Think Tech Hawaii, civil engagement lives here. Aloha, I am your host Winston Welch and I am delighted you are joining us again today for this out and about show where every other week we explore a variety of topics, organizations and events with the people who fuel them in our city, state, country and world. As a disclaimer, any views or opinions expressed by me are strictly my own and not connected with any organization. That said, joining me today in the studio is that national, international guest Hans Peter Hoeter, who is social scientist, senior scientist, associate professor and deputy head at the Department of Environmental Health, the Center for Public Health at the Medical University of Vienna. He's a doctor, an ecologist and a researcher in environmental public health. It's a lot of words to you, so welcome to this show today and thank you for joining us. Yeah, thank you for the invitation. Well, you know when we first met, I was immediately fascinated with the type of work that you do. And I think that a lot of people don't even, can't imagine maybe what it is you do do. So what kind of work do you do in an ordinary, you know, for your job? For a daily work. Daily work, yeah. I'm a researcher and lecturer at the university, at the Medical University and besides that, we do not only do our research for journals where we publish it, we have to bring our research out to the public because when it comes to environmental health, the topics they concern, these topics concern the people outside, like, I don't know, pollution in the air, outer air pollution, climate change, to nutrition facts like chemicals in pesticides and nutrition and so on.  So you're teaching typical college age students or are they graduate students? They are graduate students. We have those regular university students and, of course, we have some postdoc lecturing where, when we are teaching students for public health courses, for example. Okay. And how does the public get your information? You said part of your job is to give information to the public. This show is one way we can get information. There are different ways. First of all, when we do some research, we have always a press release on our results. This is right now one of the targets of our university, that we think that it's not only for the specialists who are reading those journals, it is for the public. And so we do press release and, of course, if there is some emergency issue in Austria, for example, is there a problem with mobile phones? And there are some organizations who wanted some talk or presentations. We stand for that and we are doing that presentations in order to give information which is scientifically based. Okay. And your university is a public university, meaning it's supported by taxpayer dollars? That's correct. And therefore, the task is for me obvious, especially for public health. It has in the name public health public. So we do not only make our research in our small rooms. Okay. And so how did you get interested in this work? What's your background that you became involved in? First of all, I studied ecology. And after two years, all my colleagues, they got specialized, for example, in biology, or in geology. And I thought ecology and association to human health. Is there an association? How is it? And I decided at this time that I studied medicine together with ecology. That was the starting point, actually. So you studied ecology. And ecology is the study of our environment? That's correct. That is the science of associations and connections in between our ecology, ecological system. And this is a very systemic approach to look at our world. But it's not focused on human health. It's pure nature and how does it work? And what I tried to figure out is, okay, we are here as a human being. How do we interfere? Or how can we get good out of this very intense system we are surrounded by? So you've finished your ecological studies, which would have been... More or less. I worked parallel. Oh, parallel. Okay. And then you became a medical doctor. And did you actually end up practicing medicine as well? You have to do.  So I did my specialization in environmental health, which is a perfect combination to my ecological study. What is environmental health? Environmental health is investigating environmental factors, physical, like noise, or chemical, like pesticides or industrial chemicals, and their effect on human health. Is there... Are some factors associated with a health problem? This is the main focus. And there are two approaches. One is simply curative and medical. So if we have a patient and there is some chronic disease and we are... We try to analyze the situation. And we think there might be an environmental factors which aggravates that disease. We are looking on that. This is really individual, but the other approach, which is, in my view, a lot interesting and much more interesting and much more important is the preventive approach. So we try to establish and to develop guidelines which we recommend to the policy makers to implement. In order to protect the health of the population. For example, we have a fine particle problem due to diesel exhaust, for example. Fine particle problem from diesel exhaust. So there are very super fine particles in less than 100 nanometers, let's say. Very, very fine. So we have a problem and we try to generate and develop guidelines which says if you keep the concentration of particles in this level, you can protect human health. So you have obviously studied this field quite widely. You're a teacher in it. And now that you've been studying ecological health and human health and public health, some things are coming to the top of what's important in life now. And probably you have some things that seem more important than others to you and maybe some seem even critical to you in regards to human health or I'm even probably thinking planetary health and our effect on planetary health. And one question I want to ask you later, keep in your mind is are we going to be the last generation of humans to exist as we understand it or are we so quickly destroying our environment or are you an optimist or are we going to live in a post-apocalyptic world or are you optimistic? Very, very difficult question. I must admit, but however, there are some major issues, I would say. One major issue is, of course, air pollution. When you think globally, we know that several millions are dying premature death due to air pollution, indoor and outdoor air pollution. So the outdoor air pollution is generated by our transportations and fuels. So the next step is, okay, fossil fuels, where they will come from, okay, you'll need some countries, oil countries. How is that generated? So you start with air pollution and you end up in climate change. It naturally is going from one to the other. You start with thinking about greenhouse gases, is it only coming from our transportations is no, it's coming from our food chain, for example, or nutrition. When you're following that, you will stop all of a sudden with how is our agricultural system. Is it sustainable or not? Do we need a lot of fertilizer? Do we need a lot of pesticides to generate and to produce that product? So you come to nutrition and it's really hard to say this is more important. You can, I think it's very important is that you say all of those problems we're facing is in connection with our behavior and attitude with our wishes. Is our consumption and our wishes for consumption designed like today that we think we can have everything very easy or do we consider more, if I step back a little bit, I can help myself in concerns in regard of health and I help our ecology, our ecological system. So all of these things are just very interconnected as you start to say it's air pollution caused by fossil fuels, but fossil fuels feed our plant, our nutrition environment and then how healthy is our nutrition as well. I was just watching, I think it's food ink. It was a 10-year-old documentary on Netflix a couple of nights ago and I could see that and I think most of our viewers will probably understand that our system is very industrialized, it's very mechanized, it's very fossil fuel dependent also for fertilizers and chemicals as well used to kill pests or maybe some herbal things. So all of this is connected and then we're consuming these products as well as now genetically modified organisms and I want to ask you about that too. So it's interesting because your work sounds like it touches on, you can't isolate just you try to isolate one thing but it's probably difficult because of these factors. Yes, you have to isolate because the fuel and everything is so complicated and the connections are very hard to understand and it's very hard to bring it up to the public. So you pick for example one issue you think which is very important for us like transportation and air pollution. So you can explain that if the level or concentrations of particulate matter is above a special limit you know that in the community there will be pre-major death account for example I don't know 1,000, 2,000 whatever. You can pick this and can bring it in order to raise awareness. It's only one aspect but when it comes to the public you can say yes this is an air pollution problem but when we try to bring a solution it's very easy for you. Transportation means that we are using cars. If you use a car for example for half a mile what's an easy alternative you can walk you can read your bicycle or whatever your bike. So you start with it's a problem air pollution and it can damage yourself and your health. On the other hand if you substitute that for example one mile you are doing it with a bike you can help to lower the air pollution and you have a co-benefit because your physical activity in the average is far too less you have a benefit for your health so you protect on one hand the environment on the other side you can do something very easily cost efficient promoting your own health so the public becomes personal that's right it's the aim because otherwise when we are talking about problems to abstract yeah so if we say instead Hans Peter walked to the store and on the way to the store you're going to meet the butcher the baker and the candlestick maker you're going to make some new friends have some connections talk to people with their dog yeah you're going to have a lot of sort more social connections social that's a psychological psychosocial aspect of transportation right so and then maybe it leads into another area might be okay well instead of fossil fuels let's get some solar here or maybe I don't know wind a small wind farm on your ceiling and if you are following that thought it's of course important to make the way more attractive it's not attractive if you walk one block I don't know with no side with no sidewalk without anything yeah small sidewalk yeah hundred cars next to you yeah there is no green space nothing there is no shop anymore because they are gone yeah this is a next feature that you think that you see that city planning walking on the other hand less physical activity with our children is connected in that way it's very interesting and it and it is a way to bring the the abstract to the personal and then the personal back to the planning and saying that's correct I'm walking along here but the sidewalk isn't here there's no shops like it's dangerous to walk here so we need to fix this somehow or create a separate bike lane that's safe or whatever it is so obviously this is one of one really good example of how we can take this these complex issues that are facing us and we'll get to this after the break because we will take a break here but of how what can sometimes I think all the information out there all the noise so much information what can I do to make a difference so when we come back we're going to talk about that a little bit more along with some other things that we haven't touched on you're obviously a very deep thinker and really valuable the lucky that the that the university has you and that our society has you because you're you're you're asking very serious questions and able to communicate thank you for also being so fluent in English appreciate that because my German is I gotta say it's not good 50 50 anyway well thank you we are going to take a short break I'm Winston Welchess is out and about on the think tech live streaming network series and we're talking with Hans Peter Hooter who is here on a vacation but actually learning a lot about Hawaii so we'll be back in a minute stay tuned for more of the story hello I'm Yukari Kunisue I'm your host of new Japanese language show on think tech Hawaii called Konnichiwa Hawaii Worldcasting live every other Monday at 2 p.m. please join us where we discuss important and useful information for the Japanese language community in Hawaii the show will be all in Japanese hope you can join us every other Monday at 2 p.m. Aloha Aloha I am Howard Wigg I am the proud host of cold green for think tech Hawaii I appear every other Monday at 3 and I have really really exciting guests on the exciting topic of energy efficiency hope to see you there we're back Ken we're live I'm Winston Welch and this is out and about on the think tech live streaming network series and we're talking with Hans Peter Hooter senior scientist associate professor and deputy head at the department of environmental health center for public health medical university of Vienna he's an ecologist a medical doctor and a researcher in environmental public health and I thank you again for being here with us today and taking time out of your your vacation which is here and but you give a lot of presentations around the world I think and on these topics so now that you've come here to Hawaii and you've seen this a paradise that we have here what are your initial impressions and are there anything that you would say right away for our policy makers here's an idea that maybe you haven't thought of or here's something you're doing really good or both let's start with a very personal impression okay when I was walking at the street and the shops are open and cold air is pouring out of the shop of those shops yeah I think if it comes to climate change and sustainable thinking this is really not understandable inside it's like you are entering a refrigerator the doors are wide open and you have an ac which has to work and I know that the consumption of electricity for this is enormous it's enormous so this is a very easy thing that first of all it's too cool inside yeah which is not good for human health employees yeah for them it's not good for a customer because you come from very hot very hot to very cold yeah and this temperature difference is far too big okay so if you are reducing that problem so you're increasing the temperature inside you save a lot of energy a lot of money so I do not understand why the shops are doing this it's interesting only completely strange for me okay so close the doors and don't leave on the air conditioner so cold the air condition is you need to increase the temperature inside yeah the same with so everybody I know that air conditioning is in the US and in some Asian countries very important yeah but wherever I'm going and observing temperature difference and outside far too far too big too much too much so first second this is a beautiful island no doubt but the transportation system is not that which I would expect in an island with this reservoir of nature as far as I got to know Hawaii is advertising its nature so how does that is in line with the transportation system which is built which is based only only more or less except for the buses on individual motorization yes I don't understand that and I think this is a must to change we have more cars than people on this island more registered vehicles it's not wandering yeah it's a it's a big problem and in fact Hawaii has I think the worst traffic gridlock in the country we compete with Los Angeles but there's you know there's a million people on this island and it's only this big so it's it's a it's a good question and a hard one and as we are looking at increasing populations here as we drove from Waikiki to downtown and I told you there's going to be another 11 towers planned just in one small area maybe 20 or 20 and you know in the next five or 10 years this is an this is an enormous challenge I know that because you have a built structure and how do you change that into a environmental friendly transportation system I know this is a challenge but actually when you look at the figures and even if you say or climate change I don't care it's a question of health of the people here we know that car dependency is associated with for example obesity because there is a lack of physical activity yeah so even you say oh I don't care for oil resources fuel whatever it comes down to the health of the people so you might have some people actually that leads to something so we need to look at how we're rebuilding our or retrofitting our our urban environment to have more walkability more trees somehow small scale small scale small scale areas where we can walk to shops and to medical appointments and have the smaller neighborhoods and for example and very important for your children because yes the development of the children I know it's in Austria it's something better something in Vienna is is worse yeah but when it comes to transportation traffic parents are afraid to bring to leave the children alone at the street sure because just because of danger yeah it's a danger it's a risk so we need to have safe places okay they stay home they look at their smartphone or a tv and then you have another problem so transportation system and with a transportation system I think city planning is is is combined with that is one of the major issues we have to think about and I think we're we're working on it here in Hawaii we're we're looking to get right now we have about 20 21 canopy cover of trees in the urban area but it's been decreasing every year because mostly of development they cut down the trees we're looking at trying to get back to 35 percent canopy by 2035 and do our part for for the the heat urban heat in island index where the concrete is making it very hot in here so that's one area because if it's too hot to walk outside guess what we're not going to walk outside old people can't go outside kids can't go outside dogs can't go outside and they the use of air condition will increase and it has to increase has to increase because you cannot stay as with when when you when you are older and maybe you have a lung or a heart disease in a hot apartment yeah it's impossible so the the idea to bring in a lot of plants is the same as you bring in a natural air condition so this is the first you have to do and what what what's important for me you do not need to invent all that measures I know books of that plan to treat everything and and how which one where how many square meter everything is here yeah this is I think always the message to the politicians or decision makers just do it do not have to invent it yeah please look at best practice here yes best practice yes but just think about it it's worthwhile to do that yes it's important it's critical I think in fact to do it because our cities are going to become unlivable if we don't do it we're looking at some climate change whether you believe it's human made or not and in fact we have a major political party and a president of the nation who says the climate change is not human made and that the climate change may not even be real now the the pentagon has identified climate change as one of the top threats facing the nation which is interesting from a military perspective WHO and and all how do you deal with how do you deal with colleagues and with with people who are smart who say Hans Peter come on that's just it's fake it's fake news it doesn't exist humans have existed for you know 100 000 years the climate change is a little bit now and then it used to Europe used to be an ice now it's going to get a little bit warmer this is all not true how do you deal with that as a scientist trying to give science-based information okay first of all in the last couple of years it becomes more and more difficult to bring up the scientific evidence to the politicians not because it's too complicated but if it's something which is not really nice or which you or an issue where you say ooh we have to go against the cars and you have to go against some too hard inside or chemical industry yeah leave it yeah so uh the thing we are observing is that it's more doubt on evidence even this evidence that's 100 percent yeah it's not at all say you know very high percent super high percentage yeah but you cannot it may be there is some some doubt yeah uh is for us a very big problem because sometimes I'm saying okay maybe in the next time is then is two plus two really four yeah so we just where do it end it up yeah go to the solution directly we have to um we have either you are discussing with those colleagues yeah and I have to say back home uh it's scientists 98 99 percent says yes that is a problem and it's human weight so we're hoping the truth wins yeah we hope that but it's really a big problem for us well I because you are you are there is a lot of work into that science and if the science is not taking as it is why are we working on that well don't give don't give up on speeder because we I think the truth will prevail of course it has to people see it for what it is as we leave today and we have to close what is the one thing that I can do if there's one thing or maybe three very simple things I can do in a couple words to make a difference because all this is out here but what can I do as an individual first of all more respect to to the nature okay the second is very simple when it comes to transportation more work okay think about that another thing why turn on your turn off your air condition when you're leaving the house okay and the other thing is um eat less eat less yeah okay well and it's true I know the studies show us yeah alternate day fasting and all types of things so walk more need not to be fasting yeah it's only a little bit limitation it's we are here and maybe okay one will well really simple and I wish we had more time to explore these topics maybe you'll come back to Hawaii again and we can but I'm afraid we have to wrap it up today so we're going to walk more we're going to eat less we're going to be more conscious of respect of the environment and each other so I really appreciate you coming on the show today um we've just barely touched on all of issues I encourage people to go to the internet and find out more about them for themselves what they can do to make a difference so I'm sorry folks we are out of town it's awful we have to wrap it up I am Winston Welch this is out and about on the think tech live streaming network series and we've been having a very interesting discussion with the super smart and nice guy Hans Peter Hooter who's a medical doctor and researcher doing very interesting work on environmental public health and we hope that you've enjoyed today as much as I have so thank you for tuning in we welcome your feedback thank you to our broadcast engineer the lovely Robert McLean our technical producer Ian Davidson our floor manager Eric Calander and to Jay Fidel our executive producer who puts it all together I'll see you here in a couple of weeks where we're going to have another interesting show on out and about aloha everyone


Hi there, and welcome to this video where we're going to do another example of an optimization problem. And this one is fairly heavy on the trigonometry, it turns out. It's always worthwhile to get a little bit of a review of our trig when we can, and problems that involve trig are very, very common in the real world anyway, so we might as well get this really mastered. So here's a very basic problem. We have a triangle here. It's an esosceles triangle. Two of the lengths of the sides are three and three. We're not given the length of the third side, but we are given an angle between the two sides that have length three, that angle is theta. And the question is what angle theta maximizes the area of this triangle? Before we do any mathematics on this, let's just go over to Geogebra and convince ourselves that this really matters, this really is an optimization problem. I probably have a sense that changing the angle in this triangle does change the area, but I need to convince myself first of all that the area can reach a maximum value, but at some point once the angle starts getting larger, the area does not keep getting larger. So I've got this set up. Here's the triangle from the problem. It's a esosceles with side length three over here, side length three over here, and although it's not labeled this angle in between here at point A prime is theta. I've got theta set up as a slider here, and just watch the area of the polygon here as I change the theta. If I slide theta all the way back to zero, obviously there's no triangle at all, but if I start increasing the angle, it grows and grows and grows, and so right about here and it begins to drop again. Okay, so there is an angle value. It's difficult to say exactly what it is. That was the largest value I managed to get by messing with my slider, but that's not really precise. So theta around 1.6 seems to give a maximum area. It's pretty clear from looking at this that I don't need to let theta go any less than zero, and I don't really need to let theta grow any larger than pi, because theta is equal to pi. It's 180 degrees and it just flips around and becomes the same triangle again. So I'm looking for the value of theta maybe on the interval from zero to pi that maximizes the area. With that in mind and being personally convinced that the area does actually reach a maximum, let's go back to the slides now and set up the problem and do some math. Okay, so now back to the picture of my problem and we're going to try to find the angle theta that maximizes the area. Now let's work through this in an organized way so we don't lose track of things. So here I've drawn the picture that helps. So I have the triangle with the sides labeled and the angle labeled. Now I want to first of all identify the quantity that I'm trying to optimize here, and that is area. Okay, area, and I'm going to denote that with an A. A for area. Now what I want to do is look in the problem and think about any formula or relationship that I know of that would possibly tell me how to find this area, and probably the one that jumps first of mine for most people is that this is an area of a triangle and it's one-half times the base times the height. However, we haven't really put the base and the height in the picture, so let's do that real quickly here. The base is just the length of this side here on the bottom. We don't know what that length is actually. It's tempting to say three, but we don't know this is an equilateral triangle, just an isosceles triangle. So that big thing down there is B. And then H is what we get when we go to the vertex up here and drop a perpendicular down to the base, and that's what H is. So I have area in terms of base and height. This is kind of far off from what I want because I know that area changes as the angle changes, and it's a relationship between area and angle that I'm interested in. So at this point, my goal here is this is a perfectly fine formula for the area of a triangle. Don't get me wrong here, but it's not really useful in my problem because it doesn't have the angle in it. So my intermediate goal here, before any calculus can reasonably take place, is to take this area formula and convert it into a formula that has area on one side and theta on the other. Right now, theta is nowhere in sight except in the picture. So I need to go to the picture and relate the base and the height of this thing back to theta, and this is where the trigonometry comes in. What I'm going to do is focus on the, let's say the right-hand half of this triangle here. So let's just pull this triangle out, split it in half, and this is what we would have. There would be a right triangle. This side length is still 3. This side length is h. The bottom side length is half of the base. So that's b over 2. And because this is an esosceles triangle, this angle up here is also cut in half. So this angle is theta over 2. So when I snap that triangle in half along the dotted line and look at the piece that's left over, I have this little right triangle here. I think I can use this right triangle to relate b back to theta and also h back to theta. If I can do that, then I can relate everything on this right-hand side back to theta. So let's see what I can do here. Well, first of all, looking at what I know about trigonometry, I have a right triangle here and this angle up here is theta over 2. And the adjacent side to that angle is h and the hypotenuse is 3. So I know one thing, and that is that the cosine of the angle theta over 2, that's the angle in this picture, is equal to the adjacent side divided by the hypotenuse length. So I do get something here. I know that h is equal to 3 times cosine of theta divided by 2. Now, I can feed that back into the formula here and I'm one step closer to having my objective, which is to have a formula that phrases a area in terms of only theta. Now, the b is what's next here, but I think I can use some more trig to help me out with that. The same triangle would say that the sine of theta over 2, okay, sine is going with old Soca Toa, that's the opposite side divided by the hypotenuse. And so if you simplify this, this is telling me that b is equal to 6 sine theta over 2. Okay, now we're talking and I can put that right back into here. So now I actually have a nice formula that gives me area in terms of angle. It may need to be simplified a little more, but we can work with it at first here. Area is one half, instead of base, I just now found the base was equal to 6 sine theta over 2 times the height, and the height is 3 cosine theta over 2. And, of course, that simplifies to 9 sine theta over 2 times cosine theta over 2. Now, there are more simplifications we can do and I'm going to do that on the next slide. Here's where we left off. A is the area of the triangle is 9 times sine theta over 2 times cosine theta over 2. If we wanted to, we could proceed through the problem now without doing any further simplification, but there's one trig identity that we can pull out here that makes this really, really simple to work with. And it is the identity that says that for all angle values x that 2 times the sine of x times the cosine of x is equal to the sine of 2x. Now, why do I bring that up? Well, I see that I have a sine times cosine of the same value of an angle, so I think I can simplify here. If I just set x in this trig identity equal to theta over 2, what that gives me is 2 sine theta over 2 times cosine theta over 2 is equal to the sine of 2 times theta over 2. Does my making a substitution? And so what that lets me say here is that the sine of theta over 2 times the cosine of theta over 2 is divide both sides by 2 and I get 1 half. And then on the inside, these 2's cancel out and I have sine theta. So now I can make a nice big substitution right here and say that the area of my triangle is 9 over 2 sine theta. Really, really simple formula here. So now I have achieved my objective. Notice no calculus has taken place yet and that's really true for many optimization problems and most of it is just set up and trying to simplify as much as possible. However, I'm ready now to proceed with the calculus because the quantity I'm trying to optimize, that's area, is now phrased as a function of a single variable theta and that's where I wanted to be. So now what we're going to do is the following. We're going to try to find the absolute maximum value of this function, A, on the interval from 0 to pi because remember we said that the angle gets bigger than 180 degrees, it's just the same triangle, just flipped around one of the sides here. So what is the absolute maximum value of this function on that interval? Well, recall how we found global optimization. We had to find the critical values of this function inside that interval and then evaluate those along with the end points of the interval back into the original function. So now we're going to switch into calculus mode and take the derivative with respect to theta. So A prime of theta is equal to 9 halves cosine theta. That is the only calculus step that takes place in this entire problem. So it's totally easy, but we really have to whack through a lot of underbrush to get to it. Okay, so let's think about where this function has its critical values. Well, that would be where the derivative is either 0 or undefined. Now, the derivative is just 9 halves cosine theta. That's defined for all values of theta. So where is this equal to 0? Well, it's where cosine of theta is equal to 0. And that happens infinitely many times, but only once inside the interval from 0 to pi. And that's at theta equals pi over 2. So that's the one and only critical value of my area function inside the interval. So now I'm going to take it and go over and make a little table of values of pi over 2 and a, all right? And I'm going to evaluate in here my critical value, pi over 2, and then the two endpoints, 0 and pi. And a, remember, is over here, 9 halves sine theta. Now, the sine of pi over 2 is 1, and so the area there is 9 halves. The sine of 0 is 0, and so is the sine of pi. You might have noticed that. When I, back in georgibor, had a slider either at 0 or at 108 degrees, there was no, the quote unquote triangle was just a straight line. There was no area at all. And so we've actually done it. We have found that the area of this triangle is maximized when theta is equal to pi over 2, and the maximum value of the area is 9 halves. Now, let's go back to the georgibor picture and see if that works, given what we've just computed. We just made a bunch of calculations that showed that this triangle has a maximum area of 9 halves, and it happens when theta, the angle up there at a prime, is equal to pi over 2. But we should never totally trust our computations until we double check them with a physical model or something visual. So what I'm going to do here is just move the slider until I think that it maxes out the area, and it seems to max out at 4 and a half, which is 9 halves. And I note this by going to a calculator that pi over 2 is about 1.57, and given the decimal accuracy I have here on georgibor, that would round to 1.6. So this does actually fit. The visual tool here corroborates our calculation. So let's do a brief recap of this fairly complex problem here. We first of all, in any optimization problem, want to identify the quantity that we're being asked to maximize or minimize. In this case, we're being asked to maximize area. And so the next step in the problem is to pull out anything and everything we know about that quantity. And very readily here, we can identify that area is equal to 1 half base times height. Now, however, this may not be ready for calculation yet. The goal now is to phrase area, the target quantity I'm trying to optimize in terms of exactly one variable, namely the variable that is being manipulated. Here, it was easy to come up with a formula for area in terms of two variables, but first of all there are two variables, and neither one of those variables was the theta that was mentioned in the problem statement. So my immediate goal was a lot of algebra and a lot of trigonometry, eventually trying to get a formula that looks like what you see here in the blue circle, where area is on one side and an expression involving only that angle is on the other. Once we do that, we have a very easy step to take a derivative, and the goal of using the derivative is to find the global maximum and minimum values of my function on that closed interval on which it's defined. And once we do that, we have both the maximum area itself and the angle at which it's maximized. Thanks for watching.


everyone and welcome! This is Melissa Armo and I thought I would review here the play of the day here which is Target. Unusual activity here in the gap. Let's just take a look at it. I'm gonna show you here what it did. Stock reported early this morning was gapping down then flipped then really wasn't gapping down at all. It was almost neutral then ended up opening kind of neutral little down fell hard and definitely looks lower here now. Holding 73 which is a good area for it to hold target today on target if it target today on target target today on target if it continues to drop is guess what 71 this is setting up again right now you could short this here and put a stop at 73 10 73 15 just to be safe again target is 71 if it continues lower not sure really where this goes in the bigger picture but for today target was a short and was busy doing stuff today late call in this worked really really nice worked but again the biggest rocks you get here in the morning okay here in the morning is where you get most of the biggest drops which is why I like to play the morning I was involved with some things was on Cheddar TV this morning but ended up seeing this boom climate late stop over 73 actually the people that were still in it actually held did a quick trade in here late late okay late late moves happen in here but I think it's just better to do the morning and quit and that's why I focused on that period between 930 and 10 so was able to get a quickie here today in target for a scout sometimes when you don't get the move early you can do a late one like that this trade that I called though with a stop over 73 is still on for people that are still in it it actually is back down near the entry price and is looking good so 71 is likely for target today if it continues to drop market is ify here I'll go over that in a minute but congratulations to everyone that did this today it worked it was good it fell it was a quick one if you get in late and sometimes you missed the first move in the morning it's always good to do it a quick one I call it a scout but that's what I like to do if I'm late either way it was a nice profitable trade and actually so far March has been a hundred percent win ratio every trade that I've called so far in March's work today is March 6 the last two months January February we're really good months too so we'll see what happens here we're on a good run gonna continue to stay focused focused and we'll see where we go the next month have a great day everyone if you're interested in learning my method and joining the live trading room as a Golden Gap class student you're eligible to join the line trading room you can email me at Melissa at the stockswush.com have a great day everyone


What's going on everyone? Sam here with Lane Sports Guard, Drippin' 22, Panini, Select, Football Hobby, 3 box break, number 19, random team stat. There's a look again at your RAM results. As always, you can find those on the website under the results tab, as well as the link in chat. That's an oxymoron, Jelani Woods, Foss Gardener, Sylvah, Kyle Pitts, and Garrett Wilson, Field Level Rookin. 49, 49, Bobby Wagner for the Rams. Super tag of my low end, Jair Alexander. You were the Duncan. Christian Watson, Alec Pierce, Silver Club Level, Resol Rookin. 3-1, Barney, Drake London, 2-1, 49, Club Level, Tri-Colour, the Falcons. Sylvah, Davis Mills. I did. Barney Cooper, Crystal Lavey, Rookie. Sylvah, Snapshots, Jalen Hurts, Silver, Chase Claypool, DJ Moore. Yeah, 11-45. Cole Strange to 35, White for the Patriots. Sylvah, Sondhaskins. Devon Bush, Justin Fields, Silver, Sam Howe. There's Micah Parsons, 2-49. There's 2-2-99, Tyrell Edmonds. Silver Auto, nice one there for the Steelers. Yeah, thank God we got Flacco and we did, because oh my God. Yeah, Kyle Buller. Oh, jeez, there was quite the carousel for Flacco. Oh, yeah. So, 1-99, K Von Thibodeau, Rookie Jersey Auto for the Giants. Can he pick it, Rookie? There's an XRC. Desmond Ritter, Silver Jamal Williams, Stefan Diggs, XRC. Defense 2, gonna be Devin Witherspoon for the Seahawks. Devin Witherspoon. Yeah, Troy Smith would have been cool to see succeed. Seahawks are hit. Yes, Jermaine Johnson to 1-99. John Runyon, blah, blah, blah. Simba Dylan Parham, and Kenneth Murray. I'll double check that after this vlog. Pretty sure. White's Tom Brady, nice. 7 of 35, congrats, Tampa. Going to Sean G, there you go, Sean. Hell yeah, man. Matt Stafford, Silver and Lewis Seen, and Mark Vanjers, I'm pretty, I'm like 99% sure. Landerson, yep, Devin Witherspoon, fifth overall. Perfect. Maybe I'll rock a Ravens jersey tomorrow. Rock my Anquan Bolden jersey. My Mark Ingram jersey, my Mark Ingram Color Rush jersey that I got for $30, fairly zappy. You don't have to re-cap that, it's zappy. To 1-99, Hassan Haskins, Silverado. And Mark Cooper, Olavé Rookie. Silver, Terry McLauren, Field Double, Scary Terry. Ah! Sauce Gardener. Absolutely. Jack Frescott, C-149. Silver, Cam Jordan, and Nick Bolton. Gold, the Darius Smith. Nice one there, that is 10 of 10. Former Raven, Grats on that Vikings, Andrew Thomas, Silver, Amonra, and Ed Ingram. The jerseys are sweet. What's up, Drew? How you doing, buddy? Blue, Derek Stinkley, welcome, welcome. 2-99. I'm doing well. Silver, Badger, Judy, and Mark Ingers, Manjers, Reed, Proble, Redwood, Blue, Redwood, Splatter, chocolate tomorrow. Nice. Yeah, I got a Ray. Red, Kenny Pickett, nice one there, 2-99. And congrats, Steelers, going to Brian B. Silver, K-Von, Tobin, and Bree, Saul Rookie. Yeah, 22 selects, pretty clean, I agree with that. Silver, Cameron Dicker, Bush, some Weston. There's a, Kenny Pickett, Lime Green, Davis Mills, 2-49. Cadarius, Tony, 2-199, Jersey Auto for the Chiefs. That's Juan there. Add a 22 select, or just in general. 22 select, ooh, there's a lot that came out of 22 select. Joe Burrow, Jay Jettos, ooh, Amon Ross, St. Brown, Numbers Game Auto. The hell, I haven't seen this before. That's pretty dope. Alliance, nice. Pulled a 1-1 to Lave, that was pretty good. I don't know, there's been a few. Pick a plane, what would you be your fave? I don't even know how to answer that. Desmond Ritter. What? Purple, Tyler L. Geer, 75. What are we doing? Seriously. Silver, Kirk Cousins, and two a tag of Iowa. 1-1 to Lave, probably the best so far out of 22 select. Silver, Bobby Wagner, Drake Young, Drake Jackson. I don't think we currently have NFL right now. Silver, Desmond Ritter, Silver, Khadir Kahau and Joe Mixon. Not for sale, this is a group break. No, it was a, I think it was a Premier level. Premier or a club, one or the other, I forget which one. It goes NHL, dot, dot, dot, can you read? I said, yeah, we have NHL. So yeah, it's a hand read. Dot, dot, dot. Yes, dot, dot, dot. There's 49, Nick Bolton. Kenneth Walker. Silver, Devonta. No, this is hobby, not first off the line. I don't think we have any first off the line, actually. Charles Cross. Scholar Thompson to 75. Silver, Damian Pierce. And Kenneth Murray. Sauce Gardner, 52, 75. Jumbo, White Jersey, nice one there. For the Jets. Silver, Son of a Knight in base, oh god. Yeah, yeah, actually on the Steelers as well. DK, Darren Waller, upside down base. Silver, DJ Moore and Justin Herbert. Right after this, it is sold out already though. Christian Watson. Silva, Kyle Hamilton. There's Gabriel Davis to 149, or 199. There's only one card for that numbers game. Silver, Devonta Wyatt. So that's what, like, it's only Amanra. Silva, Jay Jettis. Silva, Trey Hendrickson and Saquon. Two, or Maroon, Vilas Jones, Jr. to 149. Silver, Julio and Nicholas Petit-Farre. Silva, George Kittle. Tagan, Quinteriana. I don't know where his brother is there. It's a whole strange to 249. Franchise's Numbers. Chavon Curse for the Titans. Devonta Smith. Kenneth Walker. I don't know, to be honest. That's true. That's gonna be a Jersey Auto, Bailey Zappy. Nice one there for the Patriots. You can recap it as that. Stefan Diggs. Ooh, that's gonna be something. Silva is Derek Sting, Miles Garrett. That is gonna be one of one, Bailey Zappy. Artistic selections. Cohen O'Leary S. and the Patriots. Nice one there. Hell yeah, there it is. One of one. It's, I think, number 15 on the year out of select, one of ones for me. 15th, one of ones I pulled out of select. Not bad, not bad. Congrats, Larry. Last pack, Mojo, right there. Uno de uno. On a super short-printed case hit, one of one. That's where it's Buck Allen. Oh, God. Probably somebody I know, the board. Uh-oh. Quick recap here. We had Saus Gardner, Bobby Wagner, Bailey Zappy, Chavon Curse. Numbers game, Amon Ross Saint-Round. Super short print, I have to imagine on that one. Yeah, from Contenders, that's weird. Cool, though. Kaderious Tony, Son Haskins. Defense two, going to the Seahawks is Chavon Witherspoon. Chavon Sibido, Torell Edmonds. We had the Kenny Pickett, 299, and a Juan de Juan, Bailey Zappy. For the Patriots, that'll do it for the break, guys. Thanks again for the film. Up next, 10 Box Tuesday.