Good morning and welcome to the chart of the week video with me David Madden Today's date is Wednesday the 10th of June 2020 and the time has just gone 9 30 British summer time And this week's chart of the week is the Australian dollar versus the Japanese yen The Aussie yen and the reason why I want to talk about this currency pair Was because the Australian dollar is considered to be a typical example of a risk on currency Which basically means whenever traders are bullish about the the state of the global economy or their optimistic I think their prices of assets such as stocks and metals are going to rise The Aussie the Australian dollar tends to push higher on the flip side that divide the Japanese yen tends to be a risk-off currency So whenever traders become fearful about the state of the global economy or dessert or the selling pressure in stocks and or metals You often see The Japanese yen before well because it's it's considered to be or deemed to be a lower risk currency It's kind of a safe haven currency So I think this is an interesting currency pair given that one one side of it is kind of risk on the other side of it is risk off If we take a look at the price action for the last few months since mid-march So nearly for nearly three months now We've seen a solid upper trend in the Australian dollar versus the Japanese yen and the fact only in the last couple of days Did we see the currency pair hit its highest level in over a year? So it's quite clear that the Trend has been to the upside things are looking quite bullish although we did see a Bit of a pullback in the last couple of days the Australian dollar lost ground versus Japanese yen But I lost the lost ground across the board in the last couple of days due to rising Political tensions between Australia and China China is obviously a large a major Export destination for Australian goods. So any kind of political rumblings between those two countries could have negative economic impacts And a negative economic impact on the Australian economy So so what I wanted to discuss in this in this in this video is You know, what are the potential interesting interesting price points that are on potentially on the horizon in the near term You know, are we going to see a continuation of the wider upper trend in the Aussie end or are we going to look for our reversal? Or the most recent declines that you've seen is that just a pause in the wider upper trend or is the beginning of something Could it be the beginning of something larger? So if you take a look at the price action in the last couple of days We've had a fairly decent fairly decent move to the downside yesterday Take a look at the MACD Histograms MacD indicator. We can see that the the negative move in the on the currency pair has been confirmed by the decline in positive momentum So if you do look to press on lower from here and should we take out yesterday's low in at 74 It's about 47 with Kubanaki heading back towards this red line here the Trinity moving average and that comes into play at 72 spot 24 And if you do have a decent break below that we could head back down towards This area here whereby where the 100 a moving average and the 50 moving average both converge And as you can see both metrics the 100 a moving average and the 50 moving average have both acted as decent support levels in the past So if we if metrics have been act of in a pretty decent level of support in the past It makes them more likely that they'd be decent levels of support in the future although there are no guarantees So these are potential price areas to keep an eye on for to the downside should we see a decent move lower But keep in mind Mark has been in a solid upward trend for nearly three months and we haven't had a very large pullback We've had a few small but we haven't had a large one But mind you there's no guarantee that we are going to have a large pullback It's quite possible that this pullback that we saw yesterday this move lower Could be just a small pullback before we look to press on higher again And if that is the case should be pressed on higher from here We can if we take out the highs of the last couple of days, we keep looking heading up towards 78 And then if you go beyond that we could be looking heading up towards 80 If you are going to be trading this currency pair or in fact any any any any instruments on the financial markets in the next day So please be mindful that later on today at 1900 British summertime the Fed reserve will have their interest rate decision And the press conference will follow 30 minutes later. Thank you for listening. Say say stay safe Have a good trading week and good luck


Hello and welcome to the session I am Deepika here. Let's discuss a question which says, choose the correct option and give justification. In given figure, if Tp and Tq are the two tangents to a circle with centered O so that angle P Oq is equal to 110 degree then angle P Tq is equal to A 60 degree, B 70 degree, C 80 degree and D 90 degree. So let's start the solution. Now given Tp and Tq are the two tangents to a circle with centered O. Therefore, Tp is equal to Tq because the lengths of tangents drawn from an external point to a circle are equal. Let us give this as number one, in given angle P Oq is equal to 110 degree, now join O T. Now we know that the tangent at any point of a circle is perpendicular to the radius to the point of contact. Therefore, angle O P T is 90 degree similarly, angle Oq T is 90 degree. So in right angle T O P and T Oq we have again O T is equal to O P common. So by RHS is congruent to triangle by sector of angle P O 110 degree as 90 degree and angle T O Pq as 55 degree. So we have angle P T plus 55 degree because the sum of the three angles of a triangle is 180 degree. Angle P T O is equal to 35 degree plus 35 degree which is equal to 70 degree. Since our option B is correct and this is our answer. I hope the solution is clear to you. Bye and take care.


David here at the City Golf Day 2022, how's the day been so far? Wet, in a word, just played three holes and it's just stopped raining, it's soaking, it's not raining for three weeks. It certainly has done today but yeah it's great now it's fine up, it's sort of great to be here and we're having a good time anyway. Enjoyable during the week to get out on the golf course, come rain or shine and have a bit of fun, see some new faces that you've not seen before and some old faces that you've probably not seen in a while as well. Yeah it's good to catch up with a few people, I'm the same group as Dave Baldwin today, I've obviously known for a long time from his time at the City so yeah we've got a lot to catch up on and it's great to do that over a game of golf. Being excellent, the two lads that we're playing with are very good so they've made us feel them more like at home I think. So yeah really looking forward to it. Team mates on the field, team mates now on the golf course as well, the connection's still there do you think Barry? Yeah it's always there, I see Gary down at Cluck Eat now when we're playing golf together. I have a couple of beers in that and it's nice to come back on a golf day like this. Play with two lads who are playing really well and yeah enjoying it. Well look great, yeah I'm fine, not wet or miserable, actually it's stopped raining now so everything's going to pick up but it's been a rough start. Much easier in the sun then here at the City Golf Day? Yeah just a bit easier but I mean the wash hour's forecast but I didn't know it was going to be a monsoon type of thing but hopefully it'll stay off now for the rest of the day and we can enjoy it. It's been a great day so far when we first came out. I think the heavens opened and we got a little bit wet but of course it's in great nick and we're all enjoying it. Decent team together as well haven't you talked us through that and obviously familiar with the people that you're sharing a course with today? Yes I think we've got a couple of ringers, I think Glyn's playing off 22 but he's playing off about 12 I think. So hopefully we've got half a chance. No we're really enjoying it and yeah it's great to be out here and change of scenery for everyone. How's the day gone so far on the course you're doing all right? I think when you play golf you have good days and bad days so yeah yeah what golf does it brings you back with with one good shot and yeah it's a really nice track and you know just enjoying it like I said. I think the organisation of it's fantastic just about from the rain this morning so I'm going to lodge a complaint about that. That was absolutely torrential rain but no it's fantastic I think the golf club deserve a lot of praise. They've done they've done some hard work to get it into the condition that it is now and it's it's a great credit to the you know golf club itself. It's been good apart from probably the first four holes when the torrential rain greens were flooded and but no it's been it's been good the golf ain't so good but no it's it's lovely now so it's a good company. A good company you're around familiar people as well I guess it's easy to hit it off when you with people you know playing with people you know. Yeah I was seeing the gaffers group there's a few people I know as well from previous golf days that I've been to so good to see a few of them so we've got I think we've got dinner after this of weeks so I'll speak to a few and a few in the bar so no it's it's I think every club sort of does it but no it's courses in and decent Nick as well so it always helps. Nice to take a break from the pre-season training as well we've only been back a couple of days but I think particularly some of the players will be feeling like it's a lot longer. Yeah it was it was obviously yesterday was just sort of testing obviously usual testing stuff whereas today we were out in the grass got to see the goalkeepers today so had a good hour with the goalkeepers given a bit of a bit of aerobic stuff so no it was good it's it's what it's what you want to do so body's feeling a bit tired now especially golfing as well doesn't help but no it's it's something I'm looking forward to getting going as as the weeks go by. Now are you finding it back here in like we say the the dual row when you first started a player and the coach but predominantly as we say over the course of the first few days part of the coach and set up and like we said today taking more of a hands-on approach with the the goalkeepers as well. Yeah it's going to be different especially obviously the way last year last time I was here was just a player which focused solely on that but now my aim is to whoever's going to be playing to make sure they're ready for the game obviously Harry's there at the moment so Harry Harry I've got to make sure Harry's right and if if I need to be I'll just try and be as best Nick as I can but look I'm I'm not here to tell the manager look I want to play I won't be back when when you go to the coaching role it's it's 90% coaching it's 10% to play out you know what I mean when it's player coach so it's one I did last year and one I enjoyed and obviously winning the league and getting promoted was was a highlight so hopefully it can be two years on the track would be nice. I'll try and keep keeping in touch with what happens at city anyway and you know try and get down to some games so catch up with some people people there as well but yeah it's great to do on a day like like today when there's no pressure and there's no nothing else to focus our minds on other than they're knocking a little white ball around the field. People's competitive edge comes back out doesn't it? He does yeah I'm guilty of that as well. I actually came as a guest to a Bradford City games during the season where I met up with loads loads of players from my time in the 80s but it's yeah I've seen Tyredall and Gary Watson again today which is always good to see and we've always got stories about the lads from those to you know Bobby Campbell and David Mcneven and people like that Mark Ellis Barry Gallagher's here today as well so it's good to see them it's an enjoyable day just those first three holes in the torrential realm were hideous.  Always seems to be Bobby Campbell who the stories are about and who the memories are being shared about I guess when you've got a lot of common memories that you've all shared together it it makes it easier when you've not seen people for a while and you can like we say pick up where you leave off and away. Yeah it's true I mean Bob gets a let's say he got some bad publicity quite a bit but honestly if you knew Bob he had an art as big as a lion he were a gentle giant apart from being on pitch if I didn't cross it at the right time or whatever then I would get a bullocking but apart from that he were a great fella honestly regret some of the stories have been exaggerated exaggerated and exaggerated Bob Campbell were an absolute star great lad supermate and one of the lads and he'll never be forgotten. I think obviously I live in the area so any anyone if I go out for food or whatever you can just feel there's a buzz around the city and everyone says oh what's it like how is it and it's it's been fantastic so I've seen Nate and Clark well ago we arrived quite late just before tea off because I'll see with training so I'll see a few more inside but I've seen Clarky good to see him haven't seen him for a while so I'm sure there's one or two others that that I know so but no it's it is it's a family club and that's what the morals of the club I think they build themselves on behind that so hopefully we'll crack on get a good pre-season under a belt and see what the season is in store that's why the guys wanted to to be involved in the day to be connected to the the commercial deals and the people involved and just being in and around the local area so that's that's something they're very keen to embrace and you'll see on match day that they're very keen to embrace the fans as well so um yeah I think first of many and uh yeah hopefully my golf games improves it's been a good few uh few months now as well since you applied on behalf of your father for the Robert City job and and that happened how have you found it so far in terms of seeing your dad and Glen in the dugout and being a part of of the experience is it confidence for them for you are you looking forward to next season as well yeah I think they're all very excited about the season ahead I think having 13 games as a just a little bit of an insight into what what the club is all about understand it I know understanding the culture of the of the city as well and yeah they're just all so excited about going into next season there's a buzz around the place and uh yeah hopefully results are going to follow as well so uh I think they're all excited can't wait to get going to be honest I saw Mark Mark Hughes and Glen Hodges before the before that went on the first tee and I had a little chat with them of course from knowing from Man City days so yeah I'm looking forward to the rest of the game what are you making of the work that they're doing so far Mark and Glen obviously following Bradford City last season and looking into the positivity generated from pre-season so far is really impressed yeah well I believe that season tickets sales have rocketed which is probably understandable he's he's a great manager and it's a great asset that Bradford City have got hopefully the the support that they're getting they'll be repaired at the end of the season I'm sure they've got success now with Mark Hughes and then he'll probably turn out to be quite a legend at the club but everything's geared now for success I've been talking to somebody early about the new executive officer at the club guy running the show he's done a lot of changes and made a lot of improvements so it's looking good for the for the season and hopefully they can go up straight away as somebody who's worked as you mentioned professionally with Mark Hughes put together at Manchester City how much confidence do you have in him coming into like your circle that you used to play for in Bradford City that he can be the one to turn the fortunes and do a good job here well as I just said I think it's a very true move by Bradford City he's a great asset to have I'm sure he'll get the best out of the players he can get the squad together that he wants if he can sign the players that he wants then he'll get them together get them organised I'm sure they'll even though it's his first season it'll be a successful one which looks like some good signings have been made so I think I'm like a lot of city fans that really really excited about what the what the next nine or ten months holds and you know fingers crossed this is the year that we get out of league two and keep that that progression going and you know get back in the championship at least in the not too distant future once you've played for him you know a part of your heart's always there it never it never leaves and it's good to see Mark Hughes he a lot of people surprised including himself when he came but I think he approached the club which were a great a great thing to do when this is his first full season he's got you know he wants so he'll he'll be judged on that this year and I'm wishing him him and Glen all the best if they've got as much faith as we have in these two that we're playing with today Dave and Graham he'll do all right because these lads are helping us through and right I'll tell you we need it


We are at lecture 30 today probably makes pretty good sense because this course when it's all said and done will be Somewhere in the low 60s as far as lectures or DVD type lessons So we are I think exactly at the halfway point of the semester with spring break pending So if we look a little sparse today in the classroom, I guess they just didn't read their Information properly and they thought that spring break started this morning But it actually starts this evening at the end of all the classes. So I'm sure that they would have been here But it's a clarification error So we will kind of finish up 7.7 today, I think It's a battle to get this complex Roots situation covered because some of the ammunition we need we haven't had yet So we have to kind of jump ahead and pick a couple of things out of chapter 8 and use them There's a chance you've used them before in another math or math related class But I want to take a look at them Kind of validate that they do in fact work and then use them in this particular case So here's where we are in Terms of the cases that we've covered We didn't really handle it this way But if the value under the discriminant is positive The square root of b squared minus 4ac you actually get two distinct real roots So they're real and distinct So we know what the solution looks like it looks something like this. We've handled that we've done examples with that We've even done a boundary condition problem with that. So that's first case Get the characteristic equation get the roots go directly to the solution and then find the C values if in fact we have additional information Case two is where the value under the discriminant is zero. So you don't get two roots you get a double root and So the common value for r1 and r2 it is the same So we kind of upgrade the solution a little bit and we Validated that something like that has a chance of working because of the nature of the product rule in the terms that you create When you look at the product rule. So here's our third case So we've got a negative value under the discriminant If we have real coefficients in our characteristic equation, which will always be true for this class We will have two roots that are Complex conjugates of one another So there's the nature of our two roots that we're going to deal with today So there's case three now, there's some more to that but it kind of goes jumps directly to the answer and That's too big of a leap as far as I'm concerned at this point in time So we're still in seven point seven which is in the supplement to the text We're looking at the third case of second-order linear Homogeneous differential equations. So the when I say complex roots Complex roots to the characteristic equation. So there's the nature of our two roots We've got a real part and an imaginary part you should expect something to be very different from Real numbers because these numbers are Not real at all and they're very strange when you start dealing with square roots of negative numbers especially in the exponent position because the solution Is going to look something like this and since they are distinct we can allow for The two roots in this fashion as opposed to the double root So look at the ugly thing that's going to occupy R1 and The equally ugly thing that's going to occupy the position of R2. So it turns out that it Looks like an exponential type function because we've got the base e but when all is said and done and all the simplification is done, we're going to turn out with a Trigonometric result. So that's our goal today is to take this and Simplify it in some way shape or form. So we'll come back to this But there's a couple things I want us to do that actually kind of rate a couple topics from Chapter 8 Get them enough not to get full understanding of them, but just enough to use them so that we can simplify this So here's a couple things that possibly you've seen before in another math class Or math related class that we now need to use these are Taylor series have you dealt with Taylor series before and other math classes or Maclaurin series power series that Express what e to the x is in terms of the thing that's occupying the x position So it's 1 plus x plus 1 squared over 2 factorial x squared over 2 factorial x cubed over 3 factorial and so on and this is an infinite series But you can see that it would converge if let's just take an example Let's say we want e to the I Don't know keep it simple. We could do e to the first or we could do e squared Let's do e to the first and you can see Please make this series believable. This is how your calculator operates by the way your calculator doesn't know how to do e to the x problems, but it converts this to Probably a 11th or 13th Taylor series and it computes based on what you're trying to find E to a certain power so if this is true This is e to the x then everywhere. I see an x out of be able to replace it with a 1. Is that correct? This is a series for e to the x. We now want e to the 1 so x is equal to 1 so 1 plus here's an x That'd be a 1 We'd have 1 squared over 2 factorial 1 cubed over 3 factorial 1 to the 4th over 4 factorial. Let's get one more 1 to the 5th Over 5 factorial so it's a really easy series To write out so if we wanted to e cubed everywhere we put a 1 we'd put a 3 But we know what e is approximately so it's probably makes sense for our first validation to put e to the 1 So I'll put a question mark there since we're trying to validate it so the 1 plus the 1 is 2 well we're On our way 1 over 2 factorial is 1 half. That's pretty darn close already, right? We're not very far along in the series 1 over 3 factorial. What's 3 factorial? 1 over 6 1 over 4 factorial 1 over 24 And 1 over 5 factorial 5 factorials 5 times 4 times 3 times 2 times 1 Okay, sorry. I didn't see that look on anybody's face that you know, what in the world's a factorial but Got that clarified that's 5 4 3 2 1 120. Is that right? Somebody that has their calculator out and working what's 2 plus a half plus a sixth plus 1 over 24 plus 1 over 120 Of course to get e to the first we need to let this thing run indefinitely, right? See how close we are at this point 2.716 1 6. Okay, so we're not there yet So you can envision the rest of these terms being added in and this is a legitimate Power series progression for e to the x So why do we need that? We have e to some ugly power We want to be able to write it out almost in polynomial type form So this is powers of x x squared x cubed So it's kind of an infinite termed polynomial if that makes any sense We're also going to need in The simplification. I know it doesn't look a whole lot like simplification yet I think it's going to get worse before it gets better But we're also going to need this same kind of a series expansion for the sine function Because we're going to actually end up with the sine of something and we're also going to end up with the cosine of something One way to remember this is that the sine is an odd function Not like strange or mysterious odd because the f of Negative x is the negative of the f of x Notice the powers they're all odd and notice the factorials. They're all odd So that's a handy way to remember this. Let's just try something here. Let's try the sine of pi over 6 So if this particular series works for the sine of something again This is how your calculator finds the sine of something. It doesn't know the sine function So if this is the sine of x everywhere I see an x I should be able to replace it with a pi over 6 Now let's say we stop there. We're not very far along in this infinite series, right? We got the first term Are we reasonably close? What is the sine of pi over 6? That's a fair question for a Friday When yeah, what is the number pi divided by 6? Somebody take the number pi and divide it by 6 Point five two three six We're doing pretty well already aren't we this is a half and we're at point five two three six Here's how these things plot along which will explore these in depth in chapter 8 We've got too much right? We need a half. We've got point five two three six So we're going to subtract some away. We're going to subtract in this case pi over six cubed over three factorial Guess what's going to happen? We're going to subtract away too much So what are we going to have to do we're going to have to add some back in what's going to happen? We're going to add too much back in what's the next term. It's subtracted. Oh, we subtract too much So that's how it goes it kind of converges eventually on this value point five. So let's get a Couple of terms here and see what we get Let's do these and see how close we come to the value of One half, which is what the sine of pi over six is supposed to be So what's pi over six the quantity cubed all over three factorial anybody? Didn't we subtract away a little too much right? We needed to subtract out point oh two three six But aren't we getting closer to a half? Which is what we're supposed to get closer to now. We're under one half. We have to add something back in What's pi over six raised to the fifth power? Divided by five factorial. It's not going to be very large Negative fourth So three zeros three two eight So if we were to add these up knowing that we're not even close to the entire infinite series But we've picked off the first three terms. That's pretty close right to the value of one half This thing minus point oh two three nine and add this back in. What is it point five zero zero zero two eight? Is that right? Zero zero two one three okay pretty close to one half So if we kept going we'd get each term we add in and subtract add and subtract We get closer and closer and closer to this value that we know is the sine of pi over six Doesn't prove it by the way. We're not proving these but we're at least Seeing if they're plausible see if they're believable so it seems to get us what we need to get for the sine of pi over six I don't know that we need to take our time to do the cosine as well Because it works just the same way The more terms you pick off the closer you get to the actual value that you want Notice cosine is this is an odd function. We've got odd powers and odd factorials cosine is an Even function right because the f of x is equal to the f of negative x which makes it even all the powers are even all The factorials are even so that's those are handy Memory devices to remember the power series. You don't have to remember them now that go along with sine and cosine All right, let's use this one first we've got e to a power so we want to Go back to our complex solutions to our characteristic equation and then eventually we're going to use all three of these But let's use this one first so our solution at this point just plugging in r1 By the way, if you just plug in the complex roots Then you don't really have the answer because you don't have the function what it really looks like So this is why we have to Do what we're doing here Since I've got a sun I could distribute the x so x times the alpha and x times the beta times i then I Could take what is a sum in the exponent position and kind of work backward algebraically Into a product is that correct is that equivalent to the one that's above it? We've done that enough. I don't think I need to break that up into a separate step Same thing here. I could distribute the x x times the alpha that's here and x times the negative beta times i So that's going to be e to the alpha x times e to the negative i times beta x Anything gained by doing that right there you can combine some of the okay, what what do both terms have we've got two things added together Do they both have something either they both have e to the alpha x right? So by taking that sum in the exponent position Translating it backward algebraically to the product of two things with like bases We're able to now not that it's anything major, but it's Ugly enough, so let's try to farm some of that stuff out in front if we can I'm going to call this i times negative beta x is that okay negative i beta x So here's what we off to the side we have to get Something that's going to substitute for i times Something in this case that something is beta x We'll pick the problem up back here when we get what we need to simplify this So let's say we have something e to the i Theta just so we don't have a beta and an x there yet, so we have something occupying that position According to our power series For e to the x whatever is occupying that position where x is we can put it here Put it here and put it wherever x is in that infinite Series that infinite power series So for e to the i theta it ought to be one Plus now normally it's x So now it's going to be i theta Then it's normally x squared over two factorial, so it's going to be i theta squared over two factorial i theta cubed Over three factorial, so we're using that e to the x expansion Everywhere there's an x we're putting in a an i theta Let's get one more This by the way is in the supplement they kind of make the leap to Here's what e to the i theta is but it was my guess and I think it's true that we We don't have all the background that's necessary for this, so we're trying to fill in a little bit of the gaps here So we're going to square the i. What do you get when you square i? Negative one So it's going to be negative theta squared over two factorial Next term what do you get when you take i and cube it? What's i cubed? negative i and i to the fourth what's i to the fourth is One and then things are going to start to repeat right? Because then we're going to have an i to the fifth and i to the fifth is back to i Right, so am I being redundant here? Is this something you've done in? Another math class or math related you've done this anybody you've done it, okay? But it looks like several of you haven't done this I don't I don't like mystery formulas to all the sudden appear So let's just a couple steps and we'll be able to validate this The grouping that's going to happen from this point forward is we have some terms that have i in them Every other term will have an i in it. Is that correct? And then we have terms that don't have an i in it So let's group together the terms that don't have i in them So there's one actually it is one minus theta squared over two factorial plus theta to the fourth Over four factorial is that enough of a pattern to know what's the next term is going to be and what it's s i g n is going to be Next term although we don't have it would be what? negative Theta to the sixth over six factorial and so on right we're going to have a bunch of those Every term that I've underlined Has an i in it. So let's factor the i out in front and if we do that we get a theta Then we get a theta cube sorry a minus theta cubed Over three factorial. We don't have the next term. Is that enough to figure out what the pattern is and what the next term would be? It's going to be plus Theta to the fifth over Five factorial the next term is going to be minus and it would go on forever now We need to does that look familiar at all to something I had up here five minutes ago One minus something squared over two factorial plus something to the fourth over four factorial Is that cosine? Here's here's what I had up here a while ago Does that look like what we have the terms? Excuse me that did not have an i One minus something squared over two factorial plus something to the fourth over four factorial isn't that exactly what we have? So this thing we can call the cosine of theta right because on the green paper It was cosine of x the variable was an x in the expansion. So that's a cosine of theta How about this thing that is multiplied by i does that look familiar? That should be our sine Taylor series expansion or power series expansion Sine of x is x minus x cubed over three factorial x to the fifth over five factorial and so on We don't have x's we have Theta's So Theta minus Theta cubed over three factorial that should be Sine of Theta is that okay? So those are the three things that we haven't really had in this book yet that that we need to make that leap So that's what e to the i Theta is we have e to the i Something else so everywhere. We see a Theta. We're going to have to put in a beta x and over here every time We see a Theta. We're going to have to put in a negative beta x So here's where we are. I'll put the beta x in parentheses And we are going to use That that we just kind of developed in a way So e to the i beta x I want to put a beta x everywhere. There's a Theta So that's going to be what cosine said a cosine Theta. It's going to be cosine beta x plus i sine Beta x I know you don't think it's getting better But it is getting a little bit better because we'll get be able to consolidate some terms So we made a substitution for e to the i beta x and we plug beta x in here in here That's what we've done. We need to do a similar Thing over here. We've got i times something. What's the something it's negative beta x So where there's a Theta in this expansion. We need to put in a negative beta x parenthesis So it's probably a good thing We were able to get e to the alpha x out in front because it's already a mess in there We don't need to make it any messier Let's see if we can distribute and combine like terms all in one step So we're going to have a c1 that gets sent to both of these We're going to have a c2 that gets sent to both of these We need to do one more thing before we do that Cosine beta x and cosine negative beta x are they the same thing is the cosine of something Exactly the same as the cosine Of the negative of that That's true right because it's an even function so because cosine is even Cosine beta x and cosine negative beta x are the same if they're the same I'm going to get rid of this and Just call it cosine of beta x is The sine of beta x is it the same thing as the sine of negative beta x It's the negative of it. Why because the sine is an odd function, right? So sine of negative beta x is the same thing as negative sine of Beta x So we'll get rid of that. So now everything is in terms of beta x So we're going to have a and you're not responsible for this Reproducing this development. Isn't that nice news today? That's the best news yet That now it gets a little emotion out of you So c1 is going to be distributed to this and c2 is going to be distributed to this So don't we have c1 plus c2 Cosine beta x is that correct c1 is going to be sent to this C2 is going to be sent to that. So if we factor out cosine beta x we'd have c1 plus c2 Well, these are constants. So the sum of two constants is just another constant. So we'll be able to simplify that C1 is going to also be sent to this and C2 is also going to be sent to this so we've got some sine of beta x's and Here we've got negative which let's associate that with the c2 So we've got some more sine of beta x's. How many sine of beta x's do we have? C1 minus c2 That's how many sine of Beta x's we're going to have And that takes care of everything done it didn't we use all the terms c1 they got sent to both of these terms C2 they got sent to both of these terms This is not much of a stretch at all to say that some arbitrary constant added to another arbitrary constant is a constant So we'll call that k1. This is a little bit of a stretch So we have to allow for our constants in this particular problem. I'm sorry. I forgot something didn't I? This had this had an I and this had an I right so there should be an I here In that second term So if we take c1 minus c2, that's not a stretch. That's a constant But that constant is multiplied by I if we allow for our k values to be Non real numbers then we can go ahead and say for c1 minus c2 times I We're going to call that k2. We're just opening it up and saying it's not just some normal number It might in fact be complex so we have taken a Solution that looked very exponential Because we started with e to some ugly power and e to some other ugly power and we've converted that into something that's very trigonometric and You'll see when we get to applied problems why we want a solution that is Oscillatory which this is an oscillatory function That can be affected by this coefficient out in front because something is going to have a Path or a description of its motion that is Oscillating so we want the model to match what the motion is actually going to look like so if we have two complex roots that are in the form of Alpha plus beta I In alpha minus beta I There is what our solution is going to look like the problems are going to be very easy now that we've done this battle We've identified what alpha is it's very clearly identified in the solution We've identified what we do with beta once we identify beta beta is very clearly identified in our solution So back to this sheet and let me unfold what the author says our solution should look like in case 3 So if there's a root alpha plus Beta times I and alpha minus beta times I Here's what our solution is going to look like e to the alpha x. We got that right they have c1 We had k1 same kind of deal Cosine beta x plus c2 sine beta x so it is the sum of sines and cosines And you'll see that we're going to need an oscillatory model and this is exactly what we want in the third case So let's do our first example of this type and then we'll add some boundary conditions time permitting Which I think we're going to have time to do this all the way through Let's go from the second order linear homogeneous equation To the characteristic equation that skips a couple steps What is the characteristic equation that goes along with this? That 41 is not looking too good is it we're not liking the 41 But let's see what happens Probably not going to factor. I think we can concede that fact because 41 is kind of stubborn So let's see what the quadratic formula is going to yield We know what it's going to yield because it's an example of this type So it's going to have a negative under the radical. It's not going to be a surprise. Let's just validate it negative B plus or minus B squared Minus four times a is one times c is 41 all over twice a So we've got a hundred four times one times 41 is what 164 So we've got a square root of negative 64 What are we going to call the square root of negative 64? Let's call it Steve now Ed Ed Let's call it Ed now. What would we call it? Eight I would be a better name and the fact that everything is divided by two Let me tell you what I see occasionally from intelligent young people such as yourselves somebody will make a just a radical Departure from reality and reduce ten and the two Okay, what's wrong with that? Can I just reduce the ten and call it a five and reduce the two and call it a one? So the answer is five plus or minus eight. I I'm not going to write it down because it's not correct How can I reduce numerator and denominator? It's got to be a factor of the numerator, right the entire numerator. Don't we have two terms in the numerator? So in order to reduce a two in the numerator and the denominator I've got to have it as a factor not just one of them. It's got to be a factor of both of them And now that it's a factor of the numerator and a factor of the denominator We have our two solutions. I know nobody's going to admit that you have ever actually done that Reduced the ten and the two but I've seen it enough in the 30-plus years. I've been teaching mathematics, too I almost believed that it's true But then reality kicks in and I know it's not true So we have alpha equals five Beta equals and we are always in our problems going to have complex conjugates of one another Because the coefficients of our characteristic equation will be real and that guarantees this kind of solution Beta is four you could say beta is four or negative four. It's not going to affect the solution So let's choose the easier of the two. So there's what our solution is supposed to look like in this particular category So we know what to sub in alpha and beta e to the 5x So since we've done the battle and come up with this It makes the getting from our solutions complex solutions to the characteristic equation Getting to a final solution a pretty easy process now. There is some memorization So you're probably going to have to memorize this But it's worth memorizing as opposed to trying to develop it. I think we'd get a hundred percent agreement on that Some things it's not that big a deal You know if you don't remember is it one plus tangent squared that secant squared not that big of a deal because you can take sign squared plus cosine squared equals one and 12 seconds later you can have the tangent squared secant squared identity But I think it took more than 12 seconds to develop this. So that's probably one you want to remember Let's add to this problem Some initial conditions or some boundary conditions. Let's say that we also know or we want y of zero to be one and The y of pi to be two So you know what's going to Result from this we're going to be able to solve more than likely for k one and k two So we'll have a solution as opposed to a family of solutions So y of zero equals one So x equals zero y equals one, right? So one equals e to the five zero. I never did address the test I didn't have any grading time yesterday. I am taking over a class for a teacher who's going on family medical leave So I kind of was bringing myself up to speed to take over that class for her so I'll be doing that the rest of the semester, so No grading time yesterday. I apologize for that. I do want to grade them all before I decide what to do anyway as far as just Scaling it by a certain amount of points or throwing out everybody's worst problem. So I Knew I wasn't going to have them all graded So e to the five zero is e to the zero, which is one Cosine of four times zero. That's the cosine of zero, which is one and sine of four times zero is sine of zero, which is zero we go ahead and Eat of the five zero is e to the zero, which is one so we end up with a solution k one is one so we also know that Y of pi equals two so when x is pi Y is two K one we already know so I just put a one in there not good That's what I was thinking about when I was writing down the other one I'm not liking the way the second piece of this is going to work out What happens? Why is it not good? Okay, we've got sine of four pi which is zero so we lose our K2 so we don't know what our K2 is right So I've got flawed data here. Let me see if I can find that where I got this Maybe I got it from the list of problems at the end. Maybe I can make the correction. I'm not seeing it here In this list of problems But we're not going to get a solution with this right I've got Y of Pi Well, I wrote that down wrong. Maybe it's Y prime of pi Is equal to two? Let me see what that would correct things Yeah, I'll get it corrected and we'll look at the boundary value problem But that's not going to get us that needs to change to something else because we lose our K2 and that's What we're looking for out of this equation. So something happened. I wrote down the wrong Conditions All right, I'll get that corrected and we'll look at that At another time we have one more boundary condition problem to look at and Then we'll be right where we need to be In this section so let's suppose we had this problem that bothers me that I wrote that down like that That's not good. This Doesn't necessarily have to fit in the same category. We just finished it could fit in any category since we're now done with all three cases so the characteristic equation is Can you go through the mechanism? Say that again, please. Can you go through the mechanism for that the how we get from here to here? Yeah, okay Let me get this part done.  Thank you. That's what she said, but I didn't write that down. So we've got a plus four and a plus four Isn't that what you said? Yeah At this point in time in this class today, I probably trust you more than I trust myself with values since I've got a flawed Conditions in that one problem So we have a double root, okay? Jacob wanted to know where how we get from here to here. So this is going to be quick But we know that something some original function plus its derivative Times the number plus its second derivative possibly times the number a Function that has a chance of working there is the exponential function And we could have a C in front of it, but I'll forgo that just to make this a little bit simpler So since this is the nature of what y might eventually be We need to be able to plug in its derivative and its second derivative. So that are in the next one to be our square Okay, good, and then you can factor out an e to the rx, which is never equal to zero Therefore, this is the only realistic part that has a chance of being zero All right double root. So let's jump to the solution. This is case two when we have a double root What does the solution look like? That work we will see similar Situations when we have to kind of keep going with this Philosophy of adding an x till we get a solution that actually works Hopefully my data here is good So let's see Y is two and Y prime is one. I bet you that's where my mistake was on the other problem So here's some initial conditions or boundary conditions so when x is zero y is two and When x is zero Y prime is one. So we do need to take the derivative. Unfortunately, it's got a product rule, but it should be fairly quick So when x is zero y is two So that term is zero We've got e to the negative four zero which is e to the zero which is one so C One is two Y prime. All right, here's our y value. So we need our y prime. What's the derivative of C1 e to the negative 4x? 4 Negative 4 C1 Okay, and now we have a product rule first times derivative of second plus second times derivative of first and And we want when x is zero we want y prime to be one. So y prime is one So there's a zero as a factor. So that term is gone Negative four. Don't we already know that C1 is two. So let's plug that in e to the zero is one That whole term is gone. So we've got C2 e to the zero. So that's just C2 So we should be able to solve for C2 So it looks like C2 is nine So our final solution C1 is two C2 is nine So there's our final answer to that with the given boundary conditions. Have a wonderful spring break. I will see you in a little over a week


JJ asked, can the Lightning Network rules be changed and updated easily, unlike on-chain transactions? Which require a supermajority consensus, where almost everyone has to agree for a simultaneous upgrade? Also, can different groups of users use different variations of the channel rules and form a separate subnetwork? Without maintaining compatibility with the entire Lightning Network? That is a really great question, JJ. In fact, the Lightning Network rules can be changed and upgraded quite easily. The Lightning Network is a peer-to-peer network. It does not have a consensus layer of its own. The consensus layer it uses is the Bitcoin consensus layer. So, Lightning Network rules can be changed. The transactions that are used to implement Lightning routed channels, of course, have to be valid Bitcoin transactions. They have to conform to Bitcoin's rules. Lightning can't get around Bitcoin rules, because its security depends on it. However, how you use the Bitcoin rules to form a Lightning Network channel or a route, how the routes are updated... All of that is off-chain. It is not part of the Bitcoin consensus rules, and therefore it can be modified. In fact, there are a number of different Lightning Network specifications that use different sets of rules... on how they work, essentially different standards. Most people refer to the Lightning Network as a collaboration of three different companies... with three different open-source projects under a set of common standardized specifications called BOLT. BOLT stands for Basics of Lightning Technology. You can find that on GitHub. It is a repository called lightning-rfc, which means Request for Comments. It has, if I remember correctly, 12 documents, BOLT1 through BOLT12. These specify different parts of the current Lightning Network that is running between the Bitcoin and Litecoin blockchains. That is the one that everybody is talking about in relation to Bitcoin today. That is the main and test-net-running Lightning Network we have today. That is a BOLT-compliant network, which means that all three implementations use the BOLT standard... and the specification to interoperate, so they know how to establish communications with each other, how to find their peers, how to construct a route, how to create a hash-time-locked contract... that is used to forward a payment on a payment channel, how to link together multiple payment channels... to form a route, and various other details of the system, what the time-outs should be for routes, etc. That is not the only one. There is another specification called LIT. Ethereum uses yet another specification for a network called Raiden. Within Lightning Network, beyond the BOLT specifications, there is a significant amount of research happening by a number of different groups. BOLT today uses a second-generation payment channel specification. The original payment specification was called Poon Dryja, named after the two co-authors of the paper, Joseph Poon and Thaddeus Dryja, who wrote the original specification, which required n-lock-time channels using a specific feature of the Bitcoin script. I believe the current channels are a slightly different specification that uses a check-sequence verify. There are also newer channels, written or specified, if you like, or invented, by some of the other participants in the Lightning Network protocol design, who have given it various names that are the names of the authors of those specifications. There are a number of different ways to make payment channels, and some of those rules are rather interesting. There are more advanced, additional capabilities. There are some additional specifications for doing channels that might end up becoming future BOLTs, meaning they become incorporated into the BOLT standard, which would then allow different clients on the Lightning Network to upgrade to support a new BOLT specification, for a new type of payment channel, routing algorithm, for new node discovery algorithms, for example, multi-channel funding. That is where you do a single transaction to fund multiple payment channels, for doing atomic multi-paths, which is where you send a single payment over multiple channels as a collection of smaller payments, which are atomic, which means they cannot be divided, or various other interesting things. There are Lightning Channel factories, where you can outsource the creation of channels to third parties, watchtowers, and specifications for other people watching your payment channels, without you revealing any information that is private, so you don't have to always be online. All of these are developments that are happening, and they are not part of the current BOLT specification, but may become part of the BOLT specification in the future, to improve Lightning Network. Effectively, Lightning Network right now is a very basic beta-test network, and is very far from complete. There is a lot that can be done, and a lot of interesting research. The state of research is probably two years ahead of the implementation of the live network. There are all of these proposals for doing interesting things. So, Lightning Network can evolve without the consensus-hard fork limitations in the evolution of Bitcoin, which is one of the interesting things. I had talked originally about how, because of consensus, the network development and evolution of Bitcoin itself, and other open public blockchains, over time becomes more and more conservative, and you have fewer and fewer changes that can be pushed through, which means that most of the innovation has to move to layers above. You still have to use the consensus layer in Bitcoin, but that won't change. But on the layer above, you have more opportunities for innovation, and that's exactly what's happening with the Lightning Network. Crypto S17 asks, why did the developers release Lightning Network to mainnet before completion? Crypto S17, they didn't. Basically, a whole bunch of people hacked the testnet clients and started running them on mainnet to the great consternation and complaints against the wishes of those involved in developing those clients. People rushed it into mainnet before it was complete, pushing the devs to finish it faster. I don't know if that was a good thing or a bad thing. I'm guilty of participating in mainnet before the devs wanted to release it, so there we go. Susanna asks, what would be the purpose of keeping a statement secret and later decommitting it and revealing it? Why hide and then reveal what's the benefit and give us an example? This particular concept, Susanna, which is a pre-image commitment, is used in cryptography for a number of different reasons. One example is used, for example, in Lightning Network. So, Lightning uses a concept called a hash-time-locked contract, and an HTLC or hash-time-locked contract is basically a payment channel commitment based on the hash of a secret number. You commit money that can only be redeemed if the secret, the pre-image, is revealed. The only way that the person who is at the end of the channel, or sequence of channels, can receive their money, is if they reveal the secret to the person just before them, who can then only receive their money if they reveal the secret to the person just before them, causing the secret to roll backwards through the sequence of payment channels and getting everybody paid. It gives you a guarantee that the other party only gets paid if they reveal the secret.  The same concept exactly is used in atomic swaps. For example, if I commit with another party funds on two different blockchains, let's say Litecoin and Bitcoin, in such a way that we're trying to do an atomic swap, but the only way I can cash the Litecoin they're giving me is to reveal the secret that allows them to cash the Bitcoin I'm giving them, then neither of us can cheat. That's exactly how we first commit funds to a hash, then we reveal the pre-image, and we reveal the pre-image in one of the transactions, which allows the other party to receive the other side of that atomic swap. That's a mutual guarantee that no one can cheat. On the Lightning Network, what prevents a bad actor from using the revocation transaction to steal coins? Jesse says, I've been trying to understand the game theory of the commitment transactions and revocation transactions in the Lightning Network, but I don't see why someone couldn't proactively use the revocation transaction to steal coins. Can you explain how the revocation key is only revealed if a commitment transaction is broadcast maliciously? What prevents a malicious Lightning node from intentionally dropping off the network, prompting an honest node to publish the last commitment transaction, and then popping back on to publish the revocation key and steal all the coins in the channel? Right, great. Let's talk about this. It's a bit complicated.  But first of all, there is no such thing as a revocation transaction. There are only commitment transactions. And commitment transactions are complex transactions which have multiple different spending branches, meaning that there are different conditions on which you can spend a commitment transaction. That's the first thing you have to understand. There are revocation keys. And the revocation keys are exchanged between the two parties in the Lightning connection after they sign the next commitment transaction. And in order to invalidate the previous commitment transaction, essentially to revoke the prior state, now that there is new state, and to ensure that the prior state cannot be unilaterally transmitted by one of the two parties. And here's the really important thing. It's not like there is one commitment transaction. There are always two commitment transactions, and these commitment transactions are asymmetric bilaterally. What that means is, let's say I'm Bob, and I have a channel with Alice. I have a commitment transaction signed by Alice, and Alice has a commitment transaction signed by me. And we have these on standby where we can counter sign them, transmit them to the network, and activate them effectively. But the commitment transaction I'm holding, which has Alice's signature, is different from the commitment transaction Alice holds that has my signature. And the reason it's different is because the commitment transaction that I have, that has Alice's signature on it, pays Alice first, and then delays the payment to me. And that's really, really important. Meanwhile, the other transaction that Alice holds that I have signed pays me first, and pays Alice with a delay. So the payment to Alice has a time lock on it, whereas the payment to me is instant. I can claim it as soon as that transaction is broadcast. So I have a transaction, it's signed by Alice, it pays Alice immediately, but it only has a time lock on the payment that goes to me. If I choose to counter sign that and broadcast that transaction, I'm creating both of those outputs on the network, but Alice's output can be claimed immediately, and my output is delayed. There's another output that can be claimed by Alice, but that requires the revocation key, and that one consumes all of the channel balance, and that's my punishment output, if you like. And once I've given the revocation key to Alice, if I transmit the commitment transaction, then Alice can take that one output and claim the entire channel balance with the revocation key, meanwhile I can't, because my output is still time locked. So there's this fundamental interplay where my payment is delayed by a bit, but I've given the ammunition to Alice to burn the payment completely if I try to cheat, and she can execute that immediately, whereas I have to wait. And by the time I'm done waiting, she's already executed, claimed that output, and there's nothing for me to claim, so Alice has a head start on the transaction I'm holding and can always claim it before I can. Meanwhile, I have a head start on the transaction I signed that she's holding, and she has to wait on that one, so we're always at a slight disadvantage on the transactions we hold that we can transmit unilaterally, but we're on an equal footing on the transaction the other person holds, which we can close cooperatively. That's the subtle balance in game theory in the Lightning Network.


So I had a question and I've done tons of videos on like what my time is like as a trauma PA, but specifically I was asked a question about on call.  So let's get into the video right now.  This is Dana. Welcome back to my channel. So I had one of the comments posted by one of you all. So if you have not liked my videos or subscribed or hit that notification bell to know exactly when a new video is coming out and left a comment, go ahead and do that right now. But this comment was posted by Taylor Black. So Taylor said, I'm currently an undergrad majoring in biology. I'm interested in becoming a pediatric physician assistant, but I'm not sure if physician assistants have to work on call, which is something I don't want. As a physician assistant, do you have to work on call? All right, so that is what I'm going to be answering today. And if you don't know what on call means, have no fear, I'm going to answer that question as well. But before I get into that video, I do want to say you guys need to join me on Tuesday because I will be reviewing another school. Also, I have realized that there are a ton of schools to review. And so what I'm going to do is I'm actually going to do some of these reviews live through my GTCU forum. So you're going to have to join GTCU to see some of those schools that I'm reviewing as well because there are over 300 PA programs. And I think I might even start reviewing some of the international ones as well. So that's going to bring my scope out even more. So if you're interested in knowing about all the schools, then you have to follow me on YouTube and at the same time join GTCU. So just a disclaimer for you guys that I'm going to be putting out content on GTCU as well. Okay, so Taylor, yes, sometimes PAs have to work on call. And so with that being said, it's all dependent on the specialty that you're in. So for Pete, typically a pediatric PA is working in the kind of like nine to five, eight to four, it's very much your typical 40-hour work week. So I've never seen a pediatric PA that is on call as of yet. But it's not to say that there aren't any. Maybe some of them work like shift work where it's nighttime. And so I don't know if it's necessarily on call or if they're in the NICU. Maybe they're on call there. But when it comes to being a PA in any of the surgical subspecialties, especially if you have like a private office and attending that you work with and you're like the only PA, you may have to take call. And so what does it mean to take call?  So you're going to be the one that they're calling. So call looks differently for different specialties and different people. So for me, my on call means 24 hours. I am on a 24 hour shift. And so when the ED has, you know, somebody is coming in with abdominal pain. And, you know, they did an ultrasound and they see that there are, you know, stones in the biliary duct or whatever the case may be.  And so as the general surgery, acute care surgery PA, what we have to do is not go see the patient. We have to get a history from that patient. We have to ask them like, how long have they been having this pain?  What makes it worse? You have you eaten anything because depending on how bad their gallbladder looks or their appendix looks or, you know, their obstruction looks, whatever the case may be, they may need to have surgery. And so we have to make that initial assessment.  That's how my on-call looks. I come in at 6 a.m., 6.30 a.m., like that morning and I don't leave until sometimes nine the following day. That's me. For somebody else, they might be able to take call at home. You know, it's not in the hospital. So what that means is they're at home and the same thing can happen.  And so if that is the case and you don't have access to your EMR system at home, then you actually have to go into the hospital, see the patient, go through all the steps that I went through as the acute care surgery PA, then call your attending and see exactly what they want you to do. Either staff the patient, admit them and have them booked and posted and consented for surgery that day or the following day or not. That's how it works. Now, there is also the option that you can take call from home, but you do have access to the EMR system. So you can look at all those images there. And then that means that you don't necessarily have to go in. You can look at them at home. You can see is the patient really ill? Is this something that can wait till the morning when you actually get to work because usually you're one of those PAs that are working kind of in that nine to five, eight to four job. So you're going to come in the following day. They would admit the patient to either your service or the medicine service. And then you would see them on your rounds. And so there are various different aspects of taking call. But yes, as PAs, we do have to take calls. It all depends on what specialty you're in. My call is a 24 hour call.  And yes, there is a day that I use to kind of recover and sleep and really get some good rest. But at the end of the day, I get to still spend so much more time with my family than going in five days a week and yet still having to take call every weekend or every other weekend. And that's also something that can actually happen. It all depends on the the office that you work with. If they have other PAs, if they have other attendings, maybe each of you is taking call like once a month, like one weekend a month. So you would take call for that Saturday and Sunday. And if there's any issues, the providers in the hospital will call you, get your assessment and then go from there. But it's not as bad as you would think. But it really just depends on the model that you're working under. So hopefully this answers your question. Taylor, if you have any other questions for me, you guys, you already know what to do, leave them in the comment section below. Be sure to follow me on Instagram at Adana, the PA and on Instagram to get that university. Don't forget to join me on Tuesday for the next school that I will be doing the live kind of review deep dive with you all. And I will also be posting other live deep dives of other schools on GTCU in the weeks to come. So probably on like Thursday or Friday, you'll see that as well. So if you're interested in seeing all of the various different programs, you definitely should check out GTCU. Thank you guys so much for watching. I will talk to you guys next time.


for the opportunity we have to serve in this army and to chance away from each other now please bless him and his family with unity and strength in their relationships. Please bless. On the rigid fights for the represent not only the lineage and honors of who is the senior enlisted soldier in the unit and the principal advisor to the commander. The non-commission officer in charge for Sergeant Flores will pass the callers to Lieutenant Colonel Pannerhand who will in turn pass the callers to Commence Sergeant Major Lornytis. The passing of the callers symbolizes the passing of authority and responsibility to Commence Sergeant Major Lornytis. Charging him with the responsibility and the authority that comes with his position. Charge orders for Commence Sergeant Major Luna's Lornytis. Let me know from this day forward that the commander of the Headquarters and Headquarters Battalion Second Infantry Rodriguez Combined Division has placed special trust and confidence in your patriotism, dedication, integrity, and leadership abilities. Therefore you're hereby appointed as the Commence Sergeant Major Headquarters and Headquarters Battalion Second Infantry Rodriguez Combined Division. Commence Sergeant Major Lornytis will now return the callers to the non-commission officer in charge. Ladies and gentlemen, the commander of the Headquarters and Headquarters Battalion Second Infantry Rodriguez Combined Division, Lieutenant Colonel. CSM on behalf of the tribe I'd like to officially welcome you. I don't think I could ask for a better teammate to form the tribe command team and I'm excited for the next couple of years together and what we'll be able to accomplish serving this great Italian soldiers. I will be a 360 degree leader. I will lead south to the soldiers under my care. I will lead north by influencing those with authority over me. I will lead east and west impacting my peers but most importantly I will stay humble yet vigilant and maintain in my own Compass Needle Center. Second to none, fight tonight. Copsie copsie dot. This is tribe seven signing on. Ladies and gentlemen, this concludes today's survey. There will be a reception held in the Hall of Heroes, welcoming Commence Sergeant Major Lornytis to the battalion. Thank you for your attention. Head charge of the battalion. Second to none. Ladies and gentlemen.


Everybody forced here. I think three boxes MLB definitive and chrome update jumbo number one Random teams here. It's two jumbo's one definitive. Let's randomize. We'll get right into it. Good luck everybody See a monster in this break Go eight times five and three one two three four five six seven and eight Nam queue down to Eddie P and we've got the teams eight times as well one Two three four five six seven and eight White socks down to Padres All right Nam queue white socks Frank L. Marlins national Zach G. Brewer's Frank L. Giants Peter M. Tigers Chris V. Orioles Scott F. Diamondbacks Brian G Yankees Kevin F Royals Justin D. O. Braves Kenny C. Mariners Jonathan L. Angels Kevin F. A's Gavin O. Cardinals Frank L. Phillies Raymond D Dodgers Eddie P. Red Sox twins Mark L. Cubs Justin D I. Guardians Eddie P. Metz Shane C. Jays Eugene Rangers Benjamin L. Reds Edward S. Astros Evan L. Rockies Jody M. Pirates raise Eddie P. Padres Drop that link in chat Results are up. We're gonna get started Here we go Oh Pens over here Dude Whoever broke here earlier must have just got rid of everything that was necessary Whatever that could have been Definitely not someone to chat All right, here we go Stunk good old good old faithful right there. I was gonna say like 20 minutes here. I run thought the Eagles are done Yes, even me I Was on board that that train. Oh, these are not cloning together. What is he not stuck together for? so confused full bay on the Titans Refractors Schmidt rookie for the Giants future stars torque rookie prism for the Brewers Gus Varland and Vlasquez Cogg if the membership nice Lockwave rookie auto of Graham Ashcraft for the Reds Sinsy Diaz Freeman Pasquantino rookie debut refractor Royals it is typical workplace Prism rookie Tanner BB Guardians Rookie refractor France for the Astros till some clock here. Oh, yep. It's coming back lawns out Titans Trouts all action stars great rod debut refractor for the Orioles Yellow mini diamond debut Kodai Senga very nice card for the Mets here Rookie number two of 75 prism Kelly Jansen Red Sox Julian debut refractor rookie for the Twins Rookie refractor auto diamond backs Brandon Fott before 99. There we go d-backs Michael Harris action stars in a Garrett Stubbs 23 Give it up for 23 Third and 23 give it up for a day 23 prism rookie Gavin Stone Dodgers The day Rookie refractor A's Kyle gathered all the all the breaks for tonight, too. So Anything we hit or don't hit Rookie debut refractor Gunner-Henderson Orioles The thing I hate about what's going on right now in this game is like we're playing to let the homes have one more drive We're not playing an easy one to they a lot of time. Yeah, like what are we doing? Come on prison rookie Soriano Mets. It's like saying like we're gonna run the clock over good Refractor debut Cubs Kodai sang a song Saying a song right in Sean's face For a negative odor for the Padres purple speckle Rookie to 299 Bobby Miller Dodgers auto There's a rena J rod Fairchild That's Jake's new favorite one Fairchild of mine They played a place to each other mine 75 times on a Fnatic's live all the time man 75% of the time they play the song every time Gold rookie Garrett Hill for the Tigers Gold to 50 Garrett Hill Prismendic and Rookie refractor sable Giants That was a solid box. Let's see something crazy here. All right debut patch time. Come on debut patch How much why there's so many Jake's in chat Is he on something yes, well, they got a full field to work with but two minutes 49 seconds too much Mookie Riley Jeter downs are key refractor Nationals Future star Jordan Walker Cardinals prison rookie shoemaker Braves these games right here is defense We need all of it. I think offense also helps win games, too, though You haven't right now defensive Rookie auto on Drew Monasterio Brewers Kodai Sango all-star action stars cost us in a Bobby Miller refractor debut Dodgers Hold them down. Hold them down. You gotta stop. They got plenty of time. You just got to stop them They need touchdown. That's a good thing. The bad thing is it's my home prison rookie Taj Bradley for the Rays If she to their Nardi Rookie refractor for the Marlins Jake would say gnarly Nardi Sounds like Jake's becoming Sam. Yeah It's not good God Sonny Gray Shuster rookie refractor Braves There even even him and Sam aren't doing it in chat with Lawler Yep, I just noticed that show show our blue refractor Sam Hillier to 150 for the Braves prism netto debut angels. Oh Kelsey drop it Here I hear a song coming on Are being made right now? Oh Purple rookie auto Cal Stevens in a 250 for the Phillies I'm Volpe Sam Hilliard shake it off Travis shake it off. Donnie's doing it now, too Alejandro Kirk presumed jewelry for the angels Alvarez debut refractor Mets Mad force So he went mm-hmm. Yep, Cory Joel truckier factor for the Rangers and the Rangers the Astros.  Oh We're just giving them the win. It's like here you go. Thanksgiving prison rookie Nolan Jones for the Rockies Thanksgiving early presents Really give presents on Thanksgiving Donnie's going through right now. That's weak and our Julia and twins rookie base auto you push them Go twins. Yeah, but some of homes. Yeah, exactly. It's like it was Brady. Oh So it's a flag if your pal Cal That's not a good one. It's not a good one, but gentile purple lava lamp Jake bird rookie out of 299 Rockies Prism rookie netto for the angels Vargas refractor debut Dodgers Definitive time. Are we saving those? Hell, yeah, those are great. I'm using that actually right right now. All right, y'all still a few teams left here in the Definitive breaks. I'm surprised there's still teams here Guardians Rockies Marlins and rays crazy crazy That is a Jose Ramirez jumbo jersey auto out of 30 nice hit guardians That's one of the teams available actually Definitive There we go black jersey there Green rookie auto for the Dodgers Miguel Vargas at a 25 Sweet hit Dodgers think he's got some good potential still pretty young Cubs Jersey auto 25 out of 40 Andre Dawson Two pinch stripes on a sweet hit for the Cubs now Defining images autograph for Cincinnati is gonna be Barry Larkin. There we go. Since he framed auto Aaron judge 12 of 15 Yankees That is a sick car this one's going out to Brian G Brian G a 15 framed judge auto. Oh, yeah. Oh, yeah. Oh, yeah, hangarang This is nasty to dude cardinals dual relic auto one of 10 Ozzie Smith Scott Rowland That's fire. That's fire He's got st. Louis in this one. That's Gavin. There we go Gavin Ozzie and Rowland Dual relic auto to 10 for the Redbirds Pretty solid one here. You got camo at Darvish Jersey card to 30 for the Padres and one of one name plate patch the big hurt Frank Thomas White Sox regress name QL the O in Thomas on the name plate one of one patch guard game worn Very good box there that one Magnus. Well, we'll do a recap We should have just lost the game. I was like opening night in my homes. He was throwing dimes ever just dropping pass That's got to be grounding you didn't get the line over there. No Nobody can line of scrimmage Yeah, but if someone's over there, that's still okay But it didn't Reach for that flag dude That's that's that's brutal. There we go brutal. That's what we like to see numbered cards from Chrome here bird Hilliard Senga Hill a U Darvish relic from definitive into the autos now. He had Julian Monasterio fought Stevenson Miller Ashcrafts he had a Roland and a Smith dual relic auto for the Cardinals Larkin auto for the Reds Jersey auto Cubs Andre Dawson Jay Ram Jersey auto for the Guardians here to 30 a rookie auto green at 25 Vargas Dodgers Big hurt letter patch one of one for the White Sox and A framed auto of Aaron judge to 15 for the Yankees Some mixer and mayhem right there. That'll do for number one number two coming up next. Thanks everybody


Welcome to Toffy TV, it is the Everton News Daily. Sean Dyche has given his pre-match press conference a head of Everton's game against Newcastle United tomorrow night at Gwldersham Park, a huge match in the context of the season for Everton running out of games, only six to play, but they will have been boosted by Leeds draw run one-one with Leicester last night, it means if the Blues can beat Newcastle, and it's a big ask, but if they can, they will move above both Leicester and Leeds get back out of the relegations zone. That is what is on offer for Sean Dyche tomorrow. The manager was asked today in his press conference for an injury update on the likes of Seamus Coleman and Amadou O'n Arna. This is what the Blues boss had to say on that question. Seamus and Amadou have been on the grass, will make a decision on them, and Ross is still a bit away, but has been on the grass with the sports science team and just easing back into a kind of return to training programme. There you go, hopefully both of those will be available tomorrow for Everton, makes the team stronger doesn't it, when we have all of our players available. One player who should be fully fit and ready to go is Dominic Calvert, Lew and he returned in the Nillnill draw of Crystal Palace on Saturday. He gave Everton a focal point, it was a lucky play, I thought he did really well considering he's been on for a while. He has got a good goalscoring record against Newcastle, so hopefully that is a good omen for us. Did of course have the assist last season for Alex O'Wobee's winner in this fixture. Hopefully he can make the difference tomorrow. Sean Dyche was asked about the recovery of Dominic Calvert Lew and how they can get the best out of him. This is what the manager had to say about that. Good to see Don back out there that's for sure, got more minutes in than what we thought. The tempo of the game was slightly lower than some so that we could allow that to happen. He felt good, obviously we were monitoring during the game and he's recovered from that well from the physical idea of it and the recovery period. He looked sharp against day in training. To get the best out of him, the service from wide areas needs to improve. Does it? Thanks. Do you think it needs to improve? Statistically we have improved that. The quality of chance is what I'm always focusing on. I've said it a million times. You read them stats and it says they had this many chances. I saw them. It's key chances. It's key quality moments. That's what we're trying to provide. Although I know of the stats and the facts, it's more about the quality. How many quality crosses are you getting? How many quality passes? How many quality chances are you creating? So that's what we're looking to do is always add in to the quality levels, not just the amount. And get it plays in and around him as well. Yeah, of course. Again, someone we looked to effect when we came in. There's been really strong moments of that. There's been other games when you haven't done it as well. Depending on the score line, depending on how we've pressed in the game, depending on how we've attacked in the game. A lot more goes into it than literally just finding their moments. Dominic's history suggests he'll play his part in that. For someone who'd been out a while, I thought he looked pretty good physically down at Palace. A couple of down dies and some recovery dies. And I think you'll see another step on from Dom again. There you go. The bus welcome will be back for tomorrow's game. The fans have been requesting it. It has been agreed now. Everton Place will arrive on a coach. The route is out there. It's all over social media. So if you're interested in that, make sure you check it out. But the manager has asked his opinion on the bus welcome. It's just something that's been bouncing around for a few weeks. There hasn't seemed to be a great desire for it from Sean Dyche. Or maybe even the players as well. Maybe it was his way of playing down some of the games to try and take the pressure off the players. But he has to come to it. It will be taking place tomorrow before the match. This is what he has to say about that. It was well documented last season about it. A couple of fan groups mentioned about it this season. I've got a massive respect for them because of purely from what I've seen, what I've heard from the fans. I've been away since I've been here. So they wanted to help play their part if that can make a difference. Beyond that we want the team to play their part. Obviously we're looking for the team to make a difference. But if the fans can continue the support they have then which has been fantastic then we respect that totally. Well it wasn't here but I think the atmosphere or it creates helps to create an atmosphere. But the focus remains on the whistle blowing because that alone can't win you a game. You've got to make sure that you're in the right frame of mind anyway regardless. But if the fans can help play their part on that then that's part of it. Let's hope it makes the difference tomorrow. We need every little bit of help we can get tomorrow. Finally more news on the investments. Front to day obviously we reported yesterday that there was as many as five interest of parties in buying into Everton Football Club. Alamys had reported that yesterday. The main two appear to be MSP. They seem to be the favourites. But 777 have continually been linked with buying into Everton. Full takeover has been mentioned on a couple of occasions and the Miami based firm aren't going away it seems. They have commented in the last 24 hours. They said there are rumours we're looking at a Premier League team. We are in the acquisition phase. There is general investment thesis around even being around storied franchises being around places where we think there's a lot of opportunity that either hasn't been captured or we think we can bring value to. Like I said these aren't going away it seems in this story and it's coming from somewhere. I still feel as though MSP will be the eventual victors in this. But who knows? Farad Masheery hasn't said a word really in terms of who is in the driving seat. I don't expect them to really. The reports are saying that it will be signed and sealed within the next seven days. So we'll have to wait and see which one comes out on top who we decide to go with. However it is, let's hope it signals the start of a new era at Everton Football Club on the improvements in our fortunes because it has been pretty depressing of late. That is it for the news daily. Give the video a thumbs up and subscribe if you haven't to the channel. See you later.


So last time we worked on our visuals. We added images and CSS, and now we have something that actually looks like a real block. But also, it's at this point in development where you have to start to worry about the weight of your site, because all of these images and the CSS files add weight. Add file size has to be downloaded for the site to actually appear as you like. So if you are developing on your big desktop machine with a big screen and a good network connection, everything might feel great and look great. But if you serve the exact same experience to a Moto G4 phone on a 3G network, it might feel very, very differently. So we've already talked about a bit how you can streamline your loading to make it feel faster for the user. But another thing that you can look into is caching headers. Caching headers help the browser only download the things that have actually changed. And I thought that was very important and I wanted to implement it correctly in my blog. I've already given some tips in the past on caching headers and a micro-tip, so I'm gonna link to that one in the description down below. But let's do a quick recap. So the advice that I usually give is to segment your files into two groups. The one group is the files that are entry points to your app, which is usually your HTML files. And the other group is all the rest, JavaScript, CSS, images, what have you. For the HTML files, you always want to revalidate with a server if the version that you locally have is still the most recent one. And the caching header for that is called must revalidate. So that means the browser has to check with a server if the version is still the most recent one. And if it is, it doesn't have to re-download. So it doesn't really save you time, but it does save the user's bandwidth and that's already a win. For JavaScript and CSS, you wanna put the hash of the content into its file name and then set the caching duration to a really long time. So in this example, I'm gonna choose max age and then something like 31 million. 31 million sounds big and it is big and it's roughly a year. So I'm saying these files are allowed to be served straight from cache without checking with the server for a year. And that's okay because if the file changed, the file name would change. We put the hash in there after all and that's why this caching procedure works. All these assets will be referenced by the HTML. So the browser will revalidate the HTML with a server, but if that didn't change, it can just use all the other assets from cache, doesn't have to hit the network and that will save us a lot of time. So I said the browser has to revalidate with a server, but I didn't really explain how that works. So in HTTP, there's two request headers that allow this mechanism. One is called if modified since and the other header is called if non-match. If modified since basically means I have a version cache that is from this state. If it has been changed after the state, please send it to me. If non-match basically says I have a version cache that has this specific e-tag. If the current version has a different e-tag, please send it to me. Both of these headers achieve the same effect in only downloading something when actually necessary. Just one is state-based and one is e-tag-based. I personally feel like the date-based version is a little bit less robust. So I prefer e-tags most of the time, but the problem here is that we are running a blog that is written in PHP and that means that most of our content is dynamically generated. So how would you generate a hash of the content of something that is dynamically generated? So it turns out there's actually a pretty neat trick in PHP that you can use to achieve that and I'm gonna show you how. So PHP has two functions. One of them is called OB start and the other one is called OB get clean. OB here stands for output buffer and it basically means that any output I generate will be put into a variable as long as it is between those two function calls. So that means instead of sending the output straight to the user, to the browser, I instead get it in a variable first. And then I can use this variable to calculate the SHA-256 hash of the content and this is the way how I can generate an e-tag for the content that I have generated. The only thing left to do is to do the matching myself if I actually need to send the variable or not. So I grab the if-non-match header from the request and see if my content hash and the one from the header match up and if that's the case, I just send a 304 saying no change, just reuse what you already have. And if they don't match, that's only when I actually echo the variable saying now actually do send the content to a client. We can see this in action in Chrome DevTools in the network tab. So if we clear out all the caches, basically start fresh and load our page, we can see in the network tab that we download about 300 kilobytes and that all of our requests have the status code 200. Because the cache is empty, nothing can be reused. But if we now reload the page after our caches have been warmed up, as I say, you can see that pretty much every request turns into a 304, meaning not modified. And the total download size went down to just one kilobyte because we could reuse everything that was already in cache and didn't have to download anything new. And that's pretty good, right? I think being mindful of your user's bandwidth is really important. You know when you're on this really bad hotel Wi-Fi on vacation, this is where all these techniques really help and you wish every website would use them. Next time, however, we are going back to some more front-end code and we are going to build a router. You know the thing, it takes care of transitions and making it all really shiny. So if you want to see that, subscribe and I'll see you next time.