In this module, we will discuss hydro-turbo-machines. It may be recalled that hydro-turbo-machines or those turbo-machines that handle an incompressible fluid such as water or gasoline or kerosene or any other liquid. In the first part of this module, we will discuss pumps and in particular centrifugal pumps and in the second part of this module, we will discuss hydraulic turbines. Now, as we have already seen earlier, if we apply SFE to the rotor of a turbo-machine, assuming no heat loss, we get this equation. We also neglect elevation changes across the rotor between inlet and outlet. This is usually negligibly small. So, if we do that, we end up with this expression. Now, keeping in mind the definition of specific enthalpy, which is U plus pV, where V is the specific volume, we may write this as U plus p over rho. For an incompressible liquid, rho is practically a constant. So, we may write this term, the enthalpy change, H2 minus H1 as P2 minus P1, if we assume that the temperature of the fluid remains the same as it passes through the turbo-machine. In other words, if you are looking at an incompressible fluid, let's say a liquid, which is being pumped in a pump or maybe even passing through a hydraulic turbine and there is no significant change in the temperature of the fluid and so there is no change in the, significant change in the internal energy of the fluid. So, we may write H2 minus H1 as P2 minus P1 divided by rho. So, if we substitute this here and rearrange, we get the following P2 minus P1 over rho equal to V1 square minus P2 square over 2 minus Wx dot over m dot. Wx dot is the thermodynamic work or rate at which work is done in the thermodynamic sense and this is positive for a turbine and negative for a pump or a work absorbing machine. So, we may rewrite this expression in the following manner. Gather P2 and V2 square over 2 on this side, P1 on this side and then write it like this. So, we may write it like this where the P here is the power of the machine and it is a positive number. So, the sign is accounted for here. So, the power is always a positive number and the negative sign is chosen in case it is a turbine and the positive sign is chosen in case it is a compressor or a pump that is a work absorbing or power absorbing machine. If it is a power producing machine then the negative sign is chosen. We have also chosen to write m dot as the product of the density times the volume flow rate. So, this is rho times Q. Now, since the power itself may be written as rho times G times Q times H, that is the hydraulic power, this term may be written as the head H across the turbo machine. So, in case it is a centrifugal pump, the head increases across the pump, that is P2 is more than P1. So, there is an increase in head. In case it is a hydraulic turbine, the pressure decreases across the rotor or runner. So, the outlet pressure is less than the inlet pressure in that case. So, this actually may be thought of as Bernoulli's equation applied across the rotor of a turbo machine that handles liquids with Z2 minus Z1, Z1 across the rotor being very, very small. So, this is an equation that is used quite extensively in the analysis of both pumps as well as hydraulic turbines. The brake horsepower of a turbo machine is equal to the torque T times omega, where omega is the angular velocity. So, the brake horsepower is the shaft power that is generated by the turbo machine in case it is a power producing machine or it is a shaft power that is supplied to the turbo machine because it is a power absorbing machine. So, we can define the efficiency of the overall efficiency of the turbo machine as the hydraulic power P divided by the brake horsepower. So, this is either rho GQH divided by BHP for a power absorbing machine or it is BHP divided by rho GQH for a power generating machine like a turbine. So, this is the definition of efficiency that we will use throughout. Now, let us look at the particular case of centrifugal pump. First we will develop the theory and develop certain theoretical expressions for the performance parameters, do some calculations and then compare the theoretical expressions and the theoretical characteristics against the actual characteristics of the centrifugal pump. So, the blade element of a centrifugal pump looks like this we have already seen this earlier. So, this is section or taken at a certain axial distance equal to constant in a centrifugal impeller. So, let us say at an x equal to constant section and this is what the blade element looks like this is the inlet, this is the exit. So, the angles are also marked here and the reference direction in this case is the radial direction because it is a radial machine. So, alpha 1 here is the angle that the absolute velocity makes with the reference direction and as shown here this is a negative quantity because it is in a clockwise direction. The blade angle beta 1 as can be seen here it is in the anticlockwise direction. So, this is positive and the same is true here also notice that u 1 is not equal to u 2 obviously because it is a radial machine. So, the basic idea here is given the geometric details of the impeller such as r 1, r 2, beta 1, beta 2 and the width of the rotor v 1 and v 2 and inlet and outlet and the angular speed omega we will derive theoretical expressions for the performance parameters of the pump and the performance parameters of the pump are the power that is absorbed by the pump and the head change across the impeller of the head generated by the impeller as functions of the volume flowing. So, the h versus q and the p versus q are called the characteristic curves of the pump. So, given these geometric details and the angular velocity how do we relate h to q and how do we relate p to q in a theoretical manner is what we will take up next. So, based on the velocity triangle shown notice that at any r equal to constant section if you look at the velocity triangle this is the radial component of velocity C 1 I am sorry C r 1 is equal to v r 1. So, the radial component of the relative velocity and the axial and the absolute velocity are equal and that is equal to this in this velocity triangle and it is equal to this in this velocity triangle. So, the volume flow rate at any radius r is nothing but or may be written as q equal to v r times 2 pi r times b from which it follows that v r which is equal to C r may be written as q over 2 pi r times b. Now it is also clear from here that C r the radial component of velocity is equal to C times cosine beta 2. So, I can replace C r with C cosine beta 2 or C cosine beta at any radius r and write C equal to q over 2 pi r b cosine beta. Now it is also clear from here that v theta at any radial location which is this segment here or this segment here is equal to u minus C theta at any radius. So, v theta equal to u minus C theta which is equal to u minus C sin beta from the velocity triangle. So, if I replace C with this expression I get v theta equal to this.  What is that? v theta 1 here is in the same direction as u 1 and v theta 2 is in the same direction as u 2 here. So, there is no change in direction of I am sorry v theta is in the same direction as u 1 here and v theta is in the same direction as u 2 here. So, there is no change in direction. So, there is no change in the sign of this term it remains negative sign. So, we may substitute for v theta from here. So, v theta 2 is u2 minus q times tan beta 2 divided by 2 pi r2 times v2 and similarly for v theta 1. So, this is the expression for power. If we divide this by rho gq then this is nothing but the head that is generated by the impeller. So, h is equal to p over rho gq which looks like this. Now normally the impeller is designed so that at the design point which means design flow rate and the given value of omega the flow enters the impeller radially which means alpha 1 is equal to 0. Alpha 1 is equal to 0 and it also follows that v theta 1 is equal to 0. So, we may write the flow rate at design condition like this. So, v theta 1 is equal to 0, then q may be written in terms of u and the other quantities at the inlet using the fact that v theta 1 equal to 0.  So, we set out to derive theoretical expressions connecting the head produced by the machine with q and the power for the machine with q. We have expressions like this at the design condition. We need to have expressions for all flow rates. Now if we neglect v theta 1 at off design conditions, notice that v theta 1 will not be equal to 0 at off design condition blade angles beta 1 and beta 2 and omega r1 r2 are such that at a design point or design operating condition v theta 1 equal to 0 or alpha 1 equal to 0. To all other condition it will not be 0, but for the sake of simplicity if we simply neglect v theta 1 at off design conditions then we may write h equal to this. So, in this expression we simply neglect this and we can write h in terms of q like this and p also in terms of q of course, p is nothing but rho g times q times h. So, now it is clear that this is the characteristic that we are looking for h as a function of q and it is clear from here that h is linear in q and the sign depending upon the exit angle beta 2 whether it is a falling characteristic or a rising characteristic or a constant characteristic depends upon the value for beta 2. So, if you have beta 2 equal to 0 which means that it is a radial blade at exit. So, beta 2 becomes equal to 0 then the tangent to the blade at exit lines up with the radial direction. So, it is a radial blade that means if beta 2 is 0 h is a constant for all values of q equal to q 2 square over g. Now, if beta 2 is less than 0 then we have a forward curved blade and in this case this is negative. So, this becomes positive. So, this is a rising characteristic it increases linearly with q and if beta 2 is greater than 0 then we have a backward curved blade and this is positive. So, h actually decreases with q. So, this is a falling characteristic. So, let us see how we get this connotation from here. So, we can see here that if it is a radial blade then the blade actually must look like this because beta 2 is radial at the exit 0 it has to be radial at inlet also that is the way it is going to be for the radial blade and if the blade is radial then the h is a constant and the power varies increases linearly with q flow rate q that is what we are seeing here. Now, in the case of a forward curving blade remember forward curving refers to the fact that the blade curves in the direction of rotation of the impeller. So, since the impeller rotates like this the blade also curves in this direction. So, in this case the blade angle beta 2 is actually in the clockwise direction. So, it is negative which is why we say it is a forward curving blade. So, if it is forward curving beta 2 is negative and head increases it is a rising characteristic h increases with q. Now, in case it is a backward curving blade like this it is against the direction of rotation beta 2 is in the counter clockwise direction and is positive. So, this is a falling characteristic here and at the pressure increases I am sorry the power increases reaches a maximum and then starts to decrease that is the theoretical characteristics. These are the theoretical characteristics for the centrifugal pump people. Where we have made many simplifications most notably we have assumed that v theta 1 is 0 at all conditions which is which is not a very good assumption to make, but this gives us some insights on the general trends to be expected from various types of impellers. Now, before we proceed to see the actual characteristic of a centrifugal pump let us work out an example. So, we have taken this example from Fox and McDonald, Fox, McDonald and Pritchard. So, the geometric details of the blade are given radius at inlet and outlet, blade width at inlet and outlet, blade angle at inlet and outlet, omega is also given. We are asked to calculate the theoretical head, theoretical power and flow rate and the design operating condition and the same quantities at the different flow rate of 3600 meter cube per hour. So, from the given data we may evaluate the blade speed at the inlet and outlet u1 as 2 pi n r1 over 60 which comes out to be 9.817 meter per second and u2 as u1 times r2 over r1 and it comes out to be 32.73 meter per second. So, at the design point q star is given as 2 pi u1 r1 v1 cotangent beta 1. So, if we substitute the known values into this we get q star to be 0.3045 meter cube per second and the design h is also known. So, h star is given by this expression and if we substitute the numbers this comes out to be 101.32 meters and the power required at the design operating condition is simply rho times g times q star times h star and that comes out to be 302.66 kilowatts. We are also asked to calculate the shutoff head. The shutoff head is simply nothing but the head that is generated by the machine at zero flow rate. So, that is this quantity here. So, if you look at this expression we said q equal to 0. So, the shutoff head is nothing but u2 square over g and this comes out to be 109.17 meter. Next, we are asked to calculate head and power input for flow rate of 3600 meter cube per hour which corresponds to 1 meter cube per second. So, we substitute this into the general expression for h what is that we have neglected b theta 1. So, if you substitute this into the expression for h the given flow rate is 1 meter cube per second and we get the head to be 83.4 meters and the power to be 818.154 kilowatts corresponding to this case.


Know you read the title of this video, and you're like mank and this guy just stopped talking about the switch replacing the 3ds and I get it on the surface the switch replacing the 3ds is An old topic. We've covered it in the podcast. We've covered it in other conversations and I Want to actually turn this into a full-blown Discussion this isn't based on any news or any reports or any rumors You know like there was that one rumor a while back that oh in two years The switch is gonna completely replace the 3ds and we know that Nintendo is repeatedly said the switch is not a replacement for 3ds And obviously the biggest argument is if you fully believe the switch is as a home console that you could take on the go Which is what Nintendo has consistently advertised it as so Nintendo's been pretty on par with their marketing 3ds is its own thing Switch is a portable, you know Console so it's not the same thing there could be a successor to 3ds someday yada yada yada But I'm here today because I want to make it perfectly clear my stance and my reasoning behind why I think it is logical for this switch to not only replace the 3ds, but that I feel most video game fans should want the switch to replace the 3ds and Obviously the switch is already replaced the Wii U So that's a discussion for a different time although I know there's people who own the Wii U that are mad that the Wii U promise never got fulfilled They didn't get an exclusive Zelda game. They didn't get The promise of what the game pads capabilities were fully delivered to them and I'm sorry that sucks But that's in the past and we can't keep living in the past What we need to do is learn from the past mistakes to make a brighter tomorrow And I feel like that's a great phrase when we're talking about the switch It's potential how well it's doing now and why it should replace the 3ds because we need to look at the past Both successes and failures and consider the future of the video game industry because we've been told for a long time We've had the media We've haven't had certain video gamers just beating it into our head that video game consoles are going to die That PCs are going to be the only thing that survive or gaming on smartphones and tablets Which ironically the switch is a tablet but you know starting that aside you're gaming on tablets and smart devices and Gaming PCs which would always be around for safety of the more enthusiast crowd that likes to have like the best-looking visuals and all that stuff and For the most part I understand the logic behind it I understand why people think dedicated handheld gaming devices are dying out because you know this current generation you know with the Vita kind of tanking and You know the 3ds doing half the numbers of the DS and technically being less than the original Game Boy I understand the sentiment that handheld gaming is dying out even at the 3ds itself kind of prove the market is still pretty healthy For a dedicated handheld device There's a lot of misnomers about the Direction of dedicated handheld devices in that there's a market for but the market is mostly with kids right and that's kind of How Nintendo's slowly shifting the 3ds, you know They have the 2ds XL coming out Which the only reason the 2ds even exists in the first place and of course I know the 2ds XL is already released Is that it? Kids under six could not basically use the 3d feature on the 3ds without potentially harming their eyes So it's one of those ideals out there that the 2ds Exists for the sole purpose of children in the first place and a lot of times when I see the 2ds This doesn't mean that there aren't people that own the 2ds 2ds XL that are teenagers You know young adults even older adults their course there are other people that don't give a crap about the the 3d effect And they just want the cheapest possible 3ds system they can get for the games and there's plenty of hardcore games on the 3ds So this isn't even about the library although the library for the 3ds is extremely diverse Which includes children all the adults teenagers etc. There's a lot of games targeted at a lot of different markets But that's also true if you look at smart device gaming if you open up your phone and you go to the app store There's tons of stuff for games. There's also tons of things for teenagers and adults The marketplace is just as diverse and getting more content on mobile devices than the 3ds has and I Preface this because obviously Smart device gaming is different I'm not going to call it casual because while it's true people buy phones for other reasons and then happen to play games on it Whereas you buy 3ds to play games and you might happen to watch Netflix or browse the internet on it Which I know that experience isn't very good But it does have those capabilities It's still even as an aside gaming on phones has grown and I felt like become legitimate There are several indie games that come out on phones that are just as good as the indie games that come out on consoles And we shouldn't dismiss them because maybe it's a free to try model You know a free-to-play model that's not really free to play Or has micro transactions because micro transactions exist in triple-a games So we can't pretend like this isn't permeate throughout the gaming industry So we have to sit back and think man, you know Pokemon go is not a traditional Pokemon RPG But it is it just as much of a Pokemon game as Pokemon snap was I think so how about You know even looking at Nintendo again, you know fire emblem heroes It is It's a tried-and-true game that's existed on phones before and it's no it's not a full-fledged fire emblem game But it's just as much of a fire emblem game as any other side dish fire emblem game on any other platform Will be I'd argue it's more of a fire emblem game them fire emblem Warriors is going to be So it's just a roundabout cycle where I feel like we need to dismiss the fact that first off the smart devices are Not viable gaming platforms then we get into the switch I mean look at the history of Nintendo Nintendo is Almost always had two platforms they launched the NES and then you know like a year later the Game Boy or so and That's fantastic and Nintendo is always Extremely like their handheld systems have always been their best sellers So to get rid of a common misconception. Oh, Nintendo. Just you know the switch is just going to this handheld route because They can't sell consoles while their handhelds have always been massively more popular You know, that's just the way it's always been home consoles have never been as popular as handheld gaming Period end of story all the facts in the world back this up but Nintendo's approach has also come to the point where they have driven away a lot of third-party developers It's a reality. We have to accept it. I realize there's third-party developers supporting switch some at least I realize that there's tons of indie support and we're getting high quality games the switch is fantastic I realize we had high quality games in the Wii U I realize that we've had some decent third-party support even on 3ds I understand that Nintendo has still got some support in the industry because there's still a market for games on Nintendo platforms For people that aren't Nintendo, but we also have to recognize that the market for third-party games on Nintendo has shrunk At least at the AAA level We're not getting Grand Theft Auto 5 at least not now. We're not getting dishonored too We're not getting all these other AAA games Assassin's Creed Origins We're gonna call duty this year and some of these games might come over time But right now Nintendo doesn't get these games So Nintendo is stuck in this thing where a majority of the reason that people are going to buy a 3DS that people are going to buy a Switch afford Nintendo's own content and I'm of mind in 2017 heading into 2018 coming up that Nintendo can't afford business wise Well, they can't afford it technically but afford it for the future of the company to continue to split their development on Two different platforms and we even see this with 3ds We're a lot of the games coming out for 3ds moving forward are not first-party developed their second party third party, etc Nintendo's not putting their a teams. It seems like on 3ds games right now beyond Pokemon Ultra Sun and Ultra Moon But again, that's not even a first-party company game freak is a second-party company They they kind of live in their own bubble and do their own thing and Nintendo just nods their head because they keep selling 10 Plus million units of every game they release period at least when it comes to Pokemon so moving forward I Think it's smart for Nintendo to bring all of their development teams together and focus on a singular platform And the switch is the almost the perfect platform to do this with because even if you think it's a home console You can take on the go. It's still a portable gaming device That also doubles as a home console. So there's no reason to not have all of your games come to it I mean, there's people out there that want the entire 3ds library Ported to the switch and I understand the desire because it's a portable system and for once we can have a singular Ecosystem of Nintendo systems that fits both crowds of gamers both those that want to play with it underneath their TV and Those that want to take it on the go now the one caveat is all is that I feel like if they really want this to focus on under The TV they should pack in a pro controller with it just my opinion I realized they pack in a grip for the joy cons and it works fine But I think for more traditional home console gamers They're gonna see that as kind of a lackadaisical solution and maybe not ideal and they're gonna feel like they need to turn out 70 more dollars for the pro controller. So they just include that in the box I think that would you know, maybe they'll have bundles in the future that do that I doubt it. They've never done it before but you know, there's there's always help But setting that aside the switches obviously have a lot of momentum right now, right? You know breath of the wild kicked it off the right way one to switch ended up selling Well, you know launch games tend to usually sell pretty decent because there's nothing else to play on the Platform, so of course you're gonna buy the launch games, you know, we know the bomber man sold really well at launch Yeah, we know that arms has me at least had a very good start We don't know how the sales have continued since but 1.2 million for a brand new fighting game franchise You know when our franchise like Street Fighter 5 could only sell 1.7 million to date is Impressive and then you have to consider it. We don't even a smash out yet We have pocket tournament coming which again, who knows how well that's gonna sell in comparison to the original But Mario Kart, you know eight deluxe came out and you know Splatoon 2 has been selling phenomenally. Well Even third-party games the few that have released have been selling pretty well The reason that we know about all the issues in Troll and I is because people have been buying Troll and I Because they want more to play on switch and they're hungry for content And these are the content being delivered to them and for the most part has been pretty good I think Troll and I is the first legit indie game to release that really isn't that good Even overcooked with its frame rate issues when it released Was still a really decent game if you played it in a multiplayer setting whereas Troll and I just kind of feels like a letdown No, we just had Sonic Mania come out Sonic Mania is fantastic It's a multi-platform game new take on classic Sonic amazing amazing amazing amazing so many great reviews for that game and When you encapsulate this in a bubble it feels like the switch While it's already beating out 3ds sales for this year since it released It it's one of those aspects where I realize it has some pitfalls to reach that it should be everything device I realize that the plastic screen is easy to scratch But then they didn't go with the glass screen because they didn't want kids cracking it Realize the joy cons can be too small easy to lose even with the finder on the You know your joy con has to be charged for the finder on the system to work to even buzz your joy con to find it It's it's just a system that isn't perfect and if we think about The 3ds itself. I mean it's always perfect for kids. The 3ds isn't perfect for kids for starters We have the whole issue with the 3d hurt in the eyes to those hinges have always been an issue with kids I've seen so many kids snap their 3ds hinges. It's not even funny The clamshell design is great for porting your pocket and admittedly the switch isn't this kind of thing You put in your pocket, but when I see kids playing 3ds I rarely see them put it in their pocket anymore. It's always in their backpack in a bag They're carrying we live in a society now where it's become normal to have some extra carrying thing with you whether it's a backpack or whatever and you know back of the day used to be fanny packs I don't think those have really made a full comeback But it's become normal and obviously some people have really oversized pockets But I see people carrying on bags all the time and that's where they're putting their portable devices I mean maybe not their phones will still go on the pocket But again, I think phones are kind of built for the pocket portable gaming devices don't need to be something you put in your pocket I mean the original portable gaming devices way back in the day weren't things you would put in your pocket anyways Because you could break the levers on them and all this stuff because everything was mechanical. There wasn't no digital so we're at a point now where All of Nintendo's efforts should be fully concentrated in my opinion on the switch. They should Phase out the 3ds which I think they're already doing personally, but even if you don't think they are I feel like Nintendo should be doing that because if they focus all of their first-party development you know teams and second-party teams on Switch you're gonna have a platform that has an extremely robust lineup without Including third-party indie games So now you're gonna have a system that has all of Nintendo's best games and once I mean we're getting a Pokemon RPG on it We're crying out loud You pull all these games on switch and that's gonna blow it up even more than it already is you're talking about 70 million for 3ds Well imagine that all of Nintendo's output is on switch all of the people that care about any of Nintendo's games are going to buy a Switch knowing full well They're actually going to get the content not just a promise of content because it's the only platform They support when Nintendo is down to a single platform like Sony and Xbox are You start to see a higher game output because they're not splitting their development teams over two separate devices so The switch is perfect for this as I said it satisfies handheld not entirely I understand some pitfalls and it satisfies home console again not entirely there are some pitfalls with these are the Sacrifices you give for a hybrid device and as switches proving with sales people are okay with those sacrifices because they're still getting Fantastic games that look great that play well Maybe it's not the highest resolution in the world But again Nintendo was right in 2006 when HD didn't matter yet and they're right again now that 4k while it's fantastic isn't necessarily the Correct direction here in 2017 maybe by 2021 maybe switch to with an X2 and it needs to support 4k output I don't know but we're living in an age now where I feel like Nintendo is best putting everything on a single platform And I feel like that's gonna fix a lot of the issues Nintendo has had you know We you only sold 13 million we add that 13 million to to the 3ds And now you're looking at you know a single platform that could have sold 85 million units or so that's pretty good And if you're talking about you know, some people say oh, there's no way in heck the switch could reach We numbers well the one way you could do it is if it's the only platform Nintendo makes games for if that's the case There could be a huge convergence race, you know You can get 80 to 100 million units on that system if that's the only way you're getting in Nintendo games because that's how popular in Nintendo games are and The more install-baser are the more chances for third-party games to sell and the fact that third parties have already seen success Is also a good sign Everything's looking up and up for the switch and I know some people accuse my channel Oh, you just popped up in the switch are technically this channel has been around like ten years, but Just getting technical I love the switch as critical as I am about certain aspects of it about some of the Game treatment some of Nintendo's treatment of it the switch itself. I think is brilliant. I think it is the future of Nintendo I think they're gonna ride the switch hype train for a decade or more. I think there's gonna be multiple versions This is gonna be the game boy We're gonna see the new Nintendo switch and the switch to and the switch advance or the super And super Nintendo switch or whatever Nintendo does then there's gonna be like two or three generations of switch Before Nintendo tries to do something entirely new again I'm excited by this prospect. I think this is the direction Nintendo absolutely needs to go in I think it's the direction they are going in but again, this is about the conversation So let me know in the comments below what you think about it obviously I'll pick out a comment to feature on prime comments and we'll have a conversation because I Don't want to trash the 3ds. I think it was a fantastic system that did better than I expected But we are now in 2017 the system came out in 2011 And Nintendo has a portable system. I know it's also home console But it's a portable gaming system that can do everything the 3ds can do and then some I realize it doesn't have dual screens They can make it work. It has a touchscreen. They could figure out a way if they really want to use touch controls in a game Anyways, I am Nathanian ruffle jantz from Nintendo Prime. If you like this video, you know what to do If you dislike the video hit that dislike button Subscribe for more videos like this and as always folks, I will catch you in the next one


Hello and welcome to the session. In this session first we are going to discuss geometrical conditions required to determine a circle. Circle has two forms of equation. One is the standard form and the other is the general form. And in each form the equation of a circle has three independent arbitrary constants. We obtain the equation of a circle. We know the values of these three constants. As there are three variables so we need three equations or conditions about the circle to find the value of these constants. Let us discuss a few geometrical conditions. First is three points are given through which the circle passes. Second is two points are given in the circle, a line on which its center lies and third is central line, point and radius etc are given. With each of these conditions three equations can be formed. Let us now discuss how to find the equation of the circle using the given condition. Let the required equation of the circle be x square plus y square plus 2gf plus 2fy plus c is equal to 0. Let us to establish three equations in g,f and c using the three given conditions like if we are given the three points 1A2, B1B2, C1C2 then put these points one by one in the equation of the circle then we shall get three of the right equations in g,f and c. Next we have if we are given the two points and a line on which its center lies say x plus y plus d is equal to 0 where d is any constant then we put two points 1 by 1 in the equation of the circle with this we get two equations with three variables g,f and c. Now at the center of the circle lies in the line plus y plus d is equal to 0 therefore the center that is gf will lie on it therefore we shall have one more equation in the form of g and f by having three of the right equations in three variables we can find the values next is with center line and radius etc. given we can find three of the right equations in g,f and c and by solving these three equations we can have the values of g,f and c then substitute the values of g,f and c then we will have the required equation of the circle let us now discuss the intersection of a line and a circle the points of intersection of a line and a circle can be obtained by solving the equations of the line and the circle let us discuss how to solve the equations of a line and a circle let the line given by x minus 2y plus 1 is equal to 0 cuts the circle x squared plus y squared is equal to 10 now we have to find the points of intersection and we take the following steps first we eliminate y or x whichever is simpler in this we find the value of x in terms of y from the equation of the line x minus 2y plus 1 is equal to 0 which implies that x is equal to 2y minus 1 now we substitute this value of x in the equation of the circle the equation of the circle is given by x squared plus y squared is equal to 10 now we put the value of x is equal to 2y minus 1 in this equation and we get 2y minus 1 the whole square plus y square is equal to 10 which can be written as 4y squared plus 1 minus 4y plus y squared is equal to 10 that is 4y squared plus y squared minus 4y plus 1 minus 10 is equal to 0 and therefore we get 5y squared minus 4y minus 9 is equal to 0 and thus we get the quadratic equation in y now let us solve this quadratic equation in y we will have the values of y the equation 5y squared minus 4y minus 9 is equal to 0 which can be written as 5y squared minus 9y plus 5y minus 9 is equal to 0 now taking y common from the first 2 terms we get y into 5y minus 9 plus taking 1 common from the last 2 terms we get 1 into 5y minus 9 is equal to 0 and therefore we get y plus 1 into 5y minus 9 is equal to 0 to have y plus 1 is equal to 0 it implies that y is equal to minus 1 and if we have 5y minus 9 is equal to 0 it implies that 5y is equal to 9 that is y is equal to 9 by 5 therefore y plus 1 into 5y minus 9 is equal to 0 implies that y is equal to minus 1 and y is equal to 9 upon 5 now the fourth step is let us substitute these 2 values of y to y minus 9 in the equation of line to have the 2 corresponding values of x therefore for y is equal to minus 1 we have x which is equal to 2y minus 1 can be written as 2 into minus 1 minus 1 that is 2 into minus minus minus 2 minus 1 which is equal to minus 3 and for y is equal to minus 5 x is equal to 2 into minus 5 minus 1 that is 2 into 9 that is 18 upon 5 minus 1 which is equal to 18 minus 5 by 5 that is 14 upon 5 we now have 2 pairs of values that is minus 3 minus 1 14 by 5 9 by 5 for the points of intersection of the line x minus 2y plus 1 with the circle x square plus y square is equal to 10 we can also determine the length of the intercept formed by the points minus 3 minus 1 and 13 by 5 9 by 5 I have line distance formula the length of the intercept is equal to square root of minus 3 minus 13 by 5 the whole square plus minus 1 minus 9 by 5 the whole square which is equal to minus 1 minus 1 square root of minus 15 minus 13 by 5 the whole square plus minus 5 minus 9 by 5 the whole square which is equal to square root of minus 15 minus 13 is minus 28 by 5 the whole square plus minus 5 minus 9 is minus 14 by 5 the whole square plus minus 5 minus So this is equal to square root of minus 28 square is 784 by pi square that is 25 plus minus 14 square that is 196 upon pi square that is 25. So we get square root of 980 by 25 which is equal to 196 by pi and therefore we get square root of 196 by pi is equal to 14 upon square root of pi which can also be written as 14 into square root of 5 by 5 therefore length of the intercept is given by 14 into square root of 5 by 5 units. This completes our question for you enjoyed this question.


And it's just how bad is the national teacher shortage. We don't realize how bad it is. But Carl Ackerman, who has been in academia and who has been a teacher at Punahou for years and years and years can help us appreciate that. There was an article in the Washington Post a few days ago, we're gonna dwell on that a little bit. And it's very scary stuff. Welcome to the show, Carl. Thank you, Jay. Always a pleasure. Carl, I was surprised that how bad this article depicted the problem. On the other hand, when I thought about it, I realized that we are all aware of the vectors. We are all aware of the causes. And we could have, should have, would have realized that all these things that have happened, especially during the Trump administration would lead to a national teacher shortage. Can you give us a thumbnail of at least from your experience and the Washington Post first, how bad is it and how far does it reach? You know, Jay, from that article alone, you realize that almost all major school districts, there are some exceptions, like in the Fairfax County school district in Virginia, which pays its teachers very well.  I mean, I think teacher shortages are dire right now. And, you know, there was someplace, I think, if I'm not mistaken in Texas, where they're starting to hire college, undergraduate college students, which to me is really pretty dreadful. I mean, not that college students are not great people, but I just don't think they have the wherewithal to be good teachers yet. Right, right, and you know, they're trying anything. But let's look at, you know, the geographical implications of this seems to me just looking at that article, and it's not a surprise, is that the states that have been hardest on teachers, that is the states that have had issues about masks and kids wearing masks, the states that have told teachers they could not teach certain books, those states are losing teachers. Because the teachers don't agree with the policies and the teachers feel that their efforts to educate these kids are being constrained and impeded, and they are looking elsewhere.  You can find jobs elsewhere. So I think what I get out of it is they are moving to other states that are easier to teach in, salaries are better, you know, public opinion, public attitudes and sensibilities are better. And you know, it's not a problem to get licensed now because it's kind of a recruiting, feeding frenzy around the country. If one state is short, it's gonna raid and poach teachers from other states.  And unless that state that's been mean to teachers changes its policies and funding, they're gonna lose their teachers. And this is the principles and so forth, the administrators understand it and they say farewell. So what you have is a grand migration of teachers from the states that are kind of backward about this to the states that understand they've got to pay more and be kinder to teachers. Am I right about that? Lauren, you know, Jay, the big example, and you and I know this directly, that if you were a New York City public school teacher or you are anywhere around the Boston area, teachers are well paid.  I mean, they don't get as much money as doctors or lawyers but they're paid as professionals. And, you know, in other states, you know, which includes almost the entire state of Texas or in Hawaii, they're not really given a living wage. And that's part of the problem. So, you know, you begin with teachers' conditions in most places being very on the edge anyway. And then what you throw in is you throw in COVID. And that was a big sort of unknown. But, you know, if you imagine that teaching is simply a calling, you know, to use that old Protestant Max Weber comment. And it is a calling. I mean, you don't go into teaching to make a lot of money, you just don't.  And I used to have my students go up on the second floor and shout out his name, Audubon Bismarck across the campus. That's a great moment. And just because I thought he was such a, you know, interesting character in history.  And you add COVID and you sing kids on screens. And then, you know, you're working from home and, you know, the great joy of every teacher is working with kids and being around kids. And if you destroy that in addition to paying them low, in addition to, you know, making them fill out as many public schools districts do, fill out a ton of paperwork and, you know, blame them for everything under the sun for not being good social workers or not taking care of kids who come when they haven't been fed. You know, then you have problems. And let me say this right out front. One of the best things that's going for teachers are teacher unions. Not all teacher unions do all the right things. You know, and there's always a problem with unions taking on fights that might not be in the best interests of whatever their clients are in this case as kids. And I understand all that. But it's rare that something that's good for a teacher is not good for a kid. Even better salaries makes a teacher more comfortable and they don't have to worry about a lot of things. And this is in the long run, better for children. And, you know, you don't think of teachers being greedy because they often spend their own money, which I did my entire career, their own money on providing for kids, of course. And, you know, that was doubly true in the P oil program.  I don't know why, but your story of it, that reminds me of an issue that appeared in front of the neighborhood board in my neighborhood. I was on that board for a few years. And I remember the teachers came to the board and they said, you know, we don't have enough pens and pencils in our schools. So why, right? Right. We don't have enough pens and pencils in public schools. Could you guys, you know, go through your homes and see if you have any spare pens and pencils and can you give them to us so we can give them to the kids? So what? You got to be kidding me. I pay some of the highest taxes in the country and you want me to fund the pens and pencils in the schools. What's wrong with this picture? Well, it's bad administration, it's inefficiency. Though on top of all the problems that, you know, are clear and preventable, you have this fundamental lack of good administration. And I don't think it's limited to Hawaii at all. I think it's around the country. But you know, one thing, Carl, reading that article, I thought, you know, they didn't really pay enough attention to Trump and Betsy DeVos and giving coupons for private schools in little public schools.  They were weaponized, they were attacked over books, over masks, over vaccines, all these irrational things coming down on them and they got sick and they were afraid to go to school. And parents, understandably, would do homeschooling, not just because of COVID but because the whole thing was in decline. And, you know, I think it had, tell me if you agree, I think it had a profound effect on our way of looking at public schooling in this country. And private schools became much more attractive at a time when the Department of Education, you know, was national, was down on public schools and was incentivizing private schools. And so the whole thing like turned around to some extent during Trump and COVID and bad books and the like. And I don't think that can be fixed so easily even in the time of Joe Biden. Your thoughts? You know, I had a chance to meet Betsy DeVos several times and I think that she earnestly felt that vouchers and private schools were the way to go.   They're gonna do better there than in public schools. And of course, we have great public schools across the country. I mean, if we look at our own neighborhoods, if you look at a public school like Kaiser, Kaiser. Only great with great teachers, Carl. If you lose the teachers, you lose the heart of it. This is true. And if you take good care of your teachers, but, you know, even private schools, unfortunately, Jay are getting rid of, you know, teacher housing and they're getting rid of, you know, used to be at most private schools that if you taught at a private school, your own children would be subsidized greatly and sometimes getting free tuition. I know that happened to, for me at Punahou School. But that's no longer true in a lot of cases. And so it's not just an attack on the public sector but also on the private sector. It's like, you know, when you talk about the most vulnerable, the most vulnerable at any school are the staff and the teachers. And, you know, when you start pulling back and not allowing them to have the benefits that they deserve, you know, I've always thought in Hawaii, for example, there's a lot of land at different schools and you should probably build apartments, you know, high-rise, you know, especially if you have a school like Jefferson, which is right in Waikiki, you should have a high-rise there for teachers and give them affordable housing, you know? I mean, it's, this is what private schools is to do traditionally. But, you know, the other thing is, I think that people who, you know, attach themselves to vouchers and things like this are the vouchers really gonna cover the 20,000 plus, maybe 25,000 now at Iolani or Punahou. Is that gonna really happen? And are you gonna get the diversity of kids? I'm not just talking about ethnic diversity. I think that it's really important to have socioeconomic diversity first. Are you really gonna get that at kids? So, I mean, I think that to go back to where the original issue is about shortages, Jay, I really think that the shortages are a product of teachers being in vulnerable positions to begin with all the time. And then, of course, as I said- What does vulnerable mean, Carl? Well, vulnerable means that they are not paid well. They're doing this because they believe that they have, you know, a sort of a God-given, if you were, responsibility to take care of the kids and do well with the kids. And then, what you do with these people is that you pay them a very poor salary and sometimes you take away their medical benefits and things like this. So, you know, that's what I mean by vulnerable.   Not that, you know, those, I think registered nurses, of course, have their own problems.  Suddenly, their salaries are doubled or tripled. That's a hard thing to fight against. And what keeps teachers in teaching is being the kind of hams that we all are to wanting to talk about our subjects and also the great interest in having, you know, really working with kids.  But, you know, one thing is, I think, you know, just talking about the article and your thoughts here, it seems to me these problems existed before Trump, but Trump exacerbated them. Trump revealed them to us. Trump revealed them to the teachers. And the teachers realized that the community doesn't support them the way it should. It marginalizes them not only in salary, but in general respect. And it has this strange attitude and I mean, millions of parents out there have this strange attitude is, I'll send my kid to school and the teachers will take care of everything. If they're legal obligation, that's what I pay my taxes for. And I am not gonna participate in the educational process. They gotta do it. And they gotta take all the trouble I hand out to them and they are marginalized in terms of my respect with a certain percentage of parents saying, I'm gonna teach my kid myself and I do wanna talk to you about that. But don't you think that the community in general somewhere along the line and it was exacerbated under Trump lost respect for teachers and this is being revealed now?  And, you know, not to say that's bad. It's not bad under capitalism.  But without any regard for teachers and then to have a secretary of education who was, you know, who earnestly wanted to do better for kids, but you know, basically if she could have, she probably would have destroyed public education in the United States, Betsy DeVos. Even though I think that she deeply cared about kids, but you know, the public school means you go for free and you pay through it through our collective notion of taxes. And there are many great teachers and great schools in our country that are a product of public education. I can think of my sister in Los Angeles who has the Girls Academic Leadership Academy, which is an all girls public school focused on STEM that primarily caters to kids on free or reduced lunch, which means they have challenges economically, obviously. And all these kids go on to college because you know, my sister's a good administrator. She hires good teachers and she supports them. And I think the greatest rule of thumb is that from my experiences, I also taught at Elani where I experienced the greatest administrator ever and that was David Kuhn. And David Kuhn was an Episcopal minister and his motto was that he hired good people and let them do what they needed to do. And he paid them well. And you know, there was a good sort of medical plan, dental plan and retirement plan. Private schools can do that. And I think the needle has shifted in Hawaii for sure. I mean, we have private schools that are way better than public schools and it'll continue that way in other places too.  Now, I come from the public school system in New York, which I consider in those days excellent. I'm not sure what it is today. It's been a long time, but all of my friends went to public school, the private school was just not on the radar. I can't even tell you about the private schools that were worth going to. And then I went to public college, which was excellent at the time. It was the City University of New York City. If you want, I can sing you the song, but I'll hold up on that. In any event, we all loved public schooling. It was challenging. The teachers were dedicated. New York City, as you said before, had a very high priority on teacher why? Because it was a melting pot of immigrants and people understood very clearly well that if you wanna have a decent life, you gotta get educated. And so they made the government provide those experiences for kids. And that went on for as long as I know in New York City. Not all communities have had that benefit. And some of these communities now that are shedding their teachers and sending their teachers away, allowing their teachers to be recruited out from under them, which is happening in the very same states that are going red, that are red in the political news, those that they don't have the same attitude. And that's what I wanted to talk to you about here in the last few minutes of our show. So I'm giving you a National Demographic, Carl. I'm giving you, who did you quote before? Was it Weber? Yeah. I think it's really important that it's like a great state has great art, you know? But a great state also has great education. And if you don't provide great education, you don't have a citizenry that can make good choices in terms of voting, which is the most important thing we do in our civic connection to government. And thus, government will not be as good. So if I give you a state that's not teaching critical thinking that doesn't care about educating kids, then I'm gonna give you a state that doesn't vote very well and doesn't have a government that is responsible and accountable. And I think that's what's happening. And we see it to some extent here, but other states, it's much more. I mean, imagine a state where they vote for people who go to the legislature and turn the election upside down. What's that about? And that's a failure of education, of civics education, of understanding the duty of a citizen, the way the government works. And if you don't have teachers, that gets worse. And homeschooling is not gonna cover it. I guess before we go to the larger macro, what do you think about homeschooling? Is it a viable alternative and the lack of teachers? And I will go again in September. I always go to the private school conference and I think that people who homeschool, in one sense, homeschooling, what it does is it provides a venue for parents who want to do this. It takes an enormous amount of energy. And I think that people who do this have a bent whether it's a religious, I think most often it's a religious bent. They want their kids to be exposed to a single religion that they believe in. And I, that's okay. I mean, that's their right. And I understand that. But I think they can get just as good of education in a public school. And like you, I'm a product of public schools all the way along. And I think that if you take your kid, the problem with homeschooling is, and it's a big problem, is unless you have your kids and a lot of things like soccer and activities like this, they're not gonna get the kind of socialization good or bad that you get in elementary school and junior high school and high school. I mean, imagine you missing all your friends from elementary school, junior high school and high school and all the things that you did in these areas. I mean, it's a certain point making you a better cultural person. And I lament for my own daughters who went to a K through 12 private school because I was teaching at the school, their ability to socialize and to get along with everyone. And that's what they don't, they do. But they didn't have this exposure. They didn't have the exposure that you and I had in a public school where some kids would come with a key around their neck because it was only grandma and grandpa that were taking care of them. They were rough working and they had to go home and open the door for themselves and make it. Well, the problem with public school as you described with this homeschooling is that it's a echo chamber. As you're bouncing off your parents' thought process, their level of education and they're not really qualified to be teachers and to impart to you the kind of thought process that a school at least theoretically is able to impart to you. I agree about the socialization, the diversity.  You better understand different groups. But if you only have the echo chamber at home you're missing that and you're not really prepared. I suppose there are homeschool situations which are better than others. But in general, I think that a lot of parents who believe that they are qualified to teach homeschool are not qualified to teach homeschool. What's more interesting even is that now with COVID and mass and vaccines and shootings and killings and terrorism it can happen five states away but you are nevertheless terrified it's gonna happen in your school down the block. So you're afraid to send your kid there. And so a reasonable parent would say, I'm gonna do this at home. I'm gonna do homeschooling even if I'm not really completely qualified to do it. I want my kid to be safe and alive and I don't want him to be subject to this. And I have no confidence in government to protect them there. No confidence at all. We have these second amendment issues. We have these people who need mental health who walk around with assault rifles and we let them do that and then they shoot our kids. Why should I, and the teacher is the same way. Why should I be in a place where I could get killed? It's a target on my back. In addition to all the other problems teachers suffer and the lack of respect and reasonable salaries and all the trouble the parents give teachers in addition, they're at risk for their lives. So if I were a teacher Carl, I would retire immediately. If I were a teacher, I'd go to another state where they were recruiting me with much better benefits and attitude. And I think that's happening. And thus the question that I began to pose earlier is very relevant. What happens in a nation of 330 million people where our schools are declining rapidly in front of our eyes because of government, because of all these social problems that we haven't fixed, the divisiveness, what have you, the guns, the economic issues, the lack of respect. What happens in a country of 330 million people where we don't have qualified teachers to teach our children and PS, it's getting worse. What happens in that country? I think Jay, I think you touched on a key point here and the country dissolves. Actually, that's the answer to your question. But I think that what's important is that we have to get back to a sense of letting the teachers teach what they need to teach. And I think it's extraordinarily important that teachers are allowed to teach US history in the manner that they think is appropriate. I mean, they should teach about the presidents, they should teach about the civil war, they should teach, the great thing that I think keeps people on par with what should be taught are advanced placement tests to give kids when they get into later in high school. I think advanced placement tests are good. So I think that, and people should be able to teach what they teach. And now, unfortunately, education has both been politicized in this way. People are starting to say, you can't teach that and you can't teach this. And I think always think of having taught Russian history in high school for many years. What if someone were to come along and say, well, that Fyodor Dostoyevsky, he was an anti-Semite, so you shouldn't use his books? Well, he produced really great literature. And people in the 19th century, especially the late 19th century across Europe, some of them were anti-Semites.  Well, yeah, look at the whole critical race theory debate. I should debate as to who elevated beyond where it should be. Look at that, telling a teacher he can't or she cannot discuss a given subject, even though it's a clear, established part of American history and culture, it happened. It is the reality. It is the fact. And you as a teacher are told that you can't teach it. And if you do teach it, we're gonna come and get you and prosecute you already. That is really out of the 30s in Germany. It's book burning is what it literally is book burning. And it's not just that you can't teach a critical race theory, it's that the government can come. This is like First Amendment. The government and usually state government can come and tell you what you can teach, what you can't teach, what books you can discuss, what books you can't discuss. It's not just a critical race theory, it's everything. If I were a teacher, I would say, how dare they do that to me? I'm trying to open these minds and they're telling me to close these minds. Well, Jay, let me just make a concluding comment to you about this. And by the way, I have to interject that our new superintendent is Keith Hayashi and he came from a big public high school in Waipahu and he did marvelous things with the kids in terms of getting kids into little academies and getting them working in future professions, whether that's as chefs or as nurses. So I have great hope for the next four or five years with Superintendent Hayashi, I really do. I know where his heart is and it's in a good place and hopefully that feeling will transition into some good work. But let me just go back to the notion of critical race theory and be very brief about this but to also say this, that's a phenomenon. The discussion of it is just ignorant. I just think that that's taken this one specific type of ideology that sometimes comes out of and it's true what the Republicans say that sometimes you have these ideologues at universities that are far off to the left and okay, I get that. But that's not what teachers are teaching. And if you look at the history for African-Americans in this country that were basically held as slaves until 1860, not even being freed in 1860, 1863 but it basically being kept as slaves until the end of the Civil War and then having some rights and then all those rights overturned and then having Jim Crow laws and then having lynchings and only in the early 1960s being able to have some sort of equal access to education of course with that famous 1954 Brown versus Board of Education. And with all that legacy, can you say that in 2022 everyone's on equal footing and we shouldn't discuss that history? Of course we should discuss that history and how during the actually occupation of land that was hold by Mexico or Spain or the taking over of Native American lands all of this is true. Now, can we go back into and does all things know? I don't think we should but we should know the legitimate history and historians are always doing this. You want to find out what really came before and change your monograph or change your books to reflect the newest historical findings.  They are right in saying that critical race theory should probably is too advanced for anybody below college level kids. Of course, of course, no one's arguing that but to teach history in a proper way. And also I may add that we should celebrate George Washington. We should celebrate Thomas Jefferson. We should celebrate Abraham Lincoln but the former two presidents own slaves and we should point out their errors. I mean, that's not hard to do. I mean, if you're- Race is the biggest social issue in the country and how can you turn your back on the history of it? That's an extraordinary. You know, when I get out of this though, Carl and I like to ask you one more level of things here. Let's take a hypothetical state, okay? And I'm, you know, you and I can pick a few. It wouldn't be hard to find one that fits the profile. Here's the state that, you know, we're gonna outlaw abortion as fast as we can in all ways. We're gonna dump on teachers. We're gonna dump on critical race theory. We're not gonna pay them very well but we're gonna lose them. They're gonna leave. And we're gonna have another kind of population. Poor people cannot afford to go to other states for an abortion. So they have the kids and if that's what you want from your religious point of view you have a lot of poor families having kids who will be poor and not educated. And there was one article in the paper recently that pointed out that the very same states that are arguing for, well, that are making abortion illegal and not providing additional social benefits, you know, social safety net benefits to the parents or the women who are forced to have these children. So they have more children but they have the same or a less benefit. And you think about that, what that does on a demographic basis. So my hypothetical state has more people, less educated. And of course, if they're smart, they'll leave the state but a lot of them will not leave the state for economic reasons. They'll stay there, they'll suffer through it. And over time that state and many like it will be way behind the states that have attracted the teachers way behind the states that have allowed a full discussion of American history in their classrooms and civics and government and Max Weber. Well, you know, and that will give us further divisiveness. What I'm saying is that divisiveness creates a situation where we get more divisiveness, more of a divide. And I think that's where the country is heading. So when you have divisiveness beginning more divisiveness, where do you go with this? You have two countries that are even more accentuated, more different than they are today. Well, you know, let me just begin where you begin, Jay.  And my feeling about this is that, you know, this is really another one of these questions that's sort of absurd because what this really comes down to is what a physician and a client, their client, their patient has to decide because it's a medical condition, being pregnant is a medical condition. And as far as I'm concerned, I try to not get in the way nor do I think anyone should get in the way between a doctor and their patient. I mean, I think that's really kind of craziness on the first level.  I think that I understand why people have concerns here, but I think that what the doctor and the patient should determine between them is what's good for the patient in terms of survivability and what's good in the long run for the patient. I mean, that's where this nucleus should be and it's gotten lost in a lot of other things. But I think you're right. I think the same states that don't provide for education and for teachers also don't provide for other things. What's happening is those kids in the neighborhoods that you grew up in, Jay, and that are around Boston, et cetera, and some of East Coast cities that have very good educational standards for their kids and then New York is one of the best, those kids are well educated and you could still get a great education, not only in New York, but in California too. There are city colleges, there are state colleges that are universities. And for in-state people, a lot of it is affordable. Still, the University of California is getting more expensive, but still for a lot of other places, the state system, the junior college system is very affordable. And so, we're getting two tracks. And if you don't allow people to have education, I mean, the whole basis of our democracy and our constitutional framework is based on people, well-educated and literate group of people. I think that both from the right and from the left, people should allow people to be educated and especially educated in US history and civics. And I don't think there's anything wrong with celebrating US history and saying that this is a great country and we have problems, but people can have the ability to better themselves. I still believe in the American dream, how though it's becoming harder for people. And I think that we should celebrate our constitution. We should celebrate our bill of rights. We should celebrate Martin Luther King Jr. and Cesar Chavez and all the people who have fought for really extending these rights to other groups of people who were, they may have been denied. Well, one thing seems clear, Carl. You know, these revelations that the GOP has had in the past few years, these policies that it has adopted and forced on others are missing one important element. And it becomes clear from that article, it becomes clear from our discussion today that they're missing caring for the children. They're missing caring for the children as those who will, those who have the future in their hands, those who will take our society to the next generation, to the next decade even. And the GOP seems to have forgotten that. They don't care. They don't care about the safety of the classroom. They don't care about the education of the kids. They don't care about the safety of the kids against pandemics. So what I get out is this extraordinary gap in the political consciousness of the GOP organizations and individuals. They have forgotten about the kids. And that is a lethal dose in a democracy. What do you think? I think that's true. And I think that, you know, if you stop with this, you know, bashing of books and bashing of critical race theory and leave that stuff alone because it's not really producing anything good. And instead you talk about how private schools and public schools can partner like in the Pueo program, the Ka'i program here in Hawaii and how to better kids' futures and basically really improve education for kids and allow them to do great things. And I mean, you know, it's not just, there have been social reformers who have tried to pump money into education, but they pump money in and then the money has gone mostly to educational administrators as opposed to getting to the child. And these programs I mentioned Ka'i and Pueo, there was a high percentage of the money that got to the kids, that money was spent on education and teachers and classes for the kids. And that's where I think we can have some great improvement with public-private partnerships. And that was a Betsy DeVos idea, but that's a good one. But you don't attack public education. I mean, you and I are products of K through doctorates, you have a law ministry of public education all the way through. And it was a wonderful public education. And I, you know, I savor the fact that I was able to attend the University of California, Berkeley, which is a public institution. And it's a great one. And all of our institutions could be great like this. And, you know, in Hawaii, we have Kaiser High School, which is a very good public high school. And the point is that going back to what you said about parents is that, you know, when I ran the Pueo program, what was clear to me is that parents are invested in their children's education. And that means showing up at PTA meetings. And it means, you know, focusing on what a kid is learning, you know, and this is true of many immigrant families in Hawaii and also in the rest of the part of the United States, then the kids succeed. And so I think we have to draw on entire communities, but we can't, as you mentioned, if you represent a Republican administration and you don't give teachers money or, and you start to, you know, demand certain things of teachers while taking away great salaries, while taking away salaries that are approaching medium level. And you start to withdraw all these things for teachers.  And if you keep dumping on teachers, that's the issue. And- Well, you know, there's another part of it too. I just want to mention, it just occurred to me from what you're saying. Okay, A, teachers are moving, they're moving from state to state. And where the shortage is most accentuated is where the states have lost teachers to other states which offer better recruiting packages. No, no surprise. But there's the person who was in school and who was making career choices. He was saying, let's see, what can I do with my life? You know, and in your day and mine, we could say, look, I would like to teach kids. I would like to improve their lives and give them the prospect of doing better than their parents did. You know, the old immigrant diversity prospect. That's not happening. I mean, it's that, would you ever move to one of those ex-states I mentioned, if you cared about your kids, born or unborn? No. And if you were a corporation thinking of relocating or adding a unit in some state like that, you'd have to consider that people, executives, especially middle management, are not gonna come to that state because that state is not a good state for kids, for educating their kids. So, I mean, it has all kinds of secondary implications to our society. And who in his right mind these days would choose, I'm sorry to say this, Carl, I know you've invested your whole life in it. Who in his right mind these days would invest his education, his time, his future, his career? His economic success in education. Maybe not so many as before. Carl, we're out of time. We gotta go now, but we'll come back because this particular discussion leads to all kinds of other issues. So, there's more to come, Carl. Thank you, Jay. And again, it's always a pleasure working with you and you always rise to the knighthood of menshood. So, thank you, Jay. Thank you, Carl. Dr. Carl Ackerman, really appreciate you coming on the show. Aloha. Thank you so much for watching Think Tech Hawaii. If you like what we do, please like us and click the subscribe button on YouTube and the follow button on Vimeo. You can also follow us on Facebook, Instagram, Twitter and LinkedIn and donate to us at thinktechhawaii.com. Mahalo.


Hey everyone, welcome to figure fantasy. We have our last stage here from Hell, which is funnel separation. So let's see what I have for you Okay, so you're gonna be needing a lot of damage dealing here also ensuring that all five survive So your main damage dealers here would be re Zantacain and Yolanda in the front. So let's try this one out Okay, so I was actually surprised that we did a lot of damage dealing So As you can see there how the HP of the boss just creeps very quickly, so this is so far the fastest the fastest lineup in terms of damage dealing that I have assembled for the stage so More or less, I think the best In terms of survivability, they're the best as well. So there you go. No brainer It's a three star clear and thank you guys for staying as far and take care stay safe It's the warden and I'm out of here


Well, got it together most of the time. I know how to handle most things, but this is kind of like the exception. I have denied from awareness. To me, that says that I deny the fact that there is such a thing as being out of control. Well, denied from awareness simply refers to the fact that I'm not generally aware that I'm out of control. I think it's just like some specific incidents, but actually it's the belief that they're all the time. It comes to awareness in those situations where it seems out of control, and then I pin it on that. Oh, well in these situations I feel out of control, but over here I don't. What this might suggest is that you're out of control, but you don't realize it. Well, it's not that I'm out of control, but that there's a belief in my mind that I do have a lack of control, and that most of the time I keep it out of awareness. The belief comes and goes. It's not like it comes and goes. It's not like it comes when Nancy's there and it goes and Nancy's gone. But the belief is in the mind all the time, and it only comes to awareness when there are situations that I perceive as saying, oh, now I feel out of control, and then that's over, and I go to the next situation and I say, no, now I feel fine. I take it a little bit deeper too. The first time that the out of control seemed to appear was when the ego, remember I gave you the little passage into eternity, where all those one, their crevice, tiny, mad idea, which the Son of God remembered not to let, that is the original out of control. And now that's just the wrong mind, but there's layers and layers. So it doesn't seem like every time I feel like I'm out of control and I'm feeling a little anxious, that it's just because I'm choosing the ego, I'm choosing the wrong mind. No, it seems it's because something out there on the screen. If this person wasn't that way, then I wouldn't feel so out of control. Or if things had gone differently in the world, then I wouldn't be out of control. So it's a belief that's way very, very deep in the mind. So it seems like the problem isn't my belief in being out of control. It seems like the problem is the scenario. That's why we keep calling it tracing back because it's like you're starting with Nancy, and you keep tracing it back, you're tracing it back to from the perception of the scenario to the feelings that identify, to the thoughts that I'm thinking of what I'm fearing in the future and then to the belief. So that's the tracing back because the point you want to get to is the middle. Can you want to take the ego? It's the core of this problem because until I get to the core, it's just going to keep coming back. Even if Nancy dropped off the face of the earth tomorrow, it's just going to come back in another form. When I blame fear or something in the world, it is to avoid seeing the upsets and resolution as they really are, decisions in my mind and to instead maintain an image of self, other, the world as I wish. Okay. So the upset and resolutions, it boils down to our first day when we talked about the wrong mind and the right mind. The wrong mind is the upset. It's always the source of the upset. And the right mind is always the resolution to use core terms of the Holy Spirit. This mind trick seems to displace guilt and fear, but actually maintains feelings of upset. To blame or fear an image of self, other, the world requires that I believe I am limited to a body and world of bodies and denies the spiritual abstract reality of my being. As a first step in letting go of all upset, I want to see in my mind what I thought was outside it. Being upset about a is only another attempt to make see the cause of my guilt and fear. I find a cause out here because as long as I can say, well, the cause is out there, then it takes the responsibility away from my mind. If the cause is always coming from my mind, then that sometimes can feel like I don't want it to be there. I want it to be that you're the problem or you're the problem with those people. Because it's too hard to change the mind when we get to thinking about it. Like you're saying, how can I change it? How can I see it different? And I ask myself that question. Well, that means I have to choose the right mind. So that means I have to go to this concept called forgiveness. And the way the Course explains forgiveness is really difficult to comprehend at this level of my experience. But like I'm beginning to understand it more and more and beginning able to see it. Like I just realized some things here that sort of made some shifts for me in, again, back to the bathroom and getting that squared away. So I guess what I'm saying is it's just so hard to give up what you believe and think is right and true because you had it all this time. Well, that's what you identify yourself. That's a very important piece of you. Yes, the self-concept. And then what we do is we find somebody who joins us in that self-concept and most people will. I mean, if you go tell the story and you tell about Nancy, in this group we're not going to buy it. But you go to a group of your friends and they'll say, you're right Lynette. How did you deal with that Nancy? How do you put up with her?   Get rid of that Nancy. I don't need you to hear that. So you come here and we're saying we love you too much to buy it. We're going to work this through. But the world wants the world to be true. That's really important too is that joining. You can join in the conflict and you can bring in a bunch of people to join in the conflict or you can join in the peace and fight. So number eight, upset seems valuable and justifiable when A runs counter to what I want or wanted. What I want or wanted and still or unexpected or expected is E. How I wanted A to be the solution or how I wanted this scenario to go. In this case we could put peace in there, right? Well how do you want the scenario to look? With Nancy, with these family gatherings. That she wouldn't attract attention to herself or whatever. What's the ideal scenario? Upset seems valuable and justifiable. This isn't my upper mind talking. This is my lower mind talking, right? All this is your lower mind talking. All right. So what would your lower mind have said? What have been the ideal situation? Nancy would just be normal. But right down the knee. Now we got to the bottom of it. Nancy would come in and say, hi Lynette, how are you? And sit down and never say another word. You know normal. Well I haven't. I'm boisterous. Okay, we got her sitting there quietly. What is your situation right now? I still believe in some form of lack. You better believe in it. I still believe in some form of lack, D. So I think I need E to be happy, complete and at peace. Okay, now if she asks normal, I will be happy, complete and at peace. That's all it'll take, right? Sure. My ego will buy it.  As long as she says, as long as Nancy stays quiet or home. So that leads us to the lesson. Is this belief in lack and the resulting expectation more important to me than peace of mind? Is it more important for Nancy to be quiet and at peace? At peace, my peace of mind. Well, is it? But now you're addressing. We're talking about peace of mind forever. Consistent peace of mind. Consistent. 100%. Of course not. Number nine, everything in the world works together for my good. What I think is the cause of my upset is not the cause at all. The choice to be upset is a choice not to see the cause. My belief in separation, lack, has a present decision in my mind. It's an attempt to see the cause in the past or future and the present has its effect. So the first sentence really gets to that. There's a line in the Course and there's also a line in the Bible about all things work together for good. And you probably have read about it in even other spiritualities as they talk about everything's happening for the good or divine order and different things like that. That's just a basic metaphysical principle. That's very reassuring. You might add. So if you even go back to scenario A, which is the scenario of what seems to be, here's this party or this gathering of the family and that's all working together for my good. But I have a belief in lack and I'm reading meaning into the scenarios, so to speak. And according to this meaning that I'm reading in, there's a villain there. Then I'm willing to question the meaning that I'm reading. And am I willing to take a look at, well, it's happening. It's all happening for my good. So this is a lesson for me to learn in this whole thing. And that is just how can I perceive this differently? Now, okay, a sentence says, the choice to be upset is a choice not to see the cause or my belief in separation lack as a present decision in my mind. Then the it's an attempt, that refers back to the choice to be upset. Alright, it's an attempt to see the cause in the past or future and the present as it's a fact. In other words, just thinking about Nancy. You know, you're thinking about the scenario and the emotions are coming up, the frustration, the anger, the being, you know, boxing or cornered in or whatever or those feelings are that don't feel very good. Then it's an attempt to say, no, it's not my belief in separation lack, it's the source of the subset. It's the cause is in the past or the future in the case of it could be just thinking about the past or it could be thinking about, oh my gosh, we've got to get together next week and this is going to happen again. So the mind again is not in the present. So you're upset right now even though Nancy's not anywhere near this room, but I'm just thinking about what happened in the past or I'm anticipating what's going to happen next time I see her. So I could reword that slightly and say it's an attempt to see the cause in the past or future and the present emotion is its effect. Because it's my present emotion that I'm tearing right now. Present state of mind. Present state of mind. Alright. And it says it's an attempt to see it that way. Yeah. Is what I want right now above all else, is peace.  Which is, he's a good one because I think of E for expectations. It helps me remember that. Oh, I have to question my belief, my other one's belief in my...


Hey, Vico Carver from nebulaphotos.com here. It's either really late at night or very early in the morning, depending on how you think about it. It's about 3 a.m., the witching hour. The reason I'm up at this hour is because I really want to capture this new comet that's in the morning sky for us in the Northern Hemisphere. It's called Comet Neo-Wise, and it has a really long tail. I've seen all these great photos of it online, and of course I want to take one myself. So I can't do it from my backyard here in Somerville, because there's too many trees, and this comet right now is only getting about 10 to 12 degrees above the horizon from here. And so I went into my backyard and I did this trick. This is about 10 degrees if you're measuring from the ground, and so I put the ground right here. I looked right here, and this whole area was taken up by trees. And so the comet would really just get above the tree line and wouldn't be a very good shot.  It's predicted to be clear. I haven't actually been out since I woke up, but if everything works out, you'll be seeing this video, and hopefully I'll have the picture of the comet. I'm going to be doing this with a lightweight setup, because I don't want to have to, since I'm going to be traveling, and traveling to a new place for me, I don't want to bring too much stuff. So it's a setup that I can lift with one hand. It's the Skywatcher Star Adventurer, a ball head, my Canon 5D Mark III, and the Rokinon 135 F2. And I think this will provide a good field of view for the comet, a full frame with the 135 millimeter focal length. So we'll see. This is a very popular Star Tracker. It works very well, very reliable. So I have no worries about using this. I don't think the exposures are going to be very long, but the reason I'm using a Star Tracker is because I want to be able to do something like 10 second exposure so I can really capture the comet's tail. And with a 135 millimeter lens, if you go up to 10 seconds, you're going to get streak stars if you're not tracking. So that's why I have the Star Tracker. But the comet is definitely captureable without a Star Tracker if you don't have one. So if you don't have one, don't worry about it. Just take your camera out. Try to shoot the comet, because it is really pretty bright, especially for us here in the Northern Hemisphere where we haven't had anything but pretty dim comets for quite a while. So let's get in the car, get out there, and we'll see what we can see. Hopefully no clouds. OK, I did capture a comet neo-wise. Sorry I didn't show the setup, but I was rushing to get this setup in time because the sun was rising very quickly when I arrived. And I just got off my shots before it got too bright. I was ramping down from three seconds to two seconds to one second exposures because the sky was brightening so much that I wasn't getting any contrast with the comet. But I can see in my live view that I got at least 15 or 20 shots with the tail. And so hopefully when I stack those, the tail really comes out. And it's a beautiful scene here. We're in Marblehead, Massachusetts with the light host and the boats. So again, I was using the Skywatcher Star Adventurer, my Canon 5D with the 1.35mm lens. And the reason I picked this location is because looking over the ocean, I have really good horizons for the comet. I'll zoom in here on my live view screen to show you what it looks like, just a single exposure. And then we'll get back to the house and stack them together and composite it with the landscape here that I took shots of as well to make the full picture. OK, here's what a single exposure looked like on the back of the camera. And you can clearly see the tail right there going straight up. What I am hoping is that this faint stuff in the tail really comes out and stacking, even though these pictures are pretty bright and there's not much contrast, hopefully by stacking them together using the nucleus of the comet as the registration point, I can bring out a little bit more detail.  OK, so I tried stacking, but it didn't really work out that well because due to this really aggressive sky gradient and just the fact that there wasn't much contrast, there were very, very short exposures at one to two seconds. And just I only got off like 20 of them. The stacking just really didn't do me any favors and was very hard to then combine any result I got from stacking with the foreground. So instead, what I did for this picture is I just picked the best one here, the one where it looked the most in focus and everything looked good. And I'll just show you how I process just this single exposure. Hopefully, Comet Neowise does stick around and I can do something maybe with my Astrotex 60ED at 360 millimeters focal length and really get in there on the comet and its tail and do some comet stacking and all of that. And I can make a different video for that more involved process. But I just wanted to show you how I went around about editing this sort of astro snapshot, just a single frame. It's pretty simple. All I did was I wanted a little bit more contrast. I wanted to bring out the foreground a little bit, but then also darken the sky so that there's more contrast with the comet and the stars. So first thing I did was I'm just going to add a new curves layer, curves adjustment layer, just by clicking on this button up here over here on the right. And I just want to darken the whole picture a little bit first, so I'm just going to grab the shadow point, the black point, and bring it over until I like how this looks with the comet and the stars. And I like how that looks with the comet and the stars, but down here in the sunrise part, I don't like how dark it gets along the horizon because it looks sort of unnatural. So what I'm going to do is I'm just going to click on the adjustment layer's mask. Whenever you add an adjustment layer, it comes with a layer mask already included. I'm just going to grab my gradient tool here and draw a gradient directly on the mask. And the way I'm going to draw this gradient is I don't I like how this part of the picture looks, so I want that to stay white, meaning it's going to do the full effect of the curves on the top part of the picture, but then I want it to gradually affect the bottom part of the picture less. So I'm going to click up here in the part where I want it to stay white.  Now that I'm seeing it, I think that I can add even a little bit more contrast in. So I'm just going to drag that shadow slider over even a little bit more like this. OK, so I'm happy with that. The only other thing that I really want to do is just bring out this part of the picture a little bit because it's so dark that there's not much of interest in just having a black corner like this. So the way I'm going to do that is I'm just going to duplicate the background layer by pressing Command J on Mac or be Control J on Windows and bring that above everything else. So this is back to the original picture. And I want to go ahead and add a layer mask to this layer. So I'll just do that by clicking the Layer Mask button down here. And if I fill that layer mask with black, so if I just do Edit Fill with black, you can see then this layer has no effect. I want just this part of the picture to have an effect. So I'm going to go ahead and use that gradient tool again on this layer mask and just draw a little gradient into the corner like that. And then I'm just going to brighten up that corner by adding a Curves. So I'm just going to press Command M. And I'm just going to bring out those boats a little bit like that. So that was before and that's after. So it makes a pretty subtle difference, but it just adds a little bit more of interest to that corner. And I might play around with that gradient a little bit until I thought that looks right. OK, there we go. So you can see it's just brought in a little bit of a lightening effect on that corner. Of course, since this is on its own layer, this change, I can always play around with the opacity of that layer until it's just how I want it. All right, so here is my final picture. I'm just going to go ahead and press F twice. And that's my astrosnap shot of Comet Neowise over the North Atlantic Ocean in Marblehead, Massachusetts. Hope you enjoyed this quick video for me. I just wanted to get something out there to encourage people to go shoot this Comet no matter what kind of equipment that you have. Again, if the Comet does stick around and we're able to shoot it in the early evening, starting next week, I'm going to definitely shoot this again at a higher focal length. I'm planning around 300 to 400 millimeters. Till next time, this was Nico Carver from NebulaFotos.com.