 and we're hooked up. Nice. And we should be live and we are very nice. Hi everyone, this is Gicho. Welcome to my channel and welcome to another live stream. Today, today is November 20th, 2020, and we're doing a math live stream. Open discussion, drop in tutoring session number 63-ish. And we've done a few of these before, as you can tell by the numbering. I think we're doing this for a couple of years now. And it's just me making myself available for a couple of hours, at least twice a month during the school season to help people out with mathematics if they do need help. And while we wait for notifications to come out, let me tell you what this is all about. I do have a Patreon page somewhere here. There's my Patreon page. Patreon.com forward slash Gicho, C-H-Y-C-H-O. If you want to follow this work, if you want to know what this work is about, Patreon is a great place to start. Everything's layered on mathematics. Rakka 42. I'm here, so everyone has to... Canvas. This is a math session. Everyone needs to do mathematics today. Everyone needs to do mathematics today. You're missing a zero on your 4-2, by the way. It should be Rakka 4-20, not Rakka 42. Slippy Waves. How are you doing, damn? Long time I haven't been able to stop by in a chat. What's up, Gicho? Doing well, Slippy Waves. What are you doing well? I am on Patreon, gang. I don't put anything behind paywalls. Everything's great of commons. Share, share, like. You can follow the work, and if you like what you see, and if you think this work could use your support, Patreon is a fantastic way to do so. Rakka, I tried it, was taken. Oh no, math is just impossible for me. It's not impossible. The only reason you might think it's impossible is because you've allowed the centralized education system to pollute to your mind. That is the only reason you think mathematics is impossible, because math is an innate ability. It's an innate ability. Slippy Waves. Gicho, one of my roommates got COVID. Oh no, it's been super stressful to build a system where I also don't get to say, oh yeah, yeah, just you've got to be super careful, right? We had a family member in our house, not where I live, but in a different city where they're living together. One of them got COVID, and that one was taking care of the one that got COVID, and the other person didn't get COVID. So they were very careful wearing masks, sanitizing, stuff like that. So it can work Slippy Waves. Don't stress out too much about it. Don't worry about things you cannot control, but this you can partially control by being more careful, right? Tommy. Tommy G. Harding. Tommy G. Harding. If all math teachers were as good as you, we'd have a lot more people working instead. We'd have a lot more peace in the world, I think. I think if, and that's one of the thesis regarding mathematics, I think if everyone was literate in the language of mathematics, then this world would be a much better place to live for everyone. That's my take. Okay, Slippy Waves. I want to do some math that shows investing. Tommy, 100% agree. That's one of the reasons I've been going hardcore on this, right? For 15 years or so now. I don't remember. I remember one good math teacher I had that was in grade nine, and that wasn't because she was a good math teacher. It was just because she was a great human being. She was a good teacher, period. It didn't really have too much to do about her math abilities. I want to move the mic a little closer. Is this legal? I think so, mathematics. I think mathematics is legal. We are live streaming on Twitch.tv4 slash chicholive. If you want to participate in the chat, Twitch is where you want to be at. And gang, thank you for the followers. Thank you for the subs. Thank you for being here. Thank you for the support. Thank you for the love. And when the mods roll in, mods, thank you for taking care of business. Slippy Waves, what's better to open a 401 and save money on taxes this year and pay later or pay the taxes up front? Maybe we can do this through math. Slippy Waves, investing is so personal. It's not what's better all the time. It's what's better for you. How are you going to game the system? How are you going to use the laws in place or the ways you can get around the laws legally in place? How you can navigate through the bureaucracy to make optimum use of your investment? Really, it's not just a question of, by the way, gang, this is not financial advice, even though we're going to do a personal finance video tomorrow, live stream tomorrow, or not tomorrow, two days from now, we're doing current events tomorrow. This is not financial advice, but it really depends what you're doing with the 401, right? If you're a full salary, getting a paycheck every two weeks, and you've got no write-offs, you've got no write-off, I'd maximize the 401, take the tax break, because that kicks you into a lower tax bracket. If you're taking borrowing money and you're not even working full-time to maximize your, it really depends, man. The only thing you hate, I hope you're doing well. As always, you probably know what my next question is, I'm eating olive olives, autumn olives, any snacks we did, yeah, I'm still eating autumn olives, man. I've been munching on these things like mad. We're on our last bucket. We've got one more bucket for this season to eat, vitamin C galore we've gotten this season. So they're fantastic, these autumn olives, man. Like really, this was the best autumn olive season ever, as you can tell by how much I've been eating, right? Autumn olives, and I've eaten three hamburgers today. We cooked up hamburgers during the live stream yesterday, so I cooked up three hamburgers. I ate up three hamburgers, three sandwiches, oh man, I'm so full. Actually, I ate two of them with sandwiches and one of them just a patty, a hamburger patty, so good. Don't worry, I'm not taking financial finance. System veil. How many numbers between and including one and 100 aren't divisible by any of two, three, and five? To do this problem, I'll just go sequentially up, right? That's what I would do. Take out all the even numbers, they're all gone, right? So all of a sudden, you don't have a one to 100. Take out number one, take out number two, and then take out all the even numbers. So number one and number two takes you down to 98 numbers, and then divide that by two because they're half the numbers are even, so they're gone. So now you're down to 48, right? And then divide that by three, 48 divided by three, 16, right? Can you divide it by three? No, you can't divide it by three, 48. And then I would have to think about it to see where we go from there, system veil. Lark Kim, 27, hello. I don't think I've ever written anything here, but I'm really happy about this distraction right now. Your videos always calm me down a lot and I like math, awesome. Laura, Laura Kim, thank you for popping in and saying hello. Hello, hello. V-62 piece. Okay, let me try another question that maybe you can answer through math. How is money laundered through banks and art institutions? We talked about this. Okay, well, I'll give you a little example. Okay, I'll give you and this connects up to your personal finance video, personal finance question, right? Do you ever bring mathematics into investing or is it basically a crapshoot? Do you ever bring mathematics into investing? For sure. 100%, Tommy. That's one of the places you use mathematics in a big way, right? What do you do for a living, Chichou? You're a full-time streamer? Full-time streamer? No, I don't make my money on streaming. There's a little bit of funds coming in from the content I create online that I've been doing for 15 years. We just hit our 1000th video, right, on YouTube, but I teach mathematics, mathematics and physics, mainly mathematics, and I have physics students as well, and that's what I do, a private, wild strike. What are you doing? Just wondering if it's just a UK thing. Do other countries use BEDMAS and BIDMAS? Yeah, BODMAS. We use BEDMAS, B-E-M-A-S. You guys use B-O-D-M-A-S and B-I. What's the I stand for? We use E because E is O operations, I guess. I don't know what the I would stand for. For us, it's BEDMAS, brackets, exponents, multiplication, division, division, multiplication, addition, subtraction. What strange words today, Chichou? Ah, this is mathematics, brother. But I heard the Durban poison is very good. What precisely is it? If I just does, you want to do a little enjoyment? Well, just multiply 69 by 1.3. I have no idea what that was that's going to give you. I am literally lost. Great stuff. I just started private English lessons online. So far so good. Yeah, it's fun to do and I learn a lot from my students. Interesting. In the States, we learn PEDMAS, parentheses. Ah, parentheses first. Interesting. The I is for indices, I think. Indices. Interesting. I've never heard of the indices for the I. So, so far we got, yeah, let's write this down. We got BEDMAS. We use BEDMAS. BEDMAS. So, we got BEDMAS. We got BODMAS. And what was the other one? PEDMAS. PEDMAS. And by the way, this confuses the crap out of people, right? Oh, yeah, my, oh, I want to see the brain. Hold on a second. Let me finish off my intro. I do announce these live streams 30 minutes before we go live on Parler, Elo, Mines, VK, Gabb, and Twitter. You can follow the work there. The links will be in the description of this video. For live streams where we don't have any visuals, we do upload the audio SoundCloud as podcasts, and they should be available on your favorite podcasting platform, including Spotify and iTunes. And we will be uploading this video to both Bichute and YouTube. And you can follow the work there, turn on notifications, subscribe, like, share, comment. And if you're on YouTube, you can turn on YouTube notifications and the button notifications. You can support YouTube membership, support this work through YouTube membership and the buttons there. And for those of you who've been supporting this work through YouTube membership, thank you very much for the support, as well as the people who've been supporting this work on Patreon. Thank you very much for your support. Okay, I'm going to take these guys down. I tend to forget to take these things down. So I just go off on things, right? Now, let me tell you something about this, right? Oh, I remember bot mass backwards algebra. I got a B in GCC, G-C-C-S-E. I heard kids don't learn long division anymore. They use some other method. Man, I teach all my students long division. It's ridiculously important. People say it's not, but it is. The people who say it's not, they're either really high level mathematics that they don't use the division or they've been using the calculator forever. They don't know how to do long division, right? I've had arguments with people regarding long division. They're like, oh, it's not useless. It's exercise for the mind, right? Some people consider some of the most benign exercises you do in the gym to be useless because it's not building big muscles, but they're important. Doing exercises where you're doing balance is important, but people want to go there and lift heavy weights. No, no, no. It's important, right? How many unique weights are there to arrange the letters in syllables? That's the factorial, combinatorics. Here, let me... Here, this is the one you want. S-Y-M-B-O-L-S. How many weights can you arrange this? This is just a combinatorics question and the formula I believe is this. One, two, three, four, five, six, seven. Seven factorial divided by any letters repeating. We've got two S's repeating, so divided by two factorial. It's just a formula. I don't know the proof behind it. Oh snap, Chicho got a bit shoot and a parlor. Chicho, too old. Strawberry Rhino must decentralize. Yo, Chicho, how's it going? Starsky, how are you doing? Gang, by the way, thank you for the subs. Thank you for the follows. If I don't catch them, okay? My apologies. Hopefully that method is not dividing at all and when you have to use a calculator. You don't need to use a calculator. This is seven factorials. Seven times six times five times four times three times two times one. Two factorials, two times one. That kills that. So you just do the multiplication, whatever this ends up being. Here, five times six is 30 times seven is 270. 270 times 12, whatever that ends up being. The idea of long division help when doing synthetic division later. Egg, exactly, dump weaver. And the layout on it is important. Here, I'll show you what long division is. But let me tell you something about this. Take a look at this thing. A lot of people get lost with bed mass, right? They try to do algebra and they're like, I don't understand it. And you go, oh, you do bed mass. But bed mass is only half the answer, right? You do bed mass when you're simplifying. So when you simplify, when you simplify expressions, you go this way. When you're solving equations, you go this way, right? You go this way. So if you have questions where they say simplify, you do bed mass. When you got questions when they say solve, you go this one, sam dib, right? That's the thing, right? All these absolute rules in mathematics. The only absolute in mathematics is you can divide by zero, right? And even that, you can fudge it. Okay. Free assange. Wow. Totally forgot how to do factorial until now. Actually, I forgot about them entirely. Sokotoa, can you explain basic trick? For sure. We do. Yeah. Sokotoa, sure. We'll do Sokotoa. There was one other thing I wanted to do. What was the What was someone commented? They wanted to do this. Someone asked something. I forget what it was. Okay, we'll go into Sokotoa. Is that is that clear, by the way? What I'm saying here, right? That's that. I am driven, please. Correct. Pet mass, pet mass. Did I do it right? Yeah. Pete mass, parentheses, exponents, division, multiply. And by the way, these two guys, division and multiplication have the same weight. It doesn't matter which one you do first to a certain degree. P mass. Oh, P mass. Okay, okay, okay. But again, it doesn't make a difference. P mass. Sorry, thank you. My little bit of dyslexic and I think see things backwards. Letters anyway. What one first? Multiplication. Pim, pimdas? Multiplication before division. Wow. Sokotoa gives me high school flashback. Don't think I've heard it since. We were taught pimdas, pimdas. But multiplication and division is the same weight. For example, pimdas is what's always been stuck in my head. Really? I've never heard it. Case, man. How are you doing? Division, multiplication, same weight doesn't make a difference. Addition, subtraction, same weight doesn't make a difference. Which one you do first? So for example, take a look. I'm going to do one simple example of simplifying or one simple example of solving. So you see the difference, right? Same weight. It doesn't make a difference which one you do first. Watch this. 2x plus 1 minus 3x is equal to, I'm just going to do this multiplication division. Should we do division? Sure. Oh, not equal to. My bad. Let's go over 2 and over 3. Now, watch this. What I'm going to do is I'm going to change this subtraction to an equal sign over here. So this is going to be 2x plus 1 is equal to 3x over 2 and over 3. And should we put exponents here? No, I don't want to put exponents right now because I don't have room to work it. So right now, you're going to do bed mass or peat mass or pod mass or pen dash. You're going to go this way. So you're going to do brackets first. Do we have anything to combine there? We don't. If I had this, here, let's change the subs so we actually have something to do inside the bracket. What if we had this? What if we had 2x? And this was 2x. So you do it inside the bracket first. So this becomes 3x. And over here, you do it. I'm sort of changing things up. So this becomes 2 3x over 3 is equal minus 3x over 2. I'm running out of space. And then you've got to do exponents. We have no exponents. Multiplication division. So if we had anything to simplify here, we would have. We don't. And then you do additional subtractions. So we're at the subtraction. So we do this thing. So common denominator is 6. You multiply this thing by 2. So it becomes, oh yeah, actually we do have multiplication. What am I saying? We've got the 2. Watch this. I'm going to do this in one shot. We did the brackets because we're running out of space. That was 3x. We did the brackets. We don't have an exponent. And then we've got multiplication and division. Oh, we've got 2 times this. So that's 3x times 2 is 6x. Over 3. And then you can actually do division. You can do this division here. 6 over 3 is 2. So this becomes 2x minus 3x over 2. We've got nothing else to simplify. Now you do your additional subtraction. Common denominator here is 2. So this becomes 4x minus 3x. And then you're still doing additional subtraction. So it's just x over 2. Sorry if it's really crushed up. It's just a concept I want you to appreciate. Over here, you're doing things this way. You're going to do additional subtraction first. It happens to be in a bracket 2. So that works. So this would be 2 3x over 3 is equal to 2 3x over 2. And then we've got multiplication and division. Well, we've got multiplication here and we've got division here. So it doesn't make a difference. Which way we do it? So what we can do is just kill these guys. Right? 3 kills the 3. Now we've got 2x is equal to 3x over 2. Well, that doesn't make sense if you cross multiply. Which is, again, you're dealing with addition, multiplication, division. You get 4x is equal to 3x. Well, how do we do this? Well, you can. You bring that over. Bring this over. You get 3x 4x. Let me bring it over here. 4x minus 3x is x is equal to 0. So the only answer is x is equal to 0. You solve for it. That's it. That's what you're doing. Simplifying go this way, adding solving go this way. I know the example wasn't the best, but I wanted to show both on it. This is the simplest thing I could think of right away. Practices on whatever it is you guys are working on. Don't assume it's always bed mass. It's always bed mass. It's not. Solving is the other way around. As far as Sokotoa goes, Sokotoa. Here, let me explain to you what Sokotoa is. Sokotoa represents trig ratios. That's what they're called trigonometric ratios. Trig ratios. And the trig ratios say this. Sokotoa. And I'm going to give you an analogy for this. We're not even going to go into the doing trig equations yet or expressions or solving yet. I'm going to write down what this is and then I'm going to give you an example just to see if it sticks. Right? This means sine of an angle is equal to opposite sine divided by the hypotenuse. Cos of an angle is equal to adjacent over the hypotenuse. And tan of an angle is equal to opposite over adjacent. And all that means is this. For any right angle triangle, okay, if you have an angle, we're saying that sine of this angle, we're defining it. Sine of this angle is the opposite side from this angle, which is this, opposite divided by the hypotenuse. And this is the adjacent side. Now, people get confused on this a little bit. Graham, you're gifting five to your one substantial lives community. Wow, wow, wow. Thank you for the gifts, Graham. Walsh Dragon has won, Gary from the Mitten has won, leukemia has won, weekend at Barney's has won, Finnegan Fox has won, and I've got a 100 heart pounding show love. Cheers, Graham, case math says. Thank you, Graham. Okay. Now consider this analogy, right? Because a lot of people have a hard time appreciating case matter. We've done 1000 points. Nice. By the way, case map, we're doing auctions. I'm going to fingers crossed the packing video I should have up by tomorrow. Thank you for redeeming the points. And Hannah, thank you for the 1000 bits. Crazy with work, crazy with work. So check this out. You weren't able to make. I come and go. My depression keeps me on and off Twitch randomly. Hannah, it's a good idea to unplug, really. Gang, it's a good idea not to consume even mathematics on a day. I don't want to say mathematics because it's a really good idea to consume mathematics every day. Okay. It gives you a certain perspective that you will never get anywhere else. Okay. But consider this analogy because people have a hard time digesting this, right? What does it mean? Trig ratios. What does it mean? Trig ratios. They think it's some random, you know, far off idea that really doesn't have any applications in the real world. Just doesn't make sense. Okay. Not subrino six, redeem 500 points. So it's not though. Okay. Now I've mentioned this, we're going to get back to this, but now forget this. Right? Let's assume it's me and you. Right? Let's assume me, Chicho. Oops. I'm going to spell my right, my name correctly. Right? This is what a ratio means. The important word here is a ratio. Okay. Trigonometry is just a shape with three angles in it. Right? Three sides. Polygon with three sides closed. Right? Well, let's assume Chicho has $5 and you, right? You have $40. Okay. Did I just knock 500 points to 500 points? Maybe. I don't know. This pandemic has put me into a depression. I fight every day with addiction and sadness, but I have done a long, done a long way. I haven't done cannabis in a month, but I miss it so much. My woman threatened to leave me sadly. So I'm holding on as much. Hannah, look, you're not alone. Okay. And this situation right now, global situation right now has positives to it. Okay. It's revealed a lot about our society. Don't hold on to the negatives. Right? There's so much amazing stuff going on in the world. Tune out of mainstream corporate propaganda because they'll send you into a spiral of depression because they won't tell you all the positive things that have happened. Right? People are learning new things. People are connecting online. There's alternate platforms popping up, providing multiple avenues of you to be able to find what you need of sharing information. The veil has been lifted and people now see the lies through centralized power. People are building communities. People are building their, what do you call it? They got the community gardens going. They're growing food in their backyard. They have a better relationship with the environment. They have a better relationship with food. They understand what security means. Food and community security. Hannah, there's so much amazing stuff going on. So much amazing stuff going on. And as Graham says, keep doing the best you can, man. Being nice people, please. Awesome. Thanks for backing up, Graham. And case man, thanks for taking care of business. I missed it. Spider-Man, how you doing? Hello, Chichouncha. It's Rafa live. Rafa live. How are you doing? Reincarnated. I am glad to join in tonight. I hope you're well. You too, Rafa. Or Agri Pagu. Hello, hello. Sup, y'all? Math time while I'm watching Kill. Nice. Keep joining us and you will find our way along with us. We're all together, right? Collaboration is the name of the game. Collaboration is the name of the game, right? I hear that, but it's hard for me to stay positive. It's just been really hard, but I'm doing much better listening to Chichoudu math. Oddly makes me calm. Awesome. Good stuff. Now let's talk about this. Check this out. What is a ratio, right? Here's one thing that they really don't emphasize as much as they should in, let's say high school mathematics, but this should be really teaching this in elementary school mathematics, right? This is such a good game. Sugar ratios are so important for physics and for increasing your math power into Cal. Huge. And they're important to understand the concept of ratios. Now check this out. Look, let me ask you this. I'm going to give you two numbers. I'm going to give you this. Two over three, right? I'm giving you this. It's one number, really. I'm giving you this. Ask yourself, what does that mean to you? What does that mean to you? Two over three, right? There's two ways you can go with this. You can think about this as a fraction, which means this is two-thirds of a whole, part of a whole. That's what a fraction is. Part of a whole, right? So two over three means two-thirds of a whole. So if I draw a circle, right, and I break it up into three pieces, two over three means two parts from three, right? That's one way you can think of two over three. The other way you can think of two over three is as a ratio. And a ratio is not part of a whole. It's a comparison between two things, right? Compare, right? So when I say two over three is a ratio, that means two-three, right? That means two circles versus three circles, right? Two, two, three. In here, if you look at it as a fraction, there's three parts, right? Over here, if you talk this as a ratio, there's actually five things going on. Let me separate this so you realize there's two different circles. This is two, two, three. Okay, it's a different thing. It's a comparison, combined and not combined, okay? Now, these things, Sokotoa, are not fractions, they're ratios. That's important to really appreciate. So that means when you write down sine theta is opposite over hypotenuse, it means it's the length of the opposite side from the angle divided by the length of the opposite. It doesn't mean part of a whole. So if you do this, if I say, hey, what's the ratio? We're going to define a ratio right now, okay? We're going to say, can I erase this? I'm going to erase this part. Okay, take a look. Please keep in mind what a ratio is, right? So if I say, I'm going to define, I'm going to define, what should we define this at? We're going to define this as sine of chi-chou and cos of chi-chou. We're going to define this. This is what we're going to define. Should we call sine? I don't want you guys confused from this by sine theta, but I'm going to call it sine because I want to make sure you understand that this word here is just an English word or Latin word. I don't know where it comes from, right? This part is just the alphabet. It's up to us what we're defining as as, right? So I'm going to define the sine of c to be how much money you have divided by how much money I got, right? U over chi-chou, oops, chi-chou. And I'm going to define cos c as chi-chou divided by u. I keep on spelling my own name wrong. Chi-chou. I'm trying to do this speedy on Zalastar because I'm beating it like really pushing this, right? How do you graph a piecewise function? Sure, we'll do piecewise. I'm going to do it here. Piecewise. Piecewise. Piecewise are cool, right? So this is what I'm defining these at, right? So right now, based on our system, I'm going to call this absolute forever and ever and ever. If I have $5, you have $40. For every $5 I have, you will acquire $40. So if I have $10, you will have $80. Cool? If I have $15, you will have $120. Cool? So I'm setting this to be an absolute, right? This is set in stone. This ratio, 5 to 4. So right now, sine of c is u40 divided by 5, and cos of c is 5 divided by 40. Does that make sense? That's what the trig ratios are, right? Why are they important? Because let's assume we have the following questions. Question. Let's say every month I, not even, I'm not going to take it to that level. Let's assume you want to find out how much money you will have if I end up having, if this ratio stands, if I end up having $25, if Chicho has $25, if Chicho has $25, then what's sine c equal to for Chicho having $25? What would the answer be? Game. If I have $25, because sine of c is the money you have divided by money I have. So what's sine c if I have $25? What is this equal to? Well, this is the definition of sine c. The definition of sine c says it's the money you have divided by the money I have. Okay, so it's going to be the money you have divided by the money I have, and this ratio of set to be absolute, right? That means if I have $25, then we have to figure out what you have, right? Five times you have, yeah. So all you do, you say, oh, okay, this is what we need to find, but this is an absolute, and this absolute says 40 to 5, right? Cross multiply, kick the 25 up, 25, 5 goes into 25, 5 times, 5 times 40, you will have what? $200. That's what a ratio is. That's the power of a ratio. It's something set in stone, right? It's a definition set in stone. This goes into economics, personal finance. This goes into engineering. This goes into everything, biology, chemistry. This goes into everything, the concept of ratios. Okay, I really wanted to emphasize this because one of the reasons people have a hard time with so kotoa is because they don't understand what ratios are. Ratios is a comparison from one thing to another thing, right? Now, keep that in mind. Watch this. So, sine of an angle, I was much into medical math and doing prime non-param numbers, the building block of the numbers we deal with really, right? Now, take a look at this thing. The definition of sine of an angle is the opposite sine divided by hypotenuse. Definition, of course, of an angle is the adjacent side divided by hypotenuse. Ten of an angle is the opposite side divided by the adjacent side, right? Now, one place people get confused as they like to call the hypotenuse the adjacent, but the hypotenuse is the angle across from the 90 degrees, right? So, the hypotenuse is called, we call the side across from the 90 degrees, right? And always keep in mind, in a triangle, an angle controls the opposite side, right? So, this angle here controls this side here, right? If this side gets bigger, this angle gets bigger. Okay, college level trig was one of my favorite classes. The applications of trig to a circle is beautifully elegant, right? And we can kick it there if you like. Now, take a look at this thing. That's what we're defining sine of an angle to be. So, I'm going to give you a triangle. Here's a triangle. Three, four, five. And this is a legitimate triangle, right? It's a legitimate triangle. Take a look. Let's assume this is theta. What's sine of theta? What's sine of theta? I want you to tell me what sine theta is, cos theta is, and tan theta is. What's sine of theta, cos of theta, tan of theta? I want to drink some tea while you guys give us the answers. Thank you for the follows game. Like, never looked at it that way. The ratio of likewise stuff. It's the only way to look at trigonometry. It's the only way to look at trigonometry. It's their way to look at trigonometry. Why? Because that's what it is. It's drink ratios. They don't emphasize it. I don't know why the system doesn't emphasize this. It's insane to me. What's sine of theta, cos of theta, tan of theta? Give me the values, gang. I'm okay with going chill style. Sine theta, cos theta, tan theta. For sine, I can see, but cos is different. Cos, what's the definition of cos? It's the adjacent side divided by the hypotenuse. And we call this the adjacent, not that one because that one already has a name. It's called the hypotenuse. Sine theta is 3 over 5. This divided by that. Cos theta? Adjacent divided by hypotenuse. The adjacent of theta divided by that. Right? 4 over 5. Tan of theta was the definition of tan. Opposite side, opposite the angle, the side opposite the angle, divided by the adjacent to the angle. Okay? 3 over 4. Cool. Now, what does this mean? What does this mean? Right? Well, let's find out what theta is. Right? The longer hypotenuse is the smaller is cos theta then. The longer hypotenuse is the smaller it doesn't necessarily have to be smaller, this one. But the hypotenuse is always across from the 90 degrees. That's what we call the hypotenuse. Right? Opposite over hypotenuse. Cos is adjacent over hypotenuse. Tan is opposite over hypotenuse. Opposite over adjacent. Oops. I guess, man. I know. I've done that so many times, brother. I did it bad. You would make a great teacher then. Right? That's what it is. Right? Now, check this out. Let's say I give, listen to the teacher. Let's say I give you another triangle. Right? I'm going to give you another triangle. I'm going to say this angle is the same as that angle. Right? I just told you this angle is the same as that angle. Right? We don't know what that angle is yet. But this angle is the same as that angle. And the sum of the angles in a triangle equals 180 degrees. So if that's 90, that's 90, that's the same as that. Then this angle is the same as that. That we know. So this angle is the same as that. Now, I haven't told you what the angles are yet. Right? Like, I haven't given you a number for the angle. Well, this is what I'm going to tell you. I'm late. Let's go. Why are you doing it? Right? So check this out. I'm going to say this triangle is ginormous. I'm going to say this thing is 1, 2, 7, 5. Right? That's how big it is. If this was 3 meters, this one is 1,275 meters. Right? But the angles are the same. You can do it. Right? You can have a triangle with the same dimensions and make a bigger triangle with the same angles. Not dimensions, but angles. Right? Hayes, Hayes, 1, 2, 3, Chicho, your VODs, VODs keep on deleting. I wanted to re-wash your cigar stream. It was epic. I put them on BitShoot and YouTube. The reason they're deleting is because I'm only an affiliate on Twitch and the videos for affiliates automatically delete within two weeks, I think. Right? It's not up to me. As far as I know, there isn't any settings I could say. I could do on Twitch for them to stay on Twitch. I upload them to BitShoot and YouTube. Once I become a partner on Twitch, I think the videos will stay there. Okay? So we're working towards that. We're hitting all the marks. We just need, on average, 70 viewers for a month basis or something like that. We'll get it. We'll get there. Right? This could go on infinitely if it's the same angle. Exactly. You could have an infinite number of triangles. Fractals. Right? With the same angles. So this angle is the same as that. That's the same. That's the same side, but this side is huge. Well, I'm going to ask you this. What's this length and this length? Find this length and this length. Well, if the angles are the same and these are trig ratios, the definition of sign of an angle is the opposite side divided by hypotenuse. So sign of this triangle was this. Sign of this triangle, sine theta of this triangle is, one question I would have, adjacent isn't always constant as it's variable. I feel somehow confused for what I, no, these things can change the adjacent. Right? But the adjacent, the location of it is always right beside the angle. So the adjacent changes based on which angle you're in. If you're here on this angle, the adjacent side is this and the opposite is this. If you're on this angle, the adjacent is this and the opposite is this. Right? You are right on that. You are right. It's relative to your perspective where you are. Right? That's the definition of an angle. Maybe I shouldn't have used theta. I could use A. We could change this and say A. Here, A, A. Let's call this A, A and let's call this B and B. That way all of these guys become A's. Right? A, A, A. Right? Space out. Y over X for sine. Y over X, sine. Right? Sine of A is not going to be Y over X. Right? What's sine of A here for this triangle? What's sine of A for this triangle? What's cos of A for this triangle? And what's tan of A for this triangle? For this guy. It's been a few years since I've done this. It's crazy how quickly you can forget, but also how quickly it comes back. Yeah, yeah. Yeah, Connor. And it's, look, I can honestly tell you, re-learning mathematics, if you've forgotten mathematics, once you start re-learning it with fresh eyes, with eyes that have seen a little bit more of the world, wow, man. Super powerful. Dusting off some neurons I haven't fired in about the five years. Yeah. Yeah. So sine, skag bones, for sure. For sine. Yeah. Sine of A is one, two, seven, five over Y. Right? Cos of A is X over Y. Tan of A is opposite over adjacent, which is this over this. One, two, seven, five over X. Right? Makes sense. Well, if that's the case, and A, this A is the same as that A. That's why they call them A's. They're the same. So sine A is three over five, and sine A is this over this. That sine A is the same as that sine A. If that's the same as that, if that equals that, then that must equal that, because that equals that, that equals that, and that equals that. It's just ratios. Right? No? Let's do the Y. Well, let's do the Y. So this will have to equal this. Where should we do this? Let's do it here. Three over five has to equal one, two, seven, five over Y. Cross multiply. So Y, or three Y, is equal to one, seven, seven, five. Was that seven or two? Seven. One, two. One, two, seven, five times five, and then you divide by three, divide by three. Bring it over here. So Y is equal to one, two, seven, five, times five divided by three. Is that equal to two, one, seven, two, five? I'm just going to do it on a calculator here. One, two, seven, five. One, two, seven, five times five divided by three. Yeah. So Y is equal to two, one, two, five. It has to be. Oh, Y. Sorry. Y is two, one, two, five. There you go. You just found Y. That's it. And there's a little bit more just for intro trick, right? And then what does this mean, by the way? If this angle is the same as this angle, then Y has to be this. The reason it has to be this, because this divided by this is the same value as that divided by that. This is equal to 0.6, right? Then that divided by that is 0.6. The ratio stays the same. The ratio stays the same, right? For one single ratio on a constant adjacent there, the adjacent is not a variable, but the other variables are not constant until at least two of hypotenuse, I'm assuming, of tunnels or hypotenuse and angle B is declared. You need three pieces of information, one of them being a side for a triangle to be able to solve a triangle. There's six pieces of information in the triangle. There's three angles and three sides. And if you have one side at least, and two other pieces of info, there could be two sides, there could be two angles, one angle, another side, you can solve all the rest. So you can get all six bits of information in a triangle if you have three pieces of info and one of them has to be a side. That's sort of intro trick. And then if you want to find the angle, well you can do this. You can take inverse side of it, but I don't want to go there yet. I'd like to do the piecewise function as well, because if this is intro trick, this sort of gets you the starting point, right? Any questions regarding this? We could do more. We could come back to this, but we could do, let's do a piecewise function and then come back to this if you'd like. Lark Bark, how are you doing? Hey, yo, Gijo, hello there, hello, hello. I have advanced questions that may not give more information. Not me, okay? Not yet reading 1000 points. My brain always jumps to advanced trick, but you've got to get the fundamentals down first. You've got to get the fundamentals down first. One of the reasons people have a hard time with grade 12 tricks is because they don't have the fundamentals down. Where were you during my college years? Depending on how old you were, maybe I was taking college. I was in college. I doubt it though. I was in the college in the late 80s, early 90s. Let's do piecewise function. Piecewise function. On YouTube, Gijo's math videos helped me in college. Nice. Piecewise function. Let's graph two, three different functions right now. Okay, wishing well everyone. I made Lark or two now. Thank you for popping in. Take a look at this thing. I want to give you three functions. Here's function one. Y is equal to two X plus one. Let's graph this function. I hope you know how to graph this. This is an equation of a line. 36 going on 37 next month. Nice Lark break. Was I teaching math when you were 37? You're 37. I was just getting into it I think. 35 going on 36. I've decided that I'm 35 from now. This is an equation of a line. Y is equal to two X plus one. You go on one. Y intercept is one. This is Y equals X plus B by the way. I hope you guys know how to graph this. And then the slope is two over one. So one, two, and one. Here's this graph of this guy. It's a line that goes like this. Here's another thing I want you to graph. Y is equal to five. How does this look? Y is equal to five. Whoa, line slopes, more dusty brain sounds. Y is equal to five says, no, it's not a dot. That's a mistake that a lot of people make. It's a dot. It's not a dot. I've told you that this is a function and this says Y is equal to five. And when it says that, straight line on Y is equals five. It's a line. It says Y is five everywhere, all the time, forever. So you're going to go one, two, three, four, five. And you're going to go whoop. So it doesn't make a difference what X is. Y is always five. It's that absolute. Here's another function. I'm going to give you the point three and actually I'll go negative three and six. It is a function by definition. Y is equal to five function. If I said X is equal to five, we have vertical line and that's not a function. But we said we're going to graph piecewise function. So let's do this. This is a point. For a given X value, you have a Y value. Negative three and six. Negative three, one, two, three and six. One, two, three, four, five, six. And that's this function. Negative three and six. Well, I'm going to make a brand new function. And I'm going to take all these three functions and create one function. Okay. The new function I'm creating, let's call this Y1. This is Y2. And this is Y3 if you want. Y3. And it's not even really a Y3. It's a function f of X3. Right? f of X better. Well, let's use Y for now. I'm going to create a new function Y4. Y4. And Y4 is equal to this. Y4 is equal to Y1 when X is greater than three. Y4 is equal to Y2 when X is less than or equal to three, but greater than negative two. And Y4 is equal to Y3 for X less than negative two. Less than or equal to negative two. Do you see what I'm doing here? I'm creating a new function that's taking this, taking this, taking this, putting them together by defining the functions for different locations on X. Let's graph Y4. Y4. The graph of Y4 is Y1. And Y1 is really 2X plus one. Right? So I can write down 2X plus one here. 2X plus one. So Y4 is equal to 2X plus one for X greater than three. Okay. First thing you want to do when you're going to graph these things, graph this guy. Right? So you're going to go 2X plus one is one and then over to one. So there's this guy. Right? But the problem is Y4 is only equal to this for X greater than three. So let's put three here. One, two, three. So Y4 is equal to this line only for when X is greater than three. So here's three. So from here with an open circle, because it doesn't include three, you get that. The rest of this you kill because Y4 is only equal to this for X greater than three. Okay. Is that clear? Now for X between negative two and three, negative two and three, it's Y2. And it means it's equal to five. So Y4 is equal to five between negative two and three. Okay. Between negative two and it doesn't equal negative two. So open circle at negative two at five. One, two, three, four, five. So negative two, open circle to three, close circle. That's this. Cool. So Y4 is equal to five between negative two and three. And for any X is less than negative two. Right? Less than negative two. It's Y3 and Y3 is just a point. Let me just put a point there. Negative three and six. Okay. So whenever X goes less than negative three and I don't even think this is like legit terminology, but I'm just trying to show you what it looks like. Negative three and six. So negative three and six is a dot. There you go. Nope. This function, Y4 looks like that and it's made up of three different functions. That's what a piecewise function is. A piecewise function says at a certain point the function behaved differently. The function looks different. It doesn't, it's a new equation that defines that function. Right? That's all. That's what a piecewise function is. This is a pretty simple piecewise function. You're going to have multiple different types of piecewise functions. Right? Functions and definitions do create the graphs. Yeah. You have to sort of look at your functions and try to appreciate what it is it's saying. Is it your B-Day case, man? Happy early B-Day. I didn't catch the B-Day part, but that's enough. The math, math, the neurons is good on a B-Day. Right? Is that clear? And you could have tons of crazy types of piecewise functions. You could have something like this. Here's a graph. Your graph from here to here could act like a parabola and then act like a line and then be dots. And then from here become an exponential. Right? Like you could have any type of functions. CMAS 420. How are you doing? I'm not sure I speak the language you're typing. Happy MNM9. Thanks, Chichot. I could not break it down when looking at a Y4, but it is much easier when you did one, two, three. Yeah. And you have to approach it from that side. Approach it as a piecewise function. Pieces of other functions put together to define a new function. CMAS says he doesn't get it. Which part don't you get? JSA really? I have no idea what that says. Swag boy. Flicks. How do we find potential intercepts of two or more functions? Sure, let's do it. How to do quadratics? That's what he's saying. How to do quadratics? Let's do a quadratic. Here, we'll do one. Ready? Is what he said. I need to teach square functions. Square functions. I'm not sure what's square quadratics. That's what you must be referring to. And I don't know how to begin. Square root square square functions. That's what you probably mean. So quadratics. Okay, take a look at this thing. Who asked for the intersection of two lines? Swag boy. Okay, quadratics. Swag boy. Take a look at this thing. Can I incorporate intercept two functions? We'll do two functions. Sure, let's do two functions. I'm going to give you, let's find the intersection between a line and a quadratic. So we're going to put swag boy and parabolas. Yeah, swag boy and CMAS 420 together. Okay, take a look. The question is this. Solve for the following system of equations. Okay, and the system is this. Your first equation is y is equal to 2x minus one. And your second equation is y is equal to, do you know how to do simple quadratics? CMAS? x squared? Or can you do more complicated? Can you do more complicated than x squared? If you just want to do x squared, we can stick with this. If you can do a little bit more complicated, we'll do a little bit more complicated. But if you're, iffy on this, we'll stick with this. Okay, let's just stick with this. Let's stick with this. Okay, so to get a visual, okay, think about it this way. First thing you want to do is graph both things. I can do a harder one. You can do a harder one. Here, watch this. Here, we'll do one little harder one. I'm going to do this minus, and I'm going to go plus four. Okay, I'm not going to put the x term in there. You can do much harder than this. Can I do kick it up one more level? Let's kick it up one more level. Okay, I'm going to do this. Minus x squared plus four x plus four. Okay, sure. Let's just do this. I didn't kick it up full level, but this is good enough. Okay, so if you want to understand what this question is asking you for for solve for the following system of equations, it's basically asking you if these two functions intersect, where do they intersect? I'm back in four minutes. You're back in four minutes. Okay, you got to go pee. Go take a pee. Go grab a sandwich, right? Before I get into graphing this, I'm going to have a drink of water. Gang, if you eat meat, if you're diet for some reason you need a lot of protein, you're eating a lot of protein, you're going to get thirsty, drink a lot of water. Very nice. 2 a.m. in your country. Oh, wow. You got my full tension. Okay, let's do this. Watch this. So let's get an appreciation of what this system of equations, these two equations look like on a single graph. Wanted to tune in for a bit before bed. Now awesome. Let's graph this guy first. Equation one. This is y equals mx plus b. It's a line, so the y-intercept is negative one, and the slope is two over one. So one, two, and then you go over one. There's your first equation, first function. When you graph these things, number them. This is equation one. Let's graph this guy. How do you graph a parabola? Oh, we can make a table of values, but man, that's a hit and miss, right? Because you've got to get both sides of the axis of symmetry. So one way you can do this is, you can do something called completing the square. The square. And by the way, to solve this algebraically, you don't need to graph it, but we're graphing it to get a visual of what's going on. Second one has arms directed down. Yeah, because it's negative. So if you're going to complete the square to this, you're going to basically write it in a form that you can read it, right? That's what I did with this. This equation is y is equal to mx plus b. It's an equation of a line. This is the y-intercept. That's the slope. You graph it, right? You put it in the right form to be able to read it correctly to be able to graph it. So for this one, we're going to complete the square. y is equal to negative x squared plus 4x plus 4. And we've done lots of videos on completing the square. Okay, I'm going to do it speedy Gonzalez here. Okay, I'm going to write a little bit bigger so you guys see it better. And if you do chicho, completing the square, videos will pop up. That'll show you what this, how this process works. I'm going to do it quick right now. First thing you do, you put, here, I'll do this with red so you see. Let me bring out the new, I'm going to about a whole bunch of new felts, right? So you put brackets around this, the x squared and the x-turn. Can you see that well enough? I'm going to make it darker, right? And thank you for the follows. Thank you for the subs again. Now, what you're doing right now, CMAS, when you set it equal to zero, you're only going to be graphing the x-intercepts. I want you to graph this whole problem, not just find the x-intercepts. We don't need to find the x-intercepts to get this visual happening right now. Next thing you do is you take the number in front of the x-squared, bring it out. So you want the number to be in front of the x-squared to be a one. So this becomes a negative number comes out. This becomes x-squared. And because the 4x is also inside the bracket, you're factoring out a negative from this. So this becomes minus 4x. Next step is you take the negative 4 divided by 2, you get negative 2 and square it, you get 4. And then you add and subtract 4 inside the brackets. I'm not going to go too much detail with it, of why you do this. We talked about this, x plus 4 minus 4 plus 4. So you add and subtract that inside the brackets. Now what you do is you grab this guy, bring it out of the brackets. When it comes out of the brackets, whatever is in front of the brackets multiplies that, right? And that's a negative 1. So multiply by negative 1, it becomes plus 4. This is now a perfect square and it's root is negative 2. So this becomes, we can do this. Yeah, you can do this. You've done this, yes? So this becomes negative x minus 2 squared plus 8. So this is your y2, y2, because that was your y2, then here's y1, right? So now you have this in a form that you can just read it and graph it. When you're reading these things, this is a quadratic formula, this becomes your vertex. The vertex is the opposite sign of this and that, 2 and 8, 1, 2, 1, 2, 3, 4, 5, 6, 7, 8. The negative number says it opens down. The y-intercept is 4, you can go back here, set x is equal to 0, you get 4, right? So if you want to find out what y is when x is 4, just put 0 here. When x is 0, y is 4, right? 1, 2, 3, 4. So the parabola goes down like this. Parabolas are symmetrical about the line, the axis of symmetry. So if this is 2 units away, then that's 2 units away, so it looks like this. That's equation 2. That's your parabola. Now, what does it mean when it says solve for the following system of equations? It means if these two lines, if these two functions cross, now that's clear for me, awesome. Is that good? Because there's more to this a little bit, right? You're very welcome, CMAS 420. Like it's simple. You just have to follow in proper order, right? Awesome. So when it says you want to solve the system of equations, you're trying to find out if these two functions cross, where they cross. So you want to find out they happen to cross. Sometimes they don't cross, but these two things happen to cross in two different locations, here and here. So when we want to solve them, we want to find the coordinates of this point and we want to find the coordinates of this point. We want to know what they are. We know they're both x's and y's, right? So there's got to be an x here and there's got to be a y here. Let's call this x1 and y1, because that's the first point where they cross, and let's call this x2 and y2. x2 and y2, where they cross. Now when I say y2, I don't mean this function. I mean the second point, right? So all you do is say, okay, this point here, x and y, exist, right? Both on this line and on the parabola, right? It does. This point, x and y, at this x value, if you plug that in for x, you're going to get this y, and if you plug in this x here, you're going to get the same y, right? So if you're trying to find out what this point is, you're trying to find out when this y is equal to this y is equal to this y, because they're the same y. That point is on both those lines, both those functions. So all you do, you just set this equal to this. So you say, if you're going to solve this, you say solve, set y1 equal to y2. You're going to set this equal to this. That means this 2x minus 1 is going to be equal to negative x squared plus 4x plus 4. You set y1 equal to y2, right? And you solve for this now, right? And if you're solving for this, just bring everything to one side. Let's bring all of these guys to this side. So if you bring all of those guys to that side, it becomes x squared. This becomes 2x minus 4x is negative 2x. This becomes negative 1 minus 4 is negative 5 is equal to 0. How do you solve this quadratic? You can factor it manually, but I can't think of two numbers that multiply to give you negative 5 and not to give you negative 2. Oh, that's neat. I didn't think of it like that. Now, delta, cool. That's slick. Yeah, that's what it is, right? Which is crazy cool. When do they equal each other? Where on the graph do they have the same x will give you the same y? Do they have a point that exists on both this function and that function? Well, I can't think of two numbers that multiply to give you negative 5. I have to give you negative 2. So you just use the quadratic formula. x is equal to negative b plus or minus square root of b squared minus 4ac over 2a, which is negative b which is 2 plus or minus square root of negative 2 squared is 4 minus 4 times a is 1 times c is negative 5 over 2 times 1, which is equal to 2 plus or minus square root of negative 4 times negative 5 is 20. That's way faster. 4 plus 20, 24 that I used to learn. So 20, 24 over 2. I want to do this. Bring it out. Where are we going to do it? Let's do this thing here. So x, here let's do a little thing here. So right now we've got x is equal to 2 plus or minus, now square root of 24. Square root of 24. Square root of 24. 24 breaks out into 2 times 6. Sorry, 2 times 12 or 4 times 6. Let's go. 4 times 6. 2, 2, 2, 3. So square root of 24 is 2 root 6. 2 root 6 divided by 2. 2 goes into both of those. So this becomes 1 plus or minus square root of 6. That's your x value, right? Evening. Evening, Twitching Jason. How are you doing? So when x is equal to 1 plus the square root of 6 and 1 minus the square root of 6, you get this expression equal to 0. That gives you your x. Plug it into the equation, get your y. Okay. Twitching Jason, thank you for the cheers. By the way, nice cup in your upper corner. Thanks. This one, the black one. It's nice. It's a good cup. Shotgun. What are those? Shotgun. Alien beauty. Alien beauty. Alerious. Is that clear? This is what's going on when you solve the system equations. Could you show it to the camera? Yeah, sure. Let's see if you'll focus nicely. This is pretty. It's nice. It's not expensive or anything. It's just pretty. That is more understandable. I've got to learn the quadratic. You need to learn the quadratic formula. It saves you a lot of time, right? And then what you would do, what you end up having, by the way, we set this equal to this and we've got two different x's, right? x is equal to 1 plus the square root of 6 and x is equal to 1 minus the square root of 6. Well, we have two places, two different x's. When you plug it in, you get two different y's and those are the two places where the two functions cross. And that's all there's to it. Really? It's super cool. Super cool. Super cool. How do you still remember that? I've been out of school for only six years and I have zero recollection of any of that. Shotgun? Shot done? The quadratic formula? I never forgot. You end up using it so much. It's just, I didn't forget it. Sometimes I would struggle with, when someone asked me, what's the area of a circle? I was like, when I wasn't doing mathematics, I was like pi squared. And then it would go quadratic formula. Negative b plus or minus square root of b square root of 1 is 4ac over 2a. It just uses so much. Yeah, I'm glad it helps, white boy. Is repetition an effective way of memorizing work? Memorizing work? Sure. Understanding work? No. And I don't recommend going into mathematics with memorization. Thanks, Twitching Jason. I love the little bits. Right? So I don't recommend approaching mathematics through realm of memorization. I would say try to understand why things are the way they are. That's the best way to be. Okay, that's the best way to look at it. Thank you again, gang, for the follows and the subs. We, big, I like little rhymes like twinkle twinkle little star circumference equals two pi r. Ah, I've never heard that before. I use those with kids. I do. I've never even heard it before. Haha. Twinkle twinkle little star circumference equals two pi r. Ah, I love that. That's cool. I'm not the, I have mantras in math that I give people my mantras. Two of them. What's one of the first mantras you should just hum, right? The sign in front of the number goes with the number, right? The sign in front of the number goes with the number. So that's not a one. That's a negative one. That's not a four. That's a positive four. That's not a two. That's a positive two. That's not a negative X. That's a negative one, right? The sign in front of the number goes with the number, right? Do you have another negative? That's not a two. That's a negative two, right? That's not a five. That's a negative five, right? The other one is reduced before you multiply. Any book recommendations for someone designed to have a deeper understanding of basic mathematics? Swagboy, I wish I had read a book. Do I wish? I don't know if I wish. I wish I knew of a book that I've read to understand the core basic mathematics, but I didn't. I learned even though I studied mathematics, I got my minor in mathematics, I got my degree in geophysics, I really didn't understand mathematics until I started teaching mathematics, and the reason I began to understand mathematics is because students would ask me questions, they would go, Chico, why do we do this? And I didn't know the answer because I just knew we did this. So I would go online, grab books, multiple books, and do things, and think about it, go, why are we doing this? Because the answers are not obvious, they don't tell you the why, they just tell you and then after answering so many questions over the years, I began to understand why we do a lot of the things that we do do. So any good book recommendations? Yeah, but I haven't written it yet. Give me a few years. I'll write a book and I'll start recommending that book to teach mathematics and to understand mathematics, because I know they're out there. I just haven't read them. I had to figure this out by doing, by explaining. If you want good calculus books, I've done a good calculus book recommendation, but that's calculus. I use the calculus book recommendation that I recommend in that video. I've done a couple of videos of book writes, more than a couple of videos of book recommendations, and there's one main calculus book that I've used to learn, one book that I've used to learn calculus, and that's my to go to book. I don't have it handy right now. It's in another room. Shut down. I'm really good at quick math, but when it comes to these formulas, I am so lost, and then I feel stupid, but I can solve easy math problems on my head. Yeah, but formulas, I'm lost at this point. The reason you're lost shot done is because you don't know your algebra. Learn the rules of addition, subtraction, multiplication, and division. Learn algebra. Let the pen and paper. I don't teach my students to memorize or to do things in their heads rapidly under a time crunch. I tell them, let the pen and paper do the work for you. Why do extra work? When you go to the gym to work out, I have a friend that is a bodybuilder, is a fitness trainer, stuff like this. He goes, chucho people are stupid. They go to the gym, they think the best way to work out is to lift the heaviest thing they can, struggle, and they hurt themselves, torn ligaments, and all this jazz. He goes, I tell my clients, lift light. Lift it well. Do the correct posture. And that's how he teaches people to bodybuild. And the guy's done competitions doing this. So he goes, I don't want to lift more weight than I have to. I don't want to process more data than I have to in my brain when I got pen and paper that can do the work for me. I'll save that brain power to do more, you know, use it down the line, right? I'm going to remember pi equals r forever now. Twinkle, twinkle, little star. Circumference equals 2 pi r. I like that, God of gadgets. It's really weird, no matter how complicated something looks, it's always the explaining that decided whether it's hard or easy. Yeah, indeed. Skag boss. Bones, Skag bones. Hey, we got two swag. Oh, we got swag and skag. Skag swag. Good thing. My math teacher told me that tutoring and teaching is a great way of learning math. Might as quickly. Indeed. I'm just scared. Do it, really. Do it. If you want to learn math, start teaching. Can you show me the how to find gradients, please? Y equals mx plus b. You guys, you see, okay, it makes sense. Yeah, sure. Let's do y equals mx plus b. I would like you to teach at my school. Morrison. Morrison. I don't teach in an institution. I wouldn't last there. Gradients. So you're talking about slopes. Take a look at this thing. How's your time going? You should be the key, not the whole referring to your data thing. We've got time. Let's do this. Take a look at this thing. Let me draw you a line. Let's go from here to here. And make the line go continuous. So we're going from these two points. Let's call this one. Let's call this one, two, three, four. Let's call this two, three, four, four. Actually, let's make this here. We'll make this one five so we don't get confused. Six, seven, eight. Last eight. All right. So right now we have the following two, right? This point is one and five, one and five. And this point is four and eight, right? Those are the two points. Okay. So what you want to do, there's two properties of a line that you need. Y is equal to Mx plus B. And who was it? God of gadgets. You guys are calling it C. In my part of the world we call it B. And what these are, a line is a simple function, one of the simplest functions there is, right? This is the slope. The M is the slope, which is equal to Y2 minus Y1 over X2 minus X1, which is rise over run, right? Rise over run, okay? And the B is the Y intercept. The Y intercept is here for dysfunction. We don't know what it is yet, right? You actually memorize me, dude. Memorize me, dude. I can listen to you all the day talking about anything. You always grab my attention. Big Femma. Awesome shot. Shot done. Thanks for being here. I'm going to talk about pebbles on the next stream. She was too at the start. Yeah, I couldn't function in school, man. I get fired in a week if I lasted that long. That's interesting. How the English system is different. My style is Y equals KX plus M. Whoa, KX plus M. Where are you from? Cabernicus. Where are you from? It's cool. And it's super cool. Different parts of the world. Sweden, wow, wow, wow, right? So the way you do this is you want to figure out what the slope of this line is. The slope is how much you rise over how much you run. Let's zoom this in area, zoom into this area, so these were your two points. This was one and five and this was four and eight. So this was our line. I've just zoomed into this. So we have more room to work with. So the rise is how high did you go from this point to how far you went down the line? So what would the distance here be? It would be this minus this, which is Y2 minus Y1. Y2 minus Y1 divided by X2 minus X1. X2 minus X1. This is 8 minus 5, which is 3. This is 4 minus 1, which is 3. So what's the slope of this line? The slope of this line is equal to 3 over 3, which is equal to 1. Right? Rebo, hello, how are you doing? Oh, Dipper, I don't understand what you did with RAD 24 in the previous exercise. RAD 24. Oh, the square root. Yeah, sure, I'll show it to you. Sorry, but only now I can send this next because of the chat. Okay, sure. Let me take a little break from this. This is what I did with the radical. Square root. I hope it's okay. We take a little tangent from this. Send you a little tip to grab a coffee or tea on me through PayPal. Thank you very much, Shondan. I appreciate it. What's this? Square root of 24. Right? I haven't done math in such a long time, Rebo. I wish I understood the derivations and how these mathematicians reach into the ether and arrive at their revolutions. They don't reach into the ether. They use the rules of mathematics and they just bring things together and then build it and go, wow, look at what I came up with. Really, that's exactly what they do. That's all they do. Right? If you're taking a square root of 24, right? Square root, this symbol here, okay, is a radical. If there's no number here, it means two. What that means is if you have two of a kind here, you can bring them out as a single, as a one. Right? So what you do, you break these things down into the prime factor trees. By the way, if you do chicho, radicals, radicals, radicals, okay, chicho, radicals. I've done some videos on this. I did a whole series on this, but there's an ASMR video that we did. It's like hour long, maybe explains this really well. Right? And I did a whole year, summer of putting exponents and radicals together. And that does a fantastic job explaining this stuff. But take a look at this thing. This says, break this thing now. Two times 12 is 24. 12 is two times six. Six is two times three. If it's a square root of 24, it means find two of a kind. You can bring them out as a single. So here's two twos. They can come out of the symbol as a single. They merge together as one thing. And then inside, and anything you split is dead. Right? But inside, we've got two and a three. They can't pair up. So two times three is six is a square root of six. Okay. Wash this. What if I said I want the cube root of 24? Well, 24 is two times two times two times three. Two times two times two times three. Well, cube root of 24, cube root says, you're looking for three of a kind. Three of a kind can come out as a single. Here's three twos. They can come out as a two. This guy can't come out because it doesn't have two other ones to hook up with to come out. Right? So you got cube root of three left. Is that clear? I know it's just jumping right in and doing it, but that's basically what it means. Look for, okay, clear. Okay. Awesome. As far as this thing goes, come on up with the equation of this line if you want. So right now we found the slope. Y is equal to one X plus B. All we need to do is find B, the Y-intercept. You're very welcome, old dipper. I'm glad you find it useful. And its radical is super cool. And radical is just denominators in the exponents, but we'll leave that alone for now. So we want to find out what B is. The way you can find out what B is is just take a point and plug it in for X and Y. What we're going to do for both of them, we're going to get the same B. Right? Test, put in one and five, because we know that point is on the line. And do this as well, four and eight. If you get the same B, you know you did it right. Right? So plug this in. Y is five is equal to one times one plus B. Five is equal to one plus B. So B is equal to bring it over four. So this is actually at four. Comes out exactly at four. But let's do it on this side, make sure that's the case. Eight is Y, one times four plus B. Eight is equal to four plus B. Bring the four over minus four. So B is equal to four. Oh look, it's the same B. It's the same Y stuff. There is the same Y stuff. It's because we came up with the same line. We generate the equation of the line for the same two points. It better be the same Y. If these two were different, then we did something wrong. So the equation of this line is Y is equal to one X plus four. That's the equation of the line that's formed by this point and that point. That's all. Right? Y equals MX plus B. Cool. I should really go to bed. It's almost 3 a.m. I should watch the VOD tomorrow. Yeah. And you got two weeks to watch it on Twitch and I'll have it up on BitShoot and YouTube in a couple, not a couple of days, but about three or four days, four or five days. Okay. There's a lag between the time I put it on and whatnot. Oh, I got it. Awesome. God of gadgets. Again, we're almost into two hours. So let's call it a call of the stream. Okay. Nice tutoring session, by the way. This was a great session. I liked it. Thank you for the question. It should be fine for me. Oh, Sean. Yo, what were you doing? Thanks. My pleasure again. And again, I saw a lot of follows coming through. Thank you for the follows. Good math. Good math. Thank you for the follows. Thank you for being here. Thank you for the interaction. Thank you for the subs. Graham, thank you for gifting the five subs. That's amazing. Fantastic. This is amazing. I hope you get the most popular you can. Thank you. Cruz Jesus. Cruz Jesus. Am I pronouncing that right? Boastream, Wenchicho, cooking stream. Cooking stream. We just made a whole bunch of hamburgers yesterday. We did, I made 50 hamburgers yesterday. I ate three of them today. I ate like, I don't know how many yesterday. So we did like a three and a half hour cooking session. We made like tons of hamburgers, 50 hamburgers. So I cooked up 18 of them. So we're going to eat them for like a couple of days, right? Two or three days, right? And I put 32 in the freezer, right? In freezer lock bags. So there's eight of them, right? So whenever we want to have hamburgers, we had eight days more than that. We're not going to eat eight hamburgers in a day, right? So we have enough hamburgers to eat for a few days. Perfect. Cook for one day, eat for multiple days and save some in the freezer so you can have it again, right? Are they smaller? They're pretty good size. They're like this big. It's a good size. It's yummy. I took six pounds of beef, ground beef. Six pounds of beef. We had potatoes in there, onions in there, whole bunch of stuff. It was good. Very delicious. I'm not on this score at the moment and I'm missing streams. Oh no, bureaucracy kills. Bureaucracy kills. I haven't seen you forever. What's going on? Put the, what do you call it? Check out the Patreon page. I'm starting to pin the schedule on the Patreon page. So if you go to Patreon, if I have any schedules lined up, it should be the top post, okay? And if you follow on Twitch, it should send you notifications. You don't have to subscribe, but Skag bones. Preparing fruit is never bad. Saves a lot of time and you can put a lot of love and cooking you see. Yeah, for sure. It tastes better. You know what you're putting. You know what you're eating. You eat healthier. You are healthier. So important. Got to go and watch that. Yeah, it was super good. It was a fun stream. Cooking season, yeah. And different vegetables and fruits come into harvest, like different seasons. You get different fruits and vegetables and you can use them fresh, local, amazing gang. Gang, thanks for being here. If you want to know what this is about, I'm on Patreon. Patreon.com. Everything I do is layered on mathematics. This is full-on mathematics. We do a lot of other things. Mathematics. Layered on mathematics. So we're going to connect them up in one way or another, right? And we have a lot of them already. I live in South Africa, South Africa. Peace, brother. Hope you're doing well down there. 3.47 a.m. Go to bed. You need sleep. So I am on Patreon. I don't put anything behind paywalls. Everything's creative commons. Share and share alike. Okay, if you like the work there, if you like what we're doing and if you have the means to support this work, Patreon is a great way to do so. And for those of you who've been supporting this work through Patreon, thank you very much for the support. We are live streaming on Twitch, twitch.tv forward slash chico live. C-H-Y-C-H-O-L-I-V-E. If you want to participate in the chat, in these discussions, Twitch is where you want to be at. And those of you who are on Twitch, supporting this work on Twitch, following on Twitch, subscribing on Twitch, doing bits on Twitch, doing tips of coffee and tea through PayPal, Streamlabs or whatever it is, thank you very much for the support. Thanks for being here. Great discussions, great questions. Love doing mathematics. I do announce these live streams on Parler, Lo, Mines, VK, Gap and Twitter. You can follow the work there and the links will be in the description of this video. And we do have a Discord page and there's a lot of discussions taking on, taking place on different channels, different folders regarding different topics. One of them being mathematics, of course. Skagbones, thanks a lot for the stream, show a good night and have a good evening. You guys as well, gang. And good morning to our South African friends and people on the other side of the world, right? For live streams, we don't have any visuals involved. We do right now. We will be uploading the audio to soundcloud, soundcloud.com, forward slash gcho, C-H-Y-C-H-O as podcasts and they should be available on your favorite podcasting platform, including Spotify and iTunes. And we will be uploading this video to Bichute and YouTube, mathematics everywhere, right? And if you want to support this work on those platforms, you can like, share, you can follow and subscribe. You can comment, you can like. And if you turn on notifications for sure, then if we are on YouTube, you can join YouTube membership. And for those of you who've joined YouTube membership, thank you very much for the support, gang. I hope you have a fantastic evening. We got live streams hooked up for the next three days and then one more. So we got current events tomorrow evening, starting at 7.30. Personal finance, Sunday evening, starting at 7.30. We got relationships on Monday that we're going to talk about and we're going to be talking about privacy and censorship on Wednesday, gang. I hope you guys have a fantastic day and I'll see you guys in the next few streams. You can make it. Bye, everyone.