 Let's make sure we're live, and there we go. Hi everyone, this is Gicho. Welcome to my channel and welcome to another live stream. Today is December 10th, 2019, and we're doing a live stream on math. Okay, I'm just gonna pop out the chat here that way that's sitting out. So our stream for today is Drop in Math Tutoring Session for 2019, number nine. So this is the ninth one. The odds are a part of the loss count, but let's assume this is the ninth one that we're doing for this school year. And we did a whole bunch for our last school year, since we started doing live streaming really after a few months. After we got the ball rolling, we started doing math live streams. So we're gonna continue doing these. I'm just making myself available for a couple hours, usually per week. Maybe right now, it's once every 10 days or so. Two to four times a month. Making myself available for you guys, if you need any help for high school mathematics. If I can help you out, I will. And there's a certain number of people that pop in usually, most often during these math streams where, when people ask questions, they do provide answers. Some of the people know math, their mathematics is more powerful than mine. So they have better answers at times for more complicated stuff. Always tilted, how are you doing? Hey man, how are you? Doing good brother, doing good. Always happy to do a little mathematics. Always happy to do a little mathematics. And it's a nice fall day right now. We're sort of middle of the day. We're starting at 12pm by the way. I should be trying to kick these in until later in the evening for people in Canada and the United States to have access to this. But I'm busy with the students at those times usually. So I'll try to maybe sometimes do these on the weekends. Hannah, how are you doing? Hey Chico. Can you show me how to factor in quadratics? Yeah, for sure Hannah. We do top five. How's life? How's life? Dante, what's up brother? How's it going? We're going to get straight right into mathematics. Nice. St. just Germany, how are you? Welcome, welcome. Hope everybody's doing well. Longest night of the year coming up. December 21st. 11 more days. We get the longest night of the year. Cool, right? Very nice, very nice. Good, another mod here. I'm going to learn. Okay, sweet Dante. And by the way Dante, if any time you're overwhelmed just give me a heads up. Say, hey Chico, I just want to chill today. I'll take over, right? I'll make sure I'm at the bottom of the chat. If I see anything going on, we just kill it, right? It works as well. I'm slowly after a year and a bit getting a hang of the twitch rhythm and flow, right? So, and I love it. And it's fantastic, right? St. just Germany, I'm good. Let's talk about factoring. Max Gator, welcome. Why don't you shave your beard? I do at times, sure. And this is a goatee, it's not a full beard. I have had full beards many, many times. There's two full beard videos of me trimming down, right? One of them full on gone and another one converted into this, right? Lonely Piggy, how are you doing? How did the exam go? Hello, hello, I've got amazing news. Past my RCMP entrance exam yesterday didn't do as well as I liked. But the fact remains also. Congrats, congrats, brother. Nice. So you go into basic training now, I guess, right? They changed my seat at my office and now I have a window seat. Upgrade, upgrade. Congrats, top five recents, congrats. Yeah, very nice, very nice. That's a serious step, right? That's a serious hurdle obstacle gone, right? That's a few more steps. There's a few more steps, interviews and whatnot. Oh, okay. The interviews, that's right. I thought maybe they would conduct the interview. Well, I guess it's easier for them, less labor intensive for them to use sort of an automated exam to a certain degree as the first initial filter, right? So usually for large corporations or whatnot, we're our system. If you're trying to get from A to B, there's filters set in place, right? Obstacles. They're not necessarily valid, but because this whole thing is automated, right? They put obstacles in place. One of the first ones, of course, is high school degree, right? If you don't have your high school degree, that first filter, you get knocked off, right? So you play in a video game and you lose on the first level. That sucks, right? Can you give me a shout out? Say my name. Okay, I'm not going to read the whole thing because I don't know what it says, but neat? How you doing? Welcome to our stream, right? What it says, don't. You came to the wrong stream to do trolling on that level because I'm horrendous at reading names. I'm horrendous at pronouncing names, right? So I shortened everything. And we're at the end of it. You try and... It's like... I'm pretty sure it is, brother, right? Even I can do that. These trolls are so weak. I mean, they don't even hang around to get a vibe of the thing to see what's going on. They're just like... I knew someone and a conversation came up once regarding intimacy and stuff like this and we were talking about someone else and that person said he was like a rooster. In and out. These are rooster trolls, right? Oh, missed. Oops. That's funny. Should we do factoring? Hannah, what's factoring? Why are we factoring quadratics or any type of function, really? What quadratics is sort of the first wave, right? For how long will you stay living old? How long, man? I don't know. I'm shooting for 52, right? I'm shooting for 52 trolls throughout the day. They're like... They're calling me old scoundrel. They must be like two years old. Like they're just new to the world, right? Oh, by the way, if they're here, I don't know if they're here or not. We have a video out regarding perspective on life, on mathematics. So I would recommend all these weak trolls, Gicho time. Let me find you a math video we created. Which will explain to you why you, if you're a weak troll, why you might be a weak troll, right? Why there might be better opportunities for you out there. Take a look at this video. It's called, Why the Perception of Time Varies with Age. Okay. Vanessa, I hate to show my daughter got her midterm. Oh yeah, I gotta allow this. Hi Vanessa, how are you doing? Being nice boys and girls, being nice. TBF, you've got an epic great beard. Thank you. How did your dog die? What? Okay, Neat. Neat, you're out, man. I'm gonna ban you. You're out. Gicho banning is like... is like, man, you boobooed, right? You boobooed. Hey Gicho, my daughter, hi Vanessa, how are you doing? My daughter got her midterm report back last week and she dropped from an A to a B. Okay. She's in second grade. Oh, second grade. A, they're grading AB for second grade. The note from her teacher said compound addition problems. Compound addition problems. I don't know what compound addition means. Any advice on how to help her grasp it a little better? Yeah, for sure, Vanessa. She's really smart, but just has a short attention span when it comes to math. First order of business, if someone has a short attention span when it comes to math, feed them the information faster. From my experience, if someone's losing attention and they got a short attention span for math, feed the information to them faster, don't worry too much about the minor nuances, right? Kick them up to a level where they start showing interest, right? And once you got those problems going on, okay, you obviously need the pre-stuff to be able to do this stuff, right? So get them going on these more complicated problems, stuff that they might be interested in. And when they hit an obstacle that they don't know how to do, you kick them back to that specific nuance that they had to learn, teach them that, and right away they get to practice it because it's a hurdle that just overcame, right? And they do it, and they actually see how that connects back to everything else before that. And they also get to use it to connect onto more complicated concepts. That's one way of doing it, right? So keep an eye out for that. That's really important. Don't hold students that are losing attention span in math or anything else for that matter in one spot just because they're having a hard time grasping that one concept or they're getting bored of that one concept, even if they can't do it properly yet all the time, right? As long as they know how to do it two out of four times, just kick them up, right, if they're stuck on that. Preferably you need to get them doing a little bit better than two out of four, 50% of the time getting it correct. But if they continue to use it, they'll improve on it, right? The other one is this. Take a look at these videos we put out. Let me go to our playlist. If you go to your YouTube channel, I have three videos for early childhood education. And let me find them for you. Here we go. There's four videos I put out. How to teach counting. Okay, start off with this one and then... I put this out a month ago. Start off with this one and then follow the rest of these videos. I might have put this in a playlist actually, so let me see if I put it in a playlist. I didn't create an early childhood education playlist yet. I don't think so, okay? But here's the video, first video Vanessa. Take a look at this. And there's... So this one is how to teach counting. And then the next one is how to teach adding. The next one is how to teach multiplication. And the one out of that is the whole thing. Oh yeah, let me give you the whole thing. So it's three videos and it's three videos broken into pieces from this one longer video. So this is the video you want to see. I'll give you my train of thought on how to deal with kids. I usually work with grade, you know, six and up. Five is lowest I go. But depending on where you are in the world, they start teaching mathematics like really early on. Like grade one or two, you're already into adding, multiplying and dividing, right? So if that's the case, these should help you out. Hope that's okay. That's sort of my long winded to get you going on. And if you have any more questions, Vanessa, just drop me a line. Or pop into the stream either today if you get a chance to watch... I don't think you get a chance to watch them, but in the next math stream let me know where your daughter might be having problems and we'll try to deal with it right away, right? Can we time out the guy? Yeah, I banned them boys, sorry. I'm a little Jijo-ban, bog. Have you heard about the equation which some people consider the most mathematically beautiful equation? Because it puts three arithmetic operations and five fundamental... Yeah, it's the... Geez, I don't even know. It takes E1, 0, I and puts them all into one. I can't remember what it is. Hey, Chicho. Hello, Contra. How are you doing? Mask of Raven. Thank you very much for the... Twitch tier one sub. Five emotes shared. Shared reward of five others in chat. Nice. Hey, we got an emote. What is that guy? Haha, ball. Nice. Awesome. Thank you very much. My pleasure, Vanessa. Maybe I'm over-explaining it. I'll go check out the links. She was kind of heartbroken. She's used to straight A's. Yeah, that's the Mask of Raven. That equation is beautiful. It really is beautiful. And Vanessa, I don't know what type of school your daughter is in but if she's getting heartbroken in grade two, keep a close eye out on it. I've seen a lot of parents come up to me. I've had a lot of parents come up to me in either grade eight high school when their kids are entering high school or towards the end of elementary school. And they say, I don't know what happened. My son, my daughter was doing fantastic in math. They loved math. Now they hate it. And then it's extra work for my part anyway to get these kids to love math again. Because the system really grinds them down. What do you like more, algebra or analysis? I like data. I like data. I like algebra just for the sake of meditative. So they're two different beasts. Algebra is the syntax of the language. That's one reason from day one when I started creating math videos. I created something, whole math series, the videos we're producing which is called the language of mathematics, which is more concerned with the syntax of the language, the rules of mathematics, algebra. And my website that I put together, I actually have both websites, languageofmathematics.com and mathandreallife.com. If you punch those in, they take you to Chichou or math and real life. And I created another series called mathandreallife because that's really the analysis of it. So both. Common core math is in the United States literally ruined math for a whole generation and beyond. Because what they did, right? Contra, by the way Hannah, I hope you're okay. I'm factoring, I'm not dealing with it yet. I just want to take care of all that. Right? Yeah, masquerade was horrendous. But contra, they didn't just ruin math for a whole generation. Because what they did, they made more than one generation really, two, three generations illiterate in the language of mathematics. So as soon as you do that, that generation, for the most part, not all of them, but on average, illiterate in the language of mathematics and in Canada as well, right? Illiterate in the language of mathematics. And those generations grow up and have children of their own. Now they don't know math, right? So when their kids come home from school with math questions, that generation doesn't know mathematics. So it's a perpetual thing. It's a very, you know, we're not supposed to talk about politics on these math strings, but it's very typical colonial, imperialist type of maneuver, right? Because when they take over imperial nations, when they take over a land somewhere, the first thing you do, you take out a certain tradition for two to three generations and then future generations are also lost. We can see that happening with the indigenous population in Canada and the United States, right? Destroyed a number of generations and left to rot, right? Now they had to build themselves back up and they're doing a fantastic job doing it. But it takes a tremendous amount of effort to do it, right? So common core math was exactly the strategy used by imperialist nations to take over lands, right? I know it's politics and I apologize, but it is about education, right? I'd say it's more of how the education system works. A lot of math teachers here in Texas are just football coaches who didn't get a degree in mathematics. I sucked at math during high school because of this. Yeah. Snack jubu that smiles back. Snack that smiles back. Snack smiles back. It's not just Texas, it's Canada as well. I used to know some good math teachers 20 years ago. They're gone, right? Very few remain that I interact with anyway and the ones I've interacted with they're horrendous, okay? So in Canada as well, it's not just Texas. I don't know if it's a complete western world, but Canada and the United States, that's exactly what happened. Monkey see the monkey do, right? In Quebec, they implemented the reform in the teaching sector. They changed everything about anything that is, was, teach. It's so now was hard doing the transition because I was in the middle of high school when it happened. It made people who had 30% get 75% brutal. For example, teaching long division throws tons of kids off, even though I, as a math major and math enthusiast, literally never use it, ever at all. Why are we teaching it? I disagree with you there. I like teaching it. I know how to do it. One reason I know how to do it is because I teach mathematics. But it is important because it's the reverse process of multiplication, right? So it's good to complete a loop in my opinion. That's useless and annoying and makes people think math is just computation and being a human algorithm. The way they teach it I agree with you because they give them crazy numbers to divide, right? Forget about that. Give people numbers that you can get into the decimals and stuff like this and leave it at that. They just have to know that it's the reverse of multiplication which is really multiplication of division, right? Which is really just a connection to addition, right? So all three things are important to teach. Yeah, but that's just a part of the system Chico was talking about. Major underfunding of public education Common Core is just a symptom, yeah. What? Common Core is actually good, though. Not that I've seen. It might be now, but when I went to middle school eight years ago, it felt it was not a good system. I've had encounters with kids who have gone through Common Core and brutal, brutal. I've never seen a good argument against it. It was a money pit. I looked at how much money was wasted for this whole process. It's centralization of education and that's a whole branch, whole discussion on its own. The textbooks that they sell are just pure garbage that they put together. It's basically more monopolies given to certain institutions to create textbooks to provide to Common Core which is just garbage, right? If you've never heard a good argument against it you've never talked to anyone that understood it. Big or big brain. Most kids have trouble with math. Instruction is hard. Not necessarily. When you say most kids have trouble with math which kids are we talking about? Are we talking about the kids in Canada in the United States? Or are we talking about kids in Russia? South Korea? Africa? France? UK? South America? Bolivia? Brazil? Venezuela? Kids where? The one thing you have to appreciate is when people say, oh, kids are having a hard time with math if you look at the statistics oh, it's kids in Canada and the United States are having a hard time with math. The ones I've looked at but when I interact with kids from different parts of the world they don't have a problem with math. They love math. They're pretty good at math, right? So it's not the kids it's the system. That's end of story. In Quebec everyone does okay in math. French grammar, that's hard. I've had a fair bit of students from a French immersion that I've taught mathematics to some of them have a hard time with mathematics because they were English raised. The first language was English. They were trying to learn French and they were teaching mathematics in French so they had an in-between language connecting mathematics which is a language on its own to English so they lost some of the stuff in translation. By the way, I got snacks. If you're doing math have a little bit of snacks with you, okay? That's two factor. Hannah, I hope you're still around. French is, I think one of the three hardest languages to write. It's difficult. They try to teach it to me. I took it all the way up to grade 11 through high school. Fenetra. That's supposed to mean I can't even pronounce it. Window, right? Let's do factoring of quadratic functions. So let me give you a little intro and by the way, if there's math questions let us know. Make a little list here that we're going to go over but right now we're going to talk about factoring fenetra. We're going to talk about factoring quadratics. Let me give you a little intro. Factoring quadratics. This thing right here, right? And quadratics are parabolas. When they say quadratics in general this is what we're talking about, right? Something that does this, right? So if you throw a pen it'll do this, right? So that's what we're talking about, right? It's something that does this, right? So if you throw a pen it'll do this, right? So this stuff comes in handy in economics, comes in handy in kinematics, comes in handy in multiple different places, right? I always say that Japanese is in many, many ways easier to learn than French. I've never tried. Okay. So factoring the reason if you're looking and have been popping onto the math streams or if you talk to people who are trying to learn mathematics and whatnot usually one of the places that people have a hard time with there's a few different places that takes people out of the game, right? One of the places that takes people out of the game is factoring quadratics because this is really the first time you're introduced to the concept of factoring. Factoring. So it's not factoring quadratics that takes people out of the game it's factoring that takes people out of the game. The reason that most people are taken out of the game when they encounter factoring quadratics is because they don't understand what factoring really is because it's never really explained properly. Right? Or let me paraphrase that, right? Or say it in a way that's not condescending. I found with students that I work with once they understand what factoring is then they don't have a hard time factoring quadratics because quadratics are just parabolas, right? So what is factoring? Factoring is us looking at a system and breaking it down to its core properties, right? Factoring can be thought of as the same process as factoring an integer or a natural number, right? And if someone's doing factoring quadratics they've already encountered prime numbers factoring natural numbers, right? So consider this. Consider the number 28. Okay. 28. Now one of the things that happens is when you're coming into high school or whatnot or you're looking at the real number set this is called a composite number it's not a prime number and prime numbers are numbers that can only be divided evenly by one and themselves, right? So 28 is made up of other numbers. Okay? So what you can do is break down 28. So take 28 and break it down into things that multiply together to give you 28. If the number is even you can always divide it by 2. So you're going to take 28, divide it by 2 2 times 14 which gives you 28. Right? And this is multiplication between these but we never put it in because we know it's multiplication we're talking about multiplication. Now 2 is a prime number it can only be broken down into one and itself, multiply together to give us 2. So anything that fits that pattern that can only be broken down into one times itself to give itself then we don't break it down. 15 is 2 times 7. Right? So we break this down 2 times 7. Cool. So what we find out is 28 28 is really 2 times 2 times 7. Cool. Useful? Damn right it's useful. It's very very useful. Of us taking something in natural world right? And breaking it down to find out what it's building blocks are right? For example, take water. Okay. Water. So take water. Let's check it out. When I first explained to one of my friends the actual purpose of going from for example that to that rather than just the trick we found it very illuminating. Very illuminating indeed. Indeed. So on the same concept of this number take water. What's water? Water is H2O. Right? H2O. Right? Now back in the day us human beings before we understood what molecules, atoms at a time where we thought everything in the world was made up of 5 elements. Earth, wind, fire, water and wood or soil I don't know what it was. But one of them has always been water. During that period we looked at water and went that's water. We thought water was just water. Nothing made up water. Water was the thing. And then as we evolved and understood more about the world we realized that water is really pure water is really H2O. Cool. What is H2O? Break down H2O. H2O says there is H2, 2 hydrogens and an oxygen. Cool. Right? And 2 hydrogens means hydrogen and a hydrogen. Cool. What's water? It's 2 hydrogens and an oxygen. Cool. Why is this important? Well, what else can you make with this building block? Right? Because if your building block, your core building block is H2O, you have to make. Whatever you make has to have H2O in it. But if you're able to break the stand into prime factors, prime elements, then you can take parts of these and create something else. Right? You could take a 2 from 28 and a 7 from 28 2 times 7 is 14 and multiply it by 5. What do you come up with? Cool. 0, 2, you come up with 70. Oh, that means if we break down 70, it's 7 times 10. 10 is 2 times 5. So it's 2 times 7 times 5. 2 times 7 times. Cool. We just came up with a new number. Right? Guess what? We do the same thing with these things. Right? Guess what? We do the same thing with functions. Right? So on this same concept, we can take any function and try to break it down into core building blocks. Right? Let's start off with one of the easy functions. Let's start off with a quadratic. So it's breaking down the thing called factoring. That's exactly what it's called void. Right? Breaking down the thing is called factoring. It's called breaking it down to see what its core building blocks are. Right? That's it. And a quadratic is just a function that's a parabola that does this. Guess what? We have an infinite number, infinite types of functions. Here's a quadratic. A cubic does this. Power 4 does this. Power 5 can do that. You can have a line. This guy is really one of the core functions we have. Right? You could have a function that does this. Right? There are infinite number types of functions we have. And what we can do is we can factor all of them. Or we can try to factor all of them. And a line is usually considered to be the prime factor, the prime function of a lot of these functions. Okay? So the way we get into factoring for us, the first thing we try to factor is a quadratic. Because a quadratic is a parabola. And a parabola is really two lines multiplied together. Right? So in my part of the world, they teach you the lines in grade 9 if you're lucky, not really. They don't teach you that. If you're lucky, they teach you that in grade 9. But usually in grade 10, they encounter this in my part of the world. In other parts of the world, you probably do this in grade 5. Right? In some parts of the world, you don't even get a chance to do this. Right? Straight line is called a linear function, right? Exactly. Why is this called a linear function? Or the way you can remember is called a linear function. I don't know why it is, but it's called a linear function because it's a line. So consider linear functions to be your prime numbers. If you're breaking down natural numbers. Right? The first thing we're going to do is we're going to look at a quadratic. Right? So let's take a look at a quadratic. Let's take an example of a quadratic function. Now if you've been here, you know there's one quadratic function I like. Over the real number, there are polynomial factors of any degree. For example, x squared, x plus 1, cannot be factored and acts as a sort of a polynomial prime. Exactly. Yeah. Get into that later down the road. Right? It doesn't necessarily have to be a line. Sometimes you can't break things down any further. Right? And those become your prime functions. Right? It's not as simple as prime numbers. Prime functions. Right? So take a look at this. Let's take a quadratic. Let's take this quadratic. I'm going to use f of x. If this is freaking people out think of this as y. Because that's what all it is. Right? So if you want, we can just write it as y. Y is equal to x squared plus 5x plus 6. Okay? So we're given this function over the complex numbers. You can always break it down to linear factors though, which is fun. Can you masquerade it? I haven't they don't teach that anymore complex numbers in high school years so I've totally lost track of my complex number of mathematics. Right? So let's assume you're given this polynomial function. Right? The polynomial is just a smooth function. Quadratics is one of the core base polynomial functions. Right? So let's assume you're given this quadratic function. And it's a quadratic because this thing graphs a parabola. We talked about. We can talk about it further. Right? And we've done a lot of this quadratic, graphing quadratic functions. If you look up Chichot completing the square, you'll see us graphing these guys. But right now, let's assume we were given this function and this function explains some system in our world. Right? And we wanted to break it down. We want to find out if there are any prime functions within this function. Right? What's this thing made from? Right? And this is called a simple trinomial. Right? So what you do with simple trinomials, because there's only one in front of the x-square, you look for two numbers that multiply to give you six and add to give you five. Yeah, in the complex numbers, every polynomial is fully factorable, factorizable into linear factors. Awesome. I got to look further into this one. Right? So if we're trying to factor this quadratic, simple quadratic function, simple trinomial, we look for two numbers that multiply to give you six. Multiply to give you six and add to give you five. Add to give you five. And always remember the sign in front of the number goes with the number. Right? So this is positive six and this is positive five. Okay? Always start off with the multiplication part, because there's less integers. There's a finite number of integers that can multiply to give you this number than add to give you this number. Okay? Or, yeah, integers. So there's a finite number of numbers, integers that can multiply to give you that, but there's an infinite number of integers that can multiply to give you the middle number or add to give you the middle number. So don't start off with the middle number, start off with this number. List all the numbers that multiply to give you six. We got one times six. Negative one times negative six. Two times three. Negative two times negative three. Right? One times six, six. Negative one times negative six, six. Two times three, six. Negative two times negative three, six. Right? So what you do now is, hopefully this is coming out okay for you guys. Now what you do is add these two numbers. One plus six is seven. So that doesn't work. Negative one plus negative six is negative seven, so that doesn't work. Two plus three is five. That works. So just to make sure the next number is not going to work. Right? Or what it's going to equal. Negative two plus negative three is negative five. We're looking for positive five. So that's not going to work. So the two numbers that multiply to give you six add to give you five or two and three. Right? Yeah. Two and three or three and two. So all you do for this is you go, oh, this guy is going to xx plus two plus three. Right? So this broken down into prime factors is this guy times this guy. That's cool. Right? These are lines. Linear functions. Each one of these. So if we call y one is equal to x squared plus five is equal to x. Let's give this guy a name. Let's call this w. Let's give this guy a name. Let's call this z. So y is really w times z. Now you don't have to go there. I'm just doing this for visualization. And what's w? W is x plus two. Z is x plus three. Basically, God, I miss being taught something fascinating. Right? So why this is what we found out so far. Why can break down into w times z? You can think of these as different elements. Right? I miss mathematics. I'm so glad math is part of my life. Really. As someone who has been his life has been revolved around mathematics for the last couple of decades at least. Right? Man, I couldn't imagine my life without mathematics. It's good for the processing system. Really. It is an amazing B.S. detector. It's fantastic to meditate to. It's fun to play with. It improves your abilities to do whatever you want to do in life. It gives you a better understanding of the world. It's win, win, win, win, win, win, win. Win, win, win. Right? Tang, Po, how are you doing? It's amazing. Right? So consider why. We took why and for us right now why it was dysfunction. But it could be H2O. It could be water. It could be a number. It could be another compound we broke down. We broke why down into a W and a Z. Wow. Why is made up of W and Z? W, what's W? W is X plus 2. And Z is X plus 3. Right? I'm going to do a little cleaning house. And what we're going to do is we're going to graph this. Okay? Howdy chat. Amigos Sinulo. Right? So let's break this down. I'm going to erase these guys. We're going to need more space. Right? So let's break this down or erase this. Write down the core stuff that we know we found out about this. We found out that this thing is X plus 2 and X plus 3. Right? Is that big enough for you? Oh yeah, it's big enough for you guys to see. And what did we say? We said X plus 2 we called W is equal to X plus 2. And we said let Z equal X plus 3. That's a linear function. That's a linear function. A line and a line. Right? So let's graph both of these lines. Now I'm going to assume you know how to graph a line. Voyager 2. How are you doing? This is the X axis. That's the Y axis. Right? Now let's graph it using a table of values for this one and then we're going to straight up graph it there if you know Y equals X plus B. Right? Let's use a table of values for this. Now this guy, this axis, right now we're going to graph W and then we're going to graph Z and then we're going to graph Y. Okay? So if we're using a table of values to graph this X and W. Okay? Just plug in numbers for X and find out what W is. So first number, usually easy number to deal with you can plug in 0 for X. If you plug in 0 for X this becomes 0 plus 2 which is 2. If you plug in 1 for for X you're going to find out this is 3. Let's grab one. We've got one here. We've got one here. Let's grab one on this side. Negative 1 Negative 1 plus 2 is 1. And if you have negative 2, negative 2 plus 2 is 0. Right? Let's plot these points on the graph. Right? 0 and 2. 1, 2. 1 and 3. 1, 1, 2, 3. 1 and 3. Negative 1 and 1. Negative 1 and 1. And negative 2 and 0. Negative 2 and 0. Right? Okay. So this line W looks like this. This is the line W. Okay. Let's graph this guy. Okay. I'm going to erase our table of values here. If we're going to graph, let's circle this so we know what we're graphing. That's W. Here's Z, right? So let's graph Z. If we're graphing this we can use the function form notation. Y is equal to Mx plus B. Where B is your Y-intercept, M is your slope. So if you know how to read this, and it's a sentence by the way, mathematics, all of the stuff that we write down, there's sentences. They're saying something. They're telling us something. So Z is equal to X plus 3. That's the Y-intercept and the slope is 1 over 1. So here's the Y-intercept and you go up 1 over 1 which is the same slope as this guy. So you can make a line that's let me make a... Here is Z. Okay. The line Z. So we have two lines. Right? This guy's W and that guy's Z. Okay. Cool. Now, this is what this factor tells us. Right? If you notice this, we have this guy times this guy which is W times Z. Right? Which means if we take W, this line and multiply it by this line, we get that guy. And the graph of that guy, let's graph it. Should I use a different color? Let's use a different color. That's cool. Let's use this color. So we're going to graph this. Okay. The graph of this guy and this is negative 3 here for that guy, is going to go through here. Here, let's graph it using a better color. Let's graph it using brown. How did you get the slope? The slope here, here, let me do a little aside, fill in the blanks. So equation of a line is Y is equal to MX plus B. B is your Y-intercept. And M is your slope. Right? And slope is rise over run. Right? Rise over run. Okay. For this function, we had Z is equal to X plus 3. If there's no number in front of a variable, it's just 1. Right? So this is 1. And we could always make a fraction out of any number by putting it over 1. So 1 over 1. So the Y-intercept for this is Y int is equal to 3 which is here. And the slope which is M is 1 over 1. So we went up 1 over 1. Does that make sense? I hope so. Let's graph this using realm. I love it. Nice. Cool. Yes, good description. Okay. Now take a look at this. We're going to graph this guy. Now should we kick it out one more... Let's kick it out one more level of complexity so we see really what's going on. I'm going to erase these guys. Well, let me paraphrase. We're not going to kick it out one level complexity. We're going to give it a little bit more explanation as to why certain things are the way they are. Now I have a video out there. Let me get you this video. Okay. And it's called the power of 0. Cheechul. Power. Power of 0. We've done a couple of these, but here, I'll give you this one. Take a look at this video. For reference anyway. Now in this video, I'm about to let you know what it is that we're doing in this video. What the meat of that video is. And we're going to... It's going to take us like a minute to explain it. Now 0 in mathematics gives us problems. We can't divide by 0. If we divide by 0, the universe explodes. But 0 also provides us solutions. Okay. Here's a question for you. Let's say we have a times b times c times d equal to 0. How can you multiply four things to equal 0? What can you deduce? What can you conclude about a, b, c and or d? Right? At least one needs to be 0. Right? At least one of them needs to be 0. Very important. Or all could be 0. Yeah. All could be 0 as well. For sure. Right? But at least one of them has to be 0. That's not the case if this was 2. Right? Or any other number than 0. If this was 2, you couldn't say at least one of them has to be 2. That's not correct. The combination of a, b, c and d multiplying together to give you 2 is infinite. Right? The possibilities are infinite. Okay. However, as soon as we set this equal to 0 then at least one of them has to be 0. Wow. We just took an infinite, something that was infinite and reduce it down to at least one of them has to be 0. Powerful. Powerful. Powerful. Incredible. Cool. Well, how does this apply here? We'll take a look at this. Right now we have y is equal to x plus 2 times x plus 3. Right? Now let me ask you this. This is a function that plots on an x, y axis. Right? x, y grid. Right? So, ask yourself this. When does this function cross the x axis? When is this function going to cross the x axis? Just the same way you could ask this. When does this function cross the x axis? And when does this function cross the x axis? Well, this function w crosses the x axis when w is 0. Because w is this. This line is both or it's y, w, and z. Not when x is negative, but when x is 0. When x is negative for these ones, my apologies. But not just any negative. It has to be a certain negative. Negative 2. So if you want to find out this crosses the x axis, you just set w equal to 0. Because this is w equals 1, 2, 3, negative 1, negative 2. So this has to be 0, right? That's our scale. So all you do is just set w equal to 0. This becomes x plus 2. Bring the 2 over. So x equals negative 2. That's what it is. That's where we are. Negative 2. Let me use the right colors for this. That's negative 2. And this guy here, if you do it for this one, set z equal to 0. Bring 3 over. That's negative 3. Right? Cool. What's my math background? I got my degree in geophysics and a minor in mathematics. I've been teaching math for like 20 years plus high school mathematics only. Right? It's not very high. I just know how to teach high school math. Now, what about this function? Well, we haven't graphed this function yet. Right? But we can ask ourselves, okay, just curious. No worries, Bacon. Bacon slaying. Welcome to our live stream, by the way. So we have this function. y is equal to x plus 2 times x plus 3. So we haven't graphed this function yet. But let's ask ourselves, when does this function cross the x-axis? Well, this function crosses the x-axis when y is equal to 0. So let's set y is equal to 0. Let's take this guy. y is equal to x plus 2 times x plus 3. So we're going to set y is equal to 0. Right? When y is 0, we're on the x-axis. So we're asking ourselves, when does this function cross the x-axis? Well, we take this and link it up with here. Right? We have two things multiplied together to give us 0. How is that possible? The only way that's possible is if one of them is equal to 0. Okay. So you set each one equal to 0. So you can say, oh, this is true only. This function crosses the x-axis only when either this x plus 2 is equal to 0 or x plus 3 is equal to 0. That means x is equal to negative 2 and x is equal to negative 3. Oh, wow, cool. It's at the same place. Nice. So this function crosses the graph here and here. We don't know how it looks aside from that, but we know that it crosses the x-axis here and here. Okay. Very cool. Now, we can graph this using Completed Square, but I don't want to do that. I want to show you another way you can look at this whole thing. This will blow you away a little bit too. Or you should solidify your understanding of this concept. Take a look at this. Let's create a table. And by the way, this graph, let me give you a function. Do you have permutations and combinations in high school? We do. I'm not very good at it with permutations and combinations. Because they play word games with people. Right? Factoring. Let me see if I can find it with one. There it is. Here's a video. It's called Factoring Polynomials A Graphical Representation By We Factor. This is part of the Language of Mathematics series. I put this video out in 2010. Almost 10 years ago. Cool. Nine and a half years ago. And this is the function that we talked about. It's an 8 minute video that'll graphs it for you as well. But I want to show you a table format of how you can take a look at this. Appreciate what's going on here. Right? Now take a look at this. Like, wow, 2010. And that was me at a skate park with my tripod and people skateboarding around me and me doing mathematics on the walls. You were ahead of time. I just did what I did. Now take a look at this. Let's create a table. X X Y W Z Y X W Z Y It's the independent variable that both or all three of them W Z and Y are dependent on. Right? So X's are independent variable and WZ and Y are dependent on X, right? So let's find out what WZ and Y are for certain values of X. Cool? Cool. Let's plug in X is equal to 0. What's W when X is equal to 0? You put 0 in for X. So W is equal to 2. Z, if you put in 0 for X, Z is equal to because this disappears, Z is equal to 3. If you put in 0 for X here this becomes 2. That becomes 3. 2 times 3 is 6. Right? Do you see what's going on? Let's do another number. Let's plug in X is equal to 2. Okay. Should we do 2? Yeah, let's do 1 first. So we don't go too far. Oh my God. Wow, nice. So take a look at this. 1 is equal to 1. 1. Plug in 1 here. 1 plus 2 is 3. So W becomes 3. Put in 1 here. 1 plus 3 is 4. Right? What's Y? Put in 1 here. 1 plus 2 is 3. 1 plus 3 is 4. 3 times 4 is 12. Wait. Wait a second. Exactly. Why? It's just these two multiplied together. What? Let's put in X is equal to negative negative. Let's make it easy for us to multiply. I don't know what that says. Let's put in negative 8. Negative 8. When X is negative 8 negative 8 plus 2 is negative 6. Negative 8 plus 3 negative bro. Negative 8 plus 3 is negative 5. Negative 6. You could put in negative 8 here if you want but we don't have to anymore. We could just multiply these two. Negative 6 times negative 5 is 30. That's what Y is. What? 30. Negative 5. 30. Check this out. When X is 0 W is 2. Z is 3. Y is 6. 1, 2, 3, 4, 5, 6. When X is 1 are you steady? We're doing. We're just doing math, learning math. Practicing math. Meditating. When X is 1 W is 3. When X is 1, W is 3. Well, it was. We knew that. Z is 4. Well, we knew that. Y is 12. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. Right? I've been out of contact with any school subjects for nine years now. No. No, you're not mad. You're not. It'll take you two seconds to get this back. The cool thing is, I don't know about that. Hi, Gicho. Hello, QC Warrior. How are you doing? How is life? Right? Negative 8. We're not even on the board. Negative 4, negative 5, negative 6, negative 7, negative 8. When X is negative 8, W is negative 6. Right down here. Z is negative 5. Like down here, if you extend this. And Y is 30. Right? What does the graph of this look like? Does parabola look like? This stream is about mathematics. It's easy to review math unlike some other subjects. Yeah. Math should be the easiest course you take in high school. Period. University, different game. High school should be the easiest course you take because it just builds from previous years. Right? 30 is definitely out of the way for I think some better. Right? If we end up graphing this function, this is what it's going to look like. Take a look. That's what it looks like. Let me make this darker so it comes out. My pens are running out. I need to go to the stationery store. We need to go get ourselves more stationery. Having a little break from steady pun intended and I saw you were alive. So I thought I would take my little break here. Awesome QC Warrior. I'm glad. It's a nice place to show. To to et to voie. To et to voie. So that's the function. Now here's the kicker. To me this is the kicker. Right? People don't realize but this graph stuff is really important in engineering. Huge humongous. It's crazy important in economics as well. Crazy important everywhere. Right? Crazy important everywhere. And here's the kicker. We took two lines. Right? Two lines. We got a curve. Why is that? We got a curve because of the property of mathematics where if you multiply two negatives you get a positive. Right? Even in economics. So if you multiply two negatives you get a positive. Now take a look at this. Now I talk about this in the short video the eight minute video that I linked up previously. Right? Let's suck her down. But think of it this way. The zero point the factoring when you're factoring you're finding where functions cross the x-axis. That's what it is. Why do we factor? We're factoring to find where functions cross the x-axis. Right? In the most simplistic form. We're factoring to find out when functions cross each other. And these linear lines have endless possibilities. And they go on forever. Unless we give it boundaries limits. That makes sense according to our systems. But take a look at this. Let's assume this is going to be red. This might not come out well. I'm going to try green. Let's try green. The x-axis is sort of an important point. So take a look at this point. Let's extend this up. And let's extend this up. This is basically the line x is equal to negative 2 and this is x is equal to negative 3. If you look at these functions all three functions w on this side of negative 2 x is equal to negative 2 is positive because it's above the x-axis. What z is positive because it's above the x-axis. So positive times a positive gives us a positive. So we're above the x-axis. If you look at this zone from negative 2 to negative 3 w is below the x-axis so it's negative z is above the x-axis in this zone. So it's positive. Negative times a positive is negative. That's why negative times a positive is negative. That's why our function y is below the x-axis. And then as you get closer to negative 3 this number gets smaller so it's kicking up this y-value. If you go to this side of negative 3 when x is negative 3 both z and w are below the x-axis so they're both negative and negative times a negative is positive. So when you're multiplying two linear functions when you go below the x-axis they're two negatives multiplying each other to become a positive if you're talking about quadratic. So our function y has to start coming back up again. It has no choice. That's its behavior. Most scientific studies require at least knowledge of calculus which you could definitely need good graphic knowledge for. One of the main purposes of high school is to allow people to get a visual of the functions be able to graph functions and understand their behavior. Huge. And calculus just takes it a step further and finds more crucial points of functions discontinuities and limits and all that jazz. Break it over over. Time to study. I'll cash the rest of this on YouTube when it comes out. Awesome. QC Warrior. Thanks for popping by. So much information from a single equation. So much. There's so much there. But once you understand this all of a sudden wow like wow so powerful so powerful beautiful absolutely beautiful fun. I love it. I love it. And we've graphed these functions before. Let me find you a video for completing the square. That way you'll know the square. We've done this multiple times. We've done it on live streams as well. But here let me give you this link. This is an ASMR video just nice and chill going through the whole process. I'm going to have an apple that was an hour full on talking. So good. Really. So good. I'm not sure if Hannah is still here. He asked about the fact that we're a little delayed in replying. By the way, tomorrow at 9am to 11am we're doing a live stream on Julien Assange catching up on what has taken place and where we are regarding that situation. I was I came to Canada half way through grade 5 so I was really young when I came here. I didn't speak a word of English. Oops. So it blew me away really. I remember I didn't speak a word of English so I was struggling with everything. Except mathematics. I remember sitting in math class and I didn't know what was going on. This is a memory etched in my brain. Yavoid. Nice. So this is etched in my brain. Really. It blew me away at the time. Like a young chicho talking going on around them doesn't understand a word. Right? And it's time to do mathematics. And this was the first time. First class I had of math. Stayed with me for 40 plus years. And I'm sitting there in Iran the math is at a higher level. Right? Math is like universal language. 100% right? It's Raiden. Salam alaykum. Yeah Raiden, how are you doing? So I'm sitting there and they start doing math 2 plus 5. I was sitting there going what? And I started looking around. People are writing this down and writing the answers some didn't know. Or there was some multiplication there was a whole bunch of it's weird. By the way memory in the court of law just remembering something is not end all and be all of the truth being told it plays tricks on us. So it could have been 12 plus 15. Right? Whatever it was it was addition. And then we're going writing these down. Some people were putting up their hands asking questions because they didn't know how to do it. And I was like what? I thought I was on a twilight zone or something. It was just weird to me. Because we've done that in grade 2 maybe? The grade 5 halfway through grade 5 the grade 5 that I knew in Iran back in the late 1970s carried me all the way up to factoring in grade 10 mathematics that they were teaching in Canada right? Grade 5, grade 10 that's the level of mathematics the discrepancy there the inequality there crazy crazy I'm not a lawyer I have no desire to enter a bureaucratic system on that level I'm not even willing to enter a bureaucratic system on a teacher's level I just teach mathematics privately and in groups and I work with certain private institutions to help their kids learn math right? so yeah I mean in grade 5 Anuj you'd be amazed how bad the current education system in Canada is we had those common multiple and highest common factor in grade 3 Anuj where are you from? so you're an anarchist I'm a I don't want to categorize myself as certain political leaning I am definitely against decentralization India Anuj I rarely have students of who have been educated in mathematics from India that I work with that need help and the ones I do get they're in usually grade 12 and they're trying to understand the systems really well and I can help them with that 100% right? I do this I don't just teach factoring I don't teach I don't teach I connect right? so when kids need help I connect calculus was always the hardest for me for me as well I learned I failed my first year calculus when I retook it I found a really good book and I learned calculus from the book please help I'm 25 25 and 7 years you're the all connected me with math I'm 25 so in 7 years you're 25 you can learn a lot of mathematics in 7 years a lot of mathematics in 7 years apple I was an average student and scored 94 out of 110th grade food, yummy food fantastic so average student in India 94 out of 100 is that correct? try hard try your best try let me rephrase that yeah try your best I guess yeah 94 mathematics nice I would never say give I'm 25 in 7th grade jemic mathematics is on 7th grade level my recommendation is go to my website and or go to youtube and look for chicho language of mathematics start off with the first video we put out most others scored 100 I always had hard time until 4th year of high school with math until I realized it was my attitude over the classes that held me back once you give yourself into it it's so pleasant, yeah avoid agreed with that so in geometry you're part of math or does it fall more on the scientific scale it's math for sure yeah yeah yeah a lot of mathematics, branches of mathematics have come from geometry there's actually a book out there that I don't have, I've read little bits of it that fairly large article on it that had excerpts and stuff that teaches calculus with geometry once I have the time I'll track it down and learn it Khan Academy is good for learning basics yeah Khan Academy is good for learning basics if you know what it is you're looking for I would paraphrase it that way personally but here, let me give you a playlist for sure Khan Academy is good but you have to I haven't gone to their website oops I don't know what that is I haven't gone to their website on just dug down into how they begin right you can just do searches on specific things that you like that you're looking for hey sorry if I'm messing around with this YouTube changes their things YouTube does here's the playlist for language of mathematics go to the first video and the first video is way way way down there's I don't know how many videos in this how many videos in this there's 161 videos go to video number one is sorted in reverse order so the newest one are top so you want to go all the way down that's where I do introduction to language of mathematics and what it is we're going to talk about I absolutely find that a lot of people just psych themselves out when it comes to math yeah, masquerade or 100% kids, they go into panic mode it's crazy it's very weird hey I have a serious question in doubt about the math physics of the big bang can you help you and everybody else a lot of people have questions and problems with the big bang algebraic geometry is a huge part of math yeah thanks for the help on my past I hope so let us know if you need help we do these drop in math sessions on a regular basis chicho, competition is so cut through in Asia that even if you score well it's not good enough yeah and I don't like that system personally it's not inclusive it's bad for society is the smallest point sphere or anything possible also the simplest thing possible the big bang it didn't start off from a sphere it started off from a point source but that point source didn't have dimensions it was just energy it just there is no dimensions pre big bang dimensional space came to be at the moment of conception at the moment of the big bang hey chicho are you planning on doing some college level math in the future? yeah I can't pronounce that name yeah in the future I don't know when college level depending on what program you're in but calculus I'm assuming you're specifically talking about I do plan on it I just need to reach a certain level where I can spend a little bit more time on it I need to be self sustaining with this project it takes time may I ask a question about space sure of course Void when are you gonna prove the random thoughts of maybe give me about 30 years if I'm around maybe by that time I have enough my math abilities will be powerful enough to tackle some of these things right? we'll be doing live streams on my Raymond Hoth hypothesis with me shrunken down yeah it's not inclusive you're right yeah if all the energy of the universe that made matter and all was in that point wouldn't the force holding it together tap out at some point making the first thing that existed a sort of a nuclear sphere or beam structure nuclear sphere or beam structure mask of raven any thoughts on this or anyone else any thoughts on this holding it together tap out at some point what do you mean tap out at some point making the first thing that existed a sort of a nuclear sphere well theoretically we are a sphere universe sphere expanding right? Chico I need some help with trigonometric functions cosec and sec and cot okay intelligent blue bear what do you need one gravity tap and hey you honestly put it out of the metaphysical smallest point possible simplest thing possible time I don't know if the space is expanding every second hour time what exactly is it expanding into exactly what is it expanding into is it creating space as it gets going are we just a cancer and some other larger something that's growing and at some point they're going to figure out to get rid of us is that what it is like let's say you could go to the wall where it's expanding and manage to go past that wall what is beyond that wall what is it expanding into great question Star Trek has done a couple of episodes on that where they go to the edge of the universe and they see just the horizon and lots of colors we don't know no one knows no one knows be overcome be overcome at some point making the first thing that exists is sort of a nuclear sphere or bean structure I don't know what a bean structure is but again it's a sphere expanding as far as we know in Japan students are taught on abacus and really engage good that's good trigonometric functions by the way intelligent blueberry have you seen our trig playlist here let me give you the trigonometry playlist because I'm just going to touch on it right now where is our trigonometry playlist lots oh here it is jeez louise here's our trig playlist blueberry here's our trig playlist I don't have any thoughts on this because I haven't studied physics deeply enough but I think most people fundamentally misunderstand the current theory pertaining to our early universe and it would take extensive education to overcome those issues yeah I agree with you spaces like the ocean to me freaky how little we've discovered well the real problem is how to type them on a non-graph calculator oh it's just there but the thing is how can I know when to apply them in an angle or distance when to apply them in an angle or distance I'm not sure in an angle or distance but if you want to the first part the real problem is I'm having a how to type them on a non-graphing calculator all they are is just here let me erase this so if we have our sine function check this out if we have our sine function here sine theta cos theta and tan theta right? is that dark enough? I think so hopefully it's dark enough then cosecant theta is just one over sine theta secant theta is one over cos theta and cot theta is one over tan theta so all you gotta do to punch them into your calculator is just one divided by sine one divided by cos one divided by tan right? that's all they are how could the smallest point have any property at all if the thing giving such property as a property or a piece of the space of the thing you can just keep shaving it down there is no space at the origin of the Big Bang there's a possibility that General Assange will be extra at the US or suicide in jail what's your view on it first? you just want to talk that's good trinus by the way if you haven't thought through like for example the question you were asking about the Big Bang if the answer was given to you all of a sudden there is no such thing as space that should be a huge revelation to you you should not be on a live stream and asking more questions that are totally unrelated you should probably go for a walk and think about what you just discovered right? unless you're trolling which you are no brother pre Big Bang there was no such thing as space space was created at the beginning of the Big Bang that's a revelation to you that should be profound to you you should not say no that's not true you should say hey maybe Chico is full of BS I'll go look it up or if he's right oh your mind just got blown right? how's it going Chico? make how you doing? doing good brother thank you very much does that one apply always or whenever I'm giving a sum okay hold on a second oh wait a second well I walked in on a funny point you walked in on a funny point I'm just gonna copy this so blueberry what's your question does that one apply always or whenever I'm giving a sum it applies always it's the definition of it right? so for example if you have, oh what's an example we could use hello hello Jane Jason how are you doing how's everybody doing okay so we know the gold keys why is it, oh okay you're out death to non-believers I've never heard anyone call someone super funny super funny so blueberry yes this is the definition that's what it is right? that's the definition so whenever you're giving a sign of something in any type of function and by the way this is what the graphs look like and check this out I'm super disappointed for me this year because I don't have any I have a grade 12 student this year that we already did the math for and we did it speedy-go-zall style during the summer and for some reason this year I don't have any grade 12 students yet which I'm super disappointed because I'm not getting to practice this stuff so if I make any silly mistakes brain force please correct me right? doing well working and it's super rainy but been a good day so far awesome I'm enjoying this rainy weather actually I gotta go for a long walk after this so I'm gonna be walking in the rain in the cold dress warm right? so this is what the functions look like sign function looks like this goes from 1 to negative 1 right? and here's 2pi right? here's pi here's this, here's this so sign function does this right? and this is oops sign of theta versus theta those are the graphs right? so cosecant is just whatever the y value is sign theta flipped right? so first thing you do whenever you're graphing a function you find the unknowns, the boundaries, the limits the asymptotes, the holes and stuff like that then no go to points right? so all you do oh okay at pi we have an asymptote at 2pi we have an asymptote at 0 we have an asymptote because if you flip 0 you get undefined so if I ask what the cosecant of an angle of 30 degrees here let me show it to you this way as well yeah so you take the so basically you take the sign of 30 degrees and flip it right? so sign of 30 here 30 60 90 that's 1 squared of 3 and 2 that's the ratio that exists so sign of 30 oops sign of 30 is 1 over 2 so cosecant of 30 is 1 divided by 1 over 2 which is just 2 right? sign of an angle is opposite over hypotenuse opposite over hypotenuse cosecant of an angle is flip this hypotenuse over opposite over here opposite of 30 is 1 over 2 and over here is 2 over 1 right? and as far as graphs of these things go they look like this are we doing little trigonometry? little trigonometry oh I remember this so if I'm asked what that is I hope that cleared things up it is really interesting for sure I know it love trigonometry love so disappointed that I don't have anyone to teach trigonometry to right now I love delving into this stuff so disappointed sign of 30 degrees and flip numerator and denominator asymptote laugh a lot I remember the term but don't recall what it means been way too long twitching jason asymptote just basically means no go zone you can't go there it's impossible okay like ah the sound of rain hitting off the umbrella as the rich rich smell from feeding plants and nature encompasses you doesn't get better doesn't get better doesn't get better really it's beautiful it could get better sometimes put a little bit of thorninous munkin off you go right off you go I hope that helped out blueberry I hope that helped out talking a mile a minute in this stream I want to make sure we got the factoring done properly you can get as close as you want to an asymptote but never hit it close close infinitely close but you can never touch it it's like this getting close getting close never touch it I remember a lot of this from physics courses I took I've always preferred practical applications for math like physics or statistics super fun working through practical real life problems you have dangerous cutting shapes dancing along the street my G so much my G in front of passing bus yeah you gotta be careful you gotta be careful in this part it's so chill here like if you're on the sidewalk and even if you think about trying to cross the road if you just pause cars will stop it's like no no please go I'm just stopping so you talk about current events every now and then yeah for sure Anuj yeah we have to we have to there's a lot going on there's a lot going on yeah it's pretty here sweet too roads, buildings directly in front of my house and deep wooden area out back it's a nice spot nice awesome we're lucky I'm in the Midwest USA and can confirm it's like that here as well sometimes people will even cause small traffic jams at intersections because of people trying to let other people go for them yeah it's crazy I don't get it like I've seen people slam on brakes for a pedestrian and obviously they hadn't checked their rear rear mirror where all of a sudden people are like so dangerous so dangerous luckily they're driving really slow in general here so they're fender benders which is a great thing which is a good thing so tomorrow morning from 9am until 11am we're doing a stream on Julian Assange right and it's part 5 I think 5th one we've done it's more than 5th one but it's the 5th one in the series I've been doing okay if you're interested pop by you want to know what's going on that front it won't be current events but it will contain some of the things that are going on what do you guys say should we call the stream time time hour and 42 minutes take a different route home after work now too risky passing by a local school oh yeah especially if they're like in and out had one time a child just run out oh into the road seat belt almost slice me in half breaking good thing you broke though be horrendous I've never had I've never hit in a car I've never been hit thank you and I've never hit I actually have never caused an accident as far as I know anyway I have been in accidents but always it's been other people's fault and even that when someone else is fault you bear a little bit of responsibility as well scared ass out of me scared ass out of me rather not run the risk yeah agreed mek I try to avoid where children are what is the difference between pre-calculus and calculus it's just the transition there is no difference it's just mathematics they just make the separation because calculus is really introduction of time into the equations into the functions and you try to analyze how the function behaves over a certain period of time over a certain period of length before that they don't really incorporate it all together but it's all the same beast if you don't know the pre-calculus stuff you can't do the calculus stuff so it's just you need pre-calculus and pre-calculus they just take a whole bunch of mathematics and put it in that category and say that's pre-calculus thank you for being here we'll see you on the next stream or next math stream thank you for popping in I'm glad you like the mathematics by the way pre-calculus give you knowledge of graphing functions trick that you need to do calculus well yeah and that's the thing I think well is the important part here you have to have a really good understanding of functions before you can use them and that's really what calculus is right when is your sound stream sorry a sound stream tomorrow morning starting at 9 a.m. okay let me do a double check on that starting at 9 a.m. to 11 a.m. pacific time my time west coast of Canada okay so I'm just bringing up the post for some reason twitch took out their events category so you can't make events anymore you just which is weird I don't know why these platforms just keep on doing wacko things it's part 6 actually we're doing tomorrow December 11th from 9 a.m. until 11 a.m. PST okay sorry I missed most of the stream but glad I was able to no worries thank you for popping by twitching jason always tilted I know this off topic but do you have any plans of making a strawberry liqueur in the future as soon as we start getting yeah you know what the strawberry liqueur was dangerous for me I went through that thing way too fast so I'm taking a break from the strawberry liqueur making it the cornelian cherry liqueur is just as delicious the pineapple liqueur is delicious but strawberry liqueur will make maybe when I get fresh strawberries in the spring maybe I'll go buy frozen organic strawberries and make them then the event function wasn't useful yeah see here's the kicker Dante for me youtube took out there what he called annotations because they said very few people were using them but I was using them up the yin yin right I lost hour countless hours of work when youtube took those out because that's so many annotations right so I don't really put any more effort into youtube than I have to now youtube or google because they discontinued a few different things that I used to use a lot twitch just discontinued events but I was using events a lot so just because majority people aren't using it it doesn't mean it's useless but I guess they're trying to optimize profits I don't get it Julian Assange Julian Assange Julian Assange that's cute too addicting stream about Julian Assange did you ever make regular raspberry liqueur raspberry have I made raspberry I must have made raspberry once but I've never I don't remember it I don't maybe I haven't made raspberry liqueur good idea lonely piggy raspberry liqueur we need to make raspberry liqueur it'll be tart I think excellent I have an entire booklet I've kept add details now and then over the years back from mid to late 2013-14 dropped off after a while but I wrote down so much info cool blue bear sorry chicho my connection went out so I missed the entire all blueberry what it's gonna be I'll have to stream up on bit shooter youtube in the next few days okay the bottom line is money raspberry liqueur stream coming raspberry liqueur stream coming I'll work on it okay gang thank you for being here okay I never made my coconut liqueur but I did buy one of a few months ago that was incredible nice nice so if you can make it I'll see you guys tomorrow and most likely we're gonna do some kind of stream this weekend maybe a current event stream just to get people caught up okay take care chicho you too Mick you too Mick have a great day you guys as well Dante thank you for taking care of business top Fiverr was here for a while thank you for taking care of business and everybody else thank you for the conversations and thank you for everything okay thank you for the follow thank you for the subs if I didn't catch any of them okay aside from that I'll see you tomorrow if you can make it otherwise the next few streams bye for now