Good day, fellow investors. This is an extremely important video and it will discuss why I'm not investing in Tesla, NIO, Aurora Cannabis, Bitcoin, and similar investments. It's crucial to understand the difference between value investing, long-term value investing, and speculation on the other side. And therefore, even if Tesla is, yes, I know, three times, up three times over the last six months, I didn't invest in it. I missed the huge bull run up. I got a lot of comments how I am an idiot, but I'm fine with that.  That's me, and in this video, I really want to explain the key concepts when it comes to long-term wealth building and chasing investment returns, chasing speculative investment returns. You'll see the difference between the one and the other, and if you pick, you will see what you pick, but over time, all the investors sooner or later come to the long-term investing path because it's the only one that works. I'll explain the long-term investing cycle, what's speculation, what's investing, compounding the key, what does losing money mean, why Buffett always says don't lose money, and then what's risk reward when it comes to investing. To put things into context, my name is Sven Kerlin. I'm an independent investor, stock market researcher. I manage my own money, my own portfolio, and I look for companies for businesses that give me long-term sustainable growing returns over forever, in definite time. That's what I do. That is what Buffett has been doing over time, and that's also, I'm sure, my stock market research platform subscribers can tell you about it in the comments below. That's what we are looking for. We are looking for those few businesses that will do well, create extreme returns with low risk because that's what investing is all about. Let's put that into a life cycle perspective. I'm now 46, going into 47 this year, and I've been investing since 2002, and if I'm 46, I'll probably live to 100, let's say, yesterday I was looking at Charlie Munger's speech for the Daily Journal. He's in his 90s, still kicking ass, and I'll make a quick summary about that, so please subscribe and click that notification bell for long-term mindset investing on this channel. So I have another 64 years of investing ahead, so when you put 80 years of investing, 80 years for the average person now, given the health, given where we are going, and or even 60, when you put 50, 40, 60 years of investing in your life cycle, then you see, okay, I have to find a way that I invest that's sustainable over the very long-term that will keep compounding my returns, and I have to do that in a way that it maximizes my investment over the very, very long-term. You have to invest in a way that you maximize your returns over the very, very long-term. Maximizing returns means compounding, allowing for compounding, not losing money, managing risk and reward. When it comes to all of that, yes, Tesla is up 300%, but what's the risk and reward with Tesla? And just to note, I really hope Tesla does it and becomes a big player in the industry, shifts from fossil fuels to electrical. So I'm a Tesla bull for the business, for the cars, for everything. I like this exuberance when doing business. However, when it comes to investing, okay, what's the risk and reward? We have seen the stock going from 400 to below 200 and then exploding. That's the risk, reward, and thankfully there is so much money in the system so Tesla can recapitalize and get more money, more money to do what it does, not that much from the business yet, perhaps in the future, but that's not something sustainable. And those that made 300% over the last six months, great, congratulations to you, but is what you did sustainable over the long-term, is again something you have to ask yourself. Also, will you put significant part of your wealth into Tesla? I will never put 10, 20, 40% of my wealth in Tesla because the risk of losing it all is significant and once when you lose it, there is no more money there to invest in other things and that's the risk reward. And when you put that into 100 years, there will be many companies like Tesla. One out of 10 will make it or one out of 50, but 49 will probably go bust. The first rule on investment is don't lose. And the second rule on investment is don't forget the first rule and that's all the rules there are.  And that's it, don't lose money, don't lose money, don't lose money because losing money doesn't allow you to compound and compounding over time is what maximizes your returns over the long-term. Just let me give you an example here. This is 100,000 compounded over, okay, 50 years with two losses of 50% after 10 and 20 years. The difference is staggering what's that 80% difference because no losses, the two losses in year 10 and year 20 really destroy the compounding effect. So if you invest in risky businesses, you have to be careful that the compounding effect is allowed. Similarly, if there are two losses in 50 years, in year 10 and year 20, you need to reach a 14% yearly return to cover for two losses in just two years of 50%. 4% is a big difference, four versus 10% is a big difference when it comes to investing. And then compounding if you invest in businesses that grow, that's why I'm not investing in Bitcoin or physical gold because there is no yield, there is no growth, there is not a real business that we can compound into infinity. Again, same as Tesla, if Bitcoin goes to 100,000, great. All of you that have it great, you'll make a lot of money and I'm always bullish on that, I'm always positive on that because the more the merrier, the more things are positive, it's better for all of us. So I'm not against it, but I'm just telling you why I'm not investing and then if it doesn't happen, if this loses, again, goes down to 3000, that's a big loss that doesn't allow for my compounding. So I'm focused on that compounding. Yes, I know it's boring, I know it's long-term when you're talking 50 years but that's why I have just 57,000 subscribers and each one of them is extremely valuable. And if you like this, again, subscribe, if not, there are plenty of other channels here on YouTube that will talk about Bitcoin, Weedstocks, Tesla and whatever is the hot stock at the moment. If you don't want hot stocks, if you want long-term compounding, then you are in the right place. There was so much exuberance about cannabis stocks, well, this is the result. Okay, those that invested when nobody was talking about 2015 made money but most of those that invested during the hot times 2019, 18, well, this chart tells it all. And now I'm really not smart enough to do this. I'm really not smart enough to find stocks that will triple quadruple every year and then do that sustainably over the next 10, 20 years. I am smart to do this. I'm smart to compound at 10, 15, 20% what I've been doing since 2002. And I can find those good businesses with low risk that give me a good reward over time because that's where nobody's looking at. Nobody's looking at five, 10 years down the road where you can find businesses that give you 10, 15, 20% with relative low risk and everybody's looking or, okay, ARK investments, Tesla's going to go to 10,000, 20,000, whatever, that's hot, that's something you can sell immediately.  But I think it's extremely important that I keep telling that to the world and if just a few of you hear that, then I did a good job. Just another example, if you quadruple your money every year, then in five years you have a thousand times more money. If you increase your money just 300%, so what Tesla did over the last six months? If you do that over 16 years and you start with 20,000, you end up with $85 trillion, $86 trillion, which is close to the current market's capitalization. So that's why it's not sustainable. You end up owning the whole world in 16 years. You own everything. All the companies in China, all the companies everywhere, you own everything, Jeff Bezos sells you Amazon, you own everything if you can compound at that rate and I'm simply not smart enough for that. So investing is about risk and reward. You try to limit your risk, not to lose money. That's what value investing is all about. You invest in cash flows, business growth, dividends, earnings, great business models that can sustain the ups and downs of the market. We have been living in 10 years of a bullish, great market, ECB-fed printing money, low interest rates, so huge tailwinds, but when you look at investing over your cycle of 80 years, 60 years, 80 years ago, the second world war was starting. So that's something you have to keep in mind. The world will change, but if you have good, great investing principles, then you will be set for life and that's the key. If I look at what is selling, if somebody is selling risky stocks, could make you filthy rich, but yes, but what's the risk and reward of that? So to conclude, if you want me to search and that's what I do when I'm not doing videos, if you want me to search for those great businesses and even if you find a few one a year, you put it in your portfolio. You will get dividends, you will get growth, you will get earnings for the rest of your life for infinite time with low risk, high reward. That's investing, that's compounding, that's value investing. So if you wanna check what I do for less than a dollar a day, you can check my stock market research platform. If you like this mindset, investing mindset, please subscribe to the free stock market investing course that I offer. It is free, it will forever be free or because I want to help those stock market beginners. Subscribe also to the YouTube channel, thanks for watching, looking forward to your comments and I'll see you in the next video.


In the last lecture, we had talked about the coefficients of potential and capacitance. As we are getting into more formal aspects of electrostatics, we will be spending some time in looking at certain mathematical foundations, in particular two equations of electrostatics, namely the Poisson's and the Laplace's equation. As we are aware that Laplace's and Poisson's equations are rather fundamental to electrostatics, so if we have a charge distribution, if we have a charge distribution given by the density rho at certain points, then the we are aware that according to Maxwell's equations, the divergence of the electric field is given by the rho divided by epsilon 0. . Now, as we defined the electric field in terms of potential that is electric field is given by gradient of phi, where phi is a scalar function. We could immediately obtain an equation for the scalar potential, namely del square phi is minus rho over epsilon 0 del dot del. Now, this equation is known as the Poisson's equation. Now, supposing I have a region of space in which there are no sources of charge, in which case of course, this rho becomes equal to 0 and my equation then becomes del square phi is equal to 0, which is known as the Laplace's equation. Now, we have fundamental interest in looking at the solutions of these equations, that is situation where there exists charge density given by Poisson's equation and region, which are source free, where the solutions are given by the Laplace's equation. The solutions of the Laplace's equations are known as harmonic functions. What we intend to do today is to look at both these equations and look at some formal aspects of the solutions, as well as take some simple example and see how they give us the known results of electrostatics, that we have derived from more elementary considerations. Once we have done that of course, we will go over to give you the formal aspects of the solutions of both Poisson's and the Laplace's equation. Let us look at first the, what are the formal aspects? Since we deal with the del square operator, since we deal with the del square operator, we would in general be interested in knowing what is the three dimensional expansion of the Laplacian operator. Now, in Cartesian coordinate, this is very simple. So, for example, if I want to write down del square of phi, phi is the potential. In Cartesian coordinate, it is simply d square phi by d x square, that is partial, del square phi by d y square and partial del square phi by d z square. It is of course, fairly simple. Now, very often we need to look at problems which show spherical or cylindrical symmetry. These will be the two most important geometries that we will be involved with. So, for example, if we look at spherical coordinates, as you are aware that in spherical coordinates, we have variables which are r, theta and phi. Just to recall for you, r is of course, the distance from the origin. So, supposing I plot this, my reference plane is x y z, r is the distance from the origin of a point p and o p, o p makes an angle theta with z axis. Then from the point p, we drop a perpendicular to the x y plane and then I have this azimuthal angle phi which my reference x axis makes with the foot of the perpendicular that has been drawn from the point p to the point p prime on to the x y plane. So, r, theta and phi are my variables in spherical coordinates, phi is the known as the azimuthal angle. So, let us look at what happens to the expression for the spherical for the del square operator in the spherical coordinates. We will not be deriving this because they do not really add to our knowledge because there can be found in any standard mathematics textbook. So, del square phi can be written as first the radial part which is 1 over r square d by d r of r square d phi by d r. Then I have derivative with respect to theta and that is r square sin theta d by d theta of sin theta d by d theta of phi of course. Finally, the azimuthal part which is r square sin square theta d square phi, well since I am using phi for the potential let me write this phi in a slightly different way that is the azimuthal angle. So, it is d phi square well I guess that is one of the reason why many textbook use v for the potential, but this should not cause much of a confusion. So, that is our expression in the spherical coordinate and the third geometry that we normally talk about is the cylindrical geometry and in the cylindrical coordinates as you remember that our variables are rho, then of course, polar. So, this is basically a polar two dimensional polar things and rho and theta are like polar angles. So, it is cylindrical will be rho, theta and z. So, z is just the z axis which is the same similar to the Cartesian thing and rho theta are the polar the typical polar angles in the x y plane and the del square operator in polar coordinate is 1 over rho d by d rho of rho d phi by d rho plus 1 over rho square d square phi over d theta square and of course, the z axis simply remains the way it is in the Cartesian coordinates. So, it is just d square phi over d z square. Now, we will be using them quite liberally and so let us look at first what is the formal solution of the Poisson's equation. Now, we actually already know the solutions, but it is a good idea to sort of double check that the electrostatic field or the potential that we know which has been derived from Coulomb's law and that was simply that phi at the point r is given by 1 over 4 pi epsilon 0. Then the integral is to be taken over all the variables r prime in the entire space and wherever there is a charge density.  So, the integration variable is r prime and we take the integral over all space at points where there are no charge densities d rho of r prime will become equal to 0 and so therefore, it will not contribute to the integral. Now, let us look at whether this is indeed a solution of the Poisson's equation. So, what we need to do is del square phi r. Now, remember that this del square is being taken with respect to the variable r of the potential the argument of the potential function. So, this is 1 over 4 pi epsilon 0. Now, since the integration is over r prime I can always plug in take the del square inside and rho of r prime of course, does not depend upon r. So, therefore, del square operator which is a operator operation with respect to r does not take care of that.  If you recall we had shown that del square of 1 over r is given by minus 4 pi times 3 dimensional delta function of the argument.  Recall the property of the delta function that delta function if it is inside an integral then it only contributes at one point that is the point at which its argument becomes 0. And so therefore, all that I need to do is to wherever there is a variable r prime there I need to put it as equal to r because r minus r prime becomes 0 there. There is a minus 4 pi plus 4 pi that cancels out I am left with minus 1 over epsilon 0 and rho at the point r because of the delta function. As you can see that this is indeed the Poisson's equation for the potential function phi of r and so therefore, I know that this is indeed the solution of the electrostatic problem. . Now, before we go for some illustration let us look at the general structure of these solutions what are the general properties of the solutions. The one of the most important point is this. So, you know we are solving basically differential equations. Now, while solving differential equations we also need what we know as or what we call as boundary conditions. So, differential equations are always solved subject to certain boundary conditions and so we are going to state a theorem which says that that if you take Poisson's equation and you have to solve that subject to a given boundary condition then the solution of those equations will be unique. Now, the uniqueness has a great advantage if you know that the solution is unique and if by intuition or by some other way you can show that a solution or a given function satisfies the differential equations and the boundary conditions specified then you know that those are that solution is the only solution. So, now what is meant by boundary condition? Now, typically what happens is this that supposing you want to find out the solution of the Poisson's equation in everywhere in space, but in that space I have let us say a set of conductors. We are aware that that the conductors are equipotentials. So, therefore, if I have a set of conductors I could specify I could specify the values of the potentials on those conductors and of course, I supposing in addition there is an overall boundary to that volume. So, for instance I have a big volume like this. So, this is my outside boundary S and let us suppose that these are some surfaces which are conducting surfaces. So, I specify that I know the potentials at S 1, S 2, S 3 and of course, S. Now, I need to solve the problem potential problem that is the Poisson's or the Laplace's equation inside this volume which is bounded by which is exterior to the surfaces S 1, S 2 and S 3. Now, the uniqueness theorem states that the solution that you obtain will be unique, but before we go to a proof of that the it is not always necessary that the values of the potentials are given on S 1, S 2, S 3 and S. Instead what we could have is we could specify the electric field which is of course, normal to the conducting surfaces. So, the boundary conditions which are there with us are of two types. So, the boundary conditions on which are applicable on these surfaces. So, first is we specify the values of the potential. Now, when you specify values of the potentials on the conducting surfaces and the boundary these are normally known as the Dirichlet boundary condition. So, these are known as Dirichlet problems. Now, if on the other hand you specify essentially d phi by d n normal derivative of the potential which is nothing but the electric field subject to a sign these are known as the Neumann boundary condition. So, what we are going to do is to prove that solutions of Laplace's or the Poisson's equation subject to Dirichlet or Neumann boundary conditions will be unique. Now, I must point out that the type of boundary conditions that we have must be a one type. I mean you cannot have on certain surfaces Dirichlet and on certain other surfaces Neumann boundary conditions because I mean such a problem would be known by some other name like Cauchy boundary condition and one can show that the solutions then need not be unique. .. So, let us look at what is it. Now, so as the same picture is being shown on the screen. So, let us suppose that the statement that we have made is not true. That is suppose phi 1 and phi 2 are two solutions of the same differential equation namely Laplace's or Poisson's and let us also further state that they satisfy the same boundary conditions either Neumann or Dirichlet. So, now we are interested in finding out the whether this is possible. Now, let me define a solution general potential given by the difference between phi 1 and phi 2. Now, since phi 1 satisfies the Laplace's equation or Poisson's equation del square phi 1 equal to 0 let us say and del square phi 2 is also equal to 0. This tells me that del square phi which is equal to del square of phi 1 minus phi 2 that must also be equal to 0. Now, this is true whether phi 1 and phi 2 satisfy Poisson's equation or Laplace's equation. In all cases phi 1 minus phi 2 which is phi satisfies the Laplace's equation. Now, since we have made. So, this is what we want to solve for phi in my volume v. Now, since I know that on the surfaces S 1, S 2, S 3 etcetera either Dirichlet or Neumann boundary conditions are valid. So, I have phi 1 for example, if I am talking about Dirichlet boundary condition then phi 1 on S 1 for instance is same as phi 2 on S 1 and similarly for S 2, S 3 etcetera. Now, that means phi at S 1, S 2 etcetera must be equal to 0. Now, the same situation is true if instead of Dirichlet I am Neumann supposing I say that d phi 1 by d n on S 1 is equal to d phi 2 over d n at S 2. Then again by subtracting we find that d phi by d n on S 1, S 2 whatever sorry this is same surface S 1, this must be equal to 0. So, notice that once the boundary conditions are the same the potential phi on each one of the bounding surfaces or d phi by d n on each one of the bounding surfaces must become equal to 0. Now, in order to prove this let me take you back to some mathematical exercises that we have done in our first few lectures. One of the things that we proved we called it Green's first identity. What we said there is that supposing we have got two scalar fields given by let us say phi and psi then if you take an integral over a given volume bounded by a some surface S of phi del square psi plus psi del square phi integrated over the volume this is given by the integral over the surface which is bounding surface of phi d psi by d n d S. Now, recall that this is true this is true for phi psi being arbitrary scalar functions. Now, since they are true for arbitrary scalar function I am going to do the following. I am going to take phi to be equal to psi as a special case and equal to the phi that I have chosen that is phi of our problem. So, this phi is of course, the arbitrary, but this is my potential this is the phi 1 minus phi 2. Now, so let us substitute it here and see what we actually get. So, what we get is if you take this will be phi del square psi. So, I have phi del square phi plus del phi dot del phi d q r that quantity is equal to integral phi d phi by d n I made a small error here this term should have been del psi dotted with del phi for the first identity. Now, you notice this right hand side is on the surface and we have seen that on the surface either phi is equal to 0 or d phi by d n equal to 0 depending upon that type of boundary condition you have. So, whatever be the boundary condition whether it is Dirichlet or Neumann this quantity is equal to 0. Now, so that tells me that phi del square phi plus well del phi dot del phi is absolute del phi square d q r that is equal to 0, but remember that phi satisfies a Laplace's equation phi 1 and phi 2 could satisfy Poisson's equation, but phi satisfies always Laplace's equation. So, del square of phi is 0, now if del square of phi is 0 this tells me del phi absolute square is equal to 0 and we all know that I cannot have an integration which is a sum of positive quantities only and get a value 0 unless each one of the term is equal to 0. So, which tells me that gradient of phi is equal to 0 which implies that phi 1 is equal to phi 2 which is nothing, but my statement of uniqueness. Now, what I will do is this before I go to formal solutions of this problem I am going to be looking at some simple applications which you are all familiar with and the results also we know. So, this is simply reconform or reassure us that the solutions that we obtain by the mathematical process that we are going to elaborate now also gives us the solutions which we are aware of from more elementary considerations. . So, let me first pick up or take the example of a parallel plate capacitor. So, the I have this parallel plate capacitor here I have got two plates one at sorry let me take the z axis as the vertical axis. So, I have a plate which is let us say at z equal to 0 and this plate I will be grounding it and there is another plate there is another plate at let us say z equal to d this is the separation between the plates. So, you notice that and let us make a statement that directly at boundary condition is true namely the upper plate is maintained at a potential phi 0. Now, in the region between the two plates there are no sources of charge. So, therefore, in the region between the two plates I have Laplace's equation for the potential which is del square phi, but remember that since I take the plates to be infinite in dimensions the there is no x and y variation of any physical quantity that we care to calculate. So, in other words any variation that is there has to be only with respect to the z axis. So, this is nothing but this tells me this is simply d square phi by d z square and that is equal to 0 which is basically reduced to a 1 dimensional problem. Now, you can easily solve this equation as we know that this means d phi by d z is constant let us call it a and phi as a function of z is then given by a times z plus a second constant b. Now, we need to now supplement to the boundary conditions. So, at z equal to 0 phi is equal to 0 tells me that the constant b is equal to 0. Now, at z equal to d the value of the potential is phi 0 and you notice my equation is now because b is 0 the my equation is phi z equal to a z. So, put z is equal to d and on the left hand side put phi 0 which tells me that a must be equal to phi 0 by d. So, therefore, the solution of this equation for an arbitrary z is in place of a I must put phi 0. So, that is simply equal to phi 0 by d times z. So, this is the potential phi of z as a function z and this satisfies the two boundary conditions that we have talked about. Now, I can calculate the electric field in the region between the plates because I know that minus the gradient of course, the gradient in this case is nothing but the derivative with respect to z. So, therefore, the electric field is directed along the minus z direction and it is given by minus phi 0 by d times unit vector k. Now, which is consistent with the fact that my upper plate will have positive charges and the lower plates will have negative charges because this is connected to the earth and the electric field of course, is constant in the region between the plates. Now, once I know the electric field once I know the electric field I can calculate the charge density on the plates. Now, while calculating the charge density it will little careful you have to notice that the normal component of the electric field is the charged density which is basically sigma is epsilon 0 times E n. So, if you take the lower plate since on the lower plate the direction of the normal is along the positive k direction. So, my sigma is nothing but minus phi 0 divided by d and of course, there is an epsilon 0 there and on the upper plate. However, the charge density sigma is just the opposite because the direction of the normal is along the minus z direction. So, that will be plus phi 0 by d into epsilon 0. Having obtained the charge density I can simply multiply it with the area of the plate of course, strictly speaking we have taken the area of the plate to be infinite, but we can multiply it with the area of the plate and get the total amount of charge to be given by phi 0 d epsilon 0 by A. So, I get the charge and you know that so, the charge q on either plate plus or minus of course, is area phi 0 d by d times epsilon 0 and you know that the potential difference between the plates is phi 0 and this immediately gives me that if I equate this to capacitance times phi 0 it gives you your well known expression for the capacitance which is A epsilon 0 divided by d. So, this is the simplest one dimensional parallel plate capacitor problem. Now, let us continue with different example. Now, let me take an example of a cylindrical symmetry. Now, in a cylindrical symmetry I take a coaxial cable as shown on the screen. So, I take a coaxial cable of an inner radius A and an outer radius B and once again if you recall the expression that I had for the cylindrical geometry, this was given by here just recall back. So, this was 1 over rho d by d rho rho d phi by d rho etcetera. Now, if my coaxial cable is infinite then I have what is known as the cylindrical symmetry of the problem and the only dependence of various physical quantities can then be on rho which is the distance from the axis of the cylinders to whichever point you are talking about along the x y plane or in the x y plane. So, the equation that I need to solve then would be 1 over rho d by d rho of rho d phi by d rho. So, this is my del square and this is equal to well let us say I take the Laplace's equation in this case suppose it is equal to 0. I am solving Laplace's equation because my inner conductor and the outer conductors are of course, charged, but I am looking at the solution in the space in between where there are of course, no charges. So, density rho is equal to 0. So, this tells me d by d rho of this quantity this is equal to 0 which tells me again that rho d phi by d rho is a constant and let us write that constant as equal to some a. So, this gives me phi is equal to d phi by d rho is a by rho which has a solution that phi is equal to a log rho plus another constant of integration which is b. Now, once again what I do is I earth at the out ground the outer conductor which has a radius b. So, therefore, we say that phi at b is 0. Now, phi at b is 0 that tells me that 0 is equal to a log rho plus b. So, which is b is equal to minus a log rho. So, I need to of course, obtain the constant a now and that is done by saying phi in the inner conductor has a value phi 0. So, this if I plug it into this equation I get phi 0 is equal to a log rho plus b. So, phi 0 is a log rho plus b which is well we have a what I should have done is since b is equal to 0 I should have written it is a log b.  So, that tells me that a is equal to phi 0 divided by log a minus log b which is log of a by b.  So, what I get is phi is given by phi 0 log of rho by b divided by log of a by b. So, this is my potential now once again I do exactly same thing as I did earlier namely I calculate the electric field which is nothing but the negative derivative of the potential. So, the electric field E is minus grad phi, but you recall that there is really no dependence in the theta and the z. So, this is nothing but minus d by d rho of phi times the unit vector rho and this is of course, fairly straight forward to differentiate and. So, you get phi 0 divided by the constant log a by b and the log rho is to be differentiated. So, which is 1 over rho and of course along the rho direction well the normal component of that now gives me the charge, charge density which is epsilon 0 E n. Now, once again you have to realize that the normal component for the inside conductor is outward which is along the positive rho direction and the normal component for the outside conductor is along the negative rho direction and. So, therefore, this is epsilon 0 phi 0 divide now I need to calculate the charge density on one of the surfaces. For example, supposing I calculate charge density on the inside surface I get rho is equal to a. So, it is a log a by b these are charge densities and you can essentially now calculate the charge per unit length. Remember that the coaxial cables are infinite length. So, I need charge per unit length which is simply obtained by multiplying the rho with the area and which is take a unit length and of course, whatever is the area of that and that is the reason why the charge density on the inner and the outer surfaces are not symmetric that is because the outer one has a radius b and so therefore, if you take the same unit length it has a much bigger area and the inner one has a radius a which is smaller. So, you could multiply that and then of course, you know the two conductors are being maintained at a potential difference phi 0 and once again you can find out the capacitance of the cylindrical conductor. I leave the algebra to you know to be done at home as a third example let me take a spherically symmetric situation. They are all boil down to all these examples I am giving they all boil down to one dimensional problems. So, once again I have a spherical capacitor as shown here I have shown a cross section here actually the outer one has a radius b the inner one has a radius a and once again I have complete spherical symmetry. Now, spherical symmetry implies that there is no dependence on theta and phi. So, I get my del square operator as we had given an expression earlier as 1 over r square d by d r of r square d phi by d r this is equal to 0.    Now, let us let us try to evaluate this constants a and b on the outer conductor the potential value is 0. So, phi at r is equal to b is 0 which is equal to minus a by b plus capital B which is the constant which means b is equal to a by b. The second condition is the inner conductor which is phi at r is equal to a that is a constant phi 0. So, let us plug that in. So, this is equal to minus a by r is equal to a and plus b which is instead of writing b I will write a by b. So, which is equal to a times 1 over b minus 1 over a which tells me that the constant a is phi 0 a b by a minus b, but since b is greater than a let us write it as a minus of b minus a. So, this is my constant and as a result my phi at any point r is given by there is a minus sign already there.  So, which is phi 0 a b by b minus a, but with a minus sign here and divided by b which means this b cancels out. So, this tells me that phi of r phi of r is given by this expression, but actually speaking you can sort of simplify some of these expressions a little bit and get for example, you will get phi 0 a b by b minus a you have a 1 over r there and since there is a a there and there is a a b there. So, I get minus 1 over b there. So, this is the expression for the potential in case of a spherical conductor let us complete this job. So, the electric field which is minus gradient of the potential is phi 0 a b by b minus a derivative of 1 over r is minus 1 over r square, but there is a minus sign there. So, this into 1 over r square into unit vector r. Once again because of the way we have chosen our axis the normal direction is the radial direction. The inner capacitor the inner conductor has outward normal along the radial direction and the outer conductor has in the opposite direction. So, the charge density of the inner conductor is epsilon 0 phi 0 a b by b minus a into 1 over a square how much is the charge contained there. So, q inside which will actually turn out to be opposite of the charge that is contained outside is simply obtained by multiplying the charge density with the area 4 pi a square. So, that is 4 pi a square will cancel with this a I am an epsilon 0 phi 0 a b by b minus a. Well, you can show that this also is negative of q outside. So, the capacitance of a spherical conductor which is simply obtained by dividing the charge in either conductor magnitude of the charge in either conductor by the potential difference between them which is phi 0 is nothing but 4 pi epsilon 0 a b divided by b minus a. Now, suppose I have just a single conductor now this I can do by taking the outside conductor to infinite distances that is if b is very large then you notice I can neglect this a in the denominator and then this b will cancel out with that b and I will be left with the capacitance equal to 4 pi epsilon 0 times a. This is the capacitance of a single conductor actually and speaking this should not come as a surprise to us because if I have a single conductor I know how much is the potential due to that and the capacitance can be very trivially obtained from the expression for the potential of a single conductor. .. So, let us summarize what we did today we spent some time today in talking about the formal methods of Poisson's and Laplace's equation. We proved that given for given boundary conditions either of Dirichlet type or the Neumann type where the Dirichlet means give the potential values on the conductor and Neumann means give the normal component of the electric fields on the conductor. For a given set of boundary conditions this solution is unique and so what we did is to take simple exercises of problems which you had done in the past of a parallel plate capacitor a cylindrical coaxial cable and spherical capacitors and solve them by this high power methods which are of course not really necessary but this sort of gives us a confidence by looking at the fact that the results are familiar to us this gives us a confidence that the system works. In the next lecture we will be talking about the formal solutions of Laplace's equations.


Well hello there! It is Sandy and it is the summer of stamping. Ellen Hudson's got four new releases on all the Mondays in July and I'm going to be sharing each one of them with you. I'm really excited about this one. It's a partnership with Lawn Fawn and it's called Samour the Marrier. I did this card three times with this stamp set. Sometimes it just takes a while but it's got little critters, it has the little campfire, it's got s'mores and all kinds of little accessories to go with it and I use just this set of colors, believe it or not. That's all the colors that there are in there and I will be putting that picture over on the blog if you want to see what the colors are but I thought I'd share a little about how I did the stamping. First I laid all three stamps down here. I wanted the s'more in the little guy's hand so I stamped the s'more but I wiped off the part where I thought his hand would be and then I put him in there and put a sticky note over where the full s'more would be and that left me with the little paw on the sticky note so I could trim off the paw, put the sticky note back into place and then stamp it and his little paw would be in the front. I did have to do a little line work to clean things up myself because my stamping is terrible as always. I always tell you I'm a terrible stamper but then I started making my background and what I'm doing is creating a ring around the fire. The fire is going to cascade light out in an oval shape. The back half of the oval will be smaller than the front half of the oval and I'm just going to use progressively darker colors as I work toward the inside. These are E8s. That's an E89 and an E87 which are both desaturated colors and then I'm going to switch to saturated colors as I get close to the fire and saturated means it's going to have more reds in it, more strong colors rather than be more grayed out and for right now it's going to look like it's a rug. Like he's some giant round rug and that's not what it's going to be like eventually but this is setting the undertones of what I'm going to do on top of it because I want to make it look like dirt. So I put a little shadow underneath of where the fire wood is and then just blended it slightly and then comes turning it into a scene so I made a horizontal line back there so I kind of have something to gauge myself by instead of that weird oval and started making horizontal flick marks with the different colors. I just cycled through them, went through the E89 and the E87 and the YR27 and a Y23 and just kind of kept going back and forth between them making horizontal lines but you can see that under coat of the oval still remains so I still get the feeling that there's something rounded there that that's where the light came but all the stuff on top is making it look like there's more horizontal lines from the dirt so that is one of the ways that you can convey that light. I also wanted to put some water in here because it's World Watercolor Month and this is not watercolor but I thought it'd be fun to at least pretend there's some water in the picture so I put a little lake in there and I want you to notice how light the lake is going to get in a few minutes but now I'm going to put the sky in and I wanted really dark rich sky so I took a V09 and then a BV17 and just went crazy with just putting colors in here not really worrying too much about the blending getting them blended enough that it wouldn't be too noticeable if it wasn't perfect and then some B99 just as I started getting down toward that horizon line and then went in with my black marker so that I could make mountains back here in the background and the mountains you can make whatever kind of shapes you want if you want to make it a desert or a high mountains or whatever kind of campground you like to go camping at totally fine you could put trees back there all different kinds of things so now I've got this bright lake look how bright that lake got all of a sudden because color is relative to whatever is around it so I put some darker colors the the two purples that are in the sky just so that it would reflect some of that sky color because I wanted it to disappear but I just wanted it to sort of be there in the distant background and since I had the purple in my hand I threw some purple in the foreground too and then I wanted to have some grasses there so that made the the land ending up there in front of the lake and so it wouldn't be just like a hard edge and that purple didn't end up being dark enough so I went in with the black and did just some grasses just flick marks for grasses going up into the lake itself and then started bringing the colors back downward toward the fire because now I need to almost complete the other side of the circle because I hadn't really done any blending on that side of it so I worked my way from the black down to browns and then just started adding a little bit more color just to soften some of those edges and tighten in the circle because the tighter it is the smaller it's going to feel the more intimate it'll feel I put a shadow behind the hedgehog because he's blocking the light from the fire and now it's time to color the hedgehog itself now I could have colored the hedgehog and the fire first most of us would but I wanted to color him based on the colors that were in the rest of the picture I wanted to know how dark to get so I used the E87 and the YR27 so he would match the dirt and then added some lines in it using the E89 so that gave me kind of him fitting in with the whole scene and using the same yellows and same gold colors and the same brown colors then in the samore that he's holding and I have no idea I can't I can't even remember I haven't had a samore in so long so chocolate go on top of the marshmallow I think it does because otherwise you'd have the marshmallow and mushing on top I don't know which one goes on top so he might be holding us some more upside down but if he does then you know tough luck right so I made each of the pieces of wood have a little highlight on top since they'll be lit by the fire and put a little gluing into the fire itself and now for this crazy like fire thing you can make realistic looking fire by using a white pen and while it's wet use your finger to smush it and I'm just kind of pushing and twisting the lines up there and it's almost better if your pen skips because mine was skipping a little I was like oh that looks kind of cool and so I started putting just a bunch of different lines coming up from the points of the flames and then I dried it because I wanted to do something else too and I didn't want wet ink there don't ask me how I know that that will happen that'd be a problem for you I went over it with some Y17 and then started working in some of the Y02 just to start pulling some some highlights in above now you have to scribble your pen off you don't want that acrylic on the nib of your pen but then I added more white on top of it just for the top layer and then I got some yellow along with the white and I used a little bit of Copic Colourness Blender in the sky just scribbled a little bit to make a galaxy and then threw some stars in there now this is one of them that I did I colored it this whole thing several times don't ask me how mad I am at my camera for screwing it up but each time I did a little different I used different colors this one I hadn't put the lake into but I had the little guitar in his hand and the way that I stamped the guitar was the same way that I did for the Samore I stamped the guitar wiped off the top of it before I stamped it so it was empty I put the sticky note over it and then stamped him and then move the sticky note to the other side so I could stamp the bottom of him same way as I did with the Samore and decided I needed a little more yellow on his face but you know you can see the color difference I just use different colors you can use all different kinds of colors you don't have to use exactly what I used try and see what you've got this was another attempt when the camera went belly up on me and I had two of them going and I went crazy with my coloring and then found out later the footage didn't work but one of them is holding the little Samore thing and again I blocked off the bottom half stamped the top of him and then I blocked off the bottom half with stamping the Samore thing first and then around the outside I just put you know trees and branches and grasses and things so they're kind of nestled in their little camping spot so those three were fun I wish I hadn't had to do it three times to get one set of good footage but you know that's how life goes sometimes I also did the same thing in color pencil so I'm going to turn on some music and you can just watch the color pencil version this is the one that's going to go up over on Instagram and I thought I'd share it with you so let's go and do some color pencil I hope you enjoyed that and if you'd like to check out the links that are on my blog as well as in the doobly-doo and I will see you again with another video in a couple of days thanks for hitting that like button see you later


So my dad ended up taking me to the studio. I couldn't even reach the mic. We had phone books, I sat on top of the phone books. I couldn't get the notes right. So my daddy had to lay a dummy track, and I had to listen to it like four or five times. And then my dad was like, can you do it now? Yeah. Bar baby. Pay no attention to that. When you and Big Mo did that song, how did it happen for you? You were young, but how did it happen in your eyes? So I was six when we actually recorded the song. And D-Wreck and Note D actually called my dad. I was told that they were trying to use a sample. Couldn't find a sample. So my dad ended up taking me to the studio. I couldn't even reach the mic. We had phone books. I sat on top of the phone books. I couldn't get the notes right. So my daddy had to lay a dummy track, and I had to listen to it like four or five times. And then my dad was like, can you do it now? Yeah. Bar baby. And they was like, yeah, that's it, baby girl, that's it. I didn't really pay no attention. I got down, got my Barbies, went sat in the studio while they did whatever they did. When it hit was when I went home. And I don't know how they did this so fast compared to now how you got to get everything mixed in master before you even. I got home, getting ready to get in the bed, go to school, and my daddy put on the radio. And he said, listen, you got this brand new joint by your very own big mold bar baby. Future Ron, that expensive. It's the bar baby. That quick. You were so little. That's quick. And I'm just trying to figure out like, how did they get there? Now knowing what I know, like it's processing steps that just show you how much power they had back then and how the ties were. Put this on the bed. Put that on there and get it done. I got tired of listening to the song too. It got to a point where when we were getting the car to go to school and I'd hear that, I'm like, Ernie, what did you do? I went here. Did your friends know it was you? No, because I went to private school. So I went to a Christian private school. Them kids didn't know nothing. They didn't know. They don't listen to that type of music. They was trying to straight listen to whatever they were being told in that school. That's it. When I made the transition in third grade to go to public school, some of the kids knew. Yeah. But they didn't know it was me. And my daddy had instilled to me, don't tell nobody that you keep it quiet. Wow. This is a public school. Privacy. We don't know how these people are. Oh, you're talking private to the public. Yeah. And then I went to middle school. Beverly Hills Intermediate. And it's one guy named Ray Gonzalez. We want to play a game of Google. Is that all right? We're going to Google our names. I wasn't thinking. I was like, all right. We got free to do that. We got free period. You want to Google people's names? Google. You didn't even know what would pop up? We Googled everybody's name. Got some mom probably third to last. And it popped up. I know the Spencer bar babies. I was like, oh, I'm getting in trouble. I'm in trouble. What did they say when they seen it? What did your friend say? I didn't have a cell phone. I wasn't allowed to have a cell phone in school. My daddy said the only person you need to call was me. You need to call me and go to the principal's office. They got their razors, right? And they texting people. And I'm like, what are y'all doing? Ray was like, why you didn't tell us? My daddy told me not to tell y'all. I get called down to the office. Oh, you got called to the office for this? I got called down to the office. The word spread that quickly. It spread quick enough to get to my daddy's phone. I got called down to the office. I get down there. My dad and my grandmother and my daddy looking at me like. You was about, what, 10, 11, 12? I was about 11 and 12. He looking at me like, what did I tell you? It's not that hard to keep your mouth shut. And I'm trying to explain to him, it's not my fault it was Ray. And he like, who was Ray? He googled it. And then my grandmother was like, technology. You can't stop that. Right. Yeah. So he was like, what, we're going to have to have a talk with the teachers. They had to talk with the teachers. Kids treated me okay. I got a little special treatment, you know. But for the most part, kids, they treated me fine. And when I got to high school, it was a whole different ball game. When I got to high school. You were of this popularity? He was in high school with me. Oh, this is true. Dad, nigga, high school, sweetheart. This nigga, man, out of nowhere. Did he ignore you? Out of nowhere. No, he was my crush. She had a girlfriend, so he was my crush. Oh, that nigga Cheetah. Yeah. Okay. No, just kidding. I was nerdy. Like, I had the glasses. Man, I transitioned into contacts my junior year and all that stuff. So when I would see him, it was kind of like, you know, to my friends. He got a girlfriend. But what I would say with junior year, senior year, people really started finding out. You said that's that girl that was on the big mall. How did they react? What did they do? High school was a trip. Did you get any bullying? No. Somebody. It was cool with everybody. Okay. You had the people that didn't like me. I didn't really care. You had the ones that was the non-believers didn't really care either. Then you had the ones that were in the music industry that knew, that recorded at my daddy's studio and was like, nah, you good. We got you nowhere. Then you had just the ones that wanted to just say, hey, I sat with her. I took a picture with her. Yeah. But I was cool with everybody. I didn't have any problems. I wasn't a problem child because my daddy didn't have a problem coming up to the school. Yeah. He didn't either. But in high school, it was just kind of like, you seen bar baby. They treated me like a celebrity, but it was kind of like, oh, she cool. You Bernetta. Yeah. She cool. She seen too. I wanted talent shows. Wow. So I mean they would, they would show mad like North Shore show mad love on talent shows. I get up there and do my love.  You know, they rock with me. The teachers rock with me. But high school was okay. Middle school just kind of scared me because I didn't know what was going to happen. I didn't know if I was going to get in trouble about running. Sorry, daddy. Call you by your first name. Let me ask you. So, so when, when, when Big Mo died, how was that? How was, and well, let's not talk about that. Let's talk about you getting older and him still, you know, you and him having that relationship. What was that like? Um, I would get calls. Um, they kept in touch with my grandmother a lot. So I would get calls, um, making sure that those grades never dropped.  And that just wasn't from Mo. That was from all of them. Like all of them. Like who? Uncle Screw.  He was my cousin's godfather. Okay. So he was family too. He, he, he wants these money. You better keep them grades above, you know, above average. I'm letting you slide with the A minus, but baby girl education is key. Okay, Uncle Screw.  You can't come to the house with no more. You can't be doing none of that no more until you get your grades. And it was the same thing with all of them. Um, my Uncle Derek was the same way. Um, CEO of Rec Shop. Rec Shop. Them boys went home. Yeah. Progress reports and report cards was mandatory. Wow. I wanted to keep. I did. I was about to say, did you get paid for that report card? I'm still paying to this day. They let me slide with B minuses, but if it was a C on there, we had a CA talking. Like sometimes I couldn't go to the studio, but until I brought it up.


Consider the scatter plots you see on the screen right now. When you look at these different data sets, what type of shape does the data seem to form? If we were trying to connect the dots, like in this first example, A, and we try to do it in some continuous manner, what we see here is a graph that kind of looks like it's some type of exponential function of some kind, right? It does have that same kind of basic shape. And when you look at these other pictures, you kind of see the same idea as well that they appear to be these exponential graphs. All right, so this is something like that. And maybe you get something like this. These have these various different exponential growth and decay type graphs right here. And so I wanna kind of mention, how could you come up with a function to model these type of data sets if you believed your data looked like an exponential function? Well, when it comes to exponential functions, one of the most distinguishing characteristics is going to be its horizontal asymptote. So if this truly is an exponential function, that is the data model something exponential, there has to be some limiting value. So like either a maximum or a minimum value on the graph that the function doesn't seem to surpass. Now, if it's a growth model, right? I mean, we actually see two different types of growth models here. There's this one where basically emerges from nothing, or in this case, around two, and then it increases without bound really rapidly. That'd be exponential growth there. It could also be that you have this growth that's exponential, but even still, there's this limiting value. It doesn't get past something like this. So this one right here would be a good example of like population growth. That there's some baseline population, which in this case, you know, it probably would be zero, but even still, there's something like baseline that it grows off of going up and up and up and up without bound. But like this one right here, this might be something like if you take a very cold object and insert it into a hot environment, like Newton's Law of Cooling, it would start getting hotter, hotter, hotter. At first when it's really cold, it would change its temperature rapidly, but then it would slow down as you get closer, getting closer towards the reservoir's temperature right there. And then for the last one right here, again, this would be some type of decay model as you're going off towards some limiting value. Again, like Newton's Law of Cooling or radioactive decay or something like that. So you have to look for these horizontal acetotes. If there's no horizontal acetote, then it really isn't an exponential graph. So what you wanna know about an exponential function is the most general form of an exponential function is gonna look like Y equals what we'll call C times A to the X plus K, where you have some type of vertical stretch, some type of base. The only thing we know about the base is the base has to be positive and not equal to one, like so, and then there's gonna be some type of shift that goes on there, shift up and down. Now, what's nice about these exponential functions is if you wanna determine the shift, all you have to do is find the horizontal acetote. Where is the horizontal acetote? So for this one, we put it at Y equals two. For this one right here, we got it at Y equals 10 and this one looks to be about Y equals one. So we can see the horizontal shift very easily just by looking at, of course, we can look at the horizontal, the location of the horizontal acetote is the horizontal acetote's location. It's Y coordinate gives you the vertical shift for there. So the next thing to look for, I would then say is look at this number C right here. So like we observed, K equals the location, right? The location of the horizontal acetote. This number C on the other hand, you can determine C here by taking the difference. This is gonna be the X intercepts, excuse me, the Y intercepts location. Take away the horizontal acetote's location basically to take away the K. So if you take the difference between the horizontal acetote and the Y intercept, that is you take from the Y intercept the horizontal acetote, that gives you this value C. So then you'd have to look at your pictures and kind of see what do these Y coordinates look like right here. We'd have to kind of make an estimate of some kind. Something like this. So for this picture, it looks like it's gonna be like 9.5 would be my point right there. And so you take that, we're gonna subtract those then. We see that C is gonna equal 9.5, take away one. So we get 8.5 as your coefficient, okay? And then you can do similar things for these other ones. Like this one right here, you're looking like, let's say 0.5, take away 10. So you get negative 9.5. And that's good because the negative sign does indicate that it's kind of reflected downward. It's concave down compared to concave up like most exponentials are. And like this one right here, what do we wanna say it is? It's pretty close, right? So we might say something like 2.1. And so we get 2.1 minus two, which give us 0.1, like so. And so then we get these C values. And so the next thing then, then the determinant is going to be your base, right? So we have to determine the base. Now some of you might be inclined to use the natural exponential for which you have to modify your function as y equals C times E to say like the Rx plus K. You can make that adjustment. It's really okay. You can either do A or E to the R. If you wanna do exponential, like natural exponential, you can do that. That all involves some logarithms to solve for the R value right there, the rate of growth. I'm just gonna stick with just my basis arbitrary right here. In order to do this, then you just have to pick a point, right? Pick a point that looks like it's on the graph and use that as a baseline to figure things out. So like if you take this one, for example, right here, it's like feels like that's a point on there. And so it looks like three comma, I'm looking at the picture here and guessing, but we probably would have a dataset that would tell it to me. This looks like 6.5, something like that. For which then we can now work with our equation. We have y equals 0.1 times A to the x plus two, for which then if we plug in the x and the y, we're gonna get 6.5 is equal to 0.1 times a cubed, right? Plus two. And so then you can just solve for A in this equation, right? You're gonna have to subtract two, divide by 0.1 and take the cube root. You can do all of that. A little bit of a tip, if you can find the point when x equals one, that is a great point to use. So if I come over here, oh, that looks pretty good. That looks like one comma three. I like it when the x coordinates one because then you'll see y equals 0.1 times A to the first plus two, excuse me. Oh, I need to put in the y coordinate. The y coordinate turned out to be three. And then I think about when you take the first power is that you just get back in A, right? So you don't have to take any roots or anything like that. So we'll subtract two from both sides. Three minus two is one. We get 0.1 times A. And so you can divide by 0.1. So A equals one over 0.1, like so.  And so our function, our model, model first one would appear to look like from my observations, y equals 0.1 times 10 to the x plus a three. Like so. And so that gives us an equation for the first one. If we do the second one, right? We wanna pick a point. Preferably the x coordinate one is really good. Like I said, it just makes the calculation a little bit easier. It's not necessary. If we take x equals one, that'd be about this point right here. So we'll say one comma, that's about four and a half again. Again, I'm just kind of eyeballing it. We can use technology to improve this calculation dramatically. But really in this video, I just wanna emphasize how do you do it if you're just looking at it using a scientific calculator, right? Could we do this? So our C value turned out to be negative 9.5. A we don't know yet. And then our K value turned out to be 10, I believe. That's what we saw, yes. And so then we're gonna plug it out. We have 4.5, negative 9.5 divided by A to the first plus 10. So we're then gonna proceed from there, right? So track 10 from both sides. That's a 4.5 right there. So we take 4.5, take away 10. That gives you negative 5.5 equals negative 9.5 A. We're then gonna divide both sides by negative 9.5. So we get 5.5 divided by 9.5 for which that would then give us, put it in the calculator.  Again, with a computer estimate, we can do a much better estimate here. And so we then can write this down. Y turned out to be negative 9.5 times 0.57895 to the X plus 10. That equation would model the data you see right there. And then for the last example, let's finish this one up. So our equation will look like, oops, Y equals our C value on this one turned out to be 8.5. We don't know what A is yet, so that's what we have to solve for. And then our K value is a plus one. So we wanna look, again, if we can, find the point when X equals one. That way we can just kind of simplify things a little bit. So that's about this point right here. Let's say that's one and five and a half, right? Again, I'm just kind of estimating using my eyeballs for which then we're gonna plug those in there. So Y turns out to be 5.5. We get A to the first plus one. So you subtract one from both sides, you're gonna get 4.5 is equal to 8.5 A, for which then A, A should then be 4.5 divided by 8.5, for which when you throw that in your calculator, you get 4.5 divided by 8.5. That, whoops, that then gives us 0.52941. And that would then give us the equation we want. Y equals 8.5 times 0.52941 to the X plus one. And so we can model exponential functions by using the data here. My first recommendation is look for the horizontal acetote, then look for the y intercept, and then look for any other point on the graph, preferably the point one. And if you do that, we can minimize the calculations, the arithmetic necessary to model this thing. And again, this gives us a good estimate of these exponential functions that'll match the data pretty accurately. Again, we can always improve this by using statistics and computer software. But just so you have an idea of what's going on here, we're looking for parameters to fit the data, and this is how we can do it for exponential functions.


What's up everybody, Jason here for Jasper's Case Breaks.com. We just filled up 2019-20 Upper Deck Opeachy Platinum Hockey. It's a 16 box case break. Pick your teams number seven. And again, we're giving away a free Opeachy Platinum box. How to get an answer into that is just buying two teams or more in this break. So winter take all no max entries. You bought two teams. You got one entry. You bought four teams. You got two entries. Six teams get three entries, etc. etc. Full 16 box Baxter case. No veteran common ship. And again, pretty pretty nice stuff here. So we have to pick your teams here. Everybody in. Rango, Last Bomb Module, Toronto Maple Leafs. Let's print it and let's start ripping. So again, this break should take me about an hour, hour and ten. Maybe twenty. Just depending on how quick I rip. So I'm gonna try my best to get it done as quickly as possible. But after that, we have the optic football blasters that we can do. Ooh, the cardio is on. So cardio is a great, great flick. This is the first one, the second one. This is the second one, I think. Yeah, no vetship. I'm gonna say something else. Minjmans, baby. Yeah, we can also do the cello pack as well. But remember, we had to do two more after that and also sell 15 spots. So I don't think the mixture is gonna happen, but we can sell the cello and we can always create another one. But I don't think that's a problem. I think that'll sell out for sure. But definitely want to try to get those breaks on that are already close. They either have a filler, so that way we can try to work on those and get those done tonight. Optic Baseball is very nice and it's choice edition, Jarrell. Choice edition. Even damn better. Alright, third box guys. Last box and then we'll go through these four boxes, guys. There's one fourth of the break. Good luck. Sadino Chara, Inola. You got a Nino Nito Rider Arctic Freeze to 99. You got a Cam Fowler. This is a little sunset, which looks beautiful. Beautiful looking car. Taro, Conor McDavid, Kail McCarr, Kotakanyemi Rainbow, Victor Olsen, Jack O'Varana, Sturm, Wolfquist, Timo Meyer, Braun Sturm, Kenny Malkin. I've got orange checkers of Brem Burns. 21 out of 25 for the San Jose Sharks. And Sharks is Jarrell, Prohorcan, Getzlaff, Rainbow, Jack Hughes Rookie. I thought all of these came out like backwards. Quinn Hughes Rookie, Kenny Malkin, Violet Pixels of 3.99, Ferraro, Conor Timmons, Rainbow Rookie, Texier, and Klim Colston is the Rookie Autograph for the St. Louis Blues. Lafferty, Eichel, Dornfront, John the Quick, Eddick Horan. They'll be breaking after this in about an hour. Quinn Hughes. That's pretty nice. Little Violet Pixels for Vancouver. And all of Sunset. Kenny Malkin into 1.99 Red Prism. And we got Joseph Matthew. It's an update right there for the Lightning for Matthew Joseph, sorry. Matthew Sunset, beautiful looking car. Max Vox. Red Wings, David Duffy. Matt Pink, Abramov. Tyler Bertuzzi to 99. That's Arctic Freeze. Elia Sunset. I'm good accordion.  Kind of just bugs my eyes. Right new job. I'm always like trying to just like touch my eyes and finish. Barrett Hayton, Dornfront, Bargov, Mark Besser, McCarr, Olson. And we got Conor Clifton. Boston Bruins. That's Courtney. Jack Hughes, Matt Pink, Ryan Johansen, Quinn Hughes. We got Quinn Hughes and Jack are together all the time. Matthews. Red Prism to 1.99. It's about to have two autographs. Logan Brown, Otto going to Ryan Revan, Kaleman Carr, Zadina, and Ben Bishop to 1.49. All right guys, next four boxes. Yeah, well I'm taking a little longer than usual just because I want to separate the vet base from the rookies and stuff. So it makes the shipping team, sorting team's life easier. You know, so it may add an extra 10 minutes to the break, but at the same time it's worth it. We all got to chip in. Right now JR, Quinn does have better value. The only thing is that, you know, Quinn is, if I remember correctly, Quinn is a defense man, which is nothing wrong with that. But you know, Vancouver is in the playoff bubble, right? I don't think the Devils are one of the better teams at all in a while, you know, and they haven't been for the last couple of years.  He's going to develop and he's going to be pretty good.  So right now Quinn's a good buy and a good sell, but you know, I think, I think defense men's value does die down quicker than Jack. And I think what Jack is, he's a centerman. So we'll be touching the puck a lot more. But yeah, I mean, like I said, people love defense men that can score and do everything. So that's why, you know, that's why Rossman's Dolly the year before was selling for a lot at one point, although he didn't want to sign. I don't know what that was up with that. But you know, as you can see, if they don't start scoring in their next years, they don't score too much. They're not really a factor. That's when their stuff dies down. Crystal Tang, but Jack has a high because he's only 19 years old. You know, he's not playing on a really, really good team. So that also kind of affects the value. The Vancouver Canucks, on the other hand, are a young, stub team that's just hungry for winning. And you have Quinn, you have Elias Patterson, you have Brock Besser. I mean, you have some pretty strong players on that team that makes it super exciting. That's super young. You know, not that the Devils aren't young, but they still kind of have to put it all together and they have a lot of pieces missing. But I think Jack would be pretty solid. It's just you got to give him a year or two. I mean, he made the team as a 19-year-old, which is pretty solid. So that's always good. Can come out like Connor McDavid and Matthews, their rookie years. We usually don't see that. So that's why Matthews and McDavid are like, they sell for what they sell for. Because I mean, Matthew scored four goals in his first game. You know, that's pretty crazy. A Brahmoff. Ryan Pohen, 99. Haswell started here. The playoffs? The NHL playoffs? Yeah, it started like a year or two ago. A couple of games already ended. I don't know if there's any games live right now, but the playoffs half-starters. Oh, the Nuts player right now? Damn, let's watch that too. Is that on NHL Network 2? Are they on FS1? Yeah, I'm CMBC, sorry. All right, next one. A Brahmoff. Adam Fox, 99. Arctic Freeze. Kirby Dodge. Sunset. Kling Kershaw. I mean, Kling Kershaw. Kling Keller. Rad Marchand. Yeah, I think you can stream the games too, John, unlike, does Reddit still allow it? I don't remember. Reddit still does it, but Reddit usually works. And Remy, Pitlick. I have to 399. It's all over Wallstrum. Seismic Gold. 13 out of 50. It's one of my favorite cards in this product. Seismic Gold. Goody Glass, Sunset. And we got Sarelia. With Detroit. Jack Hughes. Techshade. Quinn Hughes. Jeff Skinner. Xbox. Yeah, we can finish up at NT. That's a quick break too, guys. So yeah, after this, guys, like I said, in about maybe another 40 minutes, so like around 9.15, 9.20, we'll do the blasters break. That should take me to like 9.55, almost 10 o'clock. And like I said, if you guys fill up on the breaks, I'll break them tonight. We'll do a little late night break in today. Kirby Dodge. And Techshade. 399. Violet Pixels. Goody Glass. And Ryan Poe. I want to joke your name is Ryan Redmond. We'll have Nylander. Matt Pink. Kita Gusev. Levor Hazak. Blue Rainbow. And Fox. She loves Zadina. Definitely one, maybe one and a half here. Another one for Instagram. So maybe about two and a half, three, 33 gallon bags every day. Just depends on the product that we break. So it's heavy paper based like this. It feels a little quicker. It's just no R-Boxes, NT. Well, that's easy. Johnny Goudreau. 2.99. Jack Hughes. Jack and Quinn are always linked together. Brent Stone. 9, eh? It's 1.99. And we got Trent Frederick. 1.99. And nice little rainbow rookie autograph of Blake Lazat. For my Kings and Amber. They're hating. Next box. Emerald Surge coming up. And nice. Oh, that's not Emerald Surge, actually. This is just a green out of 15 of green. What is it? Houndstooth? I almost thought it was Emerald Surge. That's not a 15 though. Emerald Surges are out of 10. It's a nice one. Another one for Blake Lazat. Kings. 12 out of 15. And Nathan Bastian. Ryan Polling. And Isaac Lundstrom for the Ducks. That's an update from 1819. All right. Next one. What makes it the best? Yeah, Chris. I'm not really so invested into it, to be honest, man. You know, I'm not saying that the Kings would have made the playoffs. There were still like like 10 points away or something. We've been trying to be like the last seeded one.  They're like eight and oh. They had built up so much ground where like the people that were into the bubble at 26, like the Kings were only like three points or four points behind them. So it's like you should have at least like finished off the season like the NBA did, you know, for at least the people that were kind of close by. But yeah, it's like whatever. But I'm just more rooting for the Leafs to try to make it. And then just because I love Ovechkin. I would say the Leafs are like my second team just to the Matthews. I know Ovechkin because I just want to see him win again and party like he did the first time around. Big girl, Olivesson. Roofer is on his way to play. Where the Islander's playing? There's Ovi speaking to him. Playing the Panthers? This could be a good one. I love me some Barcoff. Bottle roll for them in the way, man. It's $3.99, Jamie Ben. See, we're giving away that Barzell future watch, right? $9.5.10. It's a low pop. And that hockey mixer that's on the website. We were going to give away $200 and bear credit extra if it was going to fill tonight, but I'm not sure if it is. But maybe Nick will extend it and be nice and leave the $200 in there for tomorrow. But if not, at least the Barzell will give away. Well, of course. Yeah, Barcoff is very underrated. He's just such a great centerman. Nico Sturm. I don't know, Avalanche won their game today, right? Two to one against St. Louis like in the last seconds. I always just feel like the, probably Avalanche are like always one of the favorites and they just kind of just choke like for the last like three years. So, you know, like I said, Nucks are hungry and they're young. So, I wouldn't mind seeing the Canucks make a little run. Excellent. Oh, nice. Chris, thank you, man. Well, yeah, I have, I still think it has a little ways to go, but I think it might be nice enough and leave the $200 bear credit there for at least maybe tomorrow since he did post it up a little late today. But again, we're still giving away that Barzell though. That Barzell is really, really nice. Ben Bishop, Violet Pixels, Nico Sturm, Rainbow, Blu-rayne. Can you use Kezia? Red Prism, the $199 rookie. I'm pulling. Capococo, Rainbow. Kill McCarr. All right, good player for who? JR. McDavid, Rainbow. Can't go wrong with McDavid. All-time NHL favorite player. I'd have to say Copetar. But before Copetar, my favorite player was Alexander Frolff on the Kings, number 24. But when I started watching Copetar play as a king, I also really fell in love with Ovechkin. They're like one year drafted to each other. One year apart, I think. I think Copetar is 06, 07. I think he was 0506. I don't know, is Copetar 0506 too? I don't remember. One of those two years, but Ovechkin. But Copetar for sure. To me, he's very underrated. A lot of people don't really pay attention to him because he plays on the Kings, he's on the West Coast. Copetar did what he did on the East Coast. He'd have so much more praise. But he'd chillin'. Two-time San Diego champ, a couple Selkies, Jack Hughes. He actually should have won the consmite that one year. He'd actually led the Kings in points until in the 14 playoffs. It wasn't Justin Williams. I think they got their stats wrong. I think Copetar had one more point than Williams. And then Gabbard led them in goals, I think. Speaking of Copi, there it is. Out of 25, seismic gold rookie Benstrom for the Columbus Blue Jackets. Well, like in 1920, I think you kind of know more of the bigger chases, right? Kale McCarve for the Avalanche, obviously Quinn and Jack. I mean, for another years, it's kind of already, you know, players are kind of older now. So like, obviously, 18-19 Pedersen's a stud for the Canucks, best year of the year before that. You know, Matthew. So it was like McDavid the best rookie. Matthew's the next year. 17-18 was kind of a little shaky year. But he sure was the one to chase. But now he has autographs. You know, 18-19 Pedersen by far. Potokani Ami that year. Cody Glass is actually, I think one that's going to be pretty good for Vegas. I think he gets a little bit of recognition already. Three more boxes. But did he give it up or, or Nassim Khadri just scored? You know? I know Khadri scored it. I didn't get to see like a, a slow mold, how it happened. Like, was it his fault? Oh yeah, he didn't save it. That's right. Put it this way. Was it a better play or was it a bad goal? Put it that way. I don't think it's always on the goal tender. You know, the defenseman mess up and just leave a guy open. Did they not clean up the rebound? I don't always like to put the blame on the goalie. And we got Casey Middleson out of 50. Capobaco. Tech CA. Kail McCarr. Jack Hughes. Shifley. Wolfquist. Keeper. Matthew Guchuk. The punk. Yeah, James, if it sells out, I know it might say sold out, but as long as we got to sell out that little filler, which is a random number block, either right next to it or in the same category. But once that sells out, yeah, I'll break it. I don't think it's technically sold out. Did you guys sell out the filler already? No, it's done eight left, guys. This has to sell out if you want to break it. It's the random number block. It's $53. And you get a piece of all of those eight teams, which is the Astros, Reyes, Mets, Red Sox, Cardinals, Nationals, Orioles, Phillies, Tigers. That's one, two, three, four, five, six, seven, eight. That's actually 10 teams. Once we sell that out, then I can break it. And Carl Grunstrom. Awesome, Matthews. The Optic Blasters is the only thing that sold out to my last time I went through orders. If something else sold out, then I'll have to add it to the schedule. But Optic Blasters was the only other thing that I knew that sold out. So unless something else sold out, I'll add it to the break schedule once I'm done with this break here. All right, guys. The last two boxes. All right, guys. This is a 16-box Master. Gensel, Andrzej Vasilewski. And what a break for the Kings. Tobias Djarfra. One out of 50. Nice break for you. Amber with my Kings. Sega. All right, guys. Last box. What a break for the Kings. Jesus. Matt Roy, Violet Pixel Autograph. I could count at least like five Kings autographs. Ben Bishop, Matt Pink. Eric Carlson, Arctic Freeze. Molstrom, Seth Jones, Suzuki. Cliffbaum. Runstrom, Kopey. Dobson, Tavares. And an Orange Checkers of Philip Zadina. Nice. 24 out of 25. That's very nice. But everyone's had a good break, too. David Duffy. And Jesper Bofkus. Don't give up, Chris. I'm still going to be here for the next couple hours. So there's still plenty of time. All right, guys. So these are all your colors, rookies, base, stuff that will be top-loaded. Then here are your autographs and colors of bigger rookies and players that were top-loaded. A little quick hit recap. Zadina Orange Checkers, Matt Roy. Violet Pixel Autograph, Jordan Front. Runstrom, Benstrom. Seismic Gold, Cockle. Rainbow, Kale Bass. Ajax, Sturm Auto. Lumbstrom, Bastion. Blake Lazat. Out of 15. Houndstooth. Lazat, Rainbow Auto. Pohling, Kufner. Hughes. Quinn Hughes. Wallstrom, Seismic Gold. Pitlick, Pohling. Matt Pink. Logan Brown Update. Connor Clifton. Kale McCarbay. Quinn Hughes. Tarot. Matthew Joseph. Quinn Hughes Violet Pixels. Quinn Colston and Brent Burns. Orange Checkers. Now again, guys, if you did buy two or more teams, you have an opportunity to win a free box of what we just read, the PG Platinum. So let's see who's going to be part of that randomizer there. And let's give away a box. So it's alphabetized by customer name. And let's see, Amber. Got two spots. It's at least one entry. Boom, your end. Courtney, one, two, three, four, five, six. That's three entries for you. David Duffy with two. Your end. Edwin, one, two, three, four, five, six. Edwin, you got three. Draw with one. Jeremy, one. John, one. Mark with two. Matt Buckler with two. Both of you guys are in. Michael Gallucci with two. Your end. Brian Redman, you had three. So just one for you. And Will, Sabres and Rangers. There you go. So not bad. Thirteen. Customer names. There you go. Customer name and number one after. Five and a three eight times gets a free RPG Platinum box. One, two, three, four, five, six, seven and eight. Boom. Eight times. Edwin Hack, there you go. Free box of a RPG Platinum coming your way. Appreciate it, guys. Jaspy's casebreak.com.


Everything's waiting here for you. Ooh, that's a hot mug, guys. Hey guys, this is my review for last night in Soho. This is admittedly just a different setup because I actually just filmed a different Patreon video here, but I thought I might as well use it. Anyways, it's about the movie. This is the latest Edgar Wright film. This film follows a young fashion designer from rural England who comes down town to London to follow her dreams of being a fashion designer. All the while carrying some baggage. A grandmother who loves her, but is also a bit worried about her considering the mental illness history that her mother had as well as kind of the strange, more connected, medium like qualities that she has herself. And then when she comes to London, it's a bit overbearing, especially in her dorm room with the company that she keeps. So she finds a small room at the top of an apartment building. She goes to sleep and she starts to have this dream about Anya Taylor-Joy's character Sandy and how she came to London with dreams and aspirations of being a singer. And the opening scene is a 60s spectacle. There should also be noted that the main character, Elise, actually is a big fanatic of the 60s. She loves the music, the fashion, the style. Everything about the 60s is what she grew up with from records from her grandmother and her mom and that carries over into her influences. And the fact that she gets to relive the essentially these moments from Sandy's life through her dreams, I first show so much promise, show the aspiring starlet going to the big city to try and make a big kind of story. She starts to take influences from Sandy in these dreams and she incorporates that into her everyday life. She starts to change her hair, change her style, start to really reflect that of Sandy's story all the while kind of ignoring people in the current day who are trying to be nice to her, trying to be friendly with her who actually are friendly. There is one character in particular who's a really nice guy in here but there are also a lot of seedy people, one of them being Terence Stamp who is just in this movie to be a creepy old dude. But then as she starts to continue these dreams, she starts to see that Sandy goes down a dark road, a road that just keeps getting worse and worse and worse with every story. She realizes that the glitz and glamour that she was holding on for Sandy as well as her own is actually deeply buried under layers of deceit, debauchery and just seedy, ugly British people. As they get more degrading and violent, the dreams and the monsters that she sees start to bleed over into her reality and she starts to truly start to lose her marbles. When it comes to an Edgar Wright film you always know you're in for a visual treat and in terms of how he displays a story switching back and forth between Sandy and Elise. And while it takes a little while to get there, you're seeing a few of the normal tropes that Edgar Wright has with Elise getting to London. Once she has this dream, Edgar dips into that visual creativity that he's so well known for. During this opening dance number between Sandy's character and the old doctor who, it keeps switching back and forth between Sandy and Elise in the position of dancing. Now some of this obviously is done with just really fast choreography and other bits of it is done with visual effects. And I love this bleeding, this symmetry between the two, especially with mirrors.  You get connected to two different people's stories, one in the current day and one in the past. And as you start to go down this road with them, you get more and more connected to their story. And you feel this right up until the climax. I'll definitely say that the pacing of this film is fairly decent. The visual imagery is very well done. The connection slash homage love, clear love to the 60s is very much on display. But at the same time, Edgar is also willing to show what was wrong with that time, what was really hidden behind the curtain, essentially. While Anya Taylor-Joy really isn't much of a main character, we're getting her story through kind of montage assembled clips, essentially. As the dreams start to progress, I still really enjoyed her character as well as I enjoyed Elise's connection to her and just her slowly starting to lose her marbles, this connection, this medium sort of establishment that she has starting to bleed more and more where she starts seeing these faces and these people walking around her all the time. However, I will say that it actually does start to get a bit repetitive. There is a point where she has three freakouts, essentially, back to back to back, all within one kind of fluid sequence. By the second time, I was like, all right. And then the third time it happened, I'm like, okay, the story should really start moving along here because we're starting to see just the same stuff over and over again. We're not getting any further in the story. We're just seeing the same thing happen. And thankfully the movie does move on from this and I actually do like how it ends even though the movie blatantly lies to you at one point. Everything about the narrative is actually quite connected in terms of Sandy and Elise's connection, except for one very crucial bit that the movie will contradict at the end of the story. And I did feel that was a little bit of a cheap pull. I thought that maybe they could have established that differently to kind of fit that narrative more. It throws you for a loop for the sake of throwing you a loop because it needs to. Otherwise, the ending of the film wouldn't make any sense. Those are my only real kind of connections with the film. I enjoyed the acting. I enjoyed the directing. I enjoyed the story. I did enjoy some of the horror bits even though they did get a little bit too overdone. I always liked the idea of a story where someone's dreams, their fantasies become the reality but then that reality becomes a nightmare. I always liked that trick in narrative storytelling and it works decently well here even if you have seen the story done before. And so while Last Night in Soho might be not the most Edgar Wright, Edgar Wright movie you've seen, I still think it's a cool idea. I'm glad that he went with it. I'm glad that he tried something different and it's still a pretty well put together movie. In the end I'm gonna give Last Night in Soho a five out of seven. I enjoyed the aesthetic. I enjoyed the style. I enjoyed the characters. I enjoyed the story. I especially enjoyed the soundtrack. My God, this is one of those movies that makes me miss having my radio show so much because I would have played this soundtrack in a heartbeat. Anyways guys, that's all from me. What did you guys think of the movie? Tell me in the comments below. If you liked this video leave a like and if you're interested in more subscribe. Otherwise, see you guys next time.


T.F.N.N. Headline news update. Welcome folks. We had the Dow industrials finish down 36, NASDAQ off 58 S&Ps off 11 and a half, and you can expect those futures to get down a few more points coming into the close, which is another 15 minutes, folks. What you had out here is that you had a failure on price, failure on volume as they try to get into their highs once again. If we go and take a look at the spy, what you're going to see, bottom line, you got over the highs last couple of days. You got up to $300.90, and then you just gave it up, $298, bottom line is having a tough time up at these levels, and we're going into, it's the August 1st to timeframe, folks. That's your downdraft out here, $300.97 was the number. We got 3 cents over that, so your comparison is 46 million shares going into 142 million. That's where those sellers are laying. They're laying right at that level. Each and every time it goes up there, it says, you know what, man? I'll give you as many pieces of paper you want. You just give me that cash. Distribution and spades, NDX 100, 3Qs, bottom line, week-end to see, gets to a price point today of $194.42, and then just gives it up. And it looks to me like this NDX is going to be one of the movers on the way down. What's intriguing, of course, is that what we have is that we have Amazon as well as Microsoft coming out with numbers tomorrow. So those babies can move that NDX in a huge way. There's no two ways about that. We'll see what the ying and yang is out of this whole baby, but that NDX, NQZ in general looks to me like you get some massive selling inside it right now. Just from the 4 o'clock close, we just went down an additional 40 points inside the NQZ. Right now, you're down 82 points. This thing is going after the lows that were generated out here last Friday, which is 78.52, as I'm speaking, we're at 78.59 right now, folks. So that baby's going to go, we were talking a little bit earlier, right at 10 minutes of the hour. This was a confirmed ABC structure on the way down, and it looks to me like right off the bat, you're going to get this whole confirmed one on the way down. In fact, we just hit 78.53. Bottom line, you get monster selling inside these market spokes. Have a great night, have a safe night. We look forward to speaking to you right back here tomorrow morning at 9 o'clock.


How much can I earn teaching English in Greece? Due to the ongoing effects of the 2008 financial crisis, Greece is no longer the hotspot for teaching English abroad that it once was. However, it still has plenty to offer ESL teachers, including an average salary of 800-1000 euros per month, depending on experience. Until recent years, Greece was one of the most popular destinations in Europe for teaching English abroad. Unfortunately, the global financial crisis of 2008 has led to a downturn in almost every sector of the economy, including ESL teaching. Despite these setbacks, Greece still attracts a large number of foreign teachers every year due to the warm Mediterranean climate, countless stunning beaches and islands, and a relaxed approach to life. Athens is home to the biggest job market for teachers, while other cities such as Thessaloniki, Larissa, Heraklion and Corfu are also popular. Salary Although ESL teaching jobs are still relatively easy to come by, the salaries and offer have not risen substantially since the start of the financial crisis. However, the average salary for a first-time teacher of around 800-1000 euros per month should still be enough to cover all the basic expenses. Teachers with experience may find they can earn significantly more than the average sum. It is also common practice for teachers to increase their income by providing private tutoring in their free time. Hourly rates for private lessons range from 10 to 20 euros. Employers The vast majority of foreign ESL teachers in Greece are employed by private language schools known as Frontistieria. You will find over 6000 private language schools across the country catering to children of all ages, as well as a smaller number who handle business clients. As private schools are generally aimed at school children who come to improve their English skills outside of normal school hours, most positions involve teaching during the late afternoon and evening. The number of hours you can expect to spend in the classroom varies from one contract to the next, but it is typically between 20 and 30 hours per week. It is rare for contracts to include financial help with airfares, but housing support and paid holidays are often included. Private language schools generally hire teachers at any time of the year, although the peak hiring seasons are from August to October and throughout January. A degree in any subject is usually required and a Teflor or test hall certificate will also be a big advantage. It is worth noting that due to the extensive bureaucracy involved in obtaining work permits for foreign citizens in Greece, teachers with an EU passport are generally preferred by most employers. Cost of living Despite the economic downturn, Greece is still a relatively inexpensive place to live in comparison to much of Western Europe and North America. Housing costs are typically the biggest expense for most teachers working overseas, and while that is still the case in Greece, rental prices have actually dropped significantly in recent years. Utilities are another big expense, so many teachers choose to house share to reduce their overall outgoings. Imported goods, including food items, are generally expensive, but if you do your shopping at local fresh food markets, you should find much lower prices than in supermarkets. In general, the cost of living is considerably less on mainland Greece than it is on most of the islands that surround it.


with the upcoming winter storm this weekend it may look more like Christmas outside but for some springtime fun you can always visit with the Easter Bunny shoppers at the Paul Bunya mall in Bemidji can get dressed up in their best springtime outfits and visit the bunny with the very cuddly bunny i might add like visiting with Santa Claus meeting up with the Easter Bunny has become a yearly tradition for many families kids of all ages enjoy hanging out with their springtime pal tomorrow is the last chance to see the Easter Bunny before he leaves to go hiding all those baskets and eggs it's a terrific tradition and it's also a good day to come out and see the Easter Bunny because it's going to snow out there he's around all day tomorrow until five and then he goes and gets those eggs ready for everybody on sunday now the Easter Bunny will be at the Paul Bunya mall center court from 10 until 5 p.m if you enjoyed this segment of Lakeland news please consider making a tax deductible contribution to Lakeland PBS


Hi everyone, Joe for jaskiescasebreaks.com here. We finally did it. We knocked out that big number block. It was a big one. Hornets, T-wolves in the mix, plus the Kings, Thunder, and Wizards, it's a great number block. They're a good group of teams and that's how it works if you're not familiar with them. Remember Zero gets any and all redemptions, including one of one redemptions. So if you're looking for figure team four, that's coming up in a different video. Also in here, given away two spots, remember we promised those two spots. So if you click that tab, there we go. Big thanks to this group here. So we're going to do two different dice rolls. One for the giveaways, right? Someone here who bought spots straight up is going to win extra spots. And then we'll do another dice roll to randomize the full list of names, plus the numbers. All right, so this is for the giveaway. Top two, good luck. Top two after three, easy, two and a one, one, two, and three. After three, last spot, Mojo strikes again. Alan and Chris, congrats. You've got extra spots. So we'll put little rooftops next to your name. So I don't know, is the first person to buy a spot and the last person to buy a spot? You get the bonus spots. So congrats again. Thanks everybody for buying in. Okay, now let's do the randomizer for the numbers and names. And we'll put that in this official tab, the R&B tab right there on the bottom. So dice roll for this one, six and a ten, six and a four, ten times for names and numbers, one, two, three, four, six, seven, eight, nine, and tenth and final time. After ten, we got Don down to a few Chris's, six and a four, ten times for the numbers, one, two, three, four, five, six, seven, eight, nine, and good luck, tenth and final time, ten, we got one down to seven. So Don, number one, Alan with five, Ken with two, Alan with four, Eric with six, Gail with eight, Don with three, and Chris with the rest, nine, zero and seven. Let's sort by column B and again, zero gets any and all redemptions including one of one redemptions, any live one of ones will still go to you Don. Thanks everybody. I'll see you in a separate video for the impeccable break itself.


Bright pink nebula almost completely encircled the spiral galaxy. The ring structure and the galaxy's distorted spiral shape result from a smaller galaxy scoring a cosmic bull's eye, hitting the center of NGC 922 some 330 million years ago. As the small galaxy passed through the middle of 922, it set up ripples that disrupted the clouds of gas and triggered the formation of new stars whose radiation then lit up the remaining gas. The bright pink color of the resulting nebula is a characteristic sign of this process. Despite the immense number of galaxies in the universe, this is one of only a handful known in our cosmic neighborhood.