 It should be coming in a lot of soon. This is Chichou. Today is September 30th, 2019. And we're doing our third drop in math tutoring session for the year 2019-2020. The year just started. School year anyway. So we've done a lot of these in the last year. A lot of math streams. People just drop in if you have any questions. Specifically with high school mathematics, we can deal with it. Or try to deal with it, this rephrase. So I'm basically making myself available once a week, once every two weeks for a couple of hours to answer questions. Aside from that, we'll hold up until people show up. And it isn't open discussion, so the main topic is mathematics. So if we're talking about anything else, if there's a math question that pops up, we'll deal with the math question. And I'm streaming right now what time is it? It's 1.30pm Pacific time, west coast of Canada. So on the west coast, the kids are still in school. On the east coast, they just got off school, or they got off school a couple of hours ago. If you're in Europe, you're in the evening, Monday evening. So if you have any questions, it's a good place to drop those questions to start the school week, if you need help with anything. The rest of the world, my time zone, I haven't figured everything out yet. And that's it. What we did, we did a politics stream yesterday and tomorrow, we're doing a personal finance live stream. And that one starts at 1pm Pacific time. I have a plan lined up, anything to talk about today, to teach. On the last stream, we did, I feel like we did, I had something lined up. We talked about quadratics, yeah, we laid down quadratics. We talked about Pythagorean theorem, someone came by and asked about Pythagorean theorem. So we laid down sort of the foundation of what quadratics are. Two linear functions in general, multiply together to give you a parabola and stuff like this. And in the middle there, we talked about Pythagorean theorem. All of four, how are you doing? Welcome to another live stream. Hope you're having a great Monday. I'm very chill today. Very chill. Let me show you with that. I got my tea, of course. And for a snack, I got some tahini with maple syrup, right? So you take tahini and then add maple syrup to your sweetness, how sweet you like it. As much maple syrup as you like to kick up the sweetness or reduce, you know, don't kick it up to that. Mix it all up so it makes a nice little dip. And then you can eat it with a spoon. This is fantastic with a spoon, right? Or you can take bread and use this as a dip. And you just go like this, right? And you just pop that. Nice, healthy food. Fantastic, really. Intelligent blueberry, good afternoon, good afternoon. Hope you're doing well. Nicholas, how's life? Apologies I haven't been around, bro. I've been moving and switching career. How's things? You're moving around. How are you doing? Welcome, welcome. Nicholas, you're moving out of Scotland? Are you moving in with the fantastic relationship you built over your vacation? No need to apologize, bro. Life is life. Life comes, you know, sort of makes you meander a little bit. Which is a good thing, right? Which is a good thing. I hope things are going well with you. And switching careers, what are you going to do? You were doing books and stuff, collectible books and what not. I never asked you if you had a bookstore or not. Intelligent blueberry says, I'm proud to say that even before final exams, I passed two out of my six classes already. Nice. Final exams, though. Didn't the school year just start? It's amazing going to finals, knowing that you could get a zero on the final and still pass a course. The pressure relief is amazing. Which is one thing that people should really think about if they're still in school, is don't put all your weight on the final exam. You get as much of the marks as you can during the course of the school year. That way, if you're feeling sick, if you want to skip the final, if there's a concert you want to go to, if you're going to go out on an amazing date, right? You can skip the final, still get zero and still pass the course if you don't care about the marks. You haven't even had a midterm. Wow. Like, it's not even close. I have schools that haven't even written the exam yet. School did start, but I've had assignments that were worth a huge amount of percentages and two midterms. Two midterms already. What? Where are you at, intelligent blueberry? At my university, they often make it so that you need to pass the final to pass the course. Oh, the day? Okay. I've had courses where I've had the final worth 100% of my mark, so all the eggs in one basket roll on the dice. I hope I feel good that day, right? I've had other finals where the final was only worth 20%. So, if you're getting an A going into the final, you know, if you're getting an A, it's 86% of your mark, right? That's saying 90%. If you're getting 90% out of 80, so that's 72% of the total, you could skip the final, still get zero and still have 72% of the course. I'm at work just across the road from the Pentagon. Oh, my God. Would you like me to tell you, tell them anything before I leave? No. I have no desire to have any links, any communication with the Pentagon, the CIA, the FBI, any centralized authority. I'm very happy not having any links with them. But thanks for asking. Thanks for asking. Oh, yeah, I guess, here, at Calden. But don't say, Chico, I asked you. If you won't go into the lobby and just say, hey, who do I talk to to get the video footage of the plane hitting the Pentagon? I'm at Seneca. But politics for other streams. I'm at Seneca College, applied arts and technology, cool. Seneca College, I'm not sure where that is. Still in Northern Ireland, just watching houses. All is well with my partner. She watches the streams now as well. She said that tonight. Yeah, left the bookstore. Have begun training as a security guard for a private company. Cool, cool, cool. So you were at a bookstore before. Interesting. You must have a nice book collection. I know you're a fan though. That's a good idea. Don't do it. Still be, yeah, for sure. We know who you can talk to, just follow us. We will never see you again. This is probably a stupid question. What exactly is the Pentagon? It's the military branch of the US government. Where the US military headquarters, basically. It's not in Washington, DC. Where is the Pentagon? Yeah, it's on East Coast. But is it in Washington, DC? The Struct of Columbia. Is it? You don't want to. Yeah, don't. No, keep a little profile of that. If you're going through life, here's a bit of advice from an old man. If you want to live a happy life, stay off the radar of centralized power. Arlington, Virginia. That's right. That's right. Arlington, Virginia. Arlington, Virginia. Just across the Potomac from DC. Potomac. Just because I passed the classes already by being over 50%, really doesn't mean I'm just anti-up my finals already. Yeah, for sure. You should write the finals. But you never know. What if life deals you something that you have to miss the final? Yeah, half the house is books and comics displayed. Hence the pain of moving home. Man, I feel you. You have to be in good shape. You have to be in good shape. Unless you still have to box everything and then get the movers to move them. Books are heavy. Comic books are heavy. Making sure it's all box proper. You have moved a few times with your collection. Tips? Are the books going to storage or are they going to your new home that you're going to put the books up? If they go to your new home to put the books up, just label the boxes so you know where everything is. Get the movers or your friends or yourself to put the things in the right place. Okay, if they're going to storage, Nicholas, do this. Take just the cloth, right? Put some rice and baking soda in it. And then close up the cloth with a ribbon or something. Just close it off so you have like a sack. And put one of those in every box. That way it will suck up the moisture just in case the storage area is moist or they get flooding or just the air is moist. Because obviously you know that you don't want moisture to hit the books. Because moisture damages them. Pain. So put rice and baking soda in just like a cloth like this. Just put it in and then close it up. It doesn't even have to be this big. It's smaller than this. Just put it in each box. And I personally, when I took all my books, I took a cardboard box, comics I don't do that with, books. I put a garbage bag in the box and I put the comment or books in the box inside the garbage bag and I put one of those rice and baking soda cloth balls inside the plastic bag with the books. And I close it up and close off the boxes. And I've had books in storage for a long time. As you know, I showed them the videos and they all came out okay. So that's what I would do personally. And man, yeah. Sweet bro, I appreciate that. I normally handle my own books but with the job, switch, movers are doing everything so I have to leave specific instructions. Yeah, okay, cool, cool, cool. Security guard. What a different change, man. What a different change. That's huge. Hopefully it's at a good place. Hopefully it's at a good place. Good location. We're not really talking about too much mathematics, right? Mathematics discussion will kick up when we start moving towards December and early January. I'll do more of these last year. It's most likely once a week. During exam periods anyway. Because I know that's where the high demand is. Right now, the way it works in schools, most kids that are in school and most parents, you know, the school starts and stuff like this, the first intern or indication that a kid might not be doing well in school usually shows up towards the end of September, beginning of October. And then people start panicking a little and trying to find help for their kids or for themselves. Right? Nature of the Beast. For me, that was a little different. I have some clients that I've worked with for a number of years. So we start off fairly early. This year we started off crazy early. That's weird. Little keto. If the weather is good in your area, don't forget to go for a walk. Okay? Go for a walk, stretch your legs, get away from the computer, get into nature. It's a thing to do if you want to maintain good health. Okay? And if you want to be in a headspace where you can learn better, learn faster. Thank you for the follow showing by misdemean, shake something, shalik, sugar, something. Right now, I'm not looking too much away from the screen. So you can see the followers and the subscribers up. That's okay. You're welcome. So let's read your name. I'll try to practice my name reading. Maybe in about 10 years, I'll be better at pronouncing names. Shalas Shashka That's a doozy. Shalashka Shalashashka S-A-S-W-A Kelvin. Okay, for your information, T-S-A-H-Q-W-I-F-I You are on their radar now. Sorry. I don't know what that is, but it is what it is. It is what it is. It is what it is. Right? Shalash Shalash Shalash Shka Shalashashka Is that the... Is that a different language? Or a nickname? Great pick. I have been working on my math as I told you before. I'm not great with math. Working on quadratic equations and quadratic formulas is nice. Nice. Yeah, for some reason, in quadratics, there's a few different places in learning mathematics where you're in the school system where people have hiccups. People have problems. As you're learning mathematics, even from elementary school, negative numbers give people problems. Fractions give people problems. Variables algebra moving around the equal side gives people a little bit of problem initially and then once they figure it out, it's pretty easy. It's not like negative numbers and fractions. Negative numbers takes a little bit longer around. Fractions are longer. For some reason, fractions I guess is not taught properly in school. People don't have a really great grasp of fractions. Even grade 12s or university college students I've worked with. So negative numbers, fractions, algebra moving around the equal side and then you get into sort of concept of functions and lines and stuff like this and the big one is the quadratics. It gives people a hard time. Why is the sum of numbers up to N a quadratic function? Why is the sum of numbers up to N a quadratic function? Why is the sum of numbers up to N a quadratic function? I don't know if it is, is it? Masquerade? Do you think you could explain optimization? What is the English word for it? I am falling behind in math class. Optimization. I've always been bad at math but I want to do better this year. Ok, optimization. Are we talking about efficiency? Optimization. I would have to look it up. Is there a formula for it? If there's a formula, a poster formula we'll take a look at it. Otherwise I'll have to look it up to see what you mean by optimization. If we're talking about efficiency. Here's a summary. Sharaska. So this is your name. Sharaska. A slang term for suspicious hastily thrown together organization which was also applied to sacred R&D facilities and Soviet labor camps and Shashka. A type of saber from the Oshashka Caucasus for his legendary bravery and fighting ability. In tribute to Fyodor or Trollvik when put together, they create the word Shah Sharash, your name. Which then became Shaman. That is a great origin story. If you were either a supervillain or a superhero that would be your superhero or supervillain name and at some point there would be like three or four pages of background remembering how you came to be, how you picked this name. Optimization prognosis will always ask you to maximize or minimize. Oh that's what we're talking about. Maximum minimum. Yeah for sure we can do. Some quantity. Having described the situation using words instead of immediately giving you a function to maximize minimum. Just a quick Google definition of that helps. Ok, cool. Optimization like simplifying fractions. No, not. It would be simplifying fractions. It would be just simplifying. So optimization would be like this here. All of us do one. And I do have a video out on this but I'll give you. Let me find the video here. Chitro maximizing. Chitro maximizing revenue. That should bring it up. Hopefully. Oh there it is. Nice. Let me make sure it doesn't start. Here's the video. Maximizing revenue. Thanks. Oh Chitro automatic. These sessions are so late. What's up Chitro? Are they so late? I thought you were in the United States. It shouldn't be that late. It's early. For those that might need help. In school. After school. So, maximum maximum revenue. The sum of is it integers? The sum of numbers? Why is the sum of numbers at the end a quadratic function? So we're assuming these are integers. Let me write this down and then we'll look at it afterwards. Before we do that though, we'll look at the maximizing revenue. One. So, we've got this guy. One plus two plus n is equal to n and then n plus one. n plus one all over two. n plus one the whole thing divided by two. I think we don't need that many brackets there but that's what we've got. Let's do maximizing revenue and then we'll take a look at this. What's up, Chichou? What's up, Chichou? Welcome. Chichou, may I like to ask an off-topic question? You are what I would consider a very learned man. I don't know. I'm dingling compared to many people have met in my life, right? They're regarding certain topics. They're regarding living life. I've done pretty good to figure things out, right? If that's what you mean to get to a space where I am very happy with who I am, right? Someone who invests themselves personally their entire life to not just know but fully understand things. You focus on some topics for sure. I've noticed that you also greatly enjoy things of fantasy for sure. I do not share that interest but would like to understand your draw to it if you would care to explain, of course. Merlin? Merlin? Human? Merlin? Let me do this, fantasy. Let me put a little note here. Fantasy. Okay. I'll let you know. I can let you know speedy was Alistar and if you want, we'll talk about this a little bit more. I just started smoking doobie so I'm on the ground until I'm done for. I'm in Denmark. Oh yeah, Denmark. That's right, sorry I'll make. Don't be a lurk. Ping me if you need. For sure, Dante. Thank you very much. I'm in Norway. I'm a PM here too. Okay, cool. This is a math and earth wizard. I don't know about that. Just regarding fantasy, let me tell you something about fantasy. Here. Here. Amazing. Read it. If you're going to start off, well this is sci-fi. It's not fantasy, my apologies. But I hope most people when they say fantasy they also mean sci-fi. But what I'm about to say applies to... Oh sorry, this is wrong one. This is Dune Messiah. This one. Dune. Read it. Science fiction. Right? I haven't read this one yet. It's the continuation of it. It's supposed to be read a bit too. But Dune. Read it. So what is the appeal to this? Okay. In Dune and in many fantasy books many books that explore there's multiple reasons, right? One of the reasons is it explores the limits of human understanding of human imagination of human creativity. Really. I've went through school. Okay this is going to be the long version. We'll do the quadratic and maximization in about five minutes. Okay. So if you need to grab a glass of water or something apologies about this but might as well address this because it's pretty important, right? When I went to school, when I was going to school I did half of it in a Catholic school, half in a public school and stuff like that. I came across teachers and I've come across the philosophy the belief system that states that human imagination is limited. Okay. Because everything that we have in our society when it comes to tools, when it comes to technology when it comes to our social structures our mimics are mimicked from what we see in the natural world. Right? There's a period where I totally disagreed with that. There's a period that I totally agreed with that. Now, that's growing up. Now I'm in a state of mind that I believe that is very individual base. Right? If you explore your thoughts, your imagination and other people's thoughts and imaginations what you end up doing is doing either of two things right? And this is related to economics because there's mainly two types of things that give value two types of there's more but there's two main general ones right? There's two ways that the economics cycle gets the boost or product gets the boost you see business growing. One of them is you come up with something brand new or the other one is value added you take something and add something additional to it. So if you're exploring other people's psyche imagination, thoughts worlds universes that they've built initially what you're going to do unless you're a child and a child has an imagination that is vast right? Much greater than most adults they have their lives, children when they're growing up if you watch them growing up a huge percentage of their lives is an imaginary world right? I think I'm beginning to understand already but investing time into how others drain into reality you further your own life experience and knowledge 100% 100% So initially, aside from let's say you've been in the indoctrination it's not just for a while your imagination has been crushed right? And you're 100% living in this state right? If you start reading other people's thoughts and creations you can delve into those dive into those and just journey with them and if you do enough of this or if you meditate on what they've created all of a sudden you're going to start doing a little bit of value about it. You're going to start giving your own twist to their stories right? And from that imagination is really comes about what we see in our current economic system and our current political system and our social structures and everything right? And there is a tremendous amount of truth. That's one aspect of it the other aspect is there's a tremendous amount of truth being told in science fiction and fantasy right? If you want to link this up to religion there's a that whole story where you know disciples ask prophets why certain prophets use stories parables and stuff like this to talk about moral dilemmas in our societies right? or spiritual dilemmas and stuff like this and their reply in general is because we human beings can more easily relate to stories that we understand right? Then straight up saying this is bad right? So for example in Dune one of the mantras in Dune that you encounter is quote fear is the mind killer and that phrase fear is the mind killer I have no idea I'm pretty sure online you can find it how many times that phrase is stated in this book and that is one of the main theses of Dune, aside from other theses that it has aside from other points that it has right? Now, when you read Dune by the end of it you have a phenomenal understanding of what it means I mean you realize finally that fear is the mind killer now fear is the mind killer is also prevalent within spiritual texts within physical fitness within martial training within certain types of disciplines so they've taken something that's present in many other disciplines and incorporated into a teaching of a science or telling of a science fiction and there's a lot more to this as well a lot more to this phenomenal, if you want sci-fi you've never read Dune this is one of the must read books in your life read so if we were summing up to 100 they would simplify it to only 50 values so that each value is 101 summing up to 100 it would be 101 100 plus 1 99 plus 2 multiply 101 by 50 is your answer with n equals 100 make, nice, thank you mask of raven, that is the question that is the answer so for those that are watching we're going to get to the maximizing problem thank you very much for that very lucid explanation an eye-opening view of why fantasy holds an equal value to nonfiction for sure, that will work on my presence in that field, thank you again my pleasure I lived in the machine for 10 years contractor TSA, truth is we are oh that was a TSA or just a bunch of screw-offs like everyone else, my imagination is fine still active D&D games for sure also in that field either board games or video games and stuff regarding why did the sum of integers let's say natural numbers I can derive the formula but why does it for me, I always look into the summation arithmetic sequence in series when I think about these things and I just use the formulas in general but basically from odd mix reply, the solution to that why this the sum of natural numbers is a quadratic odd mix reply to this is why would a quadratic necessarily pop up I don't know I don't know if that's a philosophical question is it philosophical, it's definitely not a philosophical question why does a quadratic pop up mask of agreement if you know, post it in discord math is beautiful indeed so the solution to this or the explanation to this is the following so if you were summing up to 100 then you simplify it to only 50 values so that each value is 101 so each value is 101 each value is 101 so 50 values equaling 101 so you would go 100 plus 1 of course 99 plus 2 98 plus 3 of the 50 multiply 101 by 50 is your answer with n equaling 100 da da da da da da over 2 that's why multiply and then you multiply 101 by 50 but the punch line is this with n with n equaling 100 and what you end up getting is n over 2 which is your 50 and this is going to be n plus n over 2 that's cool this stuff still and this would be 101 of course if you're adding to n values it becomes a quadratic because this times does if you multiply this out you get a quadratic n squared over 2 plus n over 2 and that is a quadratic that is totally philosophical mathematicians don't ask why they just go down the rabbit hole just bring things in oh my god we got we got something here what does that mean mathematicians right nice question this type of stuff the why's of stuff I crunch numbers more than anything crunch numbers I don't know I like looking at systems and this is a system but this is more of a proof type of system which I've never been very good at why math is the way math is so likely originally they'd be 100 terms 1 plus 2 plus 3 plus 4 all the way up to 10 but you group the highest term with the smallest term that's right that's where you get the 50 until you get to 50 plus 51 grouping there's only 50 terms so the way you do this is this 1 plus 2 plus 3 plus 4 plus 96 plus 97 plus 98 plus 99 plus 100 so you group these guys together number 1 with number 10 number 2 with number 99 number 3 with number 98 number 4 with 97 and if we add a 5 here number 5 with 96 and all of those add up to 101 and if you're grouping 100 terms you just divided it by 2 that's where you get n over 2 right and the sum of all these numbers these groups 101 101 101 101 101 is 101 so at the beginning when you say the sum of n is equal to 1 to 100 of n you end up getting you end up getting n plus 1 which ends up being a quadratic how far are you in your math education you take call call me to rx yet which is cool this is further better explanation right instead of just telling just this is what it would be I believe or it becomes that the sum of it the function for it right let's do maximizing writing I wish we could change the topic to alien astronauts that visit the patient what it's whatever did we get mathematics from them how did we get mathematics those five axioms where they come from thought about this stuff let's talk about maximizing revenue and I'm just going to use the economics example you can use a maximizing maximizing and minimizing stuff for a number of different things two of the main ones is revenue and another one is area right what the area should we do the area let's do an area because the video link that I gave you guys this one is it still there this guy is maximizing revenue so let's talk about maximizing area let's assume we have this let's do a box I'm not going to do a box but let's do the following questions yes I'm a first year math undergrad with a lot of personal tinkering with math basically combinatorics is all about counting numbers and the fuel probably will satisfy your longer and the blind better yeah so this is what we have the following problem a farmer has fencing material that is let's say 120 meters of fencing material so either wire wire or whatever they have and they have a whole bunch of cows how do you draw cows that's my cows or sheep or something got a livestock so they have a whole bunch of livestock and they want to enclose the livestock in an area so they don't wander off disappear and let's assume we'll add a couple more levels to this because they don't add these levels in there in most general math problems let's assume each animal requires I have no idea if this is true we're not just pulling numbers out of thin air let's assume each animal requires at least 10 square meters of grazing land to be enclosed in this area so they can eat for the day and let's assume you can have a contraption enclosed area where you can pick it up and move it along and then enclose another area another week or something so you slowly move across the field wherever you are and you want to find out how many animals you can put in this enclosed area what the maximum area is you can have here the maximum area is going to decide how many animals you can put in there because if each animal needs 10 square meters to graze it takes per day per day 10 square meters is a lot per day then how many days you can keep a certain number of animals so the question can just pick up you can layer it but it's a maximum revenue problem okay and he's like that was very quiet top five are you doing I was like so what we want to do is we've got 120 meters of fencing fencing material and we want to enclose an area what's the maximum revenue we can have we're going to use calculus no calculus we're just going to use straight up quadratics so we don't know what the dimensions of this are going to be but we want it to be a rectangular shape 90 degrees we want these to be 90 degrees okay so we don't know this length we're going to call this x and we don't know that length we're going to call that y okay that's what we're going to do I'm kidding that's the dimensions of this thing okay now we have 120 meters of fencing so that's going to be x if this is going to be rectangular then this is going to be x and this is going to be y so our first equation because that's what you want to do solving problems in mathematics physics, biology, chemistry in the real world, economics, politics whatever it is you want to get variables to your unknowns and then step back look at this thing and ask yourselves what equations we can get out of this so for this there's two equations we can get the first one is the perimeter what's the perimeter of this rectangular enclosed area well it's going to be x plus y plus x plus y which is basically 2x plus 2y right so 2x plus 2y that's our perimeter now we know what our perimeter is equal to there's 120 meters so p is 120 right so 2x plus 2y is equal to 120 okay, that's our first equation but we can simplify this a little bit I have a fun problem you can try to solve with only algebra find all integer solutions a, b to the equation bruh bruh bruh it's quadratic oh it's rational there are infinite numbers so you're supposed to find a, b in variable form we'll take it, I'll try to scroll find this so here's our first equation and in general you want to find you want to simplify your equations so divide everything by 2 so this becomes x plus y is equal to 120 is equal to 60 right is equal to 60 because you divide each term by 2 just kind of curious, maybe someone in chat can answer, does cheat you'll only do math or other dropping 2 during sessions application, I love the idea of this channel and stumble upon it randomly even dude we do math we do politics, tomorrow we do personal finance and physics problems come up as well that we've dealt with okay, so basically things that are math related when we do the math streams when we talk in politics as politics comic books as comic books we do lots of cooking streams so here's one equation we're able to get from our system totally do physics I do physics, I'm going to put out a physics video soon about talking about physics books okay I got my degree in geophysics so you can also educate you in geophysics in conspiracy theories I understand that so here's one equation we got from the system x plus y is equal to 60 right one of the rules in mathematics is this 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 if you have four you need four you need five you need five so for each variable each unknown you need one equation so for example if I give this to you x plus two is equal to five you can solve that so minus two minus two so x is equal to three easy peasy that's the first type of algebra you can introduce to really you could have two unknowns let's say x plus y is equal to five and y is equal to two right and you go oh we have an x and a y that is an unknown so there's one equation with x, y and here's another equation with x, y but there's no x it's just a y so we have two equations and two unknowns so what we can do is substitute in because this y for this system and this is a system of equations is talking about one system just the way we are right so if these two equations are about this system then that y is that the same as this one if this y is the same as this y then this y is two so you can take this and suck it there so sub two equation two if this is equation two then this is equation one sub two into one so if you put two equation two into one equation two says y is two so y has to be two equation 1 becomes x plus 2 is equal to 5, and now you got, you combine two equations with two variables to generate one equation, you eliminated one variable, and you can solve for this minus 2, minus 2, so x is equal to 3. So you solve for x. That's what we're going to do for this. Okay? We haven't come up with the second equation yet, but let's talk about the second equation. Your first equation is the perimeter, right? The question is, how do you maximize this area because you want to fit as many calories in there as you want, or a lot of stock in there as you want? So maximize, you got 120 meters of fencing, maximize the area. The perimeter, the fencing is the perimeter. That's the equation relating to the perimeter of this thing. The area equation for this system is this. Equation 2, the area of this system is x times y, right? That's just an area of a rectangle, right? x times y, this times, this gives you the area of that. So that's our second equation. So if you notice right now, we got 1, x, 2, y, and we got an unknown as well. We got an a because we don't know the area of this thing, right? But we're trying to maximize this guy, so this guy's going to vary depending on what the x and the y are. Okay? So what we're going to do right now is, we're going to substitute 1 into 2. Okay? x, y. So I'm going to try to eliminate one of these variables here. Okay? Substitute equation 1 into this, so one of these variables is gone. It's replaced with the other variable. So all I'm going to do here is go take this equation 1 and go y is equal to 60 minus x. So all I did was take this guy and move it over. So y is equal to 60 minus x, right? If y is equal to 60 minus x and this y is the same as that y, you just sub it into there and you get area is equal to x times 60 minus x. So from this our equation is the following. The area of the system is equal to x 60 times 60 minus x. So what you end up doing now is multiply this guy in. You're going to get 60x minus x squared and you're going to rewrite it as negative x squared plus 60x. And this is the area relative to the xa of x. The physics physics isn't like that bad, but you know it's bad for you, but want anyways. That's funny. We have all sorts of chance here, not much in this taboo, but it's all educational and so forth. Yeah, yeah, top-diver. Thanks for stating that. It's all about education, sharing information really. That's what education is. So we got our equation. We've got an area, we want to maximize this area, maximize this function, and we have the area being represented as one variable, the x we eliminated, the y. So what we need to do now is do something called completing the square for this function. Let me erase these guys. Actually I'm going to erase this guy as well. I'm going to clean space a little bit here. Let's put our cow here. I should drunk all my books. And this cow needs 10 square meters per day. Let's bring this here. Now functions, all functions has some kind of properties. They behave in a certain way. And through mathematics what you can do is you can understand some other behavior by doing certain things. So check this out. This is a graph of this function. We're going to put the x here, and we're going to put the area here, A of x. A of x because the area is dependent on x. This is function notation. This doesn't mean A times x. It's a definition, right? We could just write A if you want, right? Because maybe you haven't been introduced to function notation yet. A, right? But when they write f of x, and f is general for function. It's a notation for a function, right? So consider the A to be f. Doesn't make a difference. This could be Frank. This could be Alfred. Right? Doesn't make a difference. Okay? f of x means this equation here that defines this function has x's in it. So it could be f of x is equal to x plus 2. So every time you increase x, x, f of x. So let's say we want to find out what f of x is when x is 1. We put in 1 for x, you get a 3. 2, 2 for x, you get a 4, right? It's function notation telling you that this function is dependent on x. You can have multiple variables in there. We could say all of 4's marks. Your marks in school are dependent on how long you study, what food you eat, how much you sleep, what teacher you have, how much exercise you do, right? And then we would have an equation here based on how your marks vary depending on all these different variables. So right now when I write A of x, I'm specifying that the area of this thing is now being represented as a function that is only dependent on x. I know I sort of went off on that, but it's a very important question you're asking. A lot of there's a little bit of a hiccup when it comes to function notation when people are trying to learn it because it's just terminology, symbolism, right? Symbols. So right now we're going to try to graph this. We're going to graph how the area of this thing varies dependent on how you change this x value, right? So if we make x really small and we have 120 meters of fencing, we have 120 meters of fencing, remember, right? So if we make x really small then y would have to be big because we're going to use up 120 meters of fencing. So let's say this x, just as an example, if we made this 10 then this is 10, so so far the x is out of 20, then the y's would have to be 50 each, right? So you could make an enclosed area like this or you could make x really big and make the y's really small. So what's going to happen is as you change the x value, the area is going to change because these shapes give you a different area. Notation is the worst. Even on the graduate notation for different things, trip me up the top. Yeah, yeah, trip me up the top for sure. And depending on if you're studying mathematics, sometimes you use the same notation depending on the teacher and how old they are and what books you're using and stuff, but then the same functions you move on to physics, all the notation changes, right? Because they're looking at specific systems now, right? So for example, let me give you two examples where you see how it changes. Well, it's so busy today, I totally missed the modification resume. Oh, I'm touching Jason, how are you doing? So let's do a couple examples just to convince ourselves what would happen with this field that we're trying to enclose, right? That's just what we had. We were going to build something like this. That's just what we make this 10, then that's going to be 10, that's going to be 50 and that's going to be 50. What's the total area for the space, right? If we have, if we're sticking with 120 meters of fencing, the total area of the space is 10 times 50 is 500, right? 500 and this is meters, this is going to be meters squared. Let's assume we had a different configuration. We made this 20 and we made this 20, right? I'm just going to show you that the area changes depending on what the x values are, right? If this is 20 and that's 20, we've used about 40 meters of 120 meters of fencing. So 40, 120 minus 40 is 80 and if these two have to be the same, then each one of these is 40, right? If you add all these up, you get 120. The area for this guy is going to be 20 times 40, which is 600 square meters. You increase your area even though you use the same perimeter, same amount of material. So land being what it is, being expensive, material being what it is, being expensive. If you're buying material and you have an open field, then it's a good idea for you to come up with the right configuration to maximize your area, right? If that's what you're looking for, because that's going to give you more crops. It's going to allow you to put more animals in there, right? Because right now in this area, we could only put in 500 divided by 10 because each one of these 10 square meters, right? We could only put in 50 of these livestock in there. Over here, we could put in 60, right? So if you're running a business, if you want to try to reduce your expenses, then 120 meters of fencing, you could put in 60 cattle, livestock in this enclosed area, then 50. Your productivity just went up, right? Your expenses went down, right? So if we're going to graph this on here, take a look at this. If this is our x-axis, here is zero, here is 10, here is 20, here is 30, here is 40, here is 50. Let's keep, take this up a little bit. 50, here is 60, here is 70, here is 80, and here, we'll just put x there, right? Now you're not going to go to 80, I'll show you how this works, right? So we're going to graph this thing. So if we set x is equal to 10, what's y? y is 500. So let's put 500 here. So when x is 10, y is 500. That's the maximum area. That's the area we can get if we set x to be 10. If we set x to be 200, or sorry, 20, then the area becomes 600. So 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000. Let's see how high it goes. 600. So when it's 20, it's 600, right? How about when it's 30? If this was 30, 30, that's 60. Oh, I'm sorry. I don't want to do 30 yet. My bad. Let's not do 30 yet. Let's do another dimension. Let's go, let's go 50, right? If we make this 50, then that's 50, the x, right? 50 plus 50 is 100. 120 minus 100. You've got 20 meters of fencing left. So you've got to split that between this and this. So that's 10 each. Oh, but that's the same as that. It's just the other way around, right? So if you make x 50, the area becomes 500. So it comes down again, right? If you make it 40, you're going to be here. If you make the 60, check this out, if you make x 60, then this guy has to be 60, right? So 60 plus 60 is 120. You have no more fencing for your y. So what you just did, if you make x 60, you just made a fence, double fence, 60 meters going down, 60 meters coming up. You got zero area. So if you make your x value 60, you got zero area. Well, that sort of sucks because you're trying to maximize your area. But maybe you want to put one fence up and another fence up behind it to deter people from entering the space, right? But that's not what our problem was. We want to maximize the area, not reduce the area to zero. And on that note, if you make the x zero, then what happens is, basically, this guy becomes the other way around. x is zero. So y is 60 and 60. So again, it's this way. So you get zero. So if you graph this thing, you end up getting something like this. This graph represents the total area of this system, depending on what you set the x value to be. So if this is the area relative to what you set the x value to be, right, then right here is your maximum area. Visually, that occurs when x is 30, right? But we're going to do this algebraically. Let's just differentiate this bad boy and call it a day. Everybody wants to do calculus. So take a look at this thing. And visually, this is what it would be. Here, let's convince ourselves that 30 is in the middle, which it is, right? 20 gave you 600. 40 gave you 600. So in the middle is 30. So if we set this to be 30, then that has to be 30. 30 plus 30 is 60. 120 minus 60 is 60. So that means each one of these has to be 30. So if you have an open field and a certain amount of material to build and close an area, your optimum dimensions or structure that you can build to maximize your area is a square, which is one of the reasons why you see a lot of buildings built at squares because that maximizes the area. City blocks and whatnot, right? And this becomes 30 times 30. The area it is 900 meter square. Well, if it's 900 meter square, and by the way, I'm going to do this manually, but might as well get the answer right now because we're there. So this would be 900. So this isn't at 70. This thing goes up. My stuff is not to scale. 900 would be 100, 200, 300, 400, 500, 600, 700, 800, 900. It would actually be up here. Let me give this better shape so it would go up like this. That looks like a nice parabola. And this point here would be when your x is 30 and your area is 900 because it's a parabola, right? But let's do this manually. The way you do this is something called completing the square. Okay, factor out and negative from this, you're going to get x squared minus 6x, 60x, 60x. And I have a few videos on completing the square. The video that I linked with the maximizing revenue, I believe we do complete the square in that video as well. But you can do, we've done a few other videos where we've done something called completing the square, right? Completing. Let me write this down so you see, can you see it here? Yeah. Completing the square. If you do chicho, completing the square, there should be at least two or three videos popping up to show you what we're about to do. Okay. So we factor out a negative, compensate for the positive, take this guy, divide it by two, you get negative 30, square it, you get 900. Okay, 3 times 3 is 900, 900. Add and subtract that inside here, negative x squared minus 60x plus 900, minus 900. This is a perfect square as root is negative 30. So this is negative x minus 30 squared. While you're doing that at the same time, you're going to kick this out. When you kick this out, you multiply by whatever is in front of the x, which is a negative number. So negative 900 becomes positive 900. So this is the area of this system dependent on x. So we're going to write it as a of x. This is what we need. What this says, if you're reading this thing, because mathematics, every equation, think of it as a sentence, right? The area of the system is dependent on x is equal to negative bracket x minus 30 squared plus 900. All of this means something. A of x means the area is dependent on x. The negative number here means that this parabola opens down. It's like this. It's not like this, but it's like this. It opens down. So it's a maximizing problem. When x is equal to 30, because you take this guy, you take this guy, you go x minus 30 is equal to zero, bring it over, x is 30. When x is 30, when x is 30, the y value, the maximum revenue becomes 900. So you read it like a sentence and that's a maximizing, sorry, that's a maximizing area problem. And the second part of the question was, we need 10 square meters per day for each cattle. So we have 900. So maximum area is 900. A max, max is equal to 900. So 900 divided by 10 means we can put in 90 cattle here or 90 livestock here in this fenced in area per day because they'll eat 10 square meters worth of food. And then the next day you just roll this fence down here and they graze there and roll the fence down here and they graze there. If you don't have time to move this fence every day, then what you can do is divide this by 10. You get 90 cattle, but you don't have 90 cattle. So you could put 30 cattle in there that you have that you might have. That means you can leave them there for three days, right? Because if they all needed 10 square meters to eat, right, per day, you divide it by 90, you could put 90 cattle in there or 90 livestock in there. But if you divide this by three, that gives you 30, 30, you got 30 square meters that they could feed on, right? So you can vary this problem multiple ways. That's a maximum problem quadratic. Cheecho, got to go, bro. Work comes early at 5 a.m. Oh, 5 a.m. Great string. If you need months, top five are still here and Dante is working. Awesome, Nicholas. Thank you very much for the heads up. Have a great sleep and I hope the work goes well. I hope the work goes well. I hope the work goes well. Olive, I hope that helped. Okay, it's fun to do this. These problems show up everywhere. Revenue for sure. This is stuff that you would do as a company if you're selling a product, if you're only interested in maximizing revenue, right? You know, you could collect, you could come up with a product, right? Sell it at a certain price. And then once you're stable, start increasing the price. See what happens with the sales. So you start collecting data, right? Let me erase this. You can always pause this and grab a screenshot if you need the notes, right? So just imagine a real life situation. Well, this was a real life situation, right? Do people troll math streams? That's very silly. Yeah, people do on it. Thanks, Giccio. This was very helpful. My pleasure, Olive. My pleasure. I don't think trolls are too particular about what they troll. Some are, some are actually. I shouldn't say that. Took notes. Awesome. What's that math about? It's about maximizing something. So just imagine here. Let's take that same problem. The mathematics is identical. That was maximizing area. Let's talk about maximizing revenue, right? Let's assume you have this product. Let's assume this is Giccio's first math module product product, right? Math. Giccio math. Giccio math. Number one. This is our first module that we're going to put up, right? Let's assume we're going to sell the sucker for $20, right? $20. I'm just going to have a little conflict with exercises and text explaining what we're doing and have the videos referenced so you can take a look at the videos. Like some knob showed up and asked people to solve an equation where the solution is for $14,069. That's funny. I don't consider that to be trolling. That's just fun, I guess. I'm fun with numbers but I don't have $20. Oh no, it's okay. All my content is available for free online and it always will be, right? Because the more people learn mathematics, the better our societies will be, period, right? But I still have to live. I still have to run this as a company. I still have to generate a certain amount of revenue because I do have other things that I would like to do with this content that we're creating, right? I need to have revenue coming in where I can upgrade my system, where I can create more modules, where I can hire people to roll things out, right? So I have to charge something, right? If there's going to be a certain type of product going out or have a little button here that we will have, right? Where it says, pay what you like, whatever, what you like, you like. And the model for this would be a little bit different than what we're talking about here. Or I do have a Patreon page, Patreon page. I have a subscribe star page. I have direct donations. I have an eBay account. So all of those function a little differently, right? But let's assume we have a module that we're going to sell for $20. Let's say I've had this module out and I'm about to put out another module, right? Here's module number two, whatever it's going to be. Our first module, I'm pretty sure I know which one is going to be, but we'll talk about it in the future, okay? So let's assume we've been selling this module for six months. Six months of data. We've got six months of data for $20, okay? Stable income coming in. But to generate, to create the second module, I need to hire somebody to do some of the graphics. I need to pre-order and stuff like this. I need to bring in a little bit more money, right? I hope one day you're saying I understand my bad English. Okay. So we need to generate a little bit more income coming in to be able to put out module number two, right? So let's assume here's $20 that we've been selling this module. And what we're going to do is I'm going to start increasing the price of the module, $1, actually let's say $2 per week to see what happens with the sales, right? So let's assume we're selling $2 and here's total sales, total. Let's assume we sold this much, whatever that much is. Let's assume we sold $1,000 per month at $20 per unit. Let's say we're going to kick it up to $22. Oops, let's do it this way. We're going to do this as a revenue, right? Let's do it this way. This is the number of sales units. Let's put this as the X, okay? This is the X. So when we're selling 20, we sell let's say 20 units. Let's say we sell 100 units at $20. This is priced at $20, okay? So this is $2,000 that we're able to generate per month. Let's play around with the data that we're collecting. Let's assume for the next month you can make the stream louder. Windows are already about at $100. It's still quiet. Yeah, the headphones is the way to go. Lester, I got the gain pretty high, okay? I don't want to bring the mic closer because I move around a lot. I might hit it and might freak people out, right? So headphones is definitely a way to go on these streams. And at some point, I'll upgrade the system. We can sell a lot of modules and upgrade the system, right? I would like to stand along with my care. I can hear a phone. Okay, good. And well, how you doing? So let's assume for the next month, I kick up the price to $22. I kick up the price to $22. Here, I kick up the price to $22 and I end up selling 95 units, right? So let's do 95 times 22. What do we end up getting? 95 times 22. 95 times 22. $2,090. Okay, so check this out. So this ends up being $2,090. $2,090. And we sold 95 units. I'm going to put that here. 95 units at $22, right? But we sold less units but made more money, right? Not bad. Let's assume we kick the price down to $18 and sold 105 units, okay? Decrease the price by $2. If you decrease the price by $2 and sell, let's do this, let's do the calculation. We got 18 times 105. 18 times 105. We get $1,890. Well, we didn't sell $5, $18. We need that to go up a little bit. I want it to be sort of 90 units. Oh, 105 units. Oh yeah, this would be, that's okay. So it would go $1,890. Now, I haven't done this. I'm not sure if I'm presenting the data. Oops, this was 105. 105 units and we made this much, right? So 105 units. Here's the X, 105. And we made $1,890. So what's going to happen here? My example sucks, by the way, but you get the general gist, right? You sell something for a certain price, you figure out how much money you're making, you play around with the price, see how many units you end up selling, okay? What you end up with is the following. I want to erase all this smack guy. I'm from Europe, so the connection might differ. Maybe. So I'm going to erase all this. I'm going to show you what the equation looks like and what the graph will look like, okay? So basically what happens is you start getting graphs like this and at some point it ends up being like this. It's a parabola and at a certain price you sell a certain number of units that's going to maximize your revenue, okay? As far as equations go, let's do it with an equation, with the variables, okay? Let me erase those. Let me give you the data. Let's assume for every $20 kickoff, sorry, not every $20. So I sell six months of data. We sold, if we sell it for $20, we sell 100 units, okay? If I sell it for $22, I sell 95 units. If I sell it for $18, I sell 105 units. So if I kick down the price on my module, I sell more units. If I kick out the price, I sell less units. But as you saw with the graph, I kicked up the price, I sold less units, but I made more money, right? This type of equation is a revenue equation. So revenue of something, R of x, and x is the number of units you have. So for example, I got five pens here. Let's say I'm selling you all five pens, or you're going to buy all five pens at $2 a pop. So that's costing you $10, right? So revenue, if you want to talk about how much revenue you make from selling a product, is the number of units times the dollar value. Right? So initially, if I was selling 100 units of $20, 100 units times $20, I made $2,000, right? Now, these things are giving us information. If you increase the price by $2, $2, up, we sell five less units, negative five less units. And this is really all we need to come up with our equation where we can figure out what the maximum revenue will be. Okay? Because we change our equation, we say the number of units now changes according to this. And we're going to call each time we change the price by $2 x. So x becomes the number of times you're changing the price. So you do a little let statement. You go let x equal number of $2 price hikes. Okay? This is our let statement, which defines our function. So for here, we're going to go, we start off $20, and we're going to increase the price by $2 every time, by $2 x. If we do that, initially we sold 100 units, we're going to sell five less units for every x. So our equation becomes, I'm going to write this a little bit bigger so you see it, our revenue equation becomes $100 minus five x times $20 plus $2 x. If you increase the price by $2, every time you sell five less units. If you multiply this out, okay, and if you graph this, you're going to get exactly what we got here. And this is going to be your maximum revenue. Whatever this is, this is r of x. And that's going to be your x, which isn't really the number of units you sold based on the way we laid out the problem. The x now is the number of times you're changing the price, right? The number of increments. So if we change the price five times, it means five times two is 10. So we kicked up the price to $30. And if we're losing, we're selling five less units for every price increment kickoff, then five times five is 25. So we sell 75 units. So you can graph that, right? You could go 75 times 30. What's 75 times 30? I should be able to do this. It's 2,250, right? Times 30. 2,250. So we're still making more money. Not really. So check this out. x. Here, let's make a table here. Let's make the table here. $20 for this guy. That was our base value. x is the number of times we're kicking up the price. And r of x is our revenue, right? If we kick up the price zero times, we're making $2,000. If we kick up the price once, one increment of $2, we're making $2,090. If we kicked up the price five times, so we're going to sell it for $30 instead of $20, we're making $2,275, right? That's our revenue coming in. Now check this out. That means the number of items we're selling now is 75 items, right? So we're selling less material. We're making more money. We're also banking 25 units relative to us selling them, selling all 100 or 2,000. So it's a double win-win, right? You make more money and you have more inventory, right? More inventory doesn't necessarily mean it's better, but in this case, it could be because we could sell those 25 units for $30. So 25 times 30 is going to be another $750 on top of this that we've sort of haven't realized yet the gains, right? So maximizing problems coming to play in many places, many places. What I don't get, how lower the price is that more people buy the item, right? Yeah. So if you reduce price, you get more customers and reduce price slightly. What's better in the future? Here's the kicker. How far are you going to reduce the price? Because this product that you're making does cost you something, right? So if you reduce it below your cost, you're losing money. If you reduce the cost to zero, right? Give it away for free. You could sell, not sell, but give away an infinite number, but you're not making any money. There's no revenue coming in. So if you're running a business, you can't just give away your product. You still have to make some kind of revenue to run a business, right? There's got to be some kind of sustainability there. You still need to make money, right? So the solution is not always to reduce price because at some point you're going to go below your cost. So you're losing money and if you're giving the stuff away, you're going to go bankrupt pretty fast, right? Quantum mechanics, hidden citizen. This is straight up high school mathematics, grade. This type of problem you do in grade. No, grade 11, grade 11, not grade 9. Some of my students, I teach this in grade 10. Some I have taught them in grade nine, but very rare. This is straight up something that anyone that's creating content, creating a product to sell has to know. May it be comic books, may it be math modules, may it be little trinkets, may it be whatever it is, right? This is math that you should have the ability to do when you come out of high school because right now with the age of technology, what we have on the internet, it is extremely important for you to be able to manage your own business, right? I started watching your YouTube video last year when I was struggling with math and it did not just help, but also gave me more respect and interest for math. Thank you for my pleasure, Olive. I'm glad it helped. I'm glad it helped. That's the whole purpose of what I'm doing. I want this whole thing of math is difficult out of people's heads because math is not difficult. Math is one of the most powerful tools that you can acquire to make sure you live a happy, prosperous, joyous life, right? And be who you were meant to be. Yes, but someone who loves buying things from you because he, she, likes you, who rather pay more might differ in your country. But in Europe, in Asia, people prefer personal connections. Lester agreed. Like, for example, the stuff I have on my eBay page, right? I know there are people who have buying some of those comics and some of them paying a little bit more than they're going market rate because they're supporting my work, right? They want that comic and they rather get it from me than someone else. Some of the other comics I've sold, they've gone out a great deal. Like, 20, 30, 40% less than what the market rate was going online. Some of them way more, 70% less, right? I sold some stuff where people got it. It was a lot of like five, six, seven comics where one of the comics was going for twice what the guy bought it for, right? I want to make money, IT consulting, but have so many questions about starting my own business. Do I have to open a business account and keep my personal bank accounts separate from my business? Or can I keep them the same? Also, can I start a business if I know nothing about accounting? Or do I need to learn that first? No, you don't need to learn accounting, but you need to know the logistics of starting a business. So your first question, do I have to open a business account and keep my personal bank account separate from my business? This tells me that you have an idea you want to do, but you really haven't looked into it at all, at all. Like you haven't looked into it at all, right? Here's the two things. Just by the way, this is not personal financial advice or anything like this, but business account and personal account are two different things, right? Open up a business account, sure, but only if you register a business name, if you have a business that you can function on there, because to open up a business account, you need the paperwork, right? The government name, official name and stuff like this to open up a business account. You can open up different types of businesses, sole proprietorship, partnership, corporation, limited company, cooperative, there's a ton of what do you call it charity. You can open up tons of different types of businesses, right? So first thing you have to do is figure out if you want to keep your finances, personal finances separate from your business finances. The second thing you have to figure out is what are the liabilities of the business that you're running. If you get your ass sued off, are you comfortable with losing all your assets or do you need the limited company protection? So if anybody sues you, if you're running a business that you don't lose your life savings, it's only the company that's getting sued, right? Should I keep my business unofficial and make some money before I start an official business? This tells me that you haven't even done one job yet, right? Start slow. Hidden citizen. Start slow. I have some business cars and I've been doing some work on the side already. That sounds okay to me, hidden citizen. No, I've been doing jobs. If you're doing jobs, then it depends what you're doing and the odds are you should probably talk to an accountant. If you're bringing money in, talk to an accountant, see where you've spent money to compensate for the revenue coming in. So you're going to write off some of the expenses that you've had for the business that you've been running. If you're running an IT business, right? Did you buy computers for IT business? If you did, those are write-offs against the money coming in. So you need to talk to an accountant to sort your stuff out, right? Or start doing a lot of research online to figure out how that stuff works. Before you get very big, important, important. One of the staff's like Tahini. School full of Tahini is a good thing. Tahini and maple syrup. That's a nice minerals. And that was with mathematics we did. I think so anyway. I wonder how much money I should be making before I make my IT consultant business official. Here's a general rule of thumb didn't say so. If you see the money in your bank account increasing, you better account for that money. I'm already happy to have a person who accepts criticism. In my country it's like a normal because people always say stay at their point. Oh, really? Yeah, criticism is the best. Ah, chicho. You should try that problem I posted earlier. Oh, yeah, that's right. You had something posted earlier. Dude, hidden citizen, you're making two K a month for consulting and you're also doing other stuff. You need to talk to an accountant. Let's take a look at that. Awesome. Touching Jason. Most people tend to worry more appeal to surface appearance items than usually running a business. Make some money first for sure. Make some money first for sure. And if you're making two K a month, talk to an accountant. You need to account for that money. Let's check it out. Let's check it out. Let's see what problem we got. The only thing I'm worried about is that if I'm IT consultant, is it bad if I don't have business insurance? Looking you to your area month. Well, they hate to break it to you, hidden citizen. It is an official business. You're bringing in two K a month and the odds are people are paying your track direct, direct transfer, interact, whatever it is, right? That's on the books. You have an official business. Someone's going to come knocking. Find all integer solutions A, B to the equation. Let's write down the equation. A squared. A squared over to AB squared minus B cubed plus one. There are infinite numbers that work. So you're supposed to find AB in variable form like A equals X squared and B equals 3X. Just an example of an actual solution. How do you go about doing this? So both A and B are X's. Is that true? Is that what we're saying? I actually don't know how to go about this. We have one equation. We've got two unknowns. You're supposed to find AB in variable form. As long as A and B are the same variables, then we can do. I'm assuming that's what you mean. If you're saying A, A is equal to X squared and B is equal to 3X. Right? If that's the case, you just substitute those guys in here. Oh no, AB are any number. My bad. Oh, AB are any number. So AB are any number. We need to find the solution to this. So AB are not this. That'd be easy for AB with these. I don't want to do that. Right? They'll be X to the power of 4 and then rest and then you just simplify. And you can't really find solutions. You're going to have to just simplify and gas and find your instructions. Oh, I don't know. How would you go about doing this? Let us know. Like they don't have to be both X's. Okay. Yeah, so they could vary. So these are variables. They could be anything. But solution to this is in what way? Like what are we trying to find to solution for them to, if there's a solution, it's got to be an equal sign here. Solution to what? Or restrictions to this. Yeah, I'm not sure what this involves, Abnik. By the way, Abnik, I listen to the, who is the Iranian mathematician, the female mathematician that got the award. That's a hint. So the equation has to be a number and try setting it up with n as a solution and have it set to 0. Try setting it up as n being the solution. So it equals n. And solve this for n equals 0, n equals 0, then a is equal to square root of n. Miriam, Mir, this guy's in my ear. Yeah. And I was driving and the radio came on and they were interviewing some of her friends and they had some interviews of her talking about mathematics. They were talking about mathematics and just listening her to her speak. I didn't realize she had, you mentioned this, but she had cancer, I believe. And the committee, the, what's the math award? I forget what the math award is. They contacted her, said that it was beautiful. Really, it was beautiful. I stayed in the car. When I got to my destination, I stayed in the car and listened to that. Oh, look at this. Look at this. Let me kill that chat. We got trolls. Look at this. We got trolls that are two years old. Two year old trolls. Oh, by the way, you trolls, it's not showing up on the screen. You realize that, right? You're just in the chat. Really? Poor guys. You guys are lonely. You're such lonely. Oh, look. There you go. There's stuff that doesn't work. Oh, bands. Did that work? Let's check it out. Oh, you guys are new. Oh, yeah. You're like two years old. You're like totally new. Oh, man. For a lot of reason, it gives great joy back. Yeah, all of them. They're kids, right? They're kids. They don't know math. They're too stupid to know math. They haven't figured it out yet. They're really young. They must be really young, right? It's not even childish. It's, it's retarded. They're actually retards. These trolls doing this for math streams. They don't have a, their, their wires are a little short-circuited and they'll stay on this retard level for a while. But yeah, Miriam won the field medal. Yeah, super cool person. Yeah, I'm like, when I listened to the interview, it was amazing. It was amazing. It's even a business image. Solid colors. That's what it's tragic. She died as a young man. Yeah. And man, Audnick listening to her speak. What a humble, humble human being. Wow. What a humble human being. Really. It was, thank you for, for mentioning her previous streams because I didn't, and I looked into her afterwards too because you'll provide a link and name and stuff like this. I wouldn't have caught that interview and the conversation with her friends that they were talking about her, if it wasn't for you, if it wasn't for you. So thank you for that. Thank you for that. Regarding this, I don't know how to do this, Audnick. I'm sorry. I'm going to look her up. Her name was Miriam. What was her last name? She's the only female to have won the field medal at the time, I believe. I don't know if anyone's Audnick has anyone who won it since then? Any other female who won it since then? She was the first female to win the field medal. This is the year, every four years it comes up. I believe this every four years, Audnick. It's awarded to someone, and every four years they pick four people to give this field medal to. So basically distributes us every year they give one to a person, but the celebrations and stuff is once every four years. It's just like the Olympics, and they take four people to give this medal to. We'd love to learn some in depth calculus. I studied that stuff. I knew it in the past, but I haven't done it for so long that I forgot it. At some point I'm going to do a series of calculus. I will, but it's going to be a while. I have to relearn everything. I have to relearn everything. Yeah, no other one has won it yet. So no other woman has won it again. Okay, okay. So the only female to have won the most prestigious math award around. If I knew math then maybe I wouldn't be in depth right now. I'm the in-citizen. I don't know. There's a lot of people that know math better than that. Like I'm in depth right now a little bit, not much. I'll paint that off. I'm going to paint that off pretty quick, but a little bit, right? So that doesn't necessarily mean. But if you want to make a lot of money, math is the way to go. Every four years I'm only given to those young. Oh yeah, that was the other kicker. I didn't know that. They mentioned this in the video and not in the video in the podcast on the radio. And less than 40, you have to be less than 40 years old to win this. I don't know why they made it less than 40. Oh, good sir. Hey, Barbarian, how are you doing? It's been long since the last stream. I hope you are well. What do you think about the Greta Thornberg? We talked about her in yesterday's stream during the politics stream. I can honestly tell you if I was her parent I would not she looked like she she's in tremendous amount of distress and fear and hopelessness. So she's in trauma right now. And if she was my daughter, I would not. I would try to shine a little bit, a little bit of light in her life to make her appreciate that what life is really about. So that problem was from the international map in IPA in like 2002. It's pretty tricky. And not only is she the first woman but also the first Iranian. And also the first Iranian. I didn't know that either. Nice. Oh man, you make me tears in my eyes. I swear. Crazy. Crazy. So this problem was from the math thing. I watched one of the videos of One Blue Three Brown that he put out from the Math International Math Olympiad where it was dots. Someone posted on Discord, super cool, where you had to prove that you know if you put random dots and you have a line going across and it rotates that you're always going to encounter. It was a pretty cool problem. Difficult. My god. It's above. These types of problems are above my mathematics. I never went into that. It went in that direction. It was too abstract for me. I really respect this channel. It was very unique in comparison to others in this problem. Thanks. Thanks kebab. That's kebabs. Thanks. Kebabs. Kebabs are delicious. Shouldn't we feel the same? Shouldn't we feel the same? To a certain degree. But she's, I don't think we should all feel the same. No. I don't think things are as dire as she has been led to believe. I really don't think so. She was in panic mode. When I watched her a few minutes, I couldn't watch too much of it. It was watching a child be abused in my opinion. And I have no desire to watch that type of thing. Being used by centralized power in a big way and traumatized. It was pretty distressing for me. Not what she was talking about. Not because of the environment. For her sake, I felt very sad, very concerned. It's less than 40 because the field model was originally designed to provide young mathematicians to take bigger risks so they have something to aspire to. Awesome. That's a great reason. That's a great reason to have business cards in citizen. I do have business cards, but I haven't used them forever. Like barely ever. If you want to see my business cards, I guess you could go to my math channel and have my business card there or something in the above. But I haven't used a business card for years, years. By the way, I wanted to tell you that I saw your video on drawing it. I gave it a try and it was really good. Awesome. Awesome. That's really good. That's really good. Yeah, it's one of the things I do every year. I use a lot of mint and food and drink and cooking and stuff like this. So I like to have a nice supply, right? And you save so much money and it smells amazing and it's always there, right? I'm glad you like. I'm glad you like. I just found you. I really like this channel. Thanks, man. I appreciate it and really appreciate the chat and the mods and everyone that's contributing and talking. I learn a lot from doing this and that I really appreciate it. Where are you from, boss? I live in Canada, west coast of Canada. Yeah, weirdly enough, I think math becoming more abstract is why I got into it. Otherwise, I'd be a physicist instead, not with the other direction on it. For me, the abstract math, I'm very, I'm a realist and I'm a dreamer as well, like fantasy, sci-fi and stuff. But when it comes to mathematics and sciences, I like hands-on, right? So the abstract mathematics just blows me away. When I take math and apply it in the real world, see the results, that to me. And I love data, data crunching. Other normal prize equivalent math prizes are the Able Prize and the Wolf Prize. Okay, cool. Normal prize equivalent math prizes. From what I understand, the Field Medal, the reason that Nobel doesn't have any awards for mathematicians was because the person, the namesake of that prize, Nobel Peace Prize and the Nobel whatever physics or chemistry, the person didn't like mathematics, so he didn't include that. As far as I'm concerned, they can go to hell. I would love to mod for this channel. It's very sensible and it would be easy to moderate. Cabab? Cabab, thank you for the offer. Right now, and for the first thing, I'm limiting the mods on this channel in a big way because we don't want to give the keys to the palace, whatever the saying is. Just hand it out to everyone and anyone, right? Because chaos can happen. We keep a pretty low key. Usually we don't get too many trolls rolling around, and I've really started to love doing the band thing. I've been trying to puzzle you posted a while ago. Mask of Remus for trying it. Nice. Spreading fear is not the right strategy to save the environment. Activists in all fields just stop scaring people to get attention and support. All of, I agree, right? It's fear-based and I totally disagree with fear-based action. Action that comes about through love is so much more powerful than through fear. Action that comes about through caring is so much more powerful than through fear. Totally understand it, no worries. How do you be a six-star man? My friend used to ride a BMX bicycle. He tried to do some crazy jumps. He ended up failing them all with some injuries. Later he learned that and he was able to hit those jumps. Yeah. See, I did a little bit of that through physics, right? As soon as you learn about the physics of a situation, you appreciate it. For me, just to let you know, for me, this exact same thing happened when I first learned how to snowboard. I don't snowboard anymore but when I was learning how to snowboard, I was in my 30s and I knew how to ski and I couldn't get a high-end on snowboarding. So I went up the mountain. I went up the chair and just went down one little turn and parked my ass on the snowbank in the trees and watched people snowboarding while puffing, right? So I sat there for like half an hour, an hour, just watched people snowboarding and I looked at the physics and I knew the physics, the shock, the shock absorber and then I got up and off I went. I started a university and a physics major actually and I ended up moving away from it. Oh really? I was bothered by that. There was never any real proof. I didn't find experiments as real justification. Oh that's interesting on that. That is one thing I don't like, right? Like Newton's laws aren't laws, they're approximations, right? It's not. There's problems associated with that. Like Maxwell's equations, the four equations that they teach, there are really 20 equations that should be in there but they truncate them and end them, approximate them. So physics is a lot of approximation which I think is a problem if we're going to talk about larger and grander things. So propaganda, to a certain degree, not propaganda. I think Guerta, whatever her name is, she's legit, she has fear but she's being used by propaganda. Did you solve it? What did you get, masquerade? I don't know if I did. I might have partially but it looks too yucky to be right. Sometimes yucky use the right answer, masquerade. Well, what did you get? If you want to check your solution and find more problems like this, the problem I posted was question two from the 2002 IMO, International Math Organization. What was it called? International Math Exam, things. Masquerade might post a solution in discord or the question. Again, this stuff is beyond me. I can't solve these types of things. I go on loops. Yeah, all the physics is approximation and it becomes even stranger when you get to things like string theory which we have no way to prove experimentally. Yeah, should I say, is it legit, automatic? Is it legit to say international math, math, Olympia, Olympia, automatic? Is it okay to say that things like string theory which we have no way to prove experimentally yet? Has it been decided that absolutely you can't prove it ever or is it because our mathematics is not strong enough or our processing ability is not strong enough to prove it yet? Is it okay to put the yet at the end or is this an absolute? String theory I would love to get into. The really. String theory. What is string theory? String theory in short, I've read one book on it and a lot of articles and short other things. String theory says this, there's two branches of physics. One of them is basically particle physics that says everything is made up of small subatomic particles in the universe. The other thing, string theory says everything in the universe is made up of vibrating strings of energy and the vibration and frequency of those strings that decide what that thing is. So what you see before you, me, is not made up of little small particles, subatomic particles and mostly empty space. That's what I am. That's what everything is mostly empty space. But I am vibrating strings of energy. Okay. I just have a is equal to b squared plus or minus. So you saw this as quadratic. Square root of b squared minus four b cubed plus one. How did you get that? I have no basis for how to approach this. So I decided to put it into the form one over stuff and then set stuff to one. Is that what you did? That's your reverb? That sounds cool. Like to me, that's crazy imagination. That's on the same level as this, right? That's on the same level as doing it because I wouldn't think about doing that. That's super cool. And now I'm struggling with this part. Yes, that's about right. Oh, wow. That's cool. We can't prove anything yet. But for example, we could have, we could have proof if we built a particle detector, the size of Jupiter next to the sun in order to take gravitons one day, maybe, right? That is what photons are, right? Vibrating strings of energy. Hello. Hello, Ben. Ben, Jim and C. Are photons vibrating strings of energy? No, I don't think photons are vibrating strings of energy. Photons are massless particles of light, are they not? Howdy, I think. Try setting it to zero. You don't want A in terms of B. You don't want A in terms of B. So you said the bottom equal to zero? But what about the rational? Do we say the bottom equal to zero? Two A v squared minus b cubed plus one is equal to zero. Is that, is that what we're talking about? I don't know. This stuff is confusing. Sometimes it's just a rearranged thing just to see if how it looks. We've been at this for a couple of hours. Thanks for the problems, Alvin, by the way. It's cool. Nice job getting close to the solution, Mask of Raven. You would get partial marks. I think they mark them out of seven. So you would have got, maybe for how far you got, you would have got like four out of seven or something. No, so it's bottom. You have to go from there. What math is this? This is called difficult math. Very difficult math, but I think we'll leave it there again. This is called a difficult math from the international math. Well, it's just algebra. Yeah, I guess it would be. But setting it up would be to the power of n minus top is equal to zero. I'll have to think about that later. Ah, okay. That's a nice form. The whole Mask of Raven knows what's going on. Last time I took math was Calculus in my script. Last time I took math was 28 years ago. Oh, I didn't go to 28 years. Yeah, at least, at least. Fun. Okay, gang. Thanks for being here. What is the next stream tomorrow, Olive? Tomorrow, we're going to talk about personal finance, starting at 1 p.m. Okay. Personal finance tomorrow at, I believe 1 p.m. I think it's personal finance, I set it up. Yeah, investing in personal finance. 1 p.m. my time Pacific time. So if you're in Europe, we're talking like eight hours later, nine hours later. How important is your business You guys think? Pretty important or it could be important. The thing that interests me the most is the Fibonacci sequence. Fibonacci sequence is fantastic. Golden ratio, right? Yeah, personal finance. Do you watch Dave Ramsey? No, Dave Ramsey. I know the name, but I don't watch Dave Ramsey. I forget who he is. Is this a cooking guy? Great. That came in too late. Yeah, sorry, Benjamin, I'm going to call him quits. Yeah, it's bedtime. It's bedtime for our Europeans from the business systems. What math education level do you have? Gordon Ramsey. Is Gordon Ramsey the cook? I don't know. I'm bad with names. I'll have to see people's faces. Gordon Ramsey is the cooking guy. I don't know Dave Ramsey then. I don't know. Maybe I do. It's a professional finance guy. I doubt it. I don't watch professional finance people. It says all that is bad. It depends on the debt. I personally don't like carrying debt, so I sort of agree with Dave Ramsey to a certain degree. I'm a PhD student, so I sort of agree with Dave Ramsey on that level because if you have debt, here, think about it this way, right? If you owe a lot of money to the bank, it's the bank's problem, right? If, like, huge amounts of money is the bank's problem. And huge amounts of money, we're talking tens of millions of dollars, right? Or millions of dollars, right? But if you owe a human being type of debt to someone, then you're there. Don't be somebody's. Live your life free. You're not free. So I do lots of math and hate myself a little. I make awesome math decisions, right? I say, how much of a week does he breathe? Yeah, I'm growing debt. Same level. Probably that's math though. That's what I'm talking about. Okay, gang, if you can make it, we'll chat tomorrow. Thank you, Autnick. Thank you, Master of Reading. Thank you, Master of Reading and Care Business. And trolls, I don't know, holy crap, math tutoring. I haven't taken a math class. That's my equilibrium class like five years ago. Well, I'm just about done with classes, so I'm going to really get into uh, research soon. That's where you really prove you're not cute. Or you go insane, right? See you guys. Thanks for sticking around, and thank you for the great conversations. Bye, everyone.