So, by the way, what was R s here in my stochastic case? So, how was that? It was like R s is equals to theta sorry, if you are going to whatever action you chose, A s transpose theta star plus epsilon right in the stochastic case that was the model. We are going to observe a noisy reward in every round. The noise, we assume some sub-question noise but what remained fixed throughout is this theta star. Because of this my rewards are all correlated across but here when I come to adversarial setting that need not be the case. What we allowed is so in the adversarial setting, we have actually get rid of this noise, yes there is no noise but this theta star could be adversarily selected by the environment. It is under an environment's control and unknown also. Here theta and it could be in adversarial it could be changing. In the stochastic case, this one also theta star also selected by environment that it held fixed throughout. What we are observing only the noisy versions of the rewards. Now, let us see how to adopt EXP 3 for adversarial case. So, the algorithm goes as following. So, input R, action set, learning rate, beta, exploration distribution and then exploration parameter. So, gamma and pi where we are used here when we try to consider this exploration distributions. Now, you do the following for t equals to 1. No, not necessarily. So, when I wrote here, I just said like this is does not depend on time, right? It is like one fixed which I am using throughout. So, this algorithm takes the action set and the learning rate eta. We will see how to set this learning rate eta and then exploration distribution and the exploration parameter gamma. So, in each round, it is going to have this distribution defined for each the probability distribution, probability defined for each of this action in this fashion which is nothing, but the linear combination of this exploration distribution plus what are the exploration, the distribution we have through these estimates, ok. So, notice this I did not explicitly mention the case what happens initially like because initially I will not have these terms, right? When I start with t equals to 1 round, this set is this summation is empty. So, we will just assume they are all uniform in the first round the way usually do, ok. For t equals to 0 round, this quantity is nothing, but 1 upon cardinality of A that is the uniform distribution. Then subsequently we are going to sample and arm A t occur from this distribution P t.  Once you observe the loss, you are going to compute this y t hat, the loss vector you are going to compute. So, sorry y t hat is what is the estimation for the loss, I mean the vector that the adversary or the environment would have selected. Once you estimate it in this fashion, we have just discussed that this is going to be an unbiased estimate or of that vector y t. Now, you go back and see what happens, what is the loss you would have incurred for each of the possible actions. So, notice that for this particular A t, you have already know that this is the loss you have observed, but you are not going to take that loss for action A t. Whatever that this kind going, this is going to give for the estimated value of y t that is what you are going to take. Like the way we did it in exp3 and then you are going to repeat this process. Yeah, yeah, yeah, action satisfied. In the we are going to use it in the statement of the regret. Okay, for this algorithm is generic, it works for anything. Like I mean even if it is this algorithm as of now only if you can compute this for A even if my capital A is uncountably many, that is fine. This algorithm as of now so, so where is the issue in this algorithm if A happens to be uncountably many terms actions. This I can't define properly, right? Because this sum could be summation over infinitely many terms. So, we will look into that aspect how to handle the case where A is uncountable or it could be a continuous set. But as long as my A is finite, this is fine, right? Everything works here. And now let's see and okay, coming to this exploration distribution that is a given to me by and the same one I am going to use it in every round. Okay, now the question is how to choose this exploration distribution, right? Naturally, if you are going to change exploration distribution for that, maybe the performance of this algorithm may change. Okay, so now, first we are going to say that there exist some good exploration distribution that will help us give a sublinear regret. And then we will see how whether indeed such an exploration distribution exist and if at all how to get it. Okay, so this is the statement, we are going to say there exist exploration. So, just I don't know there is a name, no name is don't see I am just going to call this x p lean. This is just like our notation. We are going to say that regret of exp 3 lean is upper bounded by two times. Then we can specifically set A has to be k y 3 dt and what is gamma. Okay, fine. So what this saying that see the now this is the regret this theorem requires that to state the require it requires that your action space spans your Rd and it says that there exists an exploration distribution pi and if you are going to set eta to be like this and gamma have not specified how we will see then the regret that your algorithm exp 3 lean was going to achieve is going to be of this form. It is going to be what this is going to be sublinear in T and it looks very similar to what we had for exp 3 algorithm. But what's the difference now? What is that? I mean just the regret bound. So, the D coming into picture right like the dimension earlier it was just like a square root of T. So, we have D k log k right, but that k has here that k got replaced by D. So, it is not the number of arms actually mattering us but the number of dimensions that we have to figure out because now we have linearized the rewards. So, now what matters is in what dimension the unknown parameter lies. So, once I know that how many are number of arms I can figure out the reward for everybody right. So, as long as I can find out those D dimensions the D parameters I have knowledge of all the arms. Now, how is this distribution pi right all we just said is there exist a pi such that this holds. So, for that it is bit involved we are going to just again this comes from some other result which guarantees existence of such a pi okay. So, let us briefly discuss that part. I am not going to the proof of this part you can just look into the book. This is again most of the time it is going to be very similar to what we have done it in exp 3. But of course, with little jugglery of the estimation the new kind of estimations we have bought into picture here. So, to understand this existence of how does this pi looks like. So, we have to look into some design of experiments have any of you have gone through in any of the courses you have taken the design of experiments is covered okay. So, design of experience could be like as simple as if you want to estimate some parameter with high confidence and every time you are going to play an action let us say the reward is going to be linear in this unknown parameter. So, for time being assume that the reward is going to be X transpose theta star. If you are going to choose X the reward or the thing you are going to observe is X transpose theta star but plus noise added okay. So, we already notice that when we had this is exactly the setup of linear bandits right we had. Now there what we wanted we wanted to ensure that how to quickly get a good bound on this. So, what would we say for this we say this we have VT here and what would you say we had. So, we said this upper bound by some quantity with high probability right what would we say. So, we actually said that before this we said if I am going to take theta star and theta hat and some I am some arm aim. So, we did this argument right like we did not exactly show this under very generality but under some assumptions we did show such a thing is possible right. The probability that the projection of this error on a particular arm is upper bounded is it yeah this being larger than some number is going to be very small the probability delta. So, now so we want to achieve such a thing suppose we want to achieve such a thing like I keep on observing my rewards by playing a particular action that reward is going to be simply let us say A transpose theta star plus epsilon I am going to get. Now the question how should I choosing a sequence of A's I am going to play such that as quickly as possible this is achieved. So, that means I have been able to estimate my theta hat good very fast right. So, what is this V inverse here? This is the depends on the data we have been gathering. How should I be using my data to make the observations such that my estimation error quickly falls down. Okay so this is then just this is the question about how should be I designing my experiments so that I quickly able to estimate my underlying parameters well right. Well if you just going to randomly select in every round some A's maybe that is not a good idea. What you want to do is you want to always select some actions such that the all the dimensions all the directions in this theta star are well explored. So, if you just happen to randomly play some actions maybe you may end up only exploring certain directions and also if you just do randomly you may happen to explore all the directions, but on one of the directions you have good information. But if you are going to design your experiment maybe in adaptive fashion such that as you go on you feel that some directions are not explored well. I will choose my actions such that in those directions I get better information. So, whatever the point is the way you are going to select actions in each round matters and linear pandemic exactly did this they try to select actions in each round such a way that you get a better your estimates improve from each step to the next step. So, to exactly to cover with this distribution pi we are going to state a result from this design of experiments that tell that indeed such a pi exists I mean some good pi exists and how to compute that. So, let us say I have this pi which is a map from my a to 0 1 and such that my summation of pi a is equals to 1. Now, let me define this q of pi as we already defined it it is pi of a into a at the as suppose and then I am going to define g of pi to be max over a of a norm of b of pi inverse. So, if you now map it to our linear banded stochastic banded problem oh sorry this is q pi. So, let us say this is about I want to cover with a sampling distribution pi such that my confidence bounds become tight. So, if my confidence bounds are tight can I do a cover with a better algorithm yes right because we already know that the confidence bounds are really play important role right if you have a tighter bounds then when I select my action when I am going to order them maybe like optimistically based on just the what are the estimation plus the confidence term I have. So, if my confidence terms are tight maybe the probability that I make error is also smaller. Let us say I am just going to now I want to sample my actions and observe the loss in the linear setting and now I want to estimate quickly what is the confidence I have in in these arms about the reward this quantity g of pi here in a way corresponds to that.  So, what is this let us say if I am going to think this as a confidence term and this is the largest confidence among all. Now, if I want to have a good experiment like if I want to do a good selection of my sampling through this particular pi I want this to be eventually fall start quickly falling down. So, in the design of these experiments in that terminology this usually this pi is called this design and then minimizing g of pi is called geoptimal design problem. So, just think as this is a separate problem. So, you want to know how with it you are looking for a distribution pi such that it minimizes this and what is this q of pi inverse q of pi inverse is just defined like this it is nothing but the expected value of this A transpose. So, this is just the problem like we will see how it connects to what we want to do. Now, the question is what is a good pi that minimizes this right. So, this is like as of note there is no iteration here right round 1, round 2 like I am not going like this it is just think of like one shot I want to do I want to sample my arms such that whatever this quantity here which I am calling the g of that sampling distribution is minimized. As I said this quantity I can interpret it as the confidence term corresponding to that action A and I want this to be smaller. So, this is called minimizing g of t or geoptimal design problem in the statistics or in general in the optimal experimental setup problem. Now, for this we have one result called P for this. So, we are going to the theorem uses the result from this theorem he says that assume A span of A equals to r d. So, this result may be just of independent interest to you may be you may want to use it in some other analysis also the following are equivalent ok. So, what this result says? It says these three statements are equivalent ok. It says that if pi star is the minimizer of that g here. So, we said that we are interested in minimizing this g function right. It is same as saying that at that pi star this g pi star is exactly equals to d. If this is the case it says that this pi star can be also is the is the maximizer of this quantity here. So, this algorithm actually tries to construct such a pi because as I said this pi here is the one which is going to minimize which is this term here which is an equivalent of a confidence term for me. And in every round as I go on from one round to another I want this confidence term to be smaller. So, it is going to start choosing in every round it want this to be smaller and it is going to try to cover within pi such that it kinds of minimizes this term. And this is as we said this is for one round here, but we have multiple rounds. How it does that? It is going to use that using the the set whatever I have a transpose and using the knowledge of a cube pi star. So, how exactly that overall pi is come up? It is based on this idea. As I am just telling you okay this exploration exists. So, it need to be exactly constructed and I will leave to you to look into the proof what is the exact pi that is the algorithm is using. So, what it yeah this pi is fixed yeah. So, but what they make sure is at every this pi is such that it is trying to minimize this quantity every time okay. So, you know right now you see that the way this minimization problem it defined it is only in terms of the whatever the action set I have and how it is going to define based on the norm of this. So, I am not sure like this whatever this is happening this is the pi exactly the one this algorithm is claiming which exists, but I think it is some tweak version of this it is not necessarily whatever. So, okay fine if that is the case how to compute such a pi the pi computation is already given here right it is the maximizer of this quantity which is easier to compute all you need to do is find the determinant of that and take the log and try to see which is that pi it minimizes this sorry that maximizes it. So, we know such a pi there are some good pies which is going to give us this G optimal design problem or in a way they are trying to minimize try to shrink your they are going to give a tighter confidence terms. So, the exact pie is going to be based on whatever the pi stars we are getting here based on that exactly how it is I will just leave it to you to look into the proof okay. So, okay the last part what is it says is where such a pi star exists its support is bounded by this quantity s u p p stands for support. So, will you understand what is support pi star means? So, the number of places where it is going to put nonzero values and that is going to be at most d d plus 1 by 2 when this this term is used only in the analysis it is to upper bound this. So, that means what it is actually not putting marks on all the actions right as we said the number of actions could be much much larger than the dimension okay like my dimension could be 10 but the number of actions could be 1000. But what it is saying is that this pie star is has to be defined on all possible actions right that this pie is defined on all possible actions it is saying that so suppose if you just take d equals to 10 what are these quantities 10 into 11 by 2 10 into so some 55 right even though you could have 10 into 11 yeah even though you could have like 1000 actions it is only going to put some marks on some 55 actions. So, it is not necessary that it has to put it will ask you to go on exploring all the actions okay. So, fine so it is saying that as long as you can come with a good exploration distribution and this is a standard tweak like right like the eta parameter to be set like this and also I think you can again look into that I do not have the exact value here what is the value for gamma I think it is somewhere submerged in the proof so some gamma I think it should be some function of eta like once you have this eta gamma could be set in terms of that. So, once you set it you can get a regret point of this form and we know it is we have a sub-linear regret okay. So, before we conclude on this part I just want to highlight one more aspect of these studies suppose in this setup what if the entire y t vectors reveal to you in every round. So, what I said right now in every round if you are going to take action A t what is revealed to you is y t A t from this we are going to estimate.  So, this is exactly what we started in the first class first couple of classes right. So, this is like when a label is revealed suppose so if you are if you look into the classification problem we have a set of hypothesis if a label is revealed at the end of the instance you already know how what is the loss you would have incurred by applying any of the classifiers. So, that is exactly this. So, in this case what algorithm you would have like to use if it is revealed at the end of each round you would have like to use weighted majority right. In general there are both class of algorithms which will not have time to look into that but they called follow the regularized reader. I am now talking about this case where we have this full information case what they do is in every round try to play an action that is the best so far what I mean by that. So, if y t is revealed in every round right let us say y 1, y 2, y t minus 1 till round t minus 1 this you have been revealed to you. So, what you are going to do in the next round one possibility you want to do is you want to would you like to do this and play an action in round t you want to play the action that is like arg min of this. So, what is this y s has been revealed to you in every round so far y t is not revealed to you in round t yet but you have to make an action for that round. What we are going to do we are going to see that for all the things I have observed so far which action would have given me the best possible loss and then whatever that is you may want to play that this is unregularized. But you can show that even if you just to do this case there are some instances where you may be get stuck to some bad actions but the general one could do this to allot that you may want to make this a bit smooth by bringing in the regularizer terms and one possibility for that is you may want to include a regularizer here and which is now the action. For each action you are going to define a function h now you want to minimize this and play the action and one can so you can make sure that but properly choosing this regularizer you should be able to get a good performance. So, one particular choice of this regularizer which is often used is the entropy function. So, I am right now assuming that this action sets are not probability vectors for me. So, in that case we already know that this is nothing but a i log 1 by hat how many are there. So, did you notice did you realize this formulation like where did you see this? So, now you should take this entropy exactly like this what is that you are going to get what is this a star is going to be like this is a distribution right how this a star is going to look like it is going to look like my exponentiated weights for that. So, this is going to look like my ETI is equals to what my whatever ETI whatever the loss I have observed in that round and whatever the summation of this. So, what is the optimizing value? This is just like so the a t i th component a t minus 1 i th component exponential what are the the loss you have observed for that particular i in the previous round and it is just a normalization this is just what we had observed in the weighted majority algorithm right. So, if we have this entropy we are going to get this weighted majority correspondence and in that we already know if once we have this kind of distribution we already know what should be the good value of eta right like because when we use the weighted majority we started with ok we start with such a distribution we use this distribution and then further optimize my regret by tuning this parameter eta. So, once my distribution result in this I know what is already from my knowledge of weighted majority algorithm how should be I tuning this parameter eta. So, there are class of algorithms based on this idea this regularization entropy is just one function you could think of other functions ok and like people have used something like a divergence I mean not the Kulkel divergence but there is another notion called Brigham divergence and all. So, by using different different regularization you will get different different performance ok. So, you may also want to look into that one chapter on such a regularized. So, this is called follow the regularized reader FTRL algorithm.  So, people have been using different playing with different different regularizers and coming up with different different bounds. So, you may also just want to look at. So, I am not going to give because for to define other other regularizers we need to kind of diverge into some other topics. So, we will not go into that. So, as you see that we started like looking into specific cases, but thing can be studied in more generality like what we stated as a weighted majority algorithm is nothing, but this regularized. So, why is called follow the reader because we are trying to play the reader right till that point till that point whoever is the leader you just want to play it, but it is just like taking a regularized version of that.


Now, as howling winds echo across the snow-covered beaches of the wild northwest, the Quaker Oaks Company makers of Quaker Pop Wheat, and Quaker Pop Rice, the delicious cereal shot from guns in cooperation with the Mutual Broadcasting System, present by special recording, Sergeant Preston of the Yukon. It's Yukon Gain, swept as his strongest lead dog of the northwest, breaking the trail for Sergeant Preston of the northwest mounted police, in his relentless pursuit of lawbreakers, and then on your king. Gold, gold, discovered in the Yukon, a stampede to the crondite in the wild race for riches, back to the days of the Gold Rush, and the adventures of Sergeant Preston and his wondered dog, Yukon King, as they meet the challenge of the Yukon. Our adventure will begin in just a moment. Nursing today offers an ever-widening sphere of activity. 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As the sergeant drove his canoe through the still waters of Kiribu Lake, a sudden flash of light from Bird's Landing caught his attention. Let's tell me Bird's signaling to us with a mirror, King. We'll see how well he learned his lesson while he's selling us. We've been challenged. Another series of flashes came from the Indian village on the far side of the lake. And there's good luck, King. What's he saying? Oh, another challenge. Then the fold. Well, I'd better put the suddenly blinded rest. The sergeant took his gold whistle from the pocket and spelled out an answer. WMP, that's what I'd identify as. If I could hear the whistle, it's still a good... Oh, yes, we heard it all right here. Oh, yes, we heard it all right here. Oh, he says, welcome, King. Oh, that's cool, I'd say. Welcome, too. And the fold's very good. During the next 15 minutes, as the sergeant continued paddling toward the landing, the traitor's son and the Indian boy continued to flash messages at him. When the dock was finally reached, Tommy was waiting eagerly. All right. Both you and Co-Lock were perfect. We've been practicing every day, ever since you taught us the code last spring, and how to use the mirror. Every day there was any suddenness. Didn't I make a single mistake? Only one. What? Well, one of your messages was, uh, beware of bears. Oh, I know there wasn't much sense to that one, but it's a good idea anyway. I agree, Tommy. Still, the where is spelled a... B-E-W-A-R-E, not E-A-R. Is that all it was on, Sergeant? Just filling? That's all. Oh, good. Co-Lock and I have been hoping you'd pay us a visit, too. So, will you kill me? I'll pass you... Can you send another message? E-N-R-U-G-O-I-N. You better tell Co-Lock that you was spelled Y-O-U. Oh, he knows that. He's just saving time. Going to visit us. Let me have your mirror, I'll answer him. And if you look up, Sergeant, that sounds keen.  Go on, use it. All right. Oh. That's fine. As you go over to Indian Village, will you come back and think for a few days? After that, I left Blackie at Portage City. I'll have to get back there and start for Boston. Well, anyway, you know, that's wonderful. It was during a mid-summer patrol that Sergeant Preston made that stop at the trading post in the Indian Village. And it was mid-winter before he hit Carable Lake again. This time, it was going hard and the team was glad to reach the well-packed main street of Portage City. Both the Sergeant and the dogs were looking forward to food and sleep. A large crowd in front of the Power's Cafe warned the sergeants of a troubling time. OK. Hey, what do you mean to me? Give the dog your hand. All right, old Mac. Sergeant Preston. You sure are weird. It's your name. What's the matter? That's Sally Smooy. He's taken in here about 15 minutes to go into that. Oh. Oh. Shot in the chest and beat up. I said, conduct Monday and cleared everybody out of the place. We have more to cut in the back room now. Here we are. Just a second. Yeah. Who shot him? I don't know. He passed out before he could tell us anything. Come on. I brought Sergeant Preston, dog. All right. Hello, Sergeant. Hello, dog. I'll have to go for the bullet. There's an outside chance it might come through while I'm doing it. I don't want him to move. Extended his feet, Mac. Right. His arms. All right, dog. Now, then. Badly, he's creeping around the head. Yes. There's no fracture. Possible compression. That was quick. What are his chances? That's hard to say. This wound won't get him. He lost a lot of blood. Yes, and he's shocked to consider. Lift him up gently, Sergeant, while I bandage him. So? That's fine. He didn't say anything, Mac, but he didn't have a chance. The door opened and he stumbled in and fell down on the floor out like a lightning. All right, Sergeant. Poor Simon. Looks like his lucky strike won't do him much good. And after all the years he's been prospecting. What lucky strike, Mac? The South Creek. Close to here, around the curve of the lake. Oh, I know it. You lived on this claim? Yeah, yeah. He built himself a cabin last fall. It wasn't in town this evening. No. He must have come all the way from this cabin after he was shot. I've never got out there. Did you want me to show you the way? After a while, Mac. There was only chance of us telling us what happened. Not until tomorrow at the earliest. We'd better see what we can find at the cabin. Oh, I'll take that slug, Doc. Yeah, here. 38. Oh, come on, Mac, Mac. Some were getting worse. The sergeant drove across the corner of the lake to the opening of South Creek. It was a simple matter of finding Silas Moore's cabin. A ramp was burning inside it. The front door was wide open. Okay. Well, like this side was a thing much about lamps and doors when he left here. Now, what are you doing? You haven't seen the team? Only came. I'm trying to think about the techniques of the head.  The two men and the dogs entered the cabin. The lamp was on a shelf. One of the chairs was broken. Another chair, the table, and the cot were overturned. In a far corner, two of the floorboards had been torn up. It looks like Silas put up a good fight. Barbaric. Yeah. So you're in the habit of keeping much gold here? And I can't say as to that. He sure didn't put much stock in banks. So he kept his gold hidden under the floor. And where's your bin? Someone came here and forced him to turn over the gold wire. Right, beating him up. And put a bullet through the old man before they left. See? Here you are, there he is. Jack's all covered up. It's outside. There's no telling in this thing. I want to know. Yeah? That wasn't a very hot nail, was it? No. What looks? You just print on the floor here. Yeah, a hot nail. There's another print from the ashes inside the stone. There's somebody wearing mutlix made that. And it was inside. The fence too large. Yes, you're right. Two men. At least. I think we got a sense from these prints. He might be able to pick it up outside. Let's see. Hey, boy. What? King understood the command. Snip the footprint in the ashes and then start it for the door. What's up, Jack? King, I want to look around here a little more. Quite a few supplies on the shelf. Quite a few supplies on the shelf. They don't seem to have been touched. Ah. It's hard to tell the team in a sled, Mike. I don't know. They didn't. Any suspicious characters around town lately? Suspicious? Well, I wouldn't say. Any strangers? Yeah. A couple of prospectors passed over there before yesterday. Asking questions. Well, if there had been any strikes around here. And they were told about Sabbath? Yeah. But we told them all of South Cricketman Prospect. And so I had the only pay dirt. They headed out of town for the east. They could have circled the town and come back here. There's no shoes. We're traveling life. Well, let's let a team in here. That helps. King, I think you'll be able to track them, boy. You miss storm? We'll see. All right, King. Follow the trails. We'll continue our adventure in just a moment. You should have been at the ball game today. I saw three home runs. And guess what? I got one of the home run balls. Fellows and girls, why don't you get a free baseball ticket? It's easy. Come out to the ball game as guest of a major or minor league team. Your free ticket is waiting for you right now. Inside packages of Quaker Pop Wheat, Quaker Pop Rice, Muppet Shredded Wheat, and Quaker Packleton, which has two free baseball tickets. Yes, if you are 12 years or younger, just bring mom or dad or another paying adult and see wonderful major or minor league baseball games free. Names of teams and dates are on every ticket. Get as many free tickets as you want. No mailing, no waiting. When mom buys breakfast cereal, just be sure she gets the kind with a free baseball ticket inside. That's Quaker Pop Wheat and Rice and Muppet Shredded Wheat. You get two free baseball tickets inside Quaker Packleton. So don't miss out another day. See the star players wallop those home runs. The following morning as Ben Bird finished putting breakfast on the table in the kitchen of the trading post, it was still snowing. It could hardly be called daylight. Young Tommy was out in the forest checking on his trap lines and then walked through the store to the front door to call him. As soon as he opened the door, however, he saw two men plowing through the snow toward the post. There was something about their faces that made Ben's trust him immediately. But they were travelers. The weather was bitter and the customary hospitality of the Yukon was not to be denied. Hello there. Hello. Welcome to Bird Landing. That's what you call this place? Yes, I'm Ben Bird.  That's what we expect you to do. Leave your snowshoes here. Bring them in with you. You got any food or anything hot? Yes. Well, Russell, what's the idea of a gun? That's to make you pay attention to what I say. Russell, some grubs. Sit down. There's bacon and beans on the table. I'll pour some tea for you. All right. Hurry up with the tea. Ben, did you come all the way from Portage City last night? What's it to you? Must have been hard traveling through the storm. He says it must have been hard traveling through the storm. Yes. Maybe he's feeling sorry for you. Sure. Sure, that's it. Through the forest, straight north, across the border into Alaska. That's so? He told you, didn't he? But it will be so bad from now on. We'll be traveling with dogs sledding the team. There isn't much of a trail through the forest. It's hard to follow. Well, he's still worried about his roof. But he don't wonder where we're going to get the team in the sled. He's got that all figured out. Sure. I have only six dogs. Oh, don't apologize. I can't let you have my... Maybe I'll just shoot them right now and save a lot of talk. Yeah. No, no. Take the dogs. And supplies burns. Plenty of supplies. Whatever you need. It's better. Hey, those are your dogs, parking? No, too far away. Oh, there's dogs now, right out in the back. Could be a trap or coming to trade. We'll go see. Go on. The man walked in front of the two men. The one with a gun prodded him toward the window. Never mind opening the door. You can see enough through the window. Well, he was driving the sled. You know him? He's a trap. Now listen, we'll go out in the kitchen. But we'll leave the door open. Just enough to keep you covered. Get rid of this guy fast and don't try to warn him about us. If you do, I won't. Leave it to me. He'll be careful. Come on, gang. Right? The sergeant stopped the team. King would have been working as a loose lead. He ran to the door of the trading post. The great dog knew the men they had been following were inside. The sergeant opened his partner and made sure his gun was ready for action. Then he followed King up the steps. Hello, Ben. Oh, Ben. That unusual greeting was enough to put the sergeant on his guard. Ben was standing in front of the door that led to the kitchen. King tried to circle him and get to the door, but Ben called his wife. Oh, boy. All right. Bring many pelts in today, Bill. No. Oh, you just came in for supplies, then. That's the idea. Well, what does it be? Some tea and bacon. Oh, plenty of that around. Why don't you just help yourself? Sure. The sergeant circled the counter. He sized up the situation. There were two sets of snowshoes leaning against the wall by the door. A puddle of melted snow beneath them. The door to the kitchen was open a little. Though he could see nothing, King had practically told them the men they wanted were out there. No doubt they had Ben covered. There was nothing to do but take Ben's lead, pretend to be a trapper, leave, and then return to the post after leaving his team in the forest. He buttoned his pocket, covering his uniform completely, picked up a flower sack from behind the counter, and filled it. Two slabs of bacon, five pounds of tea, and a couple of cans of tomatoes. That's enough for now. I'll be back soon. You're always welcome, sir. Ben. Sergeant, well, sure, Ben. Come on, King. Oh! Sergeant walked to the front door and opened it. At that moment, however, the kitchen door also opened. Ben was knocked aside and the shop rang out. Oh! Oh! Oh! The bullet caught the sergeant's leg, and as he fell, his head hit the door jam. He sprawled on the threshold, unconscious. Oh! Get away from me! King pleaded with the black-bearded man who had fired the shot and knocked him to the ground. He lunged through his gum hand, but the other man was in the room now. He picked up a poker from beside the stove and brought it down on King's head. It was a glancing blow, but it knocked him out. What have you done? I should have put one over on it, didn't I? All right, Guy. Almost got away with it. All right. Open a big guy's pocket. Yeah. Yeah. You were right. Beautiful. I was sure. It's Preston.  Your local. I hit him in the leg. He knocked himself out when he fell. He won't be following anybody for a long time. Suddenly, Ben turned and made a break for the kitchen. The man took after him and caught up as he reached the door. Adam! The gun fell, crashed down on Ben's head. Oh! Thanks, Chairman. Now we better get out of here fast. Here's the money, Chief. No, the trader's dogs are fresh. I'll get them hunted. I'll get the flies loaded. All right. Are you sure about the route? Across the lake to the Indian Village. The train into the forest starts there. Gonna have plenty of bacon and flour. I'll have it out in the flood by the time you have the team ready. We'll continue our adventure in just a moment. Say, why aren't you, fellas and girls, out of the ballpark these days, watching those homeruns walloped into the grandstands, eating peanuts, popcorn, and hot dogs? Come out to the ballgame as guests of a major or minor league team. All over the country, kids 12 years or younger are seeing major or minor league games free.  And you get your free baseball ticket immediately inside packages of Quaker Pop Wheat, Quaker Pop Rice, and Muffet Shredded Wheat. You'll find two free baseball tickets inside Quaker Packer 10. Names of teams and dates are on every ticket. So be guests of your favorite team at the ballpark. Crush to the storm of your mom and grab free baseball ticket packages of Quaker Pop Wheat or Rice, Muffet Shredded Wheat, or Quaker Packer 10, which has two free tickets. The more packages of these delicious Quaker cereals you get, the more free baseball tickets you get. He had completed the round of his trap lines when he heard the shots. He hurried back to the trading post and reached it just as the two outlaws were disappearing in the swirling snow that swept across the lake. Inside the store, the boy found the sergeant struggling to ride. Dad, what happened? Two crooks, killers, they shot me into a father. I saw him. Which way were they going? Across the lake. Towards the village? Yes. Then north through the forest, over the border. You'd only get a message through the Indians. There's no thunder, I can signal coolers. The wind's blowing in that direction? Yes. You're likely to hear my whistle. Tell him a message, tell him what's happened. Cool like telling his father, those men must be stuck. Here, here's the whistle. But, Dad, excuse me. I don't think so, I know what I can for you son. You get down to the shore of the lake and start sending that message. What's this? The whistle, he's calling for help. One of us. I thought he would jump for us. He won't be following us anyway. Marshal! Get the Indians out of the whistle. Get over there to find out what's the matter. Well, one of us. We might run into him any minute now. Not a chance. I'm stirring clear of the village. Look, we're coming to the shore. See the trees? But the trail... I'll find it. Our only landmark was the village. Stay over there. This is the end of the lake. If we had due east through the trees, we'd finally hit the trail. Oh! Oh! What are you stopping? Help me get the sled up the bank. No more riding for you. You put on your slow shoes and break a trail for the dog. All right. Ah, come on, here. There it is. Marshal! Hurry up! All right. Even with one of the men breaking the trail, the dogs sounded difficult to pull the sled through the system of snow in the forest. The man who was driving lashed them unmercably. Lashed you! What? The dogs pulled ironically, trying to escape the trail by to the whip. And at last, the trail was reached. We did it! Ah! Ah! Do I still have to break the trail? No, there's only about six inches of fresh snow. It's packed hard in the east. Try more board. Yeah. Looks like a good trail. We should stop soon, though. Marshal! What is that? A shot. Pull. Pull you, my pull. Keep him up ahead of us. Who's who, gonna be? Maybe an Indian. Ready with your guns. I can't see anything. I came from behind. Keep down. Watch for a gun flash and fire when you see it. I can't see anything. They're all around us. Fire at the sounds. The two outlaws never had a target. Yet it seems that the trees and the falling snow which hid their attackers so successfully could give them no protection. They left the trail to cover in the forest. It didn't help. Every few seconds, a bullet would kick up the snow dangerously close. Jake began to fire while... Cut that out. How can they see where we can? They can't see. You're telling them just where we are.  They got us around it. We haven't got a chance. Let's try to get back to the sled. Let's make a break for it. Oh, keep down. Now we've got to get out of here. Come on. Ow. I don't know. I'm lit.  Don't stand up. Stay down. Stay down. It's our only chance. We'll die.  No. Get down. Die anyway. I don't shoot anymore. You got him. I got my hands up. Don't shoot. Back at the trading post in spite of his wound, the sergeant had cared for both Ben and King. It took a great deal out of him. But when Tommy had finished sending his message and returned to the store, he bandaged the sergeant's wound. Then he rallied a little and was able to drink some hot tea the boy made for him. It's good, Tommy. Thanks. I'm dying. I'm dying. They're hurt badly, but they won't die. Look, King's trying to raise his head now. I'm dying. Don't let him get up, Tommy. That's easy, boy. It's good. I'm dying.  Nothing to be sorry about, King.  You followed the trail. You showed me where they were. I had to think of Ben, though. That's right, Sergeant. Tommy, it was all my fault. Thanks, Evans.  We're fine, Ben. What's the name of King? Dogs. I heard them, too. Could they be coming back? Go see Tommy. All right. What's the dog sign for mom? What do you see? A dog king. A dog king. What? Then they are coming back. They must have received your message, Tommy. What message? I used the Sergeant's whistle. I sent a code message to Kulak. The Indians were waiting for those cooks when they got across the lake. They're now the catchers. They're catchers, they look. Good. Good work, Tommy. All what I did wasn't easy. But if you hadn't caught me and Kulak the code, if your whistle hadn't been loud enough to carry all the way across it. Look at the dog. See the beauty?  I agree, Ben. And Hanson lives as Hanson does. Well, I'd like the whistle if this case is closed. We'll return in just a moment with a word about our next exciting adventure. Weekends are wonderful when you stay tuned to Mutual. Gay entertainment to suit every member of your family puts bright sparkle into your days of fun and relaxation. For anyone who likes quiz games, and that includes just about everyone, there's the kind you like where you can sit back and see how close the contestants come to the answer. There's music too, of course, on Mutual's weekend schedule. Lowbrow or highbrow, you can take your choice. From full-scale productions of your favorite operas and operettas with all-star singing and dramatic casts to swing-your-partner sessions of real old-fashioned barn dance jamboree, you can take your choice on Mutual. Your need for late news headlines from the field of sports as well as on the national and international scene is not neglected on the weekend either. 15-minute round-ups plus brief five-minute digest come your way regularly. Gather your family around this weekend and enjoy entertainment on Mutual where there's something for everyone, all heard every weekend over most of these stations. In mounted police headquarters where Sergeant Preston is seated in the office, the door bursts open and a man named Ben Scobietta. Sergeant, you've got to come quick. Dave Wyatt has just murdered old Milo Perth. Dave Wyatt, are you sure? Positive. I saw the whole thing through the window of the old man's cabin. Dave is still there searching for something, and Milo is lying on the floor with Dave's knife in him. Come on, King. Hard to believe Dave's a killer, but if so, it's our job to capture him. Did Dave Wyatt really murder old Milo Perth? If not, it'll be up to the sergeant to clear Dave and find the true solution of the mystery. But in doing so, he may find himself facing the guns of the real killers. Don't miss this next exciting adventure. These sergeant Preston of the Yukon Adventures are brought to you every Monday through Friday at this time by the Quaker Works Company, makers of Quaker Pop Week and Quaker Pop Right, the delicious cereal shot from guns. By special recording in cooperation with the Mutual Broadcasting System. They are a copyrighted feature of Sergeant Preston of the Yukon Incorporated, created by George W. Trenble, produced by Trenble Campbell Mule Incorporated and directed by Fred Flowerday. The part of Sergeant Preston is played by Paul Sutton. This is Jay Michael wishing you good-bye, good luck, and good health from Quaker Pop Week and Quaker Pop Right. So long. This is Mutual Radio Network All America.


In the beginning, she's doing an adapter that is awfully close to what I usually refer to as transfer, transfer from a true crime workshop where a person makes himself emotionally unavailable to you by some kind of movement, by too much overwhelming emotion, but she isn't unaffected. She's available, so take that out of your mind that just because she's swaying means she's doing something. It means she's comforting self because that release of nervous energy is comforting. There is, however, some really interesting body language when they talk about friends. That boy's gonna have more friends than he knows what to do with when he comes home. And her lead into that, the stress on that word, friends, makes me wonder, was there some kind of an altercation about his access to people that she feels guilty for? She feels something about because that comes up pretty strong in both their body language and in her stressing of the word.


Hey, this is Brett and this 2020 Ford F-150 Crew Cab Short Box XLT Sport is stock number 1-2-785 ZC. I am here at Summit Automotive in Fond du Lac, Wisconsin, you're new and used light duty truck headquarters. This 2020 Ford F-150 has the 3.5 liter EcoBoost V6 twin-turbo engine, puts out 375 horsepower. This truck has been fully-safetyed and inspected by our service shop. Has a fresh oil and filter change, all the fluid tab been checked and topped off, and this truck is 100% ready to go. I'm going to go all the way around in this video, inside, underneath, start it up, and take a look under the hood. Magnum Red Metallic is the color, shoot all my videos in 4K, so if you have HD capabilities on your computer, tablet, smartphone, or television, I highly recommend turning them on right now because it is your best way to check out the quality, condition, options, and cleanliness of the vehicle before seeing it in person. Very clean down this side, I didn't see any dents or dings on the box, doors all look really good. And if you like the video, how I do things here at Summit Auto, you can subscribe to my YouTube channel, which is youtube.com slash Summit Auto, click the bell notification so you get updates on the videos I do each and every day. And if this isn't your truck, you might just find your next one there. It comes with the 20-inch painted alloy rims, and it has Goodyear Wrangler All-Terrain Adventure tires. These are 275, 55-hour 20s, and they have probably about, I'd say, 60 to 70% of the tread left on them. Front fender is in excellent condition, I didn't see any major dents or dings on there. Headlight lenses are nice and clear, and it does have the factory fog lights. Front bumper is in really nice condition. With the painted grille, and the hood is in very nice shape as well. I didn't see any major dents on there. Passengers side front fender looks really good too. And the passengers side rim, no major scuffs or scrapes on there. Now as you go down this side of this 2020 Ford F-150, take a note of how clean that body is, how reflective and mirror-like that paint is. I take these HD videos so if you are far away or even if you're close by and you just cannot make the trip down, but you're still interested in purchasing the vehicle, you can see the truck, hear the truck, and have confidence in the vehicle that you're looking at before you even get here. So when you do get here, there's absolutely no surprises. And you can make a smart and informed buying decision from wherever you're at. And if this video helps you make that buying decision, let your salesman know that you saw the video, that it was helpful, and that Brett sent you. Back rims in excellent shape too, and the back tires have just as much tried as the front tires. And once again, if you like the video, you can subscribe to my YouTube channel in the upper right-hand part of the screen. Frame and underbody is in fantastic condition, has all the remaining factory exhaust, looks really good all the way underneath, and lower rockers and cab corners look good too. Factory painted step bars, sport package gives you the 20-inch rims, has a chrome tipped exhaust, rear bumpers in really nice shape, full towing package, which includes a receiver hitch 4-pin and 7-pin wiring. And the tailgate is in very nice condition as well. Comes with a tiger soft tonneau cover, tailgate step assist, and a very nice line-ex spray and bed liner. That's what I have on my truck, get the LED bed lighting, and that bed's in really nice shape. That bed liner goes on to the tailgate, and there's your tailgate step assist. Looks nice and solidly, and as you go down the driver's side, just as clean as that passenger side, no major dents or dings in the box once again, and for full disclosure, this back rim is in fantastic shape as well. You do get the capitalist fuel fill, which is really nice. And this one has the driver's side door code entry. We do have the code for this truck, and if you ever wanted to find out what your door code is for your 17, or maybe it's 15, to 22, up to 150, in the upper right-hand part of the screen. I've got a video showing you how to do that. Heated mirrors, built-in directional signals, inside the XLT package, gives you the gray leather interior. There are no rips or tears on the seats, and these are CATSKIN aftermarket leather seats. Power driver seat, no rips or tears. Once again, weather tech floor mats, power pedals, auto headlamps, tilt, telescopic steering wheel, power windows, power locks, power mirrors. Take a quick look at the back seats. Back seats are just as clean as front seats, no rips or tears back here. It does have the latch-child safety system for any child car seats you may have. Power sliding rear window with the built-in rear defrost. Seats are in nice shape. They fold up like so. You get husky all-weather floor mats back here that go all the way across the back, and it's a flat floor back here, which is nice if you have pets. 110-volt, 400-watt max plug-in, two USBs, and then a 12-volt power point. Child safety locks on the back doors, bottoms of the doors all look really good. I just want to show you that Magnum Red real quick. It's got kind of like a root beer almost color to it. We'll hop inside, check out the miles, the radio, and everything that this truck has to offer on the interior. Get the built-forward, tough animation there. You can see that this one has 22,428 miles, and yes, we will be putting some fuel in this truck right after this video. You do get a digital speedometer, compass display. Instrument cluster is very nice and clean. Comes with the leather-wrapped steering wheel, cruise controls and information center controls on the left, audio and Bluetooth controls on the right. This one does have the sync 8-inch radio with the factory navigation systems. Stability control, that's your start-stop capabilities. You can turn those off and on. You do have turned-out four-wheel drive, trailer brake controller, factory brake controller, heated seats. You have your different controls on the radio. So your nav, you get AM, FM, and Sirius XM radio capabilities and Bluetooth. You also have all your different mobile apps. You have FordPass Connect, Apple CarPlay, Android Auto, and this is also where your backup camera shows up, which the truck's got to be running for that to work. Anyways, down here you have two USB plug-ins, and I believe this is the 10-speed automatic transmission. Yep, this is the 10-speed. Passengers side, you get 12-volt power point, another 110-volt 400-watt max plug-in, and the passengers side, floor mat, and seat are in excellent condition as well. I don't think this truck's ever been smoked in, smells very clean, and the headliner is in nice shape, no major rips or tears up there. You do get map lights right there and your power sliding rear window button. We'll start it up and take a look under the hood. Starts right up, no check engine lights or anything like that. Here's your backup camera, and that is working nicely. I would personally like to thank you for checking out the video today, and hopefully from this HD video you will have been able to verify the quality and condition of this truck all the way around, inside, and out under the hood. We have the 3.5-liter V6 EcoBoost twin-turbo engine. Engine bay is very clean, runs very smooth. Once again, this truck has been fully-safetyed and inspected by our service shop. Has a fresh oil and filter change, all the fluids have been checked and topped off, and this truck is 100% ready to go. There is your emissions sticker. And I would highly recommend this truck from a quality and condition standpoint. And to see more pictures of this truck or one of our other 550 new and used cars, trucks, SUVs, minivans, wranglers, halftones, three-quarter-tons, one-tons, you name it, we got to go to that website right there, summitauto.com, full pictures and descriptions of every single vehicle from two locations, all at summitauto.com, and if you'd like to check out more HD videos, you can go to youtube.com slash summitauto. Remember to like, subscribe, and share on this video and all the videos that you see there. Click the bell notifications to get updates on the videos I do each and every day here at Summit Automotive. In fact, in a second, you will see a link to subscribe to my YouTube channel on the upper left. A link to more F-150 videos I've done in the upper right, a link to this vehicle on our website on the lower left, and a link to one of our latest YouTube videos in the lower right. Click those, check us out. We're super excited to help you with this ultra-clean 2024 F-150 XLT Sport in magma red metallic. Thanks again for checking out the video. Remember to like, subscribe, and share on the YouTube channel. I really appreciate it. Thanks again.


good morning everyone welcome back to my channel um my name is kenzie if you guys are new here be sure to subscribe i'm a lifestyle vlogger i attend zoe leadership college which is accredited through south east dirt it's half internship half college i'll get my bachelor's in business this summer so that is pretty much all you need to know um a daylight saving times occurred i can't say i can't speak this morning i'm not even gonna fix what i just said because i just can't talk um and so now it's really bright like it's 6 30 in the morning and it's so bright outside which is so odd i'm used to like driving in pitch black i kind of liked driving in the dark better it made me feel better about myself you know anyways i'm on my way to pilates surprise surprise taking from a daylight my favorite teacher as you guys know oh my gosh also look what i'm wearing it's funny too because after i'm wearing my hoodie like that's my outfit uh my new merch is out i'm sure i've said it in every single video link down below um so many of you guys have ordered a launch yesterday and like first off thank you guys so much to everyone who ordered you guys are so sweet like it's just so cool it's also cool because like people that i know that i'm like not even super tight with like bought it because they're like it's so cool i love it and like that's just like so cool because that's how you know like if people that you're like friends with buy or stuff i feel like that's how you know that it's cool does that make sense so anyways my back is killing me um there's something wrong but i'm on my way to class oh my gosh i'm just filming another week in my life video the podcast i listened to this morning was a skinny confidential i finished this tofya emiruso one and then i started the one they had the real jordan belford on like the real guy who leonard capio played and with wall street and i'm only 17 minutes in but it's already so good all right guys i don't feel the best um great pilates class guys i have 814 stars right now on my starbucks app i'm i'm like right outside starbucks morning on the app i'm gonna get this interest i'm gonna get this citrus defender we get a perfect bar just because but like i'm gonna eventually need coffee maybe i'll just go on lunch to get coffee i feel like that's what i'm gonna do um can for no change store i just the other day i was like i ordered from here all the time i don't get rewards and then someone's like uh you have that many stars and i was like oh yeah i'm not really gonna do much makeup like i'm gonna brush my eyebrows and put on a little bit mascara i'm filming a um what i spend it a week but like this vlog is separate so i'm tracking all that and because i'm filming this video it's actually making me way more cautious i know i'm supposed to just like buy what i buy um but you know that's kind of scary so i've been really liking those videos and a lot of you guys requested it i tweeted originally that i don't want to do it because i don't want to hate myself after um but uh here we are you know oh i'm wearing my lovey so much hoodie and i was wearing the jacket earlier if you guys want to check out the merch i'll have it linked down below also thank you so much it launched yesterday to like so many of you guys bought it and i was just like crazy like obviously you like hope that a lot of people are gonna purchase it but like so many people even people that i'm like like also like a lot of my friends i like gift it to or whatever but um like you really know it's good merch when people you're not like this tightest with but you're like friends with you're not like bestest friends with buy it because they're like no this is cool like i'm not even like super tight with these people and they're like oh my gosh no i love this i'm buying it and they like actually like bought it and that's how you know it's a really good merch because like they're under no obligation to buy it at all you know like they're not like my family so uh or like my closest bestest friend so that's how you know it's good i might put a little bit of cloud paint on this girl hates me back here i'm gonna put a little bit of cloud paint on the glossier cloud paint i'm in the starbucks parking lot also guys i forgot my brush and my gym bag i and a bra but i had another one of my car thank god i don't know why i literally never forgot anything especially in the gym bag but like look how about my hair looks today it's just not it also i'm really really enjoying um my podcast this morning it's really interesting i want to like really branch out as far as guests go the issue is i feel like i hurt myself because i'm not super niche but i feel like i'm also just like too young to really know what i want you know so that's my excuse who really freaking knows you know am i right ladies or am i right also i just have this like breakout in the middle of my nose right here and it's just like painful so that's awesome i got the citrus defender this is going to save my life we're at a new office space today we're at a new office space today so not hollywood i mean don't have to pay ten dollars for parking actually i shouldn't speak too soon because sometimes you know sometimes meters like five dollars or two hours so then it ends up being the same thing so we'll see hello everyone with my two favorite people nope not siri um we're walking into trader jose i'm so hungry during our lunch break for class quinton is my favorite student quinton is my favorite zlc student no i'm not a student i know that's the joke q doesn't get it this is my go-to wrap at trader jose here is my trader jose hall my veggie wrap and then i need to get the potatoes so i picked them up quinton's really upset that the camera missed something he just said i'll hold it up for reference oh thank you if kenzie was a potato she is sweet potato thank you q that's so sweet of you cuz you're so sweet yeah that's oh my gosh my phone's stuck how okay my phone quinton i think my phone's stuck i can't get it i guess i don't need it anymore she's been on her phone a lot lately you know oh don't even get me started actually you don't have a problem anymore quinton back in the day was really a big phone guy excuse me um people in the trader jose parking lot i'm very aggressive the last vlog the last week of my live vlog we were leaving i just edited yesterday we were leaving complaining about how everyone was so aggressive a trader jose and here we are guys it's so peaceful on the inside it is but on the outside it's really a lot okay we're heading back to class um i have to leave because everyone here hates us where this is if something's under touches the camera the screen shuts off okay there we go after class we're at Whole Foods now got the green and glowing movie beautiful friends perfect all right guys so as you saw i just went to Whole Foods with Dom um i'm actually going to some event with boohoo on thursday i got so i just found out about today and i have to go to a gifting suite because they obviously because they want us to wear their clothes so basically there's like events that you go to and sometimes they want you to wear like the clothes like their clothes so so i have to go on melrose to pick up an outfit morgan's meeting me there so we're gonna go together um i'm getting quintin too i think we might go to texas roadhouse or something tonight we're feeling wild people this hoodie is so comfy and i got so many compliments on it today even out and about in public randomly from people who have no idea that it's my hoodies all right guys i'm with my other two parent people i said this earlier because you're with just we're going to the boohoo um gifting gifting suite i don't know i can't speak you know i've always their office because i've wandered in by accident before thinking thinking it was a story and it's not called boohoo because they're sad i know what you were thinking no they're all thinking that cute things are things are clearing out the confusion um yeah i know i never it's here's the thing i love this camera because it's so much better but like it's just so big so here i am we're approaching we're approaching bye all right so we are in the okay actually the offices are really cute you guys can like barely see it but we're in the um suite i think i'm gonna go with this because i got these new black boots that you guys will see this week that would be very cute with this dress you can't really see um so it's probably what i'm gonna do have you found anything yet i have one but it's like it's a real like fallback you know so i haven't pulled it off the shelf yet oh gosh okay okay we just doordashed chick play i don't even think i've logged about the pop eyes experience i don't even want to talk about it quentin had us wait in line for 30 minutes just to not get anything so anyways because they wouldn't give us a plane he's he is just a really picky eater and they weren't able to give him a plane like uh yeah i get it it's fine so we doordashed chick play which is great so if you guys want to use my door dash code it'll be linked down below cogo you look so pretty cogo guys look at the tree merry christmas we haven't decorated yet but it's so wow merry christmas everyone santa's backwards good morning everyone my neck and back hurt so bad today i think it's because i slept on the couch but anyways good morning everyone it's wednesday it is 10 30 drinking out of my santa mug i actually have um three maybe four packages to unbox for you guys i don't need to leave for class for another hour but i need to finish getting ready obviously um today we are doing like just group devos so we have a group and we're going to blue bottle which is very exciting it's cool it's very hard people actually this semester sessions really hard and then we have lunch and then we have our creative track that i'm on but i'm gonna go during lunch and go work in the office a little bit more because i need to work on some stuff for a website anyways i'm drinking coffee i'm posting a video right now i'm wanting my hair to air dry so i don't have to like blow dry it or anything but like we'll see supposedly my new stuff from forever 21 came in and i ordered some of my cool boots guys you guys are really gonna like this unboxing i think um so i'm gonna go look for that because it might be up back i'm also making sweet potatoes right now because i need them for my lunch a lot's going on this morning guys okay and everyone i'm doing an unboxing haul which is great because i am probably gonna wear one of these things today because i actually don't want to wear this shirt the first package is from forever 21 my roommate got the coolest like cow print faux for jacket so i copied her and got the same one as always i'll have everything things down below first thing i got this white turtleneck this looks like it's going to be very see-through which will be an issue next thing i got this gray turtleneck which they're actually a pretty great quality next thing i got so as you guys probably know i think like me danielle broke morgan keaton are going to new york in december during the vlog may us get excited and i had a dream last night that like i wasn't packed or prepared it was like this whole thing and i literally freaked out and so here we are i'm going trips often like i don't know why that was a big deal so then i got the same turtleneck i might wear this today with the jacket you guys will see um and like a beige color here's the jacket well this isn't the jacket that i copied i got two jackets which is so cute so i think i'm gonna wear this jacket today and this this is the real winner the real real winner everyone but should i just wear this one to class i might i'm wearing this to new york oh my gosh guys do you see this it is so freaking cute and funny like that is so funny oh my gosh so i'm obsessed with that i would actually wear it today but it's just not warm enough unfortunately i'm really really excited for this package i saw this on a vlogger's instagram and like they're literally from amazon oh my gosh they're amazing guys look at these these are 40 dollars and they're over the knee and they're not even too crazy i'm wearing them tomorrow night but they were 40 dollars like that is actually next level the heels not too much you can wear them all the time like oh my gosh they're so freaking cute got them for 40 dollars they're gonna be on my amazon shop page because i know like so many of you guys are gonna want them because they're so cute and like i just don't know how they're 40 dollars that's so insane to me all right i got a vital protein box i love these boxes my roommate is obsessed with them too she really likes the waters a big box so you guys can see this is the collagen i literally just did a deal with them yesterday and this is just a good gift from them because you guys know how much i love them vital proteins collagen creamer which i'm excited to try this i already drank coffee this morning but i'm very pumped for this here is my collagen i have gone through an entire one of these guys and that is how much it just changes your skin like i've said this before and i'll say it again nothing has helped my skin more than a vital proteins collagen and that's how my skin's been weird lately i got matcha collagen as well which i really love i also bought some myself recently and then i have the vital proteins waters because bailey loves them so i made sure to put them in the order so excited and then i just got this package from clean and clear i love this line i wonder if i like this because i love mist but i really love this line because look at how great the packaging is like it's really incredible i'm actually pretty sure that quinton took my last one of these and he really likes them too he's actually like super into skincare um i mean i wouldn't so i'm pretty positive but i love that thank you clean and okay i've changed i'm ready for the day i haven't put my lipstick on yet um if my eyes look really odd today i don't really know why um i just curl my hair in literally 10 minutes my curler that i use is always my amazon shop page i changed into my favorite 21 tunnel neck in the new jacket that i got i know that these are princess bailey too because i was shopping there last night and i saw one and it was out of stock and i totally forgot that i already ordered this one so thank god it was out of stock you know um my leave eyes that need they're definitely a little bit big i need to go buy some more leave eyes i really want to try the agode denim too i just have so many jeans i want to try out um i need to shoot and my revolve stuff that's been sitting there my stuff is just like a little bit more cluttered than i would like and not as clean but i'm not even gonna be home until so late tonight because i have to consider coming and then um i'll be back tomorrow look i'll be here all day not really i'll have i have class and then i have like a midday break where i'll be here and then have an event tomorrow so i think i'm gonna be able to do a lot of cleaning in that time which i'm very pumped for um but this is my outfit i have my jennifer fisher hoops in my little amazon socks which a lot of you guys have been asking where they are in the amazon shop and guys i can't find them like they're off amazon now so i'm gonna look again today and see if i can add them and if i do i'll put them on an instagram story but it's so freaking annoying so i just finished the sweet potatoes and finished my lunch i made some overcooked toast because i'm definitely gonna get a drink of blue bottle but i don't want to get breakfast but i'm like really not hungry for breakfast so we'll see hopefully i mean i'm gonna have to eat this but i'm not that hungry and i finished my meal prep my lunch for today so there we go i just posted some instagram stories um of my haul today that i showed you guys so if you guys want to follow me on instagram it's just at kenzie elizabeth feel free all right oh all right guys i am this morning has been unbelievable as far as traffic goes guys okay so i left like almost an hour ago and i'm still 10 minutes away and this is normally like a 20 25 minute drive for me so i don't know what's up but los angeles needs to figure it out um anyways i'm on my way to blue bottle i'm really excited i think i'm gonna get a matcha that's the only thing that's really just making my morning because as we know traffic has really been something so yeah i'm meeting some girls there for breakfast this is like part of our program it's part of school technically but we're getting coffee and reading it's gonna be great i'm really excited for it i literally hate being late i'm never late and i'm never the person it's like oh my gosh guys sorry traffic is so bad literally ever i think this is probably my first time like in los angeles that it's been like that um i hate being late it's not me but uh you know it happens sometimes so anyways i'm on my way it is really spend something to hold it oh it makes me feel like a blocker it makes me feel like jigsaw when you hold it you're holding it for yourself it's not even on you i like to flip the thing too much work too much work take it of me just wanted to clip oh hey everyone what are you hey everyone i forgot what i was gonna say um let's go with your script i don't she forgot just wanted to do it on camera but she's over it now we're leaving i got we just finished divos it was really incredible got some matcha the bottom matcha was amazing but they just raised their prices which sucks but whatever all right guys it's now 11 30 breakfast or like our diva thing this morning was so good um had a great time i'm about to head off to class which is at our office we're in a different office this week so it's gonna be very exciting all right guys i'm out of class i had a very very awesome day at awesome i don't really i don't feel like i say that much um i had a great day in class i'm on my way to the studio just recording some intros and ads listening to a podcast on my way there um today's just a really good day like i just love life you know thank you so much taylor no i know everyone's gonna hate me for this video that's fine monday morning we launched new merch for the podcast which i love and all of you guys have been loving this is how you know it's cool this is the test so like guys i am just in the best mood today i just finished my recording it was great class was great i think it all started because coffee was so good basically this morning i was just telling these stories because we were just kind of like we just kind of ended up like encouraging each other and i'm like not a good encourager i'm just like really i'm working on it i'm not i feel like i say i'm not a words affirmation person like i'm not good at that but i actually i do it i just am not someone who's like naturally like super encouraging like i'm someone who's like i don't know what to say you know honestly it kind of depends on like who i'm talking to but um anyways this morning we were just i was just talking about all these like crazy things in life that have happened and like just like face stuff basically but just like impossible things happening and just like i don't know it was really cool not it was cool that i was talking about i mean like just stories that were really cool that have like shaped me and i don't know anyways so that was great class was great the recording was great i love going to the studio i love my dear media team like more than anything it's literally my favorite work thing ever i've had a lot of people on my team especially just like the nature of like being in digital like there's a lot of people who like you've just worked with and whatever and they are literally my favorite group of people like they're just the best so it's currently four i'm on my way to get quintin and then we're gonna get a lulu i'm actually you guys are going back on here i'm so sorry for removing um we're gonna get a lulu because i'm doing a video with them and they just gave me a gift card and i had to pick out some stuff i have literally worn lulu lemon since like middle school so it's so cool to be able to like work with them and this is like my fourth or fifth time i've worked with them this year which is so cool anyways i don't know i'm just like feeling very lucky and blessed this day this week and also i don't know i just want to describe it i feel like it's feeling off like i've said i've definitely said that a lot in these vlogs lately and i feel very myself today which is good so i'm going to pick up keo are you vlogging for me yep guys literally in the last clip i was talking about how i loved today i got a very exciting email so i'd love today even more this is really my perfect day wait what how long are we going over to oh yeah we're going to lulu lulu i don't know how to zoom so all right just got some stuff from lulu i actually got quite a bit i had a gift card and normally i feel like i only can get two sets of that now i don't know what i oh you know what so they got you something last time okay so a good day it's a great day got a lot of lemons lulu lemon what okay we're literally in the middle of my i'm gonna die so i'm gonna go thank you okay quentin we're gonna go to the hot pilates parking lot and it's in sunset plaza and there's this like oh my gosh okay so in this plaza oh i don't know what's wrong with me today okay there it's not going to be as cool because it's going to be dark when we get there but there's this really cool um are you gonna eat both of those one bars yeah i'm gonna grab them for us did you really yeah i haven't had tried the banana there's one bar sent me bars okay really quentin bars banana not bread if you guys have been watching since the summer this is really chocolate which one do you want i'm way less picky than you i haven't tried the banana i was waiting in the line 30 minutes last night and you making us get out i was telling us last today it's fine so we went to pop eyes we already told the box it's serious i oh we did last night we did but retelling it they wouldn't even make me a plain chicken sandwich like it's just so i was so hungry and i was just like no we're definitely gonna leave hectic hungry not even hungry hangry yeah but it's fine i get it you're a piqueter i understand we got your place that's fine all i want is our bird ash well my door dash code will be below anyways there's a really good view there and i'm really excited because we have like an hour until we have to be in our classes so we've got some time oh yeah meeting my one bar these are vegan too hot bodies tell me how i'm doing rumble for the first time with morgan before kenzie lets me do hoplates with her that's actually true i mean i would do rumble with you for sure and i would let you do hoplates okay comment down below for vlogmas okay i'm making it for vlogmas if you guys really want to see quentin do hoplates i mean obviously we can't vlog inside but like a lot of you guys have been saying you really just want to see it because really want to comment down below and i'll let it happen at least in the gas cup that's on you true but i've been driving out i don't know why so anyways yeah bye all right so it's fun you just dropped his phone um it's okay it worked out um i have my stuff i'm gonna change i'm going to plotties quinton's going to rumble with morgan how excited are you ready to rumble oh my gosh this is his first rumble class so he's pumped yeah we literally just sat in the car for 40 minutes in quinton freestyle if you guys have seen rhythm in a flow i think i already talked about how we love that show he played the i can't change song he thinks he can rap guys it's his thing actually honestly you're it's really kind of scary because you're not actually bad at it and i'm not just saying that everyone will say that it's quinton's like hidden talent it is and okay whoa it's gonna be oh my gosh if anyone even knows what we're talking about still in this vlog if you know you know if you know you know i'll let us know comment down below all right guys i'm currently changing just wearing a seductive set guys we're all so happy this is our new thing that we're going to do wednesday night by the way thank you mark it off wednesday night because it's a trailer too okay we'll put it in the so basically actually so basically in this little area on sunset there's equinox hotplotty soul cycle and rumble in between us three plus taylor that's where we all work out so we're thinking or like you can go to rumble so we're thinking we're just gonna do that every single Wednesday night and then go to sleep green afternoon so our new tradition you're gonna say anything right now true true okay we have a holiday roll i'm not going to eat mine right now but it's seriously the best solid i said this in every vlog i think i get one i honestly only get like one a week but still it's like a 14 dollar salad so get the bread treat yourself yeah get the bread all right guys i'm home i need to shower and just get ready for tomorrow but my it's a 10 miracle leave and a product thing that i thought i got it with plus keratin this stuff is a game changer my hair has been really dry and gross lately and this is a leaving conditioner it just completely changes your hair it's like the only hair product that i really really swear by i don't really have anything else that i like have noticed makes this huge this huge difference in my hair besides it's a 10 stuff so i'll have it on my amazon shop page this is og i've used this since like middle school but i haven't used it probably in like maybe almost a year at this point i've just been out and i just i don't know but i'm back because my hair looks rough all right guys it is showered i have a whole stack of clothes behind me but i put the leaving conditioner and it already feels so much better than it's felt so anyways really excited to come home from class tomorrow and clean my house but um it's like 9 30 i'm gonna go to bed because i have pilates at seven class we're going we're doing a bunch of cool stuff tomorrow and then tomorrow's actually gonna be a really cool day because i'm gonna clean and then i have events tomorrow night which will be fun so yeah that is what i'm doing i'm gonna go to bed now it is now thursday morning at 6 0 6 a.m i'm gonna head out there's koko it's just staring at me i'm gonna head out um in like 20 minutes i kind of believe it's a little bit too early for pilates and yeah it's gonna be a great day i'm wearing this sports jacket from forever shutting one and then these leggings you guys can get a better view right here these leggings are lululemon aligns like you don't you're not supposed to work out in aligns but you know whatever i'll be fine they're actually really not the best to work out of either but it's fine i don't need like lululemon police in the comments i already know they're just really comfortable and like i really want them on right now so it's fine all right i'm on my way to pilates it's so weird because it's bright out now and it normally doesn't get like right out until i'm walking into pilates or right park or something but i'm listening to a podcast i'm so wide awake i don't know like i mean i went to bed at like 10 but yeah i'm just having another very grateful morning i feel like i'm really annoyed but i was just thinking how lucky i am to be able to wake up in the morning i was thinking how lucky i am to be able to wake up and go to pilates in the morning this is what i mean guys i'm just in a really good mood but like seriously i feel like literally every class i'm just like grateful so yeah that's that so sorry haters if you're annoyed with me by now the light just turned green um then i have class then i have class we're going to baby to baby um i'll talk about that later i haven't been before a lot of um zoe has but i haven't and then um i'm gonna come home clean and then tonight i have events and dinner with morgan which will be fun good morning everyone um i'm out of pilates now oh i'm sorry the lighting is so weird i'm about to go into class i'm just posting some promo for my new podcast episode that went up today i did a solo one all that confidence and kind of like my journey with it in the past year i think it's a good episode so check it out my podcast is always linked down below um but yeah going in we have chapel this morning i think i'm doing announcements so i need to be there a little bit early all right guys it is now 3 p.m i'm done with class for the day this afternoon we went and volunteered at baby to baby you guys don't know what baby to baby is look it up seriously it's so cool um we just made a little like not sacks like what were they called something bags basically for newborns who needed it it basically just helps basically just helping people it's actually such a cool organization i know that honest beauty just got all the works with them and they had like all honest beauty stuff everywhere um and like diapers their kids line i heard her talk about on a podcast but anyways zoe does a lot of stuff with them and yeah it's just like a really cool thing we got to make um bags full of like supplies and like diapers and all that stuff for newborns who are gonna need it so it was really cool i know obviously to have place in la i think that there's other things that you can do if you guys want to get involved like check out baby it's really cool so anyways i'm on my way home i'm so hungry i just had a 40 i just had a 40 minute drive home so i'm listening to gals on the go right now i'm so freaking hungry i need to go home my hair you know when you have like a headache from your bun that's how i am right now i just feel awful i need to shower make lunch and get cleaning and then tonight i have an event so that is a plan all right guys so i'm home now and i just came home to a package from wonder beauty quintin loves these under i do to the under eye baggage claim gold mass so they just sent us a bunch just so funny so i'm probably going to use one of these tonight actually currently have a shower i've been doing laundry cleaning i've already cleaned up a bunch um i'm doing these summer Fridays jet lag mass currently on my face and i feel like my skin has been very dry lately and then i just made some lunch this is just salmon broccoli stew potato nature shell yeast and tahini organic tahini and then i just have water and i'm just going to sit down for a second and maybe watch a video and just chill and then i'm probably going to do like 30 more minutes of cleaning so we'll see all right guys i just got some more cleaning done i have my eye mask on they look so weird i love the chanel ones that are really cute with the chanels on them chanel whatever made some coffee with the collagen creamer so i'm gonna try that and then get some video editing done i think an hour i'm gonna try to at least get tuesday's video done so i'm not like just with that this weekend i'm so tired i need coffee really bad all right guys so i just changed i'm ready for the night i just put on some makeup and then this dress is from boohoo definitely too big so i belted it i don't love this look by any means i have to wear something boohoo so this is all i had um i just wish i had to pick something else out i don't know it's too big and i want to clip it up because it's like showing too much cleavage basically these are the 40 dollar boots from amazon that i said are like amazing i will have them linked on my shop um that's always linked down below but they're literally 40 dollars like that's actually unreal so these are my new boots i'm about to head out i'm just wearing this bell i have it tucked under for just now um this bell is actually princess poly so just need something to send you to the waist and then i'm gonna get the safety pin for right here but i'm gonna head out we're gonna get dinner um then go all right everyone can you try to fix the lining it's not great um we're about to go to dinner what is that we're about to go to dinner with morgan thank you but i appreciate the effort it looks like we're telling scary stories whoa whoa whoa anyways we're going to think for dinner i don't know why i'm really stressed out right now it's turtle next season i don't think i know anyway it's how excited are you about your first pr package i showed them it's basically christmas yeah your favorite i did one before beginning of tomorrow really wonder beauty it's a beautiful thing beautiful thing so we're gonna dinner with morgan and then the event and then home and all i just keep telling myself is it's okay because i have Pilates in the morning so she's a big Pilates girl huge huge so all right goodbye everyone she doesn't live day to day she lives Pilates session to Pilates session thank you we need to finish my phone camera guys i have this phone camera i've had the same role in it and i wanted it so badly and i used to take so many disposable so you would think i would take so many i've had the same role in it since like august so i've got to finish that tonight so then we can drop it off tomorrow and get them developed it's a good plan it's a good plan right and then we're going to the palisades actually no we're not because we're just kidding you thought we were going to the palisades you believe me yeah okay so we're out of zinc i just got my favorite meal in la the chicken my bowl is so good morgan got an assortment of things all right guys we're back from the event um i didn't bring camera and obviously it was like in a club but hope you guys enjoyed this week if my life vlog coco is jumping back there i'm in the middle of doing a lot of laundry um it's only like 1115 we left early because like i don't go to bed late so love you guys so much hope you guys enjoyed today's vlog and i'll talk to you soon bye


Now, we introduce mechanical energy. Conceptually, what we're talking about here is that there are many different forms of energy. But we can group those many different forms of energy into related categories. And one of those categories looks at the several type of energy that all relate to mechanical forces in motion. So any of those types that relate to those mechanical forces in motion, we're going to call those mechanical energy. Now, we can use several symbols to stand for mechanical energy. So for example, you could use an E with the subscript MeCH to let that know that that's the mechanical forms of energy. Some books actually use an Me to describe mechanical energy, while some just use a capital E to describe that mechanical energy. Now, there's some basic types of mechanical energy that we'll want to take a look at here. The first one being kinetic energy. And kinetic energy, again, is the energy of motion. So any object which is moving will have some mechanical energy, because it will have some kinetic energy. The other main type of mechanical energy is potential energy. We could think of this as a stored energy. So any time you've got some sort of a mechanical force and you've got energy stored, so that as soon as you release that object, that mechanical force is going to convert that stored energy into energy of motion or some other forms. We consider that a mechanical energy as well. There's two main types of potential energies that we've looked at so far in our introductory physics course. And that's the potential energy from gravity and the potential energy from springs. If we kind of put this all together and we look at the symbols that we've been using, we can define an equation which tells us that that mechanical energy is really a total of the energy we have in each one of these forms. So we look at the kinetic energy plus the potential energy due to gravity plus the potential energy due to the springs. All of those things combined together gives us our total mechanical energy. Not all energy is mechanical. And so as we look at those basic forms of mechanical energy, it's helpful to think of the fact that not all the energy we're dealing with is in mechanical form. So for example, chemical energy, thermal energy, nuclear energy, and electromagnetic energy are some other categories that we'll study at different points in physics that are definitely not mechanical in nature. Now I want to point out there are some other non-mechanical forces and non-mechanical energies. This is not an exhaustive list. So this just introduces you to the basic concept of mechanical energy.


Hi, my name is Kamala, I recently completed a short term course with NPTEL on the subject language and mind and got a certificate from IIT Madras. I came to know about NPTEL and online courses through a friend of mine. At first, I was not convinced whether courses offered by the IITs would suit me. See, I do not have a background in science streams, my background is in law. Then she convinced me that the courses offered by NPTEL include topics ranging from engineering to basic sciences to humanities and even to music. So, I decided to enrol for a course. Now, why did I register for this course? I have always been fascinated by the different modes of communication that we see all around us, not just between human beings, but also amongst animals, birds, etc. So, when I came to know that in this particular course, language and mind, we get to learn about how human mind acquires language. I was intrigued about my experience with this course. I found the NPTEL online videos very easy to use, very easy to download and I was able to watch these videos late at night, weekends, early mornings and most of the time I was able to submit assignments on time. Now, the video lessons, they were very easy to understand. In fact, I liked seeing many queries that I had in mind already getting answered in the discussion forum. Seeing my scores getting updated regularly in the progress tab was very convenient as I was able to see how my peers were doing as well. I was also getting frequent mails and text messages on any announcements about upcoming exam dates or fees, payment or upcoming assignments, etc. Now, the best part was when I got the laminated certificate by post. It was very nice to see the IIT name on the certificate. In short, this experience was quite unique in that I was able to get a certificate from the IIT without having to go to the college, follow any schedules, attend any classes and all this doing from home. At the same time, I was also able to interact with students and the faculty on the discussion forum. All said, I feel that if circumstances permit, I would enroll for more courses with NPTEL. I think all of us should. Thank you.