 and we are live. Good morning everyone. I hope you're doing well. Welcome to my channel and welcome to another live stream and this is of course Chicho and today we're doing math tutoring session drop in math during session number 64. Let's do a little mathematics and we've done a fair bit of these before and they're fun to do most definitely fun to do and the questions go all over the place for these things and what we're going to do is wait for people to roll in and this is basically open discussions so mathematics comes first first and foremost free assange free assange free assange right and we can talk about almost anything but we're going to keep politics on politics streams and certain sensitive topics on sensitive streams that we end up only uploading to bichu for now they don't get uploaded to YouTube and in 2021 we'll add a third video sharing platform to our repertoire that way people have more options to access the content just because censorship is taking hold on a lot of mainstream platforms a lot of the legacy media I guess we could call youtube legacy media to a certain degree because of the censorship aside from that welcome to another live stream let's see where the conversation takes us and again we're mainly focused on high school mathematics but we do touch topics from elementary school as well as topics and university a little bit of intro calculus a little bit of probability and statistics a lot of functions a lot of pre calc stuff and whatnot and we have like hundreds of videos available online most of them on youtube because we've been working there since uploading there since 2015 jet 7x country how are you doing welcome to another live stream and while we wait for notifications to go out for people to roll in let me tell you who I am and what this is all about or at least who I am you can find my work on patreon patreon.com forward slash chico chy ch o if you want to support this work patreon is a great way to support this project if you want to follow this work patreon is a great way to follow this or gravity of the situation how are you doing hey chico did you enjoy the obeys song that i had you listen to on youtube um god i've listened to a few stuff uh gravity uh of this situation uh i think so i think you linked it up on discord did you not if you did like if i commented i i think so i can't remember i would have to listen to the song again um that was a happy one wasn't it i can't remember now i go through so much content right and some of the uh the bring me uh the horizon song but i listen to it but i can't uh put the tune together right now but i did enjoy it for sure for sure it's it's uh there's so much uh all the snow oh yeah yeah yeah all the snow that's right is the one who suggested it on youtube that's right that's right catholic tradition this thank you very much for the twitch prime sub let's see what kind of emo we got hey we got a little santa selfie 2020 selfie it's a snowman nice awesome awesome awesome and gang i don't put anything behind paywalls everything's creative comments share share like and that is the way i began this project 15 years ago in 2005 and that is the way i will continue to do this project 15 years from now 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podcast and those audio files podcast should be available on your favorite podcasting platform including Spotify and iTunes and we will be uploading this video to both bit shoot and youtube because as of right now as far as i know youtube is not censoring any mathematics can't be promised that they won't be doing it later okay so this will go on youtube and bit shoot and you can support this work on those platforms by liking sharing commenting and if you are on and turning on notifications for sure i'm not sure if you're guaranteed to get notifications through youtube but you do get them through bit shoot i've tried that out youtube not so much but you can support this work through youtube by joining youtube membership and for those of you who support this work through youtube membership thank you very much for the support slick mick 99 hey chicho it's been a while but i love catching your math streams i'm an engineering student and currently struggling with the material engineering oh ultimate 10 10 cell strength oh my god percent elongation etc really tough stuff really tough stuff i did some of the stuff at university slick mick it's it the problem i had when i was doing this stuff i didn't really grasp the concepts of the variables that they were talking about right like they would give you these numbers these constants and these variables and the equations and you have to you just have to plug and play right just plug them in the right place but if you didn't know what the answer was you were getting and the units you had to make sure the units were in the proper um the variables were in the proper units and stuff like this and i found it difficult as well especially when it got to materials because each material was different and depending on the temperature and the pressure that they were under and stuff like this it was interesting i'm not sure you know you can pose a question and for sure you can go to our discord page and under math i'm just going to take these guys down under math and ask a question maybe people can help you out there and if i can i will but i don't i barely remember anything from that uh stuff and i don't teach that stuff in teaching mathematics right it's so it's pretty specialized the blue negative awesome i have a hard time finishing this one former third degree polynomial with real coefficients with a leading coefficient of one such that oh two plus i so it's not and one are zeros so it's not uh with real co oh real coefficients uh with a leading coefficient so let's lay this out um so we're dealing with complex numbers as well right uh dice power what about twitter it's a claim about major metric difference equations that's disputed dice power hilarious today's sunny it's disputed the the net eight hi chicho i've been watching your vids for a while but this is my first time tuning in tuning into a stream thank you very much for being here uh thought thought net eight uh appreciate dropping into the live streams and thank you for watching the videos they're phenomenal to create can't get the distribution right for for some reason oh really yeah that's what it's going to be so it's a third degree polynomial so third degree polynomial is f of x is equal to one two three and you got x's here and you can have whatever here multiply together right but we already have such that two plus i and one are zeros so two plus i yeah because i is the square root of negative one so square of negative one is plus or minus right so we got one and two plus i are roots of this function right that the zeros of this function so i is defined as the square root of negative one and square root of anything is plus and minus so really plus and minus the square root of negative one so the roots for the polynomial are x is equal to one x is equal to two plus i and x is equal to two minus not the square root of one uh actually we could do i'd rather deal i'd rather write square root of negative one are you okay with writing square root of negative one double low negative you guys are speaking a different language i just came to learn some multiplication division we're going to do multiplication in division right now we're going to do multiplication not so not so much division but we can hidden citizen we can get into the simpler mathematics uh for sure uh crafter how are you doing catholic double low negative looks like you have to the concept down finishing the problem then it's just cracking away at the algebra yeah that's all it is right so i'm just going to put down the square of negative one here double low negative okay just because when we multiply it out the square roots will disappear right i think you might want x to for the second factor so this guy is going to be you bring these guys over bring them over bring them over so you're going to get f of x is equal to x minus one you're going to get x minus two minus square root of negative one you're going to get x minus two plus the square root of negative one so far okay lock bark how are you doing ding bobber what's going on i just came for uh root retention of one to one what's what's in between 43 and 45 again you mean 44 and x x minus two i for the second factor studying every day 12 hours a day nice crafter together with physics and programming man you must be in a phenomenal state of mind or a very it might be stressful state of mind but what a unique state of mind to be in to be doing mathematics and physics like 12 hours a day like it's it's like meditation uh double little negative yeah anyway we can get after this i've tried several of these uh just can't seem to distribute each one to get the polynomial form instead of complete completely factor form so what i would do i would multiply this guy out first let's multiply these guys out first right so every term here multiplies every term there right boom boom boom boom boom boom and then so on right so let's multiply that out first and then we'll put the x plus x minus one here okay just a bad joke okay ding bobber slick mick in our engineering math class uh in college we're doing extremely complicated vectors using sine cosine and tangent obviously some real tough stuff but i cannot tell you enough how much i love math always been my favorite subject yeah i like the state of mind mathematics puts you in which is to me it's more tangible more real than the societal normal lifestyle that people live which to me seems to be contrived in for the most part right i'm i think i'm going down the right road here right should be free a song free a song free a song right so i'm pretty sure this is it then yeah it must be right so i'm going to multiply this up so this becomes equals i'm going to this is f of x by the way here right i'm going to write this really tight because we're going to need the space here x times x is x squared minus two x plus squared of negative one x minus two x this times this plus four minus two squared of negative one negative squared of negative one x plus two squared of negative one and minus negative one did i multiply that out correctly gang uh correct me if i'm wrong the only piggy how are you doing what's lonely piggy homemade homemade chocolate chip cookies honey chocolate chip cookies with apricots and these are uh check this out i put uh so scott it's homemade whole wheat whole wheat chocolate chip cookies whole wheat and coconut flour with coconut flakes and dark chocolate and apricot and they're my honey cookie recipe okay so honey whole wheat chocolate chip apricot cookies and they're really good okay and hold on doing the doing the what do you call it the 1000 video anniversary with bringing out the crab apples i cracked open a big crab apple thing and i'm eating this so super delicious super tangy that's my snack for today yes it looks like double negative says basically it's taking the complete factor form i'm making a polynomial indeed so we're going to continue with this okay how much math went into making that cookie um ratios wise a little bit great eight and nine mathematics we used you're making me if you're more hungry crafters says yeah they're really good lonely piggy fantastic maybe next time when we do redeeming points on twitch i'll do some baking and do baking uh auction chit show someone should compile all of your cooking videos into a cookbook ding bobber i plan on doing it at some point and including the mathematics in there okay flying kiwi what's up chichou how are you doing just join then welcome welcome flying kiwi what but he always has best he always has messed up catholic traditions though i get so that's what you end up getting catholic traditions so let's do this we're going to combine our like terms here all right anything kill each other these two guys kill each other negative two squared about squared of negative one and this these two kill each other these two kill each other so all the eyes are gone this and this are gone that's it so we end up getting x minus one x squared this and this can combine you get negative four x you got four and this becomes plus so it's plus five is that correct i didn't multiply the rest so let's multiply this out i'm pretty sure that's correct and then we just multiply it out so boink boink boink and boink boink boink so this becomes x cubed minus four x squared plus five x minus x squared plus four x minus five combine like terms this guy and this guy combine and this guy and this guy combined so you get x cubed minus five x squared plus nine x minus five is that correct after traditional's nice high fives right so we get the same answer and by the way gang i like when i'm multiplying stuff out i rather convert the i to the square root of negative one that way i see it visually it just makes more sense to me right dice power i think the algorithm way to solve the problem is to start with that and use long division to find the third factor but the square root of negative one is got to be plus and minus dice power right because the square root of anything is plus and minus or the even root of anything is plus and minus but i'm pretty sure the complex conjugate of the imaginary factor has to be present for the polynomial to turn out real yeah possibly i'm not sure if that's an absolute is that an absolute catholic traditions might know that and by the way the reason that the square root of or even root of anything is plus and minus is this right you asked you know ask yourself what's the square root of negative what's the square root of four so square root of four if you break it down two numbers that multiply to give you four not including one is two times two right so square root means if you got a pair inside the square root you can bring them out of single so that becomes two but the square root of four two numbers that multiply to give you four could be negative two times negative two so that's a pair as well and that can come out as negative two hence the square root of four is plus or minus two right yeah we need the conjugate to cancel out the imaginary term yeah right for that yeah but i'm not sure if uh it all it's always present is it always present it would always have to be present because in the question it said it has to be real okay yeah if it has to be real errsly errsly errsly one hi chi chou i've been recommending your content to a friend of mine who has just started studying math to be a teacher awesome awesome i hope they find it useful and my content is very much geared towards helping people teach mathematics right i i am teaching math but i sort of try to explain how it is that i'm teaching the mathematics so i hope they find it useful double or negative awesome that made more sense to me thanks chi chou catholic traditionals and dice power let me plug this in and see if we get it right be right back awesome double or negative that got it i think my problem was factoring out the that so factoring out this and then distributing three parentheses instead of just two now that uh now i can go take the quiz thanks again everyone i yield to the for awesome double or negative yeah and the kicker is when you get these these guys multiplying together don't multiply this into here first multiply these two together first because they are the conjugates so you're going to get things disappearing right and the conjugate of something is just when they when people refer to the conjugate like if it was x plus two then the conjugate of this is x minus two right you just change the middle sign right sort of the simple way of thinking about it okay should i take this down i'm gonna make it a clean board again just in case we get more math questions coming in good board a good board it served us a while over the years fantastic really fantastic really are you guys snacking on anything would this be okay x to the power of three i'm assuming is it is that supposed to be three times two or x squared right uh slick mic right any irrational solution in the form of a b c to the power of a half also known as square root c or square root c this would be a fun little problem right uh let me just double the negative right i got that part right but the damn uh Pearson software was having me go one step further and factor the combination of the two parentheses your way is faster and easier ah hey there how's your day going going well pandemic pandemic watch oh okay three x squared okay crap for Pearson night's a little comic oh you're doing chicho i taught my six year old how to play blackjack to help him count it seems to be helping yeah yeah for sure blackjack poker any card game is phenomenal to teach kids uh to learn how to play let's write down slick mix uh x cubed minus three x squared so x cubed minus three x squared minus nine x plus eleven is equal to zero minus or plus minus nine x minus nine x plus eleven is equal to zero so what are we trying to do with this she'll be counting cars into a six shoe in no time yeah uh pandemic watch and night's a little comic teacher how to play backgammon with one deck and if once she figures out how to do the counting right do do count to 21 and stuff like this and she gets really good at it teacher car counting the car counting part is this okay the simplest car counting i know and i used to do this in vegas because when i when i was playing in vegas uh they used to still only have two deck cards right and in late 1980s i was i wasn't even allowed to play in vegas i wasn't even 21 but facial hair used to get you a long way right and um simplest car counting method is this for ten jack queen and king make these positive one for aces you go plus two for two to nine you go minus one okay so what you want to do or the other way around you can make this a positive and make this a negative right negative negative when so as the cards come out for any numbers you get from two to nine just start you start with neutral zero right so you're starting with zero and as you see these numbers pop up you add one add one add one add one so the number here goes positive right when you see these guys come out you minus one minus two whatever it is so the numbers here are negative when the value of your account becomes positive in a big way right i forget what the positives were if you get positive 10 or something like this that means a lot of the small numbers are gone once you get into major positive numbers you increase your bet and the reason you do this is because in blackjack if you get an ace and any of the face cards you get paid 1.5 times your money right but if you lose to a blackjack they only take your original bet so that kicks up the probability of you winning to 54 percent more than the house right so the trick is this you do the count you also vary your bet okay now very difficult i haven't done the gambling scene for 20 years now i haven't been to vegas for like 20 years but but i've been to other casinos in the last well i haven't been to other casinos for like 15 years maybe now 10 years maybe now right but i haven't seen any blackjack tables with two decks of cards or one deck of card was ideal one deck of card or two deck of cards because this card counting method gives you an advantage over the house all right now i don't recommend teaching that to a kid but i do recommend that to teach mathematics bob's i taught my kid how to play stars at the casino luckily professor's is grading our uh scratch paper when we take the test nice if you get a sign or a parentheses or any part of the question wrong on the test it grays a whole question wrong oof i'm gonna care uh carrying a 97 percent because of him grading my scratch paper yeah paper and adjusting my grade he just wants to see we get the process not if we get a right number yeah spider man how are you doing dice power maybe my statement was slightly too strong in general the polynomial bling and bling equals bling bling bling bling is real if a times the oh dice power so this is proof of the conjugate ad e with bc is sufficient but not necessary necessary condition and you probably have to do the long division or guess and check like we did okay that's a pretty cool simple method it's a cool simple method of card counting here we use uh pierce and mastering if you get 85 percent you get plus five and if you get 50 percent you get plus two on your exam cool but you have to pass first crafter which is the only thing that matters free assange free assange free assange so let's go back to this question what was the origin of the slick mick would this be okay about right any irrational solution in the form of that aka square root of c that this could be a fun little problem so irrational solution so we're trying to solve this right if you're trying to solve this you're gonna do synthetic division okay so synthetic division i'm not sure uh is that gonna work one yeah one's gonna work right so we know one's gonna work and i'll show you how right so this is and by the way gang like people have issues with factoring they don't explain why factoring is important right let me give you a little lowdown of why factoring is important and that's the reason you learn how to factor gcf being the first type of factor and you learn right great taking out the greatest calm factor or whatnot for example right if you have multiple terms added together to give you zero right it's very difficult to solve this if they're all different terms very difficult to solve this right because these are all pluses however if you can take this expression if you can take this expression and convert it into things multiply together to give you zero right so let's assume you can take this rewrite this right into a times b times c times where's my c times c times d times e to equal zero this is easy to solve right remember this is multiplication now right times times times times why is this easy to solve because the only way you can have one two three four five or two or three or four or six or ten or a thousand things multiply together to give you zero is if at least one of them is equal to zero right one of them is zero one of them could be zero well at least one of them could be zero right so if that's the case then what you can do is say split these up and say a could be zero b could be zero c could be zero d could be zero e could be could be equal to zero and then you solve each one of these right so before we hit this up let me give you a simple example x squared plus five x plus six is equal to zero well we need to find an x value or more than one x value where we can plug it in for x and set this side equal to zero this is difficult ish if you don't do factoring you can factor this and go oh x x two numbers of multiply to give you six out to give you five is plus two and plus three is equal to zero now we've got two things multiply together to give you zero so you can set each one equal to zero so x plus two is equal to zero and x plus three is equal to zero so when x is equal to negative two and x is equal to negative three this equation is valid we can test it we can check check check for x is equal to negative left side of the equation right side of the equation the left side of the original equation is x squared plus five x plus six right so x squared plus five x plus six and the right side of the equation is zero so if we plug in negative two here negative two squared plus five times negative two plus six negative two squared is four five times negative two is negative ten plus six x, this is equal to zero. Hey, zero equals zero? This is a valid solution, right? That's what we're doing, okay? Easy. You can do a simpler question here. Let's do a simpler question where you don't even need factor, right? Or you don't need to do simple trinomial factor. We're just going to take out the GCL. What if you had this? 2x squared plus 6x is equal to zero. How do you solve for this? Well, you can take out a GCF process. How are you doing? Welcome, welcome. You can take out a GCF. GCF of this is 2x. So 2x comes out. You're left with x plus 3 is equal to zero. You got two things multiplied together to give you zero. You split them up, right? So either 2x is equal to zero and or x plus 3 is equal to zero. Divide by 2, divide by 2. So either x is equal to zero or x is equal to negative 3. That's solved. It's the solution, right? Easy. Makes sense. I hope that's clear before we move on to the third-degree polynomial, okay? For third-degree polynomial, and there's a whole bunch of different factoring techniques we use to factor polynomials, right? Or any other type of function, right? So for this, this is a degree 3 polynomial. If we can kick it down to a degree 2, we can use the quadratic formula. x is equal to negative b plus or minus square to b square minus 4ac over 2a, right? That's one of the formulas we know. So what we can do right now is try to factor this. Now, you can factor this using synthetic division. And in general, if you get any degree polynomial, the possible factors of this that you can do manually are possible factors of the last term divided by the possible factors of the leading coefficient. And the leading coefficient here is 1. So possible factors of 11 are plus or minus 1, plus or minus 11, divided by possible factors of 1 is plus and minus 1. Now, these are ones you can do manually. We can do it algebraically, right? Simply. So right now, what we got, well, these things divided by plus and minus 1 is the same thing. So possible factors of this that we can do manually are just going to be plus and minus 1 and plus and minus 11. If we can't figure it out that way, we need way more complicated methods of factoring to be able to break this thing down, right? Usually involving some kind of software. Okay. So we're going to try these guys out first. Now, just looking at this, I know positive one works, right? Because you can just do the mathematics on it. But let me explain to you how was they able to do that. Now, what does it mean when you're trying to solve this equation, right? When you're trying to solve this equation, this is a degree 3 polynomial. You can think of this as a function, x cubed minus 3x squared minus 9x plus 11, right? So what we really ended up doing is we're saying set f of x and f of x is your y. Set y is equal to 0, right? So ask yourself this, on a Cartesian coordinate system, on a Cartesian coordinate system, if this is your x and this is your f of x, which is really your y, right? When is y equal to 0? When is this equal to 0? Where are you on a Cartesian coordinate system when it's equal to 0? You want to find differential zeros. Yeah, you could do calculus on this, but we're not going to do calculus yet. Okay, we will, but we're not going to do calculus yet. I just wanted to do it using synthetic division, right? We refer to the technique you were using as the rational root theorem when I learned that. Yeah, and what it means is this. If this function is equal to 0, if this is equal to 0, it means why is 0? When y is 0, you're on the x-axis, right? If this is y is 1, 2, 3, this is negative 1, negative 2, negative 3, then this has got to be 0, right? That's what that 0 represents. Okay, the rational root theorem, right? Need some synthetic sign for doing synthetic division. You don't need it yet, right? So what we're going to do right now, okay, we're going to try out these factors because these are the factors, possible factors that we can use to plug in for x to see when f of x is equal to 0, when y is equal to 0. Synthogen, synthetic, right? So what we're going to do is let's check out f of 1. Let's find out what f of x is when x is equal to 1. Hey, what's up, buddy? Rambo, how's it going? So if we're going to do this, this is going to be 1 cubed minus 3 times 1 squared minus 9 times, oops, not negative 1, but 1, 1 plus 11, right? So 1 cubed is 1. Why is this negative 1? That should be 1, right? 1 squared is 1 minus 3 is negative 3. 9 times 1 is minus 9 plus 11. Oh, this isn't going to be... Did I write this down correctly? 12. Oh, no, it is true. 1 minus 3 is negative 2. Negative 2 minus 9 is negative 11. Negative 11 plus 11 is 0. Hey, cool, f of 1 is 0. That means when x is 1, y is 0. When x is 1, y is 0. We're here. Cool, 1 and 0. So we figured out one of the factors, right? We found out one of the factors. So what we need to do is take that factor out of this, right? Because what we just found out was this. Watch this. We just found out x cubed minus 3x squared minus 9x plus 11 is equal to 0. 4x is equal to 1, which means x minus 1. Here, let me write it this way. No, that's okay. Times something else is equal to 0. Basically, we're trying to factor that guy. So what we've done, thanks for teaching me how to count cards. You're welcome. Pandemic watch. It's hard to do it mentally to keep track of it. Think the A should be higher, maybe 2.5. You can do 2.5. It's up to you, really. You can make it a 3 if you want, right? So we need to divide out x minus 1 from this guy. And what we can do, we can do just long division, if you want, or synthetic division. We can do both of them if you want. Let's do both of them. Here, long division. x minus 1, x cubed minus 3x squared minus 9x plus 11. What do you multiply x by to give you x cubed? You multiply by x squared. So x squared. This becomes x squared minus 2x squared. Change the signs and add them. You get negative x squared minus 9x plus 11. What do you multiply x by to give you negative x squared? You multiply by negative x. So this becomes negative x squared plus x. And you don't need to bring the 11 down, but I do. Change the signs and add them. You get this kills this and that kills that. So this becomes negative 10x. Negative 10? Oh, I messed up somewhere. Oh, no, not necessarily. Did I mess up? I didn't mess up. What's going on? That's 10. You bring the 11 down. I'm going to pause this for a second. I'm going to do the synthetic division version. Think the Asia should be higher. It's not worth much these days. Of course, they use many decks. Yeah, they use many decks. It doesn't work very well. So let's do the synthetic division part. So x is equal to 1. We're going to go before I find my mistake there. Let's see what we end up getting. You take the coefficients in front here. 1, negative 3, negative 9 plus 11. Bring the 1 down. You multiply this by 1. You get 1. Add those guys. You get negative 2. That's why I put a 2 here. That's just a 1. So this would be a 2. There's my mistake. Here's my mistake. Watch this. X squared times this is x cubed. X squared times negative 1 is negative 1x squared. Then you change the signs and add them. You get negative 2x squared minus 9x plus 11. Then what do you multiply? x pi to give you negative 2x squared is negative 2x. So this becomes negative 2x squared plus 2x. Change the signs and add them. This kills this. This becomes negative 11x plus 11. What do you multiply? x pi to give you negative 11, negative 11. So this becomes negative 11x plus 11. Change the signs and add them. You get 0. So that's what remains. That's what we're going to find out here, by the way. This is negative 2. Then this multiplies this. That's negative 11. Negative 11 is 0. This is a 1 here. What we end up here is 1x squared minus 2x minus 11. I'm sorry if I lost you guys, by the way, because I'm going pretty fast through a few different concepts. But I'm assuming the person that asked this question, I think it was like Mick, you multiply the x by x to get, yeah, I just caught it. Usually it's a good idea to have two different methods going. If you're doing mathematics, especially if you're writing a test, because one situation, if it doesn't work out right, the other one might clear it up for you. In math, there are multiple ways to do things. So this guy, we can factor it now. You're looking for two numbers and multiply it to give you negative 11, add to give you negative 2. I can't think of any integers that do that. So for this, you're going to use quadratic formula, right? Rambo this year was an interesting year. Quadratic formula is x. Let's do this. Okay, I'm going to erase this part of it so we can do the synthetic division here, because we already got our expression there, right? So we just figured out what this is. This is x squared minus 2x minus 11. And we're still trying to break this up because we're trying to find out for what values of x, this will make zero. So we're going to use quadratic formula. x is equal to negative b plus or minus squared of b squared minus 4ac over 2a. So we're using this for this one. So that's going to be negative negative 2, which is 2 plus or minus squared of negative 2 squared is 4 minus 4 times a, which is 1 times c, which is negative 11, all over 2 times 1, right? So this is going to be 2 plus or minus squared of 4 times 11 is 44. Negative and negative makes a positive. So that's going to be 44 plus 4 is 48. 48 over 2. Let's break down 48. Let's break down 48 over here. Here, let's do it over here. 48 breaks down into 2 times 24. 24 breaks down into 2 times 12. 12 breaks down into 2 times 6. 6 breaks down into 2 times 3. Did I do that correctly? If we're trying to take the square root of 48, I'm sorry that this is so complicated that introduces many different concepts. No, don't be sorry. Concepts that people might not be familiar with. I was just looking for help with my own. Dude, I don't want to apologize. This is fantastic. This is the power of mathematics, by the way. This is taking concepts from grade 8, grade 9, grade 10, and grade 11, and grade 12, putting it all together into one problem, right? And what that does is puts everything at the perspective for people why it is they're studying something, right? Catholic Jesus, did you do it? Roots 1, and we're going to do it right now. Watch this. Square root of 48 is doink, doink. Square root means a pair can come out as a single, so 2, 2, 4. This becomes 2 plus or minus 4 square root of 3 over 2. 2 goes into both of them, so it's going to be 1 plus or minus 2 root 3, right? So to answer the question, the roots, which is what Catholic tradition has got, right? 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2. Yep, that's it. So the factors of this. I'm going to erase this part, gang. I'm going to take that out. I'm going to take that out. I'm going to take that out, so you see it in one shot. I should maybe tighten up my work, so I don't crunch it down, right? So what we end up having, and this was plus 11, yep. So what we end up having, if we were to factor this guy, is x minus 1 times x plus bracket 1 plus 2 square root of 3 times 1 minus bracket 1 minus 2 square root of 3, right? Yeah. Okay. I come instead, for us, I say come instead. I'm single. Awesome. Riving right now, Rambo's inviting someone to go to Germany to dance with him and process this game. So then this is equal to 0, right? So like we talked about, right? You got three things, multiply together to give you 0. I can simplify this one step first. Oh, this isn't 1. This is x, my bad. Yeah, we're not going to simplify this. It's just a bracket removes, right? So what you end up getting is, you got three things multiplied together to give you 0. You got this times this times this to give you 0. That means you can set each one equal to 0. So you got x minus 1 is equal to 0. x plus 1 plus 2 square root of 3 is equal to 0. And you got x minus 1 plus 2 square root of 3 is equal to 0. So this means x is equal to 1 is a factor. x is equal to bring them over. Negative 1 minus 2 square root of 3 is a factor or is a root where it crosses the x-axis. And x is equal to 1 minus 2 square root of 3 is an x-intercept. Right? Felix, how are you doing? Chicho, good news. I took your advice from the relationship stream about writing that girl. And note, nice. I went for a Christmas card and it went great. She wrote me one back and we've added each other on social media. Thank you very much for the idea. Awesome, Felix. I wish, brother, I wish I had the cojones to do what you did when I was younger. And I wish someone had given me that advice when I was younger. Maybe I would have done it. And kudos to you for doing it, brother. Kudos to you for doing it. Fantastic. Middle factor. Did I do it wrong Catholic tradition? Did I write it wrong? Or that one? That's fine, isn't it? No, no, no. I think that's correct. Process. Thank you for the tier one sub. Did I do it wrong Catholic tradition? Is it okay if I send you another question? I don't want to hug all the math help so I can totally leave it for the next stream. No, slick, we don't have any other math questions coming up. But I'm just going to expand this a little bit. Catholic tradition. Did I do it right? Randall, how are you doing? Let's do what kind of emote that we get. And Randall, thank you very much for the tier one sub. What did we get? Capture 2020. Nice. So check this out. What does this mean? 1 minus 2 squared of 3. What's 2 times the square root of 3? I'm just going to bring out the calculator. 2 times 3 square root. Where's my square root? So 2, just this value here. 2, the square root of 3 is 3.47, let's say. 3.47. So this is 1 minus 3.47. So if that's 1 minus 3.47, 1, 2, 1, 2, 3.47. So here's one of the x-intercepts which would be... Oh, it's negative 1. Hold on, let me erase that. Oh, no, no, that would be legit. So it's net here. Let's do this one as well. So this one would be negative 1 minus 3.47, which takes us to 4.47. 1, 2, 3, no, 1, 2, 3, 4. So here's one of the x-intercepts which is 1 minus 2 squared of 3 and 0. And the other x-intercept is 1 minus 2 squared of 3 and 0. And you want to know what the function looks like? You want to know what the function looks like? I'm drawing some Cheecho fan art. Ah, Felix, awesome. Cheecho fan art watching the stream. I'm drawing you striking down a technocrat as if you were a character from Attack on Titan. Yeah, striking down a Titan. Am I swinging around with those things? I'll send it to you on Discord when it's finished. Awesome, Felix. We'd love to see it. We'd love to see it. Attack on Titan is amazing, by the way. Have you ever made a woman? Quick process. I'll go. Good day, everyone, and enjoy math. It's beneficial for your spirit and your body. Indeed process. And again, thank you very much for the sub. Catholic tradition, Cheecho, I believe the roots are 1, 1 plus. Oh, I got 2 minuses. Oh, yes, that's right. This one should be plus. Thank you, Catholic tradition. I messed up. So this one isn't, this one is wrong. This one is over here. Because this one is because the negative one hits this guy too. My bad. Perhaps I have to. No, no, no, you got it right. I'm just gobbled up here a little bit. And this is a Cheecho brain fart happening, right? So 1 plus 3. So we're into 4.47. So 1, 2, 3, 4.47. This is the other one. So this guy becomes 1 plus 2 squared of 3 and 0. And if you want to know what the function looks like, this is what the function looks like. Okay, here we go again. Try this one, Cheecho, please. And then I can rewrite the, rewrite the night having my homework completed. Okay. Watch this before we go on. This is a positive coefficient in front of the highest degree. Okay. It's an odd power. Then the function opens up like this. So the graph of this guy looks like this. I'm going to do this in red. So you guys see it. The graph of this guy goes like this, goes through, goes, we don't know how high it goes. We got the Y intercept as 11. Let's assume it's 11. Goes up here, comes through 11, goes through this, goes down and then shoots up. To find this point and this point, we will take the derivative of this, which is calculus, and then find the zeros of the derivative. Basically, if we take the derivative of this, you would get, where are we going to write this? The derivative of this is going to be, I'm going to write it up top here. I'm going to erase this. Yeah, let's erase this. The derivative of this guy would be 2x squared minus 6x minus 9 and we're going to set this equal to zero. Right? And what you end up doing is, and this we can do, we can, ah, should we do this? Let's factor this. Minus I'll keep on building it, right? So, if you solve for this, for what x value is this function is equal to zero, you're going to get the x value of this. This has an x and a y and this has an x and a y, right? So, if you factor this guy, let's factor this guy. I'm going to factor this guy right in between here. Okay, watch this. If you're going to factor this guy, use complex trinomial factoring, we've done it, right? 2 multiplies in negative 9, so this becomes x squared minus 6x minus 18 is equal to zero. Factor this, you get xx minus minus 9. Oh no, it doesn't factor easily. We need the quadratic formula. I thought it factored easily, but it doesn't. If this was a 3, it would have factored easily. So it doesn't factor easily. So we're going to use the quadratic formula again and we have no room to use the quadratic formula. Okay? I hope that's clear everyone. Just clear as can be. If you're doing math 12, okay, and math 11. Math 11, this might be a little bit complicated. Math 12, this should be clear for you what you're doing. The calculus part, taking the derivative part, should be clear for you if you're in calculus class and free as much, free as much, free as much. So, slick, Mick, what's the other one? 3x squared. What are we doing with 3x squared? Slick, Mick. What's the scoop with 3x squared? What are we going to do with 3x squared? I'm going to pop a cookie. Oh, I didn't let us know. Apricot chocolate chip cookie. Cheecho, Cheecho's apricot honey chocolate chip cookies with whole wheat coconut flakes and coconut flour. Whole wheat flour too. Very yummy. Did I take down the differential wrong? My pooper scooper. You took down the differential wrong. It's not 2x squared. It's 3x squared. Oh, yeah, it would have been 3x squared. Poop. That's right. I'm going to Speedy Gonzales. So, it was x cubed, whatever it was, x cubed, plus, I can't remember the rest of it. But basically, if this guy comes down, it's 3x squared. And this was minus 6x, and this was minus 9. Right? I think that's what it was. And then we can just factor 3 out of this. So, this would be x squared minus 2x minus 3. And this you can factor x. Two numbers that multiply to give you negative 3 after giving you negative 2 and minus 3 plus 1 is equal to 0. So, the 2x's where we have where it came up and went down and came up would have been x is equal to 3 and x is equal to negative 1. So, this part would have been negative 1 and this part would have been 3 and negative 1, 3. And then all we would have to do to find this would be the f of 3, which was an original function. Right? So, it's pretty straightforward. Uncharted days. How were you doing? Thank you very much for the correction, Slickman. Thank you very much for the correction. Doing well. Man, when we're doing mathematics on this level, I just love it. My son is still miffed with this shift at school from algebra to geometry. Oh, really? He recently had to do some formal proofs involving centroids and medians of triangles. And I could hear him grumbling as he worked on the hilarious. I love it when you hear students go, oh, oh, oh, they get frustrated. That means they're working their brain. Right? That's a good thing. And then before they rip up the paper, you got to go give them a hand. Otherwise, they break something. It's good to challenge. Function f is such. Okay, let's check this up. Here's the next question from Slickman. Function f is such. f of x is equal to 2x cubed. I'm going to write this down. f of x is equal to 2x cubed. Let me write this down properly. Plus 5x squared plus 5x squared minus 4x minus 3. Minus 4x minus minus 3. Right? Show that x is equal to negative 3 is a root. And find other two roots. You got this. Yeah, if it's a root, Slickman, what does it mean if it's a root? What does it mean if it's a root? And anybody else, what does it mean if x is equal to negative 3 is a root? What does that mean? Grab apples. And these grab apples are great when you put the cookies in them together. What does it mean? And basically root to mean has like 5 different words. Right? Root could mean factor, could mean zeros, could mean solutions, could mean what's the word we're looking for? What's the word we're looking for? What is it? It's the one that tells you what a root is. What is it, Slickman? You got to let us know. x intercepts, exactly. Slickman, subscribe to your one. They've subscribed for three months. Woohoo! Slickman had to sub for the help on the last question also. Thanks for the subs, Slickman. x intercept, x int, if x is equal to negative 3 is an x intercept. What's f of x when x is equal to negative 3? What would it have to be if we're going to grab this? 1, 2, 3. Negative 3. The function, when it says x is equal to negative 3 is a root, it means the function goes to that point. So what's f of x? What's y? Catherine, sorry. I typed before you. That's the question I was thinking. Did not mean to be an annoying... No, that's good. We like the answer coming on. Catherine beat me to it, I think. But it's an x intercept. It is an x intercept. If it's an x intercept, then what's the y part of this point? Zero. So what we're doing here is, we're going to set this equal to zero. Three, oops, not three. Two. If I make little silly brain fart mistakes, let me know again. This is 2x cubed plus 5x squared minus 4x minus 3. We're going to set it equal to zero and we know x is equal to negative 3 makes f of x equal to zero. Which means what? Which means if we sub in negative 3 here, here, we'll do it here, f of negative 3 is going to be negative 3 cubed is negative 27. Negative 27 times 2 is negative 54. Negative 54. Negative 3 squared is 9. 9 times 5 is 45. Negative 3 times negative 4 is positive 12 and then minus 3. What is this equal to? That's going to be... Do we have it? So negative 54 minus 3 is negative 57. 45 plus 12 is 57. So this is equal to zero. So f of negative 3 is equal to zero. Cool. So we just proved that this was an x-intercept of that function. Always zero on x-axis and vice versa, I believe. And on the y-axis, x is always zero. You want a proof of that? Find the y-intercept of this function. The y-intercept of this function is when x is equal to zero. So set x is equal to zero. So f of zero when x is zero, what's y? That's going to be zero. That's going to be zero. That's going to be zero because x is zero, so it's negative 3. Cool. So it actually... 1, 2, 3. Here's the x-intercept. Here's the y-intercept. Zero and negative 3. So we found the y-intercept. We found an x-intercept. We need to find the rest of the x-intercepts. The rest of the x-intercept says this. Well, if that's an x-intercept, bring the negative 3 over, that means x plus 3 is a factor of this. So this thing breaks down into x plus 3 times something else is equal to zero. What is that something else? That's something else has to be a degree 2 polynomial because we divided a degree 3 polynomial with an x. We took out an x. So how do we find out what this polynomial is? Synthetic division or long division? Let's do both again. Let's do long division. Long division, 3... Not 3, x plus 3. x plus 3 divided into this. x cubed plus 5x squared minus 4x minus 3. What do you multiply x by to give you 2x cubed? 2x squared. This becomes 2x cubed plus 6x squared. Change the signs and add them. This kills that. This becomes negative x squared minus 4x minus 3. You're just bringing these guys down. What do you multiply x by to give you negative x squared? Negative x. Minus x. This becomes this times that is negative x squared minus 3x. Change the signs and add them. That kills that. That becomes negative x minus 3. What do you multiply x by to give you negative x? Negative 1. Negative 1 times x is negative x. Negative 1 times 3 is negative 3. Change the signs and add them and they kill each other. Zero. Cool. That belongs here. So this becomes 2x squared minus x minus 1. We can get the same result by synthetic division. The question says there may be two other roots just in case you need them. There are two other roots. That's factorable. We'll do it. But let me do synthetic division so you get synthetic division down packed as well. When you're doing this type of problem on a test, I'm going to emphasize this again. Know how to do both long division and synthetic division. It confirms your answer. If you get the same thing, right? When you do your synthetic division, you're 99.999% that you've done everything correct so far. That's a good way of knowing if you're going down the right path. If you're going to get the marks you need, it's confirmation. If they don't agree, you know you did something wrong. Figure out what you did wrong. It's a check. It's a failsafe. It's what you call it. When you're doing, if you have a company, it's called Catholic Traditions. What's it called when they do quality control? It's quality control. You're doing quality control of your own work. Learn how to do it. Synthetic division, we're going to take the coefficients in front here and we're going to use x is equal to negative 3. You take the coefficients 2, 5, negative 4, negative 3. 2, 5, negative 4, negative 3. I'm going to draw a line here so we don't get confused. Bring the 2 down. 2 times negative 3 is negative 6. Add them together. You get negative 1. Negative 1 times negative 3 is 3. Add them together. You get negative 1. Negative 3 times negative 1 is 3. Add them together. You get 0. This is 2x squared minus x minus 1. Quality control. Nice. Now we need to factor this. How do we factor this? Let me write this bigger so you see how we factor this. We don't need the quadratic formula. This is factorable. 2x squared minus x minus 1. Take the 2. Multiply by negative 1. x squared minus x minus 2. Factor this. 2 numbers that multiply to give you negative 2. Add to give you negative 1. Negative 2 and positive 1. Drop the 2 back in front. 2 and 2. Factor whatever you can and dump it. So this becomes x minus 1. This becomes 2x plus 1. So this function completely factor is so f of x is equal to 2x cubed plus 5x squared minus 4x minus 3 is equal to x plus 3 times x minus 1 times 2x plus 1. This also means your x-intercept are negative 3, 1, and negative 1 over 2. Right? There are two other real roots. And free-assange, free-assange, free-assange. Right? And if you're going to find these, 1. So 1 and 0. Negative 1 half. So here. Negative 1 half and 0. This is degree 3. Positive coefficient opens up like this. And the graph of this would look like this. Here. I'm going to draw it in red again. Let's draw it in red. This is going to go through here. Come down to a certain point and go like this. That's your function. Not to scale. Okay? Not to scale. Cool? Thank you for the help, Chichou. I better head my brain as tired after these problems. But that was some sweet math. Awesome. Slip. Learn how to do this well, man. Okay? Ridiculously important. This is pre-calc. The calculus comes in when you take the derivative and set it equal to 0. And you find these x values and you find the y associated with the x values and now you understand how the function behaves. And that's what we're looking for, right? We're trying to find out how the function behaves. That's one of the main well, THE main purpose of calculus or one of the main purposes of calculus is to understand how systems behave and functions represent systems so we can make predictions, right? Fun. Fun stuff. Catholic traditionists. Thank you for the help. I hope you like doing these random questions by the way, Catholic traditionists. It keeps us sharp, man. That's the way I look at it. It keeps us sharp, which is fantastic. And gang, if you need these as notes, you can just freeze them after the videos available. You can just freeze it, take a snapshot, and that's your notes, right? That's how I do it with my students, right? I step aside and they take a snapshot and we continue. And you have that stuff on file, right? I do great exercise for the brain. Great exercise for the brain. Love it. Love it. Love it. Here's the kicker. I told one of my students a couple of days ago, I said, listen, math is ridiculously important because it gets you. William, thank you very much for the bits. I told one of my students, look, mathematics gets you using your brain that nothing else does. And then he goes, well, that proves that math is not useful in the real world. I'm like, no, no, no, no. You're taking it the wrong way. It gets you to use your brain in a way that nothing else in the world does that you're studying right now. That makes you sharper. So when you do need to have access to this power, you have it already. It's like going to the gym and working out, making your muscle stronger, right? You become fit. You're not going to go in full capacity every day of your life, right? You know, if you go to the gym and work out and stuff like this, you've got big muscles, you're not lifting your maximum weight every time, but the power is there when you do need it. That's what mathematics is. The power is there when you do need it, right? Exercise your brain. Challenge your brain, right? Get yourself to a level where if some kind of problem comes up, you know how to handle it, right? Croomy Cury monster. Hey Chico, could you help me with a question? For sure. Let's try it out. Let's try it out. Thanks, Gryllam. Find maximum value of XYZ subject to maximum value. You need 3 equations to be able to solve 3 unknowns. I feel like Elder God would be making a pitch for creating the 9 things so too. Build your muscles and eating a lot of meat. So you got your equation here. 3X plus 2Y plus Z is equal to 12. 3X plus what? Plus 2Y. 2Y plus Z is equal to 12. You want to find your maximum value of XYZ? I don't think we have enough information, monster. So you're basically, this is a 3 variable and you're saying the volume of the variable is XYZ, right? So we got one equation. We got 2 equations. We need a third equation. We need another equation that relates X and Y together or something to maximize this. We need one more equation. Because what you would do is rewrite this in terms of X or Y or Z personally I would do it. And then the other equation you write in terms of Z are in terms of How would we do this? We need at least one more equation. And then we can maximize the volume. I was told to use the Lagrangian formula to solve this, if that helps. I don't know the Lagrangian formula. What's the Lagrangian formula? Catholic traditionals, do you know how to go about this? I don't know how to go about this. I got to look up the Lagrangian formula. What's the Lagrangian formula? Let me look it up. Lagrangian formula Lagrangian equation Lagrangian equation is a reformulation of the classical mechanics introduced by Italian-French mathematician Lagarn, an astronomer Lagarn. In Lagrangian mechanics the trajectory of a system of particles is derived by solving a Lagrange equation in one of two forms Either the Lagrange equation of the first kind, which treats constraints explicitly as extra equations often using Lagrangian multiplier or Lagrangian equation of the second kind, which incorporates constraints directly by judicious choice of generalized coordinates. Damn. I don't know this one. Let me look this up. For math, Wiki is okay. Let me see if anybody's replied. If there's just the two equations, is there infinite? I don't know if there'd be infinite. You can't do it. It's unknown. You can't define it. First time watching. Super cool stream. Thank you Mario. And welcome to our channel. It's fun. It's fun. Except this is my second and first one I watched was a couple of years ago. First one you watched was a couple of years ago. Philly. You came back after a couple of years. Right on. What language are you speaking to? I have no idea. I'm reading it. By the way, Aldergaard, you missed the whole conversation about working out. So you're taking, Lagrange equation is the first kind. It's pretty complicated. The second kind is so you're taking derivatives. So this is Lagrange equation. I'm not even going to bother writing the first kind. Lagrange equation, the second kind is d of dt of the function of, I don't even know what that symbol is called, over that qi is equal to that over, I don't even think this is, I don't even know what, I would have to look up what these terms are and everything. No, this doesn't ring a bell. I'm going to try another page. I don't know. I don't know this one. This can indeed be solved. You know this, okay, gang, Catholic traditions is going to do a live stream tomorrow to solve this equation using Lagrange equation. I don't know this. I'm sorry. Are you in the best calc? Calc 3. Yeah, this is like serious calc going on here. Basically, yeah, this is definitely beyond my math abilities. That's some advanced stuff. Gina, that's some advanced stuff. And this is of the second kind. You should see the equation in the first kind. This video gives a pretty clear example of what you need to do. Oh, dice power. You can't link up any videos. Only me and mods can link up videos or provide any links in the chat just because we're getting phishing scams and stuff coming in. So we have to put that into play. If you can link it up on our discord page on the math folder. Oh, no worries. It just shows it as what do you call it? Stars. Like on your side, you probably still see the link on the chat side. You'll see it's just stars. Like three stars, which means the link didn't come through. Let's get back into mathematics, all the God says. Paul says this is making me crazy. Yeah, mathematics is meditative. Catholic tradition is dice power. Post to discord, please. I could definitely use the refresher. Awesome Catholic tradition as gang. If you want to get this focus gang, if you want to know how to work this thing out, you got to go to our discord page in the math folder. And the math folder is in heavy topics. We should have a like topics math folder, but it's in heavy topics. And there's our discord page. Yeah, thank you very much dice power. Thank you very much. By the way, gang, at some point I'm going to once I create all my content by the way, gang, thank you for the followers. Thank you for the subs. Apologies if I haven't caught them. Okay, since I haven't caught them. Just because doing this, I have a hard, hard enough time trying to make sure I use, get the appropriate signs and the numbers in the right places. So thank you very much for the support. But just to let you know, as soon as I finish all of the content I need to create for all of high school mathematics, which is probably going to take me another 10 years or so to do, not depending on depending on how things go right, depending on how much support I can get and all that jazz how much energy I can focus into it, right? Write the modules that I need to. Okay, let's say five years at least, right? Once I finish all that stuff up, just before we get into the calculus, I'm going to start getting, relearning all the calculus that I knew before, right? Because I do have my minor in mathematics, but I've forgotten a lot of the stuff math. A lot of it. Okay, posted it in maths. Awesome dice power. I can't talk politics, but he has been reborn in Namibia. This is heavy. Marty McFly. Marty McFly. Awesome. Marty McFly. Fun. There's some fun stuff out there again. Sorry, dice power. I couldn't help you out. I wish I could, but we can only go so far, right? We can only go so far. For now anyway. For now anyway. Fun. Cookie. Cookie time. Cookie? Hi, hi. Could someone give me a quick, for your information on what it is we're discussing. Specifics on what mathematics, what math, mathematics section. We're mainly doing high school mathematics. A little bit of pre-calc for sure. Elementary school mathematics as well. A little bit of higher degree mathematics. This was much more higher degree than a little bit of higher degree than high school mathematics. So it's advanced mathematics, the question I was asked. This question anyway. We're basically doing high school math, pre-calc stuff. Honey, apricot, chocolate chip cookies with whole wheat flour, coconut flour and coconut flakes. Okay, I'm just starting to thank you. My pleasure. Barely two legs. Barely two legs. And this is basically me making, and other people by the way, there's people here that their mathematics is more powerful than mine. We're making ourselves available for a couple of hours every couple of weeks. Most of the time at least twice a month to do mathematics. We actually have another math session set up for next Tuesday. Tuesday 12 to 2 p.m. my time. We're going to do another math session. Okay, so I'm trying to get in at least two sessions a month of these things. Sometimes we do four. And free a sandwich, free a sandwich, free a sandwich. That's our nightbot reminding us to stay on top of things. These chocolate chip cookies because of the coconut flakes, they are flaky so you need like nice liquid, nice tea to legendary Rob Boss. How are you doing? Geometry, sure. We do some geometry for sure. Geometry and trigonometry are a game as far as I'm concerned. Free sausage. Where? Everybody needs to get some free sausage. Legendary Rob Boss, he won't. Maybe I was... I don't know what that is. We're taking down this complicated thing. Fun. Yeah, what type of geometry were you thinking? They need help with. We've got about another half an hour, 20 minutes left. We can definitely do if you need. Oh, free a sandwich. Sorry, I agree for a lunch. Man, I'm hungry. I want some sausages. The funny, funny, funny. Oh, man. I'm missing barbecuing. I think we're going to barbecue at some point during the winter. We've got to get the barbecue going again. German Southwest Africa. German Southwest Africa. Namibia. I figured Namibia was in Africa, what El Laga was saying. But I don't know what the Deutsche thing was. So I guess that just refers to when Germany colonized. Part of the greater Deutsche West Africa. Is it? Cool. College geometry. I'm okay for now though. Now, thanks. Okay. Depending on the geometry, I do high school geometry, trigonometry, pre-calc stuff, but some calc stuff. College geometry, a lot of it would involve integration, wouldn't it? To find the areas of shapes and stuff like this? Tumley? But you could just do straight up geometry with triangles and whatnot. Different proofs. Barely two legs. If I could sit in a recliner with a pertinent kitten while learning math in high school, I would have done so much better. Barely two legs. Everybody. Our current indoctrination centers, they're not really education centers, indoctrination centers are not designed for education. They're designed for indoctrination. They're designed to get people to submit to authority. As soon as you understand that, and as soon as you understand that you have to go through the system right now, and you can game it, right? Then once you understand how the system functions and you can game it to your advantage, then you do that until you can be free of this indoctrination and educate yourself, right? And as Barely Two Legs says, it's all about memorizing answers indeed, right? You can free yourself from it, right? And then you need to spend at least two years educating yourself into the inner workings of the world and teaching yourself science and mathematics and literature and you can do all of that. You can do serious reprogramming yourself in two years when you come out of high school, right? Even out of university you need to sit down and really process what just took place and re-educate yourself, right? Read books that really, it's very, very important. Catholic tradition is chichu. Just curious, when do students typically start to learn trigonometry, unit circle identity? Your neck of the word. They do intro unit circle in grade 11 like a small chapter, right? They learn about radians and then they stop and then they don't continue that until grade 12. Grade 12 is the main course, main section that they take when they learn about unit circles. Identities they don't touch until grade 12. So there's a small little intro in grade 11 and then it's grade 12. So grade 12 is when they deal with the unit circle, graphing sign and cosine and tangent and really understanding what the trig identities mean, what the unit circle is, learning to do proofs, using identities and stuff like that. Which is really unfortunate because that stuff is absolutely beautiful. And that is, depending on the school, they either take two chapters to teach that or three chapters to teach that. About three months yeah, two to three months of grade 12 in a 10-year school year is focused on trigonometry. That focus on trigonometry takes a lot of people out of the game. It knocks them out because they don't do it well. It's all about memorizing the unit circles and the identities and stuff like that. Which is garbage. And that's the way I was taught. I really didn't appreciate how powerful, how beautiful trigonometry was until I started teaching it and I'm like, my god why didn't they teach it to me like this? Why didn't they explain this stuff to me? Which is the reason, by the way, I have a trigonometry playlist and I'm halfway through the trigonometry module that I want to make, which takes you all the way to identities. And you can go to our trigonometry section and you can look at those things. And this ASMR format is a phenomenal series of trigonometry stuff. Gina, fun fact, I was convinced under a massive radio... I was conceived of... I was conceived under a massive radio telescope in Swatko Penand in Namibia. Really? Conceived? Oh, your parents are... your parents are cool. Philly, Philly Dojo Wait, hold up. Are you saying our education system is garbage? No way! Rolling on the floor laughing. Yep, then you know it. Everybody knows it. Seriously, everybody knows it now. Sparks. How are you doing? Good afternoon, good afternoon. Pandemic watch. You should SETI. SETI SETI. Oh, I know what SETI stands for. Extraterrest signal. What is SETI stand for? I forget. I was unteachable at school. I was suspended at age 5. It didn't get much better Elder God. You needed to eat less protein where you were younger, Elder God. You went crazy at school. But, man, I've worked with a lot of students over the years that had seriously hard time at school. And they ended up being some of the most brilliant students I've ever had. And they excelled, right? The system if you're really smart in school, you want to go faster. The system slows you down. No, no, no. Slow down, slow down. But you're your energy just wants to do, do, do. And these guys trying to hold you back. It's like trying to tame a wild stallion and they're trying to break its legs. What a horrendous system. What a horrendous system. Absolutely disgusting. They were out there looking for aliens. Ha, ha, nice. Barely two legs. All my personal fun facts are morbid and hard to believe. As far as the truth is out there, the truth is out there. Search for extraterrestrial intelligence. Search for extraterrestrial intelligence. That's right, SETI. Search for extraterrestrial intelligence. Nice. Thank you. I mostly failed math through high school until I got a tutor that taught me four years of high school math in two weeks for the ACT. And two weeks is not long enough to learn all of high school math, right? But it's long enough to pass tests, right? Are you a teacher? I've been teaching mathematics and physics for 20 plus years. Not in an institution. I'm not teaching an essentialized institution. I do private and group sessions and I work with certain schools, independent schools and I do work with certain independent schools to teach their students. But I don't go inside an institution to teach. I wouldn't last, right? Create chaos. Actually, I was very intelligent. I was like being in a room of goldfish. It is unfortunate that trig instruction in high school is often poor, so poor. Such a powerful subject in engineering, for example, trigonometry is critical in the analysis of processing of signals. Physics, too. Signal processing filters. It's everywhere. Sound, light. It's everything, right? Just use e to the power of i theta. No trig needed. Indeed, you could. But no, a trig is beautiful. They used to teach a lot more. By the way, just to let you know from what I understand from my students, because the school year shortened my part of the world, they've taken all of high school math that they used to teach in like 10 months or semester based system and they've crushed it down to 10 weeks. And because they don't have enough time to teach all that content, they're cutting back 30% of what they're teaching kids right now in school because of this whole lockdown pandemic thing. So they've already, they had already gutted math education tremendously. They don't touch e. They don't touch conics anymore. They don't do a lot of things. They've cut, they already gutted math education in my part of the world compared to like 15 years ago by 30%. Now they're gutting it another 30%. Man. Man, I wish I had you as a tutor back in school. Yeah, it's bad. It's bad. Oh, they're gone. I would head straight to the library to read books at my level after school and eventually I went to the library instead of school. Haha, nice. Yeah, it's crazy. It's such an injustice, Gina. Um, look, I'm talking with my students. I'm like, oh my God. And my students are like, yeah. Like here's one section they've cut out of one of the grades in my area. They took out personal finance. It stress rates and stuff. So in grade 11, right? So they took out the section the chapter, well we got no time to teach kids how to do personal finance and figure out interest rates and stuff. So let's throw it out the door. Crazy, crazy. The poor and stupid are an easier her to manage. Indeed, barely two legs. Yeah. As they say the masters will not teach you anything that'll set you free. It's your duty to teach it to yourself. If you are sitting there and you think math sucks or math is hard and you don't want to do mathematics, you're a fool. Right? You're a tool of a centralized state and you're a slave. Educate yourself. Period. End of story. And if you go, oh, hard, hard, yeah. Yeah, it is hard. It could be hard, but once you start doing it, oh, you get stronger and stronger and, you know, those 10 push-ups don't seem that hard anymore, right? Talk to Elder God. That's a thousand a day. Catholic traditionalist Elder God sounds a bit like my freshman year in college, except that I eventually went to the pub instead of either the library or school. I'm kidding, of course, he says. Student loan good. Think for yourself. Bad. Yeah. Gina. That's what they try to do. And free assange, free assange, free assange. Three thousand a day. My apologies. All we got. Three thousand a day. Right? Wow, wow, wow. Gang. Should we call it a stream? Fun. That was good math today. And stomp chicho. Go to discord. Find out how to use the Lagrange equation. Higher level calculus to solve that three variable problems using different methods. Right? Aside from that gang, thank you for being here. Thank you for the subs. Thank you for the follows. We got another eleven streams in the next two weeks. Sparkles. Are you ending the stream? If so, can you do a final math question for us to ponder a while we go? Yeah, for sure. Do you have one in mind? Cool stream. Philo Dojo says. Sad I discovered at the end. I'll be back though. For sure. Come back. We're going to do another math one next Tuesday, 12 p.m. And we got current events tomorrow. We got movies Saturday, movies Sunday. We got personal finance. I believe Monday. We got math Tuesday. We got what do we got? Music next Thursday. We got comic books on December 12th and 13th. We got cooking stream on the 16th. We got meditation stream on the 17th. And we got another current event stream on the 18th. No surprises. Love it. Oh, you want a surprise? Oh, comics. Yeah, we're going to do two days of comic book readings. What you have in mind? Ah, I got a comic book haul coming my way. Two of them, actually. And if they get here, we're going to read two comics from those comic book hauls. But if they don't get here, I got a lot of comic books that I'm going to choose from. So many brutal current events. What you have in mind? Lechelon. Chicho. My timing was bad. I just came at the stream ending. Oh, barely two legs. Chicho, you inspire me to go back and listen to timelessness by Fear Factory. Nice. Have the day you have, sir. Chat a day for you as well. Nice. Math question? I don't know. What should we do? What's a good math question to get you pondering? Find the solution for the following system of equations. Y is equal to 2x minus 1. Y is equal to negative 3x squared plus x plus 2. Just making sure it has solutions. Solve this system of equations. And if you solve it, post it in our discord page and I'll take a look or we'll take a look and see if it's correct. Okay? This was my first Chicho stream and I loved it. Definitely be back next time. Awesome. The same. Thank you very much for dropping by. Thank you very much for being a prime gaming I don't know if that means you're prime gaming sub or not, but thanks very much for being here and thank you for the love. Gonna screenshot. I'll look at it. I'm heading home tomorrow. Nice. The government of the university is going home between three to nine December. I'm going to hide in their midst. Perfect. Got it. Okay. Sparkles. And don't forget, when you do this, post it in our math discord, we'll take a look. Okay? If there's any problems any mistakes, we'll point them out. It should be an intersection. This is a parabola. This is a line. So this is trying to find the intersection between a parabola and a line. And there's three things that can happen. The parabola, this opens down. So let's assume that's the parabola opens down. They might not intersect. They may intersect at one point or they may intersect at two points. Which one is it? Yeah. Why was six to scare the seven? Oh, I know this. I've heard this. Because eight came next. Because eight... Oh, what is it? Because seven, eight... Oh, because seven, eight, nine. Oh, I knew it. I knew it was an eight in there somewhere. Just couldn't figure out the rest. Seven, eight, nine. I can't remember jokes. Gang, thank you for being here. If you want to follow this work, come on patreon.patreon.com. If you want to support this work, Patreon is a great way to do it. Everything's layered on mathematics. Everything's layered on mathematics. 1000 plus videos on YouTube. 400 plus streams on Twitch. Lots of mathematics there. Lots of stuff related to mathematics. Me, see how are you doing it? Long time, brother. Long time. I don't put anything behind Paywall's gang. If you follow this work and if you like what you see and if you do have the means, supporting us through Patreon is a great way to make sure we continue to do what it is that we are doing. Streaming on Twitch. Right here. The chat. If you want to participate in it, Twitch is where you want to be at. Gang, thank you for the followers. Thank you for the subs, mods. Thank you for taking care of business. And everybody, thank you for the questions and thank you for the interaction. Oh, my God. My mind is like a computer. I can remember everything. Should I add math to my credentials? Yeah. Math should be in everybody's credentials. Thus, that would be my thing I look for. If I was hiring, if someone says they know mathematics, that would be like a huge plus. Right? I do announce these live streams 30 minutes before we go live on Parler, Elo, Minds, VK, Gap and Twitter. And we do share additional content there and we do have a Discord page. You can come on our Twitch channel anytime in the chat and go exclamation mark social and it'll give you all the social links. And we have a Discord page where you can join and we've got a few different folders, channels there where people are talking about a lot of things, including mathematics. For streams, when we don't have any visuals, where we're recording a lapel mic, the audio is being uploaded to soundcloud.com forward slash chico, C-H-Y-C-H-O as podcast. It should be available on your favorite podcasting platform. VC, damn. Mr. Stream, I'll be at the next one. Awesome. We've got another 11 coming up in the next two weeks, VC, so lots of opportunity, lots of stuff to join in, including another math one next Tuesday. And we will be uploading the stream to YouTube and Bitshoot. And if you want to support this work on those platforms, you can like, you can share, you can comment. You can participate in the discussions and if you're on YouTube, you can join YouTube membership. There's a button there. And for those of you who are supporting this work through YouTube membership, thank you very much for the support. And gang, Patreon, thank you very much for your support on Patreon. I know there's been a lot of you guys there that have been supporting this work. And it is in large part because of your support we're getting there, because of the support we're getting on Twitch, because of the support we're getting on YouTube, that we're able to do this. Okay. And the direct support coming in. Thank you for being here, gang. Long live to you. Peace, everyone. And I'll see you guys tomorrow if you can make it. Tomorrow morning, I believe. 8.30am. Let's talk some politics. Bye, everyone.