My fellow Americans, during the last two years, the United States has risen from the depths of recession to one of the strongest recoveries in decades, from dark days of despair to a bright new dawn of promise and hope for all Americans. I remember saying back when things looked the worst that too much pessimism could be deadly. Some people criticized me for trying to sugarcoat bad news. I merely wanted us to remember that there's a psychological factor in recession and too much hammering at it makes recession worse. What pulled us through that ordeal, I'm convinced, was our determination to stick to our program, believe in ourselves and trust in our values of faith, freedom and hard work. Values that have never failed us when we've lived up to them. And now we're seeing the payoff. 1983 was a banner year for America, notwithstanding voices of pessimism which always found the single dark cloud in every blue sky. Those voices come from many different areas of our society. Recently, the Wall Street Journal reported on a survey of one of them, the television network's nightly news coverage of the economy during the last half of 1983. During that entire period, there were four to fifteen economic statistic stories a month, telling us whether inflation, unemployment, interest rates, retail sales or housing starts were up or down for a given month. The survey found nearly 95% of these reports were positive. However, of the 104 lengthy economic news stories in which the networks gave us their interpretation of what was happening, 86% were primarily negative. The survey found the economic news in the second half of 1983 was good, but the coverage on network television was still in recession. Now please don't get me wrong, every administration must be held accountable. None of us can be excluded from the fury of a free press whenever that's right and proper. But true balance implies consistently showing all faces of America, including hope, optimism and progress. Our economy is stronger than practically anyone predicted. The index of leading economic indicators has been up 16 of the last 17 months. Industrial production has risen 14 straight months. Housing starts climbed 60% in 1983 to the highest level in four years. Retail sales surged. Auto sales registered their best year since 1979. And we had the steepest drop in the unemployment rate in more than 30 years. In yesterday, we learned that unemployment for all workers in February dropped to 7.7%. More Americans are now at work than ever before in this nation's history. Here's one example that sums up the difference between yesterday's policies of depending on government and our approach that begins with trusting people. Last year, we were asked to raise taxes and appropriate money for a $3.5 billion program to put 300,000 people in make-work jobs over a year. We said no because incentives produce economic recovery and strong, steady growth puts more people back to work than any government program. And it has. Recovery has put as many people back to work each month as their program would in a year. We've added an average of 300,000 jobs every single month for the past 15 months and almost 400,000 last month alone. That's 4.9 million additional workers working and paying taxes. Our economic recovery has become economic expansion. And the potential for new jobs and economic growth in the future is beyond our imagination. The revolution in science and high technology is only beginning. Each time our knowledge expands, each time we push back frontiers of medicine, agriculture, and space, we will be creating entire new industries, modernizing older ones, and raising our standard of living. The issue before America in 1984 is clear. Which direction will we go now? Forward with optimism, faith, and confidence, continuing to build an opportunity society for all our people?  To serve that agenda, they need to dwell on bad news. So when good news comes, they're either dumbstruck or they pretend they didn't hear. Well, with your support, we'll keep our economy moving forward and we'll keep America's rendezvous with an optimistic future. Until next week, thanks for listening and God bless you.


What time is it? 21.24 What's the weather? With a high of 16 and a low of 14, Barcelona has few clouds and is currently 16 degrees. What is your IP address? To work lightly, address is <IP_ADDRESS> Set an alarm for tomorrow at 8 o'clock. An alarm is already set for that time. Thank you.


We're good number three Car travels 15 meter second. I'm pretty sure vi is 15 they want me to find a They've given me T and they've told me the displacement is 85 meters Is that okay, Caitlyn? I'm looking for an equation that has those in it. I think it's this one I'm gonna solve for a now. This is an awkward equation to get the a by itself, but it can be done It's not as bad as all that I would minus the vi t over you could plug the numbers in ahead of time on this one If you really wanted to but I'll get the a by itself. I would minus the vi t over and I would get this well it equals a T squared over two because I prefer it over two than a half in front and This is also one big fraction The two would move To the top and I'd have to put it in brackets because it's two times everything so far so good Sorry, no. Oh, yeah, and T squared would move to the bottom That should get you there. I hope so D minus vi t times two divided by T squared. Oh Let's find out to bracket D85 minus vi times t divided by T squared Is the answer point eight? There you go You know what we don't very often use this equation to find an acceleration Work number eight was requested number eight We kind of got to visualize what's going on and I'm almost wondering now if there was something I was not happy with the number eight, but I'm trying to remember Number eight says a child slides down a playground slide Accelerating from rest. I would probably underline the concept here from rest Reminding myself. I think vi is zero. By the way, who has number eight It's gonna have two parts while you're sliding and then while you're stopping Okay Traveling six meters and four point five seconds because I think what I need to do first is find out how fast They were going when they hit the ground. I think first in number eight. I need to find the final and It's gonna be V final squared equals. Oh, no, they gave me time. Oh, let's see what they gave me I want to find V final. I know the initial is zero. I know D is six I know T is four point five How can I use that to find the V final? Haven't I got have I got an equation that has Vi D At and V final in it. Well, no, not blatantly However, I think I can use these three here To find Acceleration if I need to I think very similar strangely enough to what I just did with Caitlyn I think I have V T D I think I can use this to find the acceleration and once I find the acceleration I can find the final pretty easily I'm pretty sure we just finished saying with Caitlyn that the acceleration was equal to 2 D minus Vi T all over T squared. I think that's what we said. I'm going from memory here Actually, that's a lie. I just rederived. I just hit the equation in my head again because I can do that to my head 4.5. Oh, hang on. No D is six six Mine times minus. Oh, this is actually even easier than that because mr. Deweyck this we have done before Vi is zero.  This is just gonna be simply two times D divided by T squared I can do lots with this So the acceleration that I get here is Two times six divided by four point five squared You know what I'm gonna go point five nine two six because this is not my final answer I'll carry a few extra sig figs and there's a lovely nine right there. So point five nine two six I'll call it that point five nine two six Which means the final when you hit the ground and I'm running out of room here But I think I can go V final equals the initial plus a TV initial was zero. I think now I can go Acceleration times four point five and I get a V final of two point six repeating I'm gonna go two point six six seven because this is not my final answer either Two point six six seven meters per second. That's what I hit the ground at Now we're hitting the ground When I hit the ground, what's my final velocity when I hit the ground? What's my initial this? What else did it tell me The distance that my legs travel is point two meters not twenty seven point two meters So I think I can do some work here. Let's see in number eight then I can say The final is zero the initial was the final at the bottom of the slide Which is the initial when I hit the ground is going to be two point six six seven a I don't know D equals point two Yes, and now I can oh Oh a Equals vf squared minus vi squared all over 2d. I'm pretty sure where yay vf is zero I'll get a negative acceleration, which is good because I am slowing down I'll get zero minus two point six six seven squared all divided by two times point two Bracket zero minus I'm going to use this value since it stored on my calculator instead of two point six six seven squared I'll use that squared divided by two times point two Lay it on me Andrew. Tell me the answer is eight point nine is the answer eight point nine eight point four Sorry Oh, I put a point four up there like a complete meat head Because I did the math in my head I can fix that I think let's see by putting a point four there I've added it is the ants is the answer that Yeah Sorry, I accidentally stuck an extra two in the bottom trying to do some arithmetic in my head forgetting that Yes, 17.7, and I guess they dropped the negative. They were just interested in the magnitude Okay Almost two G's Not quite yeah, that's about right. I think When you go down a slide you have to flex your legs and then otherwise if you keep your knees stiff it hurts I think that 20 centimeters though Brett is low from what I recall when I hit the bottom of slide Because 20 centimeters is about what that I think my knees bent more than that when I was a kid. I Don't know it's been a while Emily's going why no just yesterday. I would oh never mind nothing. I don't still play out playgrounds Any other questions I would consider that kind of a question Fair game, but it's not going to be number one on a test But towards the end. Yeah, that's good thinking. I like those and it's also I'm going to make the assumption all of you have been on a slide. So it's yay applied physics that I experienced By the way, this isn't totally accurate because what do most slides have at the bottom? They level off to prevent this Right, they have a little jog at the end where suddenly instead of being steep it levels off for about a foot and a half But but that long it's all it needs, right? But there are some Older slides and you may see them in older playgrounds often They're big wide slides and it's a straight straight down and you better stop yourself. Those are great Also fun to run up Okay, then today And you want your uh calculators out and probably in degrees introduction to vectors In physics any quantity is either a scalar or a vector Scalers have magnitude only Vectors have both magnitude And you with me right Did I miss your group? Let's try that again All right, let's continue so Vectors have both magnitude and direction which is we're going to be looking a lot at vectors this year Specifically this year We're going to start going two dimensional much more than we did in physics last year Last year most of your physics was negative To the left positive is to the right this year we're going to have things going off at angles Some quantities vector quantities displacement For example 6.5 kilometers west The scalar equivalent of displacement is a distance 205 centimeters Velocity is a vector for example Eight meters per second East Sorry for this knees on line there Speed is the scalar Eight meters per second Just making up examples Acceleration 9.8 meters per second squared down often we would just put a negative there Then I left a blank here, but I said my example is 22 seconds. What's the scalar? I want you to put here Time Time does not have direction But I saw this sci-fi film one time where they were moving backward time does not have direction, but I know moves forward At least in physics 12 Momentum so momentum How about 5.1? Didn't remember the units for momentum Whoo, you get a candy later on Kilogram meters per second because it was mass times velocity Let's add a direction. I've already done a couple of compass directions Another way that we can sometimes show a direction is to put a negative that usually means in the opposite direction that we started Not always you could have a scalar that's being that gives you a negative answer as well All that means is you lost Whatever amount you're talking about So if you get negative energy, for example, it means you lost that much energy It doesn't mean that the energy was going backwards Volume is a scalar 1.6 cubic meters force is a vector 12 Newtons at 30 degrees south of east 12 newtons at 30 degrees south of east And then work or energy is a scalar 91 Joules Jay Almost always this year when I introduce a new topic or a new concept to you one of the first things I'll give you is the units the abbreviation and scalar or vector We can add scalars like normal math. For example 6 kilograms and 8 kilograms is 14 kilograms We can't add vectors like normal math to add vectors. We have to add them Vectorially, we often have to draw a picture. We have to dope That was an acronym. I gave them yesterday. Jeanette Dalt stands for draw a little picture. Sorry Watch the lesson if you're playing How do we add vectors? There's two ways to do it One stupid and long and one clever the stupid and long way is this when we we represent vectors with arrows One way of adding the vectors would be to carefully draw them to scale using graph paper a ruler and a protractor And then carefully measure the distance between them and that would be the answer that you got when you added them together I don't want to do that Better we could use tree Oh, but by the way vectors are either written in bold font So in a textbook you'll see a vector written in bold font But to hand write handwriting bold font Emily doesn't show up exactly you can try coloring it in really whatever So the other notation is we put an arrow above the vector Except over the years we've gotten very very lazy Years and years ago. It was that but we've gotten so lazy now We just kind of put a half arrow we clue in now. It's a vector That's a vector If you just want the magnitude of a vector Believe it or not that symbolized by that symbol. Hey math 12 humans. What does that symbol mean? It's actually yet the absolute value in physics means who cares about the direction lose the negative Just tell me the magnitude which really is where absolute value comes in handy So john travels five kilometers west And then eight kilometers north What is his resulting displacement? We could get out graph paper and a scale diagram Eh, we can use trig Let's try example one here. Oh, I should read what's inside the I almost missed the punch line that box It's bold. It's big. So I'm going to raise my voice ret says this To add two vectors. We draw them tip to tail. How do we draw them Mitch? Tip to tail. Thank you. You're with me now. How do we draw them Mitch? Brett, how do we draw vectors add them? Connor, how do we draw vectors add them? Fairly sure I did this last year too with my students. It's very very key Ah, but then there's one more thing you have to remember once you've added them tip to tail The answer the resultant is from the tail of the first to the tip of the second Let's try example one here. So in example one, we have five kilometers west and eight kilometers north They're talking about direction. I always draw a compass rose whenever they start talking about direction And we're saying we want to add this five kilometers west Eight kilometers north was west and north wasn't it? Yes And you'll notice Trevor that I've drawn it Roughly to scale. I tried to make the bigger one bigger and the smaller one smaller And eights almost twice as big as five, but not quite. I drew my It's helpful to roughly draw these to scale Sometimes you just won't be able to because the diagram will be too complicated Equals This is an equation. Now. This is a bit of a weird equation. There is a plus sign We've done that for ages, but we're adding pictures. Well, we're adding vectors. This is vector math Joel, how do I add two vectors together draw them? The tail is right. You make it okay. Sure. It's a little Sorry, you're good. I don't need to bring up the Tarzan yell or anything like that. Oh good stuff What do I mean by draw them tip to tail? Well There's the five There's the tip. So I'll put the tail of the second one Right there What's the resultant? From the tail of the first one To the tip of the second one This is the vector that all car call r for resultant Now there is a lovely right angle here. That's good Remember vectors have both magnitude and direction. First, let's find the magnitude How can I find how big r is? This is something I think we're introduced to you in grade eight It's a theorem It's Pythagoras. It's named after Pythagoras. He almost certainly did not discover it for some reason. It's named after him And if you can do Pythagoras on your calculator showing no work whatsoever I'm totally good with that except I've never went on a test in our notes We'll write it out just so that when you're studying, you know what that has me in so It's going to be eight squared plus five squared equals r squared eight squared plus five squared Square root of 89 9.43. That's two or three sig figs Units Is it kilometers? Is that what it was? Now that's the magnitude. That's the scalar portion of your answer, but we also want a direction So we're going to add An at symbol like in your email address What direction is this guy traveling? It's pointing In this direction here in fact, I'm going to argue that the direction is That it's This angle theta We did review how to find an angle a couple of days ago. Is there a right angle in this triangle conor? Then I can use so katoha conor opposite adjacent to my pot news the eighth mr. Giles You're both conor g's too. That's going to be irritating Sorry I agree How about the nickel? What trig function? Toa toa sadly is not a trig function Toa is what you say when you kick your foot against something you say I stuff my toa. Yeah, you know, we don't want that Tan yes, what you do on a beach. I agree What always goes next to the trig function? the angle Which I don't know it's going to be opposite over adjacent katie if you're showing work on a test This is what you would write. I would look for this To be able to give you part marks if you've got the wrong answer if you got the right answer I'm good with whatever you did, but I would say this theta equals math 12 What does that stupid little negative one mean? Yeah, that's how you write the inverse tan you may see some british textbooks Call that the arc tan And I've occasionally seen a calculator that calls it arc sine arc cos and arc tan right above it Is that another fancy fancy word for the inverse of the tangent or this cosine or the sine but a little negative one is easier to write What's the angle? How big let me make sure I'm in degrees. I am Inverse tan of eight over five 58 degrees 58 degrees what of what? North or south east of west what of what well, we would say this See how I drew this arrow here. I started out going west And then I made the arrow go in which direction of west This is north of west vectors Example two So that's how I can add two vectors together when they're lovely right angles I think example two is also a lovely right angle So I'm going to try to say try example two on your own here really quickly. I'm going to freeze my screen And let's see if we get the same answer with my screen frozen. Let's try that again. I'm going to freeze my screen there Now it's frozen How do I add two vectors together emily draw them? Well go for it. Let's try it Sort of yeah You'll notice brian I showed a lot less work than on the previous example This is really what I would consider fairly bare minimum I don't care if you can do pipe agris in your head great And then I went straight. I knew I wanted to find inverse to find an angle anyways So I said the angle is going to be the inverse of tangent and I put opposite over adjacent right there I didn't actually bother doing this line first And I got 31 degrees south of east Now there's a second possibility For all vector questions. There's almost always two possible answers In this question here, I drew the five I drew the five first and then I drew the eight What if I drawn the eight north and then out of the five or in this question here I drew the 10 first and then I drew the six. What if I'd done them the other way around? What if I'd gone like this? six plus 10 what if I was trying to find that You'd get the same resultant of 11.7 But in this particular triangle Your angle would be That one there You would start out going south and then you've gone east It's still going to be opposite over adjacent tangent, but it's going to be Opposite over adjacent of 10 over six 59 degrees also works Or 59 degrees also works Except this is not south of east. What's this one here? This one here is start out going south and then go East of south Both of those Brett are acceptable answers I usually draw them in the order they give them to me because I figure that's what you guys will do And I'd like my work to look like yours whenever possible But I'll always take both answers on a test What are these two add to 90 if I go back to this question? Or what's 90 minus 58 in your heads, please Jacob or 32 degrees west of north that would be uh That angle right there, which is legitimate. It just all depends in the order that you're dropping I take both How many got that? Oh excellent If we add displacement vectors of length three and two meters, what's the maximum sum? What's the minimum sum you can get?  Caitlyn Convince me Okay, you know what for my because this is one of those using principles of physics right to explain questions I told you about yesterday. I think here. I'm not going to go all fancy. I'm going to draw some pictures. I would go like this Three plus Two both in the same direction doesn't have to be both positive both in the same direction Equals Five great What's the minimum vector I could possibly get if I add vector three plus vector two Minimum vector I can get adding these two together Anyway Mitch is that hand up? Oh, yeah. No, that was actually behind the sink wave investment. Yeah, sure one convince me You're right. Oh So if I go three plus Two you're saying if I go three right and two left I end up with a One sure That's a perfect explanation for my esl students Almost no english. I wrote max and min I guess but you'll notice no english there The reason I say that often my esl students start to leave those questions blank I'll make you cry. You have to try no leaving questions blank Trend page For the three vectors below draw the sum two a plus b Plus point five c Hmm Nicole, how do we add two vectors together? Tip to tail. How do we multiply a vector by a constant? What is two a? You know what it is. It's the original a except how long is it compared to the original a two a is Twice as long Multiplying a vector by a constant That coefficient easy so it would look like this That's a There's two a roughly plus Then they want me to add b Plus Point five c. I think that would be c but half as long about that ish How do I add three vectors together? Well, if they actually wanted me to calculate numbers You really can't you really want to add the first two get an answer and then add the third one But have they given me any numbers on any of these vectors? Do I actually know any of the links? I think they just want the picture. I'm going to draw them tip to tail tip to tail tip to tail. I think it would look like this two a plus b Plus point five c I think there's my resultant in red From the tail of the first to the tip of the last vector It's just doing the trig here would be a little awkward Did we ever be asked to add three vectors? Uh, I can think of one later on in the year sort of but I don't do it that way I add the first two get an answer and then add in the third one And often two of them will cancel out quite nicely if you set it up just right We can also do vector arithmetic with our equations. So it says this An object is initially moving at three meters per second east. Did we all just turn the page? Then I'm drawing a compass north east south west So it's initially moving at three meters per second east It accelerates south At 1.5 meters per second for four seconds find the final velocity by adding vf equals vi plus at Now that's the equation that we know and love but now we're going to do it Vectorially I did this one with my physics 11's last year. I think I stuck this in What's it going to look like?  Oh you were with me? I apologize then Drawing a little picture vi um, I think like that Plus What direction is my acceleration? South how big well, it's going to be a times t. It's going to be a times t It's going to be 1.5 times four Which I think is six, isn't it? 15 times four is 60 because it's 15 minute 15 Four minutes in it like 15 quarters in an hour. Is it six? So i'm going to draw a vector south How long is it going to be compared to this one? That's three long twice About there That's vi plus at can you see vf is going to be my resultant. Let's draw my triangle here How do I add two vectors draw them tip To tail V final this time is going to be that bad boy So this is the first time probably that i've given you a velocity in one direction and an acceleration perpendicular to it But i'm going to argue it's actually emily exactly what we did last year Same equation except just doing it victorially good solve it Quickly as fast as you can take shortcuts Cool. Let's keep going Let's kick it up a notch So I got a 6.71 meters per second at 63 degrees south of east or that would also be 27 degrees east of south Example three an airplane has an air velocity or engine velocity Of 200 meters per second north. So if the air is still that's how fast the planes engines can push it However, there is a wind blowing of 60 meters per second at 35 degrees south of east If I combine those two velocities, what's the plane's ground velocity or velocity relative to the ground Don't write this down here. Oh I'm going to draw a compass because I've turned the page Write that down Here's I think what we're talking about though. Don't write this part down There's my airplane pointing to the north right there The wind is blowing south of east the wind is blowing in this direction. So I think you would Try that again. Mr. Dewick There's my lasso a little button there lasso I think what you would see is the plane traveling kind of sideways Because the wind is pushing it towards the south and towards the east But the engines are pushing it north on the ground the radar would see it kind of going that way I don't think quite at that big an angle But get get the idea And I just wanted to move that around too. That's kind of cool airplane come Dulp Kara, what's belt stand for?  Here's what it's here's my hint I gave you you want to think the engine velocity plus the wind is what gives you the ground velocity What's the engine velocity according to this question? 200 plus What's the wind yuck? Well Kara, what is that last little phrase right there say? Even after the 35 degrees I want that little the letter. Yeah Say it louder. You're right To draw that I go east first with a dotted line And then I draw an arrow south of east Does that make sense? There's the vector. How big is this angle right here Kara? Yep there How long is this vector? 60 My scale is garbage because 60 is almost well. It is three times shorter than 200. So I'm going to go like that This is how you cheat and do kind of to scale afterward I want to add those two vectors How? How do I add two vectors draw them? Hit the tail I'm going to get this 200 plus 60 the resultant is From the tail of the first to the tip of the second that puppy there Mitchell. Yeah. No, yeah Question for you. Is there a right angle in there anywhere? So there's going to be sign law coast sign law, but we've got a bit more information We can add because I still haven't figured out how that 35 degrees is going to help me. Well, if I look right here I'm going to mark up my diagram right now. I don't want you to In fact, I have something to let me turn this marking on and off Kara, I think this is the angle that you said was 35. Yes See it see it see it see it Um, if this angle here is 35, what do both of these angles here add to? Ah 90 so if this is 35 right here, how big is this one right here? Aha, I've got a triangle an angle in my triangle Often for non-right angle triangles, you're gonna have to extend a few lines Sometimes you will end up with this angle being in your triangle.  Is there a right angle? So now quickly go Do I have a pair where I know both the angle and the number across from it anywhere? Emily then is this sign law? Co-sign law This is the co-sign law. What's the co-sign law? Well, we wrote it as c-squared, but what letter do I have here?  That's only the magnitude They wanted velocity they want magnitude and what? Direction Where's the direction so find the resultant where it starts And then find the nice line right next to it This black line here. What direction is it? Okay, so it's going to be of north What direction of north do I have to go to get to there? east of North so I'm going to leave a space for the actual angle itself, but I am going to write east of North because I'm also proud that I got that part And I'll put a little theta Right there. All right zay. Here we go right angle zay No Do I have a pair? I do now Because I now know are So now I can use the sign law to find an angle This is why I said you almost never have to use the cosine modified angle almost always once you've done the cosine law once You've got a pair What's the sign law going to be okay? It's going to be the sign of 55 divided by 172.73. I'll use this did 172.73. I'll use the noun round non rounded off more accurate value equals mystery sine theta divided by What side goes with mystery sine theta katie? More specific in this case Thank you katie is this one fraction equals one fraction I mean I can cross yeah cross multiply you'll get a decimal and then shift sign Theta is going to be the inverse sign of 60 times the sine of 55 divided by 172.73 So on my calculator, I'm going to go 60 times the sine of 55 divided by I still have my previous answer stored on my calculator, which is 172.72596 I'll take that one and be more accurate Oh Uh-oh I did inverse sine for some silly reason. Let's try that again And I get the sine of theta is 0.2845501 How do I find theta? inverse sine of this puppy And I get you get 16.5 degrees 16.5 degrees That's what the radar let's see A plane traveling at 173 meters per second Drifting 6.5 degrees east of north even though the plane itself is pointing to north the crosswind is moving You can do that question using components, which is probably how we taught you last year in physics 11 If you do that with components, which works it's about nine lines I'm going to argue the cosine law. You can master the cosine law much much much cleaner Significantly so Next page. It says this If you are uncomfortable with the cosine law approach You could use components This involves breaking every vector up into vx and vy If you want to use the component method Ask me later on in class and I'll show it to you I'm sensing most of you here were okay with the cosine law. I mean you got that. Okay Yes, I'm sensing most you were okay with the cosine law. It's a bit of number crunching Joe I realize that but it's mostly just typing So if you want me to do the component method with you, I will fill this page out with you later on I can also tell you kind of start your drill Brandon gonna make it Okay You get the same answer I prefer the tip-to-tail method, but you'll get full marks try the method Use the other one you like best turn the page Mr. Redmond, how do we add vectors together draw them? How do we subtract vectors? It's a trick question We don't We don't That's the short answer Instead we add the opposite if you want me to go a take vector a take away vector b What I'll do instead is going that's the same as vector a plus negative vector b where negative vector b Is vector b but with the arrow on the other end? There is Brett an actual method to subtract vectors and I learned it in college And then I found this and I went yeah, why would I teach them a separate rule when I don't need to? We can just keep using the same rule of how do we add vectors together tip-to-tail? Because you can change any subtraction question into an addition question for that the opposite So we're gonna do that A plane's ground velocity or velocity relative to the ground Is 240 meters due east? This is our last example If the wind is blowing at 80 meters per second due south, what's the plane's air velocity? Hmm Seems to mean the cold for any airplane out there The engine plus the wind gives you the ground speed or the radar speed Air or engine velocity Plus wind velocity Equals ground velocity What do they want me to find here? How would I get the air velocity by itself? minus that over We're gonna get this the velocity with respect to the air. That's what the engines are putting out Is equal to the velocity on the ground Minus the velocity of the wind We're subtracting vectors No, we're not because you know how I subtract vectors. I don't We are gonna add the opposite That right hand side is gonna be our equation. That's gonna carry help us to double What is the ground velocity? What's the radar measuring? Read the question Sean, what's the radar measuring? Direction I better draw compass because I've scrolled up So if I hear you This guy looks like this 240 Plus Sean, what's the wind velocity? How big? Direction, what's negative wind velocity then? direction Plus 80 That's going to give me my air speed That's gonna tell me How much the engines are putting out against that crosswind so that on the map I'm still able to go due east I guess this pilot is pointing his plane. I'll bet you he's pointing his plane this way So that when the wind is pushing himself it cancels out the this way portion and he ends up going due east How do I add these two vectors together Sean? Go ahead do it yourselves. I think this one will be a nice right angle And when all said and done, that's what I got Am I right? Brianna's nodding You know when you have the notes pretty good You got some game Or 72 degrees east of north would also work if we did the 80 plus the 240 So how do we subtract vectors? Well, have the opposite How do we add vectors from the tail? To the page Well, foxtrot comic I love foxtrot the guy who writes it bill amond Actually was doing his physics degree in university. He has a physics degree But also while in university he was doodling a lot and drawing a lot of comics. And so his friends said look Why don't you try getting these published? So he has a wonderful accurate nerdy math in the comics. I especially love the youngest boy jason who is an uber mega nerd It's great. So Peter the older brother is playing football with the younger brother jason. What pattern did I tell you to run? You said go 10 yards out then 10 yards to the right What pattern did you run? I went 10 root 2 yards at a 45 degree angle And are they the same thing if you had the vectors sure It's just football not math class. I think I rounded two decimal places. There's the first one The second one Jason's now the ball Okay, here's the play go 40 yards downfield then turn left and go 20 yards Then turn right and go 25 yards then turn right again and go 30 yards Then turn right and go 30 yards then turn left and go 10 yards Then turn left and go 15 yards then turn left and go 20 yards then turn left and go 50 yards And I'll hit you with the ball Peter's doing the math Won't I be right back where I started you can't throw very far Okay, here's the new play and it gets recorded back A couple of years ago. We actually ran this out in the field and you do end up right back where you started from It's raining yucky weather right now. So we're not going to it actually the math is accurate. I had to check It says homework vector addition worksheet actually first thing You get up the great big review that I gave you yesterday Jeanette, that's this bad boy here. This is due the day of the test The ultimate kinematics review. I gave it to you at the maniac class Sorry, I don't know yet. I'll always tell you a week ahead of time though But So you can't do every question on here yet. I told them which questions I covered You can now in theory do the following ones uh two four 13 15 17 24 I think that's it for now And I'm going to take a gamble here. I'm actually going to skip lesson four And give you homework from lesson four. So where it says lesson three homework vector addition worksheet I'm actually going to give you lesson four right now And I'm going to assign some quests from here taking the gamble that you remember some of this from last year and that'll give us So look up. I just gave you lesson four. This was going to be some more vectors This was going to be like the river question, but I think you all did it last year And uh, I will say this where it says handy hint change in anything is always final minus initial That's worth memorizing, but I'll flog that to death This is going to be your homework. So here are some questions you can try So I haven't reviewed finding components. I'm kind of hoping you remember But if not, I'll talk about it next class, but try number one Number two three is fine four is fine and eight is fine and I'm pretty sure You can scribble that out The answers are attached. I think yes. I hope I gave you the answers. Didn't I I think yeah So there's a few questions to try and then I have just a practice drawing your sheet for you


Hello, welcome to the session on user function in C to copy one string into another. Let's see the learning outcome. At the end of this session, the student will be able to write a C program to copy one string into another using their own function. There is one library function to copy string in C language is strcpy. In the strcpy prototype, the function is character strcpy character star destination and it is copying from the source. So the strcpy function copies the string pointed by source including the null character to the character array destination. This function returns character array destination. The strcpy function is defined in str string.h header file. For example, here strcpy in the bracket we are having str1 and str2. str1 is here destination and str2 is source. It copies the string 2 into the string 1. We will see in the program how we are using this strcpy built in function first and then we will move to the user function. Here first string copy built in function strcpy first program here directly I have shown that character s1 and character s2 has given 30 character array in the memory. So first character s1 of 30 will be stored here directly a string 1 and character s2 that is s2 variable will store string 2. Now we will use the library function. This function has copied now s2 into s1 when we are using strcpy s1 comma s2 and then we are printing that s1 that will be now copied value is string s1 is s2. Now one more program only here we are changed in the definition of the string. Here again character, source and destination they are capable of storing 100 of character and then print input string and we are getting the string with the help of get as source and then we are using strcpy that is the library function destination comma source. So source string will be copied into the destination then we are printing source as well as destination. Here output is shown input string I have given waltz now source string will be after the using strcpy source string will be waltz and destination string will be also waltz. So one more program here again the variable declaration is different. First we are used here str1 with 10 string that can have 10 character here we are directly given that string is awesome and second str2 string we are not defined here just we are given the variable for the storage. Now strcpy here we are using str2 comma str1 and second is strcpy is str3 comma well. So this well will be directly copied into the str3 and here str1 which is declared here as awesome that will be copied into the s2. So when we are putting put s str2 what will be given so whatever this copied from str1 is awesome that will be given awesome and put s str3 will be given directly whatever this well we have given the string well directly that will be copied into the str3 and when we are giving put s it will be giving str3 that is well. So up to this we have seen that we were using library function which is already built in in the c program. Now here we can see how user can write his own string copy function. So here logic will first see what is the logic we create user function to copy string for that we scan one by one the characters in the source string if the character is a null then copy character from source string to source string array to destination string array. Now destination string array size should be enough so that that can be copy the source string then once the null character is found we will stop copying this character by character from source to destination. So more elaboration here I have shown that user function to copy now first source string is here it is containing array of the string that is s1, s2, s3, s4, s5 and it is holding the string is WRT and then it is showing that null so it is a end of this string and destination string is having hello h, e, w, l, o and then null character. Now after execution of this what will happen see source string is as it is WIT with null and you can see the destination is having WIT instead of we were having hello character. Now we will write function for the string copy that is the user function you can see here include stdio.h here no need of the string.h in the main counter is initialize c and then we are having two string declared s1000 and d1000 and d1000 is already destination is having my program. Now we will print first before copying the string and then then we will go for the input a string which need to be copied by gait s now here we can see that while using while is up to the when we are not getting the null character the destination is going to be copy from the source and c is the counter that is the index from 0 then it will be going on increasing with the help of c++ and we are doing this up to when we are not having the null character and then last we will be having the null character at the end of this string once the source string is finished then we are printing the after copying whatever the string is there. So we will see the output output is before copying the string my program is there then input a string then we are having my output and then after copying into the string it will be my output so that will be source will be copied into the destination. The user function can be written with the help of function also. So here main program function so in the main program we are having declaration that include STD I would add then this declaration is about the function which we are going to use for the copy the string. Now here we can see that while copy string this is the array of the character first and array of the character second. In the main we are having the two strings S and D of size 100 and 100 then we are inputting a string get S and then we are calling once the source is there we are calling the function copy string D, S so whatever the source is here it will be copied into the D and then we are going to copy whatever the copied string that will be print. Now this is the function in the function we are having wide copy string here we are initializing the counter C is equal to 0 that is the index for the array then while it is not null we are going to copy that destination from the source incrementing the counter and then we are completing this copy and then we are copying that last character with null character. So this is the output input string welcome and then copied string we have printed is welcome. Now pause video for a second and write a function to copy a string into another using pointer here is the solution with the help of pointer also we can use we can write a function to copy string here pointers we are using target pointer and source pointer then we are checking the source pointer whenever the content of the source pointer it is showing it will be copying to the target and once it is finding the null it will be completed the copy of the string and once finishing that string we are copying the null character at the end of the string references. Thank you.


So, Candace Owen. Remember Candace Owen? You know Candace Owen. A popular right-wing talk-show host who's been at the Daily Wire for a few years now, came out of Turning Point USA. Went to Daily Wire, has a huge following. Very, very popular on the right, particularly among the MAGA right. Anyway, Candace Owen is out. Out at the Daily Wire. Probably fired, but it's not clear. Anyway, it could be mutual agreement. Could she be she quit? Not clear. Nobody's saying Jeremy Boring, who is the CEO and co-founder with Ben Shapiro of the Daily Wire, wrote Daily Wire and Candace Owen have ended their relationship. Couldn't see that one coming, huh? Anyway, she's out. And this probably has to do with the fact that she has been a vocal critic of any kind of American support to Israel. She has floated, or you could argue more than floated, with anti-Semitic comments and anti-Semitic sentiments and blaming Ben Shapiro for being more aligned with Israel than with America, similar to Tucker Carlson. I guess they get their same talking points from, I don't know, Bannon. I'm not sure who they get their talking points from. But anyway, the two of them, anyway, Candace Owen is out. The thing that probably triggered this particular action by the Daily Wire was the fact that Nick Fuentes, Nick Fuentes, known anti-Semite, not where you don't have to speculate, he just says it, known anti-Semite and general bigot and general horrible human being, praised Candace Owen for her, I guess, standing up to the ADL or standing up against some Jewish thing. And even though she claims she doesn't know Nick Fuentes, I think that was kind of, you know, when one of your hosts is being praised by Nick Fuentes, it's time to fire them, I think. So yeah, she's gone. Daily Wire now is Ben Shapiro. And of course, we have Mike Walsh. And so it's mainly kind of very religious conservatives, reactionary conservatives. And we will see, we'll see if this has any kind of repercussions, if it has any kind of impact, greater impact on the right than what it is. But yeah, you know, I'm hoping, I'm hoping that this will be a demotion for Candace Owen.  I hope she fails at whatever she does next. But that's not my expectation, because I can't stand Candace Owen. I think she's horrible and has been for a long time. She was pretty good when she first came up as kind of a voice, a voice against certain woke policies, but she's just become a horrible mouthpiece for the alt-right and a number of different things her views are just awful. Anyway, I hope she fails. And yep, it's because I envy her. No question about that. So I hope she fails. And I also expect her to succeed. I think she's doing do phenomenally well, because I think this part of the of the right, the alt-right, the MAGA right, the American, you know, isolationist, whatever, right is on the rise. So her and Tucker Carlson are going to make a great team. And they might be the future of America. So yeah, they might be the future of America. Anyway, some people think I criticize her because I envy her. She has a look. She's like a gazillion times more popular than I am. And she's a lot less intelligent. So I'm sure it's envy, right? That that is the dominant thing I feel towards Kansas. All right.


A federal high court sitting in Oqaq, the Anambra state capital, has affirmed Tukuma Saludo, former governor of the central bank of Nigeria, CBN, as the candidate of the all-progressive grant alliance, ABGA, ahead of the governorship election in this state. Saludo, who belongs to the Victoria-led faction of ABGA, had secured 740 votes. In the list, published on July 16, the independent National Electoral Commission, INAIC, picked Michael Morji over Saludo as the standard bearer for ABGA. INAIC said it based its decisions on a court First, INAIC's commissioner for information and voter education also told the cable that Musa Ubali, a judge of a high court in Jigawa state, had passed judgements in his suit, upholding the suspension of Victor Oye and affirming Jude Okeke as the party's national chairman on June 30, 2021. Okoie also cited another court order in which Bellukau, a judge at the Federal Capital Territory, FCT High Court in Kuba, on June 28, ordered INAIC to monitor the primary election of the Jude Okeke faction and comply with the results. Morji won the primaries in Okeke's faction, but delivering judgements on Monday, Chukwu Dioka, presiding judge, set the other parties in the suit, comprising Jude Okeke, Adoze and Joku, and Chukwu and Morji were meddlesome interlopers. The judge, therefore, affirmed Oye as the national chairman of the party and other INAIC to recognize Saludo as the ABGA Governorship candidate for Anambra. Now, joining us this morning to talk about all this is the former CBN Governor and now ABGA candidates, Mr Chukwu and Saludo. Good morning and thank you for joining us. Good morning and thank you. It's really a great play. Let me say al-Qaad-e-Sala to our Muslim friends and a happy holiday to our Nigerians. Okay. So how would you feel about this court judgements that has now ruled that you are the authentic ABGA candidates for the elections come November? Well, I will always say that the judiciary will always come through in the end. This is Anambra. This is the season of all kinds of court orders and court judgements flying from all over the 36 states of Nigeria. That's part of our judicial system. I don't understand it why an election in Anambra should have court orders and judgements coming from Binning Kudu, which is about a thousand kilometers from Al-Qaad where the action is, but that is the season. And so finally, I believe what happened yesterday at Al-Qaad is part of the very first, I mean, part of the very important steps in the resolution of this, what I might call, confusion that was deliberately created. Let me put it that way. Deliberately created over the past few weeks, so to speak. It is a creation of the courts that was no crisis in Africa. INEC, as you quoted the first two so-called years, was on television just about two weeks or there about a go and stated in fatically that there was no crisis in Africa. There was no dispute about the leadership of Africa. There was nothing. Africa was one united family under Victoria as the national chairman, and which was also in the INEC website and so on. Because equal year emerged through a national convention monitored and certified by INEC, the court judgment at Al-Qaad on 19th of October last year affirmed that convention and affirmed Oyeh as the national chairman. And up until now, there has been no national convention to opt on it, and a federal hike, I mean an appeal court had stated that only a national convention of a party can remove the chairman of the party. No such thing has happened. There is no court that has removed him. But then all of a sudden, how did this all emerge? So you'll work up one thing, people will apply to the same Oyeh national chairman, the only national chairman, the only national executive. Nine of us went to the secretariat, bought our forms for nomination and expression of interest. Nine of us went for the screening, and at the end they screamed out and found four of us wanted to proceed to the next stage of primaries, and disqualified five. Now, the other five, one of them, and the committee said was on feet, so wrong for primaries, let alone being governor.  I mean, that's the 11th wonder of the world, as it were. And so for me, therefore, in the context of all, when it came, I was a bit surprised at the way that INEC could actually yield today, because there were also other subsisting courts, three courts, one court final judgment by the year's chairman, there were two court orders, federal high court order and state high court ordering INEC to maintain my nomination, which it had actually received on the 2nd of July, and that INEC ignored those three, and then ignored the electoral act, which section 31, subsection 3, mandated INEC to publish my name within seven days of receipt of the nomination. It received and acknowledged my nomination on the 2nd, and it was supposed to have published my name and the particulars on or before the 9th, if my calculation is right from 2nd to the 9th, it was by electoral act mandated that the commission shall within seven days publish these particulars and so on. It fell. So I was a little bit surprised that INEC could go that far, could go this way, and then rather than decided to obey the one they caught in being good or whatever, that woke up one morning and created this chairman, and I'm just wondering if in the country today who woke up one morning and would get a quarter of that from somewhere and saying that one John Colo, Nicholas is now the president of Nigeria. Mr. Toledo, really that really is a crux of what we are was heading regarding this whole, you know, situation in Anambra state.  Well, I think only INEC can explain that. In fact, that's the point I was just making. We're saying that in this country, we know how a president is elected. We know how he's warning. We know how he is removed, validly. And then so if someday somebody wakes up in either Echiti or in Anambra or whatever high court says, one John Colo, Michael or Nicholas or whoever, is now president, is acting president of Nigeria, because that he claims to have been former vice president. We know who the vice president is, that he claims to have been former vice president, and he has sat the president and has taken over. We start regarding the person as president of Nigeria and we say we are obeying the court. That's part of the puzzle, which I think and I want to believe that ultimately INEC will come through on this because for INEC, they monitored the conversion that produced over a year. INEC has not monitored any other conversion to produce any other candidate. The electoral act requires it to do so. There is no meeting of party to elected, party candidate, party officer that INEC will not monitor according to the electoral act. He hasn't done that. They monitored the conversion that produced over a year, satisfied it, has been dealing with him and is going on the website, all the officers of the party have been on the website of INEC, up until last Friday. Now so and then you receive my nomination on the second. The second national chairman whom you recognize, you know that the law recognizes, you give him the code to upload the nomination on the second. So on the on the on the third year as national chairman of Africa, on the second he uploads my name, get acknowledgement, the electoral act requires you, mandately, to publish my name within seven days. You fail to do so. Now on the 15th of the month, the commission now meant to say, ah, the cutout that I got, whatever, from Benin Kudu. We have to obey this one. Why this regarding the court judgment earlier that meant, oh yeah, the chairman and that found that and he hasn't, by the way, the jigawa or the Benin Kudu judgment in jigawa never said, I mean, clearly spout out that Judo Keke claimed that he was deputy to one a dozean joko as national chairman and that he had now sat the Judo Keke, dozean joko and taken over from him as acting national chairman. Now for INEC, you go to the law requires that all political parties must keep on the list of their national officers with INEC. There was never any minute that the name of a dozean joko or Judo Keke was with INEC as an officer of the party. So how could you then emerge from the blues and then claim you were once you were the deputy and you have taken over and so on and so forth and INEC. But like I said, I'm confident that INEC in the fullness of time would rise up to the occasion and by the way because also the INEC in its press release following the release of the names last week did indicate that it will continue to obey court orders and judgments. Okay, fair enough, if you decided to ignore the previous three court orders and judgments in respect of Oye and my candidacy and then obey the one of Benin Kudu, now the other one has come and all fingers crossed and we watch because. So Mr. Kudu, if INEC refuses to obey this court order saying it's already standing on the one from Benin Kudu, what will be your next move? Oh well of course, I believe well if they refuse to do so, we'll see how that goes. That's on the one hand. I want to believe that there are men and women of honor and integrity there who live by their own words and by the words of the law, by the laws of Nigeria. But besides, I mean that wouldn't actually matter much whether they decide to obey or not obey, ultimately they will have to obey the laws of the land. I believe, I mean we have also of course appealed that judgment of the Benin Kudu so in Jidawa and I think like I said the share of Nigeria always comes through in the end the appeal court will take that up and probably if it has to get to the Supreme Court I believe that that would also finally we'll get justice and I'm confident that we'll be on the ballot on November 6th an election that I think from the facts on the ground we are primed to win overwhelmingly passively in terms of that and I believe that that is why this whole conspiracy and theory is to stop Saludo from being on the ballot by those who think that it's Saludo on the ballot. Actually it closes the elect options for them. Well you know there's still a couple of months till November and so we'll see how that plays out. But I want to ask about Abga itself with the little issues here that we've mentioned you know the Judo KK emergence, the Umoji's emergence also it seems like there's some cracks in the you know in the party and then people would also say that Abga may not even have such a strong hold anymore in Anambra seeing the way that politics has played and been moving in Nigeria lately. What would be your response to that? I as I said a moment ago when you talk about frankly it's a phantom faction. It's just like it's just a creation of the last two weeks sort of space up until Friday last week. INEC knows it all the Abga members throughout the country know it. They know we have one national chairman who has not been removed by anything. These were the words of Abga of INEC. There is not a crisis in Abga. So and as we speak thousands of people are joining Abga by the day in the run-up to the election this year. By the way as you speak there are about 31 self-funding uh pressure groups support groups that emerged in demand for solutions to run for office. Hundreds of thousands of members uh you know took it into their support groups and they are right there of a wired up to go for the election. And so in Abga there is no crack. There are external forces some external forces which would be expected I mean the opposition that thinks that with a soludo on the ballot and with Abga dominantly controlling no less than about 70 80 percent of the political landscape in Anambra. In the last governorship election we won 21 of the 21 local government. The last election held in Anambra happened to be the House of Assembly election after the 180 percent of the six and even could have been a lot more about 90 or that about but you know let's leave the other ones for someone. Anambra is predominantly when it comes to local elections assembly and governorship. Anambra people have almost this peculiar electoral behavior when it comes to national elections they are indifferent. When it comes to a local election they consider Abga as their own that's their own identity. Abga is our people and our people are trying to vote for Abga again and again and again 100 percent. Now the script is if you can pass this kind of decisions and particularly target if you can keep soludo harass him out of the race you may have also heard that somebody some private person went to court to say he's having criminal proceedings against soludo he didn't declare and a property that he rented for his family many years ago 2006 up until now oh he should have declared it and I don't know when you start declaring rented property as your own asset as it were all days and then trying to get the cops or the police to go to harass him and all of that they are just part of a script from external assets are unthinking now from all that we can say we don't believe I don't think any Abga member seriously believes that what is going on is up after that or that anybody else is seriously claiming to be a candidate up after that. Mr soludo you are of course a former CBN governor you know it may be for a lot of people in Anambra you know they might look at it as you know a breath of fresh air you know a young vibrant candidates you know to take over the seat of governor that might be the thinking but you know you earlier mentioned that Anambra you know sees Abga as their own so is this because of the performance of the Abga candidates that have held you know the positions in that state for a long time would you would you say that they've done very well with regards moving Anambra straightforward and I'm talking with regards infrastructural development healthcare education security and all the concerns that the electorate have would that be the reason they would continuously choose Abga or if there's a candidate that seems to have a better you know outlook with regards where he wants to take Anambra does that shake Abga's stance. Two things yes to your first part which is that Abga has served Anambra well Abga has served Anambra well from the time B2B came it took over from Big Air and you know what happened then Big Air struggled with it quite well my my own assessment despite the harassment but it was BDP then that point of point down and I'm missing him actually kidnapped the sitting governor then BDP and then he struggled and then B2B kept on the other part of that implementing the Abga manifesto that is a comprehensive development of the state B2B and a number of people adjudged him to have done well now came Governor Obiano sticking it to the net level in terms of what infrastructure in all sectors of the society despite dwindling resources when most days cannot pay salaries who just you know launched up the international effort in Anambra and international conference and and so on and so forth make a legacy project that Anambra people are saying no we want the good thing to continue so and Anambra is the only political party that the decision about who becomes their governorship candidate is taken by the people of Anambra in Anambra for Anambra and politics become too local and our people are happy they don't want it to go and that's why you see whenever you go on and all you come back to people say one Abga again now on the other thing about maybe some other person except the person is going to come from the moon to but if it is from people who are already on the terrain well I would have a sense of modesty and humility maybe on the when we all roll out our credentials our past our records of public service and our vision for the state in terms of its consolidation and continuity of the agenda then we'll see whether there is anyone else it is left for the Anambra now people to decide whether there is anybody who comes close to what we put out for them the people will decide but if what we have on ground is anything to go by the election if her today will be overwhelmingly Abga absolutely our target actually is to win the 326 words out of the 326 words the target is not the 21 over 21 it's 326 words out of the 326 words and I can then understand why the forces are aligned you know you want to sponsor a more within Abga to see if you can succeed in destabilizing it but unfortunately that isn't working I mean the Anambra people have seen through this plot they're able to decode it and know that this is this is not coming from anywhere it's isn't it funny that someone that the party screened and found to be on feet for the office is now the one who goes a thousand kilometers and the party estate caught in Jigawa orders that his name should be put on there as a candidate of the same party Mr. Saludo yes you you just talked about Abga's credentials in the past few years and that the people of Anambra stay to stand solidly behind Abga but let's talk about you as a candidate do you think the people will stand solidly behind you and what your chances might be in that elections yeah that's precisely what I said the moment they go actually the movement for me to join was actually the people's demand is a people's movement for over two years now the massive movement in the state something new in Anambra politics where the people the ordinary men are working in the markets are contributing money devoting their own resources their own talents their time and everything organizing mobilizing we have 31 such groups and about 15 of them actually have infrastructure in all the 326 words in Anambra Mr. Saludo why do you why do you think you have that support what do you think you're bringing to the table for the Anambra people that you say make them support you so much I think I will be one candidate that will be running on record of public service the people of Anambra know who Saludo is the people of Anambra recall my time at the public service as chief economic advisor to the president and as the chairman of the drafting committee that drafted the Nigerian needs national economic empowerment and development strategy that was implemented under our passenger trade jail and that so Nigerian that implementation of that so Nigerian have its unprecedented economic boom in history and they saw a governor of central bank and they saw the transformation that came with the banking system banking system to their histories before and after Saludo and they know the difference they see themselves they see how millions of people of thousands of investors can now have access to finance and so on that's all the things that we were able to create that I can go on and on we'll have time we'll have time to go through that so the people of Anambra that this is this is not the time at the time of two miles in the global economy post COVID world transition to a post oil economy when many states are having difficulty paying salaries this is not the time for learning on the job you need someone who is tried and tested and that's why they're clamoring they're asking me to come and run that asking me to come and them sir you have solved the world consultant to formally consultant to 20 international financial and development institutions and all their work there is to win I've solved the nation the grateful nation in appreciation of my example at public service honored me with the third highest national honor and with all their words globally and nationally over 200 of them and now my people say whatever you have done in the world you've done in Nigeria come home and do the same for our people and it is that call that I am answering I am going home in gratitude to God for his powerful blessing to offer my service to the people the people know solution and they know what I have done and this election will be around on record of exemplary public service and we're going to be discussing that in the fullness of time it will be talking in terms of your the audacity of our vision of I mean ambition for the state to put our state consolidate on what has gone and to continue to put our state on demand for the 200 people like a number of over 20 million of our people that's what is at stake scattered all over the world that we were our mission or the Afghan nation is to continue to consolidate to build that prosperous homeland that any of us or anywhere that doesn't feel comfortable where he is can have a livable prosperous homeland to return to all right that's why the people of Anambra think they would need a soludo to continue for wherever they are and I'm offering myself like I said in gratitude to God for his blessings and to serve my people as they have demanded all right miss assoludo um um you've of course spoken extensively with regards to your record and what you plan to do um one of the reasons you know we have these conversations is for people of the southeast and for Anambra state people to be able to hear and um um you know see you know further than just politicking um it's important and I believe it's important for every Anambra Anambarian as they are you know called to understand what the next four years of their lives will be like under the leadership of whoever it is that takes over that seat and that's why I always refer back to where you know you're coming from or where you know will you be I know it's coming from uh the minister of labor um you know criticized him and said that he had done poorly and he had filled an Anambra state stated that there is you know you know very very poor development with regards primary health care in the state and not very much has been done and that is you know um increasingly speaking now not not us so I want you to you know quickly share with us you know how how well Anambra has done with regards health care in the last four years or in the last eight years is there any hospital that you currently you know can willingly drive yourself to and say okay this is where I will you know take you know make do do my medical checkups um currently and then also you can flow from there you can also speak about the IPOB issues and the ESN and how you know that might be dealt with. Votapathy is something that the Southeast has dealt with for a long time also but let's talk about health care. It is a bit interesting when you're having the season of parties it is a friend from a governor that himself I gave him credit for focusing on some a few strategic roles he did well and probably he had these plans as I understand to go into other sectors but couldn't. Now in Anambra let's get down let me start with you talk about health care but let me first of all give you the summary in depth of the welfare of the people which encapsulates all that you talk about which is the incidence of poverty for my friends the summary of the welfare of the people is measured largely I mean there are several indicators how long they live and so on and so forth and how poor they are of course how poor they are also implication for how long they live as in case maybe let me point out the statistics summary it's not mine it's not unbegets it's not anybody's by 2010 the national burial statistics indicated that Anambra level of poverty was 53 percent of incidence of poverty means three percent of the residents were poor last year the same national burial statistics published the statistics to say that in Anambra poverty has dropped between them and last year precipitously to 14.78 that's a summary indicator of the welfare of the people under Governor Obiano since 2014 to date now we've got summary statistics and it says you can write a book about that now let's come down to the center well you've got to also go back to where are we coming from what did you have before relative to where we are today if you think it says oh you don't have prime money well there wasn't even any today you have the teaching hospitals you don't have Anambra's oxygen plants for example but they supply the rest of the country look at the incidence of a COVID pandemic that was ravaging everywhere and Anambra has the all-families place like Lagos look at our numbers and how we've managed its healthcare delivery that actually tackled much of this the infrastructure that is in place at the teaching hospital even the state teaching hospital of the state the state university teaching hospital at Amaco where a lot of the patients on COVID and so on have been treated I guess you get to give this date and the governor quite a bit of credit all right quickly talk IPOB before we go how you know you think that might affect the elections November 6 and what do you think must be done you know from the governorship level the traditional level on as indeed but also you know to handle the call for succession I think that would be I would have rest I mean because this is not a few that only three minutes four minutes 30 minutes to talk about IPOB then that's not that I would not discuss that but it is a subject that needs to be discussed I had back in 2017 about 2016 for the published book very important book from Belfra and Nigeria and all of that and during that book review I did call for a very structured conversation particularly among the Ibo elite about the Belfra and so on and when and Nandekano was when he was when he was arrested and the 10 I think in 2017 also I never knew him never saw him I've never still not met him I never met him there was all this clarity among the Ibo leaders and for me when it concerns any Nigerian and there is issue of you know rule of law and deprivation of fundamental rights I am concerned as a Nigerian and I led a team of Ibo leaders about 12 of us including but also part of talk and others and we visited him at the the prison that was the first and the last time I met him and after visiting we addressed the international press conference and called for his release and consequence of what we also call for structured conversation around this particular issue and there are alternative visions about there's some of us who kept talking about the restructured Nigerian viable Nigeria who believe the future and we are better and stronger together and I am an Africanist who believes in you know criminal states of Africa as it were but that we need to have composition around several of the issues being raised thrown out by these guys the method and what they are doing now professor so I may be speaking that's why I said just one more minute okay brilliant go ahead because we need to wrap up go ahead several people might have issues with the means or even the end of this that's a legitimate one and that needs to be that debate okay there is an Ibo when I was the chairman of the planning and strategic committee we launched the Ibo position on the restructuring of Nigeria at the women's square I read out for the position of Ibo on that location all you really that's where they are on our own sense of how a Nigerian stronger Nigeria will look like which is what we all remember but that in the context of that that needs to be a structural conversation in the run-up to the election I think that conversation will not go away we don't wish it away we have to add some I mean increasingly I was on daily basis now the elite in the south is the Hanez the everybody that's a conversation we must all get involved all right because we can't cross from land without a peaceful homeland absolutely and I think that is a subject that I as a person and together with our other leaders around the southeast and the leaders in Nigeria that we need to have these robust conversations to continue to make our country our nation and more affect society all right I think that's a that's a good place to to uh to land uh professor Chukrumasoludo thank you very much for your time this morning thank you congratulations on the court order and I would love to speak with you again uh just before the elections proper call judgment call judgment we'd love to speak with you before the elections proper all right and happy salad once again thank you all right still will also take a short break when we come back we're moving into a different conversation entirely and that is from Bishop Kuka and his response to the Nigerian government we'll talk about it after the short break stay with us


A warm welcome to the fourth session of the fourth module in signals and systems. Now, in the last two sessions, we have introduced two new transforms, one which generalizes the discrete case and one which generalizes the continuous case. Let us review a few ideas, because we must get the comparative picture clear. Incidentally, in my exposition of this subject, I am going to take these two transforms in parallel. I am going to deal with them together, looking at them one after the other. That is because there is a lot of similarity, but there are also important differences and you must understand both the similarities and the differences. So, let us begin. So, the plus transform, so the plus transform for signal x t is given by the integral over all time, x t multiplied by e raised to the power minus s t dt, where s is a complex constant and we saw that s could be written as sigma plus j omega. So, s is a complex constant expanded as sigma plus j omega and then we could interpret this. Of course, this must converge and the convergence depends on sigma. We can also view this as we saw to be the Fourier transform, the Fourier transform of x t into e raised to the power minus sigma t for appropriately chosen sigma. Now, we also specified that a Laplace transform is always an expression and a region of convergence. Now, you know it is very important. We illustrated the sampling in the previous discussion. There is an expression and there is a region of convergence. The region of convergence is the one that we might think can be ignored, but no, that is very important because if you do not specify the region of convergence, you could be dealing with the wrong signal. So, let us take an example. We will just repeat the inference that we drew in the previous session to make this clear. We saw. Now, you know we are going to bring in some notation here. When we write like this and we will do it several times in future, script L, it means take the Laplace transform. So, when we take the Laplace transform of e raised to the power of t, u t it gives us 1 by s minus 1 with the region of convergence. The real part of s is greater than 1 and we shall often further abbreviate this by writing r e in bracket s is greater than 1. This is a short form for real part of s greater than 1. Of course, you could also say sigma is greater than it all mean the same thing and we also saw minimally modifying what we did in the previous discussion that minus e raised to the power of t u minus t when Laplace transformed gave us 1 by s minus 1 once again, but with the region of convergence real part of s is less than 1. So, the region of convergence matters. You had the same expression 1 by s minus 1, but with the two different regions of convergence you are essentially talking about two different signals. Of course, I do agree that the two signals are in some sense derivatives of the same wave form they are really derived from one exponential, but there is one right sided exponential and one left sided exponential. One exponential whose domain is on the right side of 0 and the other whose domain is on the left side of 0 the fundamentally different signals. In fact, what this also brings to notice let us sketch both these sequences together now on the same graph we will get something interesting there. So, this is the time axis this is the point t equal to 0 we begin from 1 and when you exponentially grow you get e raised to the power of t u t and then you could exponentially decay, but on the left side and you get e raised to the power of t u minus t and of course, you can visualize how e raised to the power t u minus t multiplied by minus 1 looks that would look like this. So, these are exponentially decaying, but left towards and this is exponentially growing right towards. Now, you will also notice that this would anyway have a Fourier transform in fact, the Fourier transform is the same as its Laplace transform putting sigma equal to 0 or putting real part of s equal to 0 and in fact, you know this is also reminiscent of what we have done just previously right now. In this case for this region of convergence here real part of s equal to 0 is included, but here it is not that also tells us something about what we just said that this does not a priori have a Fourier transform. You need first to constrain it or hold it down however, in this case no such holding down is required it would have a Fourier transform as we have said. So this also brings us to the observation that the Laplace transform is indeed a very good generalization of the Fourier transform because for those signals that have a Fourier transform they also have a Laplace transform, but there are many other signals which would not a priori have a Fourier transform which now do have a Laplace transform after holding them down. And what are we really saying in terms of which signals are amenable at least the Laplace transform if not to the Fourier transform let us capture that idea now. So, we are saying a signal which can be made absolutely integrable after multiplication by a suitable decaying exponential is amenable to Laplace transformation.  So, you need you should be able to multiply it by a suitable decaying exponentials where it becomes absolutely integrable if that happens that function has a Laplace transform or at least we are assured that there is a convergence in the Laplace integral of course, we are talking about quote unquote reasonable functions that we often encounter in nature we most of time encounter in nature not some pathological cases where you know you have essentially the function not being integrable. So, let us not get into those pathological case, but otherwise you know for all the reasonable function that we encounter in nature wherever the function might not itself be absolutely integrable, but on the multiplication by a decaying exponential makes it absolutely integrable in such a case a Laplace transform is possible. So, you know it does not have to be just a simple exponential like you had here it could be something on one region something on another something on another. So, you know you could for example visualize the Laplace transform something like this and I give this to you as an exercise. So, you could think of a signal which begins at t equal to 0 with the value of 1 it continues to have the value of 1 and darkening it all this while up to t equal to 1 and then grows exponentially from that point onwards. First write the expression for this wave form and then find the integral interesting. Now, let us make a similar summary for the Z-transform so, the Z-transform the Z-transform of a sequence x of n is summation n going from minus to plus infinity x n into Z raise the power of minus n it is often denoted as capital X of Z and this is also an expression or a function of Z together with the region of convergence. Once again we must emphasize the region of convergence matters the same expression with different regions of convergence could correspond will correspond in fact to different sequences. We have seen examples. Now, we shall deal more elaborately with these transforms in the subsequent sessions. Thank you.