In the single peak preferences, we have looked at a interesting mechanism called the median voting rule in the previous module. And we have seen that that particular voting rule satisfies certain desirable properties, most prominently the strategy proofness and on-to-ness. And in this module, we are going to look at the this additional property of anonymity and we we are going to characterize these three properties strategy proofness on-to-ness and anonymity. We are going to ask the question which kind of mechanism satisfy these three properties together. And we will see that it is going to be the median voting rule. So, this is significant because we have seen in the unrestricted domain in the Giverts Southerway domain that even if you want to satisfy strategy proofness and on-to-ness, then the only mechanism that you are going to settle with is the dictator sheet. Clearly, median voting rule is not a dictator sheet. So, this is the power of the restricted domain. Once we focus our attention only to those domains which which are single peak, we will see that these three properties are uniquely characterized by the median voting rule. So, this is a result due to Mula 1980. It says that a strategy proof social choice function F is on to and anonymous if and only if it is a median voting social choice function. So, in this module, we are going to prove this at least a part of this and we will continue the proof in the next module. So, the first thing that we are going to do is the reverse direction or is the if direction. That is if we are given that a median voting rule social choice function which we have defined with the use of those phantom peaks, we know that it is strategy proof from the previous theorem. It is anonymous certainly because it is only looking at the looking at the peaks and it does not matter which peak belongs to which agent. If you interchange the or permute these agents, this just means the collection of the peaks remains the same only then the agent levels get interchanged. So, as long as those peaks are unchanged, the outcome does not change. So, this is clearly anonymous. It is on to as well because if you pick any arbitrary or native A, so let us say we are looking at a specific outcome A, then we can construct preference profiles and here is how we are going to construct it. We are going to put the peaks of all the players at A and because there are N players and N minus 1 phantom peaks, then always the median is going to be at this point A and it will be A irrespective of the position of those phantom peaks. And therefore, we actually constructed this P some preference profile P where the outcome is going to be A. So, and you can change it according to whichever alternative you pick. If you are picking B, you put all the agent peaks at B and so on. So, this is certainly on to anonymous and strategy proof. So, the direction, the forward direction is what we are going to discuss in detail because this is presumably the much harder direction. So, what is we are supposed to prove here? We are given a social choice function which is mapping from this restricted domain, the single picked domain to the set of alternatives and this social choice function is already known to be strategy proof, anonymous and on to. Now, a few things that we will be using throughout this proof. So, let me tell you the broader picture of what we really need to do in this case. We will have to essentially construct those phantom peaks because we are given the player peaks, we cannot change the player peaks. We have to pick the appropriate phantom peaks such that the social choice function can be written as a median of those phantom peaks plus the player peaks. That is what our objective is. And now based on the cases whether this median itself is a phantom peak or an agent peak, we will have two different cases and we will handle them one by one. So, let us first define what is the PI0. So, this is just a notation. This means that agent I's preference has all the peaks at the leftmost position. So, leftmost with respect to that common ordering over all these alternatives. So, you are putting all the peaks on the leftmost position. So, this profile is the one where the peak is on the leftmost position. And then from then onwards it is a single peak preference. So, the preferences go down in this way. Similarly, you can define. So, this 0 and 1 is the two extreme points of the domain of all the alternatives. And similarly, you can also define the P. So, this is PI0 and this is PI1. The peak is on the rightmost position with respect to the same common ordering. And all the alternatives lie somewhere here. Now the proof as we said is going to be constructive and we are going to construct the median voting rule which needs the phantom peaks to be designed such that the outcome of an arbitrary social choice function which satisfies these three properties strategy proofness and anonymity and oneness that matches the outcome of the median social choice function. So, here is our construction of the phantom peaks. How are we going to do that? So, let us consider the jth phantom peak and this is how we are going to construct that. So, we are looking at the first n minus j peaks of the. So, this first n minus 1 n minus j peaks are essentially all the peaks that are on the left most side. So, let us consider. So, we are using the same social choice function f that is already been given to us. Now we are putting. So, if you give a preference profile to it, it will give out a specific alternative and that is what we are going to consider as the phantom peak. Now, how are we choosing those preferences such that the preference profile gives out yj is the following. So, we have the first player's peak is to the left most, second player's peak is at the left most until n minus jth agent and then from then onwards n minus j plus 1 onwards until n. So, there are j peaks remaining they are all on the right most position. So, this is how we are defining the jth phantom peak and similarly if you keep on increasing j.  So, the first one will be where you have n minus 1. So, all the points until n minus 1 they have the peaks are at the left most position and the last one is on the right most position. When you are at the end n minus 1 that means you are only having the first agent's peak to be on the left most everything else is on the right most. So, and sequentially you are going from. So, one by one you are moving some of this right left most peaks to the right most peak. So, that is how the yj is defined and of course, after you choose this preference profile you apply f on it. Now, f is arbitrary we do not really know and we will have to argue that essentially this certain properties that we have discussed before. If they are satisfied then this yj and also the agent peaks will essentially match the same one as the median border outcome. The first claim that we are going to make is that all these yj's and yj plus ones. So, all these yj's have a monotone non-decreasing relationship and this inequality is with respect to the same common ordering over all the agent all the oddities the common ordering over all the oddities. So, it is saying that yj can be exactly equal to yj plus one or it should be on the left hand side of yj plus one these are the only two possibilities. And this is not very difficult to see the whole point is that we can we have defined this yj is in that way so that it becomes non-decreasing. So, what is so we have already seen what yj is up to the agent n minus j it is the left most peak and after that everything is right most. So, if I want to define in yj plus one then what will happen is that we will have one more agent. So, this will also essentially get converted into one and up all the agents up to n minus j before n minus j they are all all having the peaks which are at the left most position. And one thing that I forgot to mention is that this agents which agents have which peaks does not matter because we already have the anonymity. So, without loss of generality any agent can have any of these peaks as long as the collection of the peaks are the same we are we are happy. So, due to strategy proofness and this is an important point we have used this kind of a thing before. So, you notice that for player n minus j this particular outcome is an outcome when he is reporting his valuation to be this this one. So, if you consider that agent n minus j has this preference which is at the left most position then ideally that agent should prefer the current outcome which is given by this social choice function according to this preference ordering more than yj plus one because in yj plus one then we will consider as if that agent that n minus j the agent is misreporting something else. And because social choice function is truthful strategy proof then this relationship should hold. And now we are exploiting the fact that this preference profile has a very specific structure. It is a single peak preference which has the left most position to be the to be the most preferred and it is monotonically decreasing from left to right. Now if you if you have any according to this preference profile if you have yj to be more preferred than yj plus one then it has to be that yj is on the left hand side compared to yj plus one. This is quite self-explanatory. So, with that essentially we have proved this I mean you can repeat this argument and yeah. So, for any j starting from one to n minus two this relationship of less than or equal to will hold. All right. So, now we are getting into the actual proof we will save this result we will reuse it whenever it is needed. So, let us now consider an arbitrary agent profile which starts from p1 to pn. So, n agents have their own preferences and we are going to denote by this lower case pi their peaks. Now, the claim is that if you have this f satisfies this strategy performed to miss an anonymity then fp should be the median of all these agent peaks and be the corresponding phantom peaks. This is the final claim if we can show it then we have proved that the theorem by Mula. And again we can we can assume without loss of generality because of this property of anonymity it does not really matter who has which peak. We can without loss of generality consider the natural ordering of these agents to be in the increasing order of their preferences. So, again this increasing order of their peaks is with respect to that common ordering over all these alternatives. So, let us also define this a, a to be an outcome which is a median of all these agent peaks and also the phantom peaks. We will essentially have to show that this is the this is equal to f of p. So, as we said there could be two cases the median could be a phantom peak. So, let us say a is equal to y of j for some j in the in the set. So, what does a median mean? So, median means that you have total n minus 2 n minus 1 point. So, n agent peaks and n minus 1 phantom peaks then out of this 2 n minus 1 points this median is sitting exactly at the center which is at the nth position. So, there will be n minus 1 points on the left and n minus 1 points on the right. And now if you look at, so if you say that yj is the medium median then we also know that there are j minus 1 phantom peaks before it because all these yj's are monotonically non-decreasing. And so therefore, the, so here we will have to have n minus 1 total peaks. So, if j minus 1 of them is essentially phantom then n minus j has to be the agent peaks. Similarly, on the right hand side it has to have n minus 1 total peaks and we know that the n minus 1 minus j number of phantom peaks are there. So, there should be exactly j agent peaks. Fair enough. Now, we, so we can actually say that this yj is nothing but that a that we have to find. And all these peaks, so all these peaks because we have already ordered them in that way. So, all this n minus 1, n minus j agent peaks on the left and the rest of the peaks in this order are on the right. Now, we are going to use a similar transformation. We know what yj is, yj is by the definition as we have defined yj, applying the f, the social justice function on this preference profile. And then what we are going to do is we are going to look at what happens if you replace the first player's preference with its true preference, with its the preference that we are actually willing to prove. So, just change one preference in the whole set of preferences to p1. And let us say that is denoted by b. Now, what do we know? So, by strategy proofness, because under this preference profile if player one had this preference, then yj should have been more preferred than any other outcome because then this will be something like p1 is a misreporting. So, of course, yj has to be preferred than b under this preference profile of this agent. And again, using the same argument that this means that this preference is on the left most, the peak is on the left most position, so yj must be on the left hand side of b. Now, again by strategy proofness, now we are going to use the strategy proofness at this preference profile. So, this might be confusing if you are looking at it for the first time. We are just considering as if this player, player one, if it had this particular preference profile, then if it misreports to some other preference profile, that will not be beneficial according to that preference profile. So, if that player really had p1 0, then what we concluded here is that under that preference ordering, that player would have preferred yj more than b. But whenever your preference actually changes to p1, then we are going to say that, you should prefer this one more than yj under this preference profile, preference of that player. So, we can write again by the same strategy proofness, we can argue that b is more preferred than yj under this preference of that player. So, if that preference is this, then misreporting is worse than reporting it truthfully. Now, what we can observe that p1, we have already seen this, we have that is the reason we have ordered all this agent peaks and we have also seen this relationship. Certainly p1 is less than or equal to yj, it leads on the left hand side. So, p1 is the peak of this is going to be on the left hand side of yj. And that implies because it is single peak, b should be less than or equal to yj. So, why is that true? So, you have the peak somewhere here and yj is on the left hand side. So, if b was on the right hand side of yj because of the fact that this is single peak, that should have been less preferred than yj. This is clearly true because of the preference has this single peak nature. It can never be the case that b is living here and the peak is on the left hand side of this point yj, this alternative yj that we are looking at and still b is more preferred than yj. So, therefore we can conclude that b is on the left hand side. So, it can be somewhere here or it can be here, but it can never be on the right hand side. And because b has to be less than or equal to yj and in the previous conclusion we have made yj has to be less than equal to b, then it must be the case that b must be exactly equal to yj. So, we can repeat this argument for the first n minus j agents. So, we are going to replace this p20. So, the second agent's preference with p2 and the given preference of that player. And because we now know that b is equal to yj, so the first one is yj, we can repeat the same arguments to show that if we do it, then that will also be yj. And we can repeat this argument until n minus jth agent to get that that is equal to yj. Now, we are going to show for all pj's. So, not only up to jth agent, but all the agents up to n. So, now we are going to consider. So, after we have approved that this is yj, then we are going to replace it, replace now the preferences from the right hand side. So, now we look at the pn, the preference of player in replacing that with this first preference. Now, we apply a very similar argument, we can now show, I mean, we know that because of strategy proofness, yj has to be more preferred under this preference than the outcome b. And because of the fact now this preference is nothing but the right most, so the p key is at the right most, then it better be the case that now what you are preferring less should be on the left hand side. So, yj has to be on the left hand side, so yj should be somewhere here, let us say, and b has to be less than on the left hand side than that because this is a single big preference. And similarly, if you apply the pn and use the fact that the this peak was on the right hand side of yj and you know because of strategy proofness b has to be at least as preferred or strictly more preferred than yj, then this and this inequality holds, then it must be that is that yj must be on the left hand side because of b because again for the same reason that you have the peak p of n which is on the left hand side of yj. And because of the fact that now b is more preferred, b has to be leaving somewhere on this side. It cannot be here because then single peak will single pickness will force that that is less preferred than yj. So, yj now stays on the left hand side of b and together these two things we can conclude that b is equal to yj. So, we are also proved that b we are also done proving that b is exactly equal to yj and this is the way this proof percolates. So, now you can go to the pn minus 1 and replace up to this agent in minus j plus 1 and then at the end we will have all the preferences that you wanted to show and that is exactly equal to the yj which is the median of all these peaks phantom as well as the agent peaks. All right. So, that proves first part we will next see the case where it is the agent peak, the median is the agent peak.


Now here's one big mistake that students make. I definitely made this in medical school. Now for a second, imagine if you were gonna run a race. Perhaps if it's like a half marathon or a marathon, it usually comes with kind of a course map with elevation mapping. So you can kind of already know where the hills and the downhills are going to be and use this to plan how you're going to run your race. Now think how backwards this would be if a runner decided to look at that map and said, on the uphills, I'm gonna run faster. On the downhills and the flat parts, I'm gonna run as slow as possible to conserve energy. This is a clear example of poor energy mapping. And as students, we do this all the time. On a daily basis, you'll probably have a slump in the mid afternoon, as most of us do. And usually on a weekly basis, around that Thursday to Wednesday to Friday slot, your desire to be a student is as low as possible. But despite knowing this, the types of tasks you give yourself on a weekly basis are probably the same day to day, hour to hour. But just like an effective runner, if you understand the course map, you can decide what tasks you do at specific parts of the day to complement when your energy is going to be the highest. For instance, if you find that your retention is high as doing tasks like flashcards or practice questions, you need your energy to also be high at those points.


This is Breaking News, Green Growth Brands to offer 11 Canadian per share in stock for Aphria. I have to thank the people. You guys brought this to my attention. You told me rich, breaking news. Both Green Growth Brands and Aphria are halted. I said pardon and I did the research. I did the due diligence and you are correct. Oh my goodness. I knew I liked Green Growth Brands. I didn't know I liked it this much. Oh my goodness. They've been on fire going up every single day and maybe now we know why because they plan to acquire Aphria. Let's see if it is trading after hours. So it finished down slightly 6.41% which is really weird because it was up all day. And then Aphria, so it got halted and then Aphria got halted and people started messaging me rich. What's up with Aphria, Rich? It's going up after market. Rich, I hear Green Growth Brands is taking over Aphria and I'm like what? Green Growth Brands is taking over Aphria. Now it's not showing here after hours trading but apparently it is up big after hours. Let's read the news. The offer is valued at 11 Canadian per Aphria share. Significant and compelling 45.5% premium to Aphria's closing price on December 24, 2018. Expect Aphria to explode tomorrow. Canadian 300 million concurrent financing in Green Growth at $7 per share creates the only large scale operated to bridge US and Canadian markets. No other Canadian LP operates at scale in both markets. This will explode both stocks tomorrow. Expect them to explode. Exantic Biopharma Inc. Otherwise known as Green Growth Brands doing business as Green Growth Brands Limited under the symbol GGB in Canada, GGBXF in America. Announced today, it has concurrently intends to make an offer to purchase all of the issue and outstanding common shares of Aphria Inc, APHA in America on the New York Stock Exchange and APHA in Canada. The offer will provide Aphria shareholders with 1.5714 common shares of Green Growth. The Green Growth shares for each Aphria share and represents premiums of 45.5% over Aphria's closing price on the Toronto Stock Exchange TSX on December 24, 2018. And 46% of Aphria's volume weighted average price on the TSX for the last 10 trading days ended December 24, 2018. The offer values Aphria at approximately 2.8 billion US, 2.1 billion in America, 2.8 billion Canadian based on a valuation of $7 per share for Green Growth shares. Wow, I'm mind-boggled right now. I knew I loved this company. I brought it to you first, it keeps going up and now they're looking to take over Aphria? What? We believe our offer will create value for both Aphria and Green Growth shareholders. What a genius.  We are confident that the significant premium we are offering and the opportunity to participate in the growth of a stronger combined company are so compelling that we are taking our offer directly to Aphria's shareholders. Says Peter Horvath, otherwise known as Genius, CEO of Green Growth, taking advantage of Aphria while they're hurt, Genius. Together we can unleash synergies between our teams, assets and geographies, forming a combined enterprise that will accelerate our collective growth strategies in Canada and the US and overseas. Green Growth expects to complete a concurrent broker financing of 300 million Canadian at a price per share of $7 to both illustrate confidence in the value of the consideration under the offer and to fund the business growth of the combined entity. Green Growth expects the certain of its existing shareholders will commit to backstop the 300 million financing concurrently with the execution of a business combination agreement with Aphria or the take up of shares under the anticipated offer. Prior to announcing its attention to take the offer directly to shareholders, Green Growth engaged Aphria's board to attempt to negotiate a friendly business combination that included, among other things, a very short exclusivity period to allow both parties to seriously consider the combination. A full go shop provision in favor of Aphria and the preservation of Aphria's management and commitment to board representation at the combined company. Aphria shareholders should be aware that Green Growth offered that upon a friendly business combination with support from Aphria's board, Green Growth would invest 50 million in equity at an Aphria per share value of $11 Canadian. Why a combined Green Growth and Aphria is better for shareholders? Combining Aphria with Green Growth is the fastest way to create significant value for shareholders for both companies. The combined entity creates an unparalleled North American player with Canadian and US operations. Aphria has a large footprint in Canada and supply agreements with all provinces and the Yukon territory and strong strategic partnerships establishing whole sale supply agreements. Green Growth operates vertically integrated cannabis operations including cultivation, manufacturing and retail assets in Nevada, including recently being awarded seven retail cannabis dispensary licenses. Together the pro forma company will have a strong foundation, extensive retail relationships and infrastructure to capture significant future growth as international markets evolve. Increase scale footprint and creates the preeminent US consolidator the combined company will be the largest US operator by market capitalization and the only North American cannabis operator. Wow, I'm literally mind boggled right now. Combines Aphria's cultivation and production capacity with Green Growth's retail strength. The combined company will marry Aphria's low cost cultivation and near term production capacity with Green Growth's vast retail known how to capture market share while maintaining lean margins. Aphria's current cash cost program is 130 Canadian and expects to further decrease to 95 cents Canadian per gram with projected annual capacity of over 250,000 kilograms by early 2019. Aphria Q1 2019 investor presentation dated October 11, 2018. Green Growth's strong management team has a proven track record of delivering at the retail level and is already operating a best in-class dispensary in Las Vegas. Poised to benefit from trans-formational cannabis related regulatory changes in the world's largest cannabis market, Green Growth will soon be rolling out a consumer focus line of CBD products initially focused on topicals and balms and is well positioned to benefit from the further pro cannabis US regulation in the near to midterm. Unites best in-class management teams, Aphria's pharmaceutical and greenhouse operational experience and Green Growth's proven retail expertise. Aphria's team is comprised of veterans in the greenhouse industry and proven operators of large pharmaceutical companies. Green Growth's CEO held senior positions at a number of well-known retailers including Designer Shoe Warehouse, Inc. and Elle Brands, Inc., Victoria's Secret. Additionally, Green Growth's largest shareholder, the Scottenstein family has deep relationship in the retail sector. What are the benefits to Aphria shareholders? Wow, we need a drum roll. While Aphria shareholders may be discouraged by recent events and having seen their investment significantly impacted, they should be aware of the immediate benefits of the offer and reasons to tender. Significant and immediate 45.5% premium to market price, meaningful ownership position in a combined entity that is poised for further growth, potential for further downward share price impact if the offer is not accepted. Whoa, that is interesting. Green Growth believes it already has support for the offer from Aphria shareholders holding approximately 10% of the outstanding Aphria shares. Green Growth has additionally acquired a meaningful toe-hold position in Aphria. It is expected that following the offer, Green Growth will continue to be listed on the Canadian Security Exchange under the symbol GGB. This is huge. If you have any questions, need help, Aphria shareholders should contact Kingsdale advisors with a phone number right there. Intention to make an offer. Wow, this is huge breaking news. We bring you the news and we bring it to you first. This is breaking news. Green Growth brands putting an offer to acquire Aphria at $11 a share when Aphria is currently trading in Canada at $6.60, a 45% premium. What do you think about this news? Breaking news, and of course, your boy, Rich, is breaking you this news. First, I'm mind-boggled by this news. I need to digest it. I'll come back alive with you guys again to talk about it, but I have to break it first to let this news circulate.


This is stock number 10280. We are here at Summit Automotive in Fond du Lac, Wisconsin. You're new and used Jeep Wrangler headquarters. Today we are checking out this really cool super clean 2017 Jeep Wrangler Unlimited Sport. This one has a Moab Industries conversion package on it and from this HD video you will be able to tell just how clean this Jeep is all the way around and some of the really cool features that go along with this particular Jeep. Hypergreen is the color we shoot all of our videos in 1080p so if you have HD capabilities on your computer tablet or smartphone device turn them on right now because it is like you're right here looking at Jeep with me and definitely your best way to check out the vehicle before seeing it in person. Hypergreen really good looking color as the Enfab steps on it. MB beadlock rims and it has mud claw radial MT 37 by 12 and a half R17 LT tires with right around half the tread left maybe a little bit more on the front here. You got the Moab custom hypergreen painted shocks. You have the Fox 2.0 shocks with the reservoirs. This is a six inch lift done by Moab Industries. Obviously has the LED light bars in top the LED side lights and you also have some more LED fog lights and stuff here has a XRC 9500 pound winch DVB front metal bumpers has Dana 44 axles in the front sway bar disconnects and it has eaten front and rear lockers on it suspension is very clean has the engine is very clean as well no leaks or anything like that frame and underbody is in excellent shape custom grille custom hood has a cowl induction on there no dense or dings passenger side rim is in really nice condition and as you go down this side of the Jeep you can see just how clean the body is how reflective and mirror like that paint is we take these HD videos so if you are far away or even if you're close by and just can't make the trip down you can still see the Jeep here the Jeep and have confidence in the vehicle that you're looking at before you even get here frame and underbodies very clean back here didn't see any dents or dings in those doors this has a custom DV8 or DVB DV8 maybe off-road one piece hard top with the slanted back there looks really good on this Jeep take a look at the rear suspension these are 488 gears in the front and rear has a DV8 metal bumper receiver hitch so this is a brand new tire so you can see just how much tread is on that compared to the ones that are on it so lots of tread on those tires back rim matches all the rest pretty nice shape the rear gate is an excellent condition as well back storage area is very clean and it does have the storage back here too and your spots for your roof bolts if you had a normal top on here but this one has the DV8 custom top this does open up like so shocks work really nice does have the rear to frost shuts nice and solidly solidly heavy-duty tire carrier on here as well and on this side of the Jeep just as clean as that passenger side the hard top is in excellent shape all the way around this back rim pretty nice condition as well and down the rest of this side of the Jeep very clean has heated power mirrors the n-fab steps are a nice condition as well I didn't see any chipping or rust or anything on them has I think they're carbon fiber fenders on here those are definitely not factory fenders inside you have catskin leather black leather seats with the hypergreen stitching Moab industries stitched into the backrest as well no rips or tears on the seat we have rugged ridge all-weather floor mats throughout here your controls for the LED lights on the roof and front winch there as we hop inside here you can see that this Jeep only has 9,891 miles you get some nice grab bars up here ox gourd grab bars right here these are your eaten lockers they do work just try them out has the Android 12 inch tablet radio AM FM radio this one also has the navigation system on it and really a nice nice addition to this vehicle power windows you have your climate control stability control downhill assist control 4x4 shifter on the floor 5-speed automatic transmission and the passenger seat and floor mat are very clean as well I like the hypergreen stitching in the seats really a nice accent to those seats has the insulated hardtop so you got all that carpeting there keeps you warmer dampen some of the sounds and everything with that the windshield is nice and clear of any chips or anything like that it will take a quick look at the back seats the back seats are just as clean as the front seats and are the custom black with the hypergreen stitching you got latch child safety system for your car seats back here and a rugged ridge all-weather format back here as well these seats do fold down for extra storage and you can see that they go down really nice and flat if you got to carry a bunch of extra stuff and we'll take a quick look under the hood I would personally like to thank you for checking out the video today and I hope from this video you will been able to tell just how clean this Jeep is all the way around inside and out so you can make a smart fine decision and under the hood is the 3.6 liter pentastar v6 motor engine bays very clean runs very smooth this Jeep has been fully safe to and inspected by our service shop has a fresh oil and filter change all the fluids have been checked and topped off the vehicle has been gone through mechanically 100% and is 100% ready to go to see more pictures of this Jeep or one of our other 450 new and used cars trucks SUVs minivans wranglers half tons three quarter tons one tons you name it we got it go to our website www.summitauto.com full pictures and descriptions of every single vehicle from two locations all at summit auto.com and if you'd like to check out more HD videos you can go to youtube.com slash summit auto remember to like subscribe and share on this video and all the videos that you see there in fact in a second you will see a link to subscribe to our YouTube channel on your left a link to more Wrangler videos like this one on your right if you have not been to our website on the bottom link to this vehicle on our website click those check us out and we really look forward to helping with this super cool super clean 2017 Jeep Wrangler Unlimited Sport with the Moab conversion package thanks again


But like Pimp, China loves to steal intellectual property. That's a fallacy. China was not stealing intellectual property. The Western countries were hanging over intellectual property to China. They've been doing that for the last 30-40 years. Cheaper to build here. You don't need to pay people living wage. Or the living wage of China was a lot less than the living wage in the United States or Europe or anywhere else. So they willingly decided to build their factories in China. Okay. China was like, okay, sure. Thanks. We'll do it. Right? And then they said, oh, you have to sign these contracts saying you're gonna abide by our intellectual rights. China's like, right? Yeah, okay. Sure. We'll just bring in our people, take a look at how you do things and copy it. It wasn't stealing.  If the people in that country hand over that technology, that's not stealing. Thank you very much.


Hi and welcome to the session. Let's work out the following question. The question says a square piece of tin of side 18 centimeter is to be made into a box without top by cutting square piece from each corner and folding up the flaps. What should be the side of square to be cut off so that the volume of the box be maximum also find the maximum volume of box. So let us start with the solution to this question.  Let V be the volume of the box so formed then V is equal to 18 minus 2X the whole square into X. This happens because we see that suppose this is the square piece of tin. Now it is of side 18 centimeter now it is to be made into a box without the top by cutting square pieces from each corner. So suppose we cut these square pieces from each corner and let their side be X X and so on. Now since volume is given by length into breadth into height or we can say length will be 18 minus 2X similarly breadth will be 18 minus 2X into height will be X so this is how we get this. Therefore we can say that dV by dx is equal to 18 minus 2X the whole square into 1 plus 2 into 18 minus 2X into minus 2 into X. This is equal to 18 minus 2X the whole square minus 4X into 18 minus 2X this is equal to 18 minus 2X into 18 minus 2X minus 4X this is equal to 18 minus 2X into 18 minus 6X. Now, for maximum or minimum values, dv by dx should be equal to 0. This implies 18 minus 2x should be equal to 0 or 18 minus 6x should be equal to 0. Now this implies that x is equal to 9 cm and this implies that x is equal to 3 cm but x equal to 9 cm is not possible because if we cut 9 cm, 9 cm from each side that will be 18 cm then we would not be able to form a box out of it. So therefore we can say that x is equal to 3 cm. Now the second derivative that is d2v by dx2 will be equal to 18 minus 2x into minus x plus 18 minus 6x into minus 2. Here we apply the product rule. This is equal to minus 144 plus 24x. Now d2v by dx2 at x equals to 3 is equal to minus 144 plus 24 into 3 that is equal to minus 72 which is negative or we can say which is less than 0 therefore volume is maximum x equal to 3 therefore the maximum volume is equal to 18 minus 2 into 3 the whole square multiplied by 3 that is equal to 144 multiplied by 3 that is equal to 432 cm cube. So our answer to this question is that volume is maximum at x equal to 3 and maximum volume is 432 cm cube. So I hope that you understood the solution and enjoyed the session. Have a good day.


All right, so here we are, Westfield Stratford, London. I'm gonna show you how to do vegan in a food court. Everyone's got a food court in a shopping mall near you. Let's do one here, let's go. Vegan pretzel available here. All right, so behind me here is the boost juice bar. They've got plenty of juices, plenty of smoothies. Make sure they don't put honey or yogurt. But yeah, boost juice bars, good for smoothies. Let's go to the food courts just up here. Okay, now most food courts are pretty much the same, all right? First off on the left, sushi. You find any sushi place. They do vegan sushi at every single sushi place. You make sure they don't put mayonnaise or anything that's not vegan, any sort of weird fish stuff on there. But let's go have a look. And over here you can see pieces of fish being cut up, you know, ripped out of the ocean and suffocated and stabbed to death, packed up into pieces to be put in sushi when you can have vegetables in sushi, tofu in sushi. So many things you can have in sushi that aren't murdered animals from the ocean, destroying the environment, destroying the ocean, cruel as anything, full of mercury. Why choose rotting dead fish when you can have vegan sushi? Boom, straight away, a vegan box. Most places do a vegan box now. You don't want to eat any murdered fish here. Look, mercury fish, suffering, death, no point. A vegan box, delicious, look at that one. Really good. You can always get edamame beans as well. A little seaweed salad as well. Or you can ask them to prepare you some vegan sushi. Amazing, sushi is a really good vegan option. You can get it, every single sushi place will do you vegan sushi. So let's go, check out the sign. Sushi place will always look after you. All right, let's go. So right behind me is a burrito place.  Burrito place is amazing. Put lots of salad in there. Check it out. This place here does jack fruit burritos. But yeah, burritos are an amazing choice. Burritos. Vegan approved. I've got vegan options on here. Okay, so here, this is an Indian place behind me. Just ask our staff, look, vegan. I'm sure that the dial, you can ask if they put any ghee or any dairy, but Indian will always have some vegan options. So you just got to talk to the staff and ask them, you know? Plenty. So there's been packed of pieces of bird, covered in spices and stuck in a tandoor. You can easily have instead of tandoori murdered animal, you can have tandoori tofu, tandoori seitan, you know? Tandoori whatever other plant alternative other than pieces of flesh from an animal. Falafel are usually always vegan. So if you find a little year-os place, a little falafel place, hummus falafel in a wrap, with some tabbouleh, always nearly 99% of the time a falafel is going to be vegan. Just ask them, if they put any dairy or eggs in it, that would be weird, because it's not actually part of the ingredients of a falafel, but they're like a little fried chickpea ball. Also, most falafel places do hummus. Hummus is a staple in the vegan diet. You're not really vegan unless you eat hummus with everything. So yeah, little Lebanese places like this, they've usually got falafel and hummus and bread. Go hard. With pizza places, usually the dough will be dairy free, but you can ask them for a vegetarian without cheese. Usually they can have vegan cheese. Here we go. This menu here has vegan cheese. So they do vegan cheese on the pizza here. First pizza place we found in this food court does vegan cheese for the pizza. So pizzas are usually good. You get pasta at a pizza place, usually too. You can get a margarita, pasta in the Palatana. But anyways, they do vegan pizza here, amazing. So Vietnamese street food. If you get Vietnamese Chinese food, Southeast Asian food, you can get some noodles, some rice, some stir-fried tofu. Just make sure there's no fish sauce, no eggs in the noodles, anything like that. They usually got vegan options. Here you could probably get a vegan noodle soup, a famous Vietnamese soup called pho. It's usually made with beef stock, so just check. But let's check the menu. Here we go. So they've got a little VG. Can be made vegan, can be made vegan, can be made vegan. I was just looking at, just having a look at the vegan menu here. Yeah, yeah. The ones with the VG can be made vegan, yeah? Yeah, yeah. So spring rolls, salad rolls, summer rolls. Lot of tofu dishes here. See, they've got a pho here. Tofu dishes, really easy. Look, here's even noodles, vermicelli noodles. They've got a VG next to them. They can be made vegan. So plenty here. Yeah, look at those birds just hanging up there, skinned and roasted.  And right next to them is rice and tofu and vegetables. And there's no need to hack the heads off of birds to have food. There's no reason to stab pigs in the throat and gas chamber them to eat their body parts.  It's all completely unjustified and cruel and unnecessary. Vegan options galore in a food court. When you go to the food court, make the right choice. Oh wow, this has got plenty. Suitable for vegans.  This place here called Tost. This is chicken, this is chicken, this is chicken, this is chicken. See? So you can make all these wraps vegan with falafel. Good old falafel, saving the day. They've also got smoothies and juices here. Amazing. Really nice. So every single restaurant we've been to so far has had vegan options on. Except for this place. I don't think this place is very vegan friendly. Nah, this place here, not very vegan friendly, but that's okay. Not all places are. This place isn't. So this place here, I can't pronounce it. Or something like that. But this place is like a sandwich joint here in the UK. You might have something similar where you're from. Most sandwich places now, cafe styles will have vegan friendly sandwiches. I'll show you what they've got in here. Ho ho ho, look at this. A vegan Christmas lunch, look at that. That looks epic. Vegan, oh wow. Oh no, this is veggie. Okay, so they've got it. Veggie and vegan separated, which is good. These are all the animal body parts that you don't want to be eating. Merry Christmas, not so merry for the animals. Let's have a look here, ooh, ooh. Eggs are not vegan, obviously. Ah, here look, avocado and toast. Wow, that looks really nice. Avocado and toast. Oh, this one's a vegan sandwich too. Ah, good old falafel. Save the day again. A falafel flatbread. They've got little aside bowls in here. These are vegan as well. Fruit salad, fruit salad. Oh, look at these, dude. Check them out.  Pea and mint soup, vegan. You know what, I might get one of these right now. Have they got calories on that? 50 calories per 100. I'll just get one of these to test. Nice. First get this please. I'll just take that away, thanks. Ah, no thanks, that's fine. How many vegan options for milk do you have here? Just rice and soya, rice, coconut and soya. Ah, cool, okay. Any of these cakes vegan? Oh my God, those cookies are. Ah, no, that's just veggie not vegan, so I was just seeing that these are vegan. Ah, wow, awesome. Yeah, that's cool. I'll just have these please. Thank you very much, bye bye. Still a little taste test of this soup. Oh my lord, that's amazing. Wow. Okay, so that's how you do vegan at a food court. That was so simple, vegan options everywhere. You look for a baked potato, some sushi, some pasta, some pizza. Just ask the people behind the counter if you're not sure. Most places have got vegan options now. I know I'm in the UK, UK's really good. Australia's fantastic, the US is fantastic, but if you just talk to the staff and say, hey, this is what I don't want to eat as a vegan, I don't want dairy, I don't want this and that. Most places are good burrito places, Asian food, you go for it. Indian food, so good. Vegan at a food court, simple as, there's no reason to be eating exploited, chopped up, murdered animal bodies anymore. 2019, get with the times.


The Plateau State Governor, Simon LaLong, has condemned the use of social media in threatening Nigeria's democracy. The governor said these are the ones he organized to commemorate Nigeria's democracy day on Saturday at the government house in Jaws. LaLong said some Nigerians were using social media to propagate their personal interests at the detriment of upholding the democratic values of Nigeria. The governor said that Nigerians should be responsible, careful and guard the country's democracy jealously. He said that Nigeria would not disintegrate contrary to negative narratives infiltrating the polity.


You get that chair there. There are a number of other things that produce you a problem. You have to make them all go away. There's another part of the job that's a lot of fun, though. And that is that you go to Camp David. And what I've been doing on Camp David is picking up acorns. I've got a big bag of acorns in the desk drawer there. And every morning when I come down, I put a few handfuls out there on the porch outside. And squirrels come up and get the acorns to take them out and bury them with it. When they need them later on. Well, won't you open them? Nice family. And one other thing, to have the energy to keep doing the job. That's the presidential season. That's a jar of jelly beans. Well, I appreciate you getting your energy. Now, use a few acorns to hold the tree. They tell me that they bury them in the lawn and that they can find them in the true of the snow. Remember, wherever they bury them. And I watched out here and see them take them in the lawn. And it's the cutest thing to put them in the yard.  What's your thing to do with it? Go ahead there. Yeah, don't forget your yellow bean there for lunch. As you used to say. How do you do? Publish them in the paper. Not taking the crests or anything like that. In the morning, they just don't want to meet you. Well, they've got a lot of public. Because you know what it wasn't? It wasn't the conscious decision on our part that set it. The conscious decision was to let those men who were going to be in demand and were responsible for the mission to not have a civilian's back there looking over their shoulders telling them what to do. And they said, they're in charge. And we're not going to second guess them. And they made the decision. Well, I thank you very much. Thank you, Mr. President. This is kind of a second moment. I'm also going to hand out Dr. Davis and I will form the order of royals, but I'm thinking about the name, so I never got around to do it. Well, thanks. Thank you very much, Mr. President. And thanks for all the support. Really, one, really, one highest for many years. You've influenced my thinking on economics. Well, I'm pleased to think that, in your case, they're very grateful that Mr. Satcher told me the same thing. Well, I think the first time I met her, some several years ago in England before she was prime minister, we discovered that we had the same approach to economics. Of course, you are the two hopes for the future of mankind. A little blessing. Thank you very much. Just encourage you to tell me once again that I shouldn't raise taxes until we're out of this recession. Well, I don't know. You admit it's a problem to bring me more in person than the others. I have to admit it. If you had a free head, that would be against it, but maybe the armament is more important. Oh, well, then I have to deal with it. That becomes necessary. Yes, I know that. I should remember the long time that I took this opportunity and to give me a little souvenir in pair of cufflinks with the presidential seal. Very well, yes. This is a good one. That's the thing. Thank you very much. Thank you very much. Nice to see you as your own professor, who's telling me about the first president of the U.S. government, 60 years ago to the month. Without them, you might be interested to know what they told the president. I could choose the presidents whose portraits would be on the one that was on the first act, show us what their was, Calvin Coolidge. You know, you may be interested in your part of Calvin Coolidge, then, to see if the rules of a magnetic economic association, the poor man stood there shaking hands, 400 people in one afternoon. Well, I think he's been probably one of the most misunderstood and least appreciable. But he's being rediscovered, that's so good. That's a brilliant history of the last 80 years by a man called Paul Johnson in London. And he has discovered among other things the merits of cutting wood. And incidentally, my own AB degree was in economics. Well, what? So I continued my studies by reading you. Good to see you. Thank you. Thank you, Mr. President. We're bringing in front of the audience. There's just four of them. That's a little more of a shame.  I don't think you're saying that. That's a good one. Thank you very much.  Are you? Mike, do you need the water, Dennis? Good to see you. Can I come in? How are you? Good to see you. Good to see you. Dwayne Woodard. I'm starting to say the wrong name. That's not all, Mr. President. I'm pleased to see you again. Nice to see you again. Welcome in, sit down. The Vice President's chair, it's almost time to go on. Mr. President, we wanted to talk to you today about the crime bill and the supports of the majority of the bill, especially the bill reform sections and the sentencing reform and the forfeiture provisions. And we're particularly interested in the Justice Assistance Act provision because that will enable states to do work in our own vocalities. With those programs, those crime programs have been so very successful in the past, like crime prevention and repeat offenders and those kinds of things. We could certainly use that Justice Assistance Act money for our programs. We also are very appreciative of the federal state relations that we've enjoyed, especially when we drug


No, this is forge here. Wait was that supposed to stop there? Oh, okay. It goes. No. I have to go all the way up here Okay, I'm gonna run the money. Aren't I cannot upgrade this node? Why can't I upgrade this node? I got the materials. I was clicking the wrong one. Oh I was clicking the wrong one. I thought that was gonna roll me back. I bet I saw the words roll back. I'm sorry chat I'm sorry. All right. Now. We need to the good stuff foosium and Yeah, foosium ore. I don't know where that is 32,000 we need to tell and regrowth plates. All right. I now have a plan. Oh, we got this we got this So I have to do optional quests in that zone Like it's like they're not there Can I do these? Because these will go there. These are what a wild spar ways. Can I do this one pretty in pink? Will they give me credit towards that quest? Do investigations there are better than the optionals? I agreed, but I I gotta go see if I have some I Don't think I'll have any Let me go check. If you guys got some I'll definitely tag along Hmm, but I don't think I'll have any any for that area for that high level. I mean, let's see Uh, does it say where here? Yeah. Are those recess Coral Highlands Yeah, wild spire ways. Here we go. See these are two star Three star. I think I have to do one for coral Highlands Right. I'll just recess ancient forest Wild spire waste all all my wild spire wastes are small Rotten veil. Let me look for that one rotten veil Yeah, you can tell the areas I haven't been to that much Because all of my all of my investigations are low level like wild spire wastes. I haven't done much there For in terms of hunting Yeah, rotten veil, I don't have anything All right, if you guys can take me to if you got investigations for wild spire wastes or rotten veil I'll be down to do them I'll join your your quest I'll definitely be down to do them for wild spire wastes and for rotten veil investigations.  Probably didn't I did do it. I need to make more um more catalysts Right, this is bitter bug and honey. I think yeah, let's just take all of this All the bugs and with that catalyst I can make I think Poison Ammo to but I don't think I can use that on this gun. I think I can yeah, I can okay Let's take a word man. I miss poison man. Let's take it with You got pink rathian and rathian and Diablos or black Diablos Let's do pink rathian. Oh, oh, I think people DC. I Think everybody DC'd like everybody left at the same time when you posted that quest everybody left I'm trying to join the quest game. Let me click it. Oh, man Please let me join this Okay, that seemed to work. I think we're broken. All right, so I'm not leader I'm so used to being leader Exciting oh, oh Why would you do this to me? Who is this? Why is everybody here? What's going on? What's my name? I'm gonna go over here for a minute. That's okay with you guys. I gotta eat Uh Right, they just put me in the middle of two monsters. This game's evil Evil Disconnected all right. I got a remake. I knew something was up. I Knew something was up. I love I just wasted this food, but if I abandon quest, I should get it back, right? Return to HQ No, I don't want to finish it. I Want to I want to play with others man. I'm gonna I'm gonna reset. I'm gonna reset the the session Resetting this session is like a temporary fix You might get one you might get one hunt out of it You get one hunt and then all of a sudden everything breaks This game man. Oh, it could be so great if they could just fix this. Oh Because the majority of the players are playing solo now, man So they want to deal with this. Well the people having connectivity issues I can say the majority of players, but everybody says having connectivity issues You know It's like please I love multiplayer, especially with heavy bow gun man.  We reset the session because everybody DC by everybody. I mean People that were in here with me and now I'm down to 40 frames per second for absolutely no reason Connect the issues man. Oh, he's already in here. I was not a big deal. Oh, we got captured this one All right, so I got to be careful and not go Buck wow should I grab trunk bombs and Shock trap are the flies on the right here. I don't think so Show me the footprints Oh now it is Can you talk to these dudes? I can't talk to them. They all hate me. Let's track him. Hello. Oh, what's up, Michael? You obsessed with this game. Oh man It's very addictive. It is addictive. It's like It could be better though. That's the frustrating is like these stupid network problems and the mouse issues just Just make you wish it was a PC game first from that perspective. I know I'm being selfish Hello pink racy in Wow this dragon is amazing he May kill me Unsubscribe I may have heard them. I may have heard them really bad chat May have to find the elder dragons. He's a little bit easier. I gotta say after I get smacked around a little bit You won't be poisoning me sir I'm gonna run. Oh Good timing. Good timing little guy. Good timing little guy. Let's Stick it but no but no but I don't have Stuff to craft with what's going on? Have I burned through all my mats already? That's been all day farming. Oh, that's what you're gonna do. I took damage there. That's weird If I didn't reload, I don't know what happened there. I know I have enough mats. It's so weird that I don't Thanks for the heels It's so weird. All right, I'll do worry about it later. I've been crafted I don't know. I had like 300 of that stuff. I had like 300 of the of the of the nuts I don't think I refilled. I think that's what happened came out of lurker. I gotta read this If somebody comes out of lurk to say something you know is good No, but all right, is he drooling? I hope he's drooling Why not try to fire there? I think I got the wrong gun No, I could do pierce everyone three. This is the right gun All these excuses coming out of my mouth. Oh, this is bad. This is bad Good time to reload Yeah, yeah, yeah, do it now do it now. Yeah reload now boy. Good job. Good job. Good job. I'm gonna run I'm gonna run this way I'm gonna assume the defensive position like these guys over here. Yeah, we're just we're gonna run we're gonna run to our to our juice box To our juice box. Yeah, you won't make me reload. I'm reloading now Maybe not bad idea. Okay. Wow Wow, just just just Wowsers jet just wowsers I'm running over him to drink some my juice box Why? Oh, I definitely never know wait Maybe I did. What am I missing? I got the nuts.  I have no clusters. I don't have stuff to make clusters So we gotta do so fashion way I guess Pierce I got no no big hitters man. I'm sorry Like everything's gone. How did that miss me? Oh, we got captured. Hold on. We got captured. I forgot I was about to kill him man. I was looking for my traps.  Okay, um Come on alert. I agree this game could be better, but I said the same about the console release I prefer the older monster hunter games Scale sack carapace Rathian Ruby is that a gym chat did I get another gym? Chat I think that's another gym Man I'm just on the gym train today I thought they were supposed to be rare rare rare. Oh that triggered myself. I'm not even All right, give me that progress. Oh, there it is. That's what I want to see That's what I want to see. All right. Let me check my inventory here because I feel like Yeah, I'm missing stuff Oh, yeah Um Okay sticky ammo. I thought that's all I needed to make sticky ammo So if I wanted to make sticky ammo one, I thought all I needed was that So why did I have stuff to make stuff there? It was all working so well. I think I'm out of something and I can't figure out what I got gunpowder stuff Yeah, all you need is this I don't know gunpowder level three Which I have none of Oh, that might be it. Hold on Maybe I need to craft more gunpowder Even though I have the stuff to make gunpowder, maybe I need something to start with Oh Yeah, I think that's it I think I didn't I have the nuts to make gunpowder Which is the uh I think I do Yeah, I have the blaze nuts To make the gunpowder, but for some reason Yeah Why can I craft ammo? I'm confused why I could not care. I couldn't craft ammo in the field. I got the blaze nuts for the gunpowder Let me let me just try to craft it without being in my box. Hold on. Let's see sticky ammo one sticky ammo two So I craft this sticky ammo three Huh, so I have to actually have to make the gunpowder now Okay, I ran out of the gunpowder. I think I understand I have to have a certain amount of gunpowder To make that but I also Okay, I just got to craft some more and then uh my Loadout will probably be fine Let's do like a 200 I guess That might be too much Yeah So now if I come out here What's up, dude? I'm doing good. I'm just working out my loadout here I should have sticky ammo three Oh, I know it's not craftable. Why not? What did I just Oh I gotta reload the loadout. All right. Let's do it. So now I have the gunpowder in here. I have 80 That's what the problem was. All right. So I was putting gunpowder here. I ran out blah blah blah. Yeah. Yeah, okay. We're good Okay, so we're making progress. We need just need to repeat that Um, can we do that investigation again or do you have another one for wild spire waste or rotten veil? Or if anybody does I need a I need a high level investigation for wild spire waste and rotten veil


In your perspective, how do you see Israel bolstering the effort? You said regulators are also pushing the industry, otherwise it's always the vice versa. How do you see the Israeli ecosystem taking green shoots as well as leapfrogging from what the US has with respect to the cannabis explosion that we are seeing in the medical space? The answer is very simple. The fact that in Israel, according to regulation, you can couple all your products with clinical trials and make the whole difference in the world. Because right now we have products which went into rigorous clinical trials, showed efficacy, showed side effects, profile, showed the PK results, the safety results. And when you want to sell those products globally without those findings, your product doesn't hold much because basically you are just selling a plant. We are not selling plants, we are selling products which are coupled with clinical trials, with double-bank placebo control clinical trials in various indications and that's the source and that's for success. And that source for success wouldn't be accomplished without the regulator which is heading the camp. If I need to rate the Israeli regulator, the Ministry of Health, I will give them AAA compared to any other regulator which is treating the cannabis as a hot potato and is trying to avoid messing with it and leaving it to others. And this is the nature of success in Israel. The ecosystem which allows us to take each one of the products into clinical trials and then take it globally.


25 years ago not a single planet outside the solar system had been detected. But remarkably we now know of thousands and have studied many in surprising detail. ESO's observatories in Chile have been at the forefront of this enormous expansion in knowledge and their state-of-the-art instruments are continuing to discover and study the extraordinary diversity of exoplanets. This is the ESOcast, cutting-edge science and life behind the scenes at ESO, the European Southern Observatory. Looking up at the night sky, people throughout history have wondered if there are planets and especially planets bearing life beyond the solar system. Astronomers have also asked themselves these questions and many more. Are planets common or very rare? Do they resemble planets in the solar system or are they totally different? Frustratingly, until very recently, observational techniques were not advanced enough to be able to answer any of these questions. But in 1995 this changed overnight. The first exoplanet orbiting a sun-like star was detected. The monumental discovery was made by Geneva-based astronomers Michel Mayor and Didier Kélo around the star 51 Pegasi. The exoplanet named 51 Pegasi B has around half the mass of Jupiter and travels around its parent star in just over four Earth days. But this was only the beginning. The initial trickle of discoveries became a flood. Thousands of exoplanets have since been detected in a huge variety of sizes and orbits. Many of these discoveries have been made by ESO's observatories in Chile. But the hunt for exoplanets is a challenging one. These alien worlds hide in the shadows, giving off little or no light of their own. Any light that they do emit is swamped by the overwhelming brilliance of their parent star. However, advanced observational methods can be used to spot these elusive exoplanets. The weak gravitational pull of an exoplanet in orbit causes its parent star to wobble back and forth. This tiny motion causes a small shift in the star's spectrum which extremely sensitive spectrographs, such as ESO's harps, can detect through radial velocity tracking. Harps, installed on the ESO 3.6-metre telescope at the La Silla Observatory is the world's foremost exoplanet hunter. It's the most successful finder of low mass exoplanets to date. In 2010, the instrument discovered the richest planetary system yet. The system, located over 120 light-years away around the sun-like star HD-10180, contains at least five exoplanets. There is also tantalising evidence that two more planets may be present in this system, one of which would have the lowest mass ever found. Planetary transits can also be utilised by astronomers to indirectly detect distant worlds. When an exoplanet passes in front of its parent star, as seen from the Earth, it blocks a small fraction of the star's light from our view. This creates a dip in the brightness of the star, which can be measured. In addition to determining the size of an exoplanet, planetary transits can reveal the composition of an exoplanet's atmosphere. The atmosphere around a super-Earth exoplanet was analysed for the first time by astronomers using the very large telescope. The planet, which is known as GJ 1214b, was studded as it passed in front of its parent star, and starlight passed through the planet's atmosphere. This starlight revealed that the planet's atmosphere is either mostly water in the form of steam or is dominated by thick clouds or hazes. Directly observing an exoplanet is a monumental feat, but one that was first achieved by ESO. The very large telescope obtained the first-ever image of a planet outside the Solar System. 2M1207b is five times more massive than Jupiter. It orbits a failed star, a brown dwarf, at a distance 55 times larger than the Earth to the Sun. ESO's telescopes are equipped with state-of-the-art instruments, but to remain at the forefront of exoplanet research, ESO has recently commissioned two new instruments for the VLT. Sphere is able to find and study faint planets masked by the glare of their host stars. And in the near future, the Espresso Spectrograph will arrive at the VLT, where it will surpass harps. The European Extremely Large Telescope, which is currently under construction in Chile, will take the hunt for exoplanets even further. Once operational, this 39-meter telescope could detect Earth-like planets and possibly evidence of alien biospheres. The search for planets outside the Solar System constitutes a key element of what is possibly the greatest question of all. Is there life elsewhere in the universe? Over the past 20 years, our knowledge of exoplanets has advanced dramatically, but the quest for Earth-like planets and those that harbour life remains one of the great frontiers of astronomy. Are we alone? We do not know, but the answer is almost within reach.


And when the night comes, it's time for you to come and sit with us. And when the night comes, it's time for you to come and sit with us. And when the night comes, it's time for you to come and sit with us. And when the night comes, it's time for you to come and sit with us.


Determine the power required for a 1,150kg car to climb a 100m long uphill road with a slope of 30° from horizontal in 12 seconds under 3 different situations. In the first situation we are considering a constant velocity across the entire process. In the second situation we are considering the car going from rest at the bottom of the hill to 30m per second at the top of the hill. And in our third situation we are considering a situation where the car starts at 35m per second and ends at the top of the hill at 5m per second. In our analysis we are told explicitly to disregard friction, air drag and rolling resistance. So we have a hill, the hypotenuse of that hill is 100m and its slope is 30° from horizontal. The car is starting the process at the bottom of the hill and ending the process at the top of the hill. I'm going to define my system as the car itself and I'm going to assume that the mass of the car doesn't change throughout the process, therefore I have a closed system. Furthermore I recognize that I'm going to treat this as a transient process because time matters and I'm going to establish the process as starting at state 1 which is a state point in time and space and ending at a state point that I'm calling state 2 because I'm particularly clever when it comes to naming my state points. In my list of assumptions so far I have closed system. Remember from our discussion of open versus closed systems and transient versus study processes that the default state of the universe is an open system undergoing a transient process. So when you're treating something as an open system that's not really an assumption that you're making you just aren't making any assumptions about simplifications regarding the system. Similarly when you are treating something as being transient it's not really an assumption that you're making. The assumption that you make is simplifying reality to being a steady state process or simplifying reality to behaving as a closed system and not having mass across the boundary. Does that distinction make sense? So I'm running down closed system as an assumption because we are modifying the default state but I'm not listing transient as an assumption because I'm not modifying the default state. In situation A I'm saying v2 is equal to v1. In situation B I'm saying v1 is 0 and v2 is 30 meters per second and in situation C I'm saying v1 is 35 meters per second and v2 is 5 meters per second. So I will first set up an analysis in the abstract case and then we will simplify it for A, B, and C individually. And that analysis as you can probably imagine is going to start with an energy balance on the car. Like with all energy balances we start with delta E is equal to E in minus E out. For our purposes here we aren't distinguishing between different subcategories of energy entering nor exiting. We are just treating it as energy entering the system and increasing its kinetic and potential energy. So the E in doesn't have to be broken apart. It's just the category that we are solving for. And at that we aren't even solving for the magnitude of energy entering. We are trying to determine the power required. So instead of energy we are going to want to write this in terms of in terms of rate of energy entering E dot in. Therefore we are treating E dot in which is E in over the duration if we look at the entire process all at once. And writing E in as E dot in multiplied by duration. And then we are neglecting energy exiting because we don't have enough information to determine it anyway. And like in the previous example we are saying that the energy change of the system which could be delta U, delta KE and or delta PE is not going to include internal energy. So we are neglecting any internal energy changes of the car during this process. So I will list that as an assumption as well. We can't neglect kinetic energy, we can't neglect potential energy. And by the way it's important to note that we are distinguishing that assumption as the change in internal energy is zero. It's not that we are saying there is no internal energy, we are just saying whatever it is it isn't changing. Similarly in the previous example when we assumed that the change in potential energy was zero we are not saying there is no potential energy, we are just saying the change is zero. That's going to be important for part A where the change in kinetic energy is zero. It's not that it isn't moving, that there is no kinetic energy, it's just that whatever the kinetic energy is at the beginning it's the same at the end. Anyway. So we have the change in kinetic energy of the car plus the change in potential energy of the car is equal to the rate of energy entering the car times the duration during which that rate of energy enters. And that is what we are using as our tool for all three analyses. If we solve this for ii.in what we're saying is the average entering energy rate must be delta ke plus delta pe divided by duration. So the power required to accomplish this process which is the rate of energy entering the system is the change in kinetic and potential energy divided by the duration of the process. I know the duration is 12 seconds in all three cases. All I have to do now is determine the kinetic energy change for all three parts and the potential energy change for all three parts. Let's begin with part A where we are climbing the hill at a constant velocity. So the cruise control is locked, velocity isn't changing, whatever it is at one it still is at two. So ii.in which is delta ke plus delta pe divided by 12 seconds is going to simplify down to just the change in potential energy divided by the duration. Again, it's not that there is no kinetic energy it's just that it doesn't change. So the total change in potential energy would be the mass at state two times the gravitational acceleration at state two times the height at state two minus the mass at state one times gravity at state one times the height at state one. All divided by the duration and because I've assumed it's a closed system that the mass doesn't change the mass can be factored out and I think it would be reasonable to assume we have standard gravitational acceleration so I will call that 9.81 meters per second squared then I can factor out both mass and gravity and write this as mass times gravity times delta h or delta z if you prefer divided by duration that's something we can compute we know the mass is 1150 kilograms we know gravity is 9.81 meters per second squared the change in elevation here is not 100 meters it is 100 meters multiplied by sine of 30 degrees and then we are dividing by 12 seconds and it doesn't specify what unit it wants for power so because everything else is in metric we will express an answer in the metric unit system the relevant unit for power would be watts or more likely for cars kilowatts so I'm going to shoot for a kilowatt as my destination and as a general rule it's best to start at your destination and work backwards for these unit conversions I'm going to start with a kilowatt recognize that it is 1000 watts and then I will break apart my secondary dimensions into primary dimensions so I will write a watt as a jewel per second because that is how a watt is defined if you don't remember that off the top of your head it is listed on your conversion factor sheet right here and and then I recognize that a jewel is defined as a newton times a meter which is also on my definition sheet and a newton is a kilogram meter per second squared which surprise surprise is on your conversion sheet so we've started with 1000 watts that's a kilowatt and we've broken it all the way apart into its primary components what cancels what jewel cancels jewels newtons cancel newtons kilograms are going to cancel kilograms meters and meters cancel meters and meters second squared cancels seconds and I guess let me try that again second squared cancels second squared and the singular second cancels the singular second that leaves me with kilowatts as my answer so I'm going to pop up the calculator zoom out just a scosh and let's calculate a number here we go 1 1 5 0 times 9.81 times 100 times sine of 30 and I'm already in degrees but I will add the degree simple just for good measure and then I'm dividing by 12 times 1000 that will give me an answer in kilowatts and I determine it takes 47 kilowatts on average to accomplish this process so I'm going to call that e.in the rate of energy entering on average that would accomplish this process that power is going to increase for part b wherein in addition to accomplishing this change in potential energy I'm also accomplishing an increase in kinetic energy the process begins at rest and ends at 30 meters per second so I will start part b the same equation I used for part a before I simplified it and I will write this as ke2 minus ke1 plus pe2 minus pe1 all divided by 12 seconds and total kinetic energy can be written as one half times mass times velocity squared so ke2 would be one half times m2 times v2 squared ke1 would be one half times m1 times v1 squared and then pe2 would be mass 2 times gravity 2 times h2 minus pe1 would be mass 1 times gravity 1 times h1 all divided by 12 seconds per duration so again closed system I can factor out the mass gravity I can factor out gravity I could actually go even further and pull mass all the way out but I don't want to do that for a reason that'll make more sense in a second here so one half times mass times v2 squared minus v1 squared plus mass times gravity times h2 minus h1 divided by delta t so for convenience here I can split my denominator and write this as one half times mass times v2 squared minus v1 squared divided by delta t plus mass times gravity times h2 minus h1 divided by delta t and the cool thing about this is that this term is what we just calculated it's 47 kilowatts so all we have to do to answer this question is figure out how much it would take to increase the kinetic energy in this process and add it to the change in potential energy that we already know furthermore for part b v1 is zero because the process begins at rest so this really becomes mass times v2 squared divided by two times duration plus 47 kilowatts my mass was 1150 kilograms and I'm divided by two multiplying by the velocity at state two which was 30 meters per second which I will write as 30 squared meters squared per second squared divided by 12 seconds and again my goal is to get to kilowatts so I'm going to break out kilowatt into 1000 watts again and a watt into a joule per second then a joule into a newton meter again and a newton into a kilogram meter per second squared again newton cancels newton joule cancels joule watts cancels watts second squared cancels second squared kilogram cancels kilograms meter squared cancels meters and meters and I wrote the seconds in the wrong spot a little bit too quick there a watt is a joule per second not a joule times a second okay then seconds cancel seconds and I'm left with kilowatts and then to that I'm adding 47 kilowatts so if I pop up my calculator again and I calculate 1150 that is 1150 times 30 squared divided by two times 12 times 1000 I get 345 eighths thank you calculator 43.125 kilowatts which when I add that to 47.0063 I get 90.1313 so to accomplish this process the engine has to require on average 90.13 kilowatts 43 of those kilowatts are going into increasing the kinetic energy of the car about 47 are going into increasing the potential energy of the car then for part c I'm going to open a new page here and I'm going to copy over my equation and my approach is going to be largely the same the biggest difference here are my actual velocities themselves so in part c the car begins at a velocity of 35 meters per second and ends at a velocity of five meters per second so we begin in the same way we have the change in kinetic and potential energy divided by duration and I'm grouping those together factoring out mass and gravity and we pick up here where we got rid of v1 last time the difference here now is that I am talking about a change in velocity terms squared so I'm going to write this as one half times 1150 kilograms then I'm going to divide by 12 seconds here for good measure and then I'm taking v2 which remember was five squared minus v1 which was 35 squared meters squared per second squared and then the same unit conversion soup we begin with kilowatts and a kilowatt is a thousand watts and a watt is a joule per second and a joule is a newton times a meter and a newton is a kilogram meter per second squared and then once I calculate that quantity I add 47 kilowatts to it so watt cancels watt joule cancels joule newton cancels newton meters and meters cancels meter squared second squared cancels second squared and seconds cancels seconds and kilograms cancels kilograms leaving me with kilowatts so heck of it now is a bad time to go to sleep it's time to wake up we got math to do I'm taking 1150 multiplied by the quantity five squared minus 35 squared and then I'm dividing by two times 12 times a thousand and I am missing a parentheses and for that first part I am getting negative 115 seconds which is negative 57.5 and then I add to that 47 and I get a result of negative 10 so while I'm writing that down take a minute to ponder what that means so a common mistake for thermal one students would be to ignore the minus they have a tendency to ignore a negative sign if they don't expect it and that's a really bad habit to get into the negative signs are very important especially when we are talking about energy changes like this the fact that the change in kinetic energy was negative implies that we are getting energy out of that decrease in kinetic energy that change in kinetic energy is going to supply the energy for the increase in potential energy what that means is if we start at 35 meters per second and we don't touch the accelerator at all we will reach the top of the hill at a velocity higher than five meters per second because that negative delta was a larger magnitude than the amount of potential energy change required that means we have to supply breaking power the engine would have to work to decrease the kinetic energy in order to only reach five meters per second at the top of the hill instead of something higher than that you could also think of this as we are getting 10 and a half kilowatts out of this situation if we had an electric vehicle and we were able to recover that breaking energy we could get potentially 10 and a half kilowatts of the course of this process


Hello everyone this is Ahmed Dan of AhmedDan.com. You're watching one of my Australia travel videos and today I'll show you some roadside scenes. After returning from the great ocean road trip I'm heading towards Ballarat which is Victoria's third largest city. Ballarat is an outdrive from Melbourne. Sowering hill in Ballarat, a small city from the 1850 gold rush in Australia, is preserved as it was back in those days. You'll be able to go back in time and experience a gold mine city. I'll have lots of videos from sovereign hill gold city. Experience time and life in this recreated gold township of the 1850s with me. Thank you for watching this video. Forget about subscribing to this channel. Forget about liking this video. I'll see you shortly.