of squared by Squaring it or square rooting it right square root is the opposite of square So if you square root this side, you got a square root that side cool. So now we got on this side x minus b because the square root kills the squared is equal to square root of k minus y w over q times z over c What's left? We've got to take care of this Well, that's x minus b. How do you get rid of negative b minus b? You add b So you're going to grab this to who can bring it over it becomes plus b. So x is equal to square root of k minus y w over q times z over c Plus b. That's your x. I hope that's clear This is genius j okay Also, uh uncle sweetheart a wavelength of y on An x y axis is like sticking a rod into a globe the further away this The peaks and valleys are further apart less intense peaks where the rays intersect Valleys the middle of the empty spaces and sorry pertaining to her. Yeah, it sounds like it I gotta go to discord and see the visuals of it man Now that we know how light travels we know how sound radio Travels too chicha gonna rewrite the physics book. I hope you do man. I'll read it. This is genius Vegan hunter god is the b within the square root. No the b is outside of square root. Remember the square root was here That's now one complete term You just needed to get this on that side. So that's not inside the square root because it wasn't inside this Square root. It was inside here All right, it wasn't on that side. So it's the last step that you need to do Okay, I hope that's clear I hope that's clear Aside from that gang. I hope this helped the problem is I can't prove any of it I'm not Learned in the language of mathematics, but the concept is common sense. Well, sometimes common sense is not Correct Okay, I learned a lot of new things. Yes. It's it's you're an amazing my pleasure man. I try my best anyway right Gang, we are live streaming on twitch twitch.tv 4 slash chico live if that x had Square root of x how would we move a square root? Oh if this was squared or square root watch this I'm gonna change this up Square root square root square root square root square root. How do you get rid of square root? You square Right, so you square everything and that means you got to square this whole thing So x would equal this whole thing squared That's what you would do Okay And Free a search free a search right Gang Okay, awesome. I'm glad that makes sense. Thank you. My pleasure We are live streaming on twitch if you want to participate in that chat twitch Is where you want to be at and gang. Thank you for the follows. Thank you for this for the subs even I understand that's awesome Thank you for the subs. Thank you for being here fun. Thank you for the discussions. Thank you for the love Thank you for sharing your perspective on things and I'm now at the quadratic formula. Awesome I really mean it would have thrown you My twitch prime if I hadn't used it are no worries. No worries. I'll be here for a while, man I'm going to be here for a long time next time. Thank you very much Okay, and mods. Thank you for taking care of business. Okay I do announce these live streams 30 minutes before we go live on parlor. Hello mines vk gap and twitter And we do share additional content there as well So you can follow the work there and we do have a discord page And anytime you want you can come on to our Twitch page irrelevant of where streaming or not and go to chat chat and type in Explanation mark social and all the links will pop up and all the links will be in the description of this video Okay, and there's a lot of people sharing a lot of information on our discord page. You're welcome to join We do upload the audio for live streams when we do open discussions with no visuals We have visuals right now No visuals to soundcloud.com or slash chicho ch y ch o and they should be available on your favorite podcasting platform and we will be uploading this video to youtube and Bitchute and a third platform most likely coming early 2021 and if you want to support this work on those platforms you can subscribe you can share you can like you can Comment you can turn on notifications guarantee to give them get them through a bit shoot not so much through youtube And if you're on youtube you can join youtube membership and there's a button there And for those of you who've joined youtube membership. Thank you very much for the support gang I hope you guys have a fantastic fantastic day night evening morning and we're we're back In two days and we're going to talk music and on the weekend saturday sunday We're doing comic book readings and then we're going to do a cooking session and meditation and More current events politics. Can you give us a 20 second overview of? What bit shoot is Bit shoot is a video sharing platform that is free speech platform. They're not censoring information Think of bit shoot as being the equivalent of youtube in 2005 2006 the youtube started off in 2005 Got bought up by google in 2006 and it was a great platform to share information For a number of years until the censorship kicked in right so all of my content is not uploaded to youtube Because of censorship because we don't want to get the platform there right we've got a thousand plus videos on there Hundreds of math videos content that we created. So we don't want to risk being the platform there So everything is being loaded on bit shoot if the things are too sensitive They are not going on youtube right now the sensitive stuff is the current event discussions that we're having Sometimes during some of the other streams a little bit of politics Comes in and we talk about certain things that we cannot talk about on youtube So those don't get uploaded to bit shoot to youtube either Okay, and there are no advertisements on my videos on bit shoot There are on youtube. It's supposed to be only at the beginning But youtube is putting them in at the in the middle as well. Okay, and it's just a free speech platform right now there's a lot of politics and different Perspectives on there that some people might not agree with but there's a lot of people like me that are uploading on there as well There's ASMR content on there. There's Educational math content on the content on there and stuff like that. Okay. That's what bit shoot is It's just another video sharing platform meditation string feel like sounds cool Will it be like a guided meditation or just a discussion? It's going to be I'm going to show you one of the meditations that I used to do. I want to get back into it So this is a great opportunity for me to get back into it and it's basically a standing tai chi meditation I'll show you guys how I end up doing it and then we'll see where it goes from there, right Open discussion makes sense. It's good that there is an alternative would be good platform for political It's a phenomenal platform political discussions I watch more videos on bit shoot now than I do youtube because I consume a lot of politics and economics videos. So That's where I go to to watch most of my politics economics videos now. Okay, they're not on youtube because youtube's been killing a lot of channels okay, gang I hope you have a fantastic next next couple of days and I'll see you guys in a couple of days if you can make it We're doing meditation. I think or on the weekend where we're going to do some comic book readings Bye everyone