 What time is it? 11 o'clock. Hi everyone, this is Chichou. Welcome to my channel and welcome to another live stream. Today is September 22nd, the second day of fall 2020 and it's 11 a.m. PDT, PST, Pacific West Coast time, Canada, West Coast of the United States and Canada and we're doing our math drop and tutoring session number 59. Let's do some mathematics related mainly to high school mathematics. We do go lower as well to elementary and we do a little bit above post-secondary. We're usually trying to stay away from calculus unless it's like really intro calculus which I'm slowly getting into. A little bit of stats as well is okay, not too hardcore and computer experimentations I try to stay away from personally. It's not my forte. Aside from that, welcome to another live stream. While we wait for notifications to go out, I'm just going to let you know who I am, what this is all about. I am on Patreon, patreon.com, forward slash chichou, c-h-y-s-c-h-o. The foundation of what I'm doing is mathematics. This is it. This is the core of what I'm building everything else up on, right? Hello, young Paul Axe. How are you doing? Welcome to another live stream and I do sort of provide my thesis on or my vision on my Patreon page in the front page I guess and you can follow the work there and if you think this is a worthwhile project to put your resources in, put your funds in. Patreon is a fantastic way to support this project. I don't put anything behind paywalls, everything is great of commons. Share and share all like you can follow the work and after a while. If you come to the conclusion that this is worth supporting, Patreon is it. Okay, we are live streaming this on Twitch, WorthCoronet. How are you doing? Welcome to another live stream. Hold on who's, how are you doing? Hello, hello and we are live streaming this on Twitch, twitch.tv forward slash chichou live, c-h-y-c-h-o-l-i-v-e. If you want to participate in the chat as you see it coming up here, Twitch is where you want to be at and for those of you who've been supporting this work through Twitch by subscribing, by donating, by bits, by dropping these tutoring, these live stream sessions really if it's math or not related to math. Thank you very much for the support and for those of you who've been supporting this work through Patreon. It is mainly because of your support that we're able to continue this work and grow slowly. Elder god, how are you doing? I do announce these live streams 30 minutes before we go live on LOMinds, VK, Parler, Gabb and Twitter for now. You can follow the work there. I do share additional content there and all the links will be in the description of the video once it's loaded to Bichu in YouTube and it will be loaded on both and we have a little bot which Elder God just shared on our chat on Discord where if you do exclamation mark social and we'll give you almost all of our social links if you are on those platforms. Felix, how are you doing? What's up Chucho? How's your day weekend? Days going fantastic. Check this out. I got up this morning. Yesterday I went Cornelian cherry picking and this morning I get up early. This morning I made some Cornelian cherry jam. Rock and roll. This is a delicacy. If there's any Iranians, Armenians out there that see this they'd be knocking on my door. Chucho, give us some of that Cornelian cherry. Fantastic. I just made it this morning and I'm sampling it and it's really good. I picked, I went for two rounds last week or yeah a week and a half ago or so. I picked about three pounds that I turned into liqueur. Cornelian cherry liqueur phenomenal and yesterday I wouldn't pick another eight pounds of Cornelian cherries. It's the last time the harvest is done. It's getting ripe and I turned that into jam this morning. So very happy about it. Very happy about it. Lonely Peggy, how are you doing Chucho? Good to see you as always. How's the temperature? Temperature's doing fantastic. Plants are loving it. Buds are coming in beginning bigger. Thorin, hello, hello Chucho. Got my notification. Awesome. Welcome, welcome to another live stream throwing. Thanks for dropping in. Two in a row. We got five more to go after this one this week, right? On charter days, say Chucho. Hope you and chat are well. Been a long time since I caught a stream. Yeah, on charter days. You've been busy, I hope, in a good way, right? Felix, that looks so good. Never had Cornelian cherries before. Are they similar to, no they're not. They're very tart and they have a medicinal feel to them. Like if you get tummy ache and if you get flu or something in Iran, Armenian, you, they sort of, you know, this is something that if you can get access to it, you grab and you eat and it's got seeds in it. And it's good for the tummy. Okay. Very unique taste. It's got a tart taste to it. Okay. And these are the seeds, the dolphin. Hi, Chucho. Good to see you. Good to see you too as well, dolphin. Always good to see a dolphin. So it's really delicious. Okay. Sean Yo, 71. Hello, hello, Cheryl. How are you doing? Hi all. I'm glad. O.T. is still warm there. O.T. temperature, O.T. We had forest frost. You had frost yesterday, Cheryl? What? I can't remember having frost this early. Frost already? Man, I hope we don't get frost here. If we do, I gotta bring some plants in. I gotta make room to bring some plants in. Frost, that's too early. Felix, not sure if I can pick them up here in the UK, but I'll look around. Definitely sound, look good. Yeah, for sure. Persian stores might have the gems. I doubt it if you can get fresh corn, alien cherries. I really doubt it. Spider-Man, how are you doing? Spider-Man, I got a comic book haul that came in. It's waiting at the post office. I might cut the stream short today a little bit. Okay. Maybe an hour and a half, hour and 45 minutes. That'll give me time to go grab the comic book haul and bring it here. And if I can do that, I might do an unannounced comic book haul live stream before the video game live stream tomorrow or later on this week. I gotta do it in the next couple of days because I want to leave feedback for the seller. Diet tag, hello? Is it me? Is it me you're looking for? Is it me you're looking for? Oh, that's from a song. I forget what it is. You don't pull on this. I'm sad I missed the current event stream because it was at four in the morning for me here and I have school. Luckily, I have the awesome video on demand. And I will upload that video on BitShoot, most likely tomorrow. I have another thing I want to upload to BitShoot today if I get the chance. And then tomorrow I'll have the current events live stream up tomorrow. It was a fantastic stream yesterday, by the way. And we're in USD zone 7. It's weird for Cheryl. That's crazy, Cheryl. This is too early for Frost. Man, some of my plans are the buds are in. I want them to get bigger. I hope we don't get hit with Frost. Felix, video game live stream. Been waiting for this for ages. What games are you playing? I'm not playing any games. I'm going to show you the video games I have that have made it with me this far since the 1980s. So, it's basically my video game collection. And they're all in boxes. They're just random, just everywhere I picked up. From the 1980s, I picked up some in the 1990s, I believe. I picked some up in the 2000s, picked some of 2010s and all that jazz. Yes, I made live stream. Finally, Megan Cupcake. How are you doing? I like your name. Skellig, how are you doing? How are we doing? You're doing good. You're doing good. Eating cornini and cherry jam and drinking dark Persian black tea. Life is sweet. Well, the tea's not sweet, but the cornini and cherries are sweet. For live streams where we don't have any visuals, like the way we do right now, we record on a lapel mic on an external recorder and upload the audio to soundcloud.com forward slash chico, C-H-Y-C-H-O as podcasts for those that want to listen to the live stream open discussions and audio format, and they should be available on your favorite podcasting platform, including Spotify. The audio for this, it will not be loaded onto SoundCloud right now anyway. Maybe when I retire and I can do a lot more backend work, I'll grab the audio from this and load it up as well. We'll see. Who knows? A couple of decades from now. And this video live stream will be uploaded to YouTube and Bitchute. I can't see us talking about anything that the YouTube censorship will knock us for. So it's mathematics streams, math, content will almost always. I don't think we've done one that we haven't uploaded to YouTube yet. We might because there's some touchy subjects that require a little bit of mathematical logic to kick in there for us to get a better perspective of what's going on, but we haven't done any of those yet. So all the math content will be uploaded to YouTube and everything goes on Bitchute. And if you are on YouTube and Bitchute, you can support this work by subscribing, following, liking, sharing. And if you're on YouTube, you can support this work by joining YouTube membership somewhere here. There's a button there that you can join YouTube membership. Aside from that gang, welcome to another math stream. We're going to do anywhere between two to four days a month to help people out with mathematics, mainly high school mathematics and elementary school mathematics, if it comes up, and a little post-secondary if we can manage it. And there are times that there are people here that know dropping our math tutoring sessions that know mathematics better than I do. And on our Discord page, people have been helping each other out, okay? Davish. Hello, hello, hey, Chicho. So we're doing some math today. We're doing some math today. And physics is also on the table as well. Audio with animation. I see it in 2040. Maybe. It would be fun. It would be fun, Elder Young. That would be crazy cool. Luma, how are you doing? How are you, Chicho? Doing well. Thank you very much. Here for the math. Awesome Montreal player. By the way, gang, no matter what we're talking about, you got math questions. Drop them. We'll deal with it. Math supersedes everything else. And please remember, politics on politics streams, finance streams, and what not. No politics on the math streams, please. Okay. Unless there's a mathematical analysis we can do on it, but we would have to get confirmation on the numbers and what not. So no matter what we're talking about, if you have questions regarding mathematics, just let us know what they are, and we'll deal with them. Garbage at math. But I know that what I want to get into, I need to be good at math. Megan, what do you want to get into? And which part of math? It's like, when you say I'm garbage at math, it's like saying I'm garbage at English because mathematics is just a language. So pretty sure you're not garbage at English because it doesn't make sense. The sentence just doesn't make sense. You either know a language, know it a little bit, know it well, know it really well. So what level are you in regards to knowing the language of mathematics? Are you just beginning? Do you just need to learn the alphabet like ABCs? Shadow Franox 21. Thank you very much for the bits. 10. What is 2 times 69? 138? Did I get it? 2 times 69 is a couple of couples having a good time. Felix, could you explain how to find points of intersection of two straight lines with simultaneous equations? For sure, let's do it. Oh my god, 138. I love it. By the way, the camera, because it's a whiteboard, will go in and out of focus. Apologies if it goes out of focus. If I notice it, I'll try to bring it back focused by doing my hands. Yay. Again, thanks for the bits. And if not, it will come into focus. Now, what Felix is asking for is something called systems of linear equations. So just imagine this, just short little background. If I ask you to solve something, let's say I ask you to go solve. So I say solve the following equation. 2x plus 5 is equal to 7. Let's make it 17. So if I say solve this, you go, oh, okay, you got to isolate the x. That's what solving means. Solving means get x by itself or get the variable y itself. Skeletal. Could you go into trigonometry too? Sure. Let's put it up here. Trig. What level of trig, Skeletal? Are we talking about the grade 12 trig or grade 8 trig? Like right angle triangles, Pythagorean theorem or functions, trigonometric functions, right? Megan, I'm bad at math then. I need to know physics level math because I'm interested in astrophysics space. Okay, cool. Hey, Spider-Man, Megan says. Megan, let's deal with your thing. So you want to go into astrophysics, so I'm going to put a little note here. Physics. I'm just going to put physics here so we deal with it. Physics. So we've got a couple other topics that we're going to talk about after we talk about systems of linear equations. Solving two lines, right? Just starting out so basic. So basic. Okay, done deal with the trig, okay? Now consider this. Always keep this in mind, by the way, gang. In mathematics, there's two types of questions really that you get when you're starting out mathematics in high school and stuff like this. One of them is to simplify. Simplify. And the other one is to solve, right? Simplify means crunch, crunch, crunch, crunch, right? Crunch, crunch, crunch, until you reduce it. So for example, simplify could be this. Four over six. Simplify this fraction. Well, you can reduce this fraction. So simplify also means reduce. So four over six is two over three. That's simplify. They could say simplify this, two x plus four minus three x plus seven. And this is more combining like terms, right? So you're going to reduce this thing. And two x minus three x is negative x. Four plus seven is plus 11, right? So simplify means reduce. Also means combine like terms, right? Simplify could be two x plus one times three x minus one. This is expanding, right? So simplify could also mean expand, right? And this, you multiply this by this, this by this, this by this. So six x squared minus two x plus three x minus one. And then you combine like terms, you get six x squared plus x minus one, right? So simplify basically means crunch, crunch, crunch, reduce it to a simplest form. Okay. That's what simplify means. Solve means get the variable by itself. And when they say solve, this has an equal sign in the question. So this would be solving because in the question that you're giving you, there's an equal sign. So solving basically means get the variable by itself, which basically means in most cases, we use x to solve something. Already lost on three. That's like ancient Greek. Don't worry about this. I'll explain this. I'm just giving examples of what's going on. This is just multiplying a binomial by a binomial, Megan. So, you know, you could go on and get way more complicated stuff, but we're not going to. I'm just giving examples of simplify could mean multiple things. And all those multiple things mean explain it more simply, the simplest way you can possibly explain something. That's what simplify means. Solving means get the variable by itself. And usually a lot of times we use x as the variable, as the placeholder for something that varies. That's what they call variable. And when you're solving for something, usually you get x or w or y or z or whatever it might be, x equaling something. That's what solving means. So keep this in mind. Now, that said, I could give you one equation. Just one simple equation here and say solve for this. What does solving mean? Means get x by itself, right? Okay. So to get x by itself, you got to undo what's being done to it. So what you do is you grab this guy, bring it over here. So line up your equal sign, you're going to get 2x on this side. This becomes 17 minus 5. Line up your equal sign. You got 2x is equal to 12. And then divide by 2, divide by 2. So x is equal to 6. Congratulations, you just solved for x. So if you plug in 6 for x over here, you can check, by the way, check. You go left side. This is the left side of the equation, left side of the equation. And this is the right side of the equation. If you go the left side of the equation is 2x plus 5. And the right side of the equation is 17. And you're going to check for x is equal to 6 to see if this works. You just substitute 6 in for x, right? So you're going to get 2 times 6 plus 5. 2 times 6 is 12 plus 5 is 17. Oh, look. The left side is 17. And the right side is 17. This is a valid solution. Right on. That works. Okay? That's what solving is when you get one equation, right? What Felix was asking, I believe it was Felix who asked it. Felix, could you explain? Yeah. So Felix was asking is, can we solve, here I'll read the question again, could you explain how to find points of intersection of two straight lines with simultaneous equations, right? Now, simultaneous equations will leave a loan. So basically the question is, well, not leave a loan, but we'll talk about it. But it doesn't need to be simultaneous equations, right? Could you explain how to find points of intersection of two straight lines? And what that means is this. This is this question. You could get another question saying solve for the following system of linear equations for the following system of equations or for the following two lines, meaning find a point of intersection if there is one. So they could give you this. Solve for the following two equations combined. y is equal to 3x minus 1 and y is equal to negative 2 over 3x plus 4, right? So when they say solve for this system, for this system, right? And system means more than one thing, right? Zain, Mohammed 345. Hi, sir. Hello. Hello. How are you doing? Zain, welcome to a live stream, right? So when they say solve for the system of equations, okay? I mean, year 11 in England. Nice. When they say solve for the system of equations, what we have right now is two variables. Remember, solving for something means get the variable by itself. If we're trying to solve for the system, there is in this system an x and a y. So we have two unknowns. Over here, we only had one unknown. Rule in mathematics. If you have one unknown, you need one equation to solve it. If you have two unknowns, you need two equations to solve it. If you have three unknowns, you need three equations to solve it. Four unknowns, four equations to solve it, and so on and so forth, right? That's things backwards in that. I have problems, so I go to special needs high school. Okay, Zain. So right now, we have two unknown variables, x and a y, right? So we need these two equations to be able to solve both for the x and the y. Now, if I gave you this, I gave you only one of them, and I said, solve for this equation, you couldn't solve for it because there was only one equation and two unknowns, right? You would need the second equation. There is a second equation. Now, there are two ways that you can solve this equation. Let's do a graph of it first, so you understand what's at play here. I have a math problem someone gave me to try and solve, but it literally looks like alien language to me. Could I put it in discord? For sure, Megan. And after we do this, this, and this, you can give it to us, and maybe we could do it right now if we got taught, right? I'm in Canada, Zain. Do you know how to do this? If you do, fantastic. Take a look at this. I'm going to give you a quick little review rundown on it. If you don't, pay attention. Pretty important. Okay, take a look at this thing. There's two ways to solve for this, right? Now, the first thing you want to do is graph it. And both of these graph lines, there's x to the power of one, y to the power of one, we know it's a linear equation, a line. So first of all, let's graph this here. Very general. We're not going to scale. We're not going to be very accurate with the graph. We just want to get an idea of what it looks like, right? To graph a line, we're going to use the format y equals mx plus b, right? Let's draw a line here. Do a little break. This is one thing I do to separate different problems, right? So we know the second problem starts here. So we're going to use y equals mx plus b. y is equal to mx plus b. For those of you that know this, that's the general equation of a line. The b represents the y intercept. The m is the slope of the graph. Awesome, Megan. Okay. So if you're going to graph these guys, you go to the y intercept first. The sign in front of the number goes with the number negative one. And then you do the slope. The slope is rise over one. Okay. Three over one. One, two, three, and over one. So there's line one. Okay. And always a good idea if you're solving these systems of linear equations, graph it quickly if you want just to get a visual so you know approximately in which quadrant the answer is going to be and if there is going to be a solution. Okay. Math equation to understand. Oh, you meant Elegant. I meant I reverse engineer math question to understand it better. And that's a great way to do it. Luma. Which fork of mathematics do you think is best to learn to use in day-to-day situations? Statistics. Statistics is probably the most important branch of mathematics in everyday life. We graph this one. That's equation number one. Equation number two. Y intercept is four. One, two, three, four. And then from the Y intercept, you do the slope. Negative two over three. One, two, one, two, three. Here's equation number two. Okay. This tells us that this line intersects this line, which is exactly what they want as the answer. When they ask your question to solve for a system of equations, they're asking you to find out where the two lines cross or two graphs cross, if they cross at all. By graphing it quickly, we figure out that, oh yeah, there's a solution right here. X and Y. What that means is this point right here, where both lines cross each other, that X and Y works for this equation and works for this equation. That point right there exists on both this line and this line. That's what they mean when they solve for a system of linear equations or solve for a system of equations. Now, before we go solving for this algebraically, keep this in mind. There's three things that can happen. When you're solving for systems of linear equations, one of the ways I was taught to find the Y intercept was to put both equations in the form Y equals an X plus B, then make them equal to each other, yes, since they are both Y, and that doesn't find you the Y intercept, that finds you the Y where they cross. The Y intercept, as soon as you put them in the form of Y equals an X plus B, the Y intercept is your B. Solve for X, then substitute the X value back in one of the equations to solve for the Y. Yes, not Y, sorry, point of intersection, yeah, Felix, point of intersection. G chose Fragonard with the European heritage. Yeah, check this out. So that's what we want to find, right? So at this point, if we plug in this X here, it's going to give us this Y, which is the same as that. If we plug in this X here, it's going to give us the same Y as well, right? Two ways to solve for this. One of them is substitution, the other one is elimination. Now, before we get into solving for this, keep this in mind as soon as you see system of linear equations. There's three things that can happen. And if you think about this, you'll appreciate what it is, right? There is one graph. I'm going to draw all three systems here, three ways that this can work out. If I give you two lines to say solve for them, the two lines might cross, right? And give you a point that exists on both lines. The only way this will happen is if they have different slopes, different M, right? So the only way this happens is different slope. The other thing that can happen is the two lines might be parallel and they might have different Y intercept. So their M's might be the same, but their B's might be different. If that happens, then the two lines are parallel because they have the same slope and there will be no solution. So this has one solution. This has no solutions, no solution. And the way this will happen is if you have same slope, M, and different B. So as soon as you write them in terms of Y equals MX plus B, we saw that they had different slopes. So we would have known that it was case one where there was going to be a solution, right? The third thing that can happen is if they have the same M, same slope, and the same Y intercept. Well, if they have the same slope and the same Y intercept, they're just the same line, right? So they're on top of each other. So this would be line one and this would be line two, right? What that means is there's an infinite number of solutions because there's an infinite number of points that exist both on equation one and on equation two, right? So this happens, there's infinite, infinite solutions, and this happens when they have the same slope, same M, and same Y intercept, right? B. Keep this in mind. This knowledge and this knowledge, Y equals MX plus B is sort of what you need as a precursor before you try to solve this algebraically because it gives you a lot of information regarding your problem, right? Now, now that we know this, we know that there is a solution, let's solve for it because if there was no solution, you wouldn't even bother trying to solve for this. You would say no solution. It means they don't cross. If there's an infinite number of solutions, if you rewrite it and it has the same slope and the same Y intercept, you would say, oh, there's an infinite number of solutions. So you don't even have to do the work. That's why it's important to know all these three possibilities, right? Because it could save you a lot of time. You don't have to go and do a whole ton of work to find out that there is no solution because all you've got to do is look at the slopes, right? Now, there's two ways to solve for this. I love cute girl toes. How are you doing? I wish I didn't. That's all my teachers sometimes. Stop pissing off your teacher's gang, okay? Most of them are trying their damnedest to get this information across, right? Two ways of solving for this. One is called substitution. Substitution. The other one's called elimination. Elimination. Now I'm going to try to fit it all in here. It might be tricky. If it gets too crunched up, we're going to go back up here, okay? Brackets, observation, divide, multiplication, subtraction. Take a look at this thing. Substitution is this. Set one Y equal to the other Y, right? If you write it in terms of Y equals an X plus B, you can substitute this Y for this Y, because they're the same Y, right? So what you end up doing is you set Y1 equal to Y2, because what you're trying to do is find the same Y, right? I should write this bigger so you see it. Let's write this. This point here is X and Y, right? So at this point, at this point, Y1 will equal Y2. And if you're trying to find that point, then just set Y1 equal to Y2. Force it to be that thing, right? I don't know about never changing. I heard they're going to come out with some new numbers soon. I hope they have a good time with it. So you're going to set Y1 equal to Y2, right? Well, what's Y1 equal to? Y1 equals this, 3X minus 1. So all you do, you go 3X minus 1 equal to, what's Y2? Y2 is 2 over 3X plus 4. Well, negative 2 over 3X plus 4, right? For the next little bit, I'm turning off chat gang. Watch this. I'm just taking chat off the video so you can pay attention to this, right? So right now we set Y1 equal to Y2. Well, all we've got to do now is this is one equation with one variable. So all we got to do is solve for X. Solve for X, i.e. get X by itself, right? So what we ended up doing by doing substitution, we took two equations with two variables, got rid of one of the variables by substituting in their expressions for each other, right? So we combine two equations with two variables to create one equation with one variable. Cool. So all we got to do now is just solve for X. The best way to solve for this, if you have a fraction in an equation, get rid of your denominators. Multiply by the common denominator. The common denominator here is 3. So I'm going to multiply the whole equation by 3. This becomes 9x minus 3 is equal to negative 2 over 3 times 3. The 3s kill each other, becomes negative 2x plus 12. So 3 multiplies every term here and then you're going to get X by itself. So you're going to grab negative 2x, bring it over, grab the 3, bring it over there. This becomes plus 2x. 9x plus 2x is 11x, and 3 comes over, negative 3 comes over, becomes plus 3. So this becomes 15. And then you divide by 11, divide by 11. So X is equal to 15 over 11. You just found the X, where they cross each other. Okay. Elder God, thanks for timing out. Zane. I think he was stuck in a loop. For sure, Elder God. I would have called it through the YouTube. Mr. Gaming, YouTube. Our YouTube channel is this. Hey, that didn't work out. Mr. Gaming, I have a test and I need help. Is there a way I can share it or email it? The test? Well, we're not going to do the test for you. That's for sure. However, we've got a ton of videos on our YouTube channel where you can go in there and find certain appropriate topics, a lot of stuff. You can go to our Discord and ask questions if you need help with something, right? On Saturdays, do we have a troll just come back? It was a troll for sure. Or he wasn't doing too well. I do multiply 3 both sides. We multiply toes. This is one way to do equations. I'm going to take this off and I'm going to do some of the calculations here. Check this out. The whole point, one of the things, anyway, mathematicians like to do is make life easy. You want to simplify things as quickly and with as little brain power as possible. So watch this. What if I gave you an equation? All right. First of all, ask most people what they don't like about mathematics. What part of mathematics they don't like? They say fractions. I'll show it to you, toes. You choose the three because it wasn't a variable. It was a common denominator. So take a look at this thing. By the way, I'm taking little tangents here and there to clarify things. Keep in mind, we solve for x in this equation. We've solved for the x. We still need to find a y. So we're not done this yet. But to answer this question here, why we multiply by 3, what if I gave this to 1 over 2x plus 3 over 4x is equal to 7 over 6 minus 1 over 3x? I said solve this equation. You'd be like, okay, we've got lots of fractions here. I don't want to deal with fractions. Right? Fractions add a little bit of more difficulty because you've got to find a common denominator. You can combine these guys by going to do common denominator and all that jazz. So as a general rule, to simplify the solving process, this is solve. To simplify your algebra, if you get fractions in an equation, multiply the whole fraction by the common denominator. Make sure it's an equation, not an expression. An equation meaning there's an equal sign in the equation. And the reason you're able to do this is because you can do anything to one side as long as you do it to the other side. It's a teeter-totter, the equal sign. Equality. Whatever you do on one side, you've got to do it to the other side. So what I do is look at this, go 2, 4, 6, 3. The common denominator between 2, 4, 6 and 3 is 12. So I'm going to multiply the whole equation by 12. So multiply the whole equation by 12. 1 over 2 times 12. 2 reduces 12 down to 6, so it's really just 6 multiplying this. This becomes 6x. 4 goes into 12 3 times, so it's just 3 multiplying this, plus 9x. 6 goes into 12 twice, so it's really just 2 multiplying this, that's 14. 3 goes into 12 4 times, so it's really just 4 multiplying this, 4x. Wow! This is a lot easier to deal with. Holy Kamolis, right? Chadoff is good for visual clarity. Awesome, Elder God. We're going to keep it off for now, okay? I left then came back, now I don't know what's going on. And Megan, here's the kicker. Gang, if you're sitting in math class, really, if you're sitting in math class, try to stay focused. When you're doing a problem, try to stay focused because mathematics is a layered process, right? You don't want to miss any simple concepts that all of a sudden throw you off. Not for like two years, no more. Megan, don't worry, it'll make more sense. Seriously, when we start doing physics, if you want to deal with physics, it's just algebra, you'll see. Seriously, it's bad, I was so into it, then I had to leave for a second. Okay, this I'm just giving an example of how to deal with equations where there's fractions, which basically, most people don't like fractions, right? So for example, let's assume you get this question, they tell you without the 12 up there, right? They tell you to solve for x. Well, simplify the equation, multiply the whole equation by the common denominator, and that gets rid of all your fractions. Now you don't have any fractions. Easier to deal with. 9x plus, sorry, 6x plus 9x is 15x. This you can't combine anything on either side, and then bring all the x's to one side, plus 4x. So that's 19x is equal to 14. Divide by 19, divide by 19. So x is equal to 14 over 19. Okay. That's the reason why we multiply by the common denominator. It makes the algebra a lot easier, right? Going back to our problem, we combined equation one and two in here. We set y1 equal to y2, came up with one equation with one variable, which means get x by itself, multiply by the common denominator, which was three to get rid of our fractions. Got to here, solve for x. What we need to do now is find the y associated with the x, because if you're in a Cartesian coordinate system on an xy axis, you can't just have an x equaling something or a y equaling something unless it's a line. If it's a point, you need an x and a y, they're married, they go together, right? It's a map, right? You can't find someone's address if they just give you the number, or if they just give you the name of the street. You need both the name of the street and the number of the house, right? That's your x and y coordinate, okay? So all we do, since we found the x is equal to 15 over 11, we substitute this either into y1 or y2. So let's do the work here, so you see it, and then we'll do it using elimination, okay? So all we do now is sub into 1 or 2. They're both going to give you the same answer, right? So let's sub it into 1. If we sub it into 1, y is equal to 3, the x is 15 over 11 times 15 over 11 minus 1. So this is multiplying fractions, 3, which is just really 3 over 1, times 15 over 11, becomes 45 over 11 minus 1, and you just got to add these guys as a common denominator, as 11, that becomes 45 minus 11 multiplied by 1 by 11 to give you 11, so you're going to multiply top by 11, right? So 45 minus 11 is 34 over 11, that's your y. So the solution to this system of equations is 15 over 11 and 34 over 11. What does that mean? 15 over 11 is 1 and 411th, which is the coordinate here, right? 1 and 411th, and 34 over 11 is 3 and 1 11th, 3 and 1 11th. If you're simplifying, which is where this is, right? If this was 1, then that's 1 and 411th, and this was 1 to, how did we do it? My graph sucked, so it would be 1, 2, 3 and 1 11th, which is here. So we found the solution to the system of linear equations, which is really, just find the coordinate where they intersect, taking some notes to jog my memory. Seriously, it's bad. I was into it then. No worries, Megan. By the way, Megan, once it starts clicking, it will click. I'm going to turn chat on again. Cheryl, Megan, would you like us to post a question you shared in Discord? Yeah, what was the question you shared? I don't know, but should we do trig? So is that okay? Oh, we didn't do elimination. Let me show you how elimination works. Let's do it up here. Watch this. This was doing using substitution, right? This was substitution. Elimination means combine these equations in a way where you eliminate one of the variables, which is really what we did anyway. We eliminated one of the variables, but they like to, when they teach you mathematics, they like to separate things, categorize things, give them English names to say, this is this, this is this, this is this, right? So it's just another method, a different direction where you could have got to the same solution, right? So what you would do is say, okay, equation one is this. Equation one is y is equal to 3x minus 1. Equation two is y is equal to negative 2 over 3x plus 4. So what you can do is either add or subtract both these equations to kill them. Zane, are you back? Sir, I subscribed. Are you on YouTube and you got interesting videos, sir? They are really good. And when you do live streams, what days and what types, my schedule changes, Zane. I do shift work. I'm not your regular Twitch streamer, where I have certain days and set times where I stream. I fit them in according to what my schedule allows me to do. Okay? I don't time me out. I'm on time you out. Because we're talking about stuff, you should, instead of being, because you were talking about yourself a lot, right? Which is okay. But when the lessons going on, you said you didn't know how to do this, right? Then you should have been paying attention to learn how to do this. And if this was Greek to you, if it didn't make sense, you should pay attention anyway. Because by paying attention, you might pick up a little bit of notes here and there that will help you out later on to learn another process. Okay? Really, Zane. Mathematics is not a linear learning thing. Mathematics basically occurs like evolution. There's big steps in all some of the thought process, right? All of a sudden there are aha moments where you just get it, right? And once you get it, everything else makes sense. It is Zane. It is powerful. It is powerful. Okay? It is powerful. Learn it. Really. Do it. Do it. And I'm going to turn off chat again to explain elimination. Watch this. Instead of setting this equation equal to this equation, instead of setting y1 equal to y2, setting this equal to this, let's get rid of the fractions first, right? What we could do, by the way, is just subtract equation 2 from equation 1. Here, I'll show you two of them, right? So let's assume we're going to use elimination. We're going to subtract this equation from this equation. Draw your line and say you're going to do subtraction, minus, right? Subtract this from this. So y minus y gives you zero. 3x minus negative 2 over 3x. Let's do this on the side. 3x minus negative 2 over 3x. Simplify that, right? You try to crunch it. Common denominator is 3. This becomes 9x. Negative and the negative becomes positive, plus 2x, which is equal to 11x over 3. So if you subtract 3x, go 3x minus negative 2 over 3x, you get 11x over 3. Negative 1 minus 4 is negative 5. Does that make sense so far, right? If you like, you could put the question up, sir. Sure. That's the link? Okay, let's take a look. Let me finish this and I'll take a look. And I agree math is extremely powerful, Megan says. You do a mind-boggling amount of things with the power of math, indeed, right? So all you got to do now is, now you have one equation with one variable. You just got to isolate x. Okay, again, we have a fraction. I'm going to get rid of the fraction. I'm going to multiply the whole equation by 3. 0 times 3 is 0. 11x over 3 times 3 is 11x. Negative 5 times 3 is negative 15. Grab the negative 15, bring it over. 15 is equal to 11x. Divide by 11. So x is equal to 15 over 11. What? Same answer, right? Same answers down here. 15 over 11. We just used a different process. Okay. Now, watch this. Let's assume we didn't want to kill the y. Let's assume we wanted to kill x, right? Eliminate x. Where should we do this? Okay, trig and physics. I'm going to do it on the side here, but remind me if I forget, trig and physics we're going to do once, right? Watch this. I'm going to rewrite both these equations. Actually, I'm not going to rewrite it. I'm going to multiply, actually, I'm not going to multiply anything with equation 1. Equation 1, I'm going to keep the same. Here's equation 1 is y is equal to 3x minus 1. However, equation 2, again, I don't like fractions. I'm going to kill the 3. I'm going to kill the fraction. So I'm going to multiply the whole equation here by 3. Okay? So multiply by 3. So equation 2 becomes y times 3 is 3x is equal to negative 2 over 3. x times 3 is negative 2x and 4 times 3 is plus 12, right? Then we're going to try to eliminate x. Okay? So here's how we're going to eliminate x. We're going to make them look the same, right? We want them to be the same value but opposite sides. That way, instead of subtracting the two equations, we're going to add the two equations. They're going to kill each other, right? So that's 3x. That's negative 2x. So what I'm going to do is I'm going to multiply equation 1 by 2. I'm going to multiply equation 2 by 3. This is what it's going to do, right? So equation 1, we multiply by 2. So this becomes 2y is equal to 6x minus 2. We've got to multiply the whole equation by 2, right? Equation 2, we're going to multiply by 3. So that becomes 9y is equal to negative 6x plus 36. Take a look at this thing. This is 6x, 6x. This is negative 6x. So if we just add these two equations together, the x's kill each other, right? So 2y plus 9y is 11y is equal to 6x takes out negative 6x. This becomes 34. What do you do now? Divide by 11. Divide by 11. So y is equal to 34 over 11. What? That's the same answer as here, right? We get the same answer, right? So your solution again is 15 over 11, which is your x, and 34 over 11, which is your y. That is the point where the two lines intersect. Does that make sense? The x's kill each other. Sorry, I just have to say it. War of the roses, right? They just hate each other so much, they kill each other. Let's do trick. Let me erase all this. And I think it was Felix that asked that. I hope this went through it well enough, Felix. Is there any questions you got on this? Okay. Is there anything you want to know further regarding this before I take this down? I'm going to take a sip of tea, and if you're still here, think about it. Or anybody else, gang. If you have any questions about this, let me know right now. We deal with it, I clarify. Otherwise, we're going to trick, and then we're going to go to physics. Okay. Maybe we'll do physics first. Just drop something from Megan, because what I want to do with physics just to make something, hopefully it'll be a little pointer, Megan, to give you a little go, oh, that's all it is? Okay. And who was it that asked about trick? Who asked about trick? And whoever asked about trick, are you okay with us doing physics first and then trick? If not, if you're on time crunch, we'll do trick first and then go to physics. Okay. You guys let me know which ones you're okay with. As well as adding, subtracting, you could divide out two equations, multiplying probably not. Yeah, multiplying no, it gives you more complicated, but you can definitely divide out as well. So you could go this equation divided by that equation, the y kill each other, y over y is one. Right? So it gives you a ratio. It's, yeah, it's a little different. Go for it. Go for the physics first. Oh, okay. Yeah, that's right. Skillet. Flow physics first, done deal. Let's do physics. I'm taking this guy down. Oh yeah, there was a link that Cheryl provided. So let me click on that link. But Megan, let me give you a little intro to physics and let me click on that link to see if it's even going to be related. Where is that link? Evaluate the piecewise definition file. Oh, piecewise. This is mathematics at the following point. Five. So this is more mathematics, less physics, Megan. The problem I showed wasn't physics. I don't think someone I know sent me that, but the part of physics I'd like to know more about is relativity and gravity. Everything, really, I don't even know where to start. I'm going to give you a little intro to physics. I'm not going to do relativity and gravity right now. Okay. But I'm going to give you a little intro to physics for you to appreciate what physics is, Megan. Okay. Small world though. Could you break down the math behind for me? For mentation process? I don't know, legendary Rob Boss. The fermentation process. I haven't looked at the mathematics behind it. Just the start will be awesome. Okay, Megan, take a look at this thing. I'm going to give you an equation. Okay. Sweet dreams, Zane. If you got to go to bed, take a look at this thing, Megan. I'm going to give you an equation and this is what physics is. Okay. Cheecho could probably do some math on what the odds are of two people being in the same city for a channel, for a channel of 33 viewers. Funny. Take a look at this thing. Right. And by the way, Megan, physics is all about units. Right. So physics is all about units. Okay. And what are units? Units are how we understand a system to be. Period. Right. So if we're measuring distance, in general, we say use meters. If you're in the United States, you use feet. Right. Or inches or miles. Right. If we're going to weigh something, in general, you're going to use kilograms unless you're in the United States and two other countries, I believe you're going to use pounds in Canada. We use pounds as well. Right. If you're going to use volume, it's distance cubed. Right. So physics is all about units. You need to know your units because your units tell you what that system is about. And if you understand the units, it means you understand the system. Okay. Got it. Now, take a look at this thing. I'm going to give you an equation I'm just making up. Right. Let's assume a box squared plus three triangles is equal to four diamonds cubed. Okay. That's our system. What are the units of boxes? Well, they're boxes. Triangles are triangles. And the units of diamonds are diamonds. Okay. You could think of this as being meters, seconds, kilometers. Doesn't make a difference. Or kilograms. Right. Whatever the units are. And then I'm going to tell you the following, give you the following word problem. This is the equation that relates boxes, triangles, diamonds together. Right. And I'm going to give you the following problem. Two boxes and three triangles are interacting. How many diamonds do we get? Right. This might seem silly what I'm doing right now, but just bear with me for a couple more minutes. Right. So two boxes and three triangles are interacting in some kind of physical manner. How many diamonds do we get? Right. And I've already explained to you that boxes and triangles interact with diamonds based on this equation. Okay. So all you got to do to find out how many diamonds you get, it's sub in two for box and three for triangle. So you end up getting two squared plus three times three is equal to four diamonds cubed. Two squared is four plus nine is equal to four diamonds cubed. 13 is equal to four diamonds cubed divided by four. So 13 over four is equal to diamonds cubed and cube root both sides. So diamonds is equal to the cube root of 13 over four. And the units for that would be diamonds or whatever it is. Right. That's what physics is. You get a whole bunch of equations and they give you in a work problem. They tell you what certain things are or you do experiments, you do readings, or you average out a certain data set you have to get an average approximation of whatever variable it is, the unit it is that you're looking for. And then you plug the stuff into your equation, the relationship that you have between all those variables and get an answer. And you can only do that if you understand certain systems. So for example, let's do F equals MA. Force is equal to mass times acceleration. Force is equal to mass times acceleration. That's Newton's laws. I think it's number two. Force is equal to mass times acceleration. Right. What's the units of force in this equation? Okay, there's disclaimers here. Right. You have to understand what force is. What's force? Force the units and units they used to put in square brackets. Right. But I'm going to write it here. Let's write it here. Right. So physics is all about units. Right. Force to be able to use this equation. Right. Two. For this equation to be valid. Force has to be in Newton's. Mass has to be in meters per second squared. Oh, sorry. Mass has to be in kilograms. Acceleration has to be meters per second squared. I remember a YouTube video of this. Nice. So force, the units of force have to be Newton's. And that's an N. Okay. Mass has to be in kilograms. And acceleration has to be in meters per second squared. Okay. So we would ask, here's a question. Right. Force of 10 Newtons accelerates, accelerates an object to 100 kilometers per hour. Let's make this 1000 Newtons. So a force of 1000 Newtons, 1000 Newtons accelerates an object to 100 kilometers per hour. What's, what's the mass of the object? Smudge. What's the mass of the object? How are you going to do this? Right. Well, we have an equation that relates force, mass, and acceleration. For us to be able to use this equation, we need the force to be in Newton's. We need the mass to be in kilograms. And we need the acceleration to be meters per second. We've been given a problem where they did give us the force in Newton's, but they gave us the acceleration in kilometers per hour. So we can't just do this. This would be wrong. If you went, okay, here's an equation that relates mass, force, mass, and acceleration. F is equal to MA. Then just plug in the numbers. So 1000 is equal to mass because that's what we're trying to find times 100. This would be wrong. Why? Because the acceleration is in the wrong units. Acceleration has to be meters per second squared. So before we do this, okay, we need to convert. Ah, Megan, you said 1000 kilograms, but we need to convert 100 kilometers per hour to meters per second. So in physics, there's a lot of unit conversion. Okay, you're trying to calculate a bunch or something. We did this right. We need the neutral measurement. We need the neutral measurement, right? So a huge part of physics is being in the right unit to be able to use the right equation that relates all of your variables together, your boxes, triangles, and diamonds, right? So first order of business is converting kilograms 100, 100 kilograms, kilometers per hour to meters, oh, hour squared, by the way, hour squared to meters per second squared. We need to convert kilometers per hour squared to meters per second squared. Okay, so how do we do that? That's just straight up unit conversion, right? Now, if you want to think about it, do it this way. Hour squared means hours times hours, right? So first order of business is convert kilometers to meters. And the way you use unit conversions is a velocity, right? No, it's an acceleration, kilometers per hour squared. Sorry, I forgot the squared when I wrote down the problem, my apologies, right? It acceleration has to be distance over time squared. Okay, so that had to be kilometers per hour squared. Okay, so first thing we're going to do is convert, here, I'm going to turn on chat again so everybody sees all the different types of questions coming up. Okay, velocity is a vector, velocity is a vector, acceleration is a vector, right? It's 1000 kilometers in one megameter, one megameter, I guess so, right? So 1000 meters per kilometer, right? So if you're going to multiply this out, this is just straight up fractions. I think, I think the two in the sentence is throwing me off. Two, oh, an object, two, ah, no, that works. Accelerates an object, two, oh, yeah, that's right. Accelerates an object, oh yes, I wrote this down wrong, the wording is horrendous. And this is why some books are brutal, right? A force of 1000 newtons is accelerated, is accelerated, a force of 1000 newtons is accelerated, oh, how do we word this? I'm going to reword the problem, so it works. Bitstorm, thank you for pointing this out, right? A force of 1000 newtons two is wrong. So what's the easiest way to do this? My English sucks, by the way. See this, physics is awesome, it's so interesting. Accelerate it at one. Accelerate is accelerated at, that's right, at, oh no, 1000 newtons accelerates an object at, that's right. So I got to just change this to at, at 100 kilometers per hour squared. Thank you, correct my English gang if I make stupid mistakes like this. Visually interesting, I'm really bad at this stuff, so hopefully this isn't a silly question, but why do we use kilograms but not kilometers? Why does it need to convert to just meters? It's a standard unit, right? It's the standard units of measurement that we use, and what is newtons by the way? Check this out. Newtons is just kilograms times meters per second squared, so just imagine if Newton at the time decided that acceleration was going to be measured at kilometers per hour squared, then the Newton, one Newton would have been kilograms meet kilometers per hour squared. So it's just convention, okay? And the reason they use this convention is because in general it works out well, okay? Just see the numbers, the words cannot be calculated, just see the numbers all that God says. I don't know, it's been a while for me, right? That's why visually interesting, okay? So Newton and Newton is equal to kilograms times meters per second squared. That's just a convention that we have, okay? And the whole world, and they call this SI units, standard international units or whatever stands for, right? So for us to convert kilometers per hour squared to meters per second squared, we've got to get rid of kilometers first. So you're going to put kilometers here, right? And how do we going to convert kilometers to meters? We want meters up top, you're going to go one kilometer is equal to 1,000 meters. So kilometer kills kilometer, we've got meters up top. That's the unit we wanted. Congratulations, we got the right unit in the top. We've got to kill hour squared. How do we going to convert hours to seconds? Okay, we need hour up here, right? And hour, I don't usually go directly to seconds, I go from hour to minutes. So minute, right? So one hour is 60 minutes, right? But this is hours squared, right? So we don't need just one hour over 60 minutes, we need two of these guys. So all I'm going to do is I'm going to square this, right? And this becomes hour squared, minute squared in the bottom. So the hour squared kills the hour squared. But then we have minutes squared in the bottom, and we want seconds squared. So we're going to put minutes here, and we're going to convert minutes to seconds. One minute is equal to 60 seconds, but we don't need to just kill minutes. We need to kill minutes squared. So we're going to square this guy as well, squared. Okay, for college this week, and really nervous, CD Rome. Don't be nervous. Okay, go into it, do your best, steady your hardest, and go into an exam knowing that you're trying your best. That's what you should do. The only time, well, nervousness does come in if it's important and whatnot, but if you work really hard, really, don't procrastinate and use your time efficiently and steady as hard as you can. That should eliminate a lot of the anxiety for people when you go and write a test, because a test is really just saying, man, show us what you know. You great, so for sossus, thank you very much for the bits. Megan, I think I can say my brain is humming right now. Laugh a lot in a good way. Awesome, Megan. So we got to multiply this out to be able to get our meters per second squared. 100 times 1000, you just add two zeros at the bottom. So all of this, here's an equal sign, equals. Here's our 1000. I'm going to add two more zeros. So that's 100,000 up top divided by 60 squared times 60 squared. That's going to give us meters per seconds squared. Makes sense. You're just converting from 100 kilometers per hour squared to meters per seconds squared. Now, I can simplify this a little bit. That's 100,000 over 60 squared is 3600, 60 squared is 3600, meters per second squared. Two zeros kills two zeros. Two zeros kills two zeros. What's 36 times 36? I don't know what 36 times 36 is. This seems pretty small, but it is what it is. It does seem pretty small, but it is what it is. It is slowly starting to click. Awesome. So I'm just going to do this. I'm not even going to bother using a calculator. So the force, if we're going to sub stuff in because we can now sub it in, actually let's convert it. Let's do this. 36 times 36 times 36. One, two, six, nine. One over one, two, no, nine, six, nine, six meters per second squared. That's really slow. Did we do this correctly? I think so. Yeah, pretty slow, right? Need a calculator bot. Thank you. I'm going to give it my best shot. Okay, CD wrong. Good luck, by the way. So what we want to do is calculate the mass of the object. Now we can use this formula. Force is equal to mass times acceleration. Everything is in the right units. So the force was 1000 is equal to mass times one over one, two, nine, six. You don't have to put the units in. You already have the units calculated. You know everything is in the right units. Solve for m. You just multiply everything. Again, it's a fraction of the denominator. Cross multiply this up, really, if you want. This is really 1000 is equal to m over one, two, nine, six. Take this, kick it up, right? So the mass is, wow. It is what it is. The mass is one, two, nine, six, one, two, three kilograms. What? Did we do something wrong again? A force of 1000 newtons accelerates an object at 100 kilometers per hour squared. What's the mass of the object? The mass of the object is 1,296,000 kilograms. It's 10. 10, 10, 10, 10, 10, 10, 10, 10. Oh, it's 10. I killed too many zeros. 10. Thank you. So we eliminate one. Wrap dormant. Nice. Thank you for that. So this is going to be 10 here. This is going to be 10. And then we're going to divide by 10. So this was 10. Let's kill the kilograms here. We're not there yet. Divide by 10. But still, it seems like a lot to me. So one zero kills one zero. So one, two, nine, six, zero, zero kilograms. So the mass of the object is 129,600 kilograms. Right? Something is wrong. I make little mistakes, game. My apologies. When I look here and I look there, I sometimes drop a zero. See it? I dropped this zero. Oops. When you're doing problems, look at the problem. Don't let your eyes wander. Okay. Your trigonometry videos from some years ago helped me a lot when trying to learn that in school. Awesome, Zom. Glad to hear. Now correct. Awesome. Thank you very much for the correction, by the way. Okay. This is the general gist of physics. Okay. Really? This is the general gist of physics. Okay. Should we do trig? Let's do trig for our closing. Okay. By the way, gang, thank you for the follows. Thank you for the subs. Apologies if I'm not catching it. I'm sort of trying to keep my eyes on the problem so I don't make any silly mistakes. Right? Megan, I hope this helped, by the way. Okay. Now, trigonometry. Watch this. Let's talk about right angle triangles for now. 129 tons. 129 tons. It looks complicated when you break it down. It's not. That's what physics is. You just have to understand the system at play and the units at play. Heavy. Heavy. Take a look at this thing. Triangles. Let's deal with right angle triangles for now. And a lot of the stuff we're going to talk about applies to general triangles, but just simplicity right now, since we're doing trig. Let's talk about right angle triangles. Okay. Right angles means this line and that line are crossing at 90 degrees. Now, take a look at this thing. First thing to know about triangles, there's six pieces of information in a triangle. There's three sides and three angles. Right? In general, in my part of the world, the angles they write as capital letters and the size they write at small case letters. Right? So let's assume this is angle A. When they put it at the point, that's the angle they're talking about. Angle B and angle C. Right? So angle C is 90 degrees. Now take a look at this thing. Here's a triangle. Apologies about logos and stuff. I don't promote any products, but it is what I'm using. Right? So take a look at this thing. Let's assume this is a right angle triangle. I don't know. Let's assume here's a right angle triangle. Right? I'm going to decrease this angle. Right? I'm decreasing this angle here. The side that decreases is this. Right? If I increase this angle, the side that increases is this. And vice and the other way around, if I decrease this angle up here, you're going to see this side decreasing. So an angle controls the opposite side in a triangle. Right? Important. Not the opposite angle, but the opposite side. So this angle here controls this side. And the way we make that connection, because they're linked up, we say that this is side A. Small case letters for the sides. This angle here controls this side B. And this angle here controls this side C. Okay. An angle in a triangle controls the opposite side of a triangle. Okay. That should be clear. Right? If you change an angle, this side gets smaller or whatnot. Right? Now, a couple of relationships you need to know. The sum of the angles in a triangle is 180 degrees. That's absolute on a plain Euclidean geometry, which is map, flat surface. Right? So equation number one is sum of angles. That's like angles, short version of triangle equals 180 degrees. So for example, if I give you the following, if I say this is 110 degrees and this is 30 degrees, what's this angle? Right? Here's a question mark. What's this angle? Well, the sum of the angles in a triangle is 180 degrees. So add up those two. 110 plus 30 is equal to 140. And this plus this plus this has to equal 180. So all you do is go 180 minus 140 is 40. So this angle is 40. You can do that with any triangle, which is on a flat surface. Right? So this angle plus this angle plus that angle is equal to 180 degrees. Right? Another way you could write this is A plus B plus C is equal to 180. Right? A plus B plus C is equal to 180 degrees. Okay. The other relationship you have, are you a teacher, lecturer in math or physics? I teach privately both math and physics. The other relationship we have is a Pythagorean theorem 2. The relationship is this. This side squared plus this side squared is this side squared. And that only works for right-angle triangles. There has to be a 90-degree angle. Right? They have to be perpendicular. That's what right-angle means. Right? So for right-angle triangles, right? Angle triangles. A squared plus B squared is equal to C squared. Right? This side squared plus that side squared is equal to that side squared. That's just the relationship we have. Right? Visually, it means this. Here. If I say this is a square, right? And this side is 3. What's the area of the square? Right? Area of the square is this times this. Damn. I'm late. Hello, Danji-cho. Perceival du grau. Hello, hello. Right? This is going to be 9. Because for a square, right? The area is this times this. Right? And if they're the same, if this was x, then this would be x squared, the area. Right? Well, this relationship here says this. For a right-angle triangle, if this is A, B, and C, A squared would just be A times A. This would be A. So this area, B would be B times B, has to be equal to C times C. Right? So this square plus that square equals that square. And my drawings are not to scale if this is 90 degrees. Okay? That's another relationship we have. We also have three other relationships. Okay? The relationships are this. Sine of an angle, theta, is equal to the opposite side, opposite side divided by the hypotenuse. Cos of an angle is equal to adjacent side divided by the hypotenuse. Tan of an angle is equal to opposite side divided by the adjacent side. Okay? They call this the trig ratios. Because ratios are just fractions. Right? One thing divided by another thing. It's a comparison. A ratio is a comparison. Think about it that way. Right? So sine of an angle, right? For a right-angle triangle, it has to be a right-angle triangle. So sine of A of an angle is the ratio of the opposite side divided by the hypotenuse. And the hypotenuse is the side across from the 90 degrees. In this drawing, it's C. Right? So sine of an angle, right? It's just a relationship. Standard is the opposite side, the side that it controls, divided by the hypotenuse. Cos of an angle is the adjacent side divided by the hypotenuse. Now adjacent to the angle A is both this side and this side. But this side already has a name. It's called the hypotenuse. So we don't call this the adjacent side. We call this the adjacent side. Okay? So cos of an angle is the adjacent side divided by the hypotenuse. Tan of an angle is the opposite side divided by the adjacent side. This holds true for any triangles that are congruent, which are identical. So for example, if I give this to you, here's two triangles. Right? I'm going to say this is 30 degrees. If this is 30 degrees and that's 90 degrees, what's the angle here? Well, this plus this has to equal 180, right? 90 plus 30 is 120. 120 minus 180 is 60 degrees. So this is 60 degrees. Okay? So let's assume we have the following legitimate triangle for this with the links being the following. Okay? One square root of three and two. And square root of three is just a number, right? If you punch in square root of three in your calculator, you're going to get one point, something, something, right? So let's assume this triangle exists. And it does, right? This is one of the special triangles you have to learn. And then what I'm going to do, I'm going to give you another triangle. And I'm going to say, hey, the angles for this triangle are the same as those, that triangle up there. However, this is a bigger version of that triangle. This is a little version of this, right? And I'm going to say this side is five, right? And I want you to find x and y. I want you to find these two sides. Well, according to our trig ratios, sine, cosine, tan of an angle is the ratio of the opposite side divided by the hypotenuse, adjacent divided by hypotenuse, opposite divided by adjacent, right? So take a look at this. For this triangle, we have sine of 30. Let's use sine, right? So we're going to go for this triangle. Sine of 30 degrees is equal to, is equal to what? The opposite side divided by hypotenuse. So opposite of 30 is one and the hypotenuse is two, is one over two. Okay. Take a look at this triangle. This triangle also has a 30 degrees. So sine of 30 degrees here is the opposite side, five divided by the hypotenuse, which is y, right? 30 degrees. This says sine of 30 is one over two. This guy says sine of 30 is five over y. They're both sine of 30s, right? If they're both sine of 30, then if sine of 30 is one over two, then this sine of 30 is also one over two, right? So you can just substitute this for this because that's sine of 30. So one over two is equal to five over y. Oops, five over y, right? I'm going to bring it here. One over two is equal to five over y. So if you want to solve for y, cross multiply this baby up. So one times y is y, two times five is 10. Oh, look, we just solved for y. That's 10 because the sine of an angle is always going to be the ratio of the opposite of the hypotenuse. It's a standard for a right angle triangle. No matter how large or how small that triangle is, if it's a right angle triangle, the sine of 30 degrees is always going to be one over two. I don't care what size that triangle is, right? Does that make sense? I hope that makes sense. And when you take your calculator, take your calculator and punch in one divided by two, which is 0.5, and then take the sine of it, an inverse sine of it. We don't want to do that. Take the inverse sine of that thing, you're going to get the angle. One thing I struggled with when I studied this was that I didn't understand that this only goes for right angle triangle. Yeah, it has to be right angle triangles. These three things are only valid for right angle triangles. That's your basic general intro to trick. And if you want more on this, I do have a trick playlist and I made some trick videos a long time ago, back in 2008 or something, basic stuff that builds on top of this. This should give you a nice understanding of what's going on. And there's one other thing we have here. Here, let me erase this. I'm going to erase these guys, okay? So let's take these guys down. Take a look. There are times when you want to get the angle by itself where you have two sides, right? Right angle triangle. Here's angle theta. Let's assume this is six and this is seven, right? Still like, thanks for going through it. We're about, is this video going to get uploaded? This video is going to be uploaded in about, not tomorrow. Tomorrow? No, the next day, most likely. So today is Tuesday. Most likely Thursday it'll be up on YouTube and Bitshoot. And you should be able to watch it on Twitch for the next two weeks, okay? Maths, math is discord. Where can I see that play? The playlist you can find here. Here, if you go to YouTube channel, my YouTube channel, okay? I have a trigonometry playlist, okay? And in the bottom of the trick playlist, the first part of the trick playlist is more grade 12 mathematics. And then I linked up the earlier stuff I did, which was the basic trigonometry in the bottom of that playlist. You can also go to the language of mathematics playlist. Let me bring it up. Let me bring this up. I'll give you the link to the language of mathematics playlist because it's some of the early videos that I put out. Let me get that playlist for your language of mathematics. And there's a table of contents that I have on my main page. And this is in reverse order. How many videos here? 161. And trigonometry, trigonometry. It starts off with language of mathematics, introduction to trigonometry. So language of mathematics 14 and 15. This is the 14th math video I put up and I put this up in 2007. Wow, wow, wow. Here's introduction to trigonometry, but it's more of an introduction to geometry. And here is the first sort of video on right angle triangles where we do the intro and then you can continue to work from there. Follow the work from there. Okay. And my table of contents is here. Where is it? Let me bring this up. I'll give you the link. It's on blocks by right now. Math, where's my math? Math. And if you go to language of mathematics, you'll want to take a look at series one, video number 14 and up. And here's the table of contents for those videos. Okay. I hope that gets you to where you want to go. Now take a look at this thing. If you want to find the angle, you can still use the ratio, right? You have the opposite side and you have the hypotenuse. So you look at this, you go opposite of hypotenuse, you got it here. So you can go sine of angle theta is opposite over hypotenuse, six over seven. And to get theta by itself, what you got to do 2007 the year math was revitalized. My pleasure Oz 999 to get theta by itself. This doesn't mean sine times theta. It means sine of theta to isolate theta. You do something called sine inverse of six over seven and that button, sine to the power of negative one, but it's not really to the power of negative one sine inverse of six over seven. You can go six divided by seven and then take the sine inverse of it. It'll spit out the angle, right? Gina, how you doing? Hey Chichou and chat. The three squared and four squared equals five squared always works well for Pythagorean calculations. Yeah, indeed. It's called a, what's it called? Pythagorean? Oh, I forget what it's called. Oh, there's a word for it. The Pythagorean. Oh, I forget the word in English Pythagorean. It's Pythagorean, but there's a special word for perfect Pythagoreans, Pythagorean theorem for sure. But they call it perfect Pythagoreans like three squared plus four squared is equal to five squared, right? And I think, what's the other one? 12, 5, 12 and 13. Anyway, it's the English words trying to explain mathematical concepts. Yeah, Pythagorean triples, I think. Perfect triples, Pythagorean perfect triples or something like this. Crafter, I think that's correct. If I recall. Fun. Gang, should we call the string? What is the shortest distance to your heart? Randy and Choco one. What's the shortest distance to my heart? I don't know. I don't know if there's a shortest distance. Cornelian cherry jam I made this morning. Very yummy. Look, I picked these yesterday. Probably pickles. Very yummy. Gina. A straight line. Megan, I'm sorry to break this into the math, but did I miss the movie suggestions and stuff? Oh, the movie stream. There's four movies we've got to watch. What are they? Breakfast Club, Tombstone, El Topo, and Forbidden Planet. Most likely, our movie stream is going to be in the next set. It's called Cornelian cherries. It's tart. It's not really cherries. It's, I guess, the same family as cherries, maybe. That's why they call it Cornelian cherries. But it's very tart. They have a nice night. Thanks. I made a whole bunch of jars. I converted about eight pounds into jam this morning. I'm very excited for it. The shortest distance from one point to another point is always a straight line. Wing Chun. Yay. They're berries, right? Yeah, they call them Cornelian cherries. So they must be berries. They've got the fruit and then the seed on the inside. All right, solid one seed. Delicacy in Iran. Good for the tummy. If people have colds and stuff like this, we eat that. So I always try to always have a jar of that in the house minimum. So if we get to the last jar, we don't crack it open. Sort of use it as medicine. Yeah, very good Megan. Very good. Young Polax. It's not like to make for myself is some mozzarella and dribble, some oil on it and finish it off with pepper and salt. Ooh, nice. Young Polax. Delicious. No carbs. No crackers or bread. Gang, let's call the stream. Thank you for the questions. We did fantastic math today, by the way, gang. Awesome. We covered three topics, which was really good. There was a whole bunch of people that were subbing. Gang, thank you for the subs. We're going to be doing anywhere between two to four days a month. So you're welcome to pop in and we'll be doing a lot more of these. Okay. I feel that you appreciate science. I try to. Great stream. Untry the days. Good to have you back, man. As always, as always. Gang, I'm on Patreon. If you want to support this work, Patreon is a fantastic way to support this project. Patreon.com forward slash Chicho. CHY, CHO. I do have sort of my thesis set up there where you can see what I've created since 2007, creating the math videos and everything that I'm doing is really layered on mathematics. We've got about a thousand videos on YouTube and at least four or five hundred of those are mathematics. The rest of them, at least another 200 or so are layered directly on top of the mathematics, right? Because with math, you're a free human being if you're literate in the language of mathematics. So this, my first time here, Randy, thanks for dropping in and thank you for the sub if you subbed or followed and whatnot, right? So if you want to support this work, Patreon is a great way to support this project. I don't put anything behind paywalls. Everything's creative commons. Share and share alike. Okay. We are live streaming on Twitch. If you want to participate in the chat as it's happening, Twitch is where you want to be at. And again, gang mods, thank you for taking care of business. Thank you for the follows. Thank you for the subs. Thank you for the bits. Okay. And this because of the support we're getting from Twitch and Patreon and in different platforms, YouTube membership and direct donation and stuff like this, we're able to do this work and grow. I do announce these live streams on LOMinds, VK, Parler, Gatt and Twitter. And we do share additional content and all the links will be in the description of the video. Randy, thank you very much for the tier one sub. Appreciate it a lot. For live streams, we don't have any visuals. We do upload the audio to SoundCloud.com forward slash Chico, C-H-Y-C-H-O as podcasts, as people have requested for them to be available. Okay. And we will be uploading this video to YouTube and BitShoot. It will make it past the centers on YouTube and everything goes on BitShoot. And if you are on BitShoot and YouTube, you can support this work by subscribing, following, turning on notifications. YouTube doesn't send notifications out all the time, but BitShoot does, right? And if you're on YouTube, you can support this work by joining YouTube membership. Again, thank you very much for the questions, for the participation. Thank you for paying attention. And we've got another five streams coming up in the next five days. Three of those are me showing you my gaming collection. If we go through it in two days, we'll talk about comic books. Okay. And I might do a comic book on announced live streams sometime either tomorrow or next day. We'll see how it goes. Gang, I hope you guys have a fantastic day and I'll see you tomorrow if you can make it. I'm going to bring the boxes down in a living room and we're going to go through some of the games that have made it with me for the last 40 years. Okay. Both PC and console games. Bye everyone.