New post-war old Dutch cleanser famous for chasing dirt presents Nick Carter famous for chasing crime Every week at this time two great names are joined as new post-war old Dutch cleanser brings you one of the most resourceful and daring characters in all detective fiction Nick Carter master detective You Haven't noticed anything at all unusual share nothing I can think of mr. Carter not even some little thing that's out of the ordinary The only thing I've seen different is that a lot of folks who never wore glasses or wearing them now They're wait a minute sure if they like the folks have suddenly taken to wearing glasses That's right mr. Carter if that's the answer I was looking for new glasses come on come on wear to catch a murderer and there's no time to lose And Now the case of the failing eyes today's adventure starring Lon Clark as Nick Carter brought to you by new post-war old Dutch cleanser This early summer morning a sleek new car drives into the yard of a small farm in western, Pennsylvania A man of the woman get off briskly carrying notebooks and sheets of official looking documents They approach the tall old farmer who was watching them curiously and explain their business crystal. Good morning, sir Morning, I hope we're not intruding Permit us to introduce ourselves. My name is Lake and this is miss Branson. Good morning. Morning, ma'am We're research experts for the federal foundation. Mr. Mr. Thomas You've heard of the federal foundation, of course Well, the federal foundation is engaged in a nationwide survey of public health Mr. Lake and I one of 1500 teams of research scientists covering the entire time So if you've got half an hour to spare we'll get our information as quickly as possible and move on ready Alan Yes, okay. All right physical condition of farm Excellent drainage good. That's a chemical disposal plant back there. Mr. Thomas. Yeah, I thought so splendid Electricity. Oh, yes. Yes. I see the wiring Bottle gas for cooking excellent best conditions for maintenance of health got it out. That's right Now your own condition. It's Thomas AIDS River and dirt any recent operations or illnesses your physical condition the best I could say I can bet One moment. What is it mind if I take a close look at your eyes, Mr. Thomas my eyes Yes, I see You're having difficulty reading lately. How much Thomas? Matter of fact I do. Grant is blurred your eyes seem dim tendency to squint headache sometimes. Oh, yes. That's too bad I'm sorry, Mr. Thomas Alice. Yes put down condition of eyes bad first stage is a cataract first stage is a what cataract. Yes You mean mr. Thomas is going blind. Yes. I'm sorry cataract on the stagable symptoms No, it's no laughing matter. Mr. Thomas.  That's the same old racket, but with new trimmings. Mr. Thomas What do you mean cheap little crook? You think you were handing out this line to a room? I was a detective for 30 years before I retired to this little place Your rocket ended right now We've got an eye doctor and a hundred miles But we got a fine little jail down in town. Let's go you here. Let's go What's the letter safe after it says my dear mr. Carter in accordance with your wishes I'm keeping you in touch with news about your old friend Fred Thomas I'm very sorry to tell you that Fred is dead Then Come on. He's committed suicide on his farm sometime yesterday The note was found in which Fred stated that he had been depressed for some time owing to failure of his health Maybe he decided to get up to struggle. Well, that's impossible. I can't tell you how sorry I am to give you this news You're very sincerely worth a blink of a turn. I can't believe it. That's it That Thomas was pretty close to 70 next. Fred could be a hundred and seventy. He'd never commit suicide Well, some people when the health fail that's a Fred Thomas worked with my father. He was my father's friend and mine Fred never gave up a fight never. Well, what do you think happened? I'm not going to do any thinking until we've got facts to go on. Do you want me to write to the lawyer? No, get your bag packed. We're driving out to west bill. It's one Come in Sheriff part I'd like to talk to you. My name is nick Carter. This is my secretary patsy bone. Hello Is it detecting fire? What do you want to talk about? Fred Thomas nothing to talk about cases close But serif i'm not exactly satisfied with the facts that they said you're not No, i'm not. Ain't that too bad Look, mr.  Oh, if you've got any idea making a big show down here Excuse me, serif. I don't like to interrupt if you don't understand I've come down here to cooperate and help There are any headlines you can have them Look, serif patsy and I just checked in at the west bill hotel. Would you mind calling the desk clerk? Why should I do that? It proves that i'm sincere call him and ask him to read you the names of the people who just checked in If that doesn't satisfy you we'll get out of town. You know, I think they're crazy But uh just to get rid of you all do it Ellie get me sam wood at the hotel Yeah Sam Well, this is Joe pie. I understand the man and a woman just checked in. What's their name? Mr. Nelson crane and miss paula brown shoe salesman Well, well Thanks, sam Well, serif. I uh, I guess maybe I made a mistake mr. Carter. I uh, I apologize you and this bone Forget it serif All I want to do is to find out what happened to my old thread Fred oh, come on. Come on. We'll we'll go out the fred farm right now and buy heaven if you earn any headlines I'll split them with him This is where he was found mr. Carter the day before yesterday Mr. Parlor right old mrs. Jameson found his buddy She used to clean up for him every two days. Oh, then Fred lived alone all alone this morning Well, here's the note we found on the table But it was slumped in the chair like this one My health is going fast on 70 years old doesn't seem worth fighting anymore Sheriff, this doesn't smell right. No, this note is printed. Why wasn't it written? What about it me too? But then I remembered Fred's eyes have been going back on him. Maybe But how about the suicide he shoot himself? Yeah All right, you check the gun for prince. Yep. The gun is down at the courthouse, but I've got photos with me. Yeah 38 automatics I'm going to check with the gun all right. He's dusted the prints inside and out found fred prints all over the chart And you clear the question never one of them I think the sheriff's right me fred must have committed suicide. Oh, that's it And these photographs prove i'm right the fingerprints of that gun were placed there after fred was killed They were walked the simple matters sheriff, you know that all the killer had to do was take the dead man's hand wrap it around the gun But what makes it so sure that's what happened because the prints are too clear and sharp Especially when fred supposed to have held the gun when he shot himself too clear Yes, the recoil of the gun and his dying hand would have smudged the prints. They couldn't possibly be sharp But i'm having a right Not gonna fool the question now is Who killed fred thomas and why that's right. Let's go back to your office sheriff and start thinking I Sheriff you say fred had no enemies at all in wetville not one He was a fine man and everyone liked him and you also say he had nothing worth feeling No, nothing was wrong Then it gets down to this fred must have come across something new something bad here in wetville Whatever that was he was killed as a result We've got to find what it was. Uh, new name at mr. Carter and we'll find it So sheriff you're the man to call the turn now I am Mom But if you notice anything new or different you're unusual about wetville recently That's vicious strangers passing through new businesses. Anyway, I can't think of nothing At least nothing suspicious not even some little thing that's out of the ordinary The only thing I've noticed recently is that lots of folks who never wore glasses or wearing them now Wait a minute. Wait Lots of folks have suddenly taken to wearing glasses who never wore them before that's right Even old gem smalls got a pair. Why do you mention gem smalls in particular now because he'd be the last fella I'd expect to see wearing glasses. Why he Wait a minute Well, I wonder if that gem got them Well, he probably bought them at the oculus same as anyone else. That's just a pointless bond There ain't no oculus in wetville Well, if anyone wants glasses they drive the 16 miles over gary town The gem's been laid up for the last few months of the land bank. Uh, he couldn't get those all the time Later he bought them by mail. Not gem smalls. He'd want to see what he's buying first Sheriff, I think you've given me the answer I was looking for new glasses. I don't get you Let's go ask gem small about it. There's just one chance in a hundred that this is the something new that killed red Thomas Oh Physical condition of farm excellent best conditions for maintenance of health got it alas Now about your own condition mr. Alton eight boy over 65 Recent operations are illnesses.  I'm the best I should say I should One moment. What is it? Mind if I take a close look at your eyes mr. Alton my eyes Yeah, yes, I see You're having difficulty reading lately, huh prince blurred your eyes seem dim tendency to squint headache sometimes, huh? Yeah, that is right. That's too bad I'm sorry, mr. Alton. I've got bad news to you I knew take this down Condition of eyes dangerous birth stages of cataract. What cataract. Yes. You you mean a go blind I'm sorry, but it looks as if you know. No, not blind I cannot go blind Oh, it's not as bad as all that mr. Alton Mr You and and lady you scientific people from federal From federal foundation, you know Cheyenne. You know about eyes. Maybe Maybe you tell me how affectionately Well, there is a cure mr. Alton. We all carry me the federal foundation elixir Alice get a bottle right now this treatment when taken with a special foundation glasses retards the progress of cataract Unfortunately, it's a difficult formula to prepare mr. Alton. It's rather expensive Uh 100 dollars If the price is too much for you, no No price too much to pay for eyes You wait here. I got money from home. I get a pair of the foundation glasses Two hours In southwest 24 miles an hour parameter 29.9 one and call Very favorite you aren't again Tell her next time. She'll leave that on you. Thank you. Thank you a special warning Sheriff part But Nick Trotter warns all citizens to be on the lookout for two crooks now working the cataract record in this county A man and a woman claiming to be representatives of the federal foundation Are working through the farm and selling bogus turrets for imaginary cases of cataracts Any information that you there were about should be phoned directly to this station a reward of $1,000 will be paid Humanly I got the man. I get reward too Hello, mr. Chote, I want to call radio station right away Yeah, I hear a note, but I think I've been reward. You get the radio station big, please I think crooks is here on my farm now So you get money It's the right tag $100 for me now. I take $1,000 of them I certainly cut the roll above Good working. Yeah, he's not called Hang up that receiver quick You're in a jam, but there's one ray of sunshine At least this big mouth didn't get through to Nick Carter The two crooks stand over Olson's body and Nick is 70 miles away. We'll see what happens next in just a moment Now back to the case of the failing eyes today's adventure with Nick Carter Brought to you by new post-war old Dutch cleanser It's four o'clock in the afternoon Heavy thunderclouds are fully covering the sky as Nick's long black convertible scorches down the roads eating up the mile to Olson's farm How much further sheriff? Just a few more minutes, mrs. Bart You know, Nick, I keep thinking about that phone call to the radio station People kind of make fun of the way local phone operators in the country gossip and listen in to local conversations Yeah But if that mrs. Chote, you know the local operator hadn't been in the habit of listening in on what people were saying He wouldn't have been able to relay Mr. Olson's message to us Well, I'm still worried about Olson. All right, what do you think happened to him?  Uh, ease up, mrs. Carter. Here's Olson's place Golly, thank heaven that's over 70 miles and 73 minutes. That's traveling. Oh, it sure is. Come on This is uh, Ed Laher here, local police officer. Ah, Ed Ah, so finally going there again. Yeah, this is Nick Carter and mrs. Patsy Bourne, Ed Laher How do you do? How's Olson, mrs. Laher? I don't know, mrs. Carter. But what do you mean? Seems like he ain't around nowhere, mrs. Carter. Seems like he's disappeared Well, Nick, we've uh checked the house, the barn, shed, and the chicken coop's all the buildings on the phone And he ain't many of them, mrs. Carter He must be here somewhere I'll tell you what, mrs. Laher, suppose you have your men check the rest of the farm Search all the ditches, gullies, the brookback or the orchid and so on Okay, we'll do that. Let's go, man If Olson was murdered and there's a strong chance he was, the killer may have buried his body So be on the lookout for fresh turned earth. We'll keep our eyes open, mrs. Carter All right, sheriff But you come out to the driveway that turns off the road. Uh, what's on your mind? Tire tread. Oh?  Uh, quite a mess of traction this drive Well, mrs. Carter, you think he can make anything out of them? Yeah, maybe. Let's see It's diamond pattern tread that belongs to Ed Laher's car with India balloon at some Olson's truck Well, how do you know that, mrs? I checked him while the sheriff and his men were looking for Olson's What? Oh, so that's why you didn't go with them? Yeah Now, these are the marks of my tires, these triangular treads, they're from the other officer's car Also, the ones that the straight board had banned Yeah, that's those that can come out of this car And that accounts for all our cars Right Now, look here, sheriff Here's one tire track unaccounted for It's a half-moon pattern, funny looking too And an easy pattern to identify Sheriff, let's have another look at those pictures you took at the time of Fred Thomas's murder Oh, yeah, I got them right here, Nick You want them all? Yeah, I remember one of the pictures that closed up at the dr... Yeah, here it is What? It's the pictures in tire marks How'd you happen to take that one, sheriff? Well, I'll tell you I've been reading a book on detecting and it said to never overlook a thing So when I saw these marks and knew that there wasn't Fred's car I took the picture just in case something might come up later And it has, sheriff Look closely at this shot That's the same thread Yeah, I'm telling you That same half-moon pattern And since that thread appears in both places Where we know the cataract crooks have been It's tend to one of it's the thread of their car How about that? Now what do we do? Well, this is mostly a back country district Basically all the roads are dirt Maybe we can follow this tire mark and catch up with those crooks Maybe If the rain holds off Yeah, gotta work faster, wanna beat the rain Let's see The tire marks here from the right are over left By those going out to the left That means the ones to the left are more recent Then the killers go out and turn south on the road Right, so let's get in my car and follow the track You really think they've got a chance, Nick? Yes, Betsy, if they stick to the dirt roads And if the rain holds off Straight ahead, Mr. Carter Straight ahead I can still make out the half-moon pattern The dirt they've been weaving in and out of the back road Probably add leverage to take credit for that How so? He's set up roadblocks in the 10 miles circle Right after I spoke to him on the phone Good man That means that friends are running in circles Trying to find a place to break through Oh, that's Nick Blast Oh, yeah, I gotta thank Betsy, Nick Aw, he's all garnished What? The Medicare No The rain's starting Oh, so ahead If we don't overtake them Before the next fork or cross Right, I'm afraid they'll get away Unless the roadblocks stoppin' Mr. Carter Look up there ahead Why, there's smoke Yeah, black smoke What does that remind you of, Sheriff? Uh, burnin' oil and gasoline Them crooks couldn't have cracked up Runnin' away, could they? We'll see in a moment Hold on Right It's a car, all right Down in the culvert Come on Oh, good grief, look at him Pretty well burned on Must have crashed at least an hour ago Yeah Watch the step that way I'm all right Hey, look Two bodies inside Badly burned Well, it looks like a man and a woman Oh Who's yours to dance? That's right, I'm real fogged Lights of a bumper Last few numbers on license plates Five and nine That'll check the watch Jen Small told us, Nick Yeah, I have to kill the car Without any questions Can you run in smashed in? Yeah, it looks like that's Cut them before we get it Hey, give me a hand with this door But it doesn't All right, force it open Well, a man and a woman What about all they can say now? Have to check further for identification Looks like there may as a books and bottles here In the back seat What's left of a lot of spectacles too Well, I guess nobody will ever drive a missed car again We don't know that anybody will want to drive it Any two crooks don't need a car no more Not that they're both dead I wonder whether they are What? Nick, what are the rest of you mean? Patsy, I've got a job for you This case isn't finished yet What? Are you crazy, Mr. Carr?  But let's go the door What about this, sir? What? What in the world?  How do you know? Some of the description That tears it, lady If you ever had a chance, it's gone now Come on, come on, come on, let's get off the road I don't want them to find you right away Just a couple of hours in your car is all I need Nick, where are you?   No, no, no, it's just my heart, it won't start again One story, I got all tangled up trying to get out of that luggage compartment Well, my friend, the racket's finished, and you're... You dirty... Uh-huh, no name, please After all, I could call you a three-time killer, swindler, thief, and all-around crook, but I won't I'll just call you a jailbird Feeling better now, Patsy? No, I guess so, but, Dolly, I was scared to death, Nick What? Even though we planned everything in a fan? No, I know, but... Nick, how did Jerry Lake get away with that cataract racket? How'd he manage to scare people in the polling point? Well, they only picked on the older folks, people who were suffering from the natural short-sightedness of old age All he did was describe the symptoms of failing eyesight And they thought he was describing the symptoms of cataracts That's about it Well, I don't know, I don't know What a dirty racket Oh, another thing, Nick You say it was Olson's body that was burning Jerry Lake's car That's right If he Jerry murdered the girl he worked with, left her body and Olson's body in the car when he burned it He figured by making us think he was the one who died in the phony wreck, he thought he could get clear Well, you said you knew it was a phony accident because the car was still in low gear Well, that certainly did If the wreck had been on the level and had gone off the road while they were driving along, the car would have been on high gear I didn't notice what gear it was in I just saw the dead bodies and that was that That's what most people think They look if they don't see Just like Jerry Lake What about Jerry? He couldn't see that when he put spread fingerprints on the gun, he was really putting the finger on himself As a result, he's going to get well acquainted with the electric chair Which is as it should be Well, Nick, what about the adventure that new post-war old Dutch cleanser will bring us next week? It's a story about women's fashions like women's fashions Well, they've always been a mystery to me Don't tell me they're more than a mystery They're a cause for plenty of violence You see, the fashions were being stolen And Mary Danvers said she knew who was stealing them And when we went to see her, she walked out of her apartment without saying a word And a moment later, we found her murdered in her bedroom in that same apartment Hey, wait, this is confusing enough without going any further What do you call this adventure, Nick? I call it The Case of the Quiet Rulemate Nick Carter, master detective, is presented each week at this time by the Cuddehy packing company It is produced and directed by Jacques McGregor And is copyrighted by Streets and Smith Publications Incorporated Charlotte Manson is featured as Patsy Today's script was written by Alfred Vester Original music is played by Henry Silvern This program is fictional And any resemblance to actual persons living or dead is purely coincidental This is Michael FitzMorris saying When minutes count, use new post-war old Dutch cleansers This is the Mutual Broadcasting System


This video was brought to you by my patrons. Thank you so much for your support. Hello there. In this video, we will continue the series about the four pillars of object-oriented programming. And in this video, we will talk about abstraction. So in the previous one, we talked about encapsulation. And now we will talk about the first step actually into designing a class. There is to abstract the class into the context of your application. But before diving to how we can use abstraction in Godot Engine, I will open a book so we can have a brief definition of what abstraction is commonly described as. So I will go to this book here. And here it is described as a model of a real-world object or phenomenon, limited to a specific context. This is a very good definition, but I will actually just take root of this real-world object. Because more than often, we work with just our imagination. So we want to abstract an object that doesn't have a real-world reference. So I will actually use abstraction as a model of an object or phenomenon, limited to a specific context. And this is very important to know because what you are going to achieve with abstraction is to take root of everything that is not relevant to the context of, let's say, your game. And just use what is relevant to it. So here I have in Godot a black hole. But we know that black holes are very complex objects, right? But to the context of my game, I just want to represent a black hole in such a way that it would communicate to the player that it will suck the mouse towards its center. I don't have to model the whole representation of a black hole because it's meaningless to the context of my game. I don't want to have all the physical properties of a black hole. So abstraction is a part of the designing process of a class. We will take root of everything that's not relevant that would make the application more complex that it should be. And we'll just cherry pick what is relevant to it. So the application has a goal. And we'll just use the properties and the behaviors of the object or the phenomenon that will make this goal achievable. So now let's try to abstract the sliding panel so we can see how we can use some traits of abstraction in Godot Engine. So I will close this black hole here. Don't save. And well, I will start using a simple panel class, a simple panel node. And well, since this will be an abstract sliding panel, I will prepend these words to communicate to whoever is trying to use this class that this is an abstraction of a sliding panel. It's not the concrete implementation of this sliding panel. Whoever is trying to use this sliding panel will have to implement its behavior. So I will prepend the word abstract to communicate that this is not a concrete class followed by the sliding to communicate that this is a sliding panel. It's not a common panel. And well, to slide, I can use an animation player, but I have some problems with animation players because they use absolute offsetting. And this can cause some bugs. So I don't like to do that because it's a static implementation of a sliding. And instead, I will use a twin because with twins we can take the current value of the properties of the object in runtime and use them to calculate the animation. I will also add a timer because I want the sliding panel to have a small delay between sliding in and out the screen. Now we have a sort of an abstract sliding panel. It doesn't have any behavior yet, but we have here what we need to start working with it. So if we have an engineer working with this class, it will know that, well, we will use a string and a timer to implement some of the behaviors of this sliding panel. So I'll save this class into the interface folder here, abstract sliding panel. So I will add a new script here so we can see the abstraction features that are going to provide to us so we can make sort of an abstract class. So I will create a script here and let's start abstracting this class now. So I'll take rid of these defaults here. And for the context of the game, I just want this sliding panel to slide in and out the screen. And for that, I think that I will only need three properties. I will export a vector 2. That will be the direction of this slide because maybe I can slide in so it will point down. Maybe I can slide out pointing up. Maybe I can slide on the left, on the right. So it's good to have this direction pointing. Where is the direction that this slide will happen? And by default, it will be sliding down. I will also need a float. Then what will be the duration of this sliding? Because with that, I can define how long will take the sliding. So duration, by default, it will take one second. And also I will have a distance, the distance of this sliding, right? So export float var distance, which by default will be 100 pixels. So here we have the properties that this sliding panel will have. And now let's try to describe its behaviors. With that, we will not describe how it will behave. But what are the behaviors? This is what is concerned in the abstraction phase of the designing of a class. We are not concerned with the implementation yet. We are not concerned with how it will behave. How will the behave happen? We are just concerned about what are the behaviors of this class. So in the case of the sliding panel, I will have a function that will tell it to slide. I don't know if I add slide in and out, or if I just add a mode. Maybe I can have a mode here that will be... I will add an enumerator, mode in and out. And then I will export a mode variable that will be the mode. And by default, it will be mode.in. So now I think that this sliding panel will only have this slide method. Because I think that this is basically the only thing that it does. We will try to follow the single responsibility principle that tells that a class should be concerned with one thing and one thing only. So to do that, I will describe here on the top that this is a panel that slides on the screen. And with that, we have a single responsibility to this class. And we will have here this slide method. If you leave a method blank like this, we will have some errors, right? Godot will tell that it is expecting a block inside of this function. But as I said, when you are abstracting a class, when you are just concerned about the design of the class, you are not concerned with the implementation yet. This is a part of the engineering of the class. Godot offers to us the ability to leave a method blank by using the keyword pass. This will tell the compiler or the interpreter that this function doesn't have anything and there is no problem with leaving this function blank. With that, we can focus back on the designing of the class and not on the implementation, so we can leave it like that. But if you want to make sure that an engineer will override this method, it will implement this method, making sure that this method will not be blank, you can use the keyword assert, always passing false. And I think that you can add a comment here to communicate to the engineer that this is a virtual method and shall be overwrite by children classes. So when the engineer called this method on other classes or maybe on this class, so if he ignores that this is an abstract sliding panel, this is an abstract class, when he calls this slide method, the compiler will fail because this will assert always false and it will bring the engineer to this line of code here, the line 19, and he will see that this is a virtual method and shall be overwrite by children classes. So you are designing the class to make sure that on further implementation, someone will have to override this. But abstract classes are not just meant to be used for, let's say, for designing. They are also used to provide an interface to interact with its children. So let's say when an engineer tried to implement this abstract class, let's say a concrete sliding panel overriding this slide method here, anyone that will use this concrete implementation of the sliding panel will know how is the signature of this slide method. If it has arguments or not, what are the properties of this class, what are the behaviors and the features that this class has, what it is intended to be used for just by opening the abstract slide script. So they don't have to be concerned about the implementation itself. They don't have to open a complex version of the sliding panel. They can open the abstract class and have an easy interface to interact and to understand what this class is meant to be used for. So this is the power of abstract classes to provide an interface to the user. I received some comments in the previous video that maybe I misunderstood or I confused abstraction with encapsulation. But let me describe the two in my words so we can understand how I differ both. So to me, encapsulation is to make the implementation of the class easy to understand while abstraction is to design the class into the context of the application only taking relevant pieces of it. And well, an abstract class provides an interface to interact with the class. But the encapsulation is to make this implementation easy to understand. So this is the difference for me. But if you still have some doubts or if I say something wrong or maybe something is not clear yet, please leave a comment below. I will be modding happy to be corrected to understand if I am going into the wrong direction or if I am on the right path. Let me know. Leave a thumbs up if you enjoyed the content. This will help me understand that I'm going to the right path. And also if you want to get more of this content, don't forget to subscribe and to turn on the notifications so when I release a new video on this content you will be notified. And also if you enjoy this kind of content, if you enjoy the work that I do consider becoming one of my patrons so you can support me in this journey. But that's it. Thank you so much for watching. Keep developing and until the next time.


We've had a fascinating conference. It's been organised in conjunction with FIFA, of course, who are sponsoring our initiative, UEFA, who are the European Football Association Confederation, our Italian colleagues and of course the Interpol staff as well. We brought together 50 countries from throughout Europe with representatives from their football associations, from law enforcement, the integrity officers from national football associations, as well as other interested stakeholders including the betting agencies, the lottery agencies and the gambling regulators. As a result we got a very useful cross section of views but very common agreement on the way forward and the importance of tackling match fixing more effectively from now and into the future.


Hey everyone, Dylan Schumacher, Citadel Defense, and today we're going to talk about snub-nosed revolvers. I actually left my snub-nosed revolver downstairs. However, the one of the things that I want to talk about today is that we need to stop selling, offering, insisting on snub-nosed revolvers for new slash inexperienced slash female shooters. I don't understand where this thing started or where it came from, but here's what happens, right? A woman wants to get into guns. She goes to a gun store and nine times out of ten, they lead her over to the air weight J-frame revolver section, right? Sometimes they have cute little pink grips on them or whatever and they pull out all these little tiny revolvers and she doesn't know so she starts holding them and whatever and then decides to buy one, right? And then she goes to the range and shoots it and she's like, Good God Almighty, this is a terrible experience and this is painful and this isn't fun and why does anybody like to do this anyway and then never shoots it again, maybe carries it, maybe doesn't, who knows? But there's a problem here which should be pretty apparent. Okay, let's start at the basics. New shooters don't know how to manage recoil very well by nature of being new shooters, okay? Secondly, you're going to take a air weight revolver which is known for their heavy recoil, their difficulty to aim and their difficulty to use that carries maybe five or five, maybe six rounds and you're going to give that to someone who's never shot before.  I have no idea where this started but it needs to stop. Stop selling revolvers to new female shooters. It's a terrible idea. Physics, okay? For every action there's an equal and opposite reaction so as the bullet exits the barrel all that energy is going to get translated and pushed back to you in the shooter. If the gun has a lot of mass it's able to absorb more of that velocity before it really moves into your hand, right? If it doesn't have very much mass in the case of air weight revolvers all of that velocity gets translated directly into your hand and is physically painful to shoot, not hard, not hard to grasp this concept. So again, don't know where this trend started. Don't know why it still exists but we need to stop doing that. If you want to start someone new on shooting start them on a .22 or you can start them on something like a full size 9 like a Glock 17 or even like a Beretta 92 would be really good. Those absorb recoil really well or 19-11-9 something that's going to absorb that recoil really well so they can learn what they're doing before they have to worry about these things. I don't shoot stub nose revolvers very much.  It has a very short sight radius and again you're only having maybe five rounds in the thing before you have to dump it and then stick five more bullets in there. Conversely when this is out of bullets I take a box out, I put a box in and I can keep partying.  Okay? So that's it. That's my public service announcement. Thank you for bearing with me on this rant.  Buy them an actual gun that they will enjoy shooting so they can learn how to shoot effectively so that if their time comes they'll save their life. Do brave deeds and endure.


A couple of announcements before I jump in. This is a bit of a weird one. I'm going to be saying no calculators today because there's no calculators on this test. This is the last non-calc section of any test, which means any trigger I'm going to be asking you is going to be exact value questions and special triangles and all that stuff. Also, if you go to the website pitmath.com and you click here where it says Math 12 and you click here to access Math 12 Provincial Exam Reviews and Video Tutorials. I sent these links out to you as well, I think, on the weekend or just before the weekend, like a while ago, a couple of days ago. Anyhow, Trig Part 1 Review and Trig Part 1 Review, you can find two summaries. It'll be fairly similar to what I'm doing with you today. If you just want to hear it in a slightly different way a second time or whatever, or I didn't answer the question you specifically wanted me to answer. Also, if you want, nope, never mind. These are all both Unit 1 Trig Parts 1 and 2 combined. I did give out a second half of the first review, the even-numbered pages, which for some reason didn't photocopy, so if you were away this morning, thank me later. Can you turn in the booklets to page 20? What I want to do first of all is do straight Q&A. In other words, if you glance at a question and you say, I have no idea how on earth to do this question, then I'll do it with you. And I would like to spend a bit of time probably talking about graphing, because I suspect there's still a few questions about graphing. I'm going to do that.  I'm hopeful that the cast rule and all that stuff is pretty good. And all I need to talk about with those ones, Amanda, are the curveball type questions.  On the first page here, are there any questions? And you need to be honest, because if you're the only one that doesn't understand, that's still worth asking. Are there any of these that you would be going, I would have no idea how on earth to even start this question or what to do. Yes, number three, absolutely. So this is what I'll cut and paste in the tutorial. Trig, part one, tutorial. I won't copy the whole little test bank, because some of it will be redundant. I want to save paper. Okay, I think I like this question, or I might ask you a range, which is similar, or a minimum value, but you're going to see something like this on your test. Okay, it says, find the maximum value of this. What they're really talking about is vertically how high and how low. Dominique, I said vertical, and here's how I visualize this. What's the vertical displacement? I think I'm down here somewhere. What's my amplitude? Which means I would go five up, how high would that be? Yeah, and five down, how low would that be? There's your maximum value. There's your minimum value if I ask that, or there's the range between negative eight and positive two. So if they wanted the range, negative eight, less than or equal to y, less than or equal to two. And you'll notice the three doesn't actually show up directly. It's indirectly in here. Is that okay? Any others on page one? Yeah, okay. Five, I have no idea. Which trig function is it? It's cotangent. There's a reason I have no idea. I really haven't memorized cotangent. Ah, what does cotangent go with? Here's what I've memorized about tan, besides the fact that it happens on a beach. Did I mention I was in California?  And you know what? I'll even do the, bring in the graph paper, Mr. Dewey. There it is. Heck, let's even bring in some graph paper. Heck, Mr. Dewey, let's even insert a little graph. Here's what I know about tangent. This is what I've memorized. First of all, it's shape. Okay, I got that. Sort of looks like a letter T if you stretch the T out a little bit. I kind of remember it that way. I know for a fact that tangent goes through zero, zero. And I know it has an asymptote right there and right there. Is that okay, Ellen? Where is this asymptote? This is what else I've memorized. At 90 degrees or pi by two and at negative pi by two. You see, this little part of memorization tells me an awful lot. Can you tell me the period? How long is one wave? Well, from negative pi by two to positive pi by two. Oh, period's pi. That's one tan function, not two pi, like cosine and secant and secant and cosecant. Co-tangent and tangent are a period of pi. Okay, also it has asymptotes. Where would co-tangent have asymptotes? Here and every pi because that's a period. Now, if tangent has asymptotes right there. Oh, they want the value of pi. I'm going to have to extend my graph a little bit further, aren't I? Okay, pi by two, three pi by two. Sorry, pi by two, two pi by two. Here's three pi by two. I'm pretty sure there's an asymptote like this. I'm pretty sure tangent goes through zero there again. I'm pretty sure it looks like that. Is that fairly reasonable to do? It takes a little bit of time, like about five seconds. But, you know, the five second trade-off, Sabrina, for not having memorized yet another graph, I think I'll live with that. Now, here's the key then. It looks like the tangent of pi is zero. So what would the co-tangent be? Undefined because zero has become undefined. That's one way to do it. The second way to do this would have been to simply say, you know what, tangent is defined as y over x. And if I go to my lovely little unit circle, pi is right there. What's my y-coordinate right there? Zero over, what's my x-coordinate? Negative one. What is zero divided by a negative one? When zero is on the top, that works out to zero, and then you would say co-tangent of pi was the reciprocal, one over zero, undefined. So I can get there in a couple of ways. Which way is faster? Well, probably this way. This way is more flexible in that it can handle angles that aren't necessarily on the edges here. I could probably make an intelligent guess. Any others on this page? I don't know, but number four is a weird one. I was kind of wondering if nobody would ask. Let's find out here. This is a way that I can ask you if you understand graphs without blatantly asking you to graph something. So it says, which of these values would result in it having no x-intercepts? You know what? Let's look at it with D being zero, with no vertical displacement, and then we'll ask, what happens if D changes? I would do a real quick sketch. What's my amplitude here? Which trig function? Any phase shift? That's why I started right there. Okay, it's going to look like this. Except this one with a two there, it's a horizontal compression. That's going to be a pi right there. I really don't care about horizontal, because they're saying which would not have any x-intercepts. The domain is all real. So no matter how much I shrink or stretch it horizontally, there's going to be x-intercepts. The only way I could not get any x-intercepts is to move up either so high or so low that my graph wasn't touching the x-axis anymore. If I moved two up, you know what? I got negative four to play with. I'd still have a couple of x-intercepts. If I moved three up, I'd be kind of right there. I'd still have a couple of x-intercepts. Heck, if I moved four up, I'd still be touching once right there. I'd still have a couple of x-intercepts. You know what, Brett? You're right. It is D. Five up would have no more x-intercepts. Example of a mini curveball that I would hope you wouldn't panic. I hope you would say, well, why don't I do a sketch and kind of think about things here? Turn the page. Or next page over. Any on number six or seven, whoop, or eight or, hello, try that again. Any on six or seven or eight or nine that you want me to go over. So you'll absolutely see number six, except it's going to be radians. Okay, I'll ask you to find a reference angle or a principal angle or both, or a coterminal angle. It's going to be radians though. Range. Yeah, here's a nice algebraic one. I don't know what you're thinking about. You can always ask me to do if you want to. Number eight, here's a graph. Tell me if it's the correct equation. Sure, that's fair game. Any of these? Thank you for finally asking. It's kind of pausing there going really. By the way, good news is, seven is a little curveball. Okay, and it really ties into the one that Ellen asked earlier about how range works. You see, I know that this value here, which is the lowest, came from the displacement minus the amplitude. I know that this value here, which is the highest, came from the displacement plus the amplitude. Let's try that, maybe. Oh, wait a minute. I'm not going to be able to get a whole number. I'm just going to get an algebraic expression. I'll plug that in and I'll get the a by itself and see if that helps me.  Carly, what's a plus a? I think I'd write that next. I'd plus the k to this side. You know how many k's there are as it turns out? Three of them. Get the a by itself. Apparently the a value... That's wrong. That's wrong. Over 2. Thank you. Oh, let's go back and try the same thing. By the way, I'm kind of having a feeling that probably this is the wrong answer because it'd be a fluke if they worked out to the same thing. See, you kind of think like a test. It might be. Let's do the same trick, but this time let's get the a by itself over here and plug it in to here and see what d ends up being. So if I take this guy and I rewrite it as a equals 2k minus d, and now I plug that in there, I'll get 2k minus d plus d. Sorry, let's try that again, Mr. Duc. Substituting it improperly. I'll get d minus 2k minus d equals negative k, right? I'll get a minus 2k. I'll get a plus d equals negative k. What's d plus d? 2d or not 2d? That is the question. And I have a minus 2k. If I plus it over here, I'll get that. Ah, you know what? Turns out d is k over 2. A is 3k over 2. Now I would consider that like an a minus level question. This is a curveball, but do you see how I haven't done a single thing new here? I just haven't panicked. I said, apparently they think I can figure this out. Let's pull up some grade 11 algebra. Now, honestly though, what I would have done is I would have glanced at it. I would have said, what the heck? I would have put a star next to it. I would have moved on to the next thing.  I would have worked on it for no longer than 60 seconds. I like, I found if I get my brain working on something like this, and then I move on, what happens subconsciously? Your brains keep working on it. You've all had the experience of suddenly 10 minutes later, an answer pops into your head. Really? Okay. Thanks for coming for the 10. Okay. No problem. I'll throw this online. I may be available Thursday after school. I'll find out, sorry, Thursday, ask me. How did I get that? So this goes right back to the question that you asked me earlier. I said, you know what? The range is the lowest point. Is this minus that? And the highest point is this plus that, right? Five down and five up from the amplitude. A down and A up from the, sorry, I said five down and five up from the amplitude. Five down and five up from the vertical displacement. A down and A up from the vertical displacement. Oh, and they told me what the answer was. Apparently when I went A down, I got that. And when I went A up, I got that. Is that right? This is a tough question. Don't kid yourselves. Pardon me? I like them better than them. I make far less dumb mistakes with them. Letters than numbers. Alex, I sure can. Are we okay at number nine? I hope finding the quadrant, you can sketch it and find the right quadrant, right? Number eight. Now I'll probably ask you to recognize the graph. I'll definitely ask you to graph something like in the most recent quiz. So let's see. Vertical displacement and amplitude I try and find first. Alex, how high? How low? Careful. Negative three. Total distance? Amplitude is nine, right? Nine up, nine down, nine up, nine down. Dominic, what's the amplitude? So if you go nine down, you'll be in the middle. Or if you go nine up, you'll be in the middle. The vertical displacement is six. Okay. And right away, Emily, I would go like this. No, no. What's the amplitude? What's the highest point? 15. Go nine down, right? You must have gone nine up from the middle and you must have gone nine down from the middle to get to negative three. It's got to be six, all right? And amplitude goes there. Vertical displacement goes there. So I crossed out B and C, or to B and D. Now I need to find B. Now remember, B is not the period. B is two pi over the period. How long is the period? Well, one wave goes from here to here from zero to 10 pi by three. I think the period of this graph is 10 pi by three. So I think B is going to be two pi over 10 pi by three. Vlad, how do I divide by a fraction? So this is going to be two pi times three over 10 pi. Okay, the pi's cancel and I get six over 10, which in lowest terms is what? Three over five. Is that okay? That's how I'd handle it. Although I'll be honest, I would have canceled the twos out on this line and got straight to the three over five, but that scares some of you. Some of you just like to multiply and then reduce. Okay, easy. Number nine is okay, yes. Emily, we're good. Smiling for some strange reason. Oh, your book? No, leadership? Sorry, I'll write you a note. Turn the page! Any here on 10, 11, 12, or 13? 10, how would I find coterminal angles? Add or subtract? What? Two pi, although I'd use 18 pi by nine. Here, I can do it in my head. 11 plus 18, 29 pi by nine, and 11 minus negative seven pi by nine. The answer looks like it's B. Number 11, this looks like a job for? The arc length. I can't remember it. Oh, please do, I hope. Really look for the word arc, sorry. Sure can. Okay, I want to ask you a multiple choice cast rule question, but I can't just say, hey, where is sign positive? To try and come up with four wrong answers is tough. So this is how we will ask you if you understand the cast rule. That's my way of saying I like this question. I like this question. There's going to be one something like this. Except I'm going to, well, I'll show you. The only thing I don't like about this is it's too much typing. Amanda, I would never write secant M is negative. I would write secant M is less than zero. And tan M, I would write tan M less than zero. How would I write is positive? Greater than zero, okay? So I'm not going to write out those words. Is negative, is negative, forget it. Okay, C-A-S-T. I don't have a rule for secant. Spence, what does secant go with? Cosine. Cosine is negative according to this question. That's going to be here and here. And I do have a rule for tangent. Tangent is negative. Tangent is going to be negative here and here. Where is the overlap between which two angles? What angle is this up here? Pi by 2, how about here? Between pi by 2 and pi, has to be. That's the question that I'll give you and it's probably going to be on the first page where that's how I'll test you. Do you understand the cast rule? And to make it interesting, I'll probably have one of them be a reciprocal or both of them be a reciprocal function. Is that okay? 13, sure can. Glad you're asking. So number 13, what do they want me to find? Did they give me the sine and the cosine as fractions? As soon as I see that, I'm going, oh, they gave me x and y and r. Or they could give it to me as points. We've done that on a couple of quizzes where they actually gave me something comma something, x and y and I could figure out r. But here, sine is what over what? Sine is what over what in terms of x and y and r. So I think it's y over r, by the way, Kido. I think that. Cotangent is what over what in terms of x and y and r. So I'm pretty sure that one of these, there's a negative, one of these guys is negative. So let's think here. According to this question, sine is positive. Okay, that's here and here. Cotangent and tangent is negative. Where is tangent negative here and here? Where's the overlap? I have to be in this quadrant. In this quadrant is my x-coordinate or my y-coordinate negative. Which one? Convince me. Y, how come? You're to the left, right? Because I'm to the left and I'm above, right? I'm above the x-axis. I've got to be positive y. I'm to the left of the y-axis. It's got to be negative x. Which trig function do you want me to find? Coast, Tyler, which is what? x over r. There's a couple like that in the review. There is one particularly cheap, nasty, yucky, I think slimy one. So tricky that when he did the answer key. I actually saw the stats on it because it came out on the provincials back when they used to release stats. And something like 90% of the kids got it wrong. And of those 90%, 80% picked the same answer because it had a trap within a trap within a trap. And 80% of the kids found the trap within the trap and they were so proud of themselves. And they missed the third one. Which one am I talking about, you ask? Let me go hunt for it. It's another one similar to this, but it's cheap. Bear with me for a moment, please. Oh, I hated this question. I'll recognize it right when I see it. Oh, yeah. Because it's a great discussion question. Heck, Mr. Duke, go pit page. I even remember it's at the top of the page, I think. Tells me how much I hate the question, but I can remember what it was. Got to be getting close, Mr. Duke. Yeah, this one here. This was mean. Very similar to the question Carly, you just asked me, which is why I don't mind doing it right now. It's kind of like, hey, let's review this. So they did mention the unit circle. Remember, as soon as they say that, I know r is 1. Nice. And they told me that cosine theta is m. Really, what they've told me is that's my x-coordinate. Right? Because it's x over r, but r is 1. Y is going to be the square root of r squared minus x squared. Oh, what quadrant did they tell me that we were in? What can you tell me about the y-coordinate in that quadrant? What can you tell me about the x-coordinate in that quadrant? So a whole bunch of kids chose this one, which is wrong. And here's why. The x-coordinate is negative. But what can you tell me about cosine in this quadrant? Positive or negative? Did they put a negative here at all? Then that m must have a negative hidden inside of it. It has to because cosine has to be negative. When I wrote down x equals m, that there has a hidden negative inside the variable that we can't see because we don't know what the value is. And so, yes, I agree with you. The x-coordinate is negative. But it already is because they said that statement there. The correct answer here was that one. That's a cheap one. Because everyone was so proud, they caught the negative. There's the first trap I told you about. And then they said, oh, and of course, x is negative. It's the second trap I talked to you. I just put a negative there. And they said, OK, it's that one. The third trap is actually if that was the case, they would have had to have had a negative here, too. Right? Do they? That must mean whatever number is sitting in there that's hidden must have a negative inside there already. I don't need to add an extra one. Cheap. Cheap.  What I do like, though, I think it's totally fair game to give you something like this where you have to use x and y and r and come up with an algebraic expression, either to find the points or give you the points and find the trig function. Yes. I'm going to wash my hands after that one. I hate that question. Turn the page. You going to make it Dominique, you sure? OK. You want me to go over, I will, if you want me to. By the way, this test has lots of curveballs. Don't freak out because this practice test you're looking at, there are going to be some nice easy ones, too. In other words, if you're going, no, I like this because it is actually a bit of a higher level. Vlad. Sure thing. What do they want me to find, Vlad? Of? Now, exact values is a trigger phrase. It's either special triangles like one, two, root three. But look at your answers. Are we using one, two, root three? Or you're going to be using x and y and r. And I think that's what it wants us to do here. Because I think what they've told us is that my x-coordinate is that. Yeah. My y-coordinate is that. And if they want me to find cosy-cant, well, that's going to be y over, sorry, no, Mr. DeWitt, r over y. Right? Yes? Look up. Yeah. I mean, let's become good test writers, please. I'm ready without knowing anything else. I've got a 50-50 chance of guessing right now. In fact, I've turned it into a true or false question. Same odds. Oh, and tan is y over x. Oh, what would happen to the ks? What happened to the negatives? Technically, I'm done. It's got to be a, let's actually go further and convince ourselves that we can find the root 29, however it appears. r would be the square root of x squared plus y squared. Right? By the way, if you guys are all academic kids, Joel, if you're not in the habit on a multiple-choice test of crossing out wrong answers every time you do a step, you're wasting precious time. You'll notice I finished this question. Actually, no, I didn't even, I don't think I did a third of this question, and I have the right answer. It is going to be a. Get in that habit. Of lab, the negative is going to cancel. 2k squared is 4k squared plus 25k squared, and I'm going to get this, the square root of 29k squared. Oh, what's the square root of k squared? I think I can write this as a k in front and a root 29 right there, which explains why in this one, of course, the k did vanish too. Yay, it is a. Is that okay, Katie? Did I do anything new there? No, stubborn and clever. And, you know, relaxing, not panicking, looking for certain trigger words, exact values, at special triangles, unit circle, or, oh no, look at my answers. There's no root threes and root twos.    I hate that previous question. Any others on this page? The real question is not where you're supposed to be. The real question is, are you even here right now? The alarm bell goes off. You know where it goes off? Right here. Is that one third factored out of the x? Three pi is wrong. I'd cross out a and b right now. In fact, you know what? I'd cross out a and b and then I would say, when I factor, well, let's become negative or positive when I factor it out. Positive, so it's got to be to the left. I'd circle d and I wouldn't even do the math. Right? Can we start learning to write tests that way a little bit? Well, Mr. Dewick, are they all like really? You'd be amazed how often you can quit on a question. Let me give you a great example that I assigned to you guys earlier today. It was a quadratic trig and I just did it today. Let me go find it, Mr. Dewick. Might have gone too far. I was at the top of the page. Well, even something like this one here. So this would be totally fair game on your test. But if it's multiple choice, I'm not going to finish this question at all. First thing I'm going to do is this. Cosy cant, so it's going to be re-write it. Cosy cant x equals negative 2, because I get the cosy cant by itself. Cosy cant goes with which trig function, Tyler? Sin negative. So I know the answer is here and here. Yes, that can't be right because that's not in that quadrant. That can't be right because that's pi by 3 is in that quadrant. Right?  All I'm going to do now is find the reference angle and quit. If the reference angle is pi by 3, this is the right answer. If the reference angle is pi by 6, this is the right answer. I'm not going to do anything more than that. Why would I? You guys are looking at me stunned. You guys don't write tests this way. You need to. This is how you write multiple choice tests. And you'd be amazed, especially in trig, how often you only need to do about one-third of the question. And you're done. So sin is negative there and there. Let's see. This is negative 2 over 1. Do I have a triangle with a 2 and a 1 in it? Yeah, that one right there. Cosy cant. Cosy cant goes with what, Tyler? Sin is opposite over hypotenuse. So I'm looking for a hypotenuse over opposite. That one right there. My reference angle is pi by 6. I'm done the question. I'm not going to waste my time. Why would I bother doing more? Yeah? Isn't 2 pi by 3 what? I don't care. It's still not legal. Oh, I could have crossed that out too, you're saying. Apparently I didn't even need to do that much. Thank you, Ellen, for pointing out a short cut that I missed. Trig in particular lends itself to that because there's only four quadrants to play with and because half of them are negative and half of them are positive, almost any question can turn into a true-false question, if anything else. Let's keep going back to here. So phase shift. If you did factor out the 1 third, the same as dividing by 1 third, same as timesing by 3. Which pair of functions below have the same period? Okay. What's the period of cosy cant? Don't know. Oh, Amanda, what's cosy cant go with? Have they mucked around with the x at all? Say no. Then the period here is 2 pi. What's the period of tangent? Ugly cousin. What is the period of tangent? Pi. Have they mucked around with the x at all? Say yes. Period is pi over b, not 2 pi over b, like in sine and cosine, which would be pi over 1 half, which, oh, only smokes. I'm pretty sure the answer is that. But let's keep going just for giggles. What's the period of secant? Don't know. What's secant go with, Brett? So secant would have a period of 2 pi over b. James Coase. Pi. What's the period of cotangent? Don't know. Oh, what's the period of tangent? What did we just say? Ugly cousin. So cotangent will have a period of pi over b, in this case, pi over 2. There's your period questions for all those ones, right? And having said that, turn the page. Now, this is not a great example of how I will phrase questions on your test. If you want good example of how I'll phrase questions on your test, look at review number one, part one, and then part two that you got today. I took the questions phrased similarly to the provincial exams. This is from Alberta, but this has some nice higher level questions, Alex. I think it's a good review. Any on this page that you're going to, uh-huh, don't know. Or all of them. I'm good for that too. Number 19, great question. Ugly cousin, right? And I need to make sure I read the question very carefully. It's asking which does not have the same asymptotes. Okay. Remember the tangent graph? I sketched it a little while ago. I'm just going to visualize it, because I'm trying to get you better. If you slide that two up, because that's what that is, well, that move the asymptotes at all. So A does have the same asymptotes. It's not the answer we're looking for. If you slide it Pi left, will that move the asymptotes? Well, it will. What was the period of tangent? Pi. If you slide it exactly one period, won't it now overlap with itself perfectly again like you started out with? In that one. If you compress it by a half, would that move the asymptotes? If they were here, and now we compress them to here. See, it's half you were shaking your hand. I think it does. Like I think instead of being at 90 and Pi by 2, Pi by 2, I think it'd be Pi by 4, Pi by 4. So I'm leaning towards C, but let's go process of elimination because we're good test writers. D, if you stretched tangent vertically by a factor of 2, would that move the asymptotes at all? That'd be that. Now what I'll ask you is simply, hey, what's the equation of the asymptotes? I don't like these ones. We have to do all four answers to try and find the right answer. I hate questions like that. I've tried to get those kicked off of the provincial 10 exam as much as I could. I failed, but I tried. Any others on this page? I learned some sprinkler systems are just being tested. It's just a test. Thank you. The sprinkler systems? No, that's it. If the water comes on, we're suing they're sorry behind. So yeah, there you go. We should all get soap and things, right? You know, little shampoo, right? Honestly, that water in there would be so disgusting by now. By the way, do you know how the sprinkler systems work, though? It's a very neat system. My understanding, and this might not be with this model, but the water in there is stopped off by a piece of wax, and as soon as the temperature gets hot enough to melt the wax, the water will flow. Clever. Pardon me? In theory. Meanwhile, any others on this page? Like what? Oh, number 10? 20, you mean? No. Radiance, this is technically fair game. That's a little overkill, though. What it's saying is, so instead of 10 degrees, let's say I gave you a nice angle in radiance. What would happen if we did a vertical stretch? That wouldn't change the X intercepts. And the slide. Oh, the X intercepts have moved 10 degrees left. Pi, whatever radians left, that I'd expect you to handle. Okay. Oh, instead of 3pi by 4, we moved pi by 4 radians left. Now we're 2pi by 4. Okay. So yeah, I don't think I threw one like that at you, though. Like that fair game, and that would be a fair game as a curveball. Okay. Number 18, hopefully you could answer the, you know, period. Range. Phase shift. Which ones are true? I'm guessing one of these two is false, but maybe not. Oh, I look at the answers. Only one of them is true. Should check that. Okay. Written. This would be, find the arc length in terms of pi. So I would give you this angle in radians, and it'll be multiple choice. On your written section, I've already told you. Two graphs, and then four or five trig equations to solve, which we haven't done much of yet. We'll talk about that in a second. No. 22, no. 23. This is applications of trig functions. We're going to do that next unit. So no. 24. I'm not going to ask you to find the equation from points. I would ask you to find the equation if I give you the full graph. Ferris wheel, not yet. Number one, that you guys have this on page. Okay. So I broke the course, the units up a little bit differently than they did on this particular test. So number one would be fair game. Finding, being able to solve that minus eight from both sides, divide by four, and you'll have a negative two. Hey, have I got a triangle with a two and a one in it? Yes, it's the one, two, root three triangle. Whereas C can't negative, knock yourselves out. I bet you this one as well, you don't have to do part of the question and cross them out. But this I would also put on your written so you had to do the full thing the hard way, the long way. Do you want me to do it? Yeah, cast rule, right. Exact values. Uh, no no no no no, no no, no, no, no, no. No, no, no, no, no, no, no, no, no, no. also something like this I'll do about three more you can write these down or you can watch I'll print this up when you're done if you want copies I think I'll ask you to do something like solve the risk when I make these up and it might be exactly the same one as on your test because because what well okay whatever it happens it happens there's only so many Pi by 3 ratios and Pi by 6 is angles I can come up with right let's go secant squared theta equals negative 4 over 3 for 0 less than or equal to theta less than or equal to 2 Pi Sabrina would it be okay if I had given you the question originally like this in other words could you get minus 4 from both sides if I'm gonna get secant squared by itself I don't think I will on this test I will on your next test though we'll start saying I don't have to get the trig function by itself for you all the time this is a quadratic trig how do I know it's got a squared it's gonna be four answers this time Alex how to get rid of squared what I have to remember when I square root plus or minus so this is gonna be secant theta equals problem here mr. do it get rid of the negative can't take the square root of a negative see what happens much I make these up myself plus or minus the square root of 4 over 3 and Alex what is the square root of 4 2 and the square root of 3 is root 3 I use my cast rule if I didn't have the plus or minus here Spencer I'd have to do a bit more thinking but here there's gonna be it could be positive there's gonna be four answers what are the answers oh I need a triangle with a 2 and a root 3 in it do I have one this is the 1 2 root 3 triangle which of these angles has a secant of 2 over root 3 okay secant goes with cosine adjacent over hypotenuse so hypotenuse over adjacent of 2 over root 3 the bottom one or the top one which is how big Amanda which means that's pi by 6 that's pi by 6 that's pi by 6 and that's pi by 6 can you rattle them off to me Amanda isn't that common denominator trick nice what if for giggles I said this instead of between 0 and 2 pi how about between negative 4 pi and negative 2 pi sorry to do a domain shift if I'd given this to you right away Tyler I would have ignored it temporarily I would have solved it as is and now I'm gonna subtract or add I think in this case subtract because these are too big multiples of 2 pi although I'm gonna use instead of 2 pi what's my denominator here Tyler so I'm gonna subtract and I'm even gonna get more clever than that Emily underneath here really really small I'm gonna write that this here is actually negative 24 pi by 6 and this here is actually negative 12 pi by 6 because that'll tell me when to stop why not make my life as easy as possible so 1 pi by 6 take away 12 pi by 6 what do we get is that between negative 24 negative 12 well then do it again negative 11 pi by 6 take away 12 pi by 6 by the way Katie sometimes you may find some of your angles are already in the correct domain okay good happy joy 5 pi by 6 take away 12 pi by 6 is negative 7 pi by 6 is that between negative 24 you know what I think from all of these I'm gonna have to subtract twice aren't I so 5 take away 12 is negative 7 take away 12 negative 19 pi by 6 okay Carly what's the next one then 7 take away 12 take away 12 that's right it's negative 17 pi by 6 gotta keep going till I get to the domain what and what I'm saying is yeah keep going till you get to the domain I can give you whatever domain I throw at you now I'm not gonna throw something in the negative millions or positive millions in fact even this is a bit far but yeah and I could go you know bigger in the positive direction right so Carly now you figure that out can you get the last one 11 take away 12 you're at negative 1 pi by 6 not small enough yet take away 12 more there you go the last thing I'll throw at you on your written by the way your written will have a quadratic where am I sorry hang on here your it will have a quadratic it will have a reciprocal and it will have a domain change I did all of those in one question just to save time I'll probably separate those as three separate little skills though for me there will be probably a reciprocal but I doubt it'll be a quadratic reciprocal there will probably be a domain change but I doubt it'll be a quadratic or a reciprocal and there will be a normal standard boring one with a domain change problem I can't remember I've looked at it for you and then the last thing is the alarm bells the undefined or the ones is or the zeros is for example solve 0 less than or equal to theta less than not or equal to mister do it 2 pi cosine theta equals 0 or cotangent theta equals 0 cos theta equals 0 see the first issue is is 0 positive or negative the castrel doesn't work at all I'll put a copy and send it out instead this is where we fell on our unit circle we said temporarily let R be one we called this the unit circle and if we visualize a radius slowly draw there slowly sweeping around like that cosine is what over what in terms of x and y and r x over r and since r is one it's just plain old x what this is really saying is cosine is 0 when x is 0 is x 0 here nope it's one what about up here what about here this would be of cosine theta equal negative one what about right here sure not close mr. do it theta equals you could also have arrived there by sketching you could have gone like this well here's my cosine graph where is it 0 right there and right there hey that's pi that's 2 pi that's pi by 2 and 3 pi by 2 what about a reciprocal okay where will cotangent be 0 when tangent is what it's undefined now the other way to think about it is this cotangent is x over y what would make this fraction work out to 0 when x is 0 strands enough it's going to be the same two answers this one isn't it x is 0 right there and right there so we would say theta 1 that has to be a 0 theta 1 is pi by 2 theta 2 is 3 pi by 2 and that's also where tangent is undefined the last thing I did want to talk about if you want me to is graphing trig functions but if you're okay on that then I'm also good on pausing you guys want me to do some graphing trig functions or not sorry yeah okay I'll have to import graph paper here which you guys won't have in front of you unfortunately so we'll just do it together when I hit print unfortunately the graph paper doesn't print but I'll label my points when I make these up they sometimes go so let's find out there y equals negative 3 cos 3 bracket x minus 4 close bracket plus 1 I really don't like this question because there's a 3 there and a 3 there and that would mean some kids might get the wrong answer for the wrong reason anyways I'll leave it we always started out making the list what's the amplitude here Carly I agree what's the period don't say 3 because it's not 2 pi over 3 what's the phase shift is there an alarm bell oh excellent 5 by 4 to the right what's the vertical displacement and then here's what I also added I said take the period and divide it by 4 which is going to end up being 2 pi over 12 sticking an extra 4 down there or in lowest terms pi by 6 and then I said pick a good x scale a common denominator for this this and this Amanda when I graph this I'm gonna let each square be pi by 12 and what I'm really thinking is every dot is two squares apart that okay oh and one a whole wave is gonna be times by 4 times by 4 8 squares long yes and my phase shift is going to be 3 squares right so let's see what this looks like try to bring it in some graph paper here hopefully that'll be enough and it's kind of funny I really hardly even look at the equation anymore I'm all interested in this the only thing I'm telling the time I'm gonna go back to the equations when I ask where my graphing sine cos negative sine or negative cos I start out what's my x scale so I'm not gonna label each one that's gonna be really crowded how about one two three four five one two three four five six pi by 12 one two three four five 12 pi by 12 good enough one two three four five negative six pi by 12 and I'll add more if I need to what's my vertical displacement and that is going to end up being the middle of my graph my amplitude is going to be going up and down from there in fact I could have lanced at this and told you the range was go up one and then three up three down from there and they get up to the positive four because that's my amplitude one two three one two three one two three oh that's up here you mean that's a four you're right learn to count mr. do it do it right I had the right place though okay Carly phase shift what how many squares my first point's gonna be somewhere on this line here where my graphing positive sine negative sine positive cos or negative cos starts where which one okay got sign starts in the middle positive goes up negative goes down cos starts up high negative cos out starts down low so you know what my first point is there where's my next one how many two squares right one of those middle one of those top one of those middle one of those bottom right counting in Spanish just cuz hey let's go to left where will I be here yep how about one to here how about here yep so instead of starting I try to think of oh sure I can do this I don't want to gum this up copy three pasted down here same equation negative three sign I'll do it in highlighter yellow here here here here here here here here here this is why we said any cosine graph is actually a sine graph if you phase shift it right and every sine graph is actually a cosine graph if you phase shift it right you there's always an infinite number of answers what they give you a graph and say tell me the answer that's why I'll probably make it a multiple choice for that section because you'll have only one right answer to pick from having said that I'm gonna nuke that because that highlighter won't pick properly and they're gonna freak out don't need another one or is that alright well I ask you to graph tangent you know how to find pure good and domain well I ask you to graph cosecant or secant no you don't have to find period asymptotes domain any other folks okay let me press stop here if you want to hand in the books that would be great


This e-lecture has introductory character and provides an overview of the Internet, its underlying concepts and its main services including the history of the Internet. In particular, we will talk about the central concepts behind the Internet. We will look at Internet services and identities and we'll talk about the basic functions of the Internet. The Internet is the world's largest computer network. Individual computers are linked up to a host mainframe and hosts are linked to each other through high capacity lines leased from the telephone companies. The Internet has a relatively long history so let us look at it first. The development of the Internet goes back to the 1960s when the Advanced Research Projects Agency or ARPA decided to interconnect their mainframe computers primarily for military purposes during the Cold War. In 1980, the military and the scientific parts of the ARPANET were separated leaving the ARPANET to the global scientific community. In 1989, the European Laboratory for Particle Physics or short CERN located in Geneva, Switzerland, connected to the Internet. This research center provided much of the impetus for the adoption of connectivity and distributed computing standards such as TCP-IP. We will talk about this standard later on. In the same year, Tim Berners-Lee, a graduate in physics who had joined CERN in 1984, wrote the first server and client software for what became to be known the World Wide Web or in short 3Ws or W3. The system was first made available in December 1990 and refined over the period until 1993. At this time, a standard language for hypertext creation on the Internet, the hypertext markup language HTML was established. The Internet resides on three types of machines and the software installed on them. There are servers, machines to be contacted by others. There are clients, machines that connect to servers and there are routers, the so-called pathfinder machines. Let's look at servers first. The central machines on the Internet or more precisely the software installed on them are referred to as servers. The server hardware is not radically different from that of a standard workstation. The software, however, is especially designed to access information of specific types. Depending on the software installed, servers may be subdivided into telnet servers, into FTP servers or into World Wide Web servers. Machines that connect to servers, more precisely the software installed on them, are referred to as clients. Depending on the services used, any standard personal computer with Internet access can be used as a client. The primary purpose of the client's software is to request information from appropriate servers. And then there are routers. A router is a machine dedicated to finding functional, un-congested paths for data packets through the Internet. One reason for the growth of the Internet has to do with this addressing system and its hierarchical organization into networks and subnets. Each computer has a so-called IP address or IP number. The IP number is a 32-digit binary number. Can you read that number? Possibly not. For this reason, this 32-bit value is normally represented by means of dotted octets, so eight digits grouped into one figure. One of these octets or bytes can be translated into the decimal code. In our case, the decimal code would be 131 for the first octet, 18 for the second octet, 23 for the third, and 3 for the fourth. Well, and this decimal representation is normally represented in a dotted format again, and so there is eventually the IP number. Well, and this is how it is interpreted. The largest network is indicated by the first number. The first subnet is indicated by the second number and so on. And the last number, the final number on the right-hand side, indicates the computer number in the last subnet. So if a router has to send a packet to this IP number, all the router has to know is how to send the packet to the network with the number 131. The router at network 131 will know how to get the packet to subnet 18 and so on, and eventually the packet will reach computer number 3 within subnet number 23. The interaction between two machines in the internet involves two central notions. The first notion has to do with a standard according to which data is transmitted, the so-called protocol. And then there is an exact specification of the identity necessary, the identity of each machine within the network. The protocol defines a common set of rules and signals that computers on the network use to communicate. The protocol not only tells the machines how to transfer data, but also ensures that the pieces of data that are sent are well-formed. Two protocols guarantee the successful transmission of data via the internet. The first of these is the so-called internet protocol, or in short IP. The IP specifies the format of packets, also called datagrams, and the addressing scheme. It is a set of instructions which specifies what form the data transferred must have, how connections between machines have to be opened, how data has to be transferred, and how the connection has to be closed again. Furthermore, the IP, the internet protocol, regulates that all data must be sent in packets, where each packet is a chunk of data surrounded by an envelope. The envelope specifies the unique address of the receiving machine. And the second protocol, well, that's the transmission control protocol. The TCP, in short, enables two hosts to establish a connection and exchange streams of data. The transmission control protocol guarantees delivery of data and also guarantees that packets will be delivered in the same order in which they were sent. Different packets belonging to the same body of data may arrive at their destination via totally different routes and at different times. For many kinds of interactions, this is not acceptable. To guarantee the right order of the packets, TCP puts sequence numbers in the packets, and these numbers allow the receiving machine to arrange the packets into their original order. Well, and then there are domain names. Now, for the benefit of human beings, each machine on the internet has not only a unique IP number, whose representation we discussed earlier on, but also a unique name. This name consists of dotted domains, linguistics.online.uni-marburg.de. And they have to be read from right to left, where the rightmost domain is always more general than its neighbor to the left. So the rightmost one here is DE, which stands for Germany. And within Germany, you find an institution called the University of Marburg. Within the University of Marburg, you find a virtual part labeled by the domain part online. And finally, within this virtual part of Marburg University within Germany, there is a linguistics department. Often domain names can be much simpler, like the one over here. Google.ru. Well, and they are self-explanatory. This is of course the Russian version of Google. Well, and how does this all work? When humans send messages to an internet domain, the address has to be translated into an IP number. This mapping is done by a specific software called a resolver. It sends a request to a set of machines called domain name servers. And these servers return a valid IP number to the resolver, allowing the source machine to create envelopes for the internet protocol. That's it. Well, and here are the basic functions of the internet. There are numerous functions, and most of you know these functions. And the most prominent and all-encompassing one is of course the World Wide Web. We will look at it in a second. More specific functions are, of course, email services, electronic mail, that is the transmission of messages over communication networks. You've all written emails, haven't you? So I don't have to explain this, do I? Then there is the file transfer protocol service, the transfer of files between remote machines. Because of some limitations of email, it is often practical to use a specific service to transfer files between remote machines. For example, the collaborative work on a file with one or several colleagues requires reliable file transmission. FTP, the abbreviation for file transfer protocol, is such a service. The telecommunication network, or in short, Telnet, allows clients to access remote machines. Using the Telnet service, one can use any machine that allows remote logins as a workstation. This service is particularly useful for reading one's email on a remote machine. And finally, there is, of course, the World Wide Web. This is a system of internet servers that use hypertext as a way of accessing internet facilities. There are several applications that make it easy to access the World Wide Web. There are web browsers, and there are search engines. Even though the term World Wide Web is often used synonymously with the term internet, not all internet servers are part of the World Wide Web and offer these services. So let's look at browsers first. The term browser is the short form for web browser, a software application used to locate and display web pages. The most popular browsers are displayed here with their logos. You know them all, don't you? Well, write them down. I'll give you the solution right now. Here are the labels. Opera, Safari, Google Chrome, Internet Explorer and Firefox. A search engine is a program that searches documents for specific keywords and returns a list of the documents where the keywords were found. Let's look at an example which you all know. Here is, of course, the most well-known search engine, and we typed in the word Linguistics Marburg, and here are the solutions. And we are quite proud that the Virtual Linguistics Compass is on top of the list and our YouTube channel comes next. Although the term search engine is really a general class of programs, the term is often used specifically to describe systems that enable users to search for documents on the web. Typically, a search engine works by sending out a so-called SPIDER. This is a program that automatically fetches web pages. SPIDERS are used to feed pages to search engines. It is called a SPIDER because it crawls over the web. Another term for these programs is Web Crawler. And then there is a program called INDEXER, which reads these documents and creates an index based on the words contained in each document. Each search engine uses a specific algorithm to create its indices so that, ideally, only meaningful results are returned for each query. Well, so much for the basic functions, identities and concepts behind the Internet. This e-lecture has to be considered not only as an overview but also as a snapshot. Only a bit more than two decades after its birth, the Internet has become not only the central global network but something like the knowledge store of mankind. It is growing fast and has been redefining many traditional approaches and services such as telephone, music, film, television and scientific research and, last but not least, education. This e-lecture would not have been possible without the Internet and its services where YouTube, where we will upload this video, is just one of them.


What's going on everyone Sam here late in sports cards ripping one box of 21-22 Panini select basketball for Tyler S. It's good luck here Tyler. See what we got in here for you man. Let's go Tyler Let's do it. There's a Jeff T For the Pacers nice one there. He's got I think cards with two different teams in this product Game used on that too. Got James book night to 75 for the Rookie for the Hornets nice one there Jason Tatum a red camera in Thomas. It's a 199. There's Jericho Sims on the tricolor Jared Butler, there's Herbert Jones nice one there tricolor for the Pelican fall George Scotty Bowman Silver Anthony Davis Damian Miller premier level PG-13 nice one there for the Clippers game used on that not numbered Silver Zion Sandra Jalen Suggs rookie Mitchell Robinson to the stream crash Mitchell Robinson Anthony Davis yeah reconnecting Reconnection successful all right, so give it a second Everybody filter back in You just check YouTube really quick. Yep, I'll check twitch Sure, it's which it's good. Yep. We're good. Good on twitch So here we go keep it going here No, I'll open this pack Patrick Williams we've got Davion Mitchell to 199 nice one there for the Kings yeah, good Chris to our safe future Jalen Suggs premier level rookie Perfect There's there is Garland light blue to 299 nice one there calves Miles McBride Caleb said fire over there now, too Zebra Joe Weiss can't Ja, Marant. We've got Andre drum and on the zebra premiere level Nice one there Tyler congrats, buddy drum god Yukon legend Pistons legend Cavaliers legend Sixers legend Andre drumming nice one there He would have been like probably one if he if he played in the 90s and the 80s he probably would have been like 29 all-star. He's just like he's just in the wrong. I feel bad for him. He's in the wrong air. Yeah It's like a dinosaur Yeah, I know gazelles exactly Nicola Yolkich and Franz Wagner courtside rookie nice Last one here. Good luck Tyler silver trey And Tyler hero That'll do it for your break there Tyler congrats on all the hits buddy. We'll get them right out to you


Hi everyone, Joe for jaskiescasebrakes.com coming at you with 2023 Panini gold standard football six box half case picker team number six. A lot of nice stuff in here. Yeah, that's right Chad. These have been marinating for a little bit so let's see, let's see what we got out of here. But big thanks everybody for filling up break number six. Here are the people who bought their team straight up. Big thank you for that. Kevin you ended up with last spot mojo with the chargers and you can see we did a big random number block group here and we did that in a different video but here are the results. So featuring all those teams and now it's a serial number style break. Keep that to my side right over here. Looks like my handwriting. Mark those six so we know they're from the same case and good luck. Let's see if we could use this blank card to hide some of the hits. Let's see if we can scare up some nice hits out of here. All right, it's Cameron LaTue 18 out of 75. So that's for that. So San Francisco is a random number block team. So if you're not familiar with it we go by that digit right there. Not that one but that one directly to the left of the slash right there. So that goes to eight and that'll be for Tom. And we've got Saus Gardner 30 out of 30 for the Jets. So that goes to New York Jets zero that'll be for Tom. White gold David Montgomery big piece of his jersey there 265 out of 299. That will be for Pat picked up the line straight up nice.  Once again for Pat. We got white gold Jalen Waddle 95 out of 299. That will be for Miami Miami's a number block team. So Miami five will be will be for Joel last spot mojo should be ink now Andre Reed nice 50 out of 99 old school bill also for the number block group. So that's going to be for Tom and the number zero right down there then we have a Jalen Carter two color triple relic and autograph 27 out of 149 for the Eagles at a nice game last night against the Dolphins that will be for Zachary picked up the Eagles straight up right nice star next box Jalen Carter has been banged up a little bit I think recently I don't think he played last night right but still could be a strong candidate for defensive rookie of the year. We got Ventrell Miller 93 out of 99 Tristan with the Jaguars. Patrick Mahomes six out of 75 chiefs that's going to go to Michael chiefs are back on track as well J.K. Dobbins Ravens look good yesterday double oh four out of 299 for Baltimore that's going to go to Baltimore number four and that'll be for Carlos with that extra spot that he won Nick Chubb for the Browns 189 out of 299 no to Sean Watson no problem I guess beat the Colts Thomas with the Browns Cleveland this is for you and then we got more Cleveland Browns Ozzie Newsom 30 out of 99 there you go Thomas thanks for getting the Browns straight up couple more here we got Marvin Mims 127 out of 199 it's going to go to Denver Chateau with the Broncos the last one here Sean Clifford 007 out of 149 Green Bay Packers Mike G with that one the truck that was leaving another box see who's next there's Mike Williams for Mike Williams 12 out of 99 Chargers that'll be for Kevin out for the year that's Sydney Brown for the Eagles that's for Zach 7 out of 14 I slow number on that one and now some hits we've got Chase Claypool 253 out of 299 bears embarrassing my Raiders over the weekend not like that that's going to be for Chicago 3 it's her Carlos for number 3 we got Tank Bigsby newly minted relic 165 out of 399 and that will be for the Jaguars Jaguars that'll be for Tristan in the Jags subsushi yeah we got some chrome today Tyree Kill 175 out of 199 at Chrome University I don't know if you have any Bowman Chrome if that's what you're looking for baseball Dolphins that's going to be for Dolphins number 5 that's going to be for Joel and there's Luke Schoonmaker 10 out of 24 nice relic nice autograph Dallas Eric Klicks with the boys we're trying to get some more of that Bowman Chrome Baseball I know it's a fan favorite and Jameer Gibbs 2 out of 24 Golden debut autograph for the Lions Pat picked up the line straight up nice yeah eating solace that's that's the big chase there hopefully we can get some more Bowman Chrome in the store for you to chase Philly's down to their last six outs ladies and gentlemen Craig Campbell managed to not give up any runs they need to get runners on base but train Turner flies out to center this looks like looks like it's going to a game seven ladies and gentlemen all right George Pickens four out of five on that George Pickens that's a train whistle out of fives and under get the train whistle and nobody got the Steelers straight up so Pittsburgh four on the number block for Carlos that extra spot coming in handy Carlos all aboard the Big Hit Express nice we got Bijan Robinson 20 out of 99 that's for Atlanta that'll be for Williams didn't put under the weather sometimes it's not really well 199 out of 299 Aidan Hutchinson that's for the Lions a rough day at the office try to bounce back next week against my Raiders so probably another double-digit loss for my Raiders I'm sure Justin Fields five out of 24 that's gonna be for Dub Bears that'll be Bears five and that'll be for Joel last mod mojo in that number block five right there kind of hard to see there it is a redemption here's Josh Downs 65 out of 199 that'll be for Colts five that's gonna be for Joel and then we've got a Stetson Bennett 130 out of 149 for the Rams Rams are gonna be a number block team so I'll go to Rams zero and that'll be for Tom the redemption gonna be rookie autograph it's always nice to see and T Y Tyree Tyree Wilson for my Raiders slow start to his career but he is coming off a foot injury and I think he was expected to be pressed into service after the Chandler Jones incident was expected to get a lot of snaps but this is what it is but it'll go to my Raiders Alexander with the Tyree Wilson a couple more boxes and go good luck everyone Wilson definitely has some upside though I like foam with a two out single this camp Smith 46 out of 99 dolphins that'll go to Dolphin six will be for Omar Jared got 32 out of 75 that is for Pat and the Lions Alec Pierce mother low five piece rally 20 72 out of 299 that is Colts number two will be for Omar yeah another tank big to be 299 out of 399 for the Jags Tristan and then Bryson Stott flies out and that's that those are down to their last three outs got white gold Cooper cup 24 out of 299 that's gonna go to the Rams Rams are a number block team so they'll go to Rams for Carlos with a number four then we got Colby Wooden 107 out of 199 Mike with Green Bay have Josh Downs three out of five Josh Downs train whistle that's Carlos with a number three Carlos another one all aboard the big hit express all right final box good luck 15 out of 99 Zach with the Eagles Tyler Murray 45 out of 75 before Ryan in Arizona sauce Gardner Jets 145 out of 299 Jets five is gonna be for Joel Bigsby newly minted 185 out of 399 for Tristan and the Jaguars awesome neckler gold gear rally 95 out of 299 Chargers that's gonna be for Kevin last bottom mojo all right now let's see what we got here a couple autos we got a Garrison Hurst might as touch gold ink auto two out of 24 for Ryan Heinz and the Cardinals it's pretty cool I think I've seen a might as touch autograph the last one here nice Sam La Porta autograph 55 out of 199 nice rookie auto going up Pat Wolfe picked up the Lions straight up a wolf with a lion you've been having a nice campaign nice rookie campaign and that's that boys and girls appreciate everybody getting in I'm Joe for Jasmine's case breaks calm check out the website for some more football and I'll see you next time for the next one bye bye