 Make sure we're live. Pop out the chat. Hi everyone, this is Chichou. Welcome to my channel and welcome to another live stream. Today is December 17th, 2019, and we're doing another drop-in math tutor in session 2019-2020 school year. This is number 10, okay, and it's 12 30 p.m. my time, Pacific time, and we've done a lot of these before. I'm just popping out the chat to make things easier. We've done a lot of these before and we will continue to do them. And right now in my part of world, it's sort of exam season, sort of midterms kicking in for people before they go on break for the holidays. So I thought it'd be good to do one on a Tuesday, today's Tuesday. So if there's any exams, usually it's on, you know, the last three days of the week, just before everyone finishes school, right? If you're lucky, you get the exams before the break. If you're unlucky, you're gonna get your exams after the break, which means you got a two-week gap that you have to review, to relearn things, and remind yourself what everything was about. I always like writing exams before breaks and after breaks, because you carry that, you know, if they're important exams, you're carrying that anxiety with you into the holidays, right? And you need, you know, you need to get stuff done. It's always good to come back from a break with a fresh start, not carrying over from two weeks before, right? Aside from that, we're just going to chill. If you guys have any math questions, drop us a line in the chat. There might not be too much activity going on here. Okay, Wascoi Wallet. How are you doing? Welcome to the live stream. What are your tips for partial derivatives? Wascoi Wallet, I wish I could tour you, teach calculus right now. I'm not touching calculus right now, just because I haven't done it for a very, very long time. And to do it justice, I would have to, I want to build it up from the core up, right? So I'm mainly focusing on pre-calc. That being said, derivatives, as you know, calculus is sort of introduction of time into mathematics. That's looking into how functions change with time, right? When it comes to partial derivatives, what you need to do with a lot of mathematics, really, this is just general information, but with a lot of different branches of mathematics, what you need to do is recognize the problems that you're dealing with, right? If you're studying something in math, I mean, that's the beauty of learning mathematics, right? When you're in school, when you sign up for a certain course, you know that the material coming to you from that course are related to the content of the course, right? So the best thing you can do to prep yourself for calculus for any exams you're going to write or any tests you're going to write, or any problems you want to do is familiarize yourself with the type of problems that you end up getting in this course, in this material. And that, the only way to really get that going is to do problems. You need to practice, right? Olive, how are you doing? Hi. This was a pleasant surprise. Didn't know you were going live today. Yeah. You're like nine hours ahead, Olive, aren't you? Eight hours or nine hours? Eight or nine hours? Can't remember. Depending on what party you're up. You're in Norway, right? Norway? Yeah, Norway. From what I recall, not Sweden. Don't say Sweden, the Norwegians, right? Fun. Yeah, this is going to be our sort of last math stream we do for at least two to three weeks until people get back from the holidays, right? I'm just going to chill with it. I can hate this world, man. I'd like to watch it. I am Nick, too. That's what the powers that we want you to do, to hate things. Forget about hating it. And it's up to you. You're nine hours. Okay, cool. It's 9.30 PM. 9.30? 1.32, 3.4, 5. 6.7, 8. 9. 9. 30 PM. Norwegian time. Pre-calculus stuff I like. Trig, right? Yeah, I love Trig. The holidays are the best time to do math. Not for kids who are in school. When they have holidays, they're done. Usually it takes me about a week sometimes if I'm lucky to kick-start students again into math mode after a two-week break, right? After a two-week break, you need to crank the wheels again and get people energized and thinking about things. I hate nothing, but I still want to burn it all. So I would suggest before you decide to burn anything, you should create alternatives for people to go to, right? If you dislike something, if you want to see a change in the world, right? Then create something as well, right? Don't be the Joker. And if you're pretending to be a Joker, Joker, I like the Joker. Tell that to the school age. Yeah, funny. Yeah, most kids right now, where I am, they're burnt out, really. How long has it been? September, October, November, December. They've been in school for about four months, right? And they're burnt out. They can't wait for this two-week break, really. I am Nick. Tell you what I am, Nick. One of the best things you can do to have a really amazing appreciation to what we can do in this world, really, what we can do in this world, instead of burning it down, is to learn mathematics. Learn math, spend a little time just really getting that perspective. Once you go from a non-mathematical perspective of the world to a mathematical perspective of the world, your world's going to shake up. Your reality will shake up. All of a sudden you just go, what is going on, right? And then you no longer feel like burning things down. You feel like, you feel powerful. Once you feel powerful, you tend to create more things than you destroy. I saw some of the schoolwork my cousin do, and I don't blame them for being burnt out. I can't imagine being forced to participate in that garbage. Yeah, Mask of Raven. Like, when I talk about our education system, right, to people, for me, I have a very unique perspective, right? I see, I know what should be taught. I know how it should be taught. I've been in looking at this whole system for over two decades now. I see the perspective from teachers. I see the perspective from students. And I see the perspective from parents. I know the politics behind it, and I know the economics behind it. When I talk to people about our education system, they are very, very, very few people who really appreciate what is taking place right now. Because if they really understood it, they'd be scared shitless. Okay, it is insanity, right? And then you take a look at the whole thing and go, what is possible? And the what is possible part, I see the perspective of it because I am functioning outside of this centralized education system. So I see what is possible for all of the students that I work with, right? Their imaginations, what they are capable of, their passions, right, their loves, why they hate, why they're burnt out, why they're excited, right? I see all that. And once you explain that to people to a certain degree, like, I've come close to sharing a lot of that info with you guys, but not even, right? Once you see that perspective, man, that's fuel to the fire. That's one of the things, a lot of people ask me, what motivates me? That motivates me. That is one of the greatest motivations I have, right? Here's the problem. And here's what they're trying to destroy, right? What level of math are we at here? We're talking source run, source run. I teach late elementary all the way to pre-Calc high school, right? So grade 12. I'm in the West Coast, I am Nick. Yeah, West Coast of Canada, right? So I teach, I focus mainly on high school mathematics. If everyone in the world was literate in high school mathematics, that includes grade 12 mathematics where you're graphing functions and have a taste of statistics and stuff like this, right? No calculus but pre-Calculus, right? I don't think you necessarily need calculus to have a mathematical perspective of the world, right? You can have a statistical perspective of the world, right? Just West Coast, Nick, right? West Coast. Do you have any tips on remembering the multiplication table well? Z-art for sure, right? For sure. Here, hold on a second. We created the multiplication table here, 10 by 10, 10 by 10, generating a 10 by 10 multiplication table. Take a look at this guy. This is something I put out in 2015, generating the 10 by 10 multiplication table. Okay. Oh, I know. I'm sorry. Sauceron. In this video, we called it the ASMR math, generating the 10 by 10 multiplication table, right? So we just go through talking about the multiplication table, right? And here is, and I'm going to do more on this by the way, we're going to do some practice problems on this because I started putting together a series of videos on early childhood education to a certain degree early childhood education, but includes basically teaching, counting, adding, and multiplication. And there's more coming in this playlist. I've laid it out. I just haven't got to it. Masque of Raven loves calculus. If you have calculus questions, Masque of Raven might be able to help you if he's into it. But Z-art, take a look at this table we have. And if you already know how to add and stuff, take a look at the how to teach multiplication. This is me sharing some of the techniques I use to teach multiplication. Okay, specifically this video. And I, the first three videos in this playlist, and it's ordered from the oldest to the newest. Okay, the first three videos in this playlist are basically a full video that we shot that I shot on it. I have the whole thing in one video. Okay, here I'll link you this, and you can just skip this one and go straight out into the multiplication table. Yeah, if you put up in chat, I might be able to help. Awesome. Thanks, Masque of Raven. We're getting a lot of calculus, calculus stuff. I wish I was better at my calculus, right? Why aren't mad these? By the way, thank you for the follows and subs, just in case I missed them because I move around a lot. Thanks, Chichou. I'll give it a watch. Awesome. Just remember there's symmetry in this, in the multiplication table, right? If you draw a multiplication table here, if we draw the table, let's just say it does, right? If you go straight down the perfect squares, right, this side is mirrored here. This is the axis of symmetry, and you can just go boop, boop. And always keep in mind, multiplication is just an extension of addition, right? That's all it is. Here's an addition. Rotate this thing 45 degrees, and you have multiplication, because multiplication is just an extension of addition. So if you have two times six, this means two things. It means six added together twice, and it also means two added together six times. Plus two, plus two, plus two, plus two, plus two, right? The reason we have multiplication is because mathematicians are lazy. They want to condense multiplication. I always say mathematicians. They want to condense addition, and they created the symbol multiplication to simplify this, right? So that's all it is, really. Dante, how you doing? How's life? Welcome, welcome. Thanks for popping by. Today's slow day. How many people we got here? We got seven people here. Nice and easy, right? This is the last week before Christmas. No one's at the mathematics, right? Oh, fun. I think we're at the mathematics. We can just chill. I've been going ballistic teaching my students. Been doing a lot of in-person and online stuff and whatnot, just because they got exams, right? Just because they got exams. Here, let me show you what I got for snacks. I got apples. I've been eating a lot of apples. Loving the apples. Iron Matty's math is awesome. 100% agreed. I'm standing for linear algebra final. Then I'm free. Nice. Math is awesome for sleeping. Linear Algebra, man. I like linear algebra. I had to teach it to myself because I took a course that I didn't have the prerequisites of linear algebra. It was systems of integrals, and it was crazy. Modeling things with triple integration and stuff. It was the hardest course I've ever taken in my life. I practice math on Khan Academy sometimes. For me, I've used Khan Academy videos a few times. Not that many. Maybe a dozen times over the last 10 years or something. Because I know what I'm looking for. If I know what I'm looking for, I just do a search. But usually, I want a little more in-depth stuff than I go to longer versions. Some of the professors and stuff, hardcore people teaching math, right? But it's fun. I love the fact that there's so much math content now online. It's amazing. It's amazing. It's empowering people. It's giving people the knowledge, the health they need to educate themselves in a big way. By the way, gang, we're doing another three streams this week. We're doing health tomorrow. What are we doing? We're doing health tomorrow. Here, let me give you the times since we're having a downtime. We're going easy. We're doing open discussion in food and health tomorrow, starting at 9am my time. That's tomorrow on Wednesday. On Thursday, we're doing an open discussion on current events from 11.30am to 1.30pm. On Saturday, we're doing an open discussion on Julian Assange. That's December 21st from 11am to 1am. Just to let you know what's going on there. There's a lot of also education stuff going on in the world. It's crazy. Oh no, I'll have to miss the discussion on food and health. Oh no, Mask of Raven. It's our first discussion really on, we've done cooking streams, but we've done health, I think. We've talked about health, but I think this is our first live stream specifically. Let's talk about food and health. I think it's important. We'll see where it goes. I'm going to go through at some point all these different types of live streams we're doing. We might just put a series, a set together and say we're going to talk about this, this, this, and start focusing the streams on different things. Not just current events and open discussions, but just specifically just talk about health. Talk about economics. We've got to do an economic stream, but I want to get some videos out before we go into the economic stream. I want to do some of the analysis we did on the, because I've collected, I've tabulated, I've put it into tables, the comic books we've sold, right? And I did some, crunched some numbers. I'm like, wow, wow, wow, wow, right? So I'd like to take a look at some of that stuff. I sold a little bit since I finished the table. I don't think I'm going to include that data in there. We have enough to do our analysis on it, right? So I thought we do, we do that. Everybody's already writing exams right now. It's a weird time for me to do these mass streams, by the way, just because it's, it's during the day in my time. So at least the West Coast is still in school, right? So they don't, they're not having the opportunity to pop in. At some point later on, I'm going to do these mass streams later in the evenings. I think once we go past the longest night of the year, we start getting more, more daylights, then we'll start doing later in the evening, right? I don't know if that's good or bad since I believe we disagree on organic food, GMO and such. You're okay with all, all types of food, mask of Raven? For me, I don't want GMO for sure. And I, I go towards more local eating organic and stuff, right? But to each their own, right? To each their own, whatever works. For me, I'm just getting older. I gotta watch what I eat more now, right? Like I used to be a huge generic chocolate bar muncher, right? GMOs are good in principle. The problem I find with that stuff is, because the power is so centralized, the corruption is so rampant, and the experiment, what they have done to food, the experiment hasn't run not even close to one full cycle yet. We don't know what the side effects are or some of the stuff. But we can talk about all that stuff tomorrow. Today's education, math, physics even. I've been doing some physics reviews with people. I wanted to hear, let me show you all the questions that what are my students had in a physics 12 exam quiz that he just wrote, right? Now they were doing, the section is basically statics, equilibrium and stuff like this. Hey gang, I broker, how are you doing? To me, living healthy means not drinking a bottle of vodka every evening. My tolerance of vodka always goes in humane when doing construction projects. Yeah, I broker, by the way. Unfortunately, many of us in the Western world have gone through that phase. Every criticism of GMO I find convincing are actually just criticisms of capitalism that I agree with. To a certain degree, mask of rave. And I think a huge chunk of the criticism of what we're doing when it comes to the agro business, huge chunk of that is associated with our economic system. But we can't separate that from what's taking place, right? Here's a problem that one of my students had and it's only like a two mark problem. You said it was a two mark question on a quiz that he was writing, right? And the question is this, there's a truck driving on an incline road, right? So here's the, here's the truck, here's the road. Okay. Here's the road. Let's assume this is, I don't know, obviously I'm exaggerating. If you're driving a truck going down a road like this, don't, right? I think that GMO is fine if it's regulated to keep artificial deficit away from it. So check it out. And the way that the drawing is, the truck is either going into the road or into the border coming out, right? So the truck is not driving like this. It's not going up the incline. It's driving into the road, right? Into the thing. And the question was, your tire, tire, right? So the truck is going in. And the question was, and he only gave the dimensions of the truck. And I didn't, unfortunately, I didn't ask for the dimensions. We just talked about the problem, right? And the problem only gave dimensions, right, of the truck. And it asks, what does the slope, what does the angle of this road, what's the maximum angle of this road before the truck tips over? Before the truck goes, right? And I was like, and I asked my student, I go, well, did he give any, you know, did the teacher, that's a go program driving on. And I asked my student, you know, did they give you anything else, like the weight or the coefficient of static friction or something like that? No, this was it, the dimensions. And he said he got stumped by this. It was only worth two marks. And his solution was basically, if the center of gravity, his reasoning behind this was, if the center of gravity goes past the tire, the truck will tilt, right? So this truck will tilt. If we draw another one, I drew it with the same angle. No, let me change the angle on this. I'm like, wait a second, the center of gravity is still out. So if the road was like this, and the center of gravity is here, and if it goes like this, this truck will stay on the road and this truck will tilt over. That's the reasoning he gave. Yeah, center of gravity was, it didn't, you know what, it didn't really occur to me, center of gravity, when he, when he gave me this problem. I was looking for more info, right? I was looking for coefficient static friction. I was looking for the weight of the truck. I was looking for speed, that kind of stuff. Sounds about right. Yeah. Yeah, we agreed. He said that's the argument he made. And we said, yeah, yeah, that would pretty much would be it, right? Because the mass, the weight of this thing, of the truck would hit the tire here on this side of it, on this side of it. So that would keep it on the road. Over here, the mass is on this side. So it would just continue to flip over, right? Yeah, it makes sense. That is why boxer motors from Subaru are that good. The center of gravity is low and a lot more stable. Cool. Yeah. I like, like, I've had a couple of pathfinders in my life, the Nissan pathfinders. And I found those to be really good. I used, back in the 90s, I had one and I used it a lot for geophysics going on some crazy terrain. And it did well. It did well. I thought that was a cool problem to put on a physics test. I liked it. The, one of the things with physics is it, when you do physics here, let me do one more. A lever where you want one side to be pinned down, and once more than half weight shifts to the other side or the back wheel. The lever behaves how we want, how we don't want. A lever where you want one side to be pinned down, and once more than half weight shifts to the other side. So this one's pinned down. This one is not. Right? Let me show you another type of problem he was getting. And this involved torques. Okay. You needed torques for this. So here's a type of problem. And I like, I like teaching higher level in large part when it comes to physics and mathematics, because it's, I come across problems that I have to pause and think about. It's challenging, right? It's good for the brain. It's good muscle. You're building good muscles, right? But here's one problem that he had. And this is statics, torques, forces and stuff like this, right? You have one problem where you have a plank and it's being held up with a couple of strings. There's a robot here. This is Gijo's robot. Okay. There's a robot here. And you got the plank. And the question is, what's the tension in this string and this string given the following information? Okay. The mass of this guy, let's say it's 10 kilograms. The mass of the beam is, I forget what they are, we'll just come up with our own 75 kilograms. Okay. Kilograms. The total distance of the beam, let's say at six, the distance here is 0.5. And this is 0.5 as well. 0.5 as well. The distance of the robot is let's say two meters. And is there anything else? Is there anything else? Is there anything else? No, that would be it, right? So you're given this information. Hopefully I'm not missing anything. Hopefully this is coming out. Let's see. Is this better? That's a little bit better. Six, two meters. And these are meters all of it, right? 0.5, 0.5, 10 kilograms, 75 kilograms. Oh, we do need this distance too. The distance, that's probably, oh no, no, we got that figured out. Okay, cool. So the question is, what's the tension here at T1 and what's the tension at T2? Right? So the way we laid down this problem, the way we ended up doing this problem, I like this problem because it involves torques. So there's two types of static equilibrium problems you end up getting, usually in physics. You have to think about it, right? One of them is you try to balance out the forces, right? So if you have, here, let me show you this. If you have an object, right? And there is like a force acting on it like this. Okay, this pen is done. Let's grab a different pen. So if you have a force, let's say you have a box, there's a force one acting on this box here. There's another force acting on this box here too. Let's say there's another force acting on this box here, right? And this box weighs, let's say, 20 kilograms and it's not moving. You ask yourself, okay, what, you know, what's one of these forces, right? They'll give you this one. They'll give you this one. They'll give you this one. And they'll say, if this thing isn't moving, static, what's this force here, right? And all you do with this type of problem is you say all the forces have to balance out. So you break up this one into its components, right? So this is f1y, f1 in the x direction. You break up this one into these components, right? And you say this is f3x, f3y. And this one, let's say it's just horizontal, right? Then all you do, you say all the y forces f1y must equal to f3y. Oh, you got this guy too. Sorry, my bad. And you got mg here, right? And that's acting straight down. So you say f1y plus mg has to equal f3y, right? Because that's one force acting now. That's another force acting now. And that's the only force acting up. So they have to balance this plus this has to equal that. If this thing is not moving, if this thing is not accelerating, let's rephrase, because if it's moving at constant speed, this is also true. But let's say static, right? And in terms of the x direction, the weight doesn't come into play because that's acting straight down. Then f1x plus f3x have to equal f2 in the x direction, right? The forces have to balance out. When it comes to torques, right? They come into play when we're not treating everything as a point source, right? There's distances involved. When there's distances involved, you do the same thing. The forces in one direction have to equal the forces in the other direction, right? But it's not just the forces they have to equal, it's the torques of them they have to equal, right? So the force times the distance of this times force times the distance of this have to equal each other, okay? So over here, let's erase this. What you do with this is you say, okay, what are all the forces acting on this object, right? On this system. So there's this guy here acting up. That's t1. There's this guy here acting up, right? This is t2. There's the robot's mass weight acting down, which is this guy. And the only other thing we have here is the plank acting down on this, right? And what we do with the plank is we take the plank as being a point source and we say that's in the middle acting down, okay? Now consider this. Which one of these t1 or t2 is going to have a more of a tension, right? Because if we have this, let's assume we had this model, instead of all this stuff on it, let's say we had a plank and it was laid out the same way and this was a string and this was a string. What would t1 and t2 be? What could you say about t1 and t2, right? If this is a plank. t1 and t2, they would be equal, right? If this is a homogenous plank that is not heavier on one side or anything, these two would bear the same amount of weight to hold this guy up, right? That's why, you know, I'll use gloomy reference, but when people are carrying coffins, you put three people on one side in general and three people on the other side, so no one's really carrying too much weight unless they're different heights, right? You try to, when you're getting people to carry something heavy, you want everyone to be approximately same height, so the weight distributes evenly, right? Unless they're willing to either bend down or lift up and that could create some problems, right? But if you have a homogenous plank and you got strings holding it up, then the tensions in the strings will be the same. However, let's assume we had this thing. What would happen if you put a weight here, right? Wherever you put the weight, whichever string it's closest to, that string is going to carry more weight. The tension in here would be more than the tension in here now, right? That would make sense. So for the system, T1 is a bigger force than T2. Now, if you notice, we have two unknowns here to a certain degree. We want to find both of these, and we don't have any specified pivots when it comes to torque, and pivots are basically in torque type of problems, or you basically put something as a hinge, and everything else can rotate around that. So if you have a plank here, if you have a plank, and if this thing's sitting against the wall, this would be your pivot, and then you could have forces hitting here, hitting here, and you would try to see if it's an equilibrium, then this has to equal that. This times the distance has to equal this times the distance. That's what the whole principle of torque is. So if this force is 1, this is force 2, and this distance is D2, and this distance is D1, and if this thing is in equilibrium, it's not moving, what you would say is F1 D1 has to equal F2 D2. And always keep in mind, if you want to know how torques come into play, just imagine if you have to move a gigantic boulder. Now you could sit there and try to lift it up and throw it your back. You could try to push it this way. If it's sitting on a hinge or on a slope, you could maybe push it over, but if it's all flat ground, you can have a hard time. So how do you move something heavy, large, if you can't do it physically, just manually yourself without any tools? Well, you go grab another rock, you put it in front of it, you go grab a metal rod or something, like a lever, and you stick that thing into this, under this big rock, and you go use a little lock, rock as a hinge. Why am I doing this like a drug, right? So if you have this gigantic rock you want to move, you put another rock here, you bring a hinge here, and you stand here and go pull the sucker down and you can move that. If this thing's longer, it's easier to do. If you try to pull down here, that's going to require you giving a lot more energy. It's one of the basic tools that we have that we've known about humanity forever, right? So this would be your hinge. So if you want to think about in here, this would be your hinge. This is your hinge. So if these two, if this is not moving, if this is an equilibrium, this has to equal this, then the force here would be bigger than the force here, right? Because this is further out. So it's sort of thought process as well. You want to know how the system operates, right? So you're going to keep all this in mind. The more problems you do this way, the more little nuances you remember about specific types of systems. Like there's a whole mindset behind people who are inventors, right? It requires to give the same amount of energy, but a different amount of force. Yeah, right? And the torque is what we're talking about, right? The torques have to equal each other to a certain degree. So take a look at this. So for us over here, one of the things we do when it comes to physics types of problems, we try to simplify problems for ourselves, right? We try to make things easier. The way we try to make things easier, we either label things in a certain way where they make sense, or we label things in a certain way on a drawing to eliminate the unknowns, right? So we try to get rid of the unknowns and solve the more simplified system than the one that's being presented. And one thing we can do when we're trying to solve the system to find out what the tension is here and what the tension is here, is we specifically eliminate either T1 or T2 by putting in an imaginary pivot at one of these locations. So all of a sudden, if you have a drawing, if you have a pivot, if you're applying force on the pivot, nothing's going to happen with this, right? So what we do is, for the first problem, we're going to eliminate T1, and we're going to try to solve T2, and we're going to put a hinge here, okay? So we say, you know what? Just imagine that this system was exactly this, but this point was locked, right? We're making it a hinge, and we're going to reference everything to this point. Then what we have, I'm going to redraw this down here. Let me bring out a green. I'm going to redraw this thing here just with the forces that we're dealing with, right? So we're making this a hinge, right? Here's a hinge. This is going to be difficult to erase, I think. Here's a hinge. That's one. And then I'm going to draw the plank here, right? Here's our plank, right? So we have T1 going up like that. Oh, sorry, T2 going up like that. We've got the weight of this guy coming down, and we've got the robot, and it's the center of gravity is here, but we're just going to put it on the plank, working down like this. So the torques, these two torques, the torque that is being applied at this point, at this point, has to equal the torque at that point for this thing not to move, right? So all we need now is the distances here. So this distance, that was 0.5 from here to here is 2. So this is 1.5. The distance here, if the whole thing is 6, right? And this is 0.5, right? Well, if the whole thing is 6, well, we can't do the middle at 3, right? Because we've got to account for this. So that's 0.5. So the distance here is, I should have made the numbers easier to here. And there's 0.5 there. So actually, we have to account for this as well. Here, let me erase this. Let me put it down here so we see. So if we go from here to here, right? Because the plank is going up there. That's 6 minus 0.5, which is 5.5 meters the center of gravity of the plank is going to be in the middle of this plank, excluding the weight here, because that's on this side of the hinge, right? So 5.5 divided by 2, well, 5 divided by 2 is 2.5. 0.5 divided by 2 is 0.25. So it's 2.75 meters. So this distance here is 2.75 meters. And this distance here, starting from here, that's 0.5. So that distance there is 5, right? I hope you see that. That's okay. I'm just going to erase this. So this distance here, let me draw it here, is 5 meters. Okay? We're almost finished laying down this problem. So the equation for this is going to be, let's call this R for robot. Let's call this plank for the plank, and that's T2, right? So the torque on R plus the torque on the plank has to equal the torque on T2. So the torque on R is force times distance, right? Well, the force on this is MG. The force on this is MG as well, but the M varies. So this is the mass of the robot, mass of the plank. Mass of the robot, here, let's write down the formula, mass of the robot times gravity times the distance, which is 1.5, plus the force, the mass of the plank, P, times gravity times the distance, which is 2.75, has to equal T2, the force at T2, times 5. You can barely see that. 2 light, 2 light, M, R, G, 1.5, plus M, P, G, 2.75, is equal to T2, times 5, right? And then all we do is just plug in the mass of the robot is 10, gravity is 9.8, the mass of the plank is 75 times 9.8. Those are just numbers. You divide by 5 and you got your tension on 2, right? How do you find this one? You move your pivot from here and you put it there, you measure everything from here, this way, the distances, right? And you solve for T1. Nice problem. Really, fun problem to do. You got to love physics. You got to love physics, right? Physics is just, it's just brilliant. Really, physics is just brilliant. Torque is also a practical construction planning problem. We once had a panel flip once, since the planner didn't do the calculations right. Thank God for no one was on there. Wow. So a panel on a roof, on a skylight or something, broker. Construction is, I've been around construction most of my life, most of my first 35 years of life anyway. It's an interesting place to be, or 40 years of life, maybe, right? It's a very interesting place to be, extremely dangerous, but you learn a lot on a construction site. Yeah, and a little floor panel. Yikes. Scary, scary. And who signed off on that thing, right? Crazy, crazy, crazy. And one of the things I love about physics is drawing systems, right? They draw your system and you start making notes on it and put your arrows in place. Planning is a mystery to myself. Mostly just follow the project, yeah. There's, there's, there's usually, for a lot of construction, home anyway, home, small apartment. You have the, if it's not an architect, you got your construction people who they know what they're doing, they draw it, they go get an architect to, you know, pay them like five grand to check it and put this signature on it and go to the, go to the city and they have to approve it and their people look at it and say, no, there's problem here, there's problem here, there's problem here, you need to fix that. And then the whole cycle kicks in again. One more loop, one more loop and you get approval and you go ahead, right? But good explanation to put the thought into formula. Yeah, yeah. There is, like some things you think physically they'll work. All of a sudden you realize the forces are balanced and things snap. Things snapping is the most dangerous in construction sites, from my experience anyway, because when things break, there's shrapnel flying places. Actually, let me, let me restate that. The most dangerous things, situations in a construction site are people who are new to construction. Those are the most dangerous situations when it comes to construction. When you're getting new people who've never done construction enter a work site, they're, they don't understand the safety reasons of things, right? So I find working with new people to be the most dangerous or one I did, to be the most dangerous aspect of construction. Because if everyone knows what they're doing, they've got the safety measures in place and everyone's following a protocol, accidents are on the bare minimum, right? And of course there is unscrupulous companies that cut corners and put everyone's lives at risk, but I really didn't encounter that too much. Most of the time for me was professionals contractors, so they needed to, they couldn't afford any downtime, right? They needed to be physically able to do things otherwise they're out, right? They're out. We're not going to punch in the numbers just because it's just numbers. Click, click, click, click, click, click, click, click. And for sure, when we did the problem by the way, for sure this one was more than that one. Yo, Chico, do you have the time to give me some advice? For sure, Dante. For sure. We're in chill mode right now. It's fantastic. And take any advice I give with a grain of salt, man. Like really, like, or anyone else has to give in chat as well, right? When building high rises, then they get very tolerant and careless when the height rises slowly. Always need to keep an eye on them. Yeah. Yeah, the larger the corporation that's doing the construction, I found the more, what do you call it, shortcuts they take, right? It's, it's an interesting place to be. It's an interesting place to be. Riot, how are you doing? Doing well, brother. Thank you. I have an appointment tomorrow with someone who can put me into a job training program that I need pretty desperately. I got to convince her that my desperation is over and that I can do this. What should I tell her? Oh, depression, not desperation. Now, depression is over and that I can do, do this. What should I tell her? I'll interview you tomorrow for a training program that you need pretty desperately. You need to convince her that your depression is over. What could you tell her? I think your behavior would be more an indication to her than anything you can tell her to a certain degree, right? So I would say stand up tall, right? Look her in the eyes. Don't twitch, uh, it was called fidget around too much, right? Don't be rigid. Don't be tight. Be relaxed, but carry yourself well, dress properly, shave if you need to, if you're, you know, you don't want to go there with a 24-hour thing. Yeah, always look different. Yeah, Dante, change your look. How did I end up there? The Arab New Zealand? Dante, that's really important. If you're eating, if you guys are meeting at a cafe or something, just get some kind of herbal tea or just something not too sugar high or anything like that. Just something simple. Smile, right? Don't, you know, don't look silly and go smile all the time, but be, have a good demeanor about you. Aside from that, I'm not sure, you know, if she comes out and straight out says, hey, are you still depressed? Are you still dealing with depression? You could say, no, I've come out of that phase and I'm very happy about it. And I did a lot of self-work and meditation and I'm exercising. If it comes up for sure, mention to her that you're exercising because a sure sign that you're someone's, you know, has a handle on depression is if they're exercising a little bit, right? You listen to music. You're enjoying life. You're in good health because depression has certain physical mental attributes to it, right? That physically outwardly show. Yeah, we'll try to mention that I'm exercising, eating healthy, huge, huge, huge, right? And maybe mention to her that you've worked on a couple of projects recently and finished them off and you feel great about it and whatever it might be, right? If there are things you've been doing. But that would be my take on it, Dante. I found that the best way to confront in interviews is to practice out loud in front of a mirror with the stuff I'm going to talk about in the interview in hand, practicing it. Practicing can make you more confident for tomorrow. For sure, Riot. For sure. I'd agree with Riot as well. And I hope you've done the research into the work training program, right? If you haven't, look into that program. If it comes up, just say, yeah, I've looked into the program. I'm really looking forward into going into this, going into that and talking about these things and learning more about these things and stuff, right? So look into the program as well. Just like any interview you're going to, look into the company that's interviewing you or that you're seeking a job for. You only need one good person to get you through life successfully. And one bad person in your life can also destroy everything you have built in your life successfully. Life, right? There is a certain amount of luck involved in life. If the interviewer asks, then mentioning some hobbies would be good. Yeah, hobbies would be fantastic. Nikki, how are you doing? Welcome, welcome. And don't concentrate to prove herself too much also. People pick up on what you're thinking. Just try to feel good. Whatever works for you to feel good. Yeah, that's what I would big time book her. Yeah, of course. Thanks for your time. Our pleasure, Dante. Fingers crossed it works. Fingers crossed you get in, right? And maybe think about some of the questions that she might ask you that might throw you off, right? And prepare an answer for those. Interviews are hard. For me, I've done, I've never, I haven't done an interview with a company for ever in person. I've had some people that have hired my services and, you know, organizations that I work with when it comes to teaching there, they feed me certain number of students and stuff like this, ask me questions, and I've had parents ask me what my background is and why I'm suited to work with their kids and stuff like that. I'm rightfully so for sure. They use a vetting process, right? So I've interacted in that way. And in general, my, the way I deal with it, the information that I convey to them is that, look, my focus is this. I had a lot of experience in this and I try to set their mind at ease and explain to them that if they don't like my services after the first one or two sessions, that's fine. I don't work with everyone, but my success rate is extremely high. And my focus is the student period, right? So I try to put people at ease right off the bat in a large part, mainly because I'm honest, like I try to be as honest as I can and answer the questions appropriately, right? And I don't have a time factor associated with this, right? I don't say you have to make a decision now or anything like that. So go think about it, take your time, no rush, right? Hey Chico, when you're trying to learn a new complex topic, how do you approach it mentally? I immerse myself in it, right? I literally just immerse myself in it. I, to a certain degree, I drop what I have to drop doing or put whatever I need to put on hold, on hold, until I have a good grasp of what's going on. Like there's been times, there's one thing that, like that's one thing what the school or education system is about, right? Like when you go through university and get a piece of paper that says, hey, you're trained to do this, most people in companies, high level management, they know you're not trained to do this. They know that the only thing that this paper represents is you were willing to spend money, resources, four, five years of your life to get this piece of paper, to get you through the door, so you can work in this field. That's what you're telling them, right? They know, most people know that nobody coming out of university is trained to do anything, right? It's just a matter of, are they dedicated enough to do something? So I immerse myself in whatever it is that I'm doing. I've had things in my life come into my life where they were so profound that I dropped everything. It took me a month, right? I've done this a couple of times. It took me a month to close off tons of projects and sort myself out. And I took one time, I took a year to two years off on a sabbatical to immerse myself in this thing that I encountered, to educate myself in it. And that was one of the most profound periods in my life, right? It takes energy, it takes effort. Learning is not meant to be easy. If learning was easy, it would just be called doing. It wouldn't be learning, right? But man, when you come out of that, powerful, powerful, right? Can you talk a little bit about logarithms? I've been having trouble understanding them. Yeah, for sure. Dissolving girl, let's do logarithms. I'm glad I ended up here. I'm glad you like her. I have never done an interview in my life. I've had a couple of police interrogate her when young. Good practice. Let's talk about logarithms. Dissolving girl. Now, dissolving girl, I'm going to link you to a video that we did in the past. Logarithms. But I'm going to go over that right now. Well, not all of it, but a lot of it. And there is a whole series of whole playlists I'm going to create, specifically in regards to logs, the same type of stuff that we've done for trigonometry. If you do cheat your trigonometry introduction to logs, visualize an exponential logarithmic function as graphing. Here we go. This is my intro video to logs. But I'm going to go through it right now with you. Just for you to have an appreciation for what it is. Let me sort myself up. I honestly heard someone say something like, there's no failure. You either win or you learn. Really stuck with me, huh? Yeah, pretty much. As long as it doesn't take you out of the game, right? If it's got a popsome and apple, delicious. Thank you. I'm a music theorist and I always have to interact with logs since the ear hears logarithmically. Does it, dissolving girl? That's cool. I didn't know that. I associated music with trig functions, trigonometry. But that's cool. I should look into that more. Yeah, I literally dunked my brain into machine learning starting maybe two weeks ago. Been working on building a mental model of how it works. Cool. I learned the best when I get a little obsessed with something. Yeah, for sure. Yes, our perception of sound is nonlinear. Wow. I didn't know that. That's cool. That's super cool. I wonder why. Is it the material that the ear is made from? Or our processing abilities? We are more sensitive to higher pitches in real IRRC. What does IRRC stand for? Our perception of sound is nonlinear, logarithmic. You would absolutely love studying micro tonality and just an intonation. It's so incredible. Dante, that's the Fletcher-Monson curve, which describes amplitude sensation. Really? In terms of pure frequency sensation, we hear logarithmic. Wow, because the octaves is a two to one ratio and we can hear the two to one as a distinctly different sound, but the same pitch higher. Oh man, you're getting all excited. Show me the grounds, show me what it looks like. Let's talk about logs. Let's talk about logs. Yeah, that's true. That's super cool. The way it works logs is this. In mathematics, what we try to do, musician here, I wondered about this. Nice. In mathematics, what we have, we have the opposite of things that we can do. The opposite of addition is subtraction. The opposite of multiplication is division. The opposite of something to a power of something to a certain degree is the radicals, but the radicals are really the same thing. This guy just goes, if you're going to do this, goes in the denominator of the power. Now, one of the things we do in mathematics is when we have an equation, so for example, let's say we have this, we have y is equal to 2x plus 1. So let's say we have y is equal to 2x plus 1 and this graphs a linear function. This graphs this. 1 and you go up 2 because the slope is 2 over 1, 1, 2 and over 1. This is this line. Now, one thing we like to do as human beings, we like to take things apart and take a look at them. What are they made from? Factoring. The other thing we like to do is we like to mess around with things, switch up the order of things just to see what happens. So mathematicians came along and said, hey, okay, we know how to graph a line, but hey, what happens if we take the reciprocal of this or the inverse of this? We switch the x and the y. What if our equation wasn't y is equal to 2x plus 1? What if our equation was x is equal to 2y plus 1? What does the graph of that look like? And what does that do, really? What does that do? Well, first of all, let's answer the question, what that does. What that does, if you switch the position of the x and the y, it takes any function, right? Any function. Doesn't make a difference what it is. And it flips it about the line y is equal to x. Okay, this pen is dead. I'm going to kill this pen too. Let's do this in green so you see this. So it takes y is equal to x. So when you take any type of function and switch the x and the y, what you're really doing is you're taking whatever function you have and you're flipping it about the line y is equal to x. You're letting the line y is equal to x act as a mirror, right? I like to think about it like this. You take whatever function you have, you put your fingers here along the line y equals x and you go whoop and you flip this, right? So the flip of this, let's draw this in purple I guess, the flip of this is going to look like this. That's my crappy way of drawing a line, right? So the purple is this guy flipped, which is really this guy, right? Now whenever you're writing a function, we're not going to write x equals to y plus one, you want to get the y by itself, right? So what you do is you get the y by itself. x minus one is equal to two y and then divide everything by two. So y is equal to one over two x minus a half, which is what we have here, right? This is the purple function and that's this guy because the y intercept is negative a half, from here you go up one and over two, one two, one two, where is it? Oh, up one and over two, so over here, okay? Does that make sense? So that's what we're doing when you switch the x and the y. Keep this in mind. I'm going to erase this, okay? So let's take this out. That was a linear function with drew, right? Whoa, that was a linear function with drew, right? We've got an infinite number of types of functions, right? Or infinite number of functions. There might be a limited types of functions, I don't know, category wise, there might be limited types of functions, but there's an infinite type of functions, right? Yes, yes. Smiles back, snack, snack, snack that, smiles back, snack that, smiles back, nice. No, it makes sense. Randy, what are you doing? So take a look at this. Let's say we have an exponential function. Let's say we have the following. Let's say we have a function called f of x is equal to two to the power of x and if you don't like f of x, let's use y. Oh my God, that makes sense. Let's use y, right? So let's say we have a function called y is equal to two to the power of x. That's a large function, that's huge, right? Actually, no, no, let's not do two to the power of x. Should we do two to the right? Yeah, let's do two to the power of x. Okay, let's make a table of values. Let's graph this function using a table of values, okay? Here's our x, here's our y. So let's just plug in values for x and find out what y is and we'll graph it here, right? The first one we're going to do is zero. So when x is zero, two to the power of zero is one. So when x is zero, two to the power of zero is one, right? When x is one, two to the power of one is two. x is one, one, two. x is two, two to the power of two is four. Two, one, two, three, four, four. When x is three, two to the power of three is eight. Three, that's four, we're up here, right? We're off the board. I did not expect this to be so satisfying. What a golden moment. This is that great. How are you doing? Now, we know what the graph looks like on this side. Let's see what it looks like on this side. Let's plug in values, negative one. So two to the power of negative one is one over two. Two to the power of negative one is one over two. Because anything to a negative power, all the negative does, it just flips it, right? Reminds me of crypto trading days. Negative two. Two to the power of negative two is one over four. So negative two is one over four. So it's here. So an exponential function looks like this, right? Cool. That's y is equal to two to the power of x, right? What do mathematicians do? What do human beings do? We like to flip things around, mess around with things, right? Can we do something in four dimension or higher next? Four dimension. Here's a four dimension. Ready? This is me drawn a three dimensional box at this moment. It's live streaming this on Twitch. We're in four dimensions. I just came here to say, God, I hate man so much. You should love it. Powerful. Are you talking about tensors? Tensors, if you are, at some point I'm going to learn tensors. Fair. Wow, that just blew my mind. Take a look at this. So what do mathematicians do? Mathematicians, us, we like to mess with things, right? Flip things around. That's why I'm learning now. Tensors, you're learning tensors. One day, one day in my retirement, when I'm like, I don't know, let's say 92, I'm going to start learning tensors. So, hey, that's our function. What happens if we switch x and y? I really need to know the tensors. What happens if we go x? No, let's do it here. x is equal to 2 to the power of y. Oh, wow. x is equal to 2 to the power of y. What's the graph of that going to look like? Okay, let's do a table of values. x, y. If we start plugging in numbers for x, it's going to be hard for us to solve for y. Is it not? It is. For example, let's assume x is 1. In here, we're going to have 1 is equal to 2 to the power of y. What's y? What's y? 2 to the power of what is equal to 1? Well, 2 to the power of 0 is equal to 1, so 0. So we can do it that way. Plug in values for x and try to find y, but we get problems because we can't guess most of the answers here. If we put in x is equal to 2, 2 to the power of y, 2 to the power of what is equal to 2? Oh, 1. That one's easy. Cool. What if we put in 3? So 3 is equal to 2 to the power of what? Oh, way more difficult. Way more difficult. However, one thing we can do in math is we don't necessarily have to plug in numbers for x to find y. We can just plug in values for y and solve for x. Let's do it that way. No one says we have to start on x. This is an equation relating x and y. Equation relating x and y. We can just do values for y and solve for the x. I googled what a tensors are and then closed the window. I'm going to be going back to school so my math is making me nervous. Tensors are very pretty. I think I'll try and learn them via Python nice. That's what TensorFlow is made for. Oh, riot. You're making me envious. You're making me jealous. One day I'm going to get into this, right? One day I'm going to get into this. So let's plug in values for y. When y is 0, 2 to the power of 0 is 1. When y is 1, 2 to the power of 1 is 2. When y is 2, 2 to the power of 2 is 4. When y is 3, 2 to the power of 3 is 8. Take a look. Do you see? 0, 1, 1, 2, 2, 4, 3, 8. 0, 1, 1, 2, 2, 4, 3, 8. Okay, let's try one more. 4. y to the power of negative 1, 2 to the power of negative 1 is 1 over 2. Oh, yeah. Oh, yeah. That's all you're doing. So negative 2 is negative 1 over, sorry, it's 1 over 4, right? Because when you do this, when you switch the x and the y's, what you're doing is you're doing flip about the line y is equal to x, right? You're doing a flip about this line. y is equal to x. When you're doing a flip about the line y is equal to x, you're grabbing your function and going, so this guy's going to go poof. What you're doing in terms of tables, the coordinate system, you're switching the x and the y's because that's exactly what you did. You switched the x and the y. So you switched the x and the y's, right? You're okay there so far? I think TensorFlow might not be the right start for me. Too much boilerplate. I'd rather do something lightweight and total size. So what you're doing is you're switching the x and the y. That's what that means when you switch the x and the y and the function, right? So the graph of this guy looks like this. 1 in 0, 2 in 1, 4 in 2, 4 in 2, 8 in 3 way over there, a half and negative 1, a quarter and negative 2, right? So the graph looks like this. Sorry. So we know what visually this looks like, right? Cool. Now this is called exponential functions, right? What are we going to call that? These types of functions. Anti-exponentials? What's a good word for these? I'm going to call them logs because that's what logs are. Logs are the inverse of exponentials. That's what logs are, okay? And what they do is, exactly, right? They're just the inverse of exponentials. Logarithmic functions are you switching the x and the y around for exponential functions and coming with that function. Now what we need to do is, wait, it's not gradient descent, I lie. It's linear regression, okay? Exponential functions were the hopes of every technician, not just crypto, trader, yeah. Any trader, not just crypto, any trader, right? So take a look at this. This is our function, right? And again, like the line that we had, right? We had the equation of line and we switched the x and the y, but we don't want to write the equations as x is equal to 2y. We need to get y by itself. How do we get y by itself? Let's do it. Just like exponentials, logarithms have certain rules, right? Those are rules. So let's take this function here. Let me erase this part. Give us room here so we can mess around with it. Let's see how dark is this. That's dark that will show up. A bit hard to erase though. This one's nasty. Let me find one that's going to be easy to work with. Okay, that's the same color. We'll use this one. So take a look at this. Let's take function. x is equal to 2 to the power of y. Just like mathematics, right? You can do things on one side with an equal sign as long as you do them to the other side. So what we're going to do is we're going to take logs of both sides. So this becomes log is equal to log to y. Okay. So all we've done right now because you need a little bit of preliminary log intro to this, but all we've done right now is take logs of both sides. It's like saying here, let's multiply both sides by 5. This would be 5y is equal to 5 times 2 to the power of x, right? We just multiply both sides by 5. Okay. What we're doing right now is we're taking logs of both sides. Now logarithms, just like exponentials, they have certain rules, right? One of the rules in logarithms is this. The standards says this. If you have log of a to the power of b, you can kick the b down. And this would be b is equal to log a. Oh, sorry. Not equal to. It's equal to b log a. Okay. That's one of the rules we have regarding logarithms. So for this right now, what we can do is grab the y and kick it down in front of the log. So right now you got log x is equal to y log 2. Right? And the name of the game is we want to get y by itself. So we're going to divide this side by log 2. And we're going to divide this side by log 2. So this becomes a y is equal to log x over, oops, log 2. Can you see that? Yeah. You can see it. Now, one of the things we have with this is the rules of logs is this. So you can write the exponent in front of the log. Exactly. If it's in the power, it can come down to the front of the log. And the trick with learning logarithms is learning the log rules, which is basically learning the same way you did with how to deal with exponentials. So if you had exponentials like x squared times x cubed, well, you add those guys. That's x to the power of 5. Once you know that, you know it. It's over. Logs has the same type of rules associated with it. Learn the log rules. Everything else is easy. It becomes ridiculously easy. For example, here one of the log rules we have is this. If we have log of a over log of b, let me put the small case b, you can write this as log a to the base b. It's just terminology. Well, cool. This one means I'm just going to erase this part. You can write this as log x to the base 2. So this function written in log 4, and I'd like to show it this way. If you want to convert this to log 4, you can just grab the 2, kick it down in the log base, and this just becomes, let me write it with this, y, and this guy drops. y is equal to log base 2 of x. This is this graph. Okay. This part, you can think about it this way. Grab the 2, kick it down in the base, and this guy drops. Focus. Focus. There we go. Grab the 2, kick it down into the base, and this guy drops. Okay. That's the basics of logarithms. Aside from this, there's like seven log rules that we have. You just have to know how to manipulate them, right? How to work with them, just like you did exponentials, just like you do this. Okay. Really, I know logs takes a lot of people out of the math game. It shouldn't. It shouldn't. It's, once you wrap your head around what logs are, then you're just playing around with another type of function, and there's certain rules associated with logs, and you can manipulate your function accordingly. Okay. I always find logs easier when I think log is, what power in do I have to put a to, to get b out, where log a, b, a, b of base a, with base a equals, and yeah. If I got that right way around, I'm not sure. That makes sense to me. I hadn't considered the unique operations you can do with them. Yeah. Huge, huge, huge, huge, right? It's like almost any other type of function in mathematics. There's so many functions that give us certain types of powers, certain things in the world just follow that pattern, right? I hope that helped you out, uh, dissolve in girl. If you have certain specific types of questions where you're trying to simplify things, uh, we can definitely work with it. I can erase this and show you some of the rules. So it's so useful when you need to rearrange complex energy things. Yes. Thank you so much. I really appreciate it. My pleasure to dissolve in girl. Anything to help people learn mathematics, almost anything to help people learn mathematics, right? Because it's empowering. Once you learn this, wow, pah, pah, pah, right? Man, I don't go back to work until January 3rd after today. Phew. What a relief. Nice riot. Luckily, few engineering things are truly exponential because reality rarely goes to infinity. Yeah. Bacterial growth is exponential. Radioactive decay is exponential, but all of those things have limits. They don't go on forever. They're bacteria specifically grows, grows exponentially until it consumes the holes or consumes whatever and destroys the holes and dies in itself, right? Inverse square law of sounds is exponential. Inverse square law of sounds is exponential. Inverse square laws. I don't even know what that is. All right. I got to get ready for the bed. Good night. Good night Dante. Good luck tomorrow, brother. Keep us posted. Fingers crossed. You're in the door, right? Op amp instability is what I'm thinking of. What is this math topic called? This is called logarithms. This is a logarithmic function. And this is an exponential function. Okay. Like how sound drops off as it's moving away from us. Yeah. Is that what it is? It's like the red shift? Well, sound and light is exactly the same thing. They're waves, right? Well, not exactly the same thing, but waves. Howdy, Ahmed. How are you doing? So what was that called? Inverse square law of sound is exponential. So is that the one we're referring to? As dropping off, just like redshift with the stars, with galaxies moving away, right? English is my second language and I'm moderately trying. So I'll play this game in a hard moment. Funny. Yeah. Sound falls away logarithmically. So it attenuates exponentially. Cool. So it's like gravity. Gravity is, yeah, it's to the power of two. Is this high school math? This is high school math. Yeah. Great 12 in my part of the world. Other parts of the world, probably grade 10, grade nine, maybe. Some parts of the world, you don't even touch this. Let's take it down. Let me give you some of the rules for logs, right? We've got a little bit of time left. Must cover that. High school for me. They didn't teach it to you in high school, right? Logarithms? I did this as a homeschool kid. Nice. Awesome. I hope you had a good tutor. Fortunately, education exists freely these days. Yeah. Or close to freely. Before high school. But I'm a Brit. So no idea what age HSS. My mom. Nice. Awesome. So I hope you appreciate her very, very, very, very much. A very clever lady. Sounds like she did a fantastic job, right? So take a look at this. Some of the log rules. It's just like exponential rules here. x squared times x cubed is equal to x to the five, right? Log rhythmic rules. Log AB is equal to log A plus log B. So if we had log six, right? Let's say we had log of six. We can write log of six as log two times three. And according to our law, it says log two plus log three. So log six is log two plus log three. That's cool, right? x squared to the power of three is equal to x to the power of six. Look at that. Look at that. By studying logarithmic functions in my second year of high school, and I can't remember crap. Let's crank the triple integrals or nothing. But man, it was terrible in HSS. What I learned in college was that you have to actually practice the math and do the homework. Yeah. I didn't do that as a kid. Just kind of expected to understand anything I looked at. Not the case with math. Math. You know what? Right? It starts off that way, right? People understand that. And at some point in high school, all of a sudden you need to do homework. And people haven't been trained, right? Educated enough to take on that responsibility, to do the work. Their work ethic is not there, right? One of the first things you need to do is build up the work ethic with the students. The work ethic is not there and they don't do the work. They don't do it. So we can get infinite log one out of any log n. Yeah. Log one is it's zero. I was pool hustling and bribed a couple of teachers during high school to finish school as soon as possible. And when I got older, then I actually wanted to learn things nice. Pooled man. I did a little bit of a playing pool. Eight ball and nine ball. I played a lot. Where did apprentices go in the top right corner problem? This one is x squared to the power of three, right? So they just disappear. And a power to a power, they multiply each other. Power to a power, multiply the exponents. I'm legally blind and it wasn't detected till ninth grade. Wow. I've always been very good with sciences, but I fell behind in mathematics because I was seated in the very back, oh no, of my school algebra class. I couldn't see anything. So I grew to hate math. I actually love math though. And I wish I could have had a different starting situation. I have an intuitive understanding of systems logic, but I wasn't able to see the overhead so I couldn't learn. Oh, that's unfortunate, this old girl. Again, it's a learning thing, right? It's a burden you carry, but it makes you stronger down the road, I think. And it's never too late. We just covered some stuff that you're like, wow, cool, right? Here's a couple more log stuff. I used to love algebra in college, but didn't go any further than that. That's why eventually I'm going to learn math from my favorite teacher, Rachel. That's right. So that's one rule we have. This is rule number one, right? Here's rule number two. We talked about this. Log A to the power of B. If you have a log of something to a power of B, you can take this, kick it down. So this becomes B log A. And by the way, whenever we're writing log, if I write log, where am I going to put this? Log implies is log base 10. It's like saying if I write down the square root of five, I'm not putting the two here, right? Because it implies it's the square root. There's a two there, right? Yeah, I would love to take lessons with you if you teach privately. I do dissolve and grow. I do. I have students that I work in private and I have students that I do online activity with. Blog A. Is that what it says? No. Blog A. That's right. Blog A. B log A. That's one rule we have. Here's another rule we have. Log A over log B can be written as log base B of A. Cool. Here's another rule we have. Log A to the power of log, what is that? A, B. This kills that and that just drops as B. What are some of the other rules? GP, GP, GP. And by the way, subtraction where division works the same way. If we had log, let's say five over four, you could write this as log five minus log four. I'm sort of running out of space, but I'm giving you some stuff. I have no clue what is going on here, but I think it's really cool you do this. Yeah, thanks, cool of Borg. It's just I'm making myself available for a couple of hours every week, two to four times a month. Just talk about math. In fact, if we, there's people here that know mathematics better than I do, if we can help out other people to learn mathematics, we do, to the best of our abilities. What are some of the other log rules? Try to go by memory here, right? So over four is the same as 0.25. So over four, over four, in here you mean? It means you're dividing by four or multiplying by 0.25. Often when things go over my head here, I still feel like it will plant some seeds. Yeah, yeah. Because we do try to link this up to a lot of other things as well, right? Log A, log B. No, that's, that one is not true. The Scarlet Phoenix. So I'm going to erase these. Take a look at this here. Let me erase these. That's a common mistake that a lot of people make, right? And I associate it or blame it on the division really. Check this out. So yes, that is correct. Yes, that is correct. Zachary. Yeah, exactly. Okay. Now take a look at this. The Scarlet Phoenix. You wrote this. Log A over log B equals to log A, log A minus log B. This is not correct. This is this. Log A over B is equal to this. Okay. Is equal to log A minus log B. This guy is not equal to that. This guy is equal to log A with a base B. Okay. What you wrote down is a common mistake that a lot of people make. So it's equivalent to writing this. So we wrote down log AB is equal to log A plus log B. But that doesn't mean log A times log B is equal to that. That is not correct. There are some other relations as well. Oh, I wrote it wrong. Yeah. But this is the one you want, right? That is powerful. That is powerful. Like they give you stuff like this. Here, let me give you a crazy problem. Crazy question, right? Not a crazy question, but something they give. Here, we won't make it too crazy. They'll give you stuff like this. They'll say rewrite this. Log X squared Y cubed over Z 2Z to the power of 5 cubed. Rewrite this with separate terms, right? Hey, do you compute integers in here? Compute integral. No, we're not doing it into calculus right now. Quadruple O. Sorry, viewbot. I'm staying away from calculus right now. I have G to G teacher voice alteration. Thanks so much for your demonstration. This was great for my lunch break. I'll email here about working together. It's my pleasure to solve and grow. I hope you found it useful. And thanks for bringing up the questions, by the way. It's nice having questions to deal with instead of doing random stuff. So is it true that log N equals yes? So take a look at this. Here, log, let's do this. Let's start off this way. Right? How can we rearrange this? Well, if you remember, according to one of our laws, log A to the power of B, we can kick the B down, right? This would be B log A. Well, if you can do that, then you can kick it up as well. Right? Is there a romance in mathematics? Yes. Yes. There's so much romance. By the way, hi, legendary Rob Boss. There's so much romance in mathematics that it drives people insane, literally. Right? Can you show us the proof for the love equation? I don't know if there's a one equation. I think it's more than that. Oh my God, math tutorial. I found the dark side of Twitch. See where this is going. Yeah, you see where it's going? For sure. So you can kick this up. Right? So this becomes log of one over N to the power of negative one because there's a one here. Right? What does a negative power do? It flips things. So this would be log of N. Not only rational stimulation here, but good vibes from good intent and good company. Nice. Yeah, for sure. We've got amazing people here on chat. Right? Such a pretty proof and you haven't finished yet. Yeah. This is because a to the power of negative one is just one over a. So one over a to the power of negative one is just a. Right? It flips it. Take a look at this guy. What if they wanted you they wanted you to write this in terms of just separating the multiplications and divisions stuff like this? Well, you can do this. I might use your help though. I got a huge exam on Friday and I haven't started learning it. Oh, you caught us at towards the end. What do you got? What do you got going on? Flux capacitors. Flux capacitors. I wish I did. I don't. Take a look at this. Here's one rule we're applying. We're going to take the exponent and kick it down. So this is three log x squared y cube over two z to the power of five. Right? Well, the other rule we have, we have multiplications and divisions or additions and subtractions. Right? Geometry formula. I don't know. Yes, there are plot device from back to the future. Is that what they are? I love it. So take a look. Oh, that's what it is. Flux capacitors. Can you please explain a flux? This is back to the future thing. I think so anyway. Someone brought it up. I think so. So here's our rule. We got the three out here. Well, these guys are being multiplied. These guys are being divided. So use our rule. This becomes log x squared plus log y cubed minus log of two minus log of z to the power of five. And then you can take the powers and kick them down, kick them down, and kick them down. Right? So this becomes three two log x plus log three log y minus log two minus five log z. And then you can multiply the three in to all of these guys, if you like. So that's six log x plus nine log y minus three log two minus five. Oops, not five. Fifteen log z. You can kick the three up and that becomes an eight. Two to the power of three is eight. Here we go. You can kick the nines up if you like, but leave it like that. Right? So you could just play around with that, whatever you want to do. Right? X. How are you doing? How is life? It is inside the parenthesis. Not necessarily. It's the log of this whole thing, so I can kick that down. Yeah, and over here. Can you show the reason why log function is also the inverse of base ten fun? Oh, we just did that, brother. I think we just did it. You missed the beginning part when we did logs. It is nice that most of the proofs of the log laws involve converting to exponent exponents and reversing the results to determine the log output. Yeah, example log. Yeah, we basically just did that. Like the one you want is this, right? We did a full blown explanation, but here we can do this. So log ten to the power of x. Right? So what we can do is kick this down. So this becomes log ten. And whenever we write log ten is base ten. Right? So this becomes x is equal to log ten over log ten. Right? And log ten kills log ten. So this is just equal to x. It's the split of it. I only know that with enough powerful capacitors, you can build a ray gun. Can you? Can you solve a simple potency function just so that I can get an idea of what it is? I had no idea what that was. I think that's a notation mistake. A last log. No, it would be added together to be that. Right? Oh, that's what you're talking about. Hold on a second. Let me correct this. Watch this. Okay, let me do it in red because red is coming out better right now. Let me erase these guys. The thing that I wrote before was log x squared y cubed over two z to the power of five, all of it to the power of three. Right? All of it to the power of three. Right? Now this I can bring the three down. Right? However, if I wrote this, log x squared y cubed over two z to the power of five to the power of three, I couldn't bring that down because it's the whole thing multiplied. So this would mean this times itself three times. Right? Well, you wrote down, which is log n times log n. That doesn't equal two log n. Log n plus log n, and we don't need the brackets here, is equal to two log n. This would be log n the whole thing squared. Okay. Yeah, if it was the log of the whole thing, that would work. I thought the Q was outside of it. Yeah, sorry. I should have cleared things up a little bit. Right? You're putting some powers outside log. Yeah, I didn't mean it that way. My apologies. It's just the way we use it here. Monkey Farts, how's it going? Yeah, you cannot connect the capacitor to get the needed voltage and then ray gun is a possible. Gotcha, gotcha. Yeah, that makes sense. Okay, awesome. I'm glad I would clear that up. Well, that's a notation thing. Yeah, in my part, that's what they do. They never put it here. Would you mind proving one of the log laws for us? We did the proving one of the log laws. We can rearrange things to get it. Okay, because I'm used to calculators. The parentheses on the second line seem implicit. Akia, hello, do you have a PhD? No, no. No PhD in math. I got my degree in geophysics and minor in mathematics. Thanks for going back through that. My pleasure, Xander Wolf. Chico has a PhD in cliff diving. That I would say, to a certain degree, I would give myself a master's in cliff diving, cliff jumping. Maybe third, second year, third year PhD student. Let's go engineer here. A little more complex than that. Oops, I accidentally find the message. That's funny. How do we do for time? Women live stream for like two hours. Nice. It started off slow, but we kicked it up. We started doing lots of things. That's fantastic. Right on, right on. I get happy when we do math. When it gets into our rhythm, questions are coming in. We're doing stuff. That's super fun. Teach me how math toes, right? Zoom, zoom. Hi, Chico. Long time here on your YouTube channel. Saucy Rossy. Welcome, welcome. You got an emote. Thanks to the Xander Wolf cheer. Right on. We got an emote. Oh, thank you for the bits. Xander Wolf, appreciate it, appreciate it. I hope you're enjoying these live streams, by the way. Saucy Rossy 07. Sleepy Doggy 69. Are you being silly? Love your stuff, Chico. Keep it up. We'll do. We'll do Xander Wolf. Thank you very much for the love, man. Thank you very much for the love. Ten emotes shared. Wow. Cool. This is my first math stream I've seen YouTube. Thanks for that. Oh, what's that? It looks like ha ha. Present. Nice. Oh, what's this got? Ha ha, baby. Nice. It's today's topic. We did some long rhythms. Yeah. I am a dead artist. Are you math teacher? I do teach math. Yeah. High school mathematics. Review. Reduce low echelon form of matrix. Oh, that sounds complicated. I don't know what that is. I would have to look that up. It's not it. When Chico done, do you think he'll log out? Ha ha. Nice pun, right? Fun. Chico, one of my favorite videos is when you show it how your long and short boxes are set up. And yes, the live streams are great. Awesome. Yeah, that one, my setup is still the same. Every now and then, for the comic books we put on eBay to sell, I actually, I had some stuff on, they're sort of using a, not storage, but work area sort of storage about boxes. So I moved everything and I went through one side, a few long boxes and I pulled out some of the comics that we've been selling for the last few months. Right? So it is handy. It is fun. It took a certain amount of, and it's good exercise, right? Only huge comic book collector as well. Awesome, man. Awesome. It's seriously, one of the greatest things I ever did. Saucy Rossy, I think you'd agree. One of the greatest things I've ever done in my life and one of the worst things I've ever done in my life has become a comic book collector. The greatest thing is just the joy of it. It's just amazing, the expansion of the mind and the stuff you read and what you're exposed to and just all of it, right? Fantastic. The worst part of it is, oh my god, it costs a lot of money. And you got to move these boxes around in space and stuff. But I wouldn't change it for the world. I wouldn't change it for the world, right? One of the greatest pleasures that I have in my life. It's a great joy and a job and a job. That's one way of putting it. Mathematics is my favorite subject. Nice. Can you teach me some basic math? I suck at it. Oh, Tarek, we're about to sign off on this stream. I have a whole bunch of stuff on my website. Go to the language of mathematics. If you want basic math, here's the latest playlist I put together. Just counting, adding and multiplying. And within this, if you go to my playlist, if you go to the language of mathematics, I start putting on math videos. This table of contents I'm giving you is in reverse order. And same with the other one. The newest videos are up top. But I started putting on math videos in 2008. And I covered the basic stuff there, a lot of it. But you're welcome to pop in in the next live stream we do, math live stream we do, and I can cover some of the basics with you. How about a look at the four-year transfer? Yeah, it's a great joy and a job. I just did four year today at college. Nice. Awesome. Eyebroker, thank you very much for the tier one son. You taught me some great eBay skills for buying bulk lots. I have got a lot of Bronze Age books using your awesome, awesome. You can get some amazing deals on eBay. Just distribute out the costs into shipping. You see one seller that has a lot of stuff you want, make them offers, get gigantic bucks sent to you. Can I ask you some questions in future streams, college math? As long as I can do them for sure. Now high school mathematics goes into college as well, pre-calculating and stuff. So, oh, thank you very much for gifting us up, Zachary. It's their first gifts up in this channel. Awesome. Five emotes shared. Nice. Gift shared reward to five others in chat. Nice, nice. One day I built that ray gun. Broker, if you do, let me know how you did it. I would love to have a ray gun. Thanks. We need more streams like this. We'll try our best. We've been doing a few of these. I'll do my parts as long as I can, right? I got a bunch of werewolf by night. And two more Dracula. Awesome. About a year ago, doing what you do. Nice. Awesome. By the way, Saucy Rossy, it's getting harder to find those kinds of deals. It's getting harder. Okay. Always turn in one stream. Check out our Patreon page, Tarik. You don't have to contribute to Patreon, right? Let me see if my Patreon does that have a language? It does. Nice. Go to our Patreon page. You can just follow, and if you follow, they'll send notifications to you. Right now I'm only posting on Patreon in the post section. I'm only really posting our schedule. I'm going to start posting other things as well. I just have to get my stuff set up. And you don't have to contribute and all the posts are always open unless Patreon changes the format. They did that and it was posting stuff and it was Patreon's only for a bit, which was like open. So, and you can follow the stuff on Twitch and it'll notify you and stuff. But Patreon is mainly has been the streams. And you can definitely go to our Discord page and see the streams. I do announcements about these streams about a couple of days before. So, let's call this stream game. Where are we? Thank you very much everyone for the follow subs. Okay, I dropped the follow too. Nice. Awesome Tarik. So, we already have the next three streams set up and the next math one will probably be Tarik a couple of weeks because we're going into the holidays here. So, there isn't going to be too many people doing mathematics. So, look for more math streams coming in beginning of January. Okay. And we're going to do anywhere between two to four a month and exactly the same format as we've been doing here. Thank you for being here again. Thank you for the mods for taking care of business. I know Dante is not around but thank you Dante for taking care of business. Thank you for our follow-ups. Thank you for the subs. Thank you for the bits. Thank you for the questions. Thank you for the interaction. Fantastic. Love doing these. Thank you for the streams you're showing. Thank you everyone for the good company. See you around. Awesome. See you guys around. And if you can make it, tomorrow 9 a.m. we talk about health. Thursday, I think 11 30 p.m. we do current events. Saturday, I believe at 11 a.m. Sorry, 11 30 a.m. we do current events. And I believe 11 a.m. on Saturday, we talk about Julian Assange if you can make it. And then we'll see what comes after that. Okay. Thanks for being here everyone. And I'll see you guys in the next stream. Bye for now.