Hi everyone, this is Chichiro. Welcome to another live stream and Today is September 20th, 2019 and it's our drop-in math tutoring session number two for the 2019-2020 school year That's our little intro. We've done a lot of these We've done a lot of these last year for the last year school year and we're going to do a lot for this year as well and for those of you watching on Which YouTube or any other platform that we end up loading this video on We'll probably provide some links in the description of this video If you want to reference some stuff and usually the way it works is just We sort of chill for a bit Do a little bit of greet meeting greet salutations and whatnot for a few minutes until people start rolling in and If people have math questions They can ask the math questions, and I'll try to help you guys out Okay, as much as I can Aside from that on Discord, we have a Discord page. There was someone that mentioned Mark Metals, are you doing? Hello friend? Hello? Hello? I'm glad the comic books got there on time Oh, let me change up the The chat bring it down because this was set up for I don't know what it was set up for We had it set up for And what you'll call it. I'm glad the comics got there on time And you liked and you'd like and I hope they come back at a high grade I just to finish off my thoughts there was someone that came on Discord in a math folder that we have and Amazing amazing amazing spider-man I'm sending them off.  I hope seriously Those are very high grade most of them are very high grade. I hope they come back higher than what we graded it for I'm sending it back to you Don't see what happens mark. We'll see what I would great. I hope I hope to get back After doing the twitching Jason, how are you doing? Thank you for the thoughts. Don't work. Thank you for the thoughts Starsky, how are you doing? Please message me a good address because I'll send you the graded copy dude. You don't have to for your personal collection up mark I appreciate it very much man, but You want them you bet on them up to you up to you. I don't have any of those books graded I only have like I don't know eight graded books in my collection of I don't know how many I got right King Tom, how are you doing? Mathematics I've already decided you've already decided Okay, we talk we talk we talk Aside from that just to let you guys know There was someone on discord That came on I forget who it was on our math folder that asked me if I had any videos on quadratic Equations quadratic functions and they mentioned that you know, they know I've done a few quadratic stuff and I've done a lot of quadratic stuff videos for quadratics in ASR mathematics as well as the language of mathematics Mask of Raven, how are you doing and If there aren't any, you know, we'll chill for you know, a couple more minutes Okay, if there aren't any straight up right off the bat math questions coming up. I'm gonna do a Video this video or this session. We're gonna do quadratics. I'm gonna run you through the mindset of Why We're studying quadratics what they represent how they come about and the thought process that we have to go through to Start analyzing quadratics and what they can lead up to And this is sort of going to be a condensed version of a few videos that we've put up in a language of mathematics So I'm sort of putting it all together and I'm gonna treat it the way I would Meet the students where they were getting into quadratics and they understood basically you have to know adding subtracting multiplying dividing I don't move around any cool side what a function is and all that jazz right just preliminary stuff But I'm gonna lay it on thick. Okay. If there are any math questions That you want me to deal with Ask them. I'm willing to I'm totally okay with stopping the thought process Dealing with your questions and then continuing on with the quadratics because what I'm gonna present, you know Depending on how deep I go into it It could take anywhere between half an hour to two hours Depending on how many tangents we take and whatnot, but I'm definitely open to this is dropping open map to the session Right, so I'm definitely open for trying to help you out in whatever Concepts you're trying to understand better and whatever school work you might be doing or outside of school that you're trying to wrap your head around You know What's going on? In the wrong will not especially regarding some topics that you might be dealing with Okay, I hope that's okay Because quadratics is huge quadratics is Is Oh, yeah, let me pop up this the chat that way The computer won't be working so hard so we won't hopefully I didn't lose any So Because as soon as you pop it out you lose some of the chats So we're about seven minutes in what do you guys say should we do a Little quadratics and I give you the lowdown What is going on with quadratics? What are these things? Why do so many people ask us about quadratics? Why does it take so many people out of the game? Right Why is there so many layers? Let's do okay, looks like we're good You get the last string People watching which is good. It is 1 p.m. So on the West Coast is a lot of people still in school in Central can the United States there's people just got in a getting out of school And last thing they want to do is do a two-hour drop in tutoring sessions on the East Coast They're about three hours ahead. So they got out of school. They got to get some food in them Right if you're in school So maybe you can grab some food and sit down Think about quadratics. I love that Haven't seen quadratics be introduced in forever now. Let's do this masquerade. I'm gonna show you by the way Just for you guys that are on chat masquerade and studying mathematics if I remember correctly masquerade So his mathematics is more powerful than my mathematics I just happened to be here on this side Presenting the information. So if there's any questions you have that I can't deal with maybe masquerade and Might be willing to help you guys out And we've done this a few times Let's talk about quadratics First thing you have to appreciate about quadratics about any math concept is all of mathematics is a layer on top of Five axioms five rules, right the whole universe this world that we have created That we're looking at through the lens of mathematics is based on five Everything else builds on top I took a single math class in my second year of college left on a business statistics Statistics Then forever since I've done a formal course on course on math Statistics is super important to change. I said by the way, I have a student this year that I'm doing stats 12 with So I know there's been a lot of people asking me to do statistics, right? And I mentioned that because they took it out of the core math curriculum in my part of world But ten years ago ridiculous, right? They took stats out Oh So I haven't had the opportunity to teach statistics full on statistics for like ten years so one of the reasons I haven't really dealt too deep into statistics is because Like anything if you don't use it you lose it, right? So I forgot a lot of terminology and all that jazz, but this student mind lucky for me He's taken a full blown stats course for grade 12. So I'm gonna get exposed to a lot of statistics So the odds are we're gonna start doing more statistics And lucky for me I have a student doing this so I can learn with him and he's gonna be teaching me teaching me a little bit, right? I've been working with the student for a long time smart kid Think how are you doing? Not seeing you in a while. Hope you're well doing well man school.  I'd be very interested in statistics video series from Europe But to which in Jason I want 100% one of the things I promise that I'm gonna do is Create a series on stats and create a series on calculus Stats will be easier for me to do because they do deal with it in high school Calculus, I'll have to go I don't know what they They take stats out in my experience people love learning about probability and how to understand data Mask of Raven blew me away. I was so pissed because that took away the opportunity for me to Cameras not focus that took away the opportunity for me to do stats right and mask of Raven the other thing they took out of My part of world out of the math curriculum was conics. They took conics out like 15 years ago Just imagine beautiful Beautiful conics. They took out. I was pretty pissed. I was pretty pissed Let's talk about quadratics So mathematics for us based on five rules everything builds on top, right? so the axioms I forget what the proper terminology is and Whatever it is because those those things are the core of it, right? I'm not teaching the core of it. I'm teaching what's layered on top of it Right, but we are teaching some of the basics of how to do things right regarding the axioms And we're not worried about the proofs. We're worried about how to do things, right? So when you're learning mathematics initially elementary school First things you learn is counting obviously, right? And I'm gonna put out a video series on counting adding multiplying for elementary school students, right? I've had some people come to me in elementary school that Anyway, there's a gap that I want to fill. I'll talk to you guys about that later But the first things you learn is counting and then you learn adding subtracting multiplying So you learn adding subtracting multiplying and dividing and then you learn how to move around in equals sign and you learn all the stuff for Basically numbers, right? So they give you a bunch of numbers The box could be anything and they ask you to add them subtract them multiply them divide them and then they say hey Solve them which means deal with the equals sign, right? That's what you do in elementary school and you build on top of that you learn about fractions What not you get into high school and high school is when you're doing your algebra You're learning more about the equals sign and how to solve equations, right? So if you're given numbers you do adding subtracting multiplying dividing and how to move around And then some time in grade nine in my part of the world in other parts of the world would be much earlier Some places maybe You get introduced to something called functions, right? So they take an XY axis Cartesian coordinate system and they say hey What happens if you're looking at a system and you start Analyzing that system you collect data from that system and you plot that system, right? What they do they say the X axis is just convention. You say this is the independent variable And the Y axis the numbers on the Y Coordinate system right there's a dependent variable Right and what's Y dependent on why is dependent on X of course In general usually time is on the X axis a lot of graphs you're gonna see Time is here and something else here for example your height as your you know enter the world you might be How taller little babies Like a foot I don't know how tall you're right eight inches nine inches ten inches, right? So you're this tall when you enter the world year zero Right and as you grow, you know, there's usually growth spurts, right?  I don't know if you shrink this much, but you shrink So that could be a graph of your height the X axis with the time right and the Y axis would be height and The axis the units on the axis really depends on Which part of world you're you're either gonna be centimeters meters Inches, right? That's the way it works, right? Usually you're centimeters or your inches in the United States you're dealing with inches the units and I think there's like two other countries that deal with interest convention Canada. We have a lot of inches as well, right? How tall are you they say five feet? You know, whatever it is or six to or something like this, right and huge chunk of the world is centimeters Right, so that's a general graph. You learn how to add subtract multiply divide move around the equal sign in elementary school And in grade eight they dump it on you in grade nine You do a lot more of this in fractions and whatnot, and then you start looking at functions Okay, and these are Functions, right? They could be relations as well, but in general we're talking about functions where you're looking at a system You're looking at a y variable that is dependent on an X Okay, and this is where you want to be you want to start looking at the world through the room through the Perspective of functions what are functions, right? so what happens is Because we're going to start analyzing different types of systems trying to understand how they work, right? because you could get a lot out of this if you're Studying human biology or whatever it is once you start graphing these things You're gonna see the same type of graph for human beings no matter where you are, right? You might see you know basically, I don't know if this is the graph by the way, I'm just Pulling it out of thin air, right? that's a that's the graph of a human being growth the graph of Another type of animal might be like this, right? Because if they grow up in nature, they need to Grow up pretty fast. Otherwise they get eaten, right? If you look at other mammals that they're born like deer or any four-legged animals when they're born within minutes They're walking right human beings. It takes us a year a couple of years to learn how to walk, right? There's nurturing going on there. So Different types of animals have different types of graphs keep that in mind, right? So once we learn how to do this the first question we ask ourselves is hey What's the most basic type of function? We have was the most basic type of graph we can have other than a point a function could be just a point, right? So first thing you end up doing is You got an x you got a y the x could be anything the y could be anything the y is dependent on the x and the x is independent Right, so for us to start delving into a realm of functions the first place We start looking at is how to graph out line So lines could be like this could be like this could be like this Could be vertical You start getting lines, but there's only really lines just it's a line All that matters is is direction really the slope, right? Where it where it hits the y-axis Right, so once you start getting into lines The there's a general equation for a line, which is why is equal to mx plus That's your general equation for a line. That's a slope intercept for there's different ways you can present this as well We've talked a lot about this, right? Here's a line as well a x plus By plus c is equal to zero as long as you have x to the power of one and Or while you need a Y. Well, no X to the power of one y to the power of one Right, they're not being multiplied together. This is in separate terms Okay Then you have a line in general Right, so when you get extra power of one y to the power of one you're dealing with a line Okay, now they're not multiplied together. You can't have x y equaling five. That's not a line X over y is equal to five. That's not online. They have to be Separate terms. They cannot be multiplied together, right? They have to be separate terms not multiplied together So let's graph a line The vertical line is the only line that can't be represented as a function. Yeah, I believe Straight line stuff is guessing For sure mask of Raven this one as mask of Raven is pointing out That's not a function, but it can be sort of represented as Mx plus b to a certain degree because all this is is really x is equal to a number Whatever the number is right, so it's still x to the power of one, but x is equal to a number the M the slope of this thing is Undefined it's looking down a vertical cliff, right? What would it move down into that? Straight line stuff is guessing I'm really bad at mathematics. I hope you get an appreciation for this. We're gonna Get into the quadratics. Okay, so let's graph a line. Let's graph one line And we're gonna use the slope intercept for we've talked about lines I have you change it from one form to another and graph and stuff like that But we're not going to go into that because we're building up to the quadratics, right? So let's assume we have the following line Y Is equal to 2 over 3 x plus 2, right? Now a line does this Do I play Fortnite? No I have watched it every now and then and Vex is who I watch how to play and Vex is one of the He's actually if you look if you scroll down on my twitch page with With a little banner of who's subscribed to me the most the longest pair and stuff like this Vex Has been subscribed to me for a long time. Fortnite is great The Vex ZK you couldn't have fourth night without mathematics So how could fortnight be greater than mathematics if you couldn't have fortnight without mathematics You can have mathematics without fortnight. So mathematics trumps anything You're in a math live stream mathematics trumps anything Grading of that is 2 over 3 and y-intercept is 0 to 100 percent, right? so this is the slope or as a One thing says the gradient and this is the y-intercept So if you're graphing this guy You're gonna go y-intercept. This is our y-axis. That's our x-axis You're gonna go to the y-intercept One two that's the y-intercept is coordinate is zero and two because one x is zero one two three negative one negative two negative three Three four, etc. Right? One x is zero y is two because if you set x is zero here zero times two over three Disappears so why is equal to two keep this in mind? This is a function This is an equation that represents an x and a y and how they're related, right? So for you to find out what a y is at a certain x all you do is just plug in that x and figure out what the y is Right, you could do the other way around you could plug in a value for y and find what the x value is associated with it, right? Can you explain how we can multiply divide? manipulate Infinities infinities, you know what we're gonna get into the infinity towards the end of this little Chat that we're doing with quadratics. Okay, and once I do that here. I'm gonna put a little note here Okay, infinity. We'll talk about infinity. I'll touch on it. Okay You can't really multiply Infinities divide infinities, but you can do limits Okay, masquerade one might know a little bit well a lot more about this than than I do, right? I've put out a bunch of videos on infinity by the way if you do chicho infinity There should be at least two or three videos popping up We're going to watch like watch the Is this Ultimate fighting maybe I watch them every now and then Right So why to set this zero to and the slope is two over three So to graph this all you do is find a point on the graph and then you go To the slope and do the slope so we find the one to set that from here The slope is rise over run Rise over run so from here you go up to because the rise is two and you go to the right three One two three So here is our line and this thing continues on forever, right? Unless you give it limits boundaries Pythagoras sure. Let's put Pythagoras here, too We'll do Pythagoras as well. So we got infinity and we've got a squared plus B squared equals C squared Let me take this grittings dr. P I Vinnix Let me take this to the level where we got the quadratics happening with pop back in and then we'll deal with the With the quadratics the infinity will have to wait until we get to the end. Don't pay. How are you doing? That's live So here's a line cool Nice, we got a line. We'd learn how to graph a line Let's assume we have another line Could use Pythagoras theorem to show how to do distance along your function. Ah, yes, we could let's do it Let's do a little tangent from here Thanks, masker Raven. So we graphed a line, right? Now this could represent anything Right a line could represent anything you could you could say this is looking on a map view of engineers trying to connect up point a to point B and They want to find out how much how many kilometers of road they got a lay Right, so when we say this is a slope doesn't necessarily have to be vertical. It could be on a plant map view right where the X and Y are actually To the right looking from the top down Right, this could be the highway system. So they want to go from point a to point B. And let's assume point a Here, let's put this here. Is that negative three and point B four five six Four five six is when X is six. So if I learned this will I be good at fortnight? It's the first step to a certain degree because this is a line of sight as well, right? No, I don't sorry Yeah, I'm working I do teach physics as well High school level physics. My background is geophysics From university, right? So let's assume we want to go for point a to point B I want to find out what the distance is here, right? So here's one thing we can do by the way This is a tangent. So this isn't really connected to a quadratics to a certain degree what it could be Okay, so to find a distance of this what you can do is just draw a triangle Right and realize that this is going to be 90 degrees because our Cartesian coordinate system is 90 degrees So what you could say is hey, we could use Pythagorean theorem here and go Figure out what the distance is here right Figure out what the distance is here and Use a squared plus B squared equals C squared to figure out what the distance is here, right? So first thing we want to do is figure out what this point is here What this guy is here that's a negative three This point here was six, right? Cartesian coordinate system You have to have an X and a Y. You can just have an X by itself or Y by itself because you're on two dimensions If you're in two dimensions, you need an X and a Y to be in two dimensions Are you saying that whipped cream? No, sorry, no whipped cream just nice old age going going going great Hopefully one day you will reach this level, right? There's a saying there's a saying in Armenian it says may your hair grow white which is which is sort of wishing you the best saying that Hopefully you'll reach on the ripe old age and enjoy your life Santa Claus must be fantastic at math because if he's on the North Pole he has to map out All the places he needs to go to drop off the goodies, right? So we need to find out what Y is associated with these X's right? So we'll go back to our equation here Y is equal to two over three X Plus two so we want to find out what Y is when X is negative three, right? So all you do is just plug in negative three for X So Y is equal to two over three times negative three plus two because this equation is a Relationship between the X and Y if we know the X then we'll go far in the water. Are you a math teacher? Yeah, I teach mathematics Are you from Armenia? No, I've never been to Armenia. I was born in Iran Armenian blood I'm Canadian West Coast Canadian most of my life here.   This guy should be here, right? So if we draw What is what the accurate with our graph? so if we draw this More accurately with my line This guy would go through here, so we're here cool So when X is negative three Y is zero We found our Y value here and this guy would happen So it's not really the dotted line is not really here But it's over there. So that's six Right and here's our 90 degrees So that guy goes there that guy goes there that's that Right? Stag stagsy If you pay attention to this I'll guarantee you It'll make your life a lot easier and a lot sweeter guaranteed man Guarantee if you want to be Venex if you want to be on the naughty list you should read Lobo the paramount very Christmas special You'll see what no one does to the 90 kids Okay Check this out. So we have to find the Y value associated with this as well, right? So again, we come up to the same equation 23 x plus 2 plug in the sex Y is equal to Times six plus two three goes into six three times three times two six plus two Y is equal to eight So when X is equal to six Y is equal to Eight so this point here is six and eight right and This point was negative three and zero Thanks for the bits or the bit so we found our points now all we have to do is figure out what the distance is here What the distance is there right? Let's do it. I'm gonna erase these guys Check this out Well This distance is easy to calculate Because it goes from negative three to six. So that distance there is nine. But if you want a Formula for it. Here's the formula for it This point would be X1 Y1 this point is your X to Y to right First point second point Okay Hey, aren't you the same guy who I saw in power granted seats on YouTube? Yes I am power granted sir. Let's just make up And all grand seasons coming up with winter and the fall winter in my part of world we start getting power granted We'll do more power granted eating videos Patience and I do to change Jason the brother. I can honestly tell you I can honestly tell you Once I start acquiring more patience It's amazing how my perspective changed a lot and it helped me to To deal with a lot of situations And allows you to become a little bit sharper once you become patient because you take you take people because people if if they're being a little disruptive they're being Whatever that requires you to be patient with them Usually, they're either born out of their minds.  They're lonely. There's a lot of social elements associated with that So once I find myself to be more patient It opens the door and helps those people along maybe to Break out of that. They're shallow and later on in life. You find out that they gain a lot from that It's it is what it is, right? It's the grace and the greatness that has taught me this I've got a very high A in math mathematics on last year 93 or so And I'm aiming to get a good A this year too. I'm working on differentials at the moment. Nice. Nice That's good. Do you meditate to be so patient to a certain degree different types of meditation So let's figure out what the distance is here, right? Just too nice for me to do that. Thanks. Thanks, Daddy. Thanks for chilling here with me Okay, seriously, you're gonna appreciate what we're leading with this. It's gonna blow your mind, right? And you're gonna be pissed because you weren't taught this in school, right in this fashion Okay, not just this you would have been taught to a certain degree if you had a good teacher teaching in this The dealing with the Pythagorean theorem in the distance of a line but leading up to the quadratics So let's figure out what the distance is here, right? So the distance is here. This is the horizontal you go This minus this or that minus that, right? And it's the absolute value if you're doing distances, you're not dealing with negatives right now Right. So all you got to do to find out what the distance in the x direction is and the horizontal direction is It's just go x2 minus x1, which is 6 Minus negative 3 Negative and negative is positive. So it's not so the distance this way is 9 easy What's the distance this way? Well distance this way is going to be Distance in the y direction in the vertical is going to be y2 minus y1 y2 minus y1 it's going to be this Minus this so it's going to be 8 minus 0, which is just 8 Okay, so the distance this way is 8 now my drawings are not to scan Right, that doesn't look like an 8 if this is a 9 my drawings are not to scan Right, it's the numbers that matter But how are you doing welcome to the math livestream So according to the Pythagorean theorem if you got a right angle triangle which we do Right, we got this Going up to this and we got this right So if you want to find this Let's call this c Okay Then this squared plus that squared equals that squared. That's what the Pythagorean theorem tells us for right angle triangle So all you're going to do is go a squared plus v squared equals c squared a squared let's call this a it doesn't make a difference a or b as long as the legs of the triangle So you can go 9 squared plus 8 squared is equal to c squared 9 squared is 81 Plus 64 is equal to c squared. So c squared is equal to 5 14 C squared is equal to this it was showing up there this let me write this a little bit bigger so you see it green is pretty light So c squared is equal to what was it 145 All right So if you want to find out the distance of c you just take the square root of both sides Square root square root. So c is equal to Square root of 144 is 12 square root of 144 145 is going to be 12 point something We're just going to say approximately 12 So the distance from here to here is 12 So if this is engineers that's trying to build a row trying to figure out how much the row They're going to lay from point a to point b It's going to be 12 miles 12 kilometers water ratings. That's your path I think in theory Hey, I'm doing great really interesting to see what's going on I'm really curious about the physics around Magnetism and how electrons work. Is there something you Something you do lesson zone, uh, you know what that I actually specialized in electromagnetic and magnetic methods when I'd get my geophysics degree And I love that stuff So at some point you can definitely deal with it. I do have to touch up on the terminology. I haven't done geophysics for You know 18 years or so now You're close to So close to a career so close Just random luck, right so close, but good enough Good enough for us Martin, how are you doing? Long time no see you've been busy man So that's Pythagorean theorem. So that we've done Let's kill this guy I'm going to erase these guys. I'm just going to draw the line again Okay, because I want to link this up to the quadratics So you can pause it take a screenshot or look at the video again or whatever it is So let's take this down Let's graph our line again. So we've got our line Let's draw it here wide intercept of two Slope is two over three one two one two three. Here's our line. That's that guy Now Here's what mathematicians do or here's what scientists do or here's what People who play fortnight do Once you reach a certain level of your understanding you want to go further Right and in mathematics as we talked about If you have a number Right Or anything based value What you do is you learn how to add them subtract them multiply them divide them, right? So you learn adding subtraction and multiplying dividing and how to move around in the equal sign, right? Now The way it works mathematicians Once you know how to do something You want to apply these operations to that thing, right? To that function to that system, right? So one thing mathematicians would start doing once they figured out how to draw a line They would say hey, what happens if we have another line and then we add them together Let's draw another line. Let's use a different color. Let's use Let's use purple Purple blue red red No, we'll use red for something else. Okay. Let's stick with green. Let's keep on doing green Right, I'll push a little harder. So it comes out better. So let's assume we have another line. Let's assume we have the following line Y is equal to negative Let's go negative two over three x minus three right What's that line going to look like? Well that line the y intercept is negative three the sign in front of the number Goes with the number. That's a mantra and not that I Will continue to say and I've said a lot the sign in front of the number goes with the number So that's negative three one two three right And the slope is negative two over three negative two So if positive you go up negative you go down So one two three and then over three one two three So here is this line Nice We have line one and line two Here's line two Here's line one So we could graph another line and another line and another line and another line And there's only so many lines you can graph until you go on board right And then you start going. Okay. What can I do with these lines? right Well, first thing you can do with these do what these lines is add them up right So let's assume you come up with a new function. Let's do this in purple Okay Let's assume we We're going to create a new function and the new function Is not the green line. It's not the The blue line But our new function is the purple line And what we're going to do is we're going to add The blue line and the green line to make the purple line We just want to know what what happens, right? If we take this and add it to that So our blue purple line Let's call this three Because you're not going to use different colors when you're doing the minus You're going to number them and in mathematics Subscripts are like a last name Okay, so this is y1 y2 and y3 right So y3 is the first line plus the second line So it's going to be equal to I'm still going to keep on using different colors. Just just so you see is going to be a y1 plus y2 The rest of this I'm going to do in purple Okay The purple doesn't come out any different than the blue, I guess Oops. Should we use a different color? Should we use brown? Should we use brown? Let's use brown. Maybe it'll come out better Let's see. Is brown better? Yeah, that's darker.  So this is positive negative 2 which is really minus 2 So 2 over 3 x minus 2 over 3 x.  They're done, right? So this guy kills that guy 2 minus 3 is negative 1 So y3 becomes negative 1 right So this line The slope of this if you're if you're thinking about this being as y is equal to mx plus b This part the slope is zero because the only thing we have Is the y intercept So this line looks like this. Here's y3. It's a horizontal line All right. Wow, cool We just added that line And this line and we've got a brand new line which is a horizontal line Right interesting as we're talking about the lines It made me remember something a video that is really interesting to watch if it's okay Can I mention the title of it? It's uh on youtube. It's about a math question used in a math Championship that ended up being quite the surprise for everyone. Yeah for sure And you're welcome to go go to our discord and post the video Is it okay if I link it you can't link it back On the chat here the auto bot is going to zap it the only people that can link video link Post the links are mods and me because we have you know trolls rolling in and posting links to crazy stuff, right? But you can go on discord and link the video there in the math Uh subfolder or any other folder you think is appropriate So that's the new line, right? For us, okay, awesome. Now keep in mind we could have a different line added to these guys, right? So we could do Here let's bring out Light blue. Let's see if this comes out. Okay. We could go. Hey, here's another line y is equal to Three x minus one and we could say hey, this is line four What happens if you add line four in line two? What do you end up getting? What happens if you add line four and line? Three Right, so you can do a whole bunch of stuff like this You can do combinations of multiple lines just adding up together Well, guess what you can do the same thing with subtracting the lines I linked in a math tab. Awesome. Thank you, brother. Thank you math or bat bat smoke Or sister, of course So we can subtract a couple of lines. Let's do a subtraction Just so you know how how it lays out. This is supposed to be light blue. It comes out darker Sort of I see a darker. You guys see it Sort of a brown color It will come up also for anyone that isn't in discord search this problem seems hard Then it doesn't but it really is. Okay. Cool. Cool So let's assume our new line Let's do this in Orange orange. Let's do it in red and then when you erase all this I love that. Oh, it's three blue one brown. Okay. Cool. Cool. Cool. Yeah, I've watched these videos too Mask of raven likes it as well So that's just what we have to follow. Let's say our line five Yeah, that comes out. Okay. Was line four minus line three Right So line four is three x minus one And line four was negative one Right So minus negative one, right? You see how this goes, right? Negative and negative becomes positive.  So our new line is three x. So the y intercept Is going to be zero And the slope is three over one. So you go one two three over one That's what we get if we combine this line. Oh, we didn't graph that line. Let's graph this line So line four Is negative one And then up three one two three over one So here's this line That's that line line four And line five is this guy Right So all that happened if we added line four or subtracted Line three from line four it moved the line up, right? If we added this line and that line it made a flat line If we add this line and that line it just shifts it up one, right? So it manipulates your line right You can do a whole bunch of these and then slowly you get bored adding a subtracting lines So what do my mathematicians do they go? Hey, what happens if we multiply two lines together? Interesting. Let's try that out By the way, once you multiply two lines together You're in the introduction of quadratics and I'll show you what it looks like. Okay. Let's erase all this So keep this in mind functions are things representing Different systems, so we're not going to use the light bulb. Nothing smears Lines are Functions representing systems That we want to understand that we're presenting algebraically mathematically As well as graphically So let's assume we have a simpler line. Let's assume we have the following one y is equal to 2x Actually, let's just make it No number in front of the slope. We're going to make one Let's go y is equal to no. No, let's keep it that way 2x minus three That's line one Let's assume we have the line two is x minus plus two Okay, now keep them on we can add these two lines and come up with a new line So let's graph both these lines on the Cartesian coordinate system Is our x here's a y Let's graph line one negative three one Two three the y-intercept and the slope is two over one One two over one Here's line one one one And usually you label your lines Night night. How are you doing? Been a while since I've caught your line. Good to see you. Good to see you too, brother. Good to see you too So here's line one Let's graph line two line two the y-intercept is two And the slope is one over one up one over one Here's line two This is y two Now we can add these two lines to come up with a new line. Should we do just add If you add these guys y three if y three Is equal to y one plus y two Then let me erase these slope things so they don't Confuse people If we add these guys two x plus x is three x Negative three plus two is negative one So y three would be negative one and then slope of one two three over one So we would look like this That would be y three you could subtract them Two x minus x if y four was y one minus y two Two x minus x would be x negative three minus two is negative five And that line would be y just up to be negative five and the slope one over one. It will go like this, right? Hannah, how are you doing? Now what else can we do? Check this out. We got bored of adding and subtracting lines. Let's multiply these lines multiply the lines We're going to continue Let me give us a little bit space here And then we're going to graph them Graph this and you'll see what it looks like Let's assume our new function y five By the way, thank you for your follows. Thank you for the subs. If I've missed any subs then thank you for the bits If I missed any bits, okay I sometimes don't catch the Things pop it up Let's assume our next function y five is not adding or subtracting. What topic is this? Um pat what i'm doing is um Giving an intro to what quadratics are, right? So what we started off with was just graphing a single line And then finding another line and then adding the two lines to see what the new function will look like And then subtracting the two lines to see What a new function when you subtract these two lines looks like, right? Then you can do this Until the end of time, right? You can add a subtract Lines being the most basic polynomial function that we sort of start analyzing, right? So you take one function add it to another function to see what happens Take one function subtract it from another function to see what it looks like And you do this and then once you're comfortable enough You go into the next operations, right the next operation would be let's multiply the two lines together I have from argentina. I do not understand much But it serves me for school. Awesome. Lord. How are you doing? I finally made it. Welcome. Welcome. Welcome. Welcome So let's take line one and line two And multiply them to see what we end up getting now remember When we subtracted that when we added them and subtracted them We still ended up getting lines right If you take a line add another line you end up with another line If you take a line subtract another line you end up with a line, right? What happens if you take a line and multiply it with another line? Let's take y1 And multiply it with y2 So we're going to take this 2x minus 3 and we're going to multiply it with x plus 2 Once you do this multiplication, you're going to foil this guy out expand it, right? So this multiplies this and this and that multiplies that and that You're going to end up getting 2x squared plus 4x minus 3x minus 6 This is going to be 2x squared plus x minus 6 So our new function is this and This is a moment where you go what? We took a line and multiply it with another line We took this guy and multiplied by that We took this guy and multiplied by this And we end up getting this Which is an x squared And what this is is a quadratic function This is no longer a line What this graphs Is parabolas their curves Okay Now we've done completing the square to be able to graph this line Find the Vertex and find points the x intercepts and the y intercept to Graph it right. We're just going to do it with the table of values I want you to see what it looks like when you multiply two lines And you end up getting a curve Right only in mathematics Right Not really only in mathematics because this is real life There's systems that follow this principle, right? Well, let's see what happens now At these points These are the x intercepts Because all you do is You ask yourself Hey, when does this line y2 Cross the x-axis It crosses the x-axis y zero. So if you put in zero here you bring that guy over So this is negative two Over here If you set y is equal to zero for line y1 You get zero here bring the three over three divide by two is one and a half, right? So this guy here is Three over two the x and the y would be zero and the y is zero right I have to hop off. I hope you have a fantastic video teacher talk to everyone You too twitching Jason and we're doing a couple of live streams this weekend if you're up for it We're going to do current events tomorrow and education sunday, I think so Let's find out what happens here You show me fundamental factoring cases that I don't understand Can be I hope I hope that's making sense for you Okay, now what happens is at these points The y is zero So what happens is this function also crosses those points, but let's just do a table of values try to figure out Find some more points on this what time are saturday and sunday streams tomorrow streams at 9am my time Uh, this one was one at 1 p.m. So four hours earlier, right 10 11 12, yeah four hours earlier, right? And on sunday, we're doing one p.m. Again, okay, and the sunday is education tomorrow's current events So let's just make a table of values y sorry x and y Let's plug in values for x and find out what the y is Let's plug in x is equal to negative two just to convince herself that this function is going to go through that point as well Right, if you plug in x is equal to negative two here, you're going to get two times negative two squared Minus negative two here. Let me make this a little bit more room. So you see you see it better Right as big as possible. Let's do x Here and y here and give us plenty of room on this side So negative two we're going to plug in here Two times negative two squared minus two minus six Negative two squared is four four times two is eight Eight minus two is six six minus six is zero So negative two and zero This is also a point for this function Let's plug in two three over two When x is three over two Two times three over two squared minus three over two minus six Three over two squared is nine over four You can explain later the exercise because I do not understand anything You'll see what it looks like once we graph it. I hope It makes sense a little bit. It really depends pat How far deep uh, how deep you are in your math education if you've already dealt with quadriacs or not or even lines, right? So this becomes two times nine over four Minus two three over two minus six That kills that down to two. So this is nine over two minus three over two Minus six over one common denominator is two. So this becomes two and the top becomes 12 I'm doing a lot of this metal, right? So we don't run up space Hey, this doesn't equal zero. What's going on? I made a mistake somewhere Three over two is a three over two That's the three over two three two Yeah, three over two three over two nine over four two nine over two three over two 12 wait a second What's going on? Oh because this is a plus my bad plus plus plus Right, so that's 12 over two minus 12 over two. That's zero as well So this point is on this graph as well Water from Pointer seats You don't want to drink that Hey, dude, have you watched new New it movie? It is like clown legs No I watch if you want to watch a fantastic movie watch Dave Chappelle's Block party. I watched it again a couple of nights ago. Okay. Watch Dave Chappelle's block party You should only find mental factor in cases that I don't understand it can't be Hey, that's the same one Same comment. I can show you how to factor later. We've put a lot of videos on factoring if you go cheecho factoring You'll find tons of videos up, right? Now we know this graph goes through here and goes through here. Let's find out What the graph looks like between these two points? So let's plug in x is equal to zero Okay, if you plug in x is equal to zero here I'm going to erase all of these because we found out what they were. We don't need to keep the work up, right? So this is zero This is zero Let's plug in x is equal to zero and find out what the y is If you plug in x is equal to zero this becomes zero that becomes zero that's negative six So when x is zero y is negative six one two three four five six Wow, what? point point point Okay You melted in your bed Well, that point's there. What's going on? Let's plug in another point to see because that's what you do When you find a new function you have to plug in points just to see how a function behaves Let's plug in x is equal to three and see what happens if x is equal to three Three squared. So this becomes two times three squared plus three minus six Three squared is nine nine times two is 18 18 plus three is 21 21 minus six is 15 So when x is three y is 15 like we're way up here right Now if you keep on plugging in numbers plug in negative one sure let's plug in the x is equal to negative one Okay, let's give us a little bit of space. So we're not So clumped up. This is two I'm gonna put a bracket here. So it doesn't interfere when x is negative one two times negative one squared plus negative one minus six negative one squared is one One times two is two two minus one Is negative one negative one minus six is negative seven So when you're at negative one that's negative seven If you start plugging in numbers close to that you're going to get closer to here So the graph of this is basically going to look like We could find the vertex the lowest point you just take this and not add them together divide by two So that would be Two negative four negative a half. So it comes here So basically what you're going to end up getting if you start plugging in numbers You're going to start getting things like this and this guy goes out. So our new function This function here Wide five is going to look like this. Should we do this in red?  That's a quadratic As soon as this happens Mathematicians would have gone initially first person doing this would have gone. Whoa. What's going on? Right and just imagine because mathematics allows you to analyze anything in depth Right, you could take this thing apart We didn't take it apart.  The laws of math are indeed interesting to visualize. Yeah right and Once you get this You can start Taking this function and multiplying it by a line So you could come up with a new function after you spend some time Looking at quadratics. You could come up with a new function let's call it y6 Right where you take y5 and multiply it by y1 Take this and multiply that what are you gonna get?  It does another turn right So that's how the mathematics grows for us to understand things. We're More complicated functions if you're able to break them down into the prime factors, right prime function factors You can begin to understand how that system works Okay, and for those of you that are interested quadratic functions They come into play in the real world in business where you're trying to maximize revenue In kinematics physics where you're looking at projectiles, right When you throw something if I throw this guy This follows a parabola the parabola is upside down, okay That's what quadratics are quadratics at the beginning in beginning phases And the introductory phase of learning You have to have an appreciation that all they are are really just two lines Multiply together to give you a curve and the reason that you get a curve by the way is this Let's bring up the green I'm going to make this thing look pretty messy right now Don't take your eyes off the board Break this thing down into three segments, right one of them being here One of them being between The two x-intercepts and the other one being on this side The reason that this multiplying two lines does a curve is because in here in this side why one Was positive And why two was positive you're above the x-axis, right Well, if you multiply a positive and a positive you get a positive You're in the positive y-corner y Above the x-axis In this area Why one is negative is below the x-axis, but why two is still positive If you multiply a negative with a positive You end up getting a negative so this guy Between these two points For y five is below the x-axis. It's negative on this side Why one is negative y two is negative If you're multiplying negative and a negative you get a positive Then it's y five is above the x-axis again. So it doesn't round about and comes back up again Okay, that's where the signs Come into play. I think this is pretty cool I think this is fantastic I think this is amazing Blew me away many moons ago when I first looked at it in this light Right, and I really didn't look at it in this light until I started teaching it Right, because it never really was the dominant thing that I had in mind when I was dealing with quadratics I only started looking at it this light when My students started asking me questions that I didn't have the answers for so I had to come up with Answers on my own to satisfy their curiosity and I found that this Satisfied their curiosity Right Now, how did we get here what we got here through Taking two functions two lines adding them Subtracting them And then doing other operations such as multiplying them, right? Well, what other operation do we have we've got division Let's divide two lines and see what happens Let's divide line one and line two And see what happens and that's going to link us up to infinity Okay, I'm going to take some of this down. I'm going to take most of this down after have a sip of tea Okay, I'm a little perched That took us about an hour and a few minutes to go through that And I brought out some tahini for me as a snack This one's with maple syrup Sesame seeds and maple syrup sesame tahini sauce and maple syrup, right? So sweet full of goodness highly recommend As a healthy snack Let's rewrite these two lines 2x minus 3x plus 2 2x minus 3 x plus 2 Then we're going to take the rest of this down all of it Maple syrup tastes amazing It's sweet and It's like candy In Canada one thing that happens in the winter You can go to some markets farmers markets and stuff like this and they have a block of ice Okay, and they have maple syrup and what they do is they pour maple syrup on the block of ice And it starts getting hard sort of It's malleable, but it starts getting hard So they mess around with it and they make you a candy and you get a maple syrup candy in the winter and you eat that It's phenomenal highly recommend Canadians will appreciate how fantastic that is And maple syrup has a lot of minerals and a lot of goodness in it Very good for you very good for you within reason, of course, right? Let's assume So what we've done with these two lines We've added them we subtracted them we multiplied them What are we going to do now? We're going to divide them Let's divide We're going to take this guy and divide it by that guy So we're going to go our new function y3 Is 2x minus 3 divided by x plus 2 I'm going to graph this Now keep in mind That was a line and that was a line a line and a line Right, I think y1 went like this and y2 goes like this All right, should we put them on there Let's just stay with this one Ah, no, let's put them on let's put them on very lightly Okay, here's line one negative three one two three So here's our first point the y just have and two over one one two over one So here's line one Let's draw line two line two is two And then up one over one here's line two Here's line two y2 Let me move y1 up So it doesn't interfere with our line Here we'll put y2 here Or sorry y1 here My line curves a little bit. It's not supposed to be a curve. It's supposed to be a straight line Let's do it this way so it's not confusing Y1 hopefully that's straighter Okay curves a little bit up there, but okay, let's make it straight Let's make this thing straight. Let's see this Okay Now let's figure out what this line looks like. I'm going to graph this guy Now when you're graphing these things these are called rational functions Okay, because it's one polynomial divided by another polynomial. Okay, polynomials are basically smooth functions, right? One thing you got to do with these things There's one thing you cannot do in mathematics and that one thing is divided by zero Okay, the limitation of mathematics Is no dividing by zero Alex, how are you doing? Welcome to another stream Right, we cannot divide by zero in mathematics. That is a restriction that we have So what we end up doing is whenever we get a function any type of function We always look for the restrictions What can't we do For this system because a function represents a system Right, so for this system we go, what are the restrictions? The restriction for this system is the denominator cannot equal zero Right, so you take whatever is in the denominator and you go x plus two cannot equal zero Which means x cannot equal negative two For this system x cannot equal negative two One two negative two And what we end up getting is i'm going to do this in red This becomes a vertical asymptote and an asymptote is A boundary that you cannot A boundary that you cannot touch Go through Period you can't touch it or go through it This line whatever this function is doing If it approaches it It either needs to go up along it getting closer and closer down Getting closer and closer or it stops it can't Touch it or go through it. It can appear on the other side, but it can't go through it, right? So We have a limitation a restriction. Okay, that helps us out a little bit Now there's another restriction when it comes to rational functions like this And the law says this here's let me write down the rules for this if you have a function A x the power of n plus whatever divided by b x the power of n plus whatever Okay, order from the highest degree down, right? This is an m This is an n Okay, that's a rational function. It's just one polynomial on top of another polynomial then If the power up top is bigger than the power on the bottom, there is no horizontal asymptote If the power in the bottom is bigger than the power up top than the horizontal asymptote is That y is equal to zero If the power up top is the same as the power in the bottom Then the horizontal asymptote because this was a vertical horizontal asymptote is a divided by b so horizontal horizontal Asymptote is equal to a divided by b and in this case is going to be y that's horizontal asymptote The horizontal asymptote Is a divided by b which is 2 over 1 which is just going to be 2. So we have a horizontal asymptote at y is equal to 2 So here's a horizontal asymptote So we got now four quadrants That are function can appear It can be here It can be here It can be here It can be here Now if it appears here, it won't appear there because it won't be a function of the y's And if it appears here can't be here if it appears here can't be here and vice versa, right? So all we have to do now is find points for this function to be able to graph it First point we look for is the y-intercept as long as the asymptotes don't go through the y-intercept, right? So let's find the y-intercept Let's do it here y-int To find the y-int Set x is equal to zero Okay, so this was the first thing we did. Here's the second thing we did. Here's the third thing we're doing You follow this thing What you do there's certain points you follow, right? What's that?  What you need to do is learn a little mathematics. Let's toilet seat water more mathematics I just did I just wrapped it for you If you want to watch rap brother go see david schipals block party or See david schipals block party came on 2005 fantastic Listen to the rhymes of dead presses dropping on you. Okay, or most effort time to go in, right? I look like a wise old man Don't be fooled by looks Y-intercept set x is equal to zero. I might not be a wise old man. I might just be a trickster right Set x is equal to zero So y3 when x is equal to zero for this function becomes two times zero minus three divided by Zero plus two two times zero zero minus three is negative three divided by two. So when x is zero y is negative three over two zero and negative three over two When x is zero y is negative three over two is negative one and a half Now if you learn how to graph these functions, you know what this function is going to do This function is going to look like this Now i'm going to approximate it because what you should do is find a couple more points along here Well, we can let's find another point. So we know the function goes through here. So we know it doesn't appear above this All right, let's find what Let's do a table again What y is equal to when x is equal to one When x is one y is going to be two times one minus three One plus two So that's going to be two two times one is two minus three is negative one over three When y is one or sorry when x is one y is negative third So the graph of this is going to look like this Because as you approach an asymptote The line can't touch it Or cross it. So it acts like a magnet and keeps on pushing it away. This thing gets closer and closer I thought it was great in one of your earliest videos when you put it on mathematics by most that's very fun and great so yeah, yeah, and that was uh Unfortunately, I put that on And for a while that video was the I think was the real number seven of the first videos I ever did and that album was amazing Most death and taliqo el doing I think that was from black on both sides It goes to the mathematics It's fantastic a lot of depth in that whole album right, but unfortunately you got copyright hit for a while the sound was gone and then now it's back and The video's been jacked by rc where was the copyrights to it, right, but I've kept it up, right? I had a lot of I cut a lot of my mathematics to a lot of hip-hop Yeah, black on both sides. Fantastic album. What a fantastic album, right? So this part looks like that So we know the graph is not going to appear there and this links up with infinity. We're talking about so what happens is As x gets bigger and bigger Why approaches to but never hits to right so it goes like this For ever and ever As x approaches negative two from the positive side from above negative two Y gets smaller and smaller and smaller and smaller to negative infinity Over here y approaches to over here y approaches negative infinity Let's see what happens To the y when we're on this side Of the asymptote and all you really need to do is just find one point Because the one point you find is either going to be in this quadrant Or in this quadrant Wherever it is if in this this quadrant the graph is going to do this if it's here the graph is going to be back So let's plug in x is equal to negative three So that's going to be two times negative three minus three divided by negative three plus two negative three times two Is negative six minus three is negative nine So this is going to be negative nine divided by negative one, which is nine So when y what x is negative three y is nine Right, so it's like way up here So the graph of this I hope so Yep, so the graph is going to look like this And this asymptote is going higher and higher So we just ended up graphing a rational function That looks like this right and Where did we get this function? We got this function by taking a line And dividing it by another line Taking this line and dividing it by that line. So we took two lines Out of them all that did was shift the line We took two lines subtracted them all that did was shift the line We took two lines and multiplied them and that created a parabola And we took two lines and divided them and that created a rational function that has asymptotes restrictions right infinities crazy Absolutely powerful, and that's how mathematics has come to be We start off with some basic concepts for us. It is industry subtraction multiplication division We learn what it means to graph a line And from there we're here within two steps. We're here really and we have to understand These types of systems and these are what you graph in grade 12 And grade 11 sometimes if you're lucky in my part in the world in other parts of the world You learn about these things much much Okay, that's one thing I wanted to do I wanted to For this one because the question came up regarding quadribes. So I wanted to Give a starting point for you build it up to the quadratics and as well expanding into the into the radicals and stuff Okay, I hope that makes sense I you know, I skipped over some minor concepts and some major concepts, but this is basically the Flow of logic that we're following when it comes to graphing these types of functions fun fun fun That was a nice little lesson, I think That was good What are we at? Oh, we did an hour and a half. That's good. That's good I actually should have scheduled this Strain for about an hour and a half hour 45 minutes or so I have a student that I got to go see after this like speedy bonzala style But it was fun to do. I really tried to make sure I was able to get this on here Okay, I hope that's okay with everyone. I hope that helps you out if you're looking for Sort of intro to quadribes and you can do with functions and linear functions and how it's all related Dragon safety show. What is the next comic stream? Comic stream I have to think about this. I got just to let you know where I am just a little update. I'm gonna put out an update video Um, but I was able to I lost a harder my main editing hard drive. So I transferred back things up restored some stuff Got on to the other internal Hard drive that I asked I'm gonna start editing on there. So we're doing a couple of live streams This weekend we're doing current events tomorrow. We're doing Education on Sunday talking about your education system since school started I want people to get a feel for And what I think about the education system and how they can optimize it, right for themselves I have a couple of videos. I need to shoot one of them is A review the reason I'm mentioning block party as well because I rewatched it because I'm almost finished Thelonia the Thelonious monk graphic novel that I've been reading that have been looping Thelonious monk for last over the summer for the last three months. I've been looping it phenomenal Really brilliant brilliant brilliant stuff. So I want to do a comic book video where I'm giving a review of Monk, which is basically Thelonious Monk Graphic novel on Thelonious Monk. So that's going to be a comic book video. Okay Genius pro high teacher life Nice to see some math from twitch. Very nice. Very nice indeed very nice indeed. We love doing these, right? We're going to do a lot more of these And then I'm going to make a quick video of making If all the editing goes well, by the way, I haven't done one round of editing yet If my computer doesn't crap out if everything works out fine all the Fields are filled in property and stuff like this the next video I'm going to put out is making just a quick little video It's not going to be live stream just a quick video of making cornelian cherry liqueur Okay, because I wouldn't pick more cornelian cherries So I'm going to make a cornelian cherry video Okay, nice. I just saw Monk in the shelter dude If you like graphic novels biographies And if you know his music and you have to listen to his music to have a full appreciation of what the graphic novel is like Read that graphic novel. The art is amazing. Shall I show you guys a little bit? Can you do a video dedicated to the medicinal cannabis industry in the US? I I know brother. I mean I want I plan on Doing something like that. There's a whole Uh video series that I've planned on making regarding the mathematics of prohibition Okay, and that was my plan from 2010 to put that thing together, right and everything's been wrote and that that time Canada hadn't legalized A lot of states hadn't legalized like it was legalization wasn't going on the table, right? Some people were pushing it, but Nowhere to be found, right? I plan on doing a whole series of mathematics on the mathematics of prohibition Okay, um, I gotta pull the data But we can definitely do we can talk about it for sure Okay, uh, but regarding Monk. It's absolutely brilliant graphic novel. The artwork is amazing. Let me go grab it I'm going to show you guys some pages Here's the graphic novel, right? I'm going to do a video on this Give you guys a review. You're getting a little bit of a teaser Yeah Really, so here's the first few pages, right? Very simple and then Ah, um, yeah, and it's and it's the nonious just dancing That's what I'm talking about. Yeah Keep that temple max Tubes are hot beautiful The horns charlie is nailing it and the bass is walking just right Johnny man, this cat's smoking. Wow the music Beautiful just pulls you in It's happening. It's still alive. I am still alive And I still remember my name beautiful beautiful beautiful The nonious sphere That's the intro to this right I'm I'm here. I'm almost finished it, right? That dude it is beautiful. It is beautiful. Let me find you like And there's so many different musicians in this Like they talk about some musicians in this and uh, he's jamming with some of the greats and Like I don't know how accurate this stuff is All right, but it's trippy It's beautiful man And there's like what do you call it? There's Rothschilds in this like I didn't know like there's meaning like I can't even show you this like this is just Bob Emily Really just beautiful man. Just beautiful. I think you know what hopefully in the video I'll try to remember to pick out some pages right and show you guys Like look at them It's a As a comic book lover. This was a must. This is one of the best graphic novels I've read in this genre, right? Biographies the geography I guess And I don't uh, I'm sure this is I don't know Mugs history and stuff. So there's a video I need to make for that and then Odds are I'm gonna make a video giving a little update and a little intro And because I lost the hard drive and stuff like this If you remember last year we did a whole Weekend of monopoly live streaming monopoly games, right? There's 17 videos live streams Games that I ended up uploading to Bitchute and I did segments Like 10 minute or five minute segments of them all and put them all together and loaded that on youtube Now all the live streams I didn't load on youtube at the time because youtube was going through some changes and You know black marking, you know nailing people who are uploading from twitch and stuff like this So I didn't load them on youtube But I've already loaded them on youtube. They're all private And once I do the intro to the monopoly and do a little update For about a week to 10 days. I'm just going to release All the live streams we did on last year the monopoly games that we played. Okay, so I got for the last month. I have a few things lined up. Oh, yeah, there's a video I need to do as well I'm talking about physics textbooks. So there's three videos I plan on making short videos one of them is a review of this another one is making Courtney and cherry liquor another one is talking about physics textbooks because someone's been Reminding me that I've promised to do this. So I definitely want to do it in the next couple of weeks Okay, so that's what I got lined up if all goes well If it doesn't go well, I'm going to some more comic books to be able to raise more money to upgrade my system We'll see what happens, right? You're going to do a bill Hicks breaks soon. It seems like you're going strong. I know brother I would need to do bill Hicks breaks for a while, but Computer crashing the hard drive crashing sort of said, okay, no bill Hicks breaks for you chichu I keep on going hard And I enjoy doing this right, but I do need a sort of bill Hicks breaks coming coming up soon It'll probably be during the time when I'm uploading the live streams Streams My purpose that you to explain how multiple computers can work together to find prime numbers It's an unanswered question. I made a lot of time and go to some professors And I didn't find anything useful on the web. You know what genius pro I think I haven't looked too far into deep into this other than blockchain technology and what From what I understand with cryptocurrencies and blockchain multiple computers are working to solve Problems mathematical problems, right and the computer that solves it gets the tokens and stuff like this, right? But a lot of that stuff is related to prime numbers From what I understand anyway So One place you can you probably be able to get the answers for this is look into how cryptocurrencies and blockchain technology works I think anyway, we should be there Something should be there Anyway, that's that's a quick little update for you guys if you want to know what i'm doing in the background and where i'm going um, and then once we get into that There's a whole bunch of math stuff I got lined up to do a series But I have to make sure the editing stuff is working fine for me to get into the making of Set of math videos that I want to make Because I don't want to shoot them For it not to work, right and then once that's done We're going to get back into a comic book readings. There's a whole bunch of comic books. I don't want to read So I will get into that as well I know a lot on the plate a lot on the plate man, but loving every every every every minute of it, right I wish I could freeze time and just do everything, but then it wouldn't be life right part of the beauty of life is Having a lot to do and a lot of great things to do and not finding the time to do all the great things That you want to do that way you're always left wanting, right and that keeps the spice of life going, right? Maybe it's just uh It's just a way to trick your mind to enjoy life as much as possible, but for me it works for me it works Okay gang, I think we're going to call the stream there What I'd like to do is get ready to go teach my student And I do have to set up the stuff later on tonight for tomorrow's live stream that we're going to do regarding current events in nine a.m. my time and um Um Sunday we're going to do a live stream on education just just discussion So if you have any questions regarding education Drop by on sunday if you have any questions regarding current events, what's going on? Going on tomorrow 9 a.m. And on sunday 1 p.m. Aside from that, thanks for being here gang. Uh mask of raven. Thank you very much For the help see you tomorrow. Hopefully hopefully mask of raven. I hope you guys have a fantastic weekend if you can't make it And um, I'll try to keep you guys posted as to what I'm doing in the background Okay, uh, that's it for now gang. I'll see you guys in the next video. My Anna Is any thanks for the stream and enjoyed it great great glad you enjoyed my math matters How could you not enjoy my life? It's amazing. It's amazing. It's a similar unanswered question about random numbers and radar algorithm Could uh, computation is not so well explained in practical terms on me. I know the theory but not the concrete fast I'll look into it. I'll try to look into it. I'll try to look into it When I free up some time my genius


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from body armor to life rafts, food rations to flares. The mission of the 6th Operation Support Squadrons Aircrew Flight Equipment Team is to ensure that all essential and life-saving equipment is present and ready for use each time McDale's aircrews step into a KC-135 Stratotanker. So the base mission is obviously deterrence. We help with that by the equipment that we put on the aircrafts. If it wasn't for the equipment that's out there the aircrew members wouldn't be able to fly. McDale's AFV airmen function as a lifeline to aircrews by maintaining items such as flight helmets, oxygen masks, survival equipment, rafts, harnesses and more. Each day AFV airmen step up to the challenge to ensure the safety of McDale's aircrews. If their mask doesn't work, if their life raft doesn't work, if their body armor has flaws in it or their survival vests or missing items that could be detrimental to their survival in a situation. We are the insurance policy that we hope they don't have to cash in on, but if they do we are strong in our ideals and our experience that our equipment is going to work and they're going to come back home. Through constant training and exercising McDale's AFV airmen do their part so crews can fly with confidence as they deliver unmatched air refueling support across the globe.


America is America today because of the pioneers who had the stage, the foundation for their country. And those countries they love, their country very much. So because they love their country very much, that has helped them to develop before they are today. But most of us as Africans, the moment we get something, we feel we don't belong to our community. Then we go somewhere where people have already deserved to be there earlier and to be part of that. So we have a long way to go. They now had to set aside a certain amount of money to fly myself from Africa to Europe. Was it your first time? It was my first time to go to Europe. So there in Europe I spent almost 45 days just to see what those guys are doing. Then I discovered that they are very successful because they add value to whatever they produce before they sell. So I said, well, we have fallacies in Malawi. We have a lot of low material in Malawi. Why can't I buy machinery so that they can be adding value to whatever I produce before I take it to the market? So the first thing I did was to buy a machine for processing timber. So after buying that machine, I did that business for some time. Then I said, well, I have managed to help cut down the trees. How can I help to replace them? So I had to find a way of replacing the trees which I had managed to cut it down. Then I left that business and went into other value-addition businesses. While I was doing that, I extended my family business in other areas. Then I have enough land that now I can do whatever I want to do. How many acres of farmland do you have now? Well, I have many. I have many acres. Being a farmer, while I was just a kid in land after land after land, then now I'm giving back because I'm bringing students from universities to come to my place and help them to build their capacities so that if they are done, then they have to go home with something so that they can start their own businesses. They call you an industrialist? Yeah, well, I'm everything. I'm a farmer. I'm an industrialist. Well, I do everything. So you have industries around that you can take with you to check it out? Yeah, well, I have a dairy company. I have a rice processing plant. Well, I'm doing anything possible to create jobs and train people so that they can start on their own. My next question is, how many jobs have you created so far? How many people? Well, I don't know how many people. I have some people working at the hospital. I have some people working at some processing plants. I'm doing anything possible to help people stand on their feet. Your whole goal is to make impacting people's lives? Yeah, well, I have already explained about my background. So I don't want people to go through the same way I went. So I have, at least to find a way, how can I help people to be successful in their lives? In my Bible, Matthew chapter 7 verse 12, they say, if you want people to respect you or if you need anything to do good to you, you have to start that yourself. Then people will fall. So now what I'm trying to do is, how can I come up with a platform where the young generation can start their business? How can I help those who don't have ability to do ABCD? So now that's my business. Where is this place? That's my first home. Your first home? That's when you left your parent house? Yeah, well, from the time when I left my parents' house, the first building was like that one. That one? That was my first building from the time when I left my father's home. So from there, after I was successful in my businesses and my operations, then that's when I came to build this one. At the same time, I built that white house, so it has just been renovated, but I built it for my father. Yeah. So after building that home, then I left this place. The reason was my father, he was very generous. All the money which he was getting was just distributing to the needy. So after I had started my business as a young man, I was living with him. So he would simply ask me, how much do we have in the bank? An amount, then he would just go and get half. So within two weeks all the money has been distributed to so many people. Then the other two or three weeks, he would say, what do we have?  So within three months, we could learn out of money. By just giving to people? Just giving to the people who were asking him for help. So after learning what he was doing, then I said, well, I think I need to leave this place and go somewhere and rebuild myself so that I can withstand this situation. So I left this place, I went to in quarter quarter, which is about three, four hours from here. So I stayed in quarter quarter for a number of years until I was strong enough economically that I could stand within this situation.  So from 1991, then by then I had the tracks, I had my business doing very well. So instead of coming to the village, I had to stop at my DC trading center. Then at my DC, I became so successful that I decided to leave my DC for the capital, Sitaligonga. So I've been in Ligonga for many years. Now that's when I'm saying, OK, where do I come from? Then I have to go back now to square one. So now that building is representing this one. You came back to your roots. And you transformed the whole community. That's why I'm saying, I've come up with a plan. How can we make everybody prosperous in this area? So I'm targeting now 20 kilometers radius from this area and I have to involve everybody to transform. What are the things that you've done so far in the village since you came back? Well, I have managed to build roads. My aim is to develop this area. And when I'm done with this area, I think I will help other areas where I can. So I've managed to build all of these roads here. All the roads? Yeah, in this area. Does it mean it was a path? It was just a small path. So I had to grade them and grave them. And some small bridges. I think when we're going this side, there's a sizable river. I even built a 43-meter bridge. So I had to use the wood to build it. But big tracks used that. And this road is connecting the other road to this side. So now people have access to do business and other things using this road. You remember when you used to go to school without shoes? Yeah. So this was the path that you still use? Yeah, it was a small path. Were you not scared working in the bush those times? Well, since people were very friendly in those days, we were just afraid of animals. But the people were just very generous. So even bringing a car here, it was a challenge. Sometimes we could leave a car somewhere and walk five kilometers to our home. After we had already bought our own car. So I had to work on these things in order to improve this area. I've managed to build a police station somewhere. And now I'm building a second one here. I've managed to acquire money to build the school of agriculture. I've built this school in six months. What do you mean? You built the school in six months? Yeah. How? Well, I had built so many builders, so many laborers, and I had assigned them that if you build this, this is what I'll give you. So many people came. They started working and my tracks were busy holding bricks, sand, whatever. Wow. Yeah. You built the school with the community? Yeah, I built this school. Why the name School of Agriculture? For family independence? That people were dying of hunger in 2001. So I said, well, we have water. We have good climate. We have good land. Why can't we start using the resources which God has given us to solve our problems? So that's why I came up with an idea of building a school of agriculture. That's your father's name? Yeah, that's my father's name. And with Blake? Yeah, well, he's the one who had donated the money. Oh, okay. Yeah. I had asked him that I have this dream. So I have to build a school which will just be teaching people. Then he said, okay, I will assist you. So he gave me $250,000. So I had to use my blood to use that money to build the school. How many students have passed through this school? Each year, it's about 78 students. So, you know, we take families. So when I was saying 35 to 40, it means those were families. But since each one of them is a student, then you multiply by two. We come up with eight. So since 2006 to date, so many of you have gone through here. And their lives have changed. They have enough food, and they have built good homes. And some of them have even managed to buy cars. So this is a university? Well, it's something like a college. Yeah, where we just bring in at least one in the family should know how to light. Yeah. So just one person in the family needs to learn how to write. The rest is just oral. Does it mean there's no qualification to attend to this school? Well, here, you have to know how to write. That's it? Yeah, that's it. And what about the tuition? Well, what we do here is because we have people who have been helping the school with some funds. Then he comes in. We send tracts to collect his family and goods to this school. So when he comes here, we provide a home with electricity and water. We provide a fertilizer, seeds, whatever. Then he spends the whole year here. By the end of the year, after harvest, then he's asking just to leave two bags of rice at the tuition fee. You provide everything? We provide everything.  But for him to be proud that he had paid something, then he has to give it back to the banks. I want to see the accommodation you've created for them. Is it in the same school area? We have a dormitory over there. We have those small houses you have seen all over. Those are the houses for the farmers. So it means even the land, you provide land for them? Everything you provide for them, in order for them to learn. And the same thing is happening at the Santa. I told the people that our economy is agro-based economy. So being agro-based economy, it means those guys who are investors for agriculture, they are the guys who are supposed to be in forefront to develop the systems in the country.  So I'm saying, no, you guys come here. I will find a loan to support you to produce enough chickens, enough eggs, potatoes, tomatoes, whatsoever for one year. Then after one year, then we'll see how much money you have made. Then you give back all the expenses so that you can give back to the bank where you get the money. Then 70% of the process, the student has to take it home so that he can duplicate what he was doing in my campus. That way, now he will be creating jobs for each people. So in Twix, 55 students from University have come. They are at Santa. So now I'm saying, you guys, you can see that we have hunger because the rains were too heavy and the fertilizer was washed away. So what you should be seeing is that the people are going to suffer from the hunger which is looming. So you should not just be looking at the negative part of hunger. It is an opportunity for you to grow sweet potatoes, to grow some maize on irrigation so that by the time when people will have nothing, then you have a broader way of collecting so much money from the people and provide them with the food. Then you guys, from nothing, you are going to be something. They got nursery school in here.  So definitely, indeed it's a nursery school. But I don't know if the kids are also learning about agriculture in here. Are the kids learning how to farm? Yeah, well, they just see their parents but the kids are taught what they are supposed to be taught. But as we bring the whole family, the mother and the father, they are in class, so the children learn here so that they can also learn what they are supposed to do. He has made sure that no family will be left out. So even if you have kids, they won't come here without going to school. Believe me, this is the best story I've ever done. Like I'm so blown away. I was not ready for this story. But what I keep hearing, I've seen they are using electricity and water. Do they pay for that too? No, they don't pay. You don't love that? Well, the school of agriculture, because of what we have been doing, we have some people who are sponsoring for the school. But I did everything. And now I'm looking at how can I empower this area economically. Because I've tried and many, many students, many, many students who had no fees in this area, they have been funded for more than 10 years. So we have many who have gone to university, to secondary school. Well, over a thousand students have been provided with fees from all over the region. You are also building a hotel with a mermaid lake right in front, which will attract so many people coming in here. Exactly. And I think I also have to come up with the fountains, water fountains, and also planning of having a lot of activities in this area so that the people in the long way and the other areas during weekends are able to be coming here and spend their time. What is the idea behind this hotel? Well, the idea is we have people with money in town and the other areas of the world. But how can they bring their money here? So that's why I said I think I have to put up something which should be very attractive so that when people come with money, our local people now can manage to sell their oranges. They have bananas, they have potatoes, whatever they produce. Then by the time these people will be living in this area, back to their village, at least a small amount of money, now our people will get it. Trust me, where the hotel is, if you tell me that, okay, come all the way from the long way to this place, I'll tell you I'm not coming. But when you get here, what you see, the air you breathe in, the surrounding, I mean, you won't believe that this is sitting in a village. This is the best place for you to stay. It's called... Calipano. Calipano. Yeah, Calipano means it is here. So you even built churches, different denominations or... Well, yeah.  No. And you built a Catholic church? Well, I'm building anything in this area. I want this area to be a model. You know, I suffered a lot. So I had gone through such a difficult life that it's difficult to explain. So I should not let others go through the same. You've built a great legacy. Even though you're saying that you've done nothing, what I'm seeing, this is a great legacy, that it will forever remain so that can not come. Well, yeah, it seems to be like that. But you know, it takes one man to change the area. So I feel, if I could see this road paved, if I could see many graduates coming from this area, then when I'm gone, then I see that I have left some people who are taking my place and go ahead with me when I have left. So that's how I feel. Can you please adopt me? Well, I think what you are learning from me today will help you be like me. I love it. Thank you. Inside the same village, he has built a maize mill for the community for free. So the whole community comes in here to mill their maize. But even him, when he was growing up, he has to walk for a very long distance to go mill his maize. But this is what he has done for the villagers. He's touching a lot of lives in here, man. There was nothing like this in here. He built it for them. I have traveled over 20 countries in Africa, but I've never seen anyone who eats maize. That's a maize. That's not a rat. You know, in Ghana we eat rats, the bush one. Yeah, this is the bush one. This is the bush one? Yeah. This is from the bush? From the bush. They're too small. Yeah, well, from the bush they're too small, but the rats are big. Huh? Because the rats have all the food they need. So bush ones, they don't have enough food. They don't grow maize. So, did you roast this? Yeah, it's roasted. Roasted? Do we eat it? Ah, ah, ah. No, no, no. Not today. Not today. No, no, no. Not today. Ah! No, not today. So you sell it? Yeah. One one? Yes. How much is it? 200. 250? I'm sorry, man. I try everything. Yeah. But I don't want to try this one. I try everything. I don't want to try this one. Yeah, but... Ah! They call it the African Sausage. Yeah, African Sausage. African Sausage? Ah! Ah! You know, African Sausage. Cheese. Where do you find them? In the bush. In the bush? Yeah. Yeah. Cheese, man? Yeah. I'm sorry, man. I eat everything but this one? Yeah. I'm scared. Yeah. Nah! Yeah. Thank you. Yeah. Do you guys want to try it out?