Introducing the Geo PB Wireless One-Button Panic for the Geo Alarm.  The dimensions on this device are 1.67 x 1.51 x 0.45 inches, with wrist, belt, or neck attachments included. Functions and temperatures from 32 degrees to 120 degrees Fahrenheit. Once again, ladies and gentlemen, introducing the Geo PB Wireless One-Button Panic for the Geo Alarm.


The Y254 channel on Twitter hashtag of the day is WCW or if you like the generic is Y in the morning. Now, we are going to have a conversation. Not about Chelsea when you're a machine door one nail. Not about Manchester United and how we are number five. Not even about Arsenal and how they are somehow mystically number one. That's not why we're here today. We're talking about first dates and embarrassing moments, but before that, let me allow my panelists to say something. All right. Hi. How are you? I'm fine. I'm fine. Let me start with you. What's your name? I go by the name Grabe. Grabe. Grabe. Grabe. Grabe. Grabe. Grabe. Grabe. Grabe. Grabe. Grabe. Grabe. Grabe. Grabe. Grabe. Grabe. Grabe. Grabe. Grabe. Grabe. How can we find you on social media? Social media, Facebook at Grabiotino, Twitter at Grabiotino, all the social media platforms at Grabiotino. What do you like to do in your free time? I think you have a nice feeling, good time. What do you like to do? My free time. Reading novels. Walaai. Waka. Oh, Nakatu Alejandro. These romantic, romantic ones. Reading novels. Who's your favorite author? My favorite author, he's Stephanie, he's called Stephanie, Stephanie Mayer. Okay, all right. My favorite author is, To Date Is Lee Child, but I'm hoping to expand my base and you, what is your name? My name is Emanuele Freista, I spoke with another artist, performing at the recording and a student at the University of Eldorat, going to my fourth year this September. I'm from Malaysia. Yeah, I'm from Malaysia. That's your fate. I know. That's my fate. Someone tell her, when you finish school, it's not that easy. But it's okay.  I'm a little bit practical in my way of thinking or mannerisms generally. So if it's okay, I was hoping, come on, let's have a chat with Peace Moja, Kabla Twendele. And are you spontaneous? Let's talk about your topic, when and I, or it's just the, all right, let's stick. Let's do it. Let's stick too.  Now I have faith, the fans are real, so I know how I feel. I knew singer Phil, and Simon and Peter. But wait, what I mean is I'd love to see you. That's when all my weight not because of my height, but because of the issues that you've faced me through all my time. I don't know why I'm thinking. I don't know why I'm drowning, I don't know how to suffocate, I'm busy enjoying Firstly, I'm asking you to take myben First, I'd look for the highest to the highest that I reach and I will have to try thank you, thank you all the people I know who helped me First thing first, the path to heaven in arrow. So me who first known keeps limb. Even though me watch out. But reality is, see Asia for food. Give us this day our daily bread. Heart achy kambila blue band, sit a jam. Cause I'm hungry. I'm angry with lasina dough. Dough to the greener pastures, Nelifaku feed on. Walshia slug. I'm hungry. I'm hungry. I'm hungry. I'm hungry. I'm hungry. What happened to knock on the t-shirt be opened?  Sout in a t-shirt or a fengue? Nami hapa ni mekuti? I don't sot and I'm tied. Tied to my present and past. My fake friends and enemies. My heart and flesh. The heart is willing. But the flesh is weak. The same willing heart is a wicked seat. Killa weekend na jipata na receipt. Last weekend nili kua bash. Huku anka be friend with. Ndoni kua close and at the most high. Nika feel holy. Spiritikite rimka down my throat. Ink nili kua na tumiakwa. Ndika my vision in cups. Kika kua kikombe. Kikombe kanzakua replaced na pombe. Ndiki drank. Ndome huku bukahi o vision. Matthew 5.9. I'll be a child of God. I'll see what's here. He left the 99 to look for me. But bad o niko lost. Ndaki wilderness kume jama fees. I'm born on party. I only do daily na jitagot. Yeti e yehuchunga kondo.   The life I need to live up to 100 years and still be considered young. The truth I need to tell always to be set free. The way I need to follow to seek your kingdom first. But nime choka kusik.  Naseek kua define naseek kua refine before I get swallowed by the storms. Nyokoi o else nita zama. Nita dedi na watanile tia flowers. Yeti niki wahai hawa kua ii wa ii hatafla. Was case hata maisha ii kua mboga. So before I die, nita ii mani. Bima ira mani. Nipende kuli kua zamani. Forgive me Lord for I know not what I do.  So give me faith. Give eternal life. And surely goodness and mercy shall follow me all the days of my life. And I shall dwell in the house of the Lord forever and ever. Amen. Amen. Freista.  Okay, okay, okay. I don't know if you are as impressed as I am. So Sahib Grabe, I'm going to say it in a different way Wait, wait, wait Hashtag is Sub-CW or Why in the Morning There's talent Clearly, I'm going to eat this I'm going to eat this Anyway, getting back to the topic is We're asking you I'm embarrassing you for not taking care of your first date So, you have to take care of your child You have to take care of your child and then we get into it So, the people are singing like this We have a team I'm a heart-to-heart I'm a heart-to-heart I'm a heart-to-heart because I'm a heart-to-heart I'm a heart-to-heart My real work, no fighting My real work, no fighting Right, now, I'm going to say Water is something you must remember when you get home late So, I'm going to wash my hands and I want to say Good Morning that we're focusing on Shadrack and Brian that we're focusing on Shadrack and Brian Imagine when they get home and insist that they're going to have a single room That's right There was a lot going on, all right. Tony says, way, way. So, back it up. Okay, we're going to come to that in a little bit. But so, our bodily functions, sometimes, always, sickly. Larry Mason says, had a running nose, way. Oh, wow. Finn Shelby says, all my first dates have been up to stand-ups and complaints. Judge Maitha says, Gary Shaysha Marufuta Uhuru Highway, some are cooking, way. Tony Cruz says, in other news, Chelsea, she had a speech, and some are too comments. Thanks. Kanzaku Onjaya Ango. I come with you. Way. Carla Zabron. Yes, I'm going to put here. The daughter of Jezebel, way. I live with two other far out daughters. I came to Shafiq, and I come over here. I'm almost there. Kufiq, I'm going to guide her, and I'll take her to the church. But, Kistevo, then, after I'm sipped, two gups of coke, I'm going to go to Indonesia, I'm going to surprise, I'm going to surprise, daughter of Jezebel, Kanzaku flat with me.  Did I order anything? Or did I come with them? they switched off the phone so the harassment is that they are not allowed to work the violence everyone discuss who is what in the world is happening here where? at the street first of all I am so sorry I am sorry I apologize I don't know what you are asking do people even go on dates? if you want to go on dates you can say yes you can say please let's move forward when you are in a hotel this is the first time you are in such a situation when you are at the beach you will see as if this young person is a politician you will see you will see they are not allowed to work they are not allowed to work they are not allowed to work they are not allowed to discuss how are you feeling about this story? okay when you are a child and you are in such a situation you are surely you are not allowed to work then the girl and you are not allowed to work I am sorry you are not allowed to work you are not allowed to work your baby is not allowed to work your security is not allowed and that's why how is the village? that is my security my baby is not allowed and I am not allowed to transport that's why I am asking for help yes if someone has a date I am not allowed to take a chat if you are in a transport and I am not allowed to transport if someone is not prepared work with your own money Why under something you can't afford yourself? Nasiya Nasiya Anja Hiya Nasi Baby Boy Child Limitio Whatever you want baby I got you There are situations when you are in a situation where you are in a situation where you are in a situation where you are in a situation where you are in a situation where you are in a situation where you want to know who is the best and exchange your life So you want to know who is the best Because you are so good But I always try to be smart and be smart I always try to be very smart You need to test yourself when you are in a situation where your life is not so good But anyway, this is life guys Come prepared Hashtag is, hey wife winning so go on dates nowadays. Oh, should I scare what you are going to end up out on a date? It's crazy, I'm very few. So, what do you want to do? Like, if you want to know who I am, you can just...  Come, come with me. Come with me. Come with me. Even though I'm a part of your family, as in, what's happening? Give me the experiences you have on the ground. Don't scare what you are going to do with me. It's crazy, most of the time, I'm scared and I don't want to be online dating. Ebo, explain to me how that works. I want to know, let's say, what's up with the groups, then I want to know who you are. I want to know who you are. Same for same. Same for same. So, I want to know who you are and what you are going to say. I want to know your view status. I want to know who you are and who you are. Can I know you better? The next thing I want to know is who you are, and what are your hobbies? I want to know who I am and how I get along with. I want to know who you are, and I want to know who you are. I want to know in real sense. My wife and I want to know who you are, and we want to know who you are. Is it sometimes, maybe when you watch an online show, know what to and when you have to do it because it could be the opposite is true or you know, like KACALE where they need to volunteer information and they must have something to say Is it perhaps maybe when you ask someone and I feel it's free they think you can do it they'll say you have a very good father your dad will also be happy you call him a hero and he ask her to be your crown you know, I'm allergic to you and you will be able to tell people Oh ok and take notes and instead of being as honest as you are being and you will say When he was in school, he went back to school and my mother was in the same place. He was in the same place? Most of the time, I went back to school. I was told that he wanted to go to the gym. Yes. He had a hard time with the background and he wanted to go to a gym. Yes. You know, there were times he went to the gym. Yes. So she's not going to see me and I feel like I'm already being cursed And I'm not going to be able to see her Well, I hope that she will be there And she will see the house And she will be there So I hope that she will be able to see me The date I used to go I used to go to the hotel I used to go to the park Bye, how do you guys see how they renovated the park and they are late I'm not going to pack I'm going to go on a date with my friend Does it depend on every girl who has a standard? I guess everyone has their own standard Everyone has their own preferences Some prefer to go to a hotel Some prefer to go out like in Uhoorupak There's someone who Mostly boys They want you to go to their house I don't know why It's the first date I know But as a girl As a lady You feel the insecurity and let us make it open in an open place That's why I can say we go to hotels for parks Is there an instance where perhaps you just feel special like you're not a good girl But you do feel that you're not a good girl And you feel that you're not the only one who has a standard and you're not the only one who is not a good girl who is not a good girl but you're not the only one who is feeling so special How do we address that situation? Because you're not the only one who has a character who has developed me I'm trying to tell you something You say a sex of money to make me a girl When you want to take a walk and walk in for the first time That's why I feel there's a lot of pressure because I feel very special Or the lady Even when you're at home and you're at home and there's no one around I say when a lady loves a crushy boy they start feeling and you say I guess it's that way like you know me and me like I have been this guy not him okay he started it but I'm eyeing him so I'll feel that whatever whatever So when I'm at home I think twice maybe girls think twice or I'm a thrice Please revise the story revise Is it possible that maybe I'm crushy and I'm crushy and I'm not the only one It's important I think, by the way I'll tell you something because first date I feel like the dynamic will depend on the girl So when I'm at home I have a crush on a girl at 20 dates There might be some implications maybe I'll know and I'll make mistakes But if it's the other way around I'll find that So when I'm at home I feel like I'm not the only one What do you think? Okay, I think for the for the for the for the for the for the for the for for the for the for the for the for the But the boy expensive expensive I didn't ask her to pretend she's gold. I said to myself, is she lying to you? Now, she hasn't spoken at all about it. There's a business broker. We don't have illegalITH. Keep going left with the money. God save the edgermandy! It's just because I'm a practical, I want to make a baby girl out. Now what happens, is there is a second kind of doubt? Once we give the picture in baby girl, if you ride with me. So maybe I'm on a way up a competition is a little bit stiff. So anyway, so that takes you out say I'm a high high. Just a little bit just to put it for the gram or for was up status. Would you prefer the honest one or the one who is? It's hard by the way because but for a start, not someone well. You know, the instinct of this guy is honest. I don't know if he's a fan or not. I don't know. So what would you do with the situation? Okay. Okay. Okay. Okay. And behind a rumor, this is a truth. But this is our first date in your time. Okay. Okay. Because you've got on a first date, does that immediately mean your boyfriend and girlfriend? You might not like me the way I eat first of all. Honestly, you might not like a lot of things about me. And that's okay. It's fine. We stay friends. Thanks. Thanks. I spent all this money on you. I invest. What are you bringing to the table? Discuss. Five marks. For a first date, you are there to know the other person better. Maybe I wouldn't like something about him. You know. You see, such things. So such things. There should be no pressure off. Due to the date, I owe you anything. The first thing is, I don't have a letter. High five is something behind it. Like, there is repaying. You just do it on your own. You don't have any pressure. You don't have to pay for lunch. I spent all this money on you. You don't have to pay for a first date. You don't have to pay for a first date. You don't have to pay for a first date. What happens if I don't pay for a first date? I'm not a baby boy. It's a new day and age. But if I don't pay for a first date, maybe it's not as loudly as other things have been happening. So in the instance that I pay for a first date, I pay for a first date. I pay for a first date. I don't have any pressure. You don't have to pay for a first date. You don't have to pay for a first date. I try to put myself in that situation. I'm not a baby boy. I'm a father. I'm a father. I'm a father. I'm a father. How about you, Toria? You see, I was scared to death just because... So you see, I just pushed you in the right direction. Please take over. Because I have them. See, what you want to do next is to talk to me, and to ask you a question. You can tell this guy, what do you think? You can tell this guy, what do you think if we have lunch together? You know, I have been thinking about the same, blah, blah, blah What do you think, what do you think? At the end, I will explain to you Even though you came with the proposal See, see one with traffic So, there are ways to go So, see a thing and you go to the hotel And I will tell you to go for lunch And there is a lunchtime and I will tell you to go for lunch But I will tell you, I will tell you to go for lunch Even though I will tell you to go for lunch Just be wise with the way you are Defend where you are attacking See, I will tell you Hashtag is why in the morning So, let's say the first date is successful Like, like, I will tell you to go for lunch What's next? So, directly, what do you think? See, I think if it's a boy, maybe it's a girl Do you think you can go for another date? Another date So, if the girl can respond Okay, yeah You can go for tour More dates You can tell her to join Don't rush I will send her first date Then, now we are officially boyfriend and girlfriend What do you think of your girlfriend? If she is on the left, she will have a wife If she is on the left, she will have a wife And then, is it a problem? Let's say, we have some options We have a hotel, we have outdoors But what if the first date is a club? I will judge because it's a club Not everyone who goes to the club by the way Engages in alcohol or other things However, to say in an instance If you go to the club, you will have a wife You will have a wife See what it is See, it's an inhibit You don't make decisions as fast Or as best As you come and say You don't make And remember, this is the first time You are on a date with this person Do you think it's advisable To inhibit a little bit with your choice making Do you think it's advisable?  Personally, I'm an introvert It's a place You know I don't like it DJs say you are mute So I prefer a quiet place Supermind Matters a lot In relationships and in dating You make irrational decisions Think about it before you decide And to say This before we got to this first date Now it's face to face Whether we are eating or hiking Or whatever people do on first dates How long is that supposed to last? How long do I have a sense of Veniaco, maybe a place near Zategua What they call red flags nowadays How long? How long is the distance? How long is the stroke of WhatsApp? It depends If we have mutual friends They will post And I'm the only one not seeing International Girlfriends Day high please In a situation like that Time Duration You are online dating It depends If you are alive And you see this guy is genuine When you see him In their texts In their talks They are not faking it Okay this is the way you see it I don't know how You see You are a partner But you don't know Plus You know him better They are people When you have open conversations And You know what It's two weeks I've known this person But I feel like I've known him Forever Forever But I don't know How long it will last So it depends Who you are chatting with And who you are talking to When does it become okay To start involving your friends Because let's be honest I know we say But please after that I'm sure some of you will say Stem Some of you will say Oh my gosh she's such a gentleman I don't know what to do I don't know what to do When do we start involving friends I know some of you Don't skip thoughts to begin I know some of you say From the beginning I come and date with you So when does that I come okay Gabriel I know Me I have a best friend So obviously When I'm with you I say hurry I say to you Then I say to you Immediately You don't have any features Do you have any ideas Okay Okay Hurry it I say You don't have any You don't have any features You don't have any But you don't have any You don't have any You don't have any You don't have any He's asked you out on a date But this sure has been Look at you He's asking you out on a date You don't have any You don't have any I don't have any Friendship character development Is even worse Even worse my guy You don't have any I don't have any It's necessary So Okay I'm overwhelmed That is when I Just too sad Hey I'm overwhelmed too I'm overwhelmed But I You're telling them See everything See detailed Leo I'm feeling high Because of so and so But Don't go telling them Every detail of your dating Friends are bad What happens when Before I read more comments Allow me Let's say I match with Surah Because I'm not a violent person And I'm not trying to be violent What happens if his personality Is all that Like I'm happy And then My parents They say There are different forms of Transport As in You're all the way up there with your Wants and Dis And by the way that's not a bad thing What you want is not a bad thing Don't ever let anyone make you feel Like it is But Personality Versus In his sleep But the conversation There's no story There's no Mental stimulation There's nothing Now what do we do? I don't know Okay So there's a personality But maybe A little bit But You know You have to rent For 3 months And change your pocket You have to ask for something bigger But You can't Count flies And a boat And a boat I'll go for the one with Communication is key To me I don't know I don't know I post pictures on Instagram And post them on dobes I don't know Do you have any pressure sometimes That reminds me of Valentine You cannot keep comparing yourself Your real life to someone else's Social media So someone is happy on social media But if you're at home You're nothing like It's boring It's actually So The one with The key conversation The deep conversations We have out here I'll go for him Let's Let's just start with the rent Let's just start Happy new month nowadays as a grown up From the depths of my heart Happy new month, I mean it Because I don't know I don't know I'll go for a birthday But Social media I'll go for a birthday I'll go for you I'll go I'll go I'll go I'll go I'll go I'll go I'll go You know, I'm not here But I'm here to take you For you See you with time When it comes to church I'll always be church I'll be on the front of the main I'll be on the main So for you You'd rather have someone who is Let me use the word Financially stable Financially stable but See you For you, it's about personality I'll go for personality How much do you pay for your personalization? It depends on the day Later, I'll have to pay for post-waste Invest So not all the time, you'll have to pay for your personalization I'll have to pay for my personalization I'll have to pay for my personalization You'll have to pay for it I have to pay for my personalization So as much as you're looking for the money, you'll have to pay for it I'll have to pay for my personalization I'll have to pay for your happiness I'm just a side boy You're a delegate You'll have to pay for your personalization I'm a side boy yes anyway to each man his own means I'm gonna start your place now I'm just trying to figure out how these things work okay now let me just read a couple of more comments and remember it is that white five on Facebook white two five four channel on Twitter hashtag of the day is WCW we're gonna come boy says Linda dates oh the question is Lord Nina embarrassing a little fun you can't on your first date we're gonna come boy says Linda date place Flanny then boy child a customer need to share food pay a customer same but really wanna cooler I need a shangha sure food half you are co finishing because it was a mere help you Ah that's a head this guy scared ah so maybe we'll get you indoor I'm only caught with a polyp all the way plus you know you're not going to make a noise why leave the food aha so maybe we're known and you're not gonna come out I'm always on a sleigh Oh, you're not wasting your time? I'm not wasting my time. I'm just a little girl. I don't know what to do. I don't know why. Because I'm in high school, I don't have time to eat, I'm not even eating. So I'm just a little girl. I'm just a little girl. High school. I'm just a little girl. I'm just a little girl. High school. I just want to say thank you to my wife, I'm not able to read out loud because of the way it is, but I still appreciate you. Let's talk about this one. It's a running story. Imagine visiting the last week of Wednesday. It's Friday Saturday. Saturday is the day before the event. For some reason, I had a meal on Friday. I was in a hurry. Did you eat? I was at home. I had a stomachache. I had a stomachache. It just so happened that I got sick maybe Friday night. I thought I was going to get better by then. I slept on the bed. I went to the toilet. I was in the car. Whatever remedy you have. I thought it was bad. It was bad. It was a running story. It was a disrespectful man. I was in a hurry. At that moment in time. There were side shows. What if the boy child comes to you like that? Let's be honest. Please tell me you have a running story. It's called that fun. I was in a hurry on Sunday. I was in a hurry. How are you feeling? I was in a hurry. I was in a hurry. I was in a hurry. I was in a hurry. But I understood who the woman was. You are like an excuse to have a day off. You have money but you're in a hurry. You have a running story. It was a genuinely running story. It was a genuinely running story. I understood that. You were sitting in a chair at that time. You said you were going to continue that. Let's continue. I was in the FaceBook. I was on the Twitter channel. With Twitter and Twitter. Remember the hashtag is white in the morning or WCW.   I was in a hurry to get to the bathroom So I said we move on, we move on regardless Okay Mothoni, Tricky Boy says I'm going to swim, I'm going to the very first day we met Is it that would you swim? I'm a baby, I was going to swim I'm a brownish Violence So when Oyu says avocado Is it that I'm going to swim? Yes Someone on Facebook said I'm going to book him exactly I don't know if it's an actual Kempinski Or just a name for fancy place Kempinski So I went to the bathroom and said I'm going to swim, I'm going to swim I'm going to swim, I'm going to swim I'm going to swim I'm going to swim So I went to the bathroom and said I'm going to swim So I went to the bathroom and said I'm going to swim I'm going to swim Yeah I knew it There's something else Oh At this point It's important place I think you cannot call your girlfriend You want to talk about avocado From when I was first I am wishing you two shaggs So to see my judge We have like 7 minutes to the end I really want to read all these I want to say hello to everyone I want to say hello to everyone I want to say hello to everyone I want to read your story Would you have that second date with that person again? Yes I don't know OK OK, I will affirm that communication But the point is I want to say it I want to say it You have said it like only two words You said it like that ... ... ... ... ... ... I don't want to say that. I want to say that Christopher E. Tambor is the one who gave me this date. What? Wow. He's cheating. He's cheating. I don't want to say that. I don't want to say that. Okay. The last person who says I don't want to say that. I don't want to say that. Yes. He's a little relieved about it. Caroline könnte nul she said we don't date. I don't want to say that but I don't want to say that. We'll see. We felt that pain on your behalf, we are so sorry. Raspashir, we are obsessed with you. We love you. We love you. We love you. We love you. We love you. We love you. We love you. We love you. We love you. We love you. We love you. We love you. We love you. We love you. We love you. We love you. We love you. We love you. We love you. We love you. We love you. We love you. We love you. and you rich guy with a Isaac She's, man, with Can I okay. okay. Okay, so okay, okay, okay. it's not like I'm just a child. I'm not like that. I'm a child. I'm not like that. I made a call, I told her to let me speak in the voice of a male.  I told her that I was going to come to the house with my son, and I believed in him. I told her that I was going to come to the house with my son, and I spoke in the voice of a male. I'm so sorry, I'm so sorry. Because James and Bradley Fidel came to check on me. Marley Gibson, Kida, I appreciate all of you. So very much none. I don't have much time left. Give me your handles one more time. Don't you ever let your nose out of stock after this. Imani Frista, Imani F-R-E-Y-S-T-A-R. Flista will work at YouTube, IG, Facebook, Twitter, Tiktok, have you ever done this? And you. She has a lot ofTIONs. She got her hands dirty. I don't know what you are saying I don't know what you are saying I don't know what you are saying My mom, my sis and I are watching You are watching the drama club And we appreciate everyone who has been Supportive in this journey of poetry I salute you people I love you so much Thank you Bye See you


I have not given an example coming from real life for this least square solution so let me give an example the model comes from physics Hooke's law which states that the displacement of a spring is proportional to the force that is applied okay the displacement of a spring is proportional to the force that is being applied to the spring proportional means directly proportional this is a linear relationship okay that is if L is the length that the spring moves and if W is the weight that is being applied okay if L is the length that the spring moves if W is the weight that is applied then Hooke's law states that L and W are related by this formula L is a constant times I will call it alpha 1 W plus another constant alpha 2 L is the length W is the weight. So this is Hooke's law now in order to determine the numbers alpha 1 alpha 2 see this relationship is known the unknowns are alpha 1 alpha 2 in order to determine the numbers alpha 1 alpha 2 you do experiments experiments in the lab actually attach physical weight to the spring measure the displacement substitute into this and then you can determine alpha 1 alpha 2 for that spring but what usually happens in lab experiments is that we make errors so in order to avoid errors we make more number of experiments do more number of experiments and then try to see whether we can determine this relationship okay now when you do more number of experiments typically you will get an over determined system of equations over determined means the number of equations is more than the number of unknowns typically over determined systems will be typically inconsistent that is where you have least square solution coming okay so I will give an example suppose we have the suppose the experiment has been done let us say 3 times there are 2 unknowns it is done 3 times and I have the numbers in this tabular column let us say the displacement is I have weight here displacement here okay so let us say weight and here it is the displacement let us say I have 1 gram then 3 grams 4 grams and let us say we have one more experiment so I have 4 what is the displacement displacement is let us say 2 6.5 something like 8 and let us say 11 here these are the numbers let us say these are in inches whatever so this is the table that I have from this table for this particular spring I must determine this equation okay so you substitute these into this so this is W this is L and so I have the following equations this gives rise to the following 4 equations in 2 unknowns alpha 1 alpha 2 right 6.5 6.5 inches or millimeters whatever okay then we have the following equations L on the left I have 2 equals W is 1 alpha 1 plus alpha 2 6.5 is 3 alpha 1 plus alpha 2 8 is 4 alpha 1 plus alpha 2 and finally 11 6 alpha 1 plus alpha 2 okay I have these equations now you can verify that this will be inconsistent for example let us take equation 1 and 4 subtract 1 from the other alpha 2 is gone 3 alpha 1 is 6 so alpha 1 is 2 and alpha 2 is 0 I am just taking equations 1 and 3 alpha 1 is 2 alpha 2 is 0 but alpha 1 is 2 alpha 2 is 0 does not satisfy the fourth equation so this is inconsistent okay you can actually verify by the rank condition rank of A must be equal to rank of A, the right hand side column vector that will not happen here these ranks will be different so we need to but we need to solve this you cannot discard any discard any equation here each equation is as important as the other equation because these are experiments done under the same conditions in the laboratory so you cannot discard any of those so these have to be taken as they are but then they cannot be solved so what one does is to look at the least square solution that is the solution which minimizes norm A x minus B where the norm is the 2 norm okay so I am going to leave the rest of the calculations for you to complete okay determine this is like A x equal to B pre-multiplied by A transpose in this case can you tell me just by inspection whether the least square solution is unique we have given a condition last time the columns of A are obviously leaving it okay so A transpose A is invertible and so there is a unique least square solution for this problem okay so you please complete the rest of the problem okay let us get back to this problem of best approximation and look at this notion a little deeper that it deserves but before that let us look at the concept of this orthogonality a little into a little more detail let us take V as an inner product space so this is my framework let V be an inner product space and S is a subset of W not necessarily a subspace just a subset then the orthogonal complement the orthogonal complement of S in V I am going to define this it is denoted by it is denoted by S perpendicular and this S perpendicular is given by is given by S perpendicular is the set of all vectors X in V such that inner product of X with let us say S this is 0 for all S in S, S is not necessarily a subspace just a subset I collect all vectors that are orthogonal to each vector in S that is S perpendicular the name orthogonal is clear why is it orthogonal complement that is not clear it should be clear probably by the end of today's lecture S perpendicular it is this whatever be S S perpendicular is always a subspace okay the reason is that I see the second coordinate second argument is coming from S you can think of this as this as a linear map null space of a linear map this is a null space of a linear map okay so this S perpendicular is a subspace I am going to leave that as an exercise S perpendicular is a subspace for one thing 0 is perpendicular to any set of vectors so 0 belongs to S perpendicular subspace has to have at least a 0 vector okay so 0 belongs to S perpendicular is clear you can in fact show that it is a subspace okay let us look at two extreme examples what is V perpendicular set of all vectors orthogonal to every vector in V single term 0 it must be a subspace and what is 0 perpendicular it is V it is a kind of taking the complement here and then intuitively we might think of taking the double complement when we take the double complement we intuitively feel that we should get back the same that happens in finite dimensional spaces okay so these are two extreme examples let us then look at this notion see this is important in the context of the fact that if you are in a product space and if you have a finite dimensional subspace W then there is a unique vector U and W such that for every X in V given an X in V there is a unique vector U and W such that X minus U is perpendicular to W okay so one needs to understand W perpendicular W in our case is a subspace okay in general one can define S perpendicular in this manner without being a subspace okay so let us then go back to this problem to make the following definition I go back to the problem of the best approach let V be an inner product space and W be a finite dimensional subspace let us fix X in V then we know that there is a unique U in W such that X minus U is perpendicular to W associated with this X is that U okay so let us define a mapping I will call it E, E is a mapping on V, E is defined by E of X equals U, E of X equals U what is U? U is to emphasize where U is the unique best approximation to X from W whenever we define a map we must know that if you define a map if you want to define the image of an element X then you must know that the image is unique only then it is a function the fact that this right hand side is unique comes from the result that we proved earlier that if W is a finite dimensional subspace then there is a unique U okay so U is a unique best approximation to X from W this U is called the projection of X from V on W E is called see we denoted we call this U as a projection of X on W we are calling E as a orthogonal projection map in fact it is called the orthogonal projection map so just orthogonal projection of V on W in other words for every X there is a unique U I assign a map call that E then this E is called the orthogonal projection of V on W for one thing it is not clear that E is linear we will prove a little later that E is linear okay but before we look at the proof that E is linear and also derive some other properties there is also a relationship see we will show that E is linear then we will establish a relationship between the range of E and the subspace W okay but before that we look at a complementary notion a notion complementary to the orthogonal projection E and prove the following result I will illustrate all this by means of a numerical example I will do it next after proving this theorem. Let V be an inner product space W be a finite dimensional subspace of V doubles of finite dimensional subspace of V and E be the orthogonal projection of V on W E is the orthogonal projection of V on W the mapping I will call it F F from V to V defined by you will see that this F is related to E F from V to V defined by F of X equals X minus E X it is I minus E F is I minus E this is the orthogonal projection of V on what you expect the subspace to be W perpendicular E is the orthogonal projection of V on W I minus E you will show is the orthogonal projection of V on W perpendicular remember the name orthogonal projection comes because you have projected the vector X orthogonally on to the subspace W okay it is actually an on to map we will prove it to be an on to map but right now we will simply say on V E is a projection of V on W I minus E is a projection of V on W perpendicular these are on to maps in fact okay let us prove this first the function F we want to show is orthogonal projection of V on W perpendicular which means I must consider the best approximation problem instead of that is given X in V I must look at let us call it V given X in V I must look at small V now coming from W perpendicular which approximates X okay so let me write given X in V we are seeking V okay instead of V U and V let us call okay V is not a bad idea seek V in W perpendicular such that see this time we must understand this problem but this is similar to the previous problem given X we seek V in W perpendicular such that norm X minus V is less than or equal to norm X minus I will use Z if you do not mind Z belongs to W perpendicular I seek a V in W perpendicular which approximates X from among all those vectors in a W perpendicular so this Z belongs to W perpendicular arbitrary okay now this is the this is the problem for best approximation from W perpendicular I must show that this X minus EX is the best approximation to X coming from W perpendicular is not it in order to show that this is the orthogonal projection of V on W perpendicular I must show that this right hand side in order to show that this E is or the Y how do you get the orthogonal projection of V on W the right hand side vector U is the best approximation to the X that we started with U belongs to W the problem now is I must show that X minus EX that is why I called that as U I am calling this as V I am using V for this okay so let us call this V let us call this as V then I am I must show that V given X in capital V this small V is a best approximation to X from among vectors in W perpendicular is that clear then it follows that this F is the orthogonal projection of V on W perpendicular okay okay first of all I must verify that this what is the problem there EX equal to U U belongs to W I must verify that X minus EX belongs to W perpendicular okay I must verify that X minus EX belongs to W perpendicular that is the first thing line X minus okay I will call it V V equal to X minus EX belongs to W perpendicular that is we need to prove that X minus what is EX for X there is a U once I fix the X there is a U I must show that X minus U belongs to W perpendicular where U is the best approximation to X from W but this is something we have proved before in fact U is the best approximation to X if and only if X minus U is perpendicular to W that is X minus U belongs to W perpendicular this holds which holds since U is the unique best approximation to X from W U is the best approximation U is the unique best approximation to X from W because W is a finite dimension subspace this comes from the map E but we know that this happens if and only if X minus U is perpendicular to W that is the same as saying X minus U belongs to W perpendicular so this right hand side vector belongs to W perpendicular so it makes sense to talk about this function being the orthogonal projection of V on W perpendicular of course we need to prove further that this is what do we have to prove yeah we must show that among all vectors in W among all vectors in W perpendicular this holds this needs to be proved of course but this belongs to W perpendicular has been established okay we need to show something like this precisely this I have denoted this by V so we need to show precisely this okay but let us look at that so this is the first part I must show that this holds see I will show see we want to show this what I will do is show that norm X minus Z square is greater than or equal to norm X minus V square okay I want to show norm X minus Z whole square but look at X minus Z I can write this as X I can write this as EX so I add and subtract EX EX plus X minus EX minus Z so I have added and subtracted EX see this Z comes from W perpendicular okay so for Z in W perpendicular we have this so norm X minus Z square is norm EX plus X minus EX minus Z square look at EX now the first term say I am going to apply Pythagoras theorem look at the first term first term is EX EX by definition belongs to W so this belongs to W look at X minus EX minus Z we have just now shown that X minus EX belongs to W perpendicular Z is coming from W perpendicular W perpendicular is a subspace so this vector belongs to W perpendicular so they are orthogonal so I can apply Pythagoras theorem so this is norm EX square plus norm of X minus EX minus Z square this is non-negative so this is greater than or equal to norm EX square okay but we want to show that it is greater than or equal to norm X minus V but what is V? V is X minus EX so can I write this as norm X minus V because since X minus V is X minus V is X minus EX which is EX so this is greater than or equal to norm X minus V square so it follows that norm X minus V is less than or equal to norm X minus Z for all Z in W perpendicular okay so this is the first result then if V is a projection of V on W then I minus E is a projection of V on W perpendicular we have not yet proved that E is a linear map but before we prove that E is a linear map I want to look at an example okay and then this example will kind of act as a sandwich between this result and the next result so let us look at the following. V has R3 with the usual inner product let me take W to be the subspace spanned by this vector and for convenience I will take rho vectors what I want to do is determine E okay W is given to me I want to determine E and derive properties for I minus E okay W is span of this let us say I want to look at the vector X as 1 minus 1 1 I can determine a general X itself I want to determine the projection so I will take a general X 1 X 2 X 3 I want to determine the projection E I want to determine the projection E for this problem W is given okay. What is the definition of E? E of X is U where U is the best approximation where U is the projection of X on W and I have a formula for that W is finite dimension W is 1 dimensional I will simply take an orthonormal vector just divide this vector by the norm okay so can you tell me what E X is?  It is a inner product of X with U J the norm of this is root 6 right so 1 by root 6 it will go with another 1 by root 6 so it is 1 by 6 times X with 1 to 1 into 1 to 1 which is X 1 plus 2 X 2 plus X 3 by 6 times 1 to 1 so this is E of X obviously linear okay E is linear see what I have done is to take an orthonormal basis for W W is 1 dimensional so I am just dividing by the norm which is 6 root 6 and this root 6 will come twice because X U J U J okay so this is my EX what is the null space of E what is the null space of E what is the range of E? See in general we cannot talk about range of E because we have not yet shown E is linear but in this example W E the right hand side is in W so range of E is W what is null space of E? Null space of E is a set of all vectors X such that E of X equals 0 set of all vectors X such that this numerator is 0 set of all X such that X 1 plus 2 X 2 plus X 3 is 0 this single equation 2 unknowns so there are 2 independent solutions so it is a 2 dimensional subspace what is that subspace? It is okay I will just write I will just write 2 independent vectors not necessarily orthogonal I can take 1 minus 1 1 0 okay 1 0 minus 1 is 1 vector the other one is 0 2 minus sorry 0 1 minus 2 is there a relationship between these 2 vectors and this vector they are orthogonal okay this is orthogonal to this this is orthogonal to this these 3 together will form a basis for R 3 but what is important is this is equal to W perpendicular this does not happen for a general linear transformation what does not happen the range is the subspace W null space is the perpendicular in general this does not happen but for an orthogonal projection this will be true okay you can in fact write down the formula for the orthogonal projection of R 3 on W perpendicular it is just I minus E but I also want you to observe the following E square is E can we check that quickly E square is E E square of X is E of E X that is E of E X is X 1 plus 2 X 2 plus X 3 by 6 times 1 to 1 this is scalar X 1 plus 2 X 2 plus X 3 by 6 what is the image of E image of 1 to 1 under E image of 1 to 1 under E X 1 plus 2 X 2 plus X 3 by 6 but that is 6 6 by 6 is 1 so that scalar is 1 this is just X 1 plus 2 X 2 plus X 3 by 6 into 1 1 1 which is E X that is yes so E square is equal to E if E square equal to E then I minus E the whole square will be equal to I minus E I minus E minus E plus E square but E square is E so these 2 terms get cancelled so that is I minus E. So if such operators are called idempotent operators a matrix A is said to be a transformation T is said to be idempotent of T square equals T so if T is idempotent then I minus T is also an idempotent I will leave the following problem for you to complete what is the matrix of E under the standard basis is there a structure for that matrix E square equal to E alright so the matrix will also satisfy the property but there is another structure for the matrix you can think of so E is a linear transformation you can think of associating a matrix given a basis now this matrix has a special property in this case in this example I want you to see what it is okay any guesses what is the question what is the question E is a linear transformation on R3 I can write down the matrix of E relative to let us say the standard base relative to any basis let us say the standard basis there is a structure for E there is a structure for the matrix of E I am asking you to explore you see what it turns out to be but is there any guess never mind okay so let us now prove so we have proved certain things for the numerical example that is of course E is linear we have discovered that E is idempotent then we have also observed that the null space of E is W perpendicular okay so let us prove this in the general case in a general inner product space this is happening for R3 with the usual inner product let V be an inner product space W be a finite dimensional subspace E denote the orthogonal projection of V on W then E is an idempotent linear transformation E is an idempotent linear transformation idempotent means E square equal to E what we proved in this example E is an idempotent linear transformation such that null space of E is W perpendicular range of E is W is obvious by the definition null space of E is W perpendicular and what is more important is that remember V need not be finite dimensional W is finite dimensional okay more important is V can be written as W plus W perpendicular where this plus is the direct sum which means that W intersection W perpendicular is singleton 0 intersection of two subspaces of course W plus W perpendicular is equal to V that is any element X and V can be written as a sum of two vectors one from W one from W perpendicular this will be done in a unique way because the intersection is singleton 0. Now look at go back to this definition this perpendicular was called the orthogonal complement of W this is the reason if W is finite dimensional then there is always an orthogonal complement of W orthogonal complementary subspace V may be an infinite dimensional in a product space but it can always be written as a direct sum of W and W perpendicular whenever W is a finite dimensional subspace okay if you demand W to an infinite dimensional subspace the answer is no in general but whenever W is a finite dimensional subspace you can write V as the direct sum of these two subspaces okay this should also remind this this equation should also remind you of something that we have studied before not ranked on the dimension theorem. In helical something what I am asking you this question what does this equation remind you of see dimension will be a problem V is infinite dimension possibly infinite see there is no we have not restricted our attention to V being finite dimension so we do not know whether the dimensions will add up if V is finite dimensional the dimensions will add up but V is infinite dimensional W is infinite dimensional then these things do not make sense but I am asking you does this remind you of something we have studied before forget about the perpendicular let us say I write V as W1 direct sum W2 have we done something if we are given such a direct sum decomposition see if V is written as W1 plus W2 etc Wk then we have shown that there exists k linear maps k idempotent k linear maps E1 E2 etc Ek such that E1 plus E2 etc Ek is identity then Ei Ej is 0 if I is not equal to j that we have seen and we have also seen a connection between this and Eigen values of a linear transformation okay but forget about Eigen values of a linear transformation what we have seen is a converse of what is happening now what is happening now is we have defined a map and we have defined a map on a subspace W finite dimension subspace W and through this map we are getting a direct sum decomposition what we have done earlier is a converse given a direct sum decomposition we have constructed maps we have constructed maps which are precisely idempotent okay they do not correspond to orthogonal direct sum decomposition but is a usual direct sum decomposition the difference between an orthogonal direct sum decomposition and the usual decomposition will be clear a little later that has got to do with my question that I asked earlier what is the structure of V when you write down the matrix of V okay these are intimately connected but I just want to remind you that this converse question we have seen before it is not an orthogonal projection it is it is just an ordinary projection so the question is what is the difference between orthogonal projection and an ordinary projection what is the difference between an orthogonal projection and an ordinary projection? Just think it over orthogonal projection we have seen that ordinary ... I remember having used the word projection also earlier E square was equal E square equal to E happens here also but there is something more to E again that question what is special about the structure of E the matrix of the linear transformation E that is the extra thing which connects you to the perpendicular okay. So we have seen that we have studied the converse question in a little more general sense. If V is W1 plus W2 H2 Wk then we have constructed idempotent maps E1 etc Ek which have the property that their sum is equal to identity okay. Let just remember that see you learn a new concept you need to relate the new concept with what we have studied earlier. So I am just reminding you that the converse question has been studied not in this context of perpendicular but a little more general. Sum of direct sum of several subspaces okay I will maybe just prove that it is idempotent okay. So proof I want to show E is idempotent okay but okay so let me emphasize let X belong to V then Ex is the best approximation to X from W that is Ex belongs to W okay. If X belongs to W what is Ex yeah what is Ex? If X belongs to W then X is equal to W what is Ex? Ex is U, U is X so Ex is X. If X belongs to W then Ex is X, if X belongs to W then Ex is X that itself is the best approximation. So E acts like identity on W okay what is E of E of X then for every X and W E of E of X that is E square X okay but look at Ex, Ex belongs to W, E of something and W must be itself that is Ex that is we have shown this for each X and V so E square is E okay so E is idempotent that is really straight forward, E is idempotent okay we need to show E is linear let me do that we need to show E is linear let X, Y belong to V and let us call Z as alpha X plus beta Y alpha beta coming from the field I must show that E of Z equals alpha Ex plus beta Ey it would then follow that E is linear this is a definition E of alpha X plus beta Y is alpha Ex plus beta Ey if I show this then E is linear okay let us consider X minus Ex and Y minus Ey the function the mapping F from V to V F of X equal to X minus Ex that is an orthogonal projection of V on W perpendicular these two elements are in W perpendicular these two vectors belong to W perpendicular okay X minus U really X minus U Y minus V if you want they must be orthogonal to W so these are vectors in W perpendicular W perpendicular is a subspace so a linear combination alpha times X minus Ex plus beta times Y minus Ey that must also be in W perpendicular what is this this is alpha X plus beta Y that is Z alpha X plus beta Y minus alpha Ex plus beta Ey this belongs to W perpendicular now this Z comes from V Ex Ey belong to W W is a subspace this combination is in W so this comes from W but this difference Z minus let us call it V let us call this V okay equal to V that belongs to W okay now the difference Z minus V belongs to W perpendicular that is okay what does it mean Z minus V W sorry I will use some other Y maybe no not Y Y is already there P Z minus V P equal to 0 for every P in W perpendicular Z minus V is orthogonal to every P in W is this the same as saying that V is equal to E of Z is this the same as saying if X minus U is orthogonal to W then U is the image of X under E if X minus U is perpendicular to W U is the image of X under E if X minus sorry if Z minus V is perpendicular to W it means V is the image of Z under E by definition okay we are through V is alpha Ex plus beta Ey on the one hand E of Z Z is alpha X plus beta Y so E is linear so E is linear is that clear what is E of X E of X is equal to U where U satisfies the property that X minus U is perpendicular to W I am writing E of Z equals V because Z minus U is Z minus V is perpendicular to W okay the second last part that V is a direct sum I will prove it in the next class.


This is stock number 10039. We are here at Summit Automotive in Fond du Lac, Wisconsin. You're new and used heavy-duty truck headquarters. Today we are checking out this super clean 2015 GMC Sierra 3500 crew cab short box single rear wheel. This truck has the 6 liter V8 gas motor and from this HD video you will be able to tell that this truck is extremely clean all the way around inside and out. Onyx black is the color. We shoot all of our videos in 1080p so if you have HD capabilities on your computer tablet or a smartphone device or whatever you may be watching this video on turn on those capabilities right now because it's like you're right here looking at the truck with me and definitely your best way to check out the vehicle before you see it in person. Factory 18 inch polished aluminum rims. It has Michelin LT 265 70R 18 tires. These tires have probably about 70% of the tread left. Framing underbodies in pretty nice condition. Driver's side front fender. No denser dings on that. Has factory fog lights. Front bumping front bumper parking sensors. Has a chrome trim grille. Projector lamp headlamps and the LED running lights. Passengers side fender is in excellent condition as well. Passengers side rim. No scuffs or scrapes on that. It does come with the factory chrome step bars and as we go down this side of the truck take note of how clean the body is, how reflective and mirror like that paint is. We take these HD videos so if you are far away or even if you're close by and just cannot make the trip down you can still see the truck here, the truck and of confidence in the vehicle that you're looking at before you even get here. So that when you do get here there's absolutely no surprises and you'll have seen a full HD video looked at over 40 photos and know exactly what you're getting before you even get here. So when you do get here you're all ready to go. Back rims in all right condition. Back tires have just about as much tread as the front tires. Maybe just a hair loss. Framing underbodies in pretty nice condition under here. It's like that all the way underneath. Lower rockers all look really good and it has all the remaining factory exhaust. As we come around to the back of the truck rear bumpers in really nice condition. I didn't see any denser dings on that. It does have the in bumper steps, the backup parking sensors, full towing package which includes receiver hitch four pin and seven pin wiring. Tailgate is in really nice clean condition and it does have a factory GMC soft tonneau cover. That's in pretty nice condition as well. I didn't see any rips or tears on that. It does have a spray and bed liner accompanied with a bed mat. This is a Linux spray and bed liner and if you wondering what that is that's a basically a big jug to hold water to give you weight in the back of the truck that you can fill up. Kind of looks like an inner tube you'd go tubing with but it's for traction and very clean back here. I don't think that thing's ever been used either.  No denser dings on this driver's side box side. Back rims is in pretty nice condition as well. And down this side of the truck the rest of the way very nice and clean. Love doing these videos on the black vehicles they'll always look so great when they are clean like this one is. Has a telescopic tow mirrors with built-in directional signals these pull out like so. They also fold in. Inside the Denali package gives you the light dune tan leather interior. Both of these seats are heated. Both of these seats are cooled. You get the Denali stitched into the headrest and the seats are in really nice condition no rips or tears on them. Weathertech floor mats throughout on this truck. Power windows, power locks, power mirrors. It does have memory driver seat and of course Bose sound system. Has the auto headlamps, the turn dial four-wheel drive and the factory brake controller. As we hop inside the truck here you can see a nice instrument cluster and that this truck only has 17,230 miles. You do get the digital speedometer, the heated leather wrapped steering wheel, Bluetooth and information center controls on the right, cruise controls and heated steering wheel controls on the left. Comes with the six-speed automatic transmission, the GMC and Telolink radio. You get AM, FM and Sirius XM radio capabilities. This one has the factory navigation. Also has the backup camera right there.  Here are heated and cooled seat buttons, power pedal stability control. That's for your cargo lamps, backup and parking sensors. You can turn those off and on and then it does have a downhill assist control. You get three USBs, two power points and a 110, 150 watt plug-in right there. Dual glove box, passenger seat is very clean as well. No rips or tears on that. This truck smells very clean inside. I don't think it's ever been smoked in. Has the side current airbags and that headliner is in excellent shape. So this one does have the heavy or the snowplow prep package. That's what that is right there. If you want to tell if a truck's got the snowplow prep in the GMs you gotta look for that little light right there. That indicates that it has that in the glove box. The code is VYU. Has the on-star capabilities as well. We'll take a quick look at the back seats and then we'll check out under the hood. But very clean inside. Back seats are just as clean as the front seats. No rips or tears back here. It does have the latch child safety system. Has the fixed glass rear window with the built-in rear defrost. And like I said very clean back here. No rips or tears. Has a weather tech floor mat all the way across. And it does have in-floor storage underneath that seat there. We'll take a quick look under the hood. I would personally like to thank you for checking out the video today. Hopefully from this HD video. You will have been able to tell just how clean this truck is all the way around inside and out under the hood. We have the 6 liter V8 motor. Engine bay is very clean. Runs very smooth. This truck has been fully safety and inspected by our service shop. Has a fresh oil and filter changed. All the fluids have been checked and tapped off. Truck has been gone through mechanically 100% and is 100% ready to go. To see more pictures of this truck or one of our other 450 new and used cars, trucks, SUVs, minivans, Wranglers, half tons, three quarter tons, one tons. You name it we got it go to our website www.summitauto.com Full pictures and descriptions of every single vehicle on our lot. Videos of every single used vehicle that we have all at summitauto.com. Actually all of our vehicles from two locations are at summitauto.com so check that out. We have a Ford store and a Chrysler Dodge Jeep Ram store, Beaver Dam and Fond du Lac respectively. And to see more HD videos like this one you can go to youtube.com slash summit auto. Remember to like, subscribe and share on this video and all the videos that you see there. In fact in a second you will see a link to subscribe to our YouTube channel on your left. They link to more heavy-duty truck videos like this one on your right. If you have not been to our website on the bottom link to this vehicle on our website click those check us out. We really look forward to help you with this super clean 2015 GMC Sierra 3500 crew cab short box single rear wheel Denali package. Thanks again.


This is talk number 10175. We are here at Summit Automotive in Fond du Lac, Wisconsin. You're new and used car headquarters as well as your Dodge headquarters. Today we are checking out this super clean 2015 Dodge Dart GT this vehicle has the 2.4 liter four-cylinder motor From this HD video you will be able to tell that this car is extremely clean all the way around inside and out Bright white is the color we shoot all of our videos in 1080p So if you have HD capabilities on your computer tablet or smartphone device turn them on right now because it is like you're right here Looking at the car with me and definitely your best way to check out the vehicle before seeing it in person comes with the 18 inch Painted I think they're called hyper black rims Yokohama avid tires and those tires got a lot of good tread left I'd say over 70% of the tread left on those tires 225 40 our 18s are the size if you were curious it comes with the projector lamp headlamps the projector lamp Fog lamps no denser dings or cracks on that front bumper. It is in really nice condition Passenger side fender is in nice shape as well and the passenger side rim I don't see any scuffs or scrapes on that as You go down this side of the vehicle you can see just how clean the body is how reflective and mirror like that paint is We take these HD videos So if you are far away or even if you're close by and just can't make the trip down But you're still interested in purchasing the car You can still see the car hear the car and have confidence in the vehicle that you're looking at Before you even get here. So that when you do get here. There's absolutely no surprises Very clean down that side. I didn't see any denser dings on the doors This back rim is in nice condition as well No scuffs or scrapes on that either and the back tires have just about as much tread as the front tires Maybe just a hair bit less. It's still lots of good tread as we come around to the back of the vehicle No major dense dings or scuffs on that rear bumper has the LED racetrack tail lamps and the backup camera We'll have to go unlock the doors to get in there see the trunk comes with the dual rear exhausts with the chrome tips Deck lid is in nice shape. I didn't see any dense or dings on that And as we go down the driver's side just as clean as that passenger side No denser dings in the rear quarter and this back rim for for full disclosure. No scuffs or scrapes Found the rest is side of the vehicle. No dense. No dings has the enter-and-go system the built-in directional signals in the mirrors Inside the GT package gives you the black with red stitching leather interior Both of these seats are heated. You do get a power driver seat with factory lumbar We have factory floor mats throughout auto headlamps Power windows power locks power mirrors you get the red trim Throughout the doors and dash and as we hop inside the vehicle here. You can see that this one has 30,000 41 miles you get the seven inch tft digital display with the digital speedometer there has the heated Leather-wrapped steering wheel that's in really nice condition. No scuffs or scrapes on that cruise controls on the right Bluetooth and information center controls on the left and then on the back of the steering wheel are your Audio controls this one has the 8.4 touchscreen radio This one also has the factory navigation installed AM FM and serious satellite radio capabilities This is also where your backup camera shows up And you can do your heated seats and heated steering wheel buttons there as well as your climate control And you'll notice that it does have the dual climate control there You can also do your climate control down there if you like the more tactile approach Automatic transmission Passenger seat is very clean as well. No rips or tears on that smells very clean in this car Has the power sunroof as well and up here are your home link buttons for your garage door security systems and lighting systems As well as your map lights. We will take a quick look at the back seats Do want to point out it does have remote start on the keyless entry there also part of the Entering go system Actually, we'll take a quick look at the trunk first and then we'll check out the back seats Very clean back here does come with the tire inflator kit Gotta unlock the doors first Back seats are very clean as well. No rips or tears back here. We do have the factory floor mats back here, too These seats do fold down for extra storage And go up nice and easy But we will take a quick look Under the hood. I would personally like to thank you for checking out the vehicle today Hopefully from this HD video you will have been able to tell just how clean this car is inside and out under the hood We have the 2.4 liter multi-air motor and Jim day is very very clean This car has been fully safety then inspected by our service shop has a fresh oil and filter change all the fluids have been checked and topped off The car has been gone through mechanically 100% and is 100% ready to go to see more pictures of this car or one of our other 450 new and used cars trucks SUVs minivans wranglers half tons to quarter tons one tons you name it We got it go to our website www.summitauto.com Full pictures and descriptions of every single vehicle from two locations all at summit auto calm And if you'd like to check out more HD videos, you can go to youtube.com Summit Auto remember to like subscribe and share on this video and all the videos that you see there In fact in a second you will see a link to subscribe to our YouTube channel on your left a link to more used inventory and Car videos like this one on your right if you've not been to our website on the bottom link to this vehicle on our website Click those check us out and we really look forward to help you with this super clean 2015 Dodge Dart GT. Thanks again


Hello and welcome to CMC Markets on Tuesday the 26th of January and the weekly market update and this week I'm going to be concentrating I think largely on the risk on risk off trade row row as I like to call it. We've seen a significant correlation between equity markets and oil prices and I'm going to look at that correlation I'm going to look at the key support levels on not only the German DAX but the S&P 500 and I'm also going to be looking at a proxy for the oil trade and that is Canada Yen because I think there's potential that we could have seen a potential reversal in the Canadian dollar particularly against the Yen but also I think against the US dollar as well and that sort of brings me neatly into the Wednesday FOMC meeting where Collins Zinske and myself will be holding a webinar at 3pm which is free for you to sign up for and there'll be a link on this video for you to navigate to so that you can sign up for that webinar. I'm going to make a start with the S&P 500 as we head into month end we'll we're still I think significantly above a key support level and that's borne out by this chart that I'm about to put up in front of you right now. Now this chart here is a weekly chart and I've drawn a support line through the lows in 2000 through pretty much most of 2014 currently comes in just above the 1800 level also comes in above the 200 week moving average and it's also significantly important that we're above the trend line support from the March 2009 lows so the broader uptrend that we've been in for the last six to seven years still remains intact we're still above some key support levels and until such times as those support levels break then the likelihood is we're probably going to continue to trend off that support level if we break the support level then we could well navigate lower. Moving on to the German Dachs and it's a similar sort of story again we're looking at a long-term chart and again we can I've identified a number of key support levels notwithstanding the 200 week moving average that for me is the key support level along with the 9300 area which we bounced off earlier this month so again the oscillator as in the S&P on the earlier chart is looking a little bit oversold that's not to say that it can't drift a little bit lower but certainly in on the basis of those two charts and the fact that we're seeing an awful lot of volatility in and around $30 a barrel in the oil price maybe there is some evidence of an intermediate bottom starting to come in in oil prices to get a view on oil prices sometimes it's a good idea to look at the commodity currencies and in particular the Canadian dollar and the Norwegian Kroner which can act as proxy currencies for crude oil and I think it was rather notable last week that we saw some significant reversal patterns in the Canadian dollar now the reason I've looked at the Canadian dollar against the Japanese yen is essentially because the Canadian Canada's and their export country and Japan is a net import country so from that in that context sometimes looking at charts like across like Canada yen can be instructive in terms of the overall turnaround in sentiment on a particular currency pair so let's start by looking at the daily chart and in particular at a candle last week which I've identified as a hammer now this hammer chart does appear to suggest that we could well have a base in place but we still need confirmation of that so what I've done with this Canadian dollar chart this Canadian dollar Japanese yen chart is I've moved it forward to a weekly chart now the weekly chart we've posted a bullish engulfing week now historically these sorts of candles tend to act as a positive arbiter of a rebound we still need to be confirmed and what we don't want to see is a move back below the lows that we saw last week but the oscillator is starting to look as if it's about to turn higher and that could well suggest not only a significant rebound in the Canadian dollar and that's significant in the context of its performance against the US dollar with the FOMC tomorrow and a dovish FOMC could have the side effect of pushing the Canadian dollar higher but also in the context of a significant rebound in the oil price so that's it for this week I'll expand upon a number of those themes at the webinar tomorrow at 3 p.m. Wednesday prior to the FOMC meeting until then or next week this is Michael Houston talking to you from CMC Markets


Hey guys, it's Nate, A.K. The Foot Accountant. Welcome back to the channel. It's Sunday in FIFA Ultimate Team, and you know what that means. Sundays, upgrade packs. They're one and the same. I think we're getting upgrade packs again today. We had them last Sunday, and today hopefully we get the good upgrade packs because EA Sports, I'm telling you right now, you need to release the good ones because so far, Premtats has been an L. The players are not upgraded enough and the content's been very average. So I'm gonna come out and say it right now, EA Sports, we need the good upgrade packs. I'll talk about those in a second, and show you what those are, just to get you ready for those today. Talk about what's happening with these Tots cards right now as well, because they are dropping, and also we have guaranteed ourselves the schedule for the next couple of days. Just so you guys are aware, they updated the stuff here inside of the schedule for week and week. We are getting La Liga team this season next week, and we will be getting Bundesliga the week after. Now of course, the Bundesliga vote ends this week, so I thought it was going to be Bundesliga next week, but in fact it is the La Liga team in the season coming next, so Baran, Mendi, gets your Madrid links ready for that right there. So that's gonna be coming out, quick little tidbit right there. I also wanna talk about what's going on with the stuff in the store. Stadium items in the store, which is an L. I think that's kind of a joke in my opinion, but we saw it coming because it was happening in Volta already. First things first, let's take a look at these Tots cards because they're dropping. They're dropping right now, heading into Sunday morning. Kane was just down at 5.80, I snagged one, played a couple of games with him. Luke Shaw was just 300K flat, he's bounced back up to 3.16. Salah is still very low. Ruben Diaz has dropped a lot. So has Cancelo, Gundawan and Mount. A lot of these cards are down. Now Kane went from 6.50 to 7.20 on the Friday night into Saturday morning, which I was able to flip myself. A Kane bought at 6.50, sold them at 7.10, so a little bit of profit there. I'm kind of watching some of these cards again tonight. Salah is one who is very high rated. He has a weird amount of supply and I think he just has a weird amount of panic selling too, right? If I take a look at 1.5 mil, Salah's got one, two pages. Two pages with some overnights in the low 1.4s. I really need to see this a lot in the low 1.3s if I'm gonna get involved for an overnight flip because I think again, a lot of people are selling these cards right now because they are expecting the upgrade packs today and that's something that they think could drop these prices because people are gonna sell cards if they have the opportunity to go out and pack them. I mean, look at Kane, man. Two pages, 60K up from where he's at. I mean, he was 590, 580 at 650,000 coins. He's got two pages, so that card's pretty rare. I'm watching out on Ruben Diaz right now as well because this is a card brand new to team this season. First ever Tots card and he's looking kind of interesting. I'm trying to maybe snag him right around 400K which I might have missed the boat there. There's one at 408 and I'm gonna have to snag that because he is on the rise because he was just down at 405 and then after this one at 408, the next one is at 413. So I'm really gonna watch these Ruben Diaz right now for a potential flip. Now this is a very risky play. Risky is the name of the game that I'm going with right now.  So I'm watching De Bruyne, I'm watching Sala and this Ruben Diaz. I'm probably not gonna buy too many of them but you know what, I'm gonna risk it for the biscuit man because I would still like to make some more coins before we head into team this season because again, if the upgrade packs do come out today, that's what everybody is going to be spamming. They're gonna be dumping a lot of coins into these packs because that's what people love to do during team this season is they love to spend coins on these packs. I mean, that's what I've been doing in FIFA for the past month, really been grinding up my coins, putting a lot of time in, again, taking that RTG mentality to the max, really trading. I had almost 10 million in transfer profit this last month. I went from about 3.5 million coins and we are up over 7.6 million coins right now on my account, so a huge grind on my end, making a lot of coins this last month, just so that I can get myself more coins to open up packs during team of the season. That's my big grind. Last year it really paid off packing a lot of cool stuff and people are gonna put a lot of coins into these packs just because these are the best cards that we see on a whole with the squad throughout the year and they're very packable, right? This pack weight, it's high, right? You can definitely pack a lot of these cards. So you're gonna see a lot of that this week and I think that's why you're seeing the selling right now. Now what upgrade packs could we see today? This is the one we need to see. Premium Premier League upgrade pack. It's a 20, 25K pack with all Premier League players. So 12 prem players, three of them guaranteed to be rare. Now last year we only had this exact type of upgrade pack for 24 hours coming out on Thursday. So it was like a 24 hour grind for these packs which were like quote unquote the best ones during a promo like this because if you think about it you get 12 Premier League players with three rare. I mean, yes, there's still a lot of players that are in the Premier League but your chances of packing one of these teams this season is greatly, greatly increased if that kind of pack does come out. So these are also very, very good for crafting, right? You get a lot of cards. You can put those cards into another SBC. There should be another one that comes out that should be like a, it should require like four rares and then the rest will be non-rares and it's a Premier League upgrade pack. I mean, we had it last year in FIFA 20. If you guys remember those packs, it was like a four player pack with one rare, right? And you could rinse almost all your non-rares into there which was a good one. So hopefully we get some of the league specific upgrade packs today along with the 81 plus picks, right? If we get the picks and the packs, that would be incredible. So hopefully EA delivers today because so far with the start of Premier League team this season in my opinion, it's been kind of an L, right? The players are not juiced as much as we want them to be. And we haven't actually had a team of the season player SBC. It's only been showdown SBCs, which if you look at these cards on foot bin, these cards are disliked so much. It's unbelievable. I think the timing of this content is just very poor, right? 3,000 downvotes for Alonzo and foot bin. And I think if Mariano's got the same, almost 3,500, 3,500 downvotes for both of these cards. I just think this is not timely content, right? We want to be seeing team of the season player SBCs. Now those cards look cool. Of course, they have the potential plus two upgrade for the game playing later this week, but we haven't had a single tots player SBC yet. We've had Bale flashback and then the two headliners, or sorry, not headliner showdowns. So hopefully today we get a player SBC as well, man, because I think a lot of people are wanting that, right? Lin Gardinho, Grealish, Stones. I mean, there's a huge list of players that could very easily get a team of the season player SBC. It looks like Stones is rebounding back a little bit right here. So kind of keeping an eye on this card. Same thing with Mason Mount. I know I'm switching topics very quickly there, but just keeping an eye on some of this stuff right now. It looks like Mason Mount is rebounding as well. He was just 345 and now he's up to 350. So I'm going to keep an eye on this Mason Mount here for the next little bit. Also that DS card, if I can snag one in the, 324, sign me up on a little bit of a bid situation there. 304, because I think these cards could rise up into the morning a little bit. Again, it's risky, right? It's a bit risky to do messing around with these cards, flipping them while they're in packs, but again, you're going off of hype and rarity. So that's what we're really looking for today with these two guys to see if we can get ourselves a flip on one of them. But I do think you'll see these cards rise up a little bit this morning, regardless, just because again, they are hyped up a little bit. And yeah, we're going to keep an eye on that. But of course, with the weakening set off happening, I want to take a look at a few prices and just kind of talk about, we reached that big time peak over the weekend on these cards. They got really, really high up in price. Adama was like in the high 800s, our wire was almost 700K, Tamora was 500, Luka Marge was 250, Atal was almost 800,000 coins, and you're seeing these cards drop back down now. Honestly, because I think people are expecting the upgrade packs today, they're ready to spend their coins on them. And yeah, we're just entering into that stage of this promo where you're seeing a lot of that. So that's why I think you're seeing some of the prices go down. They're still going to fluctuate, right? But with the focus having upgrade packs out, you guys know, right? When we have the 81 plus picks that come out, whenever they come out during the year, you know what happens on this market, right? It goes crazy. People stop buying cards or anything. Prices are probably going to slide down into Wednesday. If we get 81 plus player picks and good, primary upgrade packs, because everybody's going to be focused on those upgrade packs, and that's all that they're going to want to grind. So this Malcard 360 overnight, if I could really snag myself a 345, I would love it. But I might not be able to snag that price anymore. So yeah, I think that's why you're seeing some of the sell-off today. If there is good upgrade packs that are released, which I think is possible, I think you will see more of a sell-off. I really think you could see, there's a lot of coins in this market right now. But a lot of people also are going to hand me those upgrade packs.  People have got the budgets to go out and try out cards and do SBCs and stuff. Now, one thing I will say today too is watch out for fluctuations. Still, on some of your rare out-of-packs meta cards, like this Antony was just 340,000 coins. He's between 340 and 370 most of the day yesterday. Right now he's 313. I mean, if I can get this back to 340, I would love it if I can get a couple of buys down here. Like you can still kind of trade with this stuff when the market is dropping a bit. 313, that's not sitting, it's just not there anymore. But I'm gonna watch this card, right? Cause he still links to popular cards like Taglifika who was out last week and stuff like that. So if you're watching the market again today, you're probably gonna see prices dropping off a little bit more. Stuff is still pretty rare though, right? Some of your icons are rare. Some of your out-of-packs specials like this Fatih. You know, he's up, he's like 115 right now, but he was 1.2 for most of the day yesterday. So again, I would expect these prices to start to fall down a little bit. But also know that those upgrade packs are gonna take a lot of coins off the market and that's gonna be where the hype is. You guys know what happens when we have those, the player picks coming out, everybody goes bananas for them. If the packs are good, if they're OP, especially if they release a player pick, the 81 plus, then people are gonna sell stuff even more today on FIFA. Now what else could be coming out today? We could potentially see another, that icon midfielder, SBC. Now the big thing that's gonna happen today is with upgrade packs, people are gonna start crafting as well and there's gonna be more of a focus turned on SBCs. SBC fodder is still very, very low. It's actually incredibly low still.  Crazy low from where they have been. Fodder probably rises throughout the week this week. If people are doing upgrade packs or crafting the SBCs that come out, that's gonna make people just focus on the whole SBC mentality. So I think these cards could do well. If you haven't club stocked and if you want to, that could be something where you spend some coins, put some cards in your club and then either do an SBC for cheaper later on the week or you sell those cards later on the week before Friday for some profit. Because again, Friday we're gonna have more lightning rounds and more supply and more stuff like that. So that is one thing to kind of keep an eye on. Just watch out for, again, the focus during the week for this week is really just gonna turn on to these cards. Now again, just kind of early on, talking about when's gonna be the best buy time for these cards, I really think it's gonna end up being a Wednesday because there were so many people that were looking to buy Community Tots last week. And people saw how those Community Tots cards absolutely banged out of packs. Wambasaka 750, holy smokes, right? Barns 712, this guy was 450K. So in my opinion, people are gonna be going bananas for these Prem Tots cards again. And I think that Wednesday time frame is gonna be probably a time when you buy.  So you kind of have to get in early. When you see people selling and not buying and with upgrade packs coming probably today, you know, Monday, Tuesday, we're really gonna be watching that Wednesday timeframe with the guaranteed Prem League Tots. Hopefully that gets added to the code because right now we do not have that pack in the game that needs to be added to the code, EA Sports, okay? You know you're releasing that SBC, put it in the code, all right, let's go. So we need to watch out for that SBC and how it's gonna affect the market. If for some reason they were not to do a guaranteed, you know what, I'm gonna buy both of these Antonis at 313 and we're gonna do a little bit of the flip, right? I'm gonna list these both for 340 overnight because I think that is profitable and that's how you can make coins in the market as well is just with the weakening selling and stuff getting too low. I mean, we have 15K of tax right here taking to like 330 or whatever, but that's a nice small little flip that I think is a 100% gonna hit overnight tonight. So that's why I bought both of those cards right there and I'm actually gonna, well I added that 522 in my watch list, so boom, still watching that.  They're always the most expensive, the first weekend, we always know that, right? So really keeping on their prices as we're dropping off out of the weekly this weekend because people are really gonna wanna buy these too and after we have that Prem Guarantee SBC whenever that comes out, a lot of people just shift gears and saying, hey, I didn't pack who I wanted to get, now I'm gonna buy them. So also, I would watch the weekly sell-off and this is a pro tip, I'm talking about this early, we're gonna talk about it throughout the week this week. Watch your Premier League out-of-pack specials that absolutely went bananas this week. All right, and keep an eye on those because those are gonna go high again this next weekend after Tots rewards. It happens last year, it happened the year before that, it happens every year. Watch your Prem cards, man. This Zaha at 150, he was 170, right? So that's down from where he was.  If you see pretty sizable sell-off on, you know, even like an Allen St. Maximon Inform or like a Bruno Fernandez like this type of card or a KDB lower version, all of your special cards that are in the Prem that went crazy this week, you're gonna wanna keep an eye on them. This Pugba was like 370 when he was really rare. So keep an eye on those cards this weekend during the sell-off, you know, even your Kent, your Adama, your Tamori with those English links, you're a tall even, just the really meta cards as well. Next weekend should be a nice rise after rewards again, for stuff on this game in my opinion. So that's a lot of what's going on right now. Of course, we had a huge weekend and if you guys didn't catch the streams, I made almost, this is about 700K of total after-tax profit. This was 90% of this was on Friday night and Saturday. I flipped a couple of cards on Saturday, I bought this at 165 and bought this at 1.42. So not crazy flips there, but again, huge, huge profits overall in the last couple of days. So we're gonna try to flip these Antonis, flip this Rubin Diaz and make some coins overnight tonight. We're gonna risk it a little bit. Icons that are still very rare, some of your babies in mids, they fluctuate a ton, right? This Renault is at 1.8. Again, all it takes is one person on this game to wanna go out and buy one of these cards and these baby icons are so rare. I mean, this Zidane was 1.5 this weekend selling. So you're seeing some of these cards drop off a little bit out of the weekend, but they're just mega, mega rare. So I would 100% keep an eye on this stuff and watch out for just big undercuts as people are seeing upgrade packs and stuff released. There's gonna be potentials for quick flips. So that's what I would say. Be careful with the really, really high tier, you know, like this Maldini stuff that doesn't sell pretty consistently. You wanna try to flip an icon or flip a card that is like that Antony, right? That's a really important links for people that run Neres and Tagli Fico. So that's a really big card for links and stuff. That's why I'm watching him. And yeah, just watch your out of pack specials as we fall into it today. A lot of people are gonna be focused on the packs. So if you're focused on the market, there's gonna be a lot of potential to make coins there as well. So watching the market today into Saturday 100% again, watch the sell off, upgrade packs should be coming today. Maybe an icon attacker upgrade could come out as well as people know that, hey, we're gonna start grinding, SBC, crafting and stuff like that. And good freaking luck on your weekend leaks, man, because it is sweaty out there, bro. I was just four and one, now I'm four and three and I really don't have a lot of time this weekend. So I really don't wanna chalk it up for primarily tops, but I really wanna get 14 wins, but I gotta get 10 wins today on Sunday if I'm gonna make that happen. So hopefully we can make it happen. But hopefully this also is the start of the fun that is gonna happen throughout the rest this week. If there are upgrade packs and they are good, we're gonna be spamming them 100% because I wanna pack Sun, I wanna pack Kane, as many primarily tops cards as I can. Let me know down below if you're gonna be ripping packs or any other questions that you may have about this market right now. If you like this video, smash a thumbs up, of course, get in the comments and of course, subscribe if you are new. It's been Nate, The Foot Account, and I'll catch you guys later. Peace out.


Hello, GeoSci 10 students. My name is Rosie Oaks and today I'm going to talk you through how to upload your v-trip onto the pass space and also how to then create a URL so that you can submit this onto the Dropbox on Angel. So here you can see we're at the course home page on GeoSci 10 page. So in order to get to the instructions for that extra credit, we're going to click on lessons and on assignments. And you can see here these are the directions to create your own v-trip. So here are the instructions on how to create a v-trip. You can do this in several different ways. You can create a PowerPoint or create a Word document. So have a read through, create something, a trip that you've recently been on that has geological significance. And then what you have to do is you have to upload this onto the website. So the first step is that you have to create your Penn State web space. You have to activate this. This isn't automatically done. So just click on that link on the page and it brings you to this page here, the application for a web space account. And this creates a www folder on your Penn State pass space. You have to take a quiz. It has five questions. You can take it as many times as you need to until you pass. So you just click on the link here. I've already done this so it won't let me do that again to show you. Once you've completed that, you can go to your pass explorer space. So just click on the link here on the instructions page and it will take you there. So as you can see here, I have five folders on my pass explorer space. You're going to want to click on the www folder here. So as you can see, this is where you can upload your v-trip. Just click upload here. You can choose a file. Mine is on my desktop. So it's here, the v-trip. So just open that up and click upload. I already have mine on there, but we're going to upload it again just so you can see what it looks like. So you can see here this is my v-trip. So it's rogues underscore Edinburgh underscore v-trip dot pptx. And that's really important to make a note of because this is how we create our URL. So now this trip is on my pass explorer space, but this is my own personal web space. So nobody else can see this unless I create a URL. So now we have to go back to the directions page. You can see here to create the URL for your v-trip, you have to follow this format here. So let's do that together now so you can see what we do. So it's http dot www.personal.psu.edu and then forward slash your user ID. This is your Penn State user ID. Mine is RL0130. And then forward slash and then the file name and the extensions. So I'll just move this to the side. Let's go back to the pass explorer space and just double check what that is. So there we go. There's my note there. So that's rogues underscore Edinburgh underscore v-trip dot pptx. So this is then the URL which means other people can see my v-trip. I'm going to copy that and paste it into my web browser. I'm going to check that this works before I put it into the angel dropbox. And as you can see there, my v-trip is downloading there. So that means that this link works. So let's go back to the geosite 10 page on angel. Here's the dropbox right here. So just put a title, wrote v-trip, there we go. And then in the message section you can then just paste that web link that we wrote out before. You can go back to where you cut wrote it before and then we'll just copy this and paste it. And that's it. So then you can click submit and that is your v-trip complete.