I decided to use YouTube as a way to motivate my pupils, so they weren't just writing an assignment on paper and handed in, I thought it would be far more enjoyable and innovative for them to actually make a video tutorial that they could share with other people. So I teach music technology, so they were going to research how to record different instruments in the recording studio. The challenges were, I was handed the learning over to them to write, you're going to go to research, you're then going to make a video tutorial on how to do that and then we're going to share it with other people. So I thought when we just put on YouTube it's the easiest thing to host the videos, it was shared across the world. Other teachers were picking up and ever since now we've had over 70,000 hits of the pupils work. So the equipment we used for this project was used to record in the studio during school. The pupils used some video cameras, they used Windows Movie Maker then to edit the video, put it together. So they'd record each other showing how they record guitars, vocals, drums, best practice. So I became less of a teacher, more of a facilitator. The attendance figures went up, they were in school more because they felt there was a purpose. And because they were working as a team they all had their specific jobs, their specific roles. You mentioned technology to some schools and they think hundreds of thousands of pounds of money and it's not. It literally was, in my case, maybe just using a mobile phone or just using YouTube, things that were inexpensive. But the response they had from the pupils using the technology that they like. And I'm a firm believer that if we use the technology they're using at home in the classroom it switches the pupils on. It's easier, it's easier to grasp the concept of things. It's much more enjoyable as well than just sitting down writing. I enjoy the fact that we can show other people what we at the school can do. I always used to ask Mr Ritter, could he check my work? But now because we did the project I have confidence in myself that my work is fine and it's to the best of my abilities. It is a success story. It's had fantastic results from my pupils. I want to get that out now and by using it not just within my school but within the teacher network. So using partners and learning network of Microsoft, using Twitter, get it out there for other teachers to see what we're doing, sharing good practice because it does have an impact on the children. Thank you.


The Cardona State Police Command has arrested suspected attackers of the convoy of the state governor Nassir El-Rufai by suspected members of the Islamic movement of Nigeria, I.M.N., popularly known as Shiites. Spokesman for the command, DSP Mohamed Jalige, says the security officials attached to the governor's convoy cleared the Bakken Rua axis of Rigasa, Namdya Azikue Expressway after Amhutlam, suspected to be members of the I.M.N., attacked low-abiding citizens and prevented motorists from plying the route. Meanwhile, the Islamic movement of Nigeria has confirmed the killing of its members by the security operatives attached to the convoy of Cardona State Governor Nassir El-Rufai. Shi'aid leader Aliyu Umar alleged that six members were killed, nine people sustained various degrees of injuries by the security operatives while performing their weekly procession. Out for protest to remind all that our leader is still denying his rights.  And his convoy often fires on us in the presence of the Gomno, killing five people. And nine people we have seen. Aliyu claimed that the group is peaceful and low-abiding citizens, explaining that it will institute illegal action against the Cardona State Government. No, we are not blocking the road because everybody knows that we do our things in order and organize because we have our traffic that we used to clear the road. Therefore we don't block anybody's roads. We didn't block the roads. We are going to take legal action. That's what we are.


Hello and welcome to the Monday market update with me Dave Madden. Today's date is Monday the 19th of November 2018 And the time is just gone 1125 GMD We've had a positive session in Asia overnight I want to see the positive positive start to the European session this week. There are several factors going on It's pretty much a continuation of what we've done last week uncertainty around Brexit uncertainty around The U.S.-China trade relationship and also certainly in relation to the Italian budget Theresa May is still in in a It's still in the Prime Minister ship roll Adults she appears to be on on shake ground, but there's little kind of speculation circulating in relation to a leadership bid But what once again For the time being it clears that this may is going to be staying in number 10 Dallas Street for the near term In relation to the ongoing trade negotiations between the U.S. and China tension there's still a bit on the high side No kind of further Resolution to that but later this month China and the United States will be sitting down to have this have a discussion relation to trade at the GS over 20 G summer 20 on top of that the The administration in Rome it only a few tweaks to their proposed budget deficit proposed Budget plans for 2019 which were forwarded to the European Union Another bold effect to be is in buses called whether they actually want to press ahead and actually find the Italian government for essentially breaking the rules in relation to running budget deficits or increasing their budget deficit That's also playing on a veteran's minds even though all of these issues really haven't actually kind of dented They're sensitive this morning These are all issues that are kind of bubbling in the background to be fair We haven't had much actual progress from these issues in the last number of sessions So it's impacted the stock market so far, but it is looming over at the markets So I do now take a look at some of the major markets and see how things are playing out Starting off with the first 100. I'm a tension looking at a weekly chart on the first 100 Because I want to discuss this red line here at the 200 week moving average as you can see here The two week moving average actually a decent support Back here and back in March at the beginning of this year and even though it has traded below it in recently a Few weeks ago that should move back above it and we're still holding above the two week moving average Which comes to play at 69 at 65 While we hold north of that line Of the other metric is likely we could see the at the market push on higher from here And if it does we could be looking any upwards this area here at 7,220 or 7,250 The 200 week moving average is important because as as doubt theory tells you The averages must confirm each other and so we also be keeping an eye on the two week moving average for the DAX to your market As you can see here, this is the weekly chart on the Germany 30 the DAX Look this red line here is the 200 week moving average as you can see here It's really below it trade up above it and the recent sessions that should start training back below it again So it is a bit of a negative sign that the DAX is below is to the week moving average We also have the keep money at the foot 200 just above it's to move the average So the average is kind of you know, I call it to doubt theory should be from each other If both markets are above their respective two week moving averages You can be more confident markets gonna bounce back if both are below you can be more confident We're gonna see further losses, but if one's above the ones below it was just investors are a bit uncertain While we were in below the 200 week moving average on the DAX it is likely we could see further losses from here And if you do see the market fall off from here We could be looking any back down towards the October lows or perhaps even down as as low as the 11,000 Take a look at this this this chart here We could see we've seen a nice assess a nice series of lower highs all along here We could draw a trend line resistance Along here at actually a dude on a daily chart Actually because more clear if you take a line from the high in June to the high in July to the high in September We can see a nice series of lower highs. So DAX is firmly in It's our trend if you do manage to press on our here we could be looking heading up towards the kind of 12,000 mark actually the 12,000 mark would be there. They're about where the potential or the potential for Resistance when I should come to play so and he moves to the upside in the end in the DAX may run to resistance at 12,000 and if you can see continuation of the recent downward trend that we've been in we can really carry that down towards 11,000 Taking a look now at the American markets, which are in far better shape starting off the Dow Jones Take a look here in the daily chart I've drawn low between the lows of February March April May if you get this trend line long here and notice It has a fairly decent It's been well respected Try 2018 granted. We did have when the market it didn't have an aggressive sell-off in October It did actually try to blow it but notice. I didn't actually manage to put They the following the following session it didn't manage to actually close above it and since then the market as Has a decent of bounce back the market of this valley here give back some of the ground that lot It gave back some of the ground it made but it's back above this red line here to the day moving average Which comes into play at 25,123? It's looking while it holds above this trend line things are looking We could see for the gains we made that will be an optimistic sign While we hold above this red line here at the two day moving average that that also be an optimistic sign So if you press on higher from here, if you were looking at retesting the August highs So you have the October highs rather this high here Which comes to play at 26,278 and then if you go beyond that we'd be good looking at it towards Near HD 27,000 mark, which was a record high That was a set back in October if the market doesn't want to turn over on something yet yet again And we fall back blows in the 25,000 mark support might come into play from this trend line here That would be going to play in around 24,530 550 regions some in around here and a break below that Good point of further losses as I could take us back down towards the psychology important 24,000 level But speaking of the the averages must confirm each other And I'll talk about the trend line support with the play on the SP 500 and as we've as we just discussed Try line support is coming to play on the Dow Jones And if you draw a low between the lows of the SMB hundred of the lows of February 2016 with the lows of November 2016 we get this trend line here and we can see it was actually kind of almost like perfectly respected back in Late October when we had the fairly aggressive market set off So the market bounce right off that trend line there So we can take that as a positive sign that we're we've held above the trend line and while the SMB 500 holds above its trend line support and the Dow Jones holds above its channel support We can be more confident both markets are going to move on higher So service duration will provide the market bounce off the trend line support a rallied Rallyed higher pull back some of the ground that lost Between September and October. It's managed to give back some of those gains And of course you were back below the two-day moving average on the S&P 500 The dirty movie average this red line here, which comes to play at 27,000. Sorry 2764 we're back below that but we are holding above the psychology important 2700 mark so While we hold north of the trend line support It's likely we could see further we could see the wide ruffle trend continue But also it would that'll be it would be helpful every helpful if the Dow Jones were to remain above this 200 Above this channel support as well So at the S&P 500 does plan to push on higher from here But you'll be looking at retesting the recent line which basically kind of almost runs perfectly into this the 100 day moving average at 2822 so actually it's fairly decent positions if you press on higher above that you can be looking headed towards this level here We did the load here of mid-september which come to play at 2866 and then if you go beyond that we can be looking at retesting the all-time highs in around the 2934 region And he moves to the downside should you break below the trend line support like that could point for the losses And then of course if you could be like a support come to play at 2600 and then a break below that could take us back down towards the the February lows which come to play in a 2532 look now what's going on in the commodity space taking a look at With the gold market so gold that I've already aggressive sell off between April and August and market has managed to bounce back Some of the ground but it's been a bit shaky recently because it's been a fairly strong inverse relationship between the gold market and the US dollar So that's what the gold market is appears to be kind of trying to have another push hired another push out of us Another push higher, and if it does match to push out higher from here We keep looking in retesting the late October high of 1243 and if we go beyond that we can look ahead towards this metric here 1265 should we turn lower again and It's a bit could be support might come into play in around this area here at 1200 and then a break below that could bring the Mid-Mid October low so the mid-September low of 1180 into play and a break below 1180 could take us back down towards 1160 The level not seen since the middle of August I'll now take a look at what's going on in the oil market starting off with Brent crude oil So Brent crude oil is at a fairly aggressive sell-off. I'd say the least For early October until now so it's been a huge sell-off all the way down here We have seen some of the ground Managed to actually be recouped and as the market's moving higher here We can notice on the on the MACD indicator. We can see that that negative into this folding So as the market's moving higher negative into this fall So we can be more confident that this that this kind of upward move is going to continue But you manage to press on higher from here We keep looking at the resistance coming to play in around the $69 in mark area here or the 70 mine $70 per barrel mark in around here And if you go beyond that the next year to keep in our for will be this red line here at the 200 day moving average at 64 spot 14 and notice our active resistance In early November and also actors for decent support back in early August so if a metric Or a level has been important in the past it makes it all the more likely it will be important again in the future Although there are no guarantees if market does turn over on itself again. It takes out that yeah takes out the the lows in earlier early November 64 spot 63 recouping any back down towards 60 63 spot 32 Back down towards this area here 62 62 dollars per barrel for for Brentford all Take a look now at WTI WTI is even is in even worship Then then Brentford so once again the 30 aggressive sell-off notice how in a trader he traded traded lower It traded below that the utility moving average this red line here And then I'm actually gonna bounce back up into it acting as resistance And I was only the kind of them the lower high before another aggressive move to the downside so The market is kind of creeping creeping higher here if you do see the market getting to push out higher It can run into resistance in around 60 dollars a barrel that if you go beyond that is 62 50 may act as May act as resistance and then For beyond there we could be looking at the utility moving average at 67 spot 38 acting of resistance As I said previously on the Brentford chart if a metric is acted as a resistance and or support in the past It makes them more likely we could see it again in the future But once again if the market does turn over itself and take out the the recent lows The recent lows of 54 spots 73 we could be looking heading back down towards this area here 52 spot 53 and then if you go below that we could really head back towards $50 per barrel Take a look now Euro dollar So you're not at a fairly aggressive sell-off between April and August and I'm actually a bit of a decent enough come back Once again the kind of the power of the US dollar because that appears that they were going to have a rate rise in December And we could see some interest rent hikes in the Fed in 2019 coupled with Major uncertainty in relation to the potential standoff between Rome and Brussels over the Italian budgets at that spot pressure of the Euro in fact the Euro only last week fell back to a level that was last seen in June 2017 so given an indication of actually how much the market actually fell We had this set off last week. So it's it would appear that your daughter It's kind of falling back into the wider up wider downward trend Let's get that began back in April. If you do look to kind of continue to if you do look to Remain in the downward trend and should we take out the last week's low in on the kind of 112 kind of 15 regional But could be looking heading back down towards This area here in that one one spot 1110 And that if you go below that we could really head back down towards the 110 mark Anyway, to the upside may run it in resistance at this area here one spot 1510 or one spot 15 It actually varies decent support and resistance in the last few months So it makes it likely that we could see acting as resistance again in the near term Taking a look at a pound dollar. Obviously the British pound has been dragged around by the situation in relation to Brexit. So Traders are spending less time looking at the economic indicators of the UK Even though that's been pretty good and by and large they've been better than what we've seen of the eurozone But it's all the brexit uncertainty has been gonna have been dragon starting around I've taken a look here at the price action in the last few weeks We've seen a nice series of lower highs here I see that the high in November failed to take out the high in October and I have October failed to take out the High in September, so we're seeing a nice series of lower highs Although we're not necessarily seeing a series of lower lows But because the skew is to the downside and while we remain south of the kind of psychology important 130 mark Which comes into play in around here? We could see further losses on a pound dollar. I should we gonna push on lower from here We could make a target in the August low at one spot 26 10 And then if you go below that we could be looking any back down towards this area here at one spot 25 90 Any moves to the upside if you take out 130 we could make any back down for up towards the November high of spot of one spot 31 74 and then if you go beyond that we can really go towards the one spot 32 region I Take a quick look now at the week ahead and the week ahead can be found on a website if you go to the CBC markets calm and Under the news and analysis section. You'll find this article Is the week ahead article so looking ahead at the major corporate and economic events of this week So tomorrow we have easy jet out for your figures out Also tomorrow we have the UK inflation hearings hearing support also tomorrow on Tuesday, we have the Claysdale Yorkshire banking group have their funding numbers coming out tomorrow fairly busy the day tomorrow as we also have Best Buy and Target have quarterly numbers coming out on Wednesday. We are first-time figures from Babcock On Wednesday, we also have quality results from Sears on Friday. We have the flash manufacturing services PMI reports for Germany and for France and then a Friday We also have Canadian CPI and retail sales and as it is worth noting that Thursday coming up is a Thanksgiving in the US so we could so some US markets will be some US markets will be shot On top of that, we can see no very low volatility In basically global financial markets on Thursday, then also keep mind we view it we've the Black Friday It's a big day for retail in America So keep an eye on the US retail stocks and also European retail stocks as it become more popular on this side of the Atlantic It's also worth pointing out on our trading platform You keep up with kind of daily with daily updates and our intraday updates on the insights section section Which can be found here if you click on this market type here insights Other market pulse is a second option down and then also if the third option down is the chart forum Which is the section here whereby? Self and some of the other other analysts will have this to a screenshot of a particular chart by some commentary on it Invasion to production prices we could see in the future and it isn't just if anyone with an account can update chart form So even clients feel free to actually update that and we can actually interact and I have a discussion relation What do you think certain price action could be? That's it in terms of actual video before I go if you do have any comments you want to make on this video or any of the other videos So we have conducted here CMC markets, please feel free to leave a view on Google abuse. That's all for me to speak Thank you very much


We'll call them in to order. It's the Moretown Slate Board. It is Monday, July 15th. We've got a full board. We've got Sasha at the front of here as well. And we have one guest along with our TV crew, Mike Brown. So are you here for a general comment? Yes. All right. What would you have for us? I was here because Sharlene asked me a while ago if I was interested in becoming a Lister. And I met up with the Listers last week. And I'm going to try it out, at least until the end of the year when I have to decide if I want to run in the spring. So I'm here to be appointed for the interim period between now and the end of the year. Tell me why you're having an interest in it. What brought you here? I didn't really have an interest in it. I never thought I would have. But I'm a forester, so I deal with current youth a lot. I was in here talking to Sharlene about acreage discrepancy that I figured out. And she asked me if I was interested. And I went back and forth with the Listers for a while, both busy and just not with them. So I think Sharlene was very thinking I can bring some current youth knowledge to it and just have a general idea of the acreages and changes a lot. So I think that's great. And I know the Listers have passed on their mode of competence as well. I'm hoping you would seek this position. Yeah, so it's nice to find my experience pretty hectic and very flexible. So I think it seems like it'll work. Yeah, great. Good. Any other questions? Curious, are you a commercial forester or a state forester? So I'm a private forester. So I work for myself. So Lysis and Vermont are Hampshire. So I don't really work in Hampshire much, but pretty much from like Route 4 North. So up here in the wild all in the North Kingdom is where I spend most of my time, so. All right, well, I'm gonna move to a point like ground for ground. Bake in Lister position. In a second. On 3rd or 4th eye. That's 3rd eye. Welcome to the world. Yeah, you're on board. Thank you very much for taking the opportunity to come in and we look forward to working with you. Mike and Debra are great. And with your expertise, you can only help elevate kind of what we do there in town. Great. Thank you very much. Thanks a lot, everybody. Yeah. Do you agree? Yeah. You're welcome to stay for the rest of the meeting if you wish. Yeah, I've got two small kids. Yeah. I think I'll stop this morning. I thought everyone would just stay for a couple of minutes. We just wanted to confirm. This is fine. This is fine. Thank you. Thanks, guys. Have a good night. Looks like everyone else is enjoying their evening. How was it, I guess? So let's move ahead. Stir. Sasha, you got the reports, communications, for us, don't you? The only thing I have is Robin Herbick on South Hill called and actually, she stopped in. She's got a concern with a drain pipe by her driveway. What was it? Robin Herbick? Herbick, yep, H-E-R-B-I-C-K. It's at 1947. She was going to call down to the garage, too. Ray, when you're meeting with them, can you? Yeah, I was meeting with Martin this week. Yeah, and Martin's gone this week. Is that K-47 she said? Yeah. And just what she said, the culvert she was concerned of? The drain pipe? Well, that's the only thing I can think of, the culvert. Oh, yeah, that's the culvert. Check in with them and see what's up. I think she's on the top right at the corner.  Jason, do you have anything for us? Yes. First, we were talking about the road and bridge standards. The question came up of, so what's the story with Class 4 of non-hydrologically connected roads? And it turns out that many of our Class 4 roads are not hydrologically connected. That's not true. Let me just interrupt you. We have that on the agenda, the road, board, bridge standards. Okay. We've got no business. Why don't we save that for sure? Good night. Let's say, I don't know when it's appropriate to bring up any of this stuff, so let me know if this is a matter or not.  And I just wanted to mention that because she raises a good point that there's also something I wanted to bring up a caution about. So, I didn't see her. I didn't see her. Oh, okay. So, what you wrote is, as a customer of consolidated, she is very dissatisfied with new offerings and they really have no intention, as far as we know, bringing fiber to their territory in Moortown. And that is not a big thing. And she appreciates the town's way in and I don't want to speak to her, but she's surely like if some other party would bring a fiber to the area. And okay, that's all well and good. John, you probably remember when we went and talked to Weatsville Telecom, there was an issue with inviting another company into their territory because they have been making investments. So, we don't want to discourage the companies that have been doing what they should by making it less and more remunerative for putting money into their territory. So, I just wanted to bring up that trade-off and there may be some way of dealing with trying to push that in areas where investments have not been made. Could I help me ask, and maybe if someone understood what you know, how far does Weatsville Telecom go up the mountain? I think that I'm the last one. On that, and actually, I think, Brian House actually is last. So, horns and us, from horns and us. So, you don't have to do that? I saw the communication that it's all full, it's just all full. And that's why Chuck Burr was in here. So, I guess he has, I saw it. I don't know that it kind of counts as any matter in there. I don't think it's an option. I think that's all the options for that. No, no, no, there are three companies covering different areas of work down. Oh, it's being in a different place. I have no complaints about work-ass. You do work-ass? Yep, they do work-ass. What do they provide for you to work-ass? I'm glad because I've heard Yeah, can we be an internet server? I've read out what their, whatever, do you have a fiber or do you know what maximum revenue you get? I think that, yeah. I know that we spend a lot of time cooking on our computer at the same time and we never have a problem. Okay, that's good to know at least on the end that has that, the consolidating, so it's an issue. So the question is, I'm just freezing it, something to keep in mind, how to help the folks on consolidating without messing up the business model for the companies that are doing well for us. Right, yeah. Well, maybe that's where, you know, I might do, I seem to talk with Waze here and see if they can have any ambitions or thoughts of going anywhere else in town. Yeah, you know, I would start there. I'm not sure if there were one or two, but they would know. Right, they would know and if they're not allowed to, why not, and you know, let's figure out if you can't, I mean, I think, so again, you start pushing one, so I don't see it, and if they may not want these guys coming in, it's all of a sudden consolidating, like I say, you know what, let's throw in five out there. Why don't we, we should invite Waze Field Cable, you know, Waze Field Cable in one, I think, just to thank them for what they've done. I mean, I think, again, it's their business, and they're making money, obviously, but they're also active, they've provided five or four, you know, 450 homes in more town than they have in any of the other areas. So, I mean, it would be good to have an enemy for feminists, same thing for that, but also asking if we can work with them going other places in town. I know last year when you guys wanted them to come in, they said thanks, but no thanks, you can come see us. Right, yeah, just so you know, I don't know if they'll come to a meeting. Well, they may, I mean, not happen. You know, if we don't reach out, if they don't want to, maybe we will reach out to them. Me too, right. So, Sergeant, we can talk about that, if you know who to send it to, or let's do that, and then we'll, we'll plan on it in the next couple of months, try to have someone in here from Waze Field Cable, just to, you know, find out about what to do with it. Yeah, now what about that truck was pushing? Yeah, you know, I get another email actually from Jeremy. Is that who it was pushing out from Northfield? Karen Horne's post list referenced that. Yeah, that's her camera. Yeah, yeah. What was the name of that? C. C. Central Vermont. Vermont, something. Yeah, okay, yeah. So in the last week and a half, I just reconnected with him anyway, so I'm gonna bring that up. We haven't actually talked about it yet. Not anyone's post or anything, but we have already in the last week and a half connected with Jeremy. Yeah, that sounds right. Jeremy, that's it. That's it. So if they're able to do anything for us, we'd like to know too, the issue there is not breaking other things that are working for us. Right. So they reached out and they're working. So we have to get that together as well. Any other questions? When would you like to hear about what happened at the last clients community? Right now, it's good time. Okay. Unfortunately, I forgot the copy of the minutes and left them in the printer. So John and I, I think, we'll be able to figure out what we said, but one of the items we wanted to tell the select board is our next task is taking a look at how a longer term capital needs and taking a look at what that means for the town's cash flow over the next several years. And as a result, what we should do to support those needs. So that means that we're gonna start off by taking a closer look at the stuff that I do in kind of a rush for the capital, the capital report in the town's board. And if you favor taking a look at that, you may have noticed that the outdoors are kind of scary or some large needs that we'll have to deal with at some point. And then the question that comes to me, we wanna try to even out the town's cash flow over that timeframe. And that in turn, we're interested into the tax rate discussion that will probably be not this year because we haven't done the homework in the time to make any changes to the tax rate that we're sending out. But the next time, do we wanna talk in terms of a sustainable, fairly consistent tax rate that deals with our out-year needs? And that would be a long overdue to do that. So if that was one of the items, it means that there was another one in terms of where it was. No, that certainly was the biggest. That was the biggest. That was the biggest. Well, what else did we wanna do to help do what we did? We also discussed bringing it on about to the Parasets back in the city. Oh, that's what the truth was about. Yes, but not interest. Right. Not interest, right. But yeah, that was it. Yeah. Thank you. Thank you. Just 2% on... I don't know if you remember where we were. Well, specifically, we paid out money for the truck. And we definitely stated that we were going to pay back capital reserves. Sorry. No? Same thing as reserves are saved. So we stated that we definitely intend to pay that back over three years, so we didn't say anything about an additional 2% which would still be the savings to the general fund. Okay. So that way we retain the use of the savings reserve on the future by keeping it replenished. So that was the finance review to meet this recommendation on that. So we're just passing it on to the select board. All right. Now, why don't you... When you bring the minutes, we'll talk about that again, but probably it's a good idea to charge the 2%. It was the 2% on the capital reserve fund. I thought we said with a truck. Wasn't it the capital reserve fund paying ourselves back, not on the savings reserve fund? Oh, right, right. Yeah, that's right. Yeah, yeah. Okay, I knew it was mixing that up. Put in the 2% into the capital reserve fund. Yeah. Okay. It was the one we used for the truck which is the capital reserve fund, yes. We're all saving the savings reserve fund. Right. I think that was it. Right, you haven't even purchased communications. Well, I did meet with Steve McGill. We talked about the curb cut. He wanted to make it clear that he never really intended to ask the board to move the curb cut. He was more concerned about the process of not being notified when that was happening. And plus the curb cut application, for some reason had one mile from the road, which it's only four kets in a mile from the intersection of Jumper Road. But basically, he wanted to, if he's not angry, he's not angry at neighbors who wants to be the neighbor. The Japanese was angry wherever it is, not. I think he did talk to Sean a little bit about that. There was a little bit, he sprayed it. I think things are good up there. I mean, as good as they will get, I guess. Val, thanks for the really chatting with him anyway, making me find out what's going on. Did you have a chance to find out if anyone working from the time is certified to deal with that? I did not, yeah, with a small amount. I mean, I know he could buy this stuff around the store or something. I was not able to catch up with Martin about anything. That's it. Come on. Got nothing. Got nothing, come on.  Bad enough that people are going around it and that is kind of a blind spot in places. So on the, how much is that? Yeah, after it goes to dirt and pavement to dirt. I mean, in the cave or in the dirt. So if we both try to tackle that way with someone down at the gorge, maybe we'll get that done. Yeah, I'll probably remember to call somebody in the morning to please leave a message. We'll get that saved up there when it's available. Anything else, John? No, that's it. All right, I feel like why are we... Charlene, did you have anything for a general public comment at all or are you just here for the tax rate and such? Tax rate? All right. Why don't we go ahead and prove the minutes for July 1st? Anyone have any changes? Sasha, a nice job on those. Mm-hmm. Motion's on these minutes. How many do you accept the minutes of 7-1, actually? Sorry, thank you, Kelly. And you have further discussion or changes or additions? No? All in favor of the minutes? Would I? All right. Thank you. All right, so let's go ahead, talk from the tax rate. Charlene, why don't you... Well, I'm not going to talk to you as well. I think I'll turn off my coffee. Should be right in your... Should be in your class. All right. By the way, were you able to open up your email right in here? Yes, thank you very much. I appreciate that. I'm doing a... I don't know what's on my stop, right? Oh. Yeah. So, all right. So thank you for putting this together. Holds, Charlene. Is that your work promise? Is that what Charlene said? Yeah, I did it. And then she came out just to make sure that what I did was the same. Yeah. Pardon me. Any questions? Anybody? Did anyone have an opportunity to look at the email? I know John wanted that. I hope to thank you, John, for making sure. That was something. It is nice to see that the town tax rate is really right down to where we were last year. Yeah, it is. The difference is the school went up about five cents. Yep. A couple of observations on that. First is the grand list is up 4% of them. And the base budget request is up 7.5%. Show you what the grand list would do. Yeah. And to tour our listers and everyone that's keeping that stuff up to date and the group that's doing it. That's what really helps that grand list. And I think it's well worth the money that we've spent to keep that in the hands of who is it in right now at this point. I agree. And certainly with the listers working on it. One other thing I just wanted to ask everyone, particularly Charlene, is there anything we're not thinking of to include the rate because we've gotten a bit wants on that. I asked Cheryl the same thing and I kept thinking anything, not when I couldn't find anything and neither could she. I don't see anything, right? No, I just appreciate that everyone. Staying in a double look to see all right, that's what we're not doing. And the grant need I just wanted to point out that that's money that's still owed to us for the amount and revenue that we're supposed to be in this year. I talked to Dean Currier about it. It's in the process right now. Yes, we talked about adding interest to the money that we borrowed to the capital reserve. Is that in here anywhere? Or is that something we should think about in here? That's what they're working on for next year. That's what Jason was talking about. That would be included in next year. Okay. That's right. Yeah, for proof, but. Yeah, one thing we don't have any authority on. So that waits for the 2020 budget. There's doubt that's possible. What? That doesn't mean anything to Jason, but you just don't know how much to take and what to do. I think is what they said. Honestly, I can't believe it. No, for the 2%, we do know how much that is, but we don't have to worry about it. And it's difficult to do it yet. Yeah, that's a matter of fact for the, you know, once you get a kind of administrator and select board assistant, you know, that has gone from 50 hours down to nine, it's out of me. So this, you know, we have quite a bit of money there, but Charlene said it could be just as well because we may be overspending a couple of wineminds in other areas. And in the Revenant here too, this is based on right now, it starts with the streets of Town Hall, this is all going to go up too. This is just based on right now figures. Is posting the tax maps going to have any impact on the revenue number? No, and what we thought was going to happen with that isn't going to happen to the extremes anyway. But they have to us it on for right now. Your rates are changing. They just changed. Yeah, so the per page of $10 went to $15, but instead of $1 going into the preservation fund, $4 goes into it, but it's still being creased by $2 for the courts fee. So we're still going to be ahead of the game. Can we just take a quick review of the particular one items that were over? Do we have to add anything for any of those? We don't think so, but it's just... Yeah, we kind of did add, we did put all that in there. In general, I kind of remember this the other day when we came in here, I was going to come down just a few things and being at some town office is over by $1,200. And that was the sign. Now, painting the town halls. Yeah, okay, there too. The town hall, the painting is over by $4,000. Over by $4,000. The library is over by $30 on printing and optimizing. We're really not finding a whole big... It's on a million dollar budget. Right. We're off for $2,000, so I think we're doing pretty well. It's been a little over on the general town expenses by $400. So I guess my question is, do we want to add the $4,000 for the town hall to the tax rates or not impacting other lines or are we definitely good? I think it's a good season to cover that because truthfully, I usually bring in like over $20,000. But anyway, I don't think... Sounds good. Yeah. Yeah, where's... Yeah, I can hold you on. Okay. Yeah. We're gonna end here. Great. Any other questions on the tax rate? Yes. That's pretty good. Callan, how are you doing? That's me, all right. You understand it? Here's my message. Okay. I don't know if I want to discuss with this item. I hope it's just gonna pass it out to Tom, is that what I have? Sure. I don't know. Well, I'm back on you. The bin was on that. Yeah, well, we're on that. Yeah. As far as the tax rate, let's see if we can use it enough. So we get it enough. It's in there that we need a lot of the discretionary that we put it in. But that's a good question, just in case. If there are no other questions, I move to accept the tax rate of $0.439 cents as our municipal tax rate. Second. Any further discussion on that? All in favor of a aye? Aye. Aye. Good job. Good job. Good job, ladies. Good job, ladies. Thanks, Tom. Thank you. Before you move on to the next one, I know that they'd be inside of it. You're finalizing the road and bridge standards that's coming up. I just wanted to make a note on that, unless you need me to stay for something else. No, put it in the news. Sasha has, did you bring up? Yeah. The state of Vermont is asking us to accept their codes and standards. And I just wanted to point out, whether you go yay or nay, whichever way, that I did reach out to Dan Currier and asked him what our repercussions would be. That's not only on that. Yes, that's to Eno. And I just wanted to point out that Eno's in there so that I don't make up your mind because in setting the tax rate, this grant in aid is like one of the new rules. So I just wanted to point that out. We were not considering not agreeing to this specific stuff on that list. We were still discussing some of the other items, not the state does not hold anything from us. Hey, we can, we're ready to hold business right now. So we can go ahead and go ahead and discuss that. Here we go, here we go, here's what I think. One of the categories that the state doesn't make us to do and no repercussions that I'm aware of for not doing is plus four roads are divided into hydrologically connected and non-hydrologically connected. And Moortown is so wet that at first we thought there was a good chance that almost everything was hydrologically connected. So I checked into that and in fact it's not this. So if you take a look, I'm sorry about how close the colors are, I wouldn't choose that. The purple is the hydrologically connected and this stuff. Yeah, and the rest, the ones that are not colored that are not. So we have a few roads that are not connected and therefore we can meet state standards by excluding those from the road to bridge standards. What would be the point of that? It will cost us less money. How much, don't know, but it would be a good section of the road that we would not have to meet standards on. The purple is connected so the non-purple plus fours, they have to match that, they'll be mapped upon the wall. But I don't see any reason to extend the standards to the non-hydrologically connected plus four roads. If anyone can think of a reason that we should, you know, I can't. Does anybody know, if there's damage on a road from a storm, if we say nine hydrologically connected, is there a difference in what we would get reimbursed from where it was? It looked like we couldn't get a straight answer from anybody on that one. Yeah, it sounds like if you've got a maintenance plan for structural damage. Yeah. Then, and I think we'll have a general maintenance for a class four road, as long as you have the road right. As long as you have it, as far as I know, it sounds like FEMA would pay for that. Does not help anybody else read it? That's kind of what I got out of it as well, but I'm not that. A and a T were saying that we can't speak for FEMA, so right, it is what I'm doing. So one thing is that, put frankly, none of those roads are up to the standard that they're supposed to be connected. We can all help each other in the eye and say that. We have our own, I think we've adopted the state standards on mobile, but then you talk to Martin more. We have a policy for class four A, class four B, whatever. So not sure how that fits in with the standards, per se. I don't know, it seems like to me, I don't know what the price difference is, but we're gonna do that half a road this way. Why not just have them all one standard, but I guess I don't know the exact price of doing that. And whether that is, I mean, the way I look at this, if I'm looking at this right, this is the road that we built last year, the Lynch Hill, I believe it was right there, right? So that's not, according to your map, not hydrologically effective, but when you put, and it's a pretty steep hill, we put a lot of money in that hill. And that's probably the highest standard class four road we have. So, I think we should say it's hydrologically connected. I wouldn't say that that is, I would very much say that there's a lot of water to get out of the road down the hill, so. Yeah, but we're only obligated on the ones that A and R says, not the ones that we think of.  Great things made here. That's something on a long piece of land, you know? Yeah. And I don't know. Yeah, so if we ever want to maintain a piece of road to a standard higher than what we have agreed to, nothing stops us. I just don't want to commit to anything that is to sorrow. Get some dinner on that, all right? Yeah. All right. All right. All right. I understand what you're saying, Jason, but I also don't want to be caught in that. So I'm kind of a, you know, with the state, and I'm saying, well, this is non-hydro, hydrologically connected, and this is, and what the standard is, and I'm not sure if we're doing anything more or less to either of those roads at this point as far as what standard we're using. I think, and I think there's a lot of race in, I think we're better off signing on to the both of you, and John, I mean, I've been reading it, and you know. Yeah, I mean, I think that, I think we should just include the both. Well, I mean, the thing we commit to can cost us money in the future. That's the only point here. This comes up on a yearly basis that we do this. You're, the town has its own codes and standards. They want us to adopt the state codes and standards. So that, this is, excuse me, I think this is new. This is new. And this is something that, if you were to ask me, OCT is expected to cost town's money. And we need to have this body out of the first trend. Now, it's still going to cost us money, just agreeing to what they want us to agree to, but we're certainly going to do that. I'm just saying don't extend it beyond what they're asking us to agree to. So I was just guessing here, I'm gonna say 50% of our roads are- That's roughly what it looks like. 50%. So the only savings are the only differences for that last 16, 52 miles of past our roads, 16 miles. Yes. I, you know, I don't like spending more money than I have to, but I can't imagine that that 16 miles is gonna be that much of a problem. We just did it all at one standard. I mean, you're maybe just inventing to bring it up to that standard as well. In the event of a disaster, yes. You think so, right? So I'm just going to have it, that's right. But what I don't know is how much agreeing to this costs us a lot. We've heard of questions that will cost a lot, but I have no idea what it was. It could cost us, it could save us a lot. It's like if we lose our grant needs, and that's the cost of money too, but it's like I hear it exchange. Yeah, I mean, there's no question about agreeing to the stuff that costs our grants. Right. It's done to you. Yup. You do it. Mm-hmm. And that's the gradient. Where's the gradient area here? Or? Right. Well, it's on the gradient. It's plus four non-hydrologically connected. It's a five. I'm not sure of this. According to that, and it's according to Amos, Matt. Right. I'm just gonna have you say, all right, I don't know. Well, this is just a printout. I'm not sure what you're talking about. I got it. Yeah. Somewhere, someone must hang up at these points. Well, Linchill was how long of Linchill was it, they'd be on county miles, or a mile? It's probably a mile. And it was about $10,000. Right. So they're assured. I mean, to make it past the standards of hydrologically connected roads, that was the grant last year, right? To make sure Linchill had to do, though. Same. It doesn't look like it had to do, though. Right. It means some tear bubbles. Okay, so our equivalent of every mile plus the same as Linchill, which is unlikely, the 16 miles would cost it something like $60,000. Right. Well, we all, as you know, I'm alluded to it, this whole road here is not as in good shape as that, but it's great to hear. So. Mm-hmm. I don't know. How many Linchills are worse in this area? Oh, there we are, like so. It's just, unfortunately, most of our 32 miles required a lot to get to that level. Yeah. That's a problem, I think, then. Mm-hmm. We're not even talking about plus three yet. Yeah. Plus four. But there, we're gonna have a choice of one. All right, guys, what do you want to do, please? Yeah, tell us, I'm just gonna get this. Yeah, I'll get that, that's all right. Right. This almost looks like that's John Hill. No, no. Sorry, sorry. About the point of this year? Yeah, that's all right. I just want to see if this is one. So, that's out of the classroom road. That road is classroom road, I believe. And we know at least this much of this road is classroom road. Because there's, you know, this is Herringbrook. And it's all right there in classroom, so. This is Dona Berke road. It's cutting down this class. I mean, we know that's class. So, looking at this, this does not look like an annual thing to me. It just looks like a once-and-done thing. So, this isn't a re-do next year. I guess, I suppose we could withdraw it.  Do you think, do we need to speak to someone else on this, do you think? Because my idea would be, we have another couple of Mondays is on the 29th, Monday of the 29th, people could get together for an hour, because also in that same time, I want to have the road through. Yeah, I mean. Yeah, that's a good idea. And then between now and then, he doesn't come in and get just more clarification on this so that we're not making an ill-fated decision here. All right, the broadside was on Jason, thank you for some good questions, Ray. Yes, thank you. Let's try to figure this out, either have some come in or try to delve into this a little bit more. It's just the deadline in a minute. Well, the deadline for the first place. Yeah, by the way, for the 29th, Monday of the 29th. This whole thing has come up with the Clean Water and the Wiredly Committee too, in that, pretty much for you, a creed that just about every world is like delighted to be connected.  So, I mean, I really don't know how accurate this map is. I think that it is probably not accurate, but I think it's how it's defining. So that's what we'll be committing to. Regardless of whether it's accurate or not. Yeah, I think that would be really helpful. I'm gonna ask face-to-face, I think you would clarify a lot of questions. I'm sure of this. Jason, you went and keep this map here. So, right, so the tax rate, now we have employee wages to discuss. And I think I'd like to do that in the executive session. So, it would be good if I were you. I were you, yeah, thank you, Sheryl. But before I do anything to have Sasha or myself contact Dan for the 29th. Either one of you two. Okay. Yeah, I'd like to have him come to our room so we can get that, let it sit. Just as a back-up in case Dan Carter can't make it, how do you feel that just put Jim on the phone sometimes? Yeah, that's fine. Yeah. A complex problem or something like that or if there's anyone else or, yeah. Well, I'll make you go ahead and make it. I'll make a question that we're going to do in the executive session. For the purpose of the appointment or an appointment for evaluation of a couple of dollars for employees to rise in the public body to make a final decision to hire or appoint a public officer and put in an open meeting to explain the reasons for its final decision during the opening.


Now Sudan's number two military commander Mohamed Hamdan Dagelo, also known as Handeti, has said that the October coup had failed, suggesting that he would intervene if Sudan is heading for the abyss. He said he had failed to bring about change in the country and that he would do so if Sudan is heading towards the abyss. Asked about a possible candidacy in the general elections promised by the new government headed by Army Chief General Abdel Fattah al-Boheni in July 2023, General Hamdan Dagelo refused to say as General Bohem did that he would not run.


Welcome to Episode 6 of our Math 1050 College Algebra class. I'm Dennis Allison of the Math Department at Utah Valley State College. This episode covers two major topics. First of all, we'll talk about quadratic functions, some important formulas related to quadratic functions, and we'll look at some useful applications that I think are rather interesting. Then we'll switch to another topic and talk about the algebra functions, and in particular the composition of two functions that becomes important for our next episode. Well, to begin with, let's look at what I mean by a quadratic function. If I have a function f of x of this form, let's say mx plus b, you remember in a previous episode we referred to this as a linear function. But if I have a function of this form where there's a second power involved, ax squared, I think I'll say plus bx plus c. Now, this is a quadratic expression, and we refer to this as a quadratic function. And quadratic functions have graphs that are, that are parabolas. Now, let's just take an example of a quadratic function that we've actually seen a couple episodes back. Suppose I wanted to graph this function f of x equals x minus two squared minus three. Now, you may recall that this is actually a transformation of the function f of x equals x squared. And f of x equals x squared has three target points. They were at, they were at zero, zero, one, one, and negative one, one. And once I plot those three target points then I can draw the graph by just drawing a parabola that goes through those points. But this is a, this is a transformed, this is a transformation of that fundamental graph. What are the changes that I make if I want to graph this, this function? Steven? You have to go to the right two and down three. Exactly. We're going to go to the right two because I've subtracted two directly from the x. And the minus three on the end says I need to go down three. So if I graph that one right here, let's see what I would do. Let's, let's put our scale on here first of all. This is the x-axis, this is the y-axis. So I'm going to take my origin and move it to a new position. I'm going to go over two, and I'm going to go down three. So over two, down three, this is my new origin right here. So that point corresponds to the original origin. And my target points say go over one and up one to the right. Go to the left one and up one. And so when I draw my graph, it looks like this. Now, you know, before I go too far on this, where will this function cross the y-axis? I'm going to use this space over here to find my y-intercept so that I can complete this graph. You may remember that to find the y-intercept, I let x be zero. So I'm going to let x be zero. That just means calculate f at zero. And when I plug in a zero there, I get negative two squared minus three. That's going to be four minus three or one. So this graph is going to cross the y-axis at one right there. And as it turns, so that's where I'll locate that point. And this is the graph of f. Now, while we're at it, where does it cross the x-axis? Who can tell us how to find the x-intercepts? In fact, first of all, let me ask you, how many x-intercepts does this seem to have? Two. Looks like it has two. You know, I bet there's one that's very small but positive. And there's another one over here that looks like it's bigger than three the way I've labeled it. But we don't know if my graph is perfectly accurate. Well, you remember, to find the y-intercept, we let x be zero. To find the x-intercepts, I'm going to let y be zero. Now, I'm going to need a little more space for that. So let me just erase all of this on the right-hand side. And I'm going to let y be zero. And y is the same thing as the f of x, so I'm going to let f of x be zero. x minus two squared minus three. Now, one way to solve that would be to multiply this out and then either factor it or use the quadratic formula. I'll think I'll use the idea of completing the square. I'm going to add three to both sides. Let's see, that should be a minus there. And then take a square root on both sides. And I'll take both the positive and the negative square root of three because I'm looking for every possible solution. That's what x minus two is. It's equal to plus or minus the square root of three. So x is equal to two plus or minus the square root of three. So I actually have two answers. One of them, I'll call it x number one, is two plus the square root of three. And the other one, x number two, is two minus the square root of three. Now, if you find the square root of three on your calculator, I think you'll see that the square root of three is about 1.7. So x one here is about two plus 1.7, which makes that 3.7. So when I said the x-intercept was a little bit larger than three, that's fairly accurate. That's about 3.7 right here. The other number we said should be positive, but pretty close to zero. Let's just see. If I substitute in 1.7, an approximation of the square root of three, that's two minus 1.7, and that is 0.3. Yes, so that number should be, well, right about there. I didn't draw my graph quite through it, but that's where it should have been. You know, the problem with the numbers like the square root of three is these are irrational numbers, and so as decimals, they extend indefinitely, and they have no pattern to them. So when you find the square root of three on your calculator, you really don't find it exactly. You find it out to maybe eight or ten decimal places, but the last decimal place is rounded off. And this number goes on forever, and there's no pattern. So who knows what would be the next digit after the digit you see on your calculator. So it's a lot easier to just call it the square root of three, and that's considered exact as opposed to using a 1.7, which is an approximation. It's just that when I go to actually plot a number, I need to have something more than this, so I did use the approximation in that case. Okay, well, with that idea, let's consider a quadratic function, and let's see if we can just guess where its vertex lies without actually drawing the graph. Oh, by the way, the word vertex, I'm using the word vertex here, in the graph that I just drew, you remember we said we went over two, and we went down to negative three, and I located that lowest point before I drew this parabola. This lowest point, this point where the parabola turns round, that's the vertex. It comes from Greek, it has a Greek origin. So finding the vertex means to find the lowest or the highest point on a parabola. If the parabola is inverted, it would be the highest point. Okay, let's take this function. I'm going to call this function p of x, because it's a polynomial, a quadratic function is a polynomial. p of x is equal to two times x plus four squared minus one. Now, if I were going to graph this, I would shift it four units to the left, and I would shift it one unit down, and what does the two do to the graph? Stretches it vertically. That's going to be a stretch. Yes, we're going to stretch the target points up above the horizontal line through the new origin. So that says that if I were to move, let me draw that a little better, if I were to move from the origin over four to the left, and down one, what would be the coordinates of the vertex? Susan? I actually have a question. Oh, okay. Why are you moving it four to the left and not four to the right? You see, if you add a four directly on the x, then you move it in a negative direction. Now, if I had added four on the outside, I would move it straight up. I'd move it in a positive direction vertically, but it's a little tricky when you add a four directly to a variable. It moves it in the opposite direction, so I go in the negative direction. Well, I guess the question is, where's the vertex? What are the coordinates of the vertex? Negative four and negative one. Negative four and negative one. So the vertex, I'll call it point V, is at negative four, negative one. And you know, I really didn't have to draw this graph over here. I could have gotten that information directly from the equation. So I'll do one more like this. Suppose I have the quadratic function f of x equals negative one-half times x plus two squared plus five. Where's the vertex of this quadratic function, of this parabola? Sam, what would you say? I'm not sure. Okay, Matt, what would you say? Where's the vertex? Let's see, vertex would be at negative two. Negative two, yeah. And positive five. Positive five, because see, that's a shifted up five units. So if I go to the left two units, that puts me at negative two. And if I go up five units, that puts me at positive five. You notice this coefficient had nothing to do with the location of the vertex. But it does have an effect on the graph. The negative flips the parabola over and the one-half compresses it. So if I were going to move from this new origin where the vertex lies, I would go out one on either side and I would go down one-half because it's been compressed and it's been inverted. Okay, so if the quadratic function is given in this form where I have a binomial squared and a constant, this is sometimes called the standard form. I can just pick out what the coordinates of the vertex are. But suppose I have this situation. Let's say I have the quadratic function f of x equals x squared minus 6x plus, let's say plus eight. Well, this is a quadratic function. You notice it's in the form. It's in the standard form that I gave you earlier, ax squared plus bx plus c. It looks like a is equal to one, b is equal to negative six, and c is equal to eight. What's the vertex of this parabola? Well, I can't tell in this form, but if I complete the square and get it into that form, I think I could name the vertex. So I'm going to complete the square by separating the x's from the eight. Now, what number would I add right here to complete the square of that trinomial? Stephen, what would you put? 36. Wait, nine. Yeah, tell us the rule for deciding how to get a nine there. You take half of the middle coefficient and square it. Exactly. First of all, you have to have a one on the x squared. If there's a two on the x squared, I'd factor out a two, or somehow move it away from these terms. But there's a one there, so everything's fine. I take half of the coefficient of the middle term, half of negative six is negative three, and then Stephen said he squared it and then he got nine. Now, you may ask, well, gee, Dennis, can you just add a nine in the middle of a problem? Well, you can if you subtract the nine over there so that these two nines would cancel if you wanted to go back to the original problem. Of course, we don't want to go back there. I want to go forward because I want to write this as a binomial squared, and on the outside, I have a minus one. Well, now you notice this looks a lot like what I had up here. So I think I can name the vertex for the function little f. And the vertex is, let's say it's an ordered pair. What would you say it is, Lene? Three negative one. Three negative one, exactly, three negative one. So I found the vertex by completing the square. Let me do just one more of those since I think maybe a couple examples have to make that clear. This time I'm going to put a coefficient on the x squared. Let's call this function capital P of x, P for polynomial. And let's say this is 2x squared minus 14x plus 5. Okay, the question is, what's the vertex? So I'm going to complete the square. And first of all, I have to get my variables separated from the constant term 5 over here. And I'm not ready to take half the middle coefficient and square it because I have a coefficient on the x squared other than a 1. So I'm going to factor out a 2 right there. And that says x squared minus 7 in parentheses. There's a plus 5 over here. I'm not factoring a 2 out of the 5. The 2 is only being factored out of the 2 terms with x's in it. Now, I'll take half this coefficient and square it. Let's see, half of negative 7 is negative 7 over 2. And then I have to square it. And when I square it, I get 49 over 4. So the number I need to add on here is 49 over 4. So I have to counterbalance that by putting something on the other side, on the other side of the 5. Well, you know, I'm putting in not 49 over 4, I'm putting in 2 times 49 over 4. And if I double 49 over 4, I get 49 over 2. So what I've actually added in here is 49 over 2. So on the other side, I'm going to subtract 49 over 2. And if I factor this trinomial, this will be x. There's a minus in the middle. And if I take the square root of 49 over 4, I get 7 over 2. And the square of this binomial is the trinomial that you see right above it. Plus. Now, I need to simplify the two constants over here. Let's get them both over 2. 10 over 2 minus 49 over 2. So this is 2 times x minus 7 halves squared minus 39 over 2. Well, this is a little messier than the last problem because I have fractions in it, but we can still name the vertex.  This tells me I have to shift the graph to the right, 7 halves. This says I have to shift the graph down, 39 halves. So the vertex is at 7 over 2, negative 39 over 2. If you want, you could say 3 and a half, comma, negative 19 and a half. But I think it's more compact to write. These is what they call improper fractions right here. That's the vertex. Well, I've done two problems basically the same way. This one was a little bit longer because I had to contend with the coefficient of 2 there and also because I had fractions involved, makes it look a little bit more complicated. There's a shortcut to this process. Let's start over again, and I'm going to go through this procedure one more time, but I'm going to use variable coefficients. And I'll end up with a formula that'll save me all that work. Suppose we have the function f of x equals ax squared plus bx plus c. The only difference is now I'm using variables for the coefficients rather than particular coefficients. I'm going to complete the square in this expression. And so I have f of x equals the quantity ax squared plus bx and the c. I'll move to the outside, just like I did in the last example with the plus 5. What am I going to have to do before I decide what goes in this position? Factor out the a. Have to factor out the a, right. So if I factor out the a, just like in the previous example I factored out a 2, this will be x squared plus b over ax, and over here is plus c. You see, when you say factor out the a, that means you have to divide by a inside.  Well, this is looking a little nasty, but actually it works out rather nicely. If I take half of the b over a, I'll do that over here on the side, if I take half of b over a, I'm going to square that to put in the third position. Let's see, half of b over a is b over 2a, and when I square that, I get b squared over 4a squared. b squared over 4a squared. So I have to decide what to put on the right-hand side of c to balance that. Well, I'm not putting in just b squared over 4a squared, I'm putting in a times that, and a times that is, let's see, that a would cancel, that's b squared over 4a. So what I've actually added here is the product a times this rational expression, so I need to subtract that off, subtract off b squared over 4a. You notice that doesn't look exactly the same as what I put here, but it's because I'm replacing this product. Okay, let's use this space now to factor our trinomial. I have a times a quantity plus over here, c minus b squared over 4a. Let's see, can anyone tell me how you'd factor the trinomial? Stephen. x plus b over 2a. Yeah, x plus b over 2a.  You know, this looks a little bit like the quadratic formula, except in the quadratic formula, the discriminant under the square root is b squared minus 4ac, this is 4ac minus b squared, so it's similar. And also in the quadratic formula, everything's over 2a, this has everything over 4a. Well, my point is this, if I want to find the vertex, the vertex has first coordinate negative b over 2a. That's because this says in the opposite direction of the number b over 2a, because I have a plus right here, so I shift it to negative b over 2a. And to find the y-coordinate of the vertex, it would be the number, it would be the number over here. Now, rather than remembering that if you want, you can remember that formula, that's fine with me, but rather than remembering that formula, if I want to find the y-coordinate of the vertex, I just take the number that comes up here and substitute it back in for x, and I evaluate this expression at whatever that number is. So if you choose to remember this formula for the y-coordinate, that's fine, but I think it's easier personally to just take this, substitute it back into f. Let's work an example using this. I'm going to write down my formula right here, and I'll also write down this formula just in case somebody wants to use that at home. Let's see, the very first example I worked I think looked like this. I had the function f of x equals x squared minus 6x plus 8, and the formulas I'm using is that for the vertex there are two coordinates, an x and a y-coordinate. The x-coordinate is negative b over 2a. And the y-coordinate, what I suggested is you go back to the original function and you evaluate it at negative b over 2a. Now in a lot of textbooks the x-coordinate of the vertex is called h, so I'm going to put an h there, and the y-coordinate of the vertex is called k, so I'm going to put a k there. But as an alternative I said you could calculate a using the formula 4ac minus b squared over 4a, but somehow that seems sort of complicated but if you want to use that, you certainly can. Okay, let's draw a little line here and let's see how this works out. I need a value for a, I need a value for b, and I need a value for c. Let's see, Susan, what are the values of a, b and c in this problem? A is 1, b is negative 6, negative 6, and c is 8. C is 8. Yeah, you know my b looks a lot like a 6, so I hope you can see the difference there. If I calculate h, let's see, that's negative b over 2a, that's going to be negative, negative 6, which is 6, all over 2a, 2a is 2, and so I get a 3. h is 3. Now to get k, what I would do would be to take 3, substitute it into the original function, just plug in a 3, and I get 9 minus 18 plus 8. And that's 17 minus 18 is negative 1. So the vertex is at the point 3, negative 1, and I believe that's the same answer we got just a moment ago when we completed the square to find the vertex. Someone may say, could you work that to calculate k using your formula over here? Well, let's just try that and see. And I'm going to erase this space right here and see if I come up with a value for k. Okay, the formula says k is equal to 4ac minus b squared over 4a. So if I substitute in our numbers, so I have 4 times 1 times 8 minus negative 6 squared all over 4. And that's 32 minus 36 over 4. Let's see, that's negative 4 over 4 is negative 1, and that's exactly what we got over here was negative 1. So if you would like to remember that formula, that's fine. Or, the alternative is to substitute the h value into the function, and just calculate the function value there. Okay, now there are applications for this. You know, we're not just finding vertices just because we think they're fun to find, but there are actually applications for this in the real world. So let's go to the next graphic. This is a... Let's see, let's go to the next graphic for the garden problem. Yeah, this is a problem that we talked about last time when we were using a function to model a real-life situation. You remember in the last episode we described a property owner who planned to use 120 feet of fencing to construct a rectangular garden beside a garage. What would be the largest enclosed area if she enclosed all four sides? Now that's not exactly the way the problem was stated before. Imagine that I have 120 feet of fencing and let's say the fencing comes on a spool like this and let's say we're going to make a rectangular garden so that I have to fence all four sides. Then let's say I put x here and I put x here. How much fencing would be left over for the other two sides? I think it would be 120 minus 2x feet because I've used up 2x. Now I need to divide that by 2 because I'm going to put half there and half there so if I divide that by 2 then the length of each one of these sides is 60 minus x. So I'll put 60 minus x up here and 60 minus x down here. So the area of the garden we'll call it A of x is length times width. The length is 60 minus x and the width is x. And so the area is 60x minus x squared. Now let's see, for example, what if we said x was 10? Can anyone tell me what is the area of the garden when x is 10 if you plug in a 10 right there? 500? I think it would be 500. 10 here says 600 10 here says subtract off 100. It will be 500 square feet. But on the other hand, what if we say that we made this side 20? What would be the area of the garden? Well, if I put in a 20 there 60 times 20 is 1200 and 20 squared is 400. So we get a larger garden. It's 800 square feet. Well, this presents the question of what should I choose for x if I want to make the area of the garden as large as possible? What's the largest garden I can make? Well, to do that, I need to find where this quadratic function reaches its highest point. You say, does that reach a highest point? Well, this is a quadratic function and I have a negative on the square. So this is, if I graph this, it would be a parabola that opens down and that parabola has a highest point. Let's just see how that would go. Let's see the function that we had there was 60x minus x squared. Now I'm going to turn that around and call it minus x squared plus 60x and the negative right there this is a parabola that opens down. So if I graph this function the graph would look sort of like this more or less. And there's a highest point and this is the area axis, the vertical axis so there must be a maximum area right there. So if I could just determine that number, that would tell me the largest garden I could make. But that means I need to locate the vertex and see what is its y-coordinate. So what is the vertex of this parabola? Well quickly the way I could find the vertex is to take negative b over 2a to get h and then afterwards I'll calculate k.  Now that tells me the x-coordinate of the vertex. That says we should let x be 30 up here and we should let x be 30 to get the maximum area. And what is the maximum area? Well that would be the k-coordinate of the vertex, which is a at 30. And that, if I plug in a 30 over here that's minus 900 plus 1800 is 900 square feet. So if you want to make the largest possible rectangular garden the largest garden you can make is 900 square feet and you make this side be 30. By the way, what would be the length of the other side? If this is 30 what would this length be? 30. It would be 30 also. Yeah, because if x is 30 60 minus 30 is 30. In other words this is a square is what it is. Now you might say, Dennis you went all the way around the world to tell us something that we probably would have guessed intuitively that you make a square garden to get the biggest area. I agree, we did go a lot of trouble to verify that. Now let's change the problem and I think we get an answer that you wouldn't normally expect. And this is the problem that was actually posed in the last episode. The landowner is going to put the garden up next to the garage. You may remember this illustration. I'm going to, let's go to the next graphic and I think we'll see this on the screen. I'll be drawing this on my board at the same time. There's the garage. I make a rectangular garden and I come out x on top and I come out x on bottom to figure out what's the biggest possible garden we could make. Okay, let's come back to the green board and this time I'm going to put all the extra fencing on this side. And that was 120 minus 2x feet. Now the area of this garden is x times 120 minus 2x which is 120x minus 2x squared. Which is minus 2x squared plus 120x. Now I've arranged the terms in this form so I can pick out the a, the b and the c. C is zero. So to calculate the vertex h is negative b over 2a which is negative 120 over 2 times a which is negative 4, h is 30. It's the same number I had in the last problem. This should be 30 feet. This should be 30 feet. Now I could calculate k by substituting in 30 into the original function. I'll find a at 30 and let's use this form up here. If I plug in a 30, that'll be 30 times 120 minus 20 which is 30 times 60 which is 1,800 square feet. Let's see what was the answer before when we did the square? 900 square feet. Now we get 1,800 square feet. We actually double the area of the maximum area if we put the garden up against the garage wall. You see basically the reason for that is rather than having to fence from this side I could put all the fencing over here and now I'm making this twice as long. This ends up being 60 over here and 30 times 60 is 1,800. So I think now it comes in sort of holes and it says just put all the fencing on one side you can make it twice as long and so you get twice the area. Okay, another problem that we introduced last time was Galileo's problem of the projectile being thrown into a building. Let's go to the next graphic and we'll see that problem stated again. It says in the last episode a ball was tossed upward from the edge of a 240 foot building with a speed of 32 feet per second. How high will it go before it strikes the ground? Okay, let me illustrate that again. You probably remember me drawing something just like this. This building is 240 feet tall and right here we throw a ball up in the air we throw something up in the air so that it goes up, it reaches a maximum height and then it comes back down toward the ground. The question I ask now is how high will the ball go? When I first heard this problem when I was taking a mathematics course I thought that would be impossible. How can anyone know how high it'll go? I mean the thing is moving nobody's up there to see how high it'll go but we can actually do this with the fundamental formula that we introduced last time from Galileo that said h of t is minus 16 t squared plus v sub zero t plus h sub zero. If you take a course in physics you'll hear a lot more about this formula and you'll hear a lot more about Galileo. In this problem what was v sub zero? That was the initial speed. 32? 32 feet per second and what is h sub zero? 240. So this says h of t is minus 16 t squared plus 32 t plus 240. This is a quadratic function and I'm looking for the maximum height. It's a maximum because if I were to graph this this is a parabola that opens down because there's a negative on the square term. It opens down so it has a maximum height. So to find the maximum height I'll allocate the vertex. First I'll calculate h negative b over 2a which is negative 32 over 2 times negative 16. Let's see now that's negative 32 over negative 32 that's 1. Now h is the first coordinate so this represents time that would be 1 second. So after 1 second it's at the maximum height. Now what is the maximum height? I'll calculate k because k is the function value the function values give heights. I'll find h at 1. If you'd prefer to use that formula that we created 4ac minus b squared over 4a be my guest go ahead and use it but I think this is quicker.  Let's see this gives me 16 plus 240 is 256 feet that's how high the object goes. Now you might say Dennis if I go out get on top of a building 240 feet tall and if I can actually throw an object straight up with the initial speed of 32 feet per second will it actually go 256 feet high? Well you remember this function is a model and we haven't taken into account distance, wind, things like that so in a vacuum this is how high it should go in real life it may go just a little bit less than that but this is a fairly close approximation of how high it'll go if we could do this in a vacuum for example there's a vacuum on the moon there's no atmosphere on the moon then this should be accurate but on the moon I would change that negative 16 to a different negative number because the acceleration of gravity on the moon is different and that constant on the earth. Okay let's see let's go to the next topic here and that is the algebra of functions so we're going to shift gears we're going to leave quadratic functions now you know how to find the vertex of a quadratic function two ways you know that you can complete the square and write the quadratic function in standard form and pick out the h and the k or you can use the formula for each negative b over 2a and then calculate the k coordinate okay well the other topic today is the algebra of functions I'll just write that up here the algebra of functions and this is how you combine functions in various ways and this is related to sort of a preview of what's coming up in the next episode now suppose I have two functions let's say I have a function f of x equals two x minus three and I have a function g of x which is three x plus one and suppose I want to add these two functions together well if I add the two functions together I would get how many x's there I'd get five x and minus two exactly now this is this is a new function and if I wanted I suppose I could call it h of x although if I give a name like h that tells me nothing about where the function came from so instead of h I'm going to give this function a little bit more complicated name I'm going to call it the function f plus g I'll say that really fast because I'm thinking of this as a single symbol this is the function f plus g and it is the sum of f and g so it's sort of a natural name for it now the reason that's an improvement over saying h of x is because when I see h of x equals five x minus two this doesn't tell me anything about the history of the function it doesn't tell me how I arrived at it it just says it is this tells me about the moment whereas this statement tells me about how I got this function that I added two other functions this doesn't tell me what f and g are but it tells me that I added two functions to get it take for example your own name let's see we have here matt sievers matt sievers now matt is his is his given name but sievers is his family name that says that sort of in a historical context he comes from the sievers shall we say the tribe or the clan called sievers so it says a little bit about his history so matt's his own person but he belongs to a certain clan or tribe called the siever tribe probably the clan of his father because that's sort of the tradition in American culture anyway is to take your father's last name so this tells me a little bit about the history of the function that I've created here it was formed by taking f and g together suppose I were to say I'm thinking of a function I'm going to call it the function f minus g of x now this is a single function but it's name is f minus g it's a hyphenated name no actually it's not hyphenated that's a subtraction but sort of like people today have hyphenated names kind of think of it this way it's a single name what would you guess would be the rule for the function f minus g? negative x minus 4 negative x minus 4 yeah I think what steven was doing is he was subtracting those two in fact let me just fill in some details for that I think he was taking x minus 3 and he was subtracting 3x plus 1 and then he reduced that so he had 2x take away 3x is negative x and minus 3 minus 1 is minus 4 now you know sometimes I have students who say oh Dennis I see what you did you just distributed the x across the f minus g like f times x minus g times x well that's not really true because this isn't multiplication it's the function of x and we just define f minus g of x we define it to be f of x minus g of x but this was not multiplication because this is one function I'm taking a function of x and it just happens to look like multiplication but it's not that's not actually what's happening okay another situation I'm thinking of yet another function this function I'm going to call fg of x fg of x what do you think that means fg the product of the two functions it's the product yeah see when I write fg I'm thinking of multiplication so the new function I'm calling fg but it's basically f of x times g of x and if I multiply those together that would be 2x minus 3 times 3x plus 1 and that would be 6x squared minus 7x minus 3 so in this case I have the product of two linear functions as a quadratic function we could find the vertex for this but we don't want to do it so we'll leave it at the quadratic function would that be any different than if I had found f or rather gf of x the same thing by definition this would be g of x times f of x but when you multiply these in the reverse order you get the very same answer so it would still get 6x squared minus 7x minus 3 so technically I'm talking about two different functions that happen to have the same rule you can probably guess what's coming next we've just done the sum of two functions the difference of two functions the product of two functions f slash g of x yes I'm afraid you're right this is the ratio of the two functions this is going to be f of x on top and g of x on bottom so if I see f slash g it just means take the ratio of those two and that's going to be 2x minus 3 over 3x plus 1 what was the domain of the original function f all real numbers what was the domain of the original function g all real numbers but what's the domain of the function f slash g all numbers except for negative one third exactly because we can't divide by zero and this is zero if you put in a negative one third for x you get negative one plus one is zero so sometimes when you combine two functions and other functions you can have a domain that changes a restricted domain the domain of f slash g is all real numbers except negative one third in that case let's see here I'm going to draw a graph of a function that I hope will be fairly easy to read and I'm going to ask you some questions about it the graph of the function looks like this here's the x-axis here's three here's negative three I'm running out of room so I'll say that's two and this is negative two now suppose this function looks like this it goes diagonally up to this point that's the point negative two one then it goes diagonally down to this point that's it negative one and then it goes horizontally over to here and then it goes diagonally up right there okay that's that function I'm going to call f now I'm going to draw another function on top of this I'm going to make it dotted so we can tell the difference that function starts right here at negative three and it's dotted all the way over to there and then that function comes down at a 45 degree angle to two and then it goes horizontally so it's supposed to be right on the x-axis but I'll put it just above it so you can see it and it goes over to three I'm going to call that function g now just looking at that graph what would you say is f at one let's see now here's f at one f at one should be what number? negative one just looking at that graph what would you say at negative one I'm just picking negative one at random what is g? it looks like at negative one if I go up to g g at negative one is two does everyone agree? looking at that graph what would you say is f plus g at zero you say well Dennis you don't have the graph of f plus g here well f plus g is defined to be f at zero plus g at zero you remember that was the definition of f plus g at zero I'll take f at zero plus g at zero what is f at zero? negative one looks like that's negative one and what is g at zero? two g at zero is two so the answer is one f plus g at zero is one what would be g minus f at negative two let's see that would be g at negative two minus f at negative two one minus two let's see g at negative two g at negative two is how much did you say Eleni? two this one is two minus what is f at negative two f at negative two is one so I get one there also both these answers turned out to be one I didn't know that was going to happen let me ask you one more question what would be f slash g at at three f slash g at three undefined very good it's undefined it's kind of a trick question you see this is actually f at three divided by g at three f at three f at three is one g at three is zero and that's undefined what that says is three is not in the domain of f slash g this is undefined it has no value on the other hand I think I could have turned it around and said what is g slash f at three and there would be an answer because that would be g at three divided by f at three and that would be zero divided by one let's see now can you divide into zero we can't divide by zero can you divide into zero sure and one goes into zero zero times so the answer is zero in that case okay you'll see problems like this on the website when you look at episode six on the website you'll see not this particular graph it's something like it and I'll ask questions about function values let's see I guess we've talked about four ways of combining functions we could add, subtract, multiply and divide functions but now what if we take one more way to combine functions let's see the two functions I had here were help me out I think it was two x plus three and the other function was three x minus one is that what I just had two x minus three, three x plus one two x minus three thank you and three x plus one okay so here's the fourth way of combining functions it's called the composition of two functions the composition of two functions now what I'm going to do is I'm going to start off by taking g of x and then I'm going to take f of that so I'm actually taking a function of a function and this is abbreviated by putting f with a little circle dot g of x circle dot there is elevated right in the middle between the g and the f the f and the g now because g is closest to x it's the one on the inside because f is on the outside or f is further out that's why it's on the outside now the way I would evaluate this is I would work from the inside out I would substitute for g of x three x plus one and then I would take f of that let's see now f of that what would it be over here it says whatever you plug in for x you're supposed to double it and subtract three so I'm going to double this and subtract three and it looks like we're going to get six x plus two minus three I think is a negative one six x minus one now compare that with the composition g dot f of x generally when you reverse the order of a composition you don't get the same answer so I get g of this time f of x goes on the inside because it's the one closest to the x and I work from the inside out so this is g of two x minus three and now what does g do to that well g takes any number and it triples it and it adds one so I'm going to have to triple this and then add one and this time I get six x who can tell me what the constant is minus nine plus one minus eight minus eight, yeah six x minus eight they look similar but they're not the same thing so we don't get the same function it's rather unusual when the composition of two functions gives the same answer in the reverse order let's go to our last graphic well let's go to the composition f dot g of two functions f and g is defined by the rule f dot g of x f of g of x I'll work one more example here and then I think we'll have to stop this time rather than picking linear functions I'm going to pick something a bit more more involved let's say that f of x is equal to x squared plus two and let's say that g of x is equal to x over x plus one the first function is a quadratic function the second function is called a rational function because it's a ratio of two polynomials I want to calculate f dot g of x this means by definition f of g of x and now from there I just substitute for g f of x over x plus one so now f goes to work on this rational expression what does f do to any number x that I plug in? what do I do to the number I plug in? square it and add two square it and add two, okay now this time I have a rather complicated thing I'm going to have to square it and add two so that'll be x over x plus one squared and then I add two that's going to be x squared over x plus one squared plus two times x plus one squared x plus one squared you see I'm getting a common denominator here and now if I combine those and put it over one denominator let's see if I multiply that out that's going to be x squared plus two times the quantity got a square of the x plus one x squared plus two x plus one and when I combine those can anyone tell me how many x squares I'll have all together on top? three x squared, yeah three x squared and then I'll have plus four x and then I'll have plus two you may or may not want to square this denominator for this purpose it doesn't really matter if you squared, if I do square that it would be x squared plus two x plus one now that's a rather complicated looking thing isn't it and that's the composition of these two functions if I reverse the order I'll try working this in the order g dot f of x and down here in the corner I'm going to leave that answer so I can look at it in a minute this was f dot g of x I'm going to reverse the order and see how different my answer is when I put it in this order it's very rare but it can happen that in the reverse order you get the same result but I don't think it'll happen here I'm going to take g of f of x and that's g of x squared plus two now what does g do to any number inside of g well it puts that number in the numerator it puts that number in the denominator plus one so if I put this in the numerator x squared plus two and if I put this in the denominator and add one what I get is x squared plus two over what x squared plus three over x squared plus three totally different now not nearly as complicated as what I had down here so when you have a composition of two functions you have to be very careful about the order that you put them in let me just give you an example that's sort of ludicrous but it pertains to this when I got up this morning I put on my shoes and socks but no wait a minute actually that's not what I did is it because I put on my socks and then my shoes makes a difference technically if you put on your shoes and socks your socks would be on the outside so if you reverse the order of those two operations the operation of putting on your shoes putting on your socks you get a totally different outcome and the same thing holds true for compositions now the order of the functions in addition makes no difference the order of the two functions in multiplication makes no difference but it does make a difference in subtraction it does make a difference in the quotient f slash g, g slash f and it makes a difference in the composition well if I could summarize what we've done today we first looked at quadratic functions and we found how to find the vertex of a quadratic function now that's very important because that tells you the extreme value of the function the lowest or the highest then we did the algebra of functions I'll see you next time yeah we got Matt Sievers right I told him about that


Alright, we're with Doug Zeke from North Central South Dakota in Walworth County. Doug, really good to talk to you and looking forward to hearing a few more things about our common philosophy towards soils and holistic systems. But before we do that, Doug, just tell me a little bit about your operation, what you're up to right now, how many acres you farm, what are you farming? Okay, sure. Well, like Buzz said, we're in North Central South Dakota, about 40 miles from the North Dakota border, about 10 or 15 miles east of the Missouri River. We run cattle and we run them, we background them over the winter. You could say we leave them on the cow and do a cheap grazing thing on corn stalks over the winter. Then we'll run the yearlings on grass until sometime in this fall and let them go then. Crop-wise we have corn, soybeans, wheat, oats, and warm season and cool season cover crops. About four or five years ago I started dedicating a fourth of my crop land acres to full season cover crops. And that's kind of evolved into really liking the way the warm season cover crop mixes work. The sedan grass, pearl millet, German hay millet mix with six or ten other things mixed in with it. I kind of got started down this road, probably back in 2007, South Dakota No-Toe Association organized the bus tour up into North Dakota. And we went up to Gabe Brown's place and I can still picture him standing out in a cover crop field, warm season mix. It was about this tall and talking about how he was going to graze that and how he was buying less fertilizer and using less herbicide. This was the end of September. So I ran home and I rounded up some winter triticale and some hairy vetch because he said that was his slam dunk. And I ran out, planted that yet, like the first week in October and some soybean ground that we'd come by.  That's kind of where things started. After that I started going up there whenever I could because what they were saying was interesting to me. And then I got connected with the South Dakota Grasslands Coalition too. They've got a grazing school down in Oklahoma in the fall. And what I found there was the people in the grazing circle, the progressive grazing circle, were a lot of the same people that were in the progressive farming circle as far as using cover crops and cutting back on things. So it was a holistic network that was building up and not holistic floppy hat bib overalls, but holistic looking at the whole picture, you know. I was a little afraid of that term at first, but then I learned that it means looking at the whole picture. When we think of holistic, instead of thinking of radical viewpoints, what I've learned that holistic really means is looking at the whole picture, looking at how things are interconnected. And in nature, everything is interconnected.