let's grab a seat make sure we're running okay yeah should be a lot of nice hi everyone this is chicho today is march 21st happy easter happy not easter happy spring happy solstice i guess or equinox he solstice is equinox either way uh happy march 21st hello spider-man how are you i'm just gonna pop out the chat here and today we're doing a live stream open discussion well not open discussion but open discussion but math drop-in tutoring session okay and we've done a few of these and basically we're doing high school mathematics almost anything goes except hardcore statistics and permutate um calculus okay zemi 002 how are you doing catholic traditionalists how are you doing how are you doing welcome to another live stream and mathematics we've actually had a couple of people actually more than a couple of people i asked for this math stream uh which is fantastic right mask of raven how are you doing how's life welcome welcome i'm looking forward to the math stream good break from uh well a good follow from the 10 by 10 math puzzle and a good break from the more the things that have occupied people's minds on the last little while one little while last few days vc pow wow vc how are you doing how's life hope you guys are enjoying your saturday yo yo yo intro kui intro kui how are you doing hope you guys are doing well west coast of canada sunny very nice very nice it's uh interesting times we live in always always great just been playing a lot of animal crossing oh dude spider-man i saw lineups in toronto for people lined up yesterday to try to get their uh get a copy of uh animal crossing by just line up out the door going around the corner some people were abiding by the social distancing of three meters uh at least one to three meters or something some people bunched up together it is what it is right always been making how are you doing james david satin welcome welcome hope all is well doing good we did a little uh food run yesterday got ourselves some more eggs some cabbage uh some onions some veggies basically veggies is the food that doesn't last as long except with cabbage onions potatoes but some greens we got some greens and stuff are you familiar with discrete response systems uh circus stuff no i'm not unfortunately intro kui i'm not i don't think so like i might know uh if it's not calculus written it's a linear algebra i need to review my linear algebra um i know i used to know it very well right i taught it to myself and i knew it really well with determinants of matrices and stuff that's what it sounds like um discrete response systems and if there is demand for it i'll review it but i've forgotten how to do multi uh multi variable equations to solve them and stuff uh because i've been focusing on high school mathematics right wow that's insane i just got it digitally yeah no point in going out to get it if you have internet i do understand people love physical copies though yeah all of the send uh pandemic streams all of these pandemic streams must do must do right must do must do and as before if there's any math questions police post away uh we'll deal with the mathematics but it is an open discussion we can talk about you know almost anything but preferably we keep the politics and politics anyway to politics streams laplace transforms oh dude i used to know laplace transforms like uh yeah i would have to review it i used to i got my minor in math right so you know i did all that stuff but i haven't done it for so long so long right i have no idea how to pronounce your name hurt hurt i'm in the middle of that right now mask of riven is that what you're doing right now laplace transforms eight hours a day uh revisions just for levels to be canceled with teachers predicting me bees meaning i'm getting rejected by my oh dude really tachi ha it then tachi ha yeah i i got a feeling i had like some people are getting burned because of all this all these cancellations with school systems and stuff like this right so hopefully the system will sort itself out but keep in mind it's not important to go through things rapidly enjoy the process right so some people are going to get burned there's no doubt about it but take it with a grain of salt take it you know what they tell you uh don't panic through it and don't don't put the blame on you know later on if things are a little hiccupy don't just get stuck in that loop saying it was this it was this because it happened and stuff like this just roll with the punches really that's what i'm really trying to say right um as well no matter how bad things get as long as you're doing the best with the situation you're in it will improve right so if you keep on optimizing doing the best with what you've got at some point it's going to be exactly what you want or what you need right my degree is in physics laplace transforms make me sick i always be making now i gotta lick this up again i forget what it refers to i think it's yeah i can't even say uh it's got to be some kind of filter system taking from one camera function and what do you call it on top of another function no autistic how are you doing hey man just just dropping it this is actually the first time i've managed to catch your live originally found you on youtube thank you for popping by thank you for popping by i've been very active on twitch and loving it here by the way and mainly focusing on doing the live streams and loading them on youtube and bitching and stuff and trying to shoot some videos in the background and edited videos and load those up um one of the reasons just to let you know is well no we won't get into that but we took this year as well we took it this year as well for the past transform welcome we're glad to have you for sure finna ma bob bob how are you doing welcome welcome i'm turning 20 this year i feel like i'm losing time no that's what the system is trying to make you feel don't feel that way really oh that's the plastic right there um the function is equal to the integral of the function to the times e to the power oh man that's like bringing back nightmares but uh uh tequila techiha do not be in a rush to go through life that's what the system is has embedded in you break that time based education that you you've been implanted with okay that's a control mechanism enjoy the process enjoy the learning there's nobody nobody chasing you right that you have to get this done by then this but if you've set those time frames for yourself fine and dandy but be flexible more have a longer time span in mind than the shorter ones the shorter ones are okay you adjust accordingly right but try to figure out where you want to be right who you want to be how you want to interact with the world and everything else will fall into place right just make the best of what you got right as this situation develops they may uh reverse that decision yeah i agree like things are not going to play out the way a lot of people think dice power how are you doing it's a shift from the time domain to the frequency domain not a bad way of saying it oh that's the plus transform from time to frequency that's what it is isn't it from time to frequent i gotta look this up now the plus transform that oh man that rings a bell big time in mathematics though the press transform is an integral transform named afters and ventricle uh pierce simulopress it transforms the function of a real variable t to a function of a complex variable s the transform has many applications in science and engineering the process is similar to the Fourier transform yeah which is linked up to the Fourier transform and Fourier transform uh i dealt with a lot more than the Laplace transform if i remember yeah for sure i did right but that dice power what you said also applies to uh i forget who it was that feels like in a rush i'm gonna do my best to make some lemonade out of these lemons yeah minimum values of minimum values of nine minimum values of that that let me write this down i don't know if we can do that without doing calculus masquerade but i'm gonna write it down uh i'm just gonna catch up with co uh chat close to the power four uh four x that's the way we're gonna write it da da da yeah minus 12 uh cos squared that's gotta be cos squared x plus seven plus seven okay let me write this down i mean first thing i would do is just take the uh uh what do you call it uh factor it right set it equal to zero but that's going to give you the x intercepts uh the minimum values if we took the derivative of it and then we would find uh where the slope was zero is and then we set it equal to zero so if this is a function right if i remember my calculus you take the derivative of this right the derivative is basically the slope of this function and wherever this guy is going like this the slope here would be zero so you find those points right so you set the derivative of this equal to zero but is there a way to do it without calculus is there a way to do it without calculus we can graph it i think i should be able to graph it it's all perspective i do anything to go back to when i was 20 and i'm only 20 say i would not spider man i would not go back to when i was 20 i wasn't what i know now took a lifetime to learn so far all right uh i wouldn't go back to when i was 20 laplace transforms takes a function of discrete variables t to a complex variable function make the best of it enjoy the ride learn math love your hobbies that's it gina how are you doing welcome welcome laplace transforms are very useful in analyzing circuits with time-dependent elements like capacitors and inductors cool i didn't use the class transforms very much i use more Fourier transforms and i would have to look up where Fourier transforms where we use them how it applied to us uh because i didn't deal with circuitry too much i dealt with electromagnetic and magnetic methods a lot right hello there i don't have time uh time to stay but i wish you all a good day wherever you are stay safe uh stay safe i guess and healthy and enjoy some math of course of course thank you very much for dropping by handy and giving us uh wild wishes dice power applies to Fourier transforms also i think the Fourier transform is just the real part of the little plus transform or something like that cool you can okay you can do it without calculus okay we try much love you too awesome bob hello all same here when i was 20 i did a lot of stupid things and wasted my time yeah but learned from the lessons hopefully right hello chico we're on a tiny little planet in the vastness of a near infinite spans time really has no meaning agreed agree jina yeah that's a good point i am still young so i bet when i i'm older and wiser i will not think that would know hope you're making the best of self-quarantine um michigan up to 550 cases now 554 if you count death oh coolio how are you doing you can recommend uh can you recommend books on anything to learn how to do basic proofs uh i could never understand them at the freshman level math at tommy t honest i had a hard time with proofs as well i memorized proofs i didn't try to drive them except for you know minor ones right like the quadratic formula i could drive it right i could do some proofs regarding just geometry and stuff like this but when we get into when we when i was studying mathematics when we got into hardcore proofs i really had a hard time bringing it all together i remember one proof we had to do for geophysics where it took three pages like three eight and a half by eleven pages and i memorized the whole thing i because i didn't understand all the functions we were bringing in so i never really got a good handle on proofs myself either and there was never a book that anybody recommend or any books that i was given that even came remotely close to giving a better understanding of how to do proofs and need help solving for systems for math okay money man oh money man how you doing you were asking about the math stream what's the question you have regarding systems because i'm pretty sure we can do that faster than we can do this one uh distracting myself with weird wine brunch and chicho streams awesome coolio listen it sounds like a good Saturday right i'm 18 now and trying my hardest to not waste it but i'm worried that i'm trying to hard too hard and uh i'll miss the good stuff uh bob living is not wasting time really like some people like wasting time what's wasting time getting wasted every day drunk out of your mind every day for a number of years that's not good you're to a degree wasting your time right and ill health uh but you're 18 you're just starting to accumulate information really hopefully you're out of high school you're out of jail so you're experiencing life with free free quotation marks open eyes you're not wasting time you're sampling sample to your heart's content make sure whatever your sampling doesn't take you out of the game but for sure make sure you keep your eyes on the prize and whatever you're sampling make sure you're accumulating the power you need to be able to process all this information that is coming your way and to use it to your advantage that means two of the main things you have to learn is mathematics and your natural language know how to communicate because that's about communicating information okay so don't worry about too much about wasting your time just make sure you're taking care of business right if you're taking care of business you can sample whatever you want people other people might say you're wasting time some people might say that's the best way to spend your time here's a fun one prove the world is around mathematically to educate any flat earthers passing through we could do that at some point all right it's just a let me just look at the curvature look at the ship coming across right you see their top come in and then get bigger and bigger that's as simple as it gets right as someone who teaches seniors now it's really hard and try to just live in the moment try to just live in the moment how to prove it by Daniel's I was looking at graduate level statistics and it looks like nightmare it's all crazy proof uh graduate level statistics yeah there would be a lot of proofs like I didn't reach that level I went to like third year stats right I was more interested in the applying the statistics into the real world processing the data not coming out with the proofs right book of proofs by oh that's a book recommendation awesome uh book of proof by Richard Hammond oh Richard Hammond Richard Hammond is amazing hold on I just got to find his face there's a lecture series I've been watching of literature Richard Hammond and I've linked it up before does he have a book on proofs hold on this is a different Richard Hammond Hammond is Hammond not hammock Hammond it must be Hammond wait a second Hammond I think he wrote down hammock hammock is it it must be Hammond no it's not oh god who's this guy math hold on book of proofs book uh proofs oh maybe this is a different person I'm thinking of Hammock book of proofs for Richard Hammond oh no I don't know this person I don't think sorry gang it's just no no I think this is a different person okay well I don't know this book this book sounds cool hammock not Hammond okay hammock yeah I looked it up it's a different person I was thinking of thank you for the book recommendation by the way with substitution but use whatever numbers hey Chico uh money man did you post the I don't have an exact equation sure we could do that with substitution okay let me do one for you with substitution and we'll deal with the trig finding the minimum of this a lot of night night school in the Canadian edition system really didn't work for me so I feel like I know nothing not to mention if you can solve the problem will be the best generation to lead the new world just my opinion hold on I think despite the number of problems that the current generation is dealing with I feel like the younger people will come out as the most well-informed generation if we work the Kulio I have no doubt the younger generation the people have been teaching their processing speed is insane okay insane okay so they're they're much wiser than when we were kids when I was a kid just letting you know man okay I was a Canadian edition system that that that finally falling in love with math learning in my own way the Chico discord has helped me a lot okay awesome Bob awesome multi-line trinomials multi-line trinomials pain in the ass I wish we'll do one I'm not sure I wish I knew if I was allowed to share some of my online texts from my classes mask of raven for sure you can post it on our discord page mask of raven if you have posted on our discord page for sure your daily dose of cyanide what's 1000 minus 500 580 that's going to be 420 that's April 20th isn't it they don't tell you that centralized education is meaningless unless students learn what learning learning method works best for them schools tend to use the approach of what style works best for most people yeah just your desire to learn puts you far ahead of the rest yeah and the box gets smaller and smaller in the centralized education system right so if you don't fit into the box focus focus focus don't fit into the box you're considered to be this right learning something they give you a tag on that right I consider that being your processing speed is much faster than the box allows right your short circuit in this the system so the system saying oh purge purge purge I don't know if that that is that is true centralized education use the approach of what style is best for corporate interest not what is best for most people what is what is best for the system that's what the centralized education system does right and the system is run by corporations and centralized institutions so that's what they allow which is we're seeing it collapsing right now right baku baku that school prices are inflated only practical might uh practicals might require campus support rest can be done online yeah in other words the free market determines RJ definitely not free as you put it in quotation marks oh no how you're doing okay system was equations using substitution you said right substitution who said money money money money money I don't have exact equations substitution let's do a substitution problem okay let me give you an equation we're going to keep this one up here okay let's do a substitution here we'll draw a little breaker so we'll we'll do a quadratic and a linear okay so I'm going to let the chat do a sting gang if there's anything that comes up that's directed towards me after we do this example post it again when I'm reading the chat and we'll do this one we're definitely going to take a look at but let's do solving a system of equations two equate we could do three as well but let's do two equations using substitution right so let's assume we have one function which is a line which is two x minus four and let's assume our second equation is f of x is a is a quadratic right let's assume our quadratic is x squared plus 5x 56 right so 15x minus 56 plus 56 plus plus minus minus minus minus minus plus no 56 is too high let's do this hold on let's reduce this that way I can graph it properly right because I want to graph these as well okay so let's call this minus 10x minus plus 24 okay so we want to solve the system of equations so what we want to do right now what's up chichou fat boy fat how are you doing the short the short chat right so what we want to do is find out when they say solve the system of equations and we've got a quadratic and a linear sometimes it could be usually they introduce this to you with both of them being linear and we do have by the way here let me show you this one we do have videos out there where there's one of them here I'll show you this one if you look at this video this one we talk about I go through how you know what's required to solve a system of equations using two variables as well as using sorry a linear system of two equations and linear system basically of three variables right so you need three equations I'm talking about the pattern so this one is a pretty good video okay that runs you through how you end up doing this but we never I don't think we did one that's a quadratic and a linear so if you're going to graph this first of all you do this here we're going to make a general graph very simplified version of the graph right so what you would do is graph this guy so this is a linear equation y intercept is negative four slope is two right so one two three four and the slope is two so you go two up one over so that's equation number one right that's what you number the one whenever you're doing these things number your equations right when you're graphing them and always try to graph them because that gives you a better idea of if you're close to getting the equation or you're not right this one the simplest way to graph this you could use the completeness square to graph this and we've talked about this we have videos if you go chicho completing the square here completing the square completing the square you'll find at least two three videos of four five videos of us doing these right when you're trying to graph a quadratic function but there's a simpler way to graph it you just graph it based on its x intercepts right so first thing you can do is factor this thing two numbers i give you 24 i have to give you negative 10 x minus six x minus four right add them together you get negative 10 multiply them together you get positive 24 right and then what you can do is set f of x equal to zero so solve for this solve for this one this is equal to zero when you're setting f of x is equal to zero you're setting the function equal to zero that means you're setting y equal to zero because this is the y axis is really your y right so people have a hard time really appreciating what this means you can set the function equal to anything and solve for it and you're basically finding trying to find out what x is when y is whatever you set it equal to be right so how are you doing hopefully this will help you appreciate math a little more right and then the power of zero and we do have videos on that type in chicho the power of zero you'll find how we're doing this if you have two things multiply together give you zero two or more you can set each one equal to zero right so you just go x minus six equal to zero x minus four is equal to zero so x is equal to six x is equal to four those are your x intercepts right so one two three i should find out where the y enters where the x intercept is here right the x intercept here is two right let's go for equation one right if you want to find out where across is the x axis you set y is equal to zero right so zero is equal to two x minus four bring the four over four is equal to two x divide by two so x is equal to two so my graphs not to scale right so i'm going to erase this so this is one this is two this is three let's extend this a little bit further so we have the right graph approximately anyway so one two three four five six okay so that's where this function crosses the x axis and our parabola our quadratic function crosses the x axis at four and six so one two three four and six right so let's extend this guy right we're going to go into our calculations right and we're going to put equation one down here so we know this is equation one or the graph of function one right so those are x intercepts that's a parabola we know that opens up right and we know the vertex is going to be right in the middle so take the average of six and four you get five right so we know the graph goes like this right we just want to find out how far down it goes before it turns up again right so what we could do is just plug in five for x and find out what y is right and it should pop us here somewhere what i could do is pop it here f of five is equal to five minus six times five minus four five minus six is negative one five minus four is one so that's negative one so when x is five y is negative one x is five y is negative one so the graph goes like this right let's go through it right let's go through this too okay right because we've already gone through we've done the calculations for ourselves we just want to graph it to get a better idea of what's going on so our solutions when we're trying to solve the system equation our solution is where does this that's what it's asking you when does this equal this so we're trying to find out when they cross like this right we're trying to find these two points this point and this point okay how do we do this using substitution all you got to do is just set the first function equal to the second function because at this point this x is going to be the same as this x and at this point this y is going to be same as that y i'm just going to call this f of x right at this point this x is going to be the same as that x and at this point this y is going to be the same as that right i know it looks scribbly because you would have more room to play around with I'm trying to give the background as to what it is that you're doing when you're solving a system of equations. You're trying to find out if the two functions cross. When does one equal the other? Do they intersect? Are they parallel? Do they have no solutions? Are they the same thing? Do they have an infinite number of solutions? Right? So all we do to solve the system, what we can do is just go, oh, let f of x1 equal f of 2x. All you do, you set this equal to this. Does that make sense? I hope that makes sense. So in terms of substitution, I'm doing a substitution, which is, it's weird to call the substitution because you're setting equal to each other, but it is substitution to a certain degree. It's defined as substitution. We'll do a different version of substitution in the next question, a quicker one. So what you can do is here, say, let this equal to this because this y at this point is going to be equal to this y, which means at this point, this y is this y, this must equal to this. So that's what we're going to do. What's up? So I'm going to make some room for us here. Let me erase these guys.  I'm going to redraw it. What? We had minus 4, we had plus minus 10x plus 24. And this guy goes like this, and this guy goes like this, and they hit here. This is 10x. So all you got to do is set this equal to this, which means you're going to set 2x minus 4 equal to x squared minus 10x plus 24. So all you need to do now is solve for x. So what we're going to do is grab these two guys, bring them over. So this becomes minus 2x, and that becomes plus 4. So this guy becomes, if you write it, x squared minus 12x plus 26 is equal to 0. Now you got to solve this guy. Two numbers are multiplied to give you 24. I have to give you negative 12. I can't think of anything top of my head, right? Things are multiplied to give you 26 or 2 and 13, but I can't combine 2 and 13 in any way to give me negative 12, right? So what we need to do is use the quadratic formula. Quadratic formula. x is equal to negative b plus or minus square root of b squared minus 4 is c over 2a, which is x is equal to negative b. So negative negative 12 is 12. 12 plus or minus squared of negative b squared or b squared, which is negative 12 squared, which is 12 squared is 144. I like this formula. Yeah, nice formula. 144 minus 4 times a times c. 4 times a is 1 times c is 26 all over 2a, 2 times 1. So what does this become? Anybody want to punch this in? See what we get? We'll do it here too. 4 times 26. 4 times 25 is 100. 4 times 2 is 8, so that's 108. 144 minus 108. 144 minus 108. I hope I got that right. 104 not 108. Almost made a big mistake. I'm going to do mental math if I make any mistakes. Let me know. 104, right? Is that true? I got to do it. I always second guess myself. 104, right? So we got 104 and then we're going to subtract this. We get 40, right? So inside here is going to be 12 plus or minus square root of 40 over 2, right? Now square root of 40 if you do, what do you call it? Thanks, Max, for masquerading or not masquerading, bit monkey. Isn't it 28? Not 26 that I meant. Mess it up. It is 28. Thank you. Croatian. Croatian Bruce Lee comes to the rescue. 28, 28, right? So it's going to be 112, right? Is that correct? Let's bring it back. Let's bring it back, right? So 28. Thank you. 28 times 4. 4 times 25 is 100. There's 3 left. 3 times 4 is 12, so 112, right? 109, oops, 112. Subtracted to 3. So it's 32. Eagle's eyes. Eagle's eyes. 32. So we got 32, right? What's the square root of 32? This is your factor tree, right? Now we've done a lot of videos with this, reducing radicals. So let me erase this. Make some room for us, right? 4 root 2. Yeah, it's 4 root 2. Does everyone know how to do this? Not only heroes when it comes. Square root of 32. 32 is 4 times 8. 22, 222. Square root, you're looking for a pair. You can bring them out as singles. So 22 has come out as a 2. 22 has come out as a 2. There's a 2 left over. 2 times 2 on the outside, which is 4, right? So you get 12 plus or minus 4 root 2 over 2. And you can simplify this because 2 goes both into both of them. Will the examination of Cambridge postpone for later due to coronavirus? I don't know. Most likely. I'm assuming everything's going to shut down. It's been a while since I've done math like this. It's starting to come back. Nice. I'm going through a speedy Gonzalez, by the way, right? I'm all energized for some reason. All excited. A lot of things going on, right? I'll study math next year. Nice. Creation. Yeah. If you caught this mistake, good on you, man. You're way ahead of the game, right? Hey, Chichou, I was like, hello, Felix, how are you doing? Do you have more exercises to show? I'm going to start loading on exercises. After we do this, I'll mention what's going on in the background with school being closed in my students, right? Because they've been asking, I'll mention them now, they've been asking me to, because most people realize that they still need to learn the stuff, right? They're not just on vacation.  It's not a good idea to step away from mathematics or your education for a number of months and then try to come back and learn the stuff because in the future, you need these things. So the ones that are keen, the ones that see the grand picture, right? Have been asking me to start providing them with exercises and stuff so they can continue learning. So I'm going to start creating exercises for some of my students, and I'm going to start sharing those exercises on our Discord page and our Patreon page for sure. Oh yeah, by the way, I'll do a little intro to this. If you guys want to know where I am, who I am, how you can support this work, where I'm going to post a lot of content and stuff like this. We do have a Patreon page. Okay, that's my Patreon page. And for those watching this on another platform, we're live streaming this on Twitch.  To help people learn mathematics because if everybody understood mathematics, the world would be a much, much better place to live it, right? And we're announcing this on Twitter, these streams on Twitter and stuff like this, and on different platforms that are listed in the description of this video, right? Including Gav, Mines, VK, and LO. Okay, because decentralization is the name of the game, right? So let me take these down and get back to business of mathematics. Okay, so what do we got so far? We got this guy. We want to reduce this fraction. 12 plus or minus 4 root 2 over 2. 2 goes into both of these. So this becomes x is equal to 6 plus or minus 2 root 2. Those are our x's here. Okay, so this x, we just figured out what this point is. That's 6 and 6. Why is it 6? It should be 5. Or maybe not. 1, 2, 3, 4, 5. It should be 5. I might have made a booboo somewhere. Okay, do some self-experiments. Take a math exam without coffee a day apart. But anyway, for now we got 6 plus 2 root. This one's going to be going backwards. Oh no, no, no, it's still, wait a second. This should be the minus one. 2 root 2. And for this one, it's going to be, where are we going to put this? Let's put this here. For this one, it's going to be 6 plus 2 root 2. And then we have to find the y associated with this. And all you do, you punch this number into your calculator and plug it into here and figure out what the y is associated with each one of these x's. Okay, the math and coffee study. We could do it right now. We could go 2 root 2. So I'm just going to punch it in and get our y value. Okay, 2 square root. Where's my square root symbol? Where's my square root symbol? Okay, what's going on? I'm going to take a 2 to the power of 0.5 because I can't find my square root symbol. It's 1.41 times 2 and then subtract 6, which is going to be 3.17. So our x value are 3.17 and let's go plus 6 plus 6. And then plus 6 again to kick it up to the other one, which is 8.82. 8.82. So these are the numbers you plug in here to find your y. So over here, find your f of 3.17, right? So for this guy, find f of 3.17. You're going to go 2 times 3.17 minus 4. Here, we'll do it. Clear, clear, clear, clear, clear. 3.17 times 2. Exactly. I also want to fix that. 6.34 minus 4, which is 2.34. So the y value here is 2.34, which makes sense, sort of, we drew it like this. Not to scale, not to scale. So this point, the solution for this system is 6 minus 2 root 2 and that's just the number comma 2.34, which is the point on the graph where they cross. Let's do a simpler one that doesn't take up so much space and then you would do it for this one as well. Find what this value is as well, which we could do. What's the other number? 8.82. So let's do that one too. Might as well finish off this guy. 2 times 8.82 is equal to that minus 4, which is 13.64. So the y value here would be this guy here is 13.64. That's where it's here. I hope that wasn't too fast and I might have made a mistake more than one, right? But that's the general gist of it. If you want to do a quick version of a solving, let's say, a system of linear equations instead of a quadratic and a linear, here let me do one really speedy ones out less and then we're going to hit up this guy. I think it's time to give this guy a wash. Can you summarize once? Oops, late. Oh, I didn't summarize. I killed it. Sorry, BitMonkey. I killed it. But I can summarize here again the process anyway and don't forget there's here. BitMonkey, check out this video and in this video, it's part of the how to steady playlist, right? And I basically called this one recognize the pattern of how to solve an equation, right? So it has three equations with three variables and two equations with two variables. Let's just do two linear equations with two variables right now. What if you had the following equations? y is equal to 3x minus 4 and the other one would be 2x minus 4y is equal to 5, right? Let's assume if you wanted to find out if these two systems had a solution and what these two systems are, they're both linear equations, okay? Without any sports to watch, is everyone keeping up with their marble racing? I saw that video actually. Always making, always be making the marble race one. That was super cool. When a parabola is 3D space is cut by a place, how hard is it to solve? When a parabola in 3D plane is cut by a plane, no, in 3D space is cut by a plane parabola. So it's a cone, it's not a parabola. Parabola in a 3D plane is cut by, 3D space is cut by a plane. How hard is it to solve? It would just be substitution elimination I'm assuming, right? Connex sections, connex, right? It's just, so connex is this by the way. If you have, here, just take a parabola, just do it, let's do 2D, right?  If it was in 3D, you would get a circle. If you cut a parabola like this, you would get an ellipse, okay? Or cone, let's call it a cone, here, let's do a cone. Why do a parabola? Here's a cone, right? Here, let's do a cone, connex, right? That's supposed to be 3D, okay? Here's a cone. If you have a cone, right? If you cut it, here, let's do a different pencil, it's all not confusing. If you cut it like this horizontally, you get circle, right?  If you cut it like this, you would get an ellipse, okay? If you cut it in a way where you're not touching the other side, like this, I believe, you get hyperbole. They took connex out of grade 12 in my part of world, which I was really pissed about, by the way. There used to be a section 15 years ago that I was teaching in my part of world high school that it was all dedicated to connex, and they took it out, like horrendous. Oh, this is a parabola. Okay, so this is a parabola, right? So this one, we get a parabola, and the, or is it this one? Vertically, we get a parabola. That one is a parabola? Sure.  They get, they have the limits? That would be ellipse cut in half. That's an ellipse cut in half? Okay, ellipse cut in half. Sorry if I don't know this, this 15 years ago, going back by memory, right? Connex. Connex is super cool. Super cool, by the way. Okay. So take a look at this. If you're going to solve this using substitution, you're basically trying to find out when these two lines cross each other, right? You can do this here. Graphing this one's easy. One, two, three, four, up three over one, right? This one, you rewrite it in terms of y. You get negative four y is equal to negative two x plus five divided by negative four. y is equal to one over two x minus five over four, right? Negative five over four is negative one quarter, and then you go up one over two two. Right? So they cross here. Well, visually we know what it looks like now. We graphed them. So let's do it algebraically. If we don't get in this range, we know we did something wrong. And the way you can get into this range is realize at this point, this x is equal to that x, and that y is equal to that y. So all you can do say is at this point, this y equals that y, and this y equals this. So I'm going to take this and sub it into there because this y is equal to that y, which is equal to that y, right? So you just sub that into here. So you're going to get two x minus four bracket, three x minus four is equal to five, two x minus 12x plus 16 is equal to five. This is negative 10x. Bring it over minus 16 is equal to negative 11 divided by negative 10. So x is equal to 11 over 10. Did we do that correctly? I might have done it way too fast because that doesn't look like one and one tenth, but my graph is not the scale. So it might be, right? So negative 12, 16, negative 10, negative 11. Yeah, that's correct. Right? The hyperbole is when you have two cones and you cut such that they create two pieces. Okay, thanks, Mask of Raven. I wish they never took it out. I loved that section. It was amazing, right? Centralized education dumbens us all down. It's wrong, sadly. Logic bed. Right? So now what we can do is set x equal to 11 over 10 and find the y associated with it, right? So y is equal to any substitute this, either into this or that, right? If you want to make sure you did it right, substitute it into both of them. If you get the same y, you know, basically <IP_ADDRESS>.99% that you did it correctly. You didn't proofread that before stream. Start from beginning. Sorry. Connex section is used in perspective drawing. From beginning you should restart the stream. It'll be up once we're done, right? Or you can wait until the next example. That's the beauty of mathematics. You don't have to learn it all from the beginning, right? You can jump in anywhere you want. So 3 times 11 over 10 minus 4, 33 over 10 minus 4. Common denominator is 10. So that's going to be 433 minus 40. Wow. So our graph is like wrong. Why is our graph wrong? So we've made a mistake somewhere, maybe. Logic bed. I'm going to time you out. Time out.  Hey, what happened? Unauthorized command. Oh, someone did Spider-Man right on. Dude, don't take over chat. Yeah, we took care of him. That's why I keep on scanning the chat by the way. Sorry, I got him. Nice Spider-Man. That's one bad guy. I'm tied up, hanging from a post with a sign on him. Your friendly neighborhood Spider-Man took care of the business, right? I was pretty occupied. No worries, Covio. Connex geometry is used a bunch in remote sensing too. I had a grad professor who developed remote sensing stuff for the Mars rover. Really, really neat stuff. That's super cool. That's super cool. Okay, what did I do here? Did I make a mistake here with the calculations? Four. Anyway, we're getting negative 7 over 4, which gives us a negative Y, but we're in the positive. So either my graph is way off or we did something wrong. We could double check it. So right now we've got a solution of 11 over 10 and negative 7 over 4, right? So what we can do, oh, I know what I did because I put it here. This guy should have been here going up over 1, right? So definitely, I think this is going to be correct. So it's not this line because I just went to the quarter. I went to the wrong side. So it would be here. There's our line, not this guy. What we can confirm it, sub 11 over 10 here. Okay, let's do that. We could just do it here, but let's do it from the beginning that way. It works. Sub 11 over 10, 2 times 11 over 10 minus 4Y is equal to 5, 22, actually not 22, 22. Reduce before you multiply 5. So 11 over 5 minus 4Y is equal to 5. Multiply everything by 5. 11 minus 20Y is equal to 25. Bring the 11 over minus 11. Negative 20Y is equal to negative 14. Is that correct? 25, 10, 40, 20. Bring it over 11, 24. Oh, 24, 11. No, it is 11. So it's 24 and then divide by 20. So Y is equal to, well, we got something wrong. 2 goes into this 12 times, 2 goes into that 10 times. So this becomes 6 over 5. So we've made a mistake somewhere, that's for sure, because our two Y's don't agree. Right?  It's not 24. It's 14 over 20. Oh, it's 14. That's right. My bad. Look at this. 14, 14, 14. And 2 goes into that 7 times and that's a 5, which is 7, 14, 2, 4, 5. We're still off a little bit. Sorry. It's fun though. Right? It looks too complicated for me right now. Beans, how you doing?  I'll stop making mistakes in the process. Right? Speedy, talking speedy. Right? The slope of 3 should be steeper. Yeah, it should be steeper. My mistake. I'm not the, what do you call it, the most precise, I have brain farts when I'm doing a lot of mathematics. It's fun though. It's fun though. Should we do this one? We'll go slow with this one. Okay. The challenge would be to find out where I made the mistake. The mistakes are fun. They make paying attention more challenging. They do. Right? Let's do this guy. So we want to find the minimum values of this, I believe. The minimum values of this. Okay. So what's the first thing we should do? The first thing we should do is try to factor this thing, I think. Mask of raiment. What's your recommendation? First thing, try to factor or should we graph it first? We could graph it. Could we graph it? Oh, I don't know if I could graph it right now. I never understood Shimomachi, but I always wanted to. I honestly would replace cos squared with x. It looks nicer. It does. Right? So what you could do is do a let statement. Right? As VC says. Right? So we could say let cos, yeah, let's call it cos x equal w because we already got an x. Right? And if you want where it achieves those minimum values and where it achieves those minimum values, which is what x is when the minimum occurs. Right? So let's do this first. So basically what we're saying is let cos x equal w. So f of x is equal to nine w squared minus 12. Oh, sorry, w to the power four minus 12 w squared plus seven. Right? Oh, you're welcome, money man. I hope it helps. Sorry about the mistakes, by the way. My apologies about the mistakes, but it is what it is. It's a mistakeful day today. Right? So we could use factors using the quadratic formula or we could try to use the four step method. Right? It does. Okay, good. A corona day. It's a corona day. Right? So complex trinomial factoring. We'll try it out. Right? I would use would you? Mask of Raven? Okay, let's do it. So let's do it this way. Instead of saying w equals this, we're going to say w equals cos squared. So now we got, oh, I changed the square. Jeez. This would have been, if this wasn't squared, this should have been four. Right? But we don't want to the power four. We could say w is equal to cos squared. All of a sudden, this becomes cos squared and that becomes just, or w squared and that becomes w. Right? Makes it easier. Doesn't w squared combine first? I don't think you can use quadratic formula. Oh, I see. Yeah. Yeah, we could do it. I made a mistake. Sorry. So what we could do is take this, multiply by this. Right? Let's see if this is going to work. What? So we got w squared minus 12w plus 63. Two numbers that multiply to give you 63 and add to give you negative 12. Right? They have to be, if they multiply to give you positive, they're either both positive or both negative. They add to give you negative, so they're both negative. Right? Two numbers that are negative to multiply to give you 63. I can't think of anything. I don't know. I don't think it is either. Right? Not simply in terms of integers. Right? So that doesn't work. So we're going to use the quadratic formula. Quadratic formula. Quadratic formula. x is equal to negative b plus or minus squared of b squared minus 4ac over 2a. Negative b is negative 12, so it's 12 plus or minus squared of b squared is 144 minus 4 times 9 times 7. This number is going to be bigger than this number, so it's not factorable. Right? 2 times 9. Right? 4 times 9, 36, 36 times 7, 36 times 7, 42, 2, 4, 21, 25. So right now we've got 12 plus or minus squared of 144 minus 252 over 18, 12 plus or minus square root negative number. Okay, let's do it. I would just say negative, but let's do it. 252 minus 144, 2, 2, 2, 8, 0, 1. So negative 108 over 18. That's a negative number. You can't take the root of a negative number. It's a complex number. So there are, what does this mean? There are no x intercepts. So the function is above the x-axis and it's channels. Right? I'm assuming it's going to be channels or there, okay, or above the x-axis. Yay, complex plane. We are in imagined territory. Whoever assigned this problem likes torturing their students and their tutors. I can imagine what the root might be. You said 42, not 49, well, it was like, did I? Yeah, I know I say the wrong word too. Sorry. I signed it to myself. So we can't factor this. So let's take this now, okay? And that's what happens with mathematics. You try to go down a certain root, you get it wrong, you can't do it, you progress. So, Mask of Raven, how do we end up doing this? We're trying to find the minimum values. That means when f of x, y is the lowest point, right? Complete the square. Okay, let's do it. Heading to buy it now. Gicho always tortures people. No worries. I'll check this out. So we're going to complete the square to this. Let's complete the square because this is a quadratic equation, right? So, completing the square, and if you do chicho, completing the square, there's going to be at least two, three, four videos of completing the square that we have up that you can go through how to complete the square, okay? Yeah, we're going to check the discriminant first before, what do you call it? Here, let me show you what I got. Apple and peanut butter. I'm going to speedy Gonzales right now, so I don't feel like munching on anything, right? Apple and peanut butter is not fasting, and I got some of those chocolates who want to buy some more, those chocolate end pieces. Delicious. Rambo, how's it going? Watched any movies recently? Did you watch Bloodshot? Healthy two, healthy two. Peanut butter and apples, amazing, right? So, completing the square, put brackets around these guys, take the nine out, so this becomes W squared. You've got to compensate for the 12, so you divide it by nine. 12 divided by nine, three goes into both alone, so it's four over three, W plus seven. Completing? Oh, thank you, Spider-Man. You rock, right? That's at least one of them, right? So, basically, you're thinking about this. If you take the nine out, the nine is in front of the bracket, so the nine would multiply everything inside the bracket. That means to figure out what's here from there. If you take the nine out, you got to divide everything inside the bracket by nine. Okay? So, next step, because if you multiply nine in, you're going to get nine W squared minus 12 W, right? Now, what you're going to do is take this guy divided by two. It's just a process, it's an algorithm, right? So, negative four over three divided by two is the same thing as multiplied by half. Two kills this down to two, so this is negative two over three. Take this guy and square it. You get four over nine, and again, this is just an algorithm, a technique to be able to graph a quadratic function where you're being able to find the minimum or maximum value, depending if the thing opens up or down, right? So, we got this guy. Now, what you do, the algorithm tells us, take this guy, add and subtract it in there. Nine W squared minus four over three W plus four over nine minus four over nine plus seven. The reason we're adding and subtracting this number in there, because we can't just arbitrarily add a number into a function because it changes the function. The only number we can add into a function without changing that function is zero. So, four over nine minus four over nine is zero. So, we're choosing what the zero looks like. We're manipulating the equation, right? And the reason we're doing this is because we want to be able to complete the square, which means we want to create a perfect square out of this thing, okay? And we have to compensate for what we need to do to it. I'm on the board right now. Is this a code for a nuclear? No, just a quadratic formula, right? Or not a quadratic formula, a complete square, graphing a quadratic, right? So, what you ask yourself is this. Now, first thing you're going to do is you're going to grab this guy and take it out of the bracket. We don't need the negative one in there. Now, keep this in mind. When you take out of this bracket, take this out of the bracket, whatever's in front of the bracket is standing guard, okay? And anything that comes out of the bracket has to multiply this. So, it's going to be negative four over nine times nine, which just becomes negative four. Simple as that, right? The other thing you're asking yourself is you're trying to factor this guy. We tried to factor it here, but we couldn't factor it. It didn't factor properly, okay? So, you want to factor this guy. You're asking yourself what are two numbers that multiply to give you four over nine and add to give you negative four over three. You don't even have to think about it, right? It's this guy. That's the reason we circle this. This number that you divided by two is if you multiply this times this, you get this. If you add this plus this, you get this, right? So, when you do this complaint to square, circle this and circle this because you're going to use both of those numbers. Okay, both of those numbers. So, this guy becomes nine. Two numbers that multiply to give you nine over four and add to give you negative four over three. Sorry, four over nine and add to give you negative four over three is this. So, this becomes x minus two over three times x minus two over three, but that's just that squared plus three. Nice. We found our quadratic. Graph theory, Theo, I'm not sure what you mean by graph theory. I don't what do you call it? What does it exactly mean with graph theory? I'm sorry, I'm not familiar with names. I might not be able to do. If it's high school mathematics, I could do, right? So, over here, what we have, what this is telling you is. So, what's this telling you is, this is the vertex of this parabola. Okay, irrelevant of what this guy is, right? Because we reconfigured this guy to represent the parabola. Graph theory is definitely not high school. Yeah, I don't think it is either. There's, you need to know some of the graphing stuff before you get into high school, right? Before you get into graph theory, but graph theory, is that sorting, searching, algorithm, algorithm, is it? I have a question of a fate of the view. I have read about, I would like to know your opinion. I don't know what the fate of the view is. Crazy bow happen. Okay, it is comb, combatorics and informatics. Sorry, combatorics, I'm not very good at. Can we do a graph that tracks the exponential growth of coronavirus in New York City? Sleepy waves. We can do in our coronavirus live stream, we're going to do next Sunday, I think. What are we doing? We're doing it April 1st. We're going to do April 1st, right? So, if you, if you send me the info, like by that time we'll have more data. New York is just reporting slowly, right? So, if during this week and next few days, post a link to where they're tracking that information and we can definitely do it. Okay, let me finish off this guy. So, basically what we have here is a parabola that opens up. So, if it's a parabola that opens up, its vertex is going to be at positive 2 over 3 and 3. So, 2 over 3, here's 1, here's 2. So, 2 over 3 is 0.6666 and 1, 2, 3, here. And based on this, it opens up. And I'm not sure how this guy is completely going to look, but that's going to be the minimum value. Right? And the y just, wait a second, y just up to 7. Oh yeah, because this thing's power exponential. It's way up there. This would be 7. That guy would be the 1 intercept. Right? So, the minimum value is 3. And it occurs at when x or, oh, look at this. Look at this. What a mistake. This is w. Okay? When w is 2 over 3, right? But we wanted to find out what x was, right? So, we want to find out what x is. So, what we can do is go 2 over 3. Wait, did we miss, did I make a mistake? How do you know it's a parabola that opens up and not opens down? It opens up because the 9, the number in the coefficient in front of w squared is positive. If this was negative, it would open down. Right? That's good for you. Point 6 is the number of 5 bookers. So, it was math, but then it was w. The minimum value is 3, not minus 3. Oh my god, I hope, look at this. What a mistake. Brain farts, brain farts, 3. Who told me that? Theo, thank you very much for that.  Okay, so I'm going to make a mistake. So, it's 1, 2, and 3. 1, 2, 3. Right? Oh my, oh my. That's why this thing is a 7, too. Right? This guy goes like this. So, here's 7. This point here is 2 over 3 and 3. Thank you, Theo. Very much appreciate it. Right? So, the coefficient is negative or positive. Random subject. It seems the island where over 1 million king penguins, oh, crazy boathens. I can't even change gears to think that way right now. Okay. Seriously. You have to change gears to start thinking in a certain way, right? Maybe w to 0 to 1. Right? So, w to 0. So, what we're doing right now is we're gonna, we found w. w is equal to 2 over 3. It occurs when w is equal to 2 over 3 and the minimum value is 3. Right? But we also want to find out what x is when the minimum value occurs. Okay? Well, you found the minimum of 3. So, you're done as far as my original question. But you also said find the x when the 3 occurs. Right? So, the x when the 3 occurs, we have to find out what x is. So, let's go back and find out what x is when we find when the minimum is occurring for the original function. Right? So, it's 2 over 3. Let me erase all this. Let's go to here. Oh, it looks so much cleaner. Right? So, we do that. So, we found the solution to be 2 over 3 and 3. But the 3, 2 over 3 was w and f of x. We still have to find the x. So, what you do is you plug in 2 over 3 for w. So, cos squared x is equal to 2 over 3. Now, this means cos x times cos x. So, you can just take the square root of this guy. Then you're going to get cos x is equal to plus or minus squared of 2 over 3. Right? So, x is going to be cos inverse of plus or minus squared of 2 over 3. Those are going to be your x values. Okay? Now, if you want to... No, you just use a calculator for this. You just use a calculator for this. Do they study algebraic structures in Canada? Not in high school. I wanted to ask something. Algebraic structures... Again, let me know what algebraic structures are. Not in high school. We don't use that term in high school. It should be outside the cos. No, they should be there. I think they should be there. Very. I think a cos is an even function. Not sure. Not sure. Yeah, it's in the bounds. California, that's... Yeah, for sure it's within the bounds, because 2 over 3 is less than 1. No, it does. It does do something. It tells you which quadrant is right. So, if you have this... So, basically ask yourself here in trigonometry... By the way, we have a whole playlist of trigonometry, which trig I love. If you do chichu trigonometry or go to our YouTube channel, there's a trigonometry playlist where we've... We haven't solved problems like this yet, but we've done all the preliminary work for it. Okay. We've done all the preliminary work for it. So, basically, you can think about the cos axis. Cos as the x-axis. So, because cos is positive and negative, cos is going to be positive here and here, cos is going to be negative here and here. So, there's going to be four points that we're going to get solutions for. There's going to be four x-values for this. That's definitely good enough for the solution, for sure, masquerade, and I think so. But the value of x changes. It depends on the quadrant, not the value of the function cos x. But cos x, cos x, you can think of the x-axis as cos x and the y-axis as sin x. If you want to a certain degree, right? And cos is going to be positive here and here, because x is positive, and it's going to be negative here and here, because x is negative. Okay. That was Peter Gonzalez talking. I'm going to pop an apple in a peanut butter.  Very delicious. In general, if a function is even, its inverse cannot be. In general, if a function is even, its inverse cannot be. I think your calculation is wrong. Rambo. You don't. Hopefully, you're checking. Rambo. I tell all my students, or whenever I'm teaching mathematics, check, I make mistakes. Right? Please be civil. Yeah, civil is good. Deal. People can have fun. People are joking around. I'm all good with that. Oh, the even function thing. So when you said, in general, if a function is even, its inverse cannot be. That is not correct. You're correcting that. So function, if it's even, it can still be even. Its inverse can still be even. And the inverse of a function is you're flipping the x and the y's. Right? So you're doing this. I'm going to erase those. The conversation of the inverse of a function is this. Let's assume we have the following function. y is equal to x plus 1 over x minus 2. Right? Well, forget about how, ah, no. Let me give you a simpler one. That way we can do a graph of it too. Right? Let's assume we have 2x minus 3. I don't know why I'm coming to this one, but I am. Right? So if we graph this guy, it's negative 3. 1, 2, 3. And then up to over 1. Right? Here's this guy. If you want to take the inverse of this function, what you're really doing is you're flipping the x and the y. So what you're doing is you're seeing what this function looks like if you use the y equals x line. This is the line y equals x. If you take this line and say this is a mirror, what does this function look like if you flip it? Right? In a mirror. Right? So what you're really doing is you're switching the x and the y's. So what you do, the inverse of this function would be x is equal to 2y minus 3. Isolate y. So x plus 3 is equal to 2y divided by 2. Y is equal to a half x plus 3 over 2. 3 over 2 is one and a half. That's your y-intercept. One and a half. And then up one over 2. All right? So this is the inverse of that. And vice versa. And where they cross the mirror is they're the same point. Okay? So that's what the conversation is. So an even function would be something like this. f of x is equal to 2x to the power 4 plus 2x minus 1. It's even because the highest power is even. So an even function is inverse. Supposedly it can still be even. Right? Is that true? Even functions can't have inverses is a better statement. Even functions can't have inverses. This can't have an inverse? Really? What? Is that what we're talking about? Masqueraden? Are we referring to the same stuff? You can do whatever you want. No Joyce Lin. I'm assuming you are a responsible human being. Right? And you probably live at home somewhere. Right? You can do what you want. Yeah. It's not a caulking in Germany and I'm looking at math, of course. What's wrong with me? You want knowledge? You're enjoying the stream? Sign is even sign inverse exists. Okay? And others have made YouTube series to help learn basic algebra and masquerades. I'd recommend checking them out. Here's our YouTube channel by the way. Can't have inverses over the original domain. Can't have inverses over the original. Can't have. Is that absolute? Can't have inverses over the original domain and domain is the values of the x for even functions, I'm assuming you're saying. You have to restrict it. Oh, yeah, yeah, yeah, because if you have, let's assume, let's do a different color. So an even function would be something like this. Right? So I'm going to do this. Pro and slinky. How are you doing it, Chichu? You are the best. Thanks. So if you have an even function, like a quadratic function is even. Right? So here's an even function. It's a parabola. Right? If you flip this on the mirror, the graph is going to look like this. So definitely their domain, what their possible x values can be, can, is not the same. Right? Yeah, domain and range change, changes of the function and inverses. Yeah, basically the domain of the original one becomes the range of the inverse and the range of the original one becomes the domain of the inverse. Right? It is just a function. Won't be in Iraq. You have to restrict the domain of the new function for it to have an inverse. In general, it does not. Okay. Yeah, domain and range change, changes of the function. It is just a function. Won't be in America, like close, close age. Interesting. Mathematics, like I wish the math in my part of the world in high school near was a little bit more challenging than what it is right now because it's making my math abilities decrease, which is unfortunate. Subscribe to the YouTube. Nice, California. Oh yeah, by the way, gang, thank you for the follows. Thank you for the subs. Thank you to the mods for taking care of business. Sorry, I haven't been paying attention to the follows and the subs and stuff like this just because I want to get as much math done as possible. I know there's a lot of people that are missing the mathematics in times of pandemics. Right? So it's always good to stay on top of the math. It really is. It's good for the brain. Right? Serious question. Do the corona crisis, I think the global economy will cloud. Should I withdraw? I posted it, you know, someone asked in the economic section, our discord page, and we have a discord page where there's a lot of conversation taking place. Have enough cash handy so you can take care of your daily expenses for a month or two. It's not just about number of deaths which are predicted anyway. It's the fact that the exponential rate of virus spread overwhelms countries medical system. And by the way, gang, it's exactly what VC is saying. What you want to do right now is don't overload the system, right? The healthcare system because you're putting the lives of the healthcare professionals when you overload the system. Social distancing is a good thing. Chill.  May they be math chico related or someone else's streams playing video games. Just sit back, relax, take it easy. There's a storm and you need to bunker down because if you're not putting your life at risk, you're putting other people's lives at risk and if you're doing that, you're right. So chill the out and stay home if you can and stay away from people and let the storm pass because the last thing you want to do is stress out the healthcare system in your countries because once you do that, there's going to be a lot of people being hurt, okay, including healthcare professionals. I teach blood acts. I teach high school mathematics, not an essentialized education system, but in privately. Thank you very much for what you are doing, doing that quarantine. Yeah, we've someone's quarantined yourself for sure. Modern economies guarantee bank deposits up to a pretty high amount. So your bank will be fine unless you're a rooster. I wouldn't put 100% faith in that system. Okay. Do you also teach classical physics? My degrees in California nice made my degrees in geophysics. So I do teach physics as well. Certain segments I'm better at than others like circuits and stuff I'm not very good at projectile motions is fine. And then the I used to know my mag and lecture magnetic stuff way better than I do now. I probably don't even know it now just because I'm dealt with it for much forces, momentum, yeah, some anyway. We've done some physics on these live streams. A horse is tied to a corner of a square field with side length one. How much rope should you give the horse to let it reach exactly half the field? Let's check this out. I still have to go to work. Oh, no. Big chilling as usual. I don't know what that is except a bit of job. One what kilometer masquerade and two part masquerade isn't that countless? Is it a countless problem? One unit, whatever you want. So let's check this out. What's the problem? A horse is tied to the corner of a square field with side length one. Here's our horse. I need like my horse. How much rope should you give the horse to let it reach exactly half the field? So, what do you mean half the field? Half the area? Or half the distance from each? I'm assuming it would have to be half area, right? That's what you mean. Is that true? Amazing hard masquerade. Thanks. Sorry, the longest moments show up in chat. You can post on Discord. Yeah. Half the area. Yes, half the area. So half the area. So how much rope do we have to give it to reach half the area? How much rope do we have to give it to reach half the area? Half the area. I mean, half the area would be this. The problem is, I mean, you could do it this way. This is half the area, but that's not going to work because the rope is not going to reach here. If it reaches here, then it goes there. So you can't do something like that. So it has to be something like this. Let's try this out. Let's draw a diagram. Diagrams usually solve the solutions for us. So it's going to be something like this, right? Okay. So one unit. Let's call this one. One. All right. And what we're going to do is we're going to assume quarter of surface are the rope radius, the surface area of the square. Yes. Wait, I'm wrong. There's root two. So it's a circle of area two. The radius is the rope. Is it? I'm not sure. Because this area here has to be equal to this area, and A plus A has to equal total area, right? Area. So these two areas are the same. So what's the area of the square? Total area.  Instead of using one, let's use five or something. How do you find the circumference of a circle, then take a square of it? I have no idea why beans that automot grabbed that thing. For everyone in chat, the answer I got was square root of two over pi. Let's check it out. Let's check it out. So total area. Oh yeah, I was going to change this. Let's make it, I'm going to make it five. Just because five. Why circle? Because it has to be a rope, right? So it has to be a rope. So it's going to be like a radius, like this, right? That's what it would be, right? To be half the area, because it has to be pinned to one of the corners. Okay. So total area is going to be five squared for the whole thing, right? So half the area, A is going to be five squared is 25, right? 25. So it's going to be 25 over two, right? So the area is 25 over two. Now what's the area of this? Because we're trying to find R, the length of the rope, right? So what's the area of the circle if this thing went all the way around? Went all the way around. Well that's going to be a quarter of the area of the circle, right? So area circle is going to be this area, let's assume, is going to be pi R squared, not two pi R, pi R squared, pi R squared over four, right? Because it's a quarter of a circle, right? If we do this, that's a quarter of a circle, right? So we want to find R and area C of the circle, let's say a quarter of the circle, has to be equal to this. So we can just set these two guys equal to each other, right? So this is going to be R squared is going to be four times 25, or let's do cross multiplication here. We'll just do cross multiplication. That way we're not multiplying pi. Two goes into four twice. So that's going to be 50. R squared is going to be 50 over pi, and you take the square root. So R is going to be squared of 50 over pi. Is that what you've got, Master Root? Something like that. Yeah, over pi, square root of 50 over pi. So this thing is going to be square root of 50 over pi, and square root of 50 is going to be five root two, because 50, square root of 50 is two times 25, square root of 25 is five, right? So that's going to be five square root of two over pi, right? That's the radius. So you have to make the length of the rope five square root of two over pi. Does that work with you guys? I hope that's clear. And square root of two over pi. So whatever your unit is times two square root of, so if this was 500, the length of the rope would be 500 square root of two over pi. Fun question, by the way. Thanks, Mask of Raven. That's a great question. I like it. Beans. The automata is zapping your comments because you're spelling someone wrong, so I was thinking some bad words. What's the follow-up question to this, Mask of Raven? The circumference of the circle is two pi r. Circumference of the circle is two pi r, r. Newton rolled over in a coffin. Poor Newton. Is he eating apples and peanut butter? Apple and peanut butter. Nice. Wait, wait, wait. With a chocolate on top. Pandemic food. The follow-up is this. Tie a horse with the same amount of rope to the other side of the field. Prove that the area that can both go is equal to the area they both can't reach. Prove that the area they can both go, the area they can both go, is equal to the area they both can't reach. Okay, I'm going to do this in red. So they prove that the area they can both go is equal to the area. Oh, so you're saying this. So let's assume this is like this. So here's the other horse, right? So prove that the area they can both go is equal to the area they both can't go, which would be this and this. Is that correct? Mask of Raven? It's not that simple, sir. What if the length of the rope is greater than half of the square field? The length of the rope is okay for it to be. That's fine. I think the app on peanut butter is how you lure the horse to the middle of the field, so he creates the radius. When does he actually stream? I've got to go, but I want to watch him again in the future. We've got eight streams of field listed.  Here's our Patreon page, and if you go to the post section, I list all the streams that we're going to do in the post there. So I do announcements where I say our next four streams, our next two streams, the last one I did is our next eight streams. This is the first one we're doing of a set of eight. So you can find it there. Our next stream is actually here. I'll give you guys the dates. We got the current events tomorrow at 8.30pm, comic books Monday at 8.30pm. We got cooking live stream on Thursday at 12pm. We got reading comic books on March 29th at 11am. We got reading comic books on March 30th at 2pm. We got current events on March 3rd at 8.30pm. And we've got COVID-19 data we're going to look at. I guess it's a fourth live stream we're doing. We're just keeping up with the data on April 1st, Wednesday at 8.30pm. Oh, I was considering a rectangle on my mind in the last question. Oh, okay. Oh, let me take down the Patreon thing. Okay, so this problem, I cannot wait. Mask of Raven, I gotta find it. Yes, that's the question. So this is the question. Okay, cool. So we've got to think about how we do this. Case man, how you doing? How's life? Peanut butter is amazing. Pandemic seriously, it's amazing. So good. I've never eaten so much peanut butter for so many days in a row. It just feels great. Okay. Oh, I was gonna do that. I cannot wait until comic books. I think very soon I'm going to start cataloging all my books and stream this. Oh, dude, Spider-Man, that'd be fantastic. Cataloging, man. I lost track of what I got and where I got them. So long ago. I'm really excited for your comic book streams. Nice, Spider-Man. Hello, sir. Case, man. How are you, friend? Nice. So let's do this problem. I wonder how we do it. I'm thinking about it right now, but I'm not sure how we go about doing this. Let me erase, get rid of all the clutter here. Okay. So I'm gonna erase all this. We don't need all this. So we got a question. Follow-up question. Doing well. Awesome case, man. Could you add a recalculated mortality rate given a five-day offset between reported cases and reported deaths? Yeah, we could, Gina. If you could send me a reminder on Discord or post it on Discord in COVID-19, that way I'll create a column and have the data available. By the way, the fatality rate is kicked up. It's more than 4%. Now, it based on the numbers we have, right? And that's the best we can do right now. I don't want to go into a speculation of what's what. Okay. But Gina, for sure. How long before streams? April 1st is our COVID-19 stream. Tomorrow we do a current event stream. So if I have time, I'll create the column today and then just punch in the calculations and have the data pop out so we can take a look at it, right? I have an inking. You like the Punisher. Punisher. How is this question true? Let's assume the length of each rope to be equal to the length of the square. It negates the problem. But what's the length of the square? Are we talking about this side? Or are we talking about a diagonal? Like what's the length of the square, right? California Knight is my favorite character. Punisher. The length of each rope is exactly enough to let the horse access half the area of the field. Yeah. So if this was, we just did the previous calculation for this, right? So if this was one, right, or one unit, then the length of the rope, R, right, we're calling it R because it's a circle, was a square root of 2 over pi. That's what we have right now. So we're saying this, what's the length? Oh, I should use a red. What's the length of this rope half to be for this horsey to go like this? And the area here is going to be area equal to what they can't reach. We'll do. Okay. Thanks, Gina. Appreciate it. Okay. This is about 0.799. Is that what it is? So let's check it out. So saying it's got to be 0.79 if this is a one. So how do we do this? How do we do this? So we got to do it with areas again. How do we do this? The area that can both reach. This is a way more complicated problem, masquerade. No, how do we do this? So this, this length is squared of 2 over pi. If our lengths are 1, how do you negate the overlap? We're not negating it. We're trying to calculate it. Gina, we're trying to figure out what this overlap is, right? Because the question was, what is the area of this? Oh, wait a second. It's not half anymore. Was it half? The question is not too bad. Purely logical. But are we assuming each one is taking half again? Or are we going to fluctuate the radius? Oh, we're going to fluctuate it. I lost it for a second. So this isn't the radius we're going to have. We want the radius to be set in a way where the area that they both can reach is equal to the area they both can't reach. I think I presented that correctly. Is that true, masquerade? Because this isn't the radius anymore. My bad. We're not going by this. We're trying to figure out, yes, both take half. Oh, yes, both take half. So if both take half, so if both are taking half, we want to find out, what was the question again? We need to increase the radius. No, both can reach half and have the same length of rope. Okay. Yeah, sounds complicated to me too, Gina. So they can both reach half. So they both have the same amount of rope. So what's their overlap? Basically, that's what we're going to figure out, right? How much area do they overlap? How much area do they overlap? Because each is going to eat half the grass of the overlap, as long as they're friendly. 16th of the total circle. I feel the same as dub. If both take half, then area they have is fixed. And area they do not have is also fixed. Nothing to prove here. Don't try to calculate the actual area. Okay, just figure out why the overlap is equal to the both can't reach. So why, why is this and this equal to this, this area, right? So if we erase these, let's put letters in here. So if we call this C, and I'm assuming both of these would be the same, A and B, but A and B would be the same, right? They would have to be, right? So let's call this here, what's easier to convert A? So A plus A, so 2A has to equal C. 2A has to equal C. I think I wouldn't need help with this one. I don't know how to do this one. It's not coming to me anyway. The diagonal, you would have to calculate the diagonal, right? Do we calculate the diagonal? Yes, they are A equals A. Yeah, for sure. Don't think I'll break that all. Don't think, oh, man. My natural instinct is to think algebraically. I'm not sure how to think about this without algebraically. I'm still thinking algebraically, right? I'm thinking, oh, the length of the diagonal, we can figure out what the length of the diagonal is and figure out what that length is there and what that length is there and then we can get those points and do the calculation that way. I respectfully disagree, but I'm unable to provide an alternative. Yeah, I don't know how to do this. I'm with Gina. Don't think algebraically, so how could you not think about this algebraically? Geometrically, how would you think about this geometrically? How would you think about this geometrically? What was this number equal to? I'm going to punch that in. I'm going to figure out what 2, clear, clear, clear, 2 divided by, where's my pi? Pi equals, and I'm going to take the square root of it, to the power of 0.5. So it's 0.799, 0.7979. So this length is equal to 0.7979. That's the sum, right? So that distance is 0.79, that distance is 0. So I don't know how to think about this without algebraically, and I don't know how to do it algebraically. I'm just not sure you can assume 2A equals C. But I think, are we forcing it? Can we force it? For sure you could. Yeah, you know what? If it's half, then how do we know that 2A equals C? I'm assuming it would be, it would have to be set up in a way where this area equals this area, this and this, right? But does that necessarily mean that half of it is half way? If you would have to figure out what the length of that has to be for those two, this to equal that, and that to me sounds very complicated. So it's not a question of finding these areas, it's a question of finding the radius, finding the length of the rope, no? Okay, actually think about adding the total areas and smaller areas together, adding the total areas. So the total areas, what were the total areas? That's the radius. So the area for each one is going to be, area is pi r squared divided by 4, right? And r is that guy. So it's going to be pi, 2 over pi squared is just going to be 2 over pi over 4, right? So it's a half? No, which makes sense. Of course it's got to be a half. No clue, but don't focus on that. Of course it's going to be half because we want it to be half. One times one is a half, so that's a half, right? Total equals one, horse, one equals a half, horse two equals a half, yeah? You know the area of the circles and the area of the square. The area of the square is one, yes? It involves sector of the circle and intense calculation. I have no clue, but don't focus on that. True, it's still half. It's still half, right? I have to do a calculation to be, that's the way I am. I have to do a calculation and then it becomes obvious. Just draw one of the circle quadrants and the square and a diagonal to the square intersecting the quadrant of the square circle. I'm going to go for a walk. See you all later. Always be making, enjoy your walk. My explanation is that since they both add to one and they have overlap, there must be non-overlap equal to that. There must be non-overlap equal to that. There must be non-overlap. It doesn't make sense to me, just came back in. What's the basic premise of this problem? The basic premise, Bob, is this. We have a horse tied to a corner and we figured out what the length of the radius has to be for the horse to have access to, let's say, a one by one square to half the grass in the field. So we calculated that. We said the radius has to be squared of two over pi. Now the secondary question is this. If you have another horse on the other side, opposite corner, kitty corner from this corner and that horse also has a radius of square root of two over pi, which consumes half the grass here, then what is, I lose the question again, but I guess what's the area of the overlap where they both have access to the same grass where that area is equivalent to the area of the region that they don't have access to. So this area equaling this plus that to A, they don't have access to this and they have access to this area. I'm pretty sure you could use calculus to solve this problem. I think it is a calculus problem, but my calculus is not powerful enough to do this. R equals one. How come they both add to one? How come they both add to one? Because we set up our corner square to be one. I can calculate each area of the portion you have drawn. Yeah. And what two ways to get my notepad? Could you use calculus? Yeah, perfectly negates the overlap. R equals one negates the overlap. How about that? Think about it in terms of sets. The area of A union B equals the area of A plus the area of B minus area of overlap. It can't be annoying, but area of B union, area of A union B. So this area has to be equal to area A plus area B minus area overlap. Oh, no, no, no, no. Total area of A plus total area B has to be equal to area. What do you mean by union? Union? Are we masquerade? If you're talking union, are you saying union? I'm reading it like this, but the way you've written area overlap, overlap is that. So union would be the total areas, or union would be area of this and area of this. Just go corner to corner. How come is it a calculus problem? If we are taking an element, we do an integration and it varies the limit to whatever doesn't prove anything. I might write something up on this and post it in Discord later. I don't want to hijack the stream. No, it's okay, masquerade. I personally don't see it. It's not making sense to me. I love it to make sense. So if you do it right up on and post it in our Discord, that'd be fantastic. That'd be great actually. The area of the overlap doesn't matter. Each gets half in any case. Yeah, for sure, but the question is, what's the areas here? How much don't they get? I mean, we could figure that out just by using a radius, right? But this becomes tricky because these are curves, right? So it's difficult to calculate the areas. How did you get our, we got it by, we did it earlier. We did it earlier. Definitely gone over two hours. Got lost in the problem. Wait, we should call this stream, yeah? Let's call this stream game. It's a great problem. I guess we've continued this on our Discord. If Mask of Raven could let us know what the solution is, can you please explain the question I am new? Sure, or Robo. So what we did initially, that's why I keep on coming back to R equals one, this was very comforting to me during these challenging times. Good stuff, Hannah. I really think I could solve this one. So here's the problem, right? You're going to write it down and try? Okay, so here's the problem. We have a horse tied here, right? And we've made the length of the radius of the rope that the horse is tied to enough so the horse can consume half the grass in a squared field, right? And we figured out that the radius had to be square root of two over pi for the for the horse to be able to eat half the field, the grass in the field. And then we said, let's tie up another horse kitty corner to this guy over here, okay, and set the radius to be the same. The set the rope on the horse to be the same. So this horse, the red horse, can also eat half of the grass in the field. The question is this, what's the area? I'm saying what's the area because think about what's the area that they overlap, where the overlap area where they can both eat the grass is the same as the areas that they can't eat the grass, right? If we set it up so this horse can eat half the grass and this horse can eat half the grass. Are these two areas, this plus this, equal to the area over the overlap? Can you prove that basically? That's the way I'm seeing it. Let's solve this one and then call this a stream and the problem is we don't know how to solve it. I don't know how to solve it. Everyone, I'll post something in Discord later. Hopefully I'll explain it. I said, awesome mask of Raven. Awesome, because I don't know. Like right now my brain is not much. There's no way I would find it. It is an interesting problem. Yeah, draw it as r equals 1. It will make sense. So forget about this. Just say r equals 1. Okay, we do maybe on Discord. See how it goes. Second horse on top of Verdax, right? Yeah, here. That's right. So they're both tied on the corners, right? And they're coming out and they're eating the grass and they overlap in this area, right? Coolio, we're about to call this stream. I gotta, so you guys, coolio, nice. I'm one of the quadrants first. Congrats, congrats. Let's call this stream again. California Nights, we got it, right? So if you can make it, we're doing a stream tomorrow night, 8.30 p.m., current events. We're doing a stream Monday, 8.30 p.m., comic books. We're doing a stream Thursday, 12 p.m., cooking live streams in the kitchen. We're doing comic books on next Sunday and next Monday at 11 and 2. We're doing current events next Tuesday, March 31st at 8.30 p.m. And on April 1st, we look at our updated version of our data for COVID-19. And if there's anything you want us to look at, go to our Discord, post it, I'll try to create columns where we can take a look at the data. Everyone, just remember the finding actual area to go overlap isn't a question. It might be really hard. Just try to find why the overlap is equal to the area and neither can reach. I think this problem is pretty deceiving. Deceive me, that's for sure. Amazing stream. Awesome, Spiderman. Glad you loved, glad you liked. I hope you guys have a fantastic day today and if you can make it, we're on tomorrow, 8.30 p.m. Okay. I hope you guys enjoy your lockdowns if you can. Bye, everyone. Spiderman and the mods. I forget who the mods are here. Thank you for taking care of business. Thank you for the subs. Thank you for the follows. And this is our Patreon page. This is where we're doing the Twitch livestream. And we're announcing everything on Twitter and Mines and Gab and L.O.N.B.K. And the links will be provided in the description of this video once this video is loaded on the YouTube channel for now. Bye, everyone. Hope you have a fantastic day.


In 2015, the Hubble Space Telescope captured the sharpest and most detailed image ever taken of the galaxy. It shows over 100 million stars and thousands of star clusters embedded in a section of the galaxy's disk, stretching across over 48,000 light years. It traces the galaxy from its central bulge on the left, where stars are densely packed together across lanes of stars and dust to the sparser outskirts of its outer disk on the right. Zooming into the boxed field, we see some foreground Milky Way stars in the line of sight to Andromeda, and a couple of distant spiral galaxies shining through Andromeda's disk. The large group of blue stars in the galaxy indicates star-forming regions in the spiral arms. While the dark silhouettes of obscured regions trace out complex dust structures. Underlying the entire galaxy is a smooth distribution of cooler red stars that trace Andromeda's evolution over billions of years. A large number of star clusters can be seen in this analysis of Andromeda. This 150 light years across view of AP-14 and others like it are helping astronomers interpret the light from more distant galaxies that have similar structure.