 Hi everyone, this is Chichop. Welcome to my channel and welcome to another live stream. Today is October 29th 2020, and we're doing a drop-in math tutoring session number 62. Let's do a little bit of mathematics, open discussion. Okay, and as before we've done a lot of these and it's basically a drop-in math tutoring. Anybody that needs any help in mathematics, mainly high school mathematics, we've done and we do some elementary preliminary stuff, and we've gone into a little bit of post-secondary mathematics as well. And until math questions come up, basically open discussion on all fronts to a certain degree where we keep politics on politics streams. Aside from that, welcome. I hope you're looking forward to doing a little bit of mathematics. And until we wait for notifications to go out for people to pop in, let me tell you who I am. Yo, let's go. How are you doing? You're speeding on the Zalazim. Nice. Gang, I want Patreon. Patreon.com forward slash Chicho. C-H-Y-C-H-O. If you want to follow this work, box office. I got notified. Awesome. From Discord or Twitch. Box office. I am on Patreon. Patreon.com forward slash Chicho. C-H-Y. Awesome. Twitch. C-H-Y-C-H-O. If you want to know what this is all about, this is about mathematics. All of it. Okay, it may not appear so based on some of the other live streams that we're doing, but it is all layered on mathematics and my thesis basically is on Patreon. If you want to support this work, if you want to follow this work, Patreon. Patreon. It's fantastic. I don't put anything behind paywalls. Everything's great of commons. Share, share, like. You can follow the work and after a while, if you think this work is worth supporting through funds, Patreon is a great way to do so. Crafter, how are you doing? Good morning, good morning, and good afternoon. Good morning Knights of Old Kame. You're around my area, so it's good morning for you as well. Nice, nice, nice. Lack of caring. Hello friends. Hello, hello. Hope you're doing well. We are live streaming on Twitch. Twitch, Twitch. The chat that you see here, notifications going here, that's where we're at. Twitch.tv forward slash chico live, C-H-Y-C-H-O-L-I-V-E. If you want to participate in the discussion, in these live streams, Twitch is where you want to be. Okay, and for those of you who've been supporting this work through Twitch, subscribing, following, commenting, liking, coming onto this live streams, thank you very much for your support. And for those of you who've been supporting this work through Patreon, thank you very much for your support. It is a large part because of your supports that we're able to continue this work. Crafter, I'm taking a big two-day break to hopefully get motivated again. And that else is killing me. From school? Crafter? Oh, my God, I'm here, he says. Good, good, good. How are you doing? Chico, hello again. Lonely Piggy, how are you doing? Taking a wild guess. Autumn Olive today. Autumn Olive today. Autumn Olive. This has been my snack for the last week, and it's going to continue to be my snack for the last week. This thing lasts a while. Let's see if it's going to focus. I don't think it's going to focus here. Oh, there it is. Look at that beautiful autumn olive. Like seriously, like so beautiful. Look at the patterns there. I wonder if we can come up with a mathematical equation for that thing, right? And there's a lot of mathematics in nature, right, gang? And the mathematics of nature is absolutely brilliant, right? From studying outside of the classes I have. Oh, from studying outside. Yeah, it's a lot of people, a lot of pressure from the way school is set up right now, right? Bartoliani. Hello, hello again. Welcome to another live stream. Zalatan. Zalatan. How are you doing? I just finished school. Time for some after laughter lessons. Hannah, how are you doing? Long time no see. Good morning, Chichou. I became addicted to Canada, so I am taking a break for a month or two or longer. Awesome. Good idea, Hannah. I became very depressed. I do miss it, but I will move on and focus on my mental health. Yeah, Hannah. If you find yourself addicted to anything, I don't care what it is. Even autumn olives. Take a break, right? Super delicious. Crazy tart. I hope you guys are munching on some good stuff. Okay. Box office. I need to know the probability of getting a Buck Deeter yield. Buck Deeter yielding in the Pacific Northwest. Next bull hunting season increased my chances. We need to collect some data before we can do any probably analysis on it, right? Box office. You got to give us data of how many arrows you shot per year and how many Buck Deeter you've been able to hunt, I guess. What do you do with the Buck Deeter? Do you use it all up? I do announce these live streams 30 minutes before we go live on LOMinds, VK, Parler, Gap and Twitter. You can follow the work there. We do share additional information. Hannah, I went on a three-hour walk and enjoyed the alone time away from the chaos of the world. So I will do it again today over and over, even if it rains. Walking is my therapy. Hannah, me too, man. Me too. 100%. It's amazing. Zero bucks, all dough. Oh, zero bucks, all dough. Okay. Hold on. Dough is good? Yeah, you want to eat dough, not buck, right? Dye a thug. Thank you very much for the tier one sub. Zalatan, I have some buffalo chicken, mac and cheese in the fridge. Buffalo chicken, mac and cheese. Already prepped up. Is it leftover? Buffalo chicken, mac, cheese. Buffalo chicken, macaroni and cheese. So it's a casserole. It's not a sandwich. I was, all of a sudden I pictured a sandwich, like a buffalo chicken burger, but mac and cheese. Yeah, it's from Noodle's. Oh, nice. Dye a thug, my first sub in Twitch outside of my cousin. Right on, thug. Dye a thug, right on. I'm honored. Thank you. His mind is currently being blown. His mind is currently being blown. How funny. Buck's office, you want buck? Dough season is separate or fits under other criteria. It's all based on the numbers of previous seasons. Oh, wow, really? So there's got to be some serious statistics, mathematics that your state does to say, because I think they announced when hunting season begins for each one or if it's not going to begin, right? So they do definitely, you know, probability rules are a world right now, right? Big data. Oh my God, chicken buna has 95% of selling out. The other 5% is mine. Is that why you linked up and discord the picture? I recently started eating dried figs and they're so good. Oh my God, yeah, for sure. Dried figs, it's part of my routine. It's almost always have dried figs. Dried figs and dates. Those are two power foods we usually have. And man, fresh figs off the tree are brilliant, brilliant. Dye a thug. My state, my state, you can just order hunting and fishing license online. No class needed, really. Nothing. For the hunting, you must show your permit for the guns and stuff, don't you? You must have a place to enter that in. I want to get back to cannabis. I really want to. At what point should I go back to it? You know, cannabis, if zero, there's zero things they need. Zero license for hunting. Interesting. Wear very bright colors if you do go hunting, right? As far as how to look, if you find that you get addicted to something, I don't recommend you going back to it, because that means you have an addictive tendency to that thing. In my opinion, though, whatever you're addicted to, if you stop consuming it, and if you're still craving it, don't go back to it. The only time you should go back to something that you found yourself to be addicted to is at a time when you don't crave it at all, right? And don't go into a hardcore. You do a little sample, maybe pie, maybe whatever, beer, maybe, and I don't think if you're, if you find yourself you're an alcoholic, you shouldn't go back to drinking, period, right? And anything else, that's my take, right? Nope. Second amendment, rice means rifles and not needed to be registered. Even for hunting, I thought, I figure you need, but you apply for a hunting license. Yeah, you get your number, that's right. Box office, yeah, mine as well. You buy a tag from the state and you need to submit your yield to the state upon taking the animal. Okay. Then they configure the rules for next season based on how many animals were taken on the previous, okay? So that's where the mathematics is coming in. And I'm assuming there's huge fines for people who don't submit their yields, what they ended up getting, right? Because if they're not reporting it, then the mathematics, the statistics that the state is doing is flawed and that can seriously endanger the herd, right? He ate, he hate me. Cannabis helps me manage my other addictions. Yeah. For many, by the way, he hate me. Only God, the math was double speak. How can I eat 5% of a probability? What? No, but that's 5%. Chicken mon has a 95% of selling out. You should have had 95% probability of selling out. The other 5% as well. No, I think that works. Now you're confusing the crap out of me, Elder God. Find something healthy that replaces that high you're looking for. I agree with young Polax, right? Yeah, you should also have people that go rifle hunting in bull hunting season. Oh, I'm back with the Mac. This is a lot that it says. Nice. For live streams where we don't have any visuals, we do upload the audios to soundcloud.com forward slash chico, CHYCHO is podcast. Mathematics, we got visuals. The audio for this most likely is not going to go, well, it's not going to go to SoundCloud right away. At some point in the future, when I'm old and retired and have faster computers, I'll process all the audio from these and load them up to SoundCloud podcast. And this should be available on your favorite podcasting platform including Spotify and iTunes. And we will be uploading this video to both BitShoot and YouTube. And if you're on those platforms, you can support this work by following, by liking, by commenting, by sharing. And if you're on YouTube, you can support this work by joining YouTube membership with a button here somewhere. And for those of you who are supporting this work through YouTube membership, thank you very much for the support. Box office. CHYCHO has math naturally been easy to learn for you in your life? Or have you had to sit down and seriously study for the most part? Yeah, I've sat down and studied. For sure. It's, I'm not a savant. I put in the time to learn the math. And I put in a lot of time to learn the math to be able to teach it. The math is the course, the math courses I've taken are the ones that I've studied the most in my life. There was one course I took at university where I studied 10 days for it, between 12 to 14 hours a day. It was a heavy, heavy course. And I ended up getting like 57% or something. I only got to, after, I forget what it was, four and a half hours of the test, the final. I only got to 70% of the course of the exam. I didn't even get to the other 30% of the question. And the guy didn't even bell curve it. So I got 57 out of 70. So anybody that didn't get at least 50 out of 70 ended up failing if they only got to 70% of the test, right? It was a crazy course. What's on the math menu today, my guy? You know what, Doug? I'm just leaving it open. I'm thinking about, you know, planning up some lessons. I'm just hesitant on it right now because I know it just takes a little bit of extra work from my part and I'm crazy busy. But I can definitely do the lessons. I know all my lessons by heart. I just very much like all the lessons that I have, right? And I link up everything together and whatnot, right? So basically this is dropping math tutoring. I want to leave it open for discussion. Because when questions come up in mathematics, it may seem like someone wants to just learn how to, for example, factor. But that links up to polynomials. That links up to quadratics. That links up to maximizing revenue. I mean, maximizing area and all that jazz, right? So depending on how where the questions lead us, we deal with it accordingly, right? I just want to make sure it's dynamic enough and flexible enough to help people out. Hannah, thank you Chuchot. And on another, my grandpa has a 40 foot tall fig to see him climb up on a ladder at age 88. It's scary, but he swears he needs to do it. And he says, okay, you should give him a hand, brother. That class sounds like my worst nightmare. It was hardcore, man. I'm very happy to have done it. Ah, Meg, how are you doing? Welcome, welcome. Hey, Chuchot. Can't stay for long. Hope you're having a nice day. Thank you very much, Odmek. I hope you're having a fantastic day as well. Boxes. I think it's an illusion that math comes easily to anyone. Anyone who's good at it has had to work hard. Yeah. I mean, that's the kicker, right? Like people look, if you're taking courses, if you're in school and everything's coming easy for you, you're not living. Okay, that's like life. If everything in life comes easy for you, you're not really living. You're just existing. You're not challenging yourself. You're not bettering yourself. You're just doing things that are easy. Just imagine when you learn how to read for the first time, right? You know, you picked up books that like big letters and a few pages with pictures, and you read those. To read heavier books, it took time. You had to have look words up to figure out what they meant. Just imagine if you never did that. You'd be stuck in the realm of Jill and Jack walk up the hill or whatever it was, right? I struggle in pre-algebra, so I mean polynomials and etc. I'm extremely lost. The way you have to think about polynomials is just the easiest type of functions, mathematical models that we have for things that we observe in the real world. That's what polynomials are, right? All of mathematics, functions and whatnot, all of mathematics has come to be for us to better understand the world around us. The simplest types of functions that we have, and other people may correct me on this, but the simplest types of functions that we have that we can analyze in the world are polynomial functions because they're continuous functions, right? There's no breaks, there's no holes, there's no point, there's no gaps, there's no asymptotes, right? There's no restrictions, right? Aside from whatever the system, whatever restrictions the system functions under, right? Best Coatie on Twitch, Super Metal, awesome. Micro Twitch, awesome, thanks. Fun. Facial hair rocks, man. Let me grow my beard. I'll have the best beard on Twitch as well. I've never done, I don't think I've done live streams with my beard. It's always been the goatee since we started live streaming on Twitch. Maybe I'm just lazy with math. A box office, it takes effort, man. It takes effort. Ian Orr, how are you doing? What get me about math? It's really abstract. It's, how so? I find mathematics is very, you could go abstract for sure, but it's also very tangible. It's extremely tangible. Look at statistics. You take data from the real world, analyze it and get parameters for that data set. You understand what the population or the sample size is doing, right? And from understanding what the sample size is doing, you understand what the population is doing. That's not what you call it. That's not abstract. That's as tangible as it gets, right? So it really depends. Box office, not lazy. I think you probably had a bad experience or a bad teacher, Odmik says, and I agree with her. It's easy to be discouraged because math is another language that's hard for humans to learn. Initially, anyway, once you understand some of the preliminary stuff, it's easy. It's like ABC, do it, Microtwist says. Yeah, I will at some point grow back the beard again. Quentin Wolff, how are you doing? Do you think someone with a full-time job can self-study math? Yeah, nothing too complex just to understand the world around them better. Yeah, 100% Quentin Wolff. I mean, that's to a certain degree what I did. I started tutoring mathematics to get me to relearn mathematics and I just fell in love with it again or fell in love with it, really understood it, and then I just stumbled into just teaching it, right? Zalatan. I feel like the main reason that people mess up with math is that they don't take their time. Yeah, and that's in huge part the fault of the system, right? The education system, because they give people grades, they grade you, they mark you, which is to a certain degree legit. You need to know if you did something right or wrong, but not the way they apply it, right? And then they put you under the clock. So if all of a sudden the concept of mathematics makes sense to you, right? When you're sitting in class and you go, oh, wow, I get it. And then you're working on a problem that bell rings and say, move on to history. Now all of a sudden you have to stop your train of thought and go learn something else. Now coming back to that train of thought and picking it up again, man, that might be impossible to do if or very difficult to do, right? So it's in huge part the fault of our current education system. The reason why we're having so many hiccups, so much problems with it. I think I read somewhere that pigeons of all things have more intuition than humans in terms of probability. Like they solve the Monty Hall problem easier than people seriously? Automatic? That's cool. Pigeons, the flying flying rats really. If you live in a city where there's lots of pigeons, they're like flying rats. They poop everywhere, they're dirty, they eat anything. True North 93. A guy I sat next to was gaming hearthstone in every class in college and aced everything. Well, good on him. Maybe he was gaming in school and going home and steadying his ass off, right? I thought I did much better with math when I was applied to chemistry and physics classes. Not sure why though, because you could apply it, you could see it, you could visualize it, right? And that's the trick. You have to be able to, if you want to appreciate the power of mathematics, you have to apply it somewhere, right? Micro twist. Box office. Math is an art form you need to practice to be good at. For example, like in martial arts, you need to practice a lot and time and time and time again to understand it, like painting. Math is not like gym class where you need to be present to get a good grade. You need to practice it to be good at it. And by the way, this micro twist. Some people do poorly in gym class because they're not wired, geared for it, right? So they have to put in a lot of hard work. I've met people that they hate gym class. They find gym the hardest class they have, right? So even people taking gym class, some people, it doesn't come naturally, so they have to put a lot of hard work into it to do well in it. Mathematics the same deal, right? Box office to Audnick. I think you're right. Makes a lot of sense to micro twist. Micro twist. I ate tasty pigeons in each of them. Really good, really. They eat a lot there. They eat a lot there. Wow. Oh my God, I loved that my pre-advert was for a Fender guitar. Was it? Cool. That's cool. Audnick, actually, have you all gone over the Monty Hall problem before? It's really fun. The Monty Hall problem, that's the one with the three doors, right, Audnick? We covered it once during a live stream. It's a three-door one, right? I think so. I want to lay it out for us if it's a three-door one. I know I try to do this through by memory, and then I have to, because when you're trying to solve problems, math problems, it's not really the most important part. It's how the problem is phrased, right? It's how the problems phrase. If you miss one word in the phrasing of the problem, then the problem doesn't make sense. So I know I try to do it by memory once, and I messed up in some part of phrasing it, but I'll try it again. Monty Hall problem. This is the one where there was a show, share the pick of the math equation I need to work in discord. I need for work in discord. Yeah, it is a three-door, the three-door problem. Okay. Diet tag, what's the equation you need to work for work in discord? Can you post it here? The three-door problem. There's a game, there's a game show TV, TV game show that was aired I think in the 1970s, 60s, 70s, 80s, in the 80s for sure, where it was let's make a deal. It was called let's make a deal, where there's three doors, right? Door number one, door number two, and door number three, right? And you're this guy, and here's the host. Let's put a bob hat on the host. Like he just took a car on the guy's head. There you go, that's the host, right? Can you guys even see this? Is that dark enough? I should press more. The game show thing, the game show thing. Okay, cool. You're on a game show. Oh, odd mix audit for us. Okay, awesome. I'm going to read that. Okay, let me do this so it's dark enough. You're on a game show, and they're giving you a choice. I'm going to read this. Read odd mix thing. Kevin says he's 21. It looks like a shoot. I thought it was a shoot. I think it stopped on. So here's the question, right? You're on a game show where the host has put a prize in one of three doors, door A, door B, and door C. You pick door A, but then the host reveals that there's nothing behind door C. And you ask if you want to switch to door B, should you, right? So let's call these door A and B. B, consistent with the question. So door A, door B, and door C, right? So you have a choice of picking this one, this one, or that one to get the prize, right? You pick this one. So you say this guy. You pick that one, right? Right now, what's the probability of you having the prize? What's the probability of the prize being here? Okay, as soon as I see the first answer, I'll continue. Okay, hello from Ireland. Grylam 1995, hello, hello, welcome, welcome. Michael Tuastitio. Are you a math professor or an engineer? My background is geophysics with a math minor. I worked as a geophysicist and I've been teaching mathematics for like 20 years. Not a prof, no. I'm not an academic. Not that there's anything wrong with it, but I haven't gone down that path. Picking another has a higher percentage of having it. Yeah, cool. So 33%, one third. So your probability, so right now, if you pick this, the probability of the prize being in A, probability of A containing the prize is one out of three, right? Which is 33.3%. What's the probability of the prize being in here? What's the probability of the prize being in here? No, not a genius, that's for sure. So what's the probability of the prize being in B and C? What's the probability of the prize being in B and C? Two thirds, yeah, two thirds. This is before the whole shows you that it's that guy, right? So it's two thirds, two over three, which is 66.6%. Now there's something called, wouldn't it be the same probability? Oh, I see. No, because before the whole showed it to you, the prize could have been here, here, here. So each one of these, the probability was a third, right? One third. So if this one was in here, it'd be one out of three, and this one would be two out of three, two thirds, right? Now the whole says it's not in there, right? And there's something called conditional probability, and the conditional probability states this, I should have left more room. So the question would be, what's the probability of, I gotta remember my probability, how to state this? What's the probability of the prize being in B given that not in C, not in C, or A, I guess. No, given that it's not in C, yeah, given that it's not in C, 50-50, 50-50 almost got 50-50. Oh my god, I gotta look up the answer. So the question is, if it's not here, let's kill this, so if it's not here, and the game is this, right? As soon as the host says it's not in here, he gives you the opportunity to change your choice, and he says, okay, it's not in C. Now, do you want to take B instead of C, instead of staying with A, right? Variable change, variable change to a certain degree, right? So he asks you, now that I showed you that it's not in C, would you like to change your vote and pick B? Or do you want to stay with A? What's your answer? And what's the probability, this one's not working well, what's the probability of it being here and being here, right? Is it tricking you, though, could still be in it? It's got to be in one of these. Yeah, they don't trick you, it's got to be in one of these, right? This is a simple mind trick to make them think about it to no, actually. There was a woman, everybody used to say that, yeah, this was 50-50 now, and I think everyone used to say that you should change your vote, because this was a third when the initial conditions were set, but this here was two thirds, so you should go with the two thirds to a certain degree, or no, everyone was saying it was 50-50, and then there was a female mathematician, okay, I believe she was a female mathematician, that wrote an in-depth article on this, right? And I believe she published it in a newspaper, or maybe Ottmek would know this, published it in either journal or newspaper, I can't, I can't remember, Ottmek. Change your vote gives you 50% rather than 33%, it's more favorable to change the vote, because the condition has changed, but you made your choice at the beginning of the condition, right? And she wrote an article analyzing this and saying that it was a good idea, I want to read Ottmek's comment, the answer is 66%, because the probability of it being in either B and C is still 66%, C being empty means that there is a 66% chance of it being in B, right? So initial conditions, it was a third and 66, so this probably hasn't changed because you already, let's say you looked in this one first, right? So she wrote this article, and mathematicians across the world started trash talking her, right? Saying that, oh, she didn't know mathematics because she was wrong, because the condition was not 50-50 and stuff like this, and she went through it and did the proof saying no, this is still 66% here, right? Or 66.6%, this is still two-thirds probability because, let me do it with this one, this was a third, one out of three, but this was two out of three. So her advice was always choose the other door, okay? If they show you one and it's not there, and now you're down to two, always switch to the next, or if there was three here, four here, and they show you it's not a one, always switch your vote, it's a better probability of obtaining, getting the prize, right? You should always change because the chance of you picking the wrong door the first time is higher, yeah, and that's a good way of saying it actually, true north, right? Ordnika's right voice says, I'm 100% right. Yep, I'm just lurking, listening, taking the lesson, hope you're well. Welcome, welcome, and I hope you enjoyed the discussion. I think the woman was an amateur who posted it in a call, a call this magazine, it's crazy that she wasn't a mathematician. Yeah, she wasn't a mathematician? Are we sure about this, Otmek? All I remember from the story regarding the mathematics aspect of it were, was that mathematicians were saying how stupid it was and trash talking the article, and the observation, and then later on, mathematicians did the analysis, they're like, oh yeah, she's right, and that proves one huge thing in academia or in established thought patterns of our society that even the greatest dogmas in the world supported by the, by the specialists and the, and what do you call it, the experts, the authority can be wrong, right? Don't fall into dogmas, right? So you should go be, you should go be, yeah. Okay, I'm gonna, I'm gonna process, process tech in injection, molding, and I do dye setting as well. We have to make sure our chains are rated for the weight of the dye. So it's the length of the chain divided by the height from the tool to the center point of the chains equals the angle of the chains times half the width equals x, x, x being the total force being applied to each other. So in other words, what L over h is equal to a times one half w equals x. That's a mouthful dye thug. You would have to understand all the variables here. Statistical success, Allah God says. I'm actually confused. I missed the first part. Basically, you had a choice to pick between three doors, right? And you chose A. The host comes up and so there was a prize behind each door, right? The host comes up and says, okay, you chose A. There's two places that it could be. They show you C and they say it's not there. So what's the probability of the prize being in A or in B now, right? And the answer is it's still 66% in B because initial conditions was it was 66% that it was in either one of these. So just because it's not there, it just kicks this up. The probability of it. I'm back. You broad street bullies. I have to go down and buy some Swedish tacos. Tobacco, Swedish tobacco micro twist. By the way, gang, thank you for the follows. Thank you for the subs. Apologies for missing them, right? I remember she had an IQ higher than Einstein. Did she? CJ? Did she have a huge IQ? The person who wrote this article? Hello, what were they wrong about? They were wrong about the probability being because they showed C didn't have the prize. They changed the probability and said, oh, the probability must be 50-50 now. But it wasn't, right? Because the choice was made. The separation was made, right? 100% sure. I think her not being a mathematician is one of the reasons everyone thought she was wrong. Oh, is that why? Okay, she didn't have the credentials, right? Crazy, crazy, crazy, crazy. Void hook to that. I did armory works on scoops and red dots, scoops and red dots. I thought zeroing scoops were rough. So it's just zeroing the instrument, is that what it is? Audmic, yeah, maybe, but Einstein never took an IQ test and generally relatively should be more than enough evidence that he was a genius. He was a great manager, Audmic. I consider Einstein to be a great communicator. Okay, imagine thinking women are less intelligent than men. Is that what microtwits said? Women have lower IQ than men. What? Who said microtwits? You, you know, what do you call it? I think you're making fun of things, right? But anyway, that's funny. As far as Einstein is concerned, a great book is that I read was Amir something is called God's equation and it explains, goes about how Einstein came up with the theory of relativity and how he was able to prove the theory of relativity because he had an amazing imagination and it was a great communicator and he was a good manager because the mathematics was, from what I understand, more powerful than what Einstein knew. The physics was more powerful than what Einstein knew and Einstein didn't have the technical capabilities to collect the data to do the measurements, right? So he communicated with experts in these fields that got his theory, tightened up his theory and he communicated with someone that went up, went to, I think they went to South America, they went up to the mountains and they were there for three days or some island, they were there for three days and it was all cloudy. They were trying to get the reading of a certain star, right? And they couldn't, they didn't have a nice guy, right? It was all overcast and on the last day in the last hour or something, last night, last hour or something, they were able to take their measurements, maybe it's folklore and they proved Einstein's theory of relativity. If those measurements weren't taken, okay, then Einstein's theory of relativity probably wouldn't have come to light for a few years later, right? Which is super cool. I thought it was super cool. Yeah, I get it. Bipser says, R, we get trolled. Yeah, possibly. Gender has nothing to do with intelligence. Anybody that thinks that irrelevant of their gender, their dum-dums, right? JC or CJ, CJ, you should only switch if the opportunity to do so is offered in every game. Otherwise, the producers are trying to get you off of it. Maybe, maybe not. Maybe, maybe not. When I was a kid, I watched that and they gave the opportunity and all of a sudden you saw things happen, right? The person shouldn't have switched. The person should have switched. Hey, man, I did your job. Pch. Odmek, a more intuitive way to think of it is this. You are on a game show and have to pick between 100 doors. You pick door one. The host reveals that door two to 99 are empty. Should you switch to door 100? Yes, because there's a 99% chance it is in door 100. Odmek, I've never even thought about it that way. That is a brilliant way to explain it. That is a brilliant way to explain it. Awesome. I'm going to start using that, by the way. Copyright Odmek. That's a great way of explaining it, actually. I like it. Saying higher IQ than Einstein is meaningless, but she's very smart nonetheless to see this problem. Very smart, right? Very real, right? Because she wasn't an academic, probably. She was thinking in terms of how systems work, right? In the real world. Various, but the mean is same as men's. Delinger? I don't know about this. Women's IQ has less variance, but the mean is same as men's. I don't think there's any data supporting this or not. Odmek would know. Maybe someone might know, but I doubt it very much. Then how is a woman having a lower IQ than men, because it is both higher and lower? Relative to someone saying, Maryland had a higher IQ than Einstein. To void. I mean, you'll know right away, if you're wrong, when you lift the dye and it chain snaps right away, so you're never unsure. If it chain snaps, man, you're in trouble. If there's, especially if there's tension on it. If there's any type of strange chain wire that has tension in the snaps, jump on the ground and duck and cover your head, because that thing's going to take somebody out. Chicho. Bit storm. Sorry, off topic, but ordered some automotive plants. Really, two variety, ruby and garnet. Apparently, they cross-pollinate. Delivery is in January. Nice. Awesome. Automolives. Automolives. Look at this beautiful thing. Look at this thing. Look at that thing. I'm going to munch on these as it came up. Super delicious tart. Anna says, nearly every woman I've met is smarter than me. I can honestly tell you that as a man, women mature way faster than men or boys. All right. There were a lot of very mature, worldly women that I knew when I was in my 20s, but almost every man that I knew, including myself, was a dingaling. IQ is a gift for the benefit of all mankind, that's all the God says. Yo, Chicho, I have a nice question. Can you sketch? Sure, let's sketch it. Let's sketch a quadratic. So we want to sketch f of x is equal to negative x to the power of 2 plus 7x plus 25. So f of x is equal to negative x squared plus 7x plus 25. Better write it down, right? Yeah, I believe so. Cool. It's a quadratic. It's a quadratic. It is indeed. Starscape. I'm going to scroll down. Yay, automolives. Yes, the vast majority. Daniel Gurr. Yes, the vast majority of tests, stats consistently show won't have lore. These aren't just my speculations, by the way. Furthermore, it's replicated across different cultures. Men have a larger variance on most measures than women because of evolutionary benefit. What? I don't know. I think we're being trolled, man. The whilst dragon, was wondering when your next politics stream is. Would love to hear your thoughts on Jeremy Corbyn. Oh, we talked about Jeremy Corbyn when he was running, by the way. So next politics one, in the next set, we're going to do one. Most likely in a couple of weeks, the whilst dragon. Okay. UK would have been way better off. The odds are, you guys chose Jeremy Corbyn instead of the clown, right? I sure as hell was a dumb dumb in my 20s. Yeah, me too. That's so true for me now. A trolling, Daniel Gurr says. Well, let's read Odmix comment. I think so, but he's he's not spamming. He's trying to argue a case, but arguing a mathematical case on a math live stream that has no merit. It's just not going to work. By the way, Daniel Gurr, you're totally welcome to go to our Discord page and link scientific research that you think state what you are stating, right? But as far as I'm concerned, I doubted very much. Okay. And Odmix response to you is, it's wrong. There's less variance. But personally, I am very, very jaded against people saying men are smarter woman in one way or another, 100%. And the variance, like knowing statistics, what's the questions that they're asking? Where were the surveys done? Who did the surveys? Who collected the data? Who does the interpretation? Like, there are differences between men and women, right? But in terms of intelligence, hell no. The intelligence of a human being does not depend on their gender. It depends on their opportunities, on their diet, on social structures, on many, many, many things, right? And none of them are related to their gender unless you're talking about how society treats people that are different genders than men, right? In certain cultures, women aren't allowed to go to school. In certain cultures, women are objectified in a big way, right? So it has, it doesn't have anything to do with the gender, it's about the social structure of things, right? It's called a variability hypothesis. Link it up on our Discord. It's because men are more likely to be born with Down syndrome or autism, etc. More men on the tail ends of intelligence. Is there an omnic? Now, what is that related to? Is that because a lot of men work in environments? I don't know. Do you know what? I'm not even going to speculate on what this might be, right? I'm never going to speculate on that front. It could be a gazillion different things. And I doubt if on the high end of the, of the, of the distribution, you see more men with higher intelligence, because maybe in the academic world, it has been men that have been given the opportunity to excel in their academia, academic lives, right? Depending on their opportunities that they had. We're, as we've talked about this a little bit in the entheogen stream, we're just coming out of the dark ages. We are clueless. And what are the things that they're measuring, right? Are they just measuring their engineering skills, right? Or are they measuring their communal structural skills, right? Like family ability, compassion, like that compassion, empathy requires intelligence. Okay, really, it really does. Because you have to know yourself and the other to have that, that connection, right? Let's leave the politics for now. Let's leave the graphic quadratic. This thing gets my go, it gets, gets me a little riled up as well. F of X is equal to this. We want to graph this thing. Now, this is a quadratic, okay, to its cause, but in terms of modern day tests, it does exist. Daniel, girl, since you brought these, since you mentioned this, modern day tests suck ass. Okay. Our education system is horrendous, centralized, controlled garbage. And the tests that they give people is pure garbage. Okay. So based on a garbage system, giving people garbage tests, yes. I can definitely tell you it is 100% flawed. I was saying that Daniel girl was right. It's because women are born with double X chromosomes that cover up more genetic defects. While XY chromosomes don't cover that up. Is that, is that it? That's cool. I did link up some articles for us, man. Our people link up some article for us in this square. We could take a look at it, right? I don't know the biology. I didn't do well in biology. I, I like the math, right? And the physics and the chemistry. Take a look at this thing. If we want to graph this thing, there's a couple of ways we can graph this, by the way. Okay. I'm going to show you two ways to graph a quadratic. Let me make this darker. You know what? I'm going to grab another pen. Let's find a pen that's nice and dark that you see. Nope. That's not it. Nope. I don't like that either. What's this one? Oh, that's not bad. What's this one? Oh, that's definitely not good. Let's use the purple. Okay. Let me try one more. I'm going to try that one. Nope. Dark green. Oh, that's not bad either. Okay. We'll keep the dark green. We're going to do dark green again. Okay. I'm going to erase this. So I'm going to erase this again. Let's write it out. Half of x is equal to negative x squared plus 7x plus 25. That's worse. Jesus. Oh, there we go. That's nice. That's nice. That's nice. That's nice. That's nice. As for x, right? Awesome. That came out good. I'm also only taking, talking explicitly about IQ tests. To be honest, I 100% think the conclusion is a bullshit as the race science that says black people are dumber because they have lower IQ. It's silly and it's because women don't have the same opportunities as men. How many women like Miriam Miraz Zakhani haven't been mathematicians because of sexism? 100%. The person Audnick is referring to is the only, Audnick, correct me if I'm wrong, the only mathematician to win the medal, the world mathematical medal. What's it called? I forget what it's called. Audnick, please let me know. I'm still in the blank. And she was an Iranian, right? The field medal, right? And Audnick is the one that informed me of this, right? A year ago, two years ago, right? That's a heated topic. Well, I'm going to avoid it. I'm going to avoid that topic. I'm moving on to graphing quadratics. Now, take a look at this thing. We're going to grasp this thing using completing the square and then we're going to graph it using finding the x-intercepts if there are x-intercepts. Okay. And there will be x-intercepts for this. Completing the square, this is what you do. You guys enjoy your conversation. I'm going to graph a quadratic. When you're completing the square, this is what you want to do. You've got a quadratic, write it in descending order. Take the x-square term, take the x-term, put them in brackets, right? Now, what you want to do is get whatever is in front of the x-square term out in front of the bracket, right? If this was just one, then you'd leave it alone. There's nothing there, right? It's just a one. Anything other than one, you need to get it out of there, right? So when you have a negative here, it's actually negative one. So you're going to grab the negative and bring it out of the bracket. So now what we have is negative x-square. Now, because you're putting it in front of the bracket and the bracket contains both these terms, you have to adjust this to compensate for the negative in the front. So what you really end up doing is you take this term and divide it by whatever you took out, right? So divide this by negative one. So the sign changes. It becomes negative 7x plus 25, right? Then what you do, oh, there's Nassim Nikolas Talib coming up, has some good articles refuting the validity of IQ tests, but I've yet to read them. Daniel Gur, IQ test, I've never taken an IQ test and I never will take an IQ test because the IQ tests are really question dependent. I think IQ tests are garbage, tell you the truth. Literally, they're garbage. I don't recommend my students taking IQ tests when they bring up IQ test scores. I go, well, it doesn't really mean anything to me, right? IQ tests are garbage. But thanks for letting us know that Nassim Nikolas Talib has written articles about how bad IQ tests are because they're culturally focused, right? In large, they say they're not, but they are, right? Then what you do in completing the square, you take this guy, whoop, the number in front of the x term, okay? And remember, one of the mantras in mathematics is the sign in front of the number goes with the number, right? So this isn't 7, it's negative 7. You take this number out of here and you divide it by 2. Now if you can reduce this, you do. You can't reduce 7, negative 7 divided by 2, it's just negative 3.5, but I like working with fractions, right? That way I don't need to use a calculator to do things. So if you can reduce it or reduce it, if you can't, you take this number and square it, you get 49 over 4, right? Now that's the process you do. Whenever you take whatever number was here, bring it higher, divided by 2, square it, you get that. Then you're going to add and subtract this guy inside the brackets and you're adding and subtracting 49 because you can't just take a function and add a number to it. The only number that you can add to a function without changing it is number 0, right? So if you add 49 over 4 and you subtract 49 over 4, you're adding 0, right? So this becomes negative x squared minus 7x plus 49 over 4 minus 49 over 4 plus 25. Now what's the sum of this? It's 0, right? So you're not changing the value of the original function. You're just adding 0. This could be there or could not be there. It doesn't change anything up, but we're manipulating it to turn this thing into a perfect square, okay? I need to get going. Chichou, Audmick says, have a nice rest of the stream. You have a fantastic day, Audmick. And thank you for the discussions and the info. By the way, I appreciate it very much. Now what you're going to do is do this. Take the negative one, the one you subtracted out of the bracket. So you're going to take the one that's minus in front. You're going to take it out of the bracket. Now if this is coming out of the bracket, whatever's in front of the bracket has to multiply it, right? Because it's a it's a gig keeper, right? Anything that's inside has to, before when it's leaving, has to multiply whatever's in the front. So this thing comes out, multiplies negative one because this is a one really, negative one times negative one. This guy here is now a perfect square. Perfect square means this. What are two numbers? Here, I'm going to show you simplified perfect square. x squared plus 4x plus 4. So whenever you have a quadratic when you're trying to factor it, you're asking yourself, what are two things that multiply to give you this number and add to give you this number? Multiply to give you the third number, the constant by itself, and add to give you the coefficient in front of the x term, right? Well, two numbers that multiply to give you four and add to give you four or two times two. So two, so x plus two, x plus two, and we've done a lot of videos on factoring and stuff like this, right? So look into series 3a and 3b of the language of mathematics that we have on our YouTube channel, and there's a lot of videos there explaining how to do factor and quadratics and stuff, right? So if you multiply this out, you would get that out. This is a perfect square because it's the same thing multiplied by itself, right? So this guy factored becomes x plus two squared. Oops, x plus two squared, because x plus two times x plus two gives you that. That's what a perfect square is, right? So what are two numbers that multiply to give you 49 over four and add to give you negative seven? Oh, difficult, difficult, right? What are two numbers that multiply to give you 49 over four and add to give you negative seven? You don't even have to think about this. It's this guy right here. It's negative seven over two. Negative seven over two times negative seven over two is 49 over four, negative seven over two plus negative seven over two is negative seven, okay? That's the reason we circle this because we're using it, all right? When you're doing complete the square, circle this, circle this because you're using both of them. This one, you're dropping here, here and here, and this one is this factored. So in one shot, you're going to write this negative bracket x minus seven over two times x minus seven over two, which is really just x minus seven over two squared. And you're going to go negative 49 over four times one is plus 49 over four. So this is going to be plus 25 plus 49 over four. Now all you've got to do is just add those two guys now, right? If you're adding two guys, you know common denominator, here we can do it on the side, 25 plus positive 25 plus 49 over four, common denominator is four, four times, because that's over one, four times 25 is 100 plus 49. So this becomes negative x minus seven over two squared plus 149 over four, right? Now to save us space, I'm just going to erase this and put 149 over four, right? Because we're going to graph it in the bottom here, okay? So this becomes positive or plus 149 over four plus 149 over four. This is what f of x is. This is the same as this is the same as this is the same as that. They're all saying the same thing. They're all the same functions just expressed differently, right? Now why did we take this and rewrite it in this form? Because this is the form we can write things in quadratic functions to be able to graph them easily, okay? It's like saying equation of a line. Now if you're into quadratics, you already know what an equation of a line is, right? Equation of a line is y is equal to mx plus b, where m is your slope and b is your y-intercept, right? So if I give you y is equal to two over three x plus three, okay? Then what you do is you read this as a sentence and this is a sentence. It's instructions, right? The sleeping fox three, hello, hello. It's just instructions telling you what to do, how to graph this function. And what it tells you how to do this is you go to the y-intercept, one, two, three, and then from the y-intercept you do the slope rise over run. One, two, one, two, three. You just graph the equation of a line, okay? Now quadratics, quadratics have the same thing, same kind of sentence that tells you, gives you the instructions of how to graph them, okay? Hey, may I ask, what's two plus two? Oh God. Two plus two is a maximum of four. Here, we'll do a little sidetrack. Ready for this? Here's two plus two. Are we talking about vectors? If you're talking about vectors, if you have magnitude two vector going in this direction, magnitude two vector going in this direction, you add those guys up, you get zero, right? Or do you have two going this way and then you attach another two over here, then this plus this is going to be four. And you have every number between zero and four. Tomorrow might be negative one. More important question, how do you graph a quadratic? Lacking, okay? Yes, please, vectors, vectors are fun. So quadratic, graph in the parabola, is this. Alpha-vax is equal to ax minus p squared plus q. This is your general, not your general, but your vertex form of writing a quadratic function, okay? What this means is this. A is your stretch factor and your flip factor. P and q are your vertex. So what this says is this, if we're going to read it off, let's read it off and give all the points and graph this. This thing says the vertex of a parabola is the opposite sign of this and the same sign of that. So this becomes seven over two and 149 over four. So that's where the parabola, and the parabola looks like either like this or like this, right? That's what a parabola is. When you throw a projectile, if I throw this, I go, it's going to go like a parabola. All projectiles fly like parabolas, right? So what is this? Seven over two is three and a half. Two, three, four, five, six, seven, eight, nine, ten, eleven. Three and a half, right? And your vertex is 149 divided by four. What's 149 divided by four? Let's do long division. One, 49. Four doesn't go into one, but it goes into 14. Four goes into 14 three times. Three times four is 12. Subtract, you get two. Bring down the nine. Four goes into 29 seven times. So that's 28. That's one. So 37 and a quarter. So 149 over four is equal to 37 and one over four, right? Yeah, 37.25. A quarter is .25 because you take one and divide it by four, right? So 37 and a quarter. Now these are all one text. I'm going to make these texts fives. Five, 10, 15, 20, 25, 30, 35, 40, right? So we're at three and a half and 37 and a quarter. So that's 35. Here's 37 and a quarter. Okay. That's the vertex. I had to do the same as all the girls. So that's our vertex. That's the word of parabola turns down because this is negative. So if there's plus, if the number up here was positive, it would turn up. Since it's negative, it flips down. So we know that the parabola goes down. Okay. Now find your y-intercept. Y-intercept. Y-intercept is when x is equal to zero because on the y-axis, x is zero, right? Because this is your x values and this is your f of x, right? If that's one, two, three, four, five, six, seven, that's zero and that's negative one, negative two. So when x is zero, you're on the y-axis. What's our y-intercept? Our y-intercept, you can grab from here or you can sub in zero here. If you sub in zero here, you're going to have to go zero minus seven over two, negative seven over two squared and then you figure out what that is and you add it to this. Lots of work. Go to the original and sub in f of sub in x is equal to zero. Well, that becomes zero. That becomes zero. So your y-intercept is 25. So y-intercept is f of zero is equal to 25. So our y-intercept is here, right? So let's do that for now. Now, parabolas are symmetrical. I use Gaussian curvature to explain to my younger brother why folded pizza doesn't drop. I think I broke his brain. Did you at least give him some pizza? So one thing that happens with parabolas is parabolas are symmetrical, right? On the symmetrical basically means ideally, like if you're going to draw a perfectly symmetrical person, if you draw a line right down the middle, their ears are going to be the same distance apart. Their eyes are going to be the same distance apart, right? So symmetrical means one side is equivalent to the other side, right? You can flip it along its axes, right? So for a parabola, its axis of symmetry, we call that AOS, axis of symmetry. Axis of symmetry is x is equal to just the x part of the vertex, seven over two. x is equal to 3.5 is the line that is symmetrical for a parabola. So here's our axis of symmetry. Got it? So this line here is x is equal to seven over two. So our parabola, we can graph it right now by the way. We're going to at least go through the y-intercept. If we graph it, goes like this. Now we don't know where crosses the x-axis yet, right? So hold off on that. It makes so much sense, the very definition of beauty, the very definition, and we get attracted to it, right? Human beings were attracted to symmetry, right? There's a lot of theories based on this. There's people that do analysis in elections and say the most symmetrical face in most elections usually ends up winning more often than not, right? Which is crazy. So take a look at this thing. If this is an axis of symmetry, how far away is the y-intercept from the axis of symmetry? The y-intercept is sitting at the y-intercept, or the axis of symmetry, is seven over two away from the y-intercept, right? So this distance here is 3.5, seven over two. So if you go another same distance here, you end up at seven. So where are we? One, two, three, four, five, five, six, seven here. So it's going to be here. So I'm going to give you the coordinates so you see what's going on here. This point here is, yeah, exactly, rough alive, right? As a sixth grader, I don't know what this means, but at least I'm learning, at least you're learning good stuff. The sleeping fox tree. Daniel, I think Thurston said that symmetry is way of humans understanding things too big to comprehend. Possibly, possibly. So this point here is zero and seven over two. Oh no, not seven over two. Zero and 25, right here. Let me write this bigger so you guys see it. Zero, zero and 25. That's this point here. This point here is going to be 3.5 plus 3.5, which is going to be seven and 25. So we found the mirror point of the y-intercept. Now the only other thing we need to really find is our x-axis. There are other parameters you can give here. You can say, oh, what do you call it? The axis of symmetry, it opens down, opens down. It has a maximum value, maximum of, oh, this point here. This point here is seven over two and 149 over four. It has a maximum value of 149 over four. Maximum value of 149 over four when x is equal to seven over two. The domain of this thing is what are all the possible x values. Well, if this thing goes on forever, the domain is the element of the reals. The range of this thing, range is what are all the possible y values. The y values is the highest y value and everything less. So y is less than or equal to 149 over four. So now we need to find the x-intercept. We can find the x-intercept. Oh, sorry. That's okay. The sleeping fox. I hope everything's okay. No need to apologize. Elder God, age is just a number. Age is just a number. What else? You make me feel old. Oh, that's why Elder God, he doesn't, the sleeping fox doesn't make me feel old. See the goatee doesn't make me feel old. As, who says Starsky, Elder God, age is just a number. It's just a number. Yeah. It's, I've had some amazing conversations with some of my students that would blow away the conversations I've had with some of my peers at my age, right? They'd be like, what? They don't even understand what some of my students are talking about, which I'm very, very grateful for. Youth processing speed is insane. Really, the generation is coming up. True. But 11 years old was a lifetime ago. Yeah. Multiple lifetimes ago, Elder God, I'm guessing, right? So now the only thing we need to find is the x-intercepts, right? The x-intercepts, like for example, when are you on the x-axis? You're on the x-axis when y is equal to zero, right? So all you got to do is set y, f of x is your y, equal to zero, right? So if we said we could set y is equal to zero here and isolate the x or we could set y is equal to zero here and factor that thing. Now, that thing doesn't factor easily. So we would have to use a quadratic formula, right? Or we do it here. Let's do it here. I'm going to do this here, here. Okay. So you guys see it and I'm not bending down and writing really small. So check it out. Check it out. So if we want to find out when this function crosses the x-axis, you set f of x is equal to zero. So you set this equal to zero, right? And this equal to zero. So zero, and I'm going to set it equal to zero here, is equal to negative x minus seven over two squared plus 149 over four. I hope you guys can see that. Good enough, I think. We're going to grab this guy, bring it over. So this becomes negative 149 over four is equal to negative x minus seven over two squared. We're going to multiply everything by negative one and we're going to multiply both sides by negative one or divide by negative one to get rid of this negative and get rid of the negative from the brackets, right? So if you multiply everything by negative one or divide everything by negative one, this becomes positive and that guy's gone. So this is going to be 149 over four is equal to x minus seven over two squared. We're trying to get to the x. We're basically peeling a banana, right? So all you do now is you square root both sides. If you take the square root of this, the bottom is going to be two and 149, it's not perfect square, so I'm just going to leave it as a square root of 149, right? And square root of anything is plus and minus, right? So for if I write down what's the square root of four, if you say the square root of four is just two, that's half your marks. Square root of four is plus and minus two, right? Plus and minus two. Keep that in mind. The even root of a number is plus and minus, right? Plus and minus. So this becomes, here, I'm going to erase this part so we have room to work. It becomes plus and minus square root of 149 over two is equal to x minus seven over two and then I'm going to grab the seven over two and bring it over. So x or x intercept is going to be seven over two plus and minus square root of 149 over two, okay? Let me draw a separator here. So we realize that this is side work, right? So we can take that and say the x intercepts x ints are x is equal to, and they're both over two so I can combine those guys, the bottoms, right? x is equal to seven plus or minus square root of 149 over two. Now what does that mean? That means this. First of all, do you see the seven over two? What does that remind you of? What does that remind you of? Seven over two. What is that? What is that gang? What's seven over two? It's on the graph. What is it? Seven over two. It's our axis of symmetry. Is it not? Is this line here? Right? That's seven over two. x is equal to seven over two. So what this means is from the axis of symmetry, it means seven over two is the sleeping box. Awesome, by the way. It means seven divided by two, three point five. But what is this meaning based on the graph? It's our axis of symmetry. Because this thing is symmetrical across the y, the horizontal line, it had to open my, I had to open my phone before it says, so it's crying because it's symmetrical. Couldn't I've got an ad? Oh no, too bad. So if you had this, it means from the axis of symmetry, if you go plus squared of 149 over two, you're going to be here. So whatever this point is, is seven over two plus the square root of 149 over two and zero. The point, right? And this point is, this point is seven over two minus the square root of 149 over two and zero. So it's basically saying the distance here is the square root of 149 over two. This distance here is the square root of 149 over two. And you just ended up graphing a quadratic function. And this is one of the main things in grade 11 in my part of the world that you have to learn. You can't progress into higher level mathematics until you learn how to graph a parabola. Unless you go into statistics, but you still need to know how to graph parabolas. It's one of the core building blocks of progressing into higher level mathematics or anything beyond graphing parabolas. Now I mentioned to you guys that I'm going to show you two different ways of graphing this, right? Let me show you two different ways of graphing this. This is the systematic way of doing it. This is what you're, what you get taught. And it is legit. And I highly recommend knowing how to complete the square. Let me show you the other way. The other way is working it backwards. The other way is taking this guy, finding the x-intercepts, taking their average to find the axis of symmetry, taking the axis of symmetry, plugging it back into the equation, finding the y associated with the axis of symmetry. So you find the vertex. So you work backwards. Beauty of mathematics. One of the most beautiful things about mathematics is whatever you can do, you can undo. A direction that you can go in to solve something. The odds are you can go in the opposite direction and solve for the same thing. 79 con. I was always, it was always easier to me to look at such quadratic functions as that plus five. What I can read from it is that it is vertically inverted parabola intersecting x-axis in zero and seven. But it's not. Shifted up to, oh, shifted up 25. They are always symmetric. So to vertex, it is the middle between zero and seven. 3.5. Very good. Very good. Yes, this is the second solution. Very nice. That's a great way of doing it, by the way. That's a great way of doing it. Shifted up 25. I like that. Rare I see that. Rare I see that. I'm going to show you too in a way where we're going to use the quadratic formula to factor it because the quadratic formula is ridiculously important as well. Now take a look at this thing. I'm going to erase all this. I'm going to keep that there. And remember, if you need these for notes, you can always take screen caps of them. Right? 79. The sleeping fox says you broke me. One. Check it out. Check it out. Let's take out this guy. We don't need the bracket either. And this is a negative, right? And that's it. Let me take out square root of four as well. So we've got a clean board. So if you want to solve for this, you're really just basic math. Yeah. It is basic. You're not using anything as Elder God says. You're not using anything very complicated. It's just adding, subtracting, multiplying, dividing. Yeah, but I'm sixth grade. Yeah. By the way, sleeping fox, learn how to deal with fractions. Okay. If your school is telling you to use a calculator to do fractions, work in decimals, learn. I don't want to say don't listen to your school. You need to do what you, you know, you need to still get good marks and stuff like this, but learn how to deal with fractions. Ridiculously important. You'll thank us for it later. It'll make you be able to do way more complicated mathematics than having a calculator by your side all the time. Once you learn how to deal with fractions, your algebra becomes more powerful. Okay. Now one way to do this is we're going to factor this. We want to find that X intercepts. Now we can't factor this easily. So we're just going to use a quadratic formula. The quadratic formula says this X is equal to negative B plus or minus squared of B squared minus four AC all over to A. A, B, and C. What are A, B, and C? It's just A, B, and C. A, B, and C are this. AX squared plus BX plus C. So C is your constant. B is the coefficient in front of the X and A is the coefficient from the X squared. Learn their basics then adapt it to your own method later. Yeah. Agreed with Elder God. Learn the basics and adapt it to it for yourself later on. Do schools recommend calculators in sixth grade now? They do in my part of the world. It's horrendous. When I get students, the first thing I get students, I test them to see if they know how to deal with fractions. If they don't know how to deal, negative numbers and fractions. If they don't know how to deal with those, we hit those up right away. I don't care if they're in grade 12, grade 11, or grade 6. Fractions, key, essential. So this becomes this. Negative B is negative 7. Negative 7 plus or minus. B squared is going to be 7 squared which is 49 minus 4 times A times C. A is negative 1. C is 25 all over 2 times negative 1. So this becomes negative 7 plus or minus square root of 49. 4 times 25 is 100. Negative and negative is positive positive plus 100 over negative 2. Right? Now, when you have a negative in the bottom and negative here, you can just eliminate the negatives. They kill each other and these two signs flip. Right? So right now we've got negative here plus minus and negative. Well, if you write these separately, this is what it shows. Right? I'm going to do this in one shot so we can save the space. Right? So this is over negative 2 and that's over negative 2. Negative and negative kills each other. So that becomes 7 over 2. 7 over 2, ring a bell. That's our axis of symmetry. And the negative here just flips those which becomes negative and a positive which is the same thing as a positive and negative. So this thing simplifies to 7 plus or minus square root of 149 over 2. This is our, these are our x-intercepts. We already knew this. Right? We got it from before. So if we're going to graph this, here let's do this. 7 over 2 plus 1 square root of 149 over 2. Right? So 7 over 2, if you're going to write this like this, let's write it like this. 7 over 2 plus or minus square root of 149 over 2. So 7 over 2, 1, 2, 3, 4, 5, 6, 7. 7 over 2 is here. That's our axis of symmetry. All right? And you're going to go plus 149 over 2 plus square root of 149 over 2, which puts you here, wherever that number is. And minus, and that put you over here. Too bad it's not, doesn't look as symmetrical as it should. And this over here is minus a square root of 149 over 2. Right? Well, we already know our axis of symmetry because if you take the average of this, this just disappears. It becomes 7 over 2. Nice. So all we've got to do now is find what our y value is when x is 7 over 2. So let's plug it in because that's going to give us whatever the point is here. So find y or f, find y when x is equal to 7 over 2. So all we've got to do is just plug 7 over 2 up here. Right? So f of 7 over 2 is going to be negative 7 over 2 square plus 7 times 7 over 2 plus 25. I'm going to grab a seat so I can reach this stuff better. I had to wait 10 minutes to comment. Did you, Natalie? XO Natalie. Yeah, I think we have a 10 minute for new subscribers. Thank you for subscribing, by the way. Oh, sorry. We had some troll actions coming for our math streams and stuff like this. I don't know why people would be trolling math but they do. They think this is a centralized education system. Right? So we put a 10 minute timer on it, delay on it. Okay. I hope that's okay. But now that you're following, you can comment as you wish. Right? Oh, that's rude. Math trolls. I know. Math trolls. That sort of shows you how bad our centralized education system is when people try to troll math. Just like math. You must be bored out of your mind. Okay, awesome. I'm glad you like. You're okay with it, Natalie. Now, take a look at this thing. This is negative 7 over 2 squared. 7 over 2 squared is 49 over 4. So it's negative 49 over 4 plus 49 over 2. 7 times 7 over 2. That's 7 over 1. 7 times 7 is 49 over 2 plus 25. Common denominator is 4. Right? So let's go 4. This becomes negative 49 plus. Multiply 2 by 2 to give you 4. So 2 times 49 is 98. Right? 98 plus. And this was over 1. So that becomes 100. Oh, yes. Let me join this math streamer and ruin it just because I know. Right? Crazy. Lack of caring. I've been using my university's library database of download PDF versions of math, philosophy, science things. Awesome. Awesome lack of caring. Versions. I hope you're reading them as well. It's okay to data hoard and archive the stuff, but share. Right? So this becomes negative 49 plus 98 is going to be 49. Right? It's going to be 49 plus 100 over 4. So this is going to be 149 over 4. What was 149 over 4? We did it. It was 37 and a quarter. Right? So this is 37 and a quarter. I hope it was. Let's do it again. 4. 149. Right? 4 goes into 14 three times. So that's 12. That becomes 2. Bring the 9 down. 7. 7 times 4 is 28. 1. Yeah. So 37 and 1 over 4. Right? 37 and 1 over 4. That's what we had last time too. So this is here. It's 7 over 2 and 149 over 4. That's our and our y-intercept is 25. So let's put it here. So this is our problem. We just graphed it a different way. All right? Did it require less work? To a certain degree it did. Right? We didn't have to complete the square. I mean just looking at the board, this has less writing in it than the other one. Right? And you got the same information out. Okay? But completing the square is powerful. It's hard to follow just with audio. I work at the sometimes. Yeah, with math it's very difficult to follow with the audio only. You need the visual. You need the visual. Lack of caring. Yeah. I want to amass a comprehensive library of the essential fields of study. I was inspired in no small part by your channel. So, oh my pleasure lack of caring. And I'm glad you're doing it. It's important to have that information at disposal that you can use. Right? That was beautiful. She just starts keep things. It was easy. Well, I don't know if it's easy. It's you have to have an appreciation of what's going on. Right? It's not mathematics is not about monkey see monkey do. It's not about memorization. It's about understanding. Because once you understand it, you can drive everything. Right? So that's the key to mathematics getting. Understand what's going on. Understand what's happening. And you're a master of your universe. Once you're able to do that. Right? It's beautiful. It's beautiful. Really. Once you have an appreciation for all this. It's man. It's like playing a video game. And you got the magic sword. And you got an invincibility shield. You can go anywhere, do anything. You're a master of your own universe. Right? It's beautiful. It's beautiful and powerful. You want to do a profit function? Profit function how so? Profit revenue or revenue function? We got how much time do we got? We got a little bit of time we could do. Should I erase this? I'm going to erase this gang. Just in case if we want to do anything. The sleeping fox. I forget who it was that asked to graph a quadratic. But thank you for oh wait. Oh sleeping fox. You can take a screen cap. You can on the on oh sorry. You're going to ask a question. Oh no. You can ask a question. I remember the function. If you have a question. If not on the video you can what do you call it? Just take a screen cap or screen cap or just video on the man. Just look at it again. Apologies. Next time let me know. As soon as another question comes up usually I go crazy and delete things. Pi is equal to negative Q squared. But that's a quadratic again. Starsky. Are we talking about pi like Pythagorean theorem pi or pi phi? Are we talking about just a symbol f of x basically? But that's the same function. We do the same things. Are we talking about this? f of x is equal to negative Q squared plus 4Q plus 12. 4Q plus 12. I can do it speedy Gonzales style. So you can see how fast it goes. Should we do speedy Gonzales style? Let's do speedy Gonzales style. Let me try one of these pens. Let's see how dark this is. Can you see that well? I'm going to try this. Watch this. If we want to graph this. Speedy Gonzales style. Ready? Ready? I want to do completing the square. Bring the negative out. Q squared minus 4Q plus 12. Take the negative 4 divided by 2. You get negative 2. Square it. You get 4. You got negative Q. Negative Q squared minus 4Q plus 4 minus 4 plus 12. Grab the negative 4. Bring it out. Multiply by negative 1 because in the front that's a perfect square as that guy. So it's Q minus 2 squared plus 4 which is plus 16. So that's your function. And if you're going to graph it, your vertex is 2 and 16. Vertex is 2 and 16. So 1, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16. Your y-intercept is 12. 1, 2, 3, 4, 5, 6 is 12. Oh no, 12 would be up here. If that's 16, here's 12. So this is 0 and 12. The mirror would be 4 and 12 because the axis of symmetry is 2. You're going to graph it. Let's make a big dot. You're going to graph it. And we need to find these points. Your maximum revenue is 16, I guess. Yeah, that's good. Yeah, fair enough. No, no, let's do it. We're doing the speedy-goons-out stuff. We've got time for speedy-goons-out. So your maximum revenue, so Q, whatever Q is, whatever the system is, your maximum Q, speedy-boy, maximum revenue, maximum revenue, revenue is equal to 16, I'm assuming, dollars when X or Q, when Q, quantity of the object, I guess, is equal to 2. And here are your X intercepts. And the X intercepts, you can just set F of X is equal to 0. 0 is equal to negative Q minus 2 squared plus 16. Grab the positive 16 over. Negative 16 is equal to negative Q minus 2 squared divided by negative 1. So you get 16 is equal to Q minus 2 squared. Square root both sides. Square root of 16 is plus or minus 4, which is equal to Q minus 2. Grab the 2, bring it over. So you got Q is equal to 2 plus or minus 4. So Q is equal to 2 plus 4, which is equal to 16. And Q is equal to 2 minus 4, which is equal to negative 2. So this guy is negative 2 and 0. And this guy is 6 and 0. That's it. Now remember, when we did the completing the square for the first function, we went through all the little details, so covered a lot more space here. And the numbers were fractional, so we had to do a little bit of extra work. But this one seems like not as much work. So depending on the numbers that you have, how much work you need to do and how well you know the system, how well you know this algorithm, because that's all it is. It's just an algorithm. That's all. And once you understand every little part of the algorithm, you can manipulate this thing to your liking and take shortcuts where you want, because you understand what's going on. I hope that's okay. I hope that's good. Gang, should we call the stream? Should we call the stream? Let's call the stream. Tomorrow, tomorrow, we do reading. The next day, we do reading, comic book readings, Halloween comic book readings. Winners are sessions. I forget when our reading sessions are. In the next two days, we're doing comic book readings. And the comic book, oh I don't want to let me tell you when our comic book readings are. I'm just going to go to our Discord. And if you go to our Discord schedule, you'll see the schedule. And tomorrow, we're doing a comic book reading from 9 30 a.m. my time, PDT Pacific time. And on Saturday, we're doing a comic book reading starting at 11 a.m. So we're doing two comic book readings in the next two days. And then we're going to do two Julian Assange streams. One on Monday at 10 a.m. and another one on Tuesday at 10 a.m. The comic book readings are going to be Halloween comic book readings. So I'm going to pick some horror comic books. Horror and stuff like that to read. I'm going through my comic book collection now. I've been pulling some stuff out. I pulled out too many. So we're going to do most likely modern horror comic book for maybe tomorrow. And do golden age horror comic book reading for Saturday. Okay. Do you like jazz? Or oh and I'm trying to figure out times and divisions times two. You're trying to figure out I do like jazz. Jazz is amazing. Phenolius Monk. And Phenolius Monk is absolutely amazing. And some people say Nina Simone was jazz. Oh, you book. I have a Halloween party on the 31st. Nice. Awesome. Candy. Thanks for this change. You're my pleasure, Starsky. Take care brother. You too. You too. Regarding education system that sucks. I wish there was more geometrical proof of basic theorems when I was in school. Now when I know them, they look so simple and beautiful indeed. Geometric proof of Pythagorean theorem. Beautiful. Beautiful. Indeed 79 con. And with me too. I wish there was more of a lot of things in school. I'm off to Julian Assange stream, but I will be there. Awesome. I am home for Julian. Awesome. Elder God. I'm looking forward to that. I've compiled a fair bit of info. I want to go over. Yeah, have a great day. You too. You too. Love you. No homo. Indeed, that's okay. That's okay. Even the other, if it was, it's still okay. Okay. Love. I'll take love any which way. Okay gang. Gang, if you want to know what this is about, I'm on patreon.patreon.com forward slash chico. C-H-Y-C-H-O. I don't put a thing behind way of all. Everything's created commons. Share and share alike. And my thesis is laid out there. And everything's laid on mathematics. Okay. If you want to follow this work and see what it's about, you can follow without committing any funds. And if you do like what you see, and if you think this project deserves your support, you can support this work through patreon. And for those who've been supporting this work through patreon, thank you very much for your support. I appreciate it very much. It allows us to do what it is that we are doing. We are live streaming on twitch.tv forward slash chico live. C-H-Y-C-H-O-L-I-V-E. If you want to participate in the chat, twitch is where you want to be at. And for those of you who subscribe to follow it and who are here participating in these live streams in the mod, thank you very much for your support. We do announce these live streams 30 minutes before we go live on L-O-M-I-V-K, part of the gap and Twitter. You can follow the work there because we do share some additional information. For live streams where we don't have any visuals, we do upload the audio to soundcloud.com's podcast soundcloud.com forward slash chico C-H-Y-C-H-O-L-I-V-E. And this should be available on your favorite podcasting platform, including Spotify and iTunes. My love for chico is a spiral spiritual fun. I was about okay, bye. Hope you have a great one. YouTube Sleeping Fox and good luck in school. Learn your fraction of Sleeping Fox. Pay attention. Know your fractions well. Okay. You know your fractions, your master, your own domain. Okay. And this video will be uploaded to both Bichute and YouTube. And if you want to support, watch someone else. I want to watch more. Okay, enjoy it. And if you are on Bichute and YouTube, you'll be able to support this work. You can subscribe. You can follow. You can turn on notifications, share, like. And if you're on YouTube, you can support by joining YouTube membership. Gang, thank you for being here. And I'll see you guys in the next couple of days. We've got some comic books to read. Bye, everyone. Awesome. Join the discourse if you like. Thank you. My pleasure, gang. Bye, everyone.