Excuse me sir. Yes Tirpan tell me. Sir, will you do functions as a separate chapter like composite functions and all that. Yes, yes. You're after this chapter? Yes. I think I've already sent one small part to you which is even odd functions even that is not complete I'll send you one more part. Okay. Okay. Alright, so good evening. Welcome to the fourth session of differentiation. So in today's session we are going to primarily talk about approximations also called differentials. And we are going to also talk about tangents and normals. Okay. So let's get started with the concept of approximations, approximations and differentials. Okay. Now this concept is not new to you because in physics also you would have done it in last year's first chapter of physics, units and dimensions, how to find errors, etc. And the same thing would be used also to do approximations. So both these concepts of errors and approximations are linked to each other. Now how does calculus feature in over here? Let us talk about a function in general, let's say y is equal to f of x, where y is an output which is dependent on the input x. So obviously if you do a small change in the input, let's say you make x as x plus delta x. Okay. Remember we call delta x as absolute error in x, absolute error in x. So if you make a small change in x, which we call as delta x, because of that a small change in y would be introduced. That means an absolute error of delta y would be introduced in y. So delta y is nothing but absolute error in y. Okay. So how do we figure out what is this absolute error without having to undergo the full process of finding what is the value of the new y when you are substituting the new x, that is x plus delta x into your function. Okay. Now for this we are going to use our first principles of differentiation. I hope everybody remembers here that what is dy by dx? dy by dx is nothing but f of x plus delta x minus f of x by delta x, limit delta x sending to zero. Okay. I am assuming that the function is differentiable and hence the left hand derivative, right hand derivative both can be used or anyone can be used to find out dy by dx. Okay. Now this expression if you make some small changes, very, very small changes, instead of saying delta x sending to zero if we say delta x is very small, right? Delta x is a small quantity. Okay. This is a very small quantity. Okay. Rest everything I keep it as it is. Okay. Then your left hand side instead of dy by dx it will become delta y by delta x. So you can say that these two quantities can be compared to each other. You can say it can be approximately used for each other when your delta x is small. Okay. So what we say is dy by dx could be approximated as delta y by delta x. Okay. For very small values of delta x. And remember this dy by dx is calculated at the point where the error has occurred. So x is that value where the error has occurred. I'll give you an example. I'll give you an example for the same. Let us say, let us say there is a metallic cubicle container which is kept under the sun. So I'm just drawing a cubicle container, okay, which is kept under the sun and it's very hot that particular day. Okay. Now, because it is kept under the sun, this metallic container will expand, isn't it? And as it expands, its volume will change. Right. Let's say initially this container was having a dimension of two centimeters. So it's length, breadth and height were two centimeters each. Okay. So what are the volume of this container? It's a volume of the container is not going to be x cube where let's say x is the edge length. So it is going to be two cube, which is eight centimeter cube. Okay. But let's say after being in the sun for let's say an hour or so, it's, you can say new length became 2.012, 2.012 centimeter. Okay. So what will be the new volume or question can be asked in this way, what is the change in the volume? So one way to do it is obviously find 2.0 to whole cube, but that would be a painful process, especially when you are devoid of calculators. Correct. So how do we calculate such things by use of differentiation and how is differential calculus helpful in evaluating this? So because of the expansion in the side length, we can say let the, let the change, let the change in the volume, change in the volume be Delta V. Okay. If you use this formula that we have derived just now, this formula, remember why is playing or we is playing the role of why for you? So we can say Delta V by Delta X will be approximated as DV by DX at the instant when the error has occurred. Now the error has occurred at X equal to two. So initially it was two and now it has become 2.012. So you can say this term is actually your X plus Delta X. Now one small piece of advice that I would like to give you, we always write the change as plus Delta X. There's no minus Delta X because Delta X itself will be positive or negative quantity. If let's say you had kept this metallic container on a winter day outside, obviously it will contract. Correct. In that case, your Delta X would be a negative quantity. Right. But you still write X plus Delta X equal to that new value of the length of the container. Okay. Never put your external sign in place of, in front of Delta X. Don't put minus or plus. It's always plus. Okay. So in this case, if you are looking for what is your Delta V, we need to know the following things. We need to know Delta X. Delta X can be obtained from here. Originally your X was two. Originally your X was two centimeter. Okay. So your Delta X will become or you can say two plus Delta X is 2.012. Okay. Let's not write down the units unnecessarily. So Delta X will become 0.012. Okay. So this will become 0.012. This is approximately equal to the derivative of this function calculated at the point where the error has occurred. So three X square at X equal to two. I think that will give you 12. Isn't it? So Delta V would be Delta V would be 12 times 0.012, which is 0.144. Correct. So this tells you that there would be a change of 0.144 centimeter cube. Right. The positive sign indicates that there is an increment. Okay. So always you need to do plus. Right. If there was a decrement, it would have automatically come with a negative sign. So I'm repeating again. Please do not put any external sign here. Delta V comes with its own sign. Okay. So the new volume of this particular cubicle container would be 8.144 centimeter cube. I would like you to check this out if you have a phone with you or a calculator kind of an object with you. Just check whether when you cube it, how close you are to the answer. You would realize that you are very close to the answer. Okay. But we never had to do a cubing process. We found it out by the process of calculus. Is this fine? Any question here? Oh, it's matching. Very good. And if that tells me that is quite matching. Okay. So I think with this example, the fundamental of approximation and differentials is clear. Okay. Now basically, you can also try to understand this from geometrical point of view. So let's say there is a curve. There is a curve. Okay. And at a certain value of the input, the value of the function is y. Let's say at x it is y. Okay.  I'm just taking a positive change. It could be any any change. It could be a negative change also. And I want to know what is the change in my output. That means I want to know what is delta y. Okay. Now, what does this process say? It says if you want to know this change approximately, you can draw a tangent at that point. And this change that you have over here, this change you have that you have over here, let me call this as change k. This k will be approximately equal to your delta y. That is what it's trying to say. Right. I know there is always an error. There will always be some kind of an error in your finding because it is just an approximation. That's why I have written an approximation symbol here. This is approximately. Okay. Now remember, more closer you are, more your delta x is tending to zero, more this approximation will become equal to sign. Okay. So if your delta x is tending to zero, then your delta y by delta x will be equal to d y by dx at that point of error. Okay. So smaller this delta x, more close you are to the actual value. More close you are to d y by dx. Getting the point. So here if you see this is your delta x. Okay. This base is your delta x. You can say run. You have to find rise. So what do we do is we use the fact that tan theta will give you k by delta x. Okay. So dy by dx is definitely k by delta x. Correct. If you see the triangle over here, k by delta x will be tan of this angle, which is nothing but d y by dx calculated at that point. Are you getting my point? But remember, when you're trying to approximate it, it becomes delta y by delta x because k is not exactly delta y, but it is very close to it. So as a result, we can use dy by dx is approximately delta y by delta x. Don't forget to put the x value of the point where the error has occurred in your dy by dx. And therefore, this formula will be helpful for you to find your error in y. Is that fine? So with this, we can actually start solving few questions. This topic is not very difficult. Let's jump into our question directly. Find approximate value of find approximate value of value of 127 127 cube root of 127 approximate value. Many a times you will see they use the word this for this both are same thing. Okay, don't don't get confused. Both are same thing actually. Please do not use calculators and all as the purpose will be defeated. We have to find it without the use of any kind of a calculator. Okay, Aditya good. So guys, here we have to take care of two things one. In fact, three things one. What is that output input relation that you're going to build up? For example, when you see this kind of an operation, you know that your output is input to the power of one third. So this is the one thing that we need to understand. Many a times this will not be given to us. So we need to figure it out from the question. Okay, second thing is for what value of x, which is close to this? Can you find why without the use of any problem or without the use of any calculator? So tell me a value which is very close to 127 for which cube root is very easy to obtain. So you will see 125 right? Yeah, 125. You won't take 64, right? I'm sure you won't take 64. Neither will you take 225 or right? Sorry, what is seven cube 343 or 36 into six that is how much 216 that is also be very far. So the best value to start here with will be x equal to 125 because for that your y can be easily be obtained and that is five. Okay, now the problem is we don't have 125. We have a slightly deviated value and that is 127. So they're not trying to ask you what is this new value of the output? This is what we need to find out. So first we need to understand that our delta x here is plus two. Okay, now many people ask me said two is not a small value, right? So how are you trying to use it here because your delta x should be very, very small. It is basically in comparison to the x value. Your delta x is small in comparison to the x value. So two as compared to 125 that is a small quantity. That is what we need to take into account. For example, when you are dealing with, when you're dealing with let's say the frequency of a simple pendulum. Okay, what do you consider? You consider that the length of the string is very small as compared to the radius of the earth. If it is very large, your formula is going to change. Isn't it? Right? People who have done gravitation chapter. So we consider that L is very small as compared to the radius of the earth. So it's not like L is actually small as small as zero. No, it is small as compared to the radius of the earth. So in the same way, this delta x should be small as comparison to x. So now the third step would be using the formula d y by dx at the point the error has occurred. Now where has the error occurred? The error has occurred at 125. This is approximately equal to delta y by delta x. Delta x is already known to you as a two. Okay, so let's solve for delta y from it. So d y by dx, this is your y. So d y by dx will be one third x to the power minus two third calculated at 125 is equal to delta y by two. So this is going to give you one third, one third and if I'm not mistaken, this will give you 25, isn't it? Yeah. So delta y, delta y by two is equal to this. So delta y is going to become two upon 75. Okay, two upon 75. This is approximately 0.026666. You can write 267. Okay. So again, it automatically comes with its positive sign. Right? So if there was a case of subtraction, it will automatically come with a negative sign. So your new value of the output will be the old value, which was five plus 0.0267. That is nothing but 2.0267. This is going to be a new value. Okay. So you don't need a calculator in order to calculate it. Now, it doesn't mean you have become a calculator because such things will only work when your value of the new input is very close to a value which is known to you. Let's say had I given you something like 170, then probably this method will not work because there will be a large amount of error in your answer. So only when your delta x is very small as compared to x, then only you can expect a very accurate, in fact, you can say close to accurate answers to come out. Is this fine? Any questions here? Please do ask. If no, can I move on to the next question? Clear? Okay. Next question is if one degree is alpha radiance. If one degree is alpha radiance, however, if I want, I could give you alpha value that is 0.0174. But that is not required for us. Then, then, cause of 60 degree one minute is approximately equal to option A, half plus, half plus alpha root 3 by 120, option B, half minus alpha by 120, option C, half minus alpha root 3 by 120, option C, half minus alpha root 3 by 120, option D, none of the above. Let me put a poll on. Can you all see the poll? Yes, sir. Yes, sir. So 29th onwards you have your UT, right? What is the syllabus for maths? The full integration and application of integrals. And linear programming? Yes, sir. Oh, they have taught application of integrals also? There is only one exercise in that, sir. It's an easy question. I'll give you another 30 seconds to finish this off. Only 5 people have responded. Okay, at the count of 5 I'll stop. 5, 4, 3, 2, 1. Please vote. Please vote. 12 of you haven't voted yet. Okay. Good, good, good, good. Fine. See, guys, whenever you're dealing with angles, you must always deal in radiance, right? All the calculations actually should be done in terms of radiance. That's why this first information is given to you that 1 degree is 60, 1 degree is alpha radiance. As you can see, most of you have gone for option C. Let's check. So the obvious relation that you're going to have over here is y is equal to cos of x, because you're evaluating cos of something. Okay. Earlier, your x was pi by 3. That is 60 degrees. But now it has, by the way, y for that was half. But now it has gone to 60 degrees plus 1 minute. Now, if 1 degree is alpha radiance, 1 minute will be alpha by 60, correct? Okay. And they're trying to ask you what is the new value of y? Okay. So delta x is very clearly alpha by 60. So let us use the formula. Let us use the formula dy by dx at the point where the error has occurred is approximately equal to delta y by delta x. So delta y will be approximately equal to delta x times dy by dx. That is sine x with a negative sign at x equal to pi by 3. So delta x is alpha by 60 into root 3 by 2. So as you can see, there is a negative answer coming, which clearly suggests the fact that there would be a decrease in the value from half. And we all know that because cos x is a decreasing function from 0 to 90. So there will be a fault. Okay. So your new value of the output would be the old value plus delta y. Delta y will be this. So as a result, you end up getting option number C as your answer. Option number C will be your answer. Is that fine? Any questions here, anybody? Next thing that we are going to talk about is the relative error. Is the relative error. Relative error. So I think in physics also you would have learned about it. Relative error is basically the absolute error divided by the point where the error has occurred. You can also write it as this. Okay. If you multiply this by 100, then the relative error becomes percentage error. This is read as relative error in x. And if you multiply this by 100, or let's say this by 100, it becomes the percentage error in x. Percentage error in x. Okay. Now we'll take up some questions which are based on relative error. These are slightly trickier ones because I've seen people making mistakes in them. Okay. By the way, when I say delta x or when I say this, please note that this is approximately equal to dx. Okay. So when you say delta y, this is approximately equal to dy. Okay. So many a times we replace dx and dy terms with delta x or delta y. So as to make our life convenient. Okay. So this differential change in x can be approximated as delta x many a times when you know that these quantities are very, very small. Okay. But basically it is done in presence of in presence of an x because then only these quantities would be considered to be a very small quantity. Okay. Let's take few questions on the same. Then probably it'll give you a lot of idea. All of us have seen in thermodynamics adiabatic process. Correct. So for a diatomic gas undergoing adiabatic process, we know that the relationship between pressure and volume is given as PV to the power 1.4 is a constant. Okay. My question is, find the percentage, find the percentage change in volume, in volume. If the pressure is increased by, if the pressure is increased by 1%, find the percentage change. Now I'm not saying increase or decrease. You have to tell me what is happening actually when the pressure is increased by 1%. How will you solve such questions? Would you like to try first? Your voice is breaking. Yes. Yeah, please try. Please try. So what is given to us? We have been given that delta P by P into 100. This is 1. This is given to us. And what do we need to find? We need to find this. Correct. Correct, Trippan. Okay. So let's discuss this. Very good, Shruti. Very good. Okay. Let's take log on both the sides. So log P plus 1.4 log V is equal to a constant. Okay. Constants log is also a constant. Okay. Let us differentiate with respect to V. Let us differentiate with respect to V. So when we do that, it becomes 1 by P dP by dV plus 1.4 by V is equal to 0. Now, we have learned that dP by dV can be approximated as delta P by delta V. So we'll do the same thing over here. We'll write this as delta P by, sorry, delta P by delta V. Delta P by delta V. You can write this as negative 1.4 V. Let us take this delta V to the other side. Let us take this to the other side. So it'll give me delta P by P is equal to negative 1.4 delta V by V. Let's multiply both sides within 100. Let's multiply both sides with 100. And when you do that, automatically you'll end up seeing this expression which is actually given to us as 1. Okay. And they want us to find out this expression. They want us to find out this expression. So I can say here that delta V by V into 100 will be negative 1 by 1.4. This is approximated as negative 0.7 if I'm not wrong, or 7-1 whatever. Okay. So what we can say is that there is a decrement. There is a decrement of 0.71 percentage in volume. Okay. So as the pressure rises by 1%, there is a fall of 0.7% in the volume. Understood how it works? Yeah, sure. Any questions? Oh, yes. Correct. All right. Let's take the next question. If the sides and angles of a plane triangle vary in such a way that its circum radius remains constant, find the value of DA by cos A plus DB by cos B plus DC by cos C where DA, DB, DC are small increments in the sides of the triangle. I'll put the poll on for this. Please put your response on the poll. Okay. Excellent. Very good. Three people have responded so far. Nice. Yeah, yeah. Take it. I'll give you 45 more seconds from here. Please vote, guys. Last 15 seconds. 5, 4, 3, 2, 1, go. Please vote, please vote. End of poll. Almost equal responses have been given to A, B and C. Of course, the reason for D not getting any response, it is none of these. And many of us, we know very well that none of these being correct is very less. Okay. Now let's check here. What is the thing given to us? If the sides and angle both vary, but they vary in such a way that the circum radius remains constant. Right. So we all know by our sign rule. Sign rule says A by sin A is equal to B by sin B is equal to C by sin C. Okay. And this is equal to 2R. So A is equal to 2R sin A. B is equal to 2R sin B. And C is equal to 2R sin C. Okay. Now can I say DA would be 2R cos A DA. Can I say the differential change in A will be 2R cos A, the differential change in angle A. Similarly, DB will be 2R cos B DA. And DC would be 2R cos C DC. I should write a B here by mistake. In other words, which is very rhyming with the expression that we are supposed to get. DA by cos A is actually 2R DA. DB by cos B is 2R DB. And from here I can say DC by cos C is equal to 2R DC. Okay. If you add them, if you add them here, that given expression will become 2R DA plus DB plus DC. Isn't it a differential change in the sum of the angles of a triangle which we very well know that there is not going to be any change because A plus B plus C is a constant. Right. It's a fixed value. So the change in the value here would be 0. There cannot be a change in the value of the sum of the angles of a triangle. The given expression to U will be equal to 0, which is option number A. Which is option number A. But I thought it was tomorrow Venkat. Oh, it was today. Yes, any question anybody? Why are your voice coming very feebly to me? Which one sir? No, I thought your bio was tomorrow. Oh, tomorrow is GEM. Is this fine? Any questions here? Okay, looks like an easy concept, but many people make mistakes here. Let's take one more. In a acute angle triangle ABC, A and B are constants. A and B are constants. Right. But angle A and B are varying. But angle A and B are varying. Okay. Prove that. Prove that D A D capital A by under root of A square minus B square sine square A. Is equal to DB by under root of B square minus A square sine square B. Try this out. Just right done. Once you're done with the proof, just right done. See here, DA by cos A, DB by cos B, DC by cos C is clear. What is your given expression? Your given expression is the sum of these, right? So when you add this means you're adding this. DA, DB, DC means differential of A plus B plus C. Correct? Okay, that partly I doubt sir that why you took D out. Okay, when I say D by DX of sine X. Plus D by DX of X square. Can I not write it as D by DX of sine X plus X square? Yes, sir. The same way. A change in the error, a change in A value and a change in B value and a change in C value. The change in the A plus B plus C value. Okay, sir. Let me go back to the question. When is your semester exam starting? I didn't tell sir. No tentative date also? No. Okay. Okay, as soon as you get your dates, do let me know because I have to plan for your next monthly test. Very good, Tirpan. That's a one minute. Yeah, very good Siddharth, very good Ayush. Okay, let's check this. From our sign rule, we can say. Xiaomi also done, Patam also done. Okay, I'll just give you a hint from the sign rule, we can say A by sine A is equal to B by sine B. In other words, A sine B is equal to B sine A. Okay. Differentiate both sides. That means do this. Somebody's trying to say something. Hello. This will become A cos B db. Remember, there is no change in a value. So A will be like a constant. So only will differentiate sine B. So the differential of sine B is cos B db. In the same way, this will become B cos A dA. Correct. In other words, dA divided by a cos B will be equal to db divided by B cos A. So basically I brought it down to the left and I brought this down to the right. Any doubt so far? Okay, so now we can write cos of A as sorry, cos of B as under root of one minus sine square B. And we can write your cos of A as under root of one minus under root of sine square A. Correct. Let us introduce this A inside. Let us introduce this A inside. This will become A square minus A square sine square B. And this will become under root of B square minus B square sine square A. You can write this as a square of A sine B actually. And this is square of B sine A. Okay.  Is it? Yeah. So I can replace this A sine B with a B sine A. So I can write this as under root of A square minus B square sine square A. And on the same way, on the left hand side, I can write D B by under root of B square minus A square sine square B. Right. So this is what we actually were looking for and hence proved. So I think this is more than enough required for approximation and differentials. You will not find many problems on this concept. So without much waste of time, we will move on to the next concept now.


What is the goal of today's daily vlog? number one Teach you one thing YouTube teach you one thing and number two To get healthy, which means what does that mean? It means I I must Attempt to get 12 hours of sleep Tonight, which the Sun is gonna be down in about two hours I've got to go to bed early and I've got to sleep 12 hours to get rid of the sickness That's the only way I've decided that this is gonna go away. I did not sleep well last night I don't know what happened. I think maybe it was because I took a little cat nap after dinner Anyway, that is the goal the two goals for today teach you one thing The runner's not and to go to bed early so I can defeat the sickness All right, we've got the zantase here the new balance zantase bright neon green Gotta love that and then you've got the black Nike Vemero 14 So what I'm gonna do is I'm gonna take the shoelaces out of the zantase right here And I'm gonna put the shoelaces into the Vemero 14s So that you can see the contrast of the bright neon green against the black of the Vemero 14s And then we will analyze exactly how you tie a runner's knot. So let me get these out Real quick for you Have you ever heard of the runners not maybe you have maybe you have not There's a lot of new runners on this channel people that are just getting into running if so you probably have not heard of this Not maybe somebody at a running shoe store has taught you about how to tie this knot That's where I actually at the runners roost on Colorado Boulevard in Denver, Colorado 20 years ago somebody work in the floor taught me the runners knot So if you don't know it if nobody's ever taught it to you you won't you won't know how to do it and why you should do it So I like I lean in the direction of a snug fit for my shoe I like to feel pretty secure in the shoe now. I sometimes go too tight and I have to stop You know, maybe like once or twice a month I have to stop in the middle of my run and loosen my shoe just because I went a little too snug But overall I like a snugger fit through the shoe and especially in the heel Especially on the trails like when you're going up and down steep trails You do not want any slipping happening in the heel. The runners knot basically what it allows you to do is cinch C-I-N-C-H cinch down with the shoelaces the back of your shoe through the heel So with all running shoes you have eyelets going up the side of the running shoe right through here and basically these eyelets is what the shoelace goes through and Then you work your way up the shoelace lacing the shoes Until you get to the last two holes at the top of the eyelet chain So those last two holes you want to save don't put the shoelaces through yet Basically, you're going to cross over one more time to the second to last eyelet with the end of the shoelace put it through and Now instead of going back across the shoe with the rest of the shoelace You're going to want to string it through the last eyelet at the very top on the same side and then what is that going to create? It's going to create a loop at the top of your eyelet chain This loop is what's going to allow you to cinch down your shoelaces So you can have a snug fit through your heel once you have created both loops at the top of the eyelet chain on both sides Of the shoe you're going to take the extra shoelace that's left There's you know There's probably going to be four or five inches and you're going to send it across the shoe to the other side and Yes, thread it through the loop that you just created on the other side of the shoe Do that on one side and then go across to the other side so what you've just created with these two loops is a Basically a pulley system where you're creating tension between both sides of the shoe that allow you to cinch down Slowly don't go too tight, but cinch down slowly so that what's going to happen is these shoelaces are going to pull the back of the shoe Toward the front of the shoe and that's going to create that nice snug feel through the heel so that you don't feel any Slipping happening through the heel because you really that's like the worst is when your heel is coming up just a little bit in the back of your shoe and That is the runner's knot and then of course at the very end once you have cinched down and you feel like you're secure You can finish off tying the shoe like you normally would and then you're nice And don't forget to double knot now tip of the day Don't forget to double knot so that is the runner's knots And I know it's kind of hard to describe through words and images through a video if you were here in person It'd be a lot easier, but I'm telling you I've been doing this knot for 20 years and I love it And I use it for all my shoes my trail shoes my road shoes my racing shoes and it just creates a slightly extra snug feel through especially through the heel which I love and it Honestly, I think it helps me actually stay off of my heels when I'm racing because it kind of forces you up on your toes a Little bit because you're just nice and locked down that nice lockdown feel and the question of the day Do you use the runners knot? Have you ever heard of the runners knot if you have not heard of the runners knot? Will you try it? And if you do let me know down in the comments. I'd appreciate it Man, I just I had I had to come outside and get some fresh air It being sick and cooped up inside for the last two days or whatever.  Okay guys I was sick a couple days ago, and so I forgot I'm still sick But I forgot the comment of the week and so here we go. This is from Turkish churros nice name I like that and this is in connection to yesterday's question of the day about who is your favorite runner of all time And this is what he said I Was going I was going to say Kipchogi or Steve pre-fontaine But when you mentioned hometown heroes, I immediately thought of my high school coach Darryl general He was a 214 marathoner and he tied a record by qualifying for five consecutive Olympic trials which means he was highly competitive for almost two whole decades his entire career He worked three jobs Including coaching at a local high school. I was lucky enough to have him as my coach and without his influence I would not still be running today. He wasn't the fastest or most famous runner of all time But he is my favorite runner of all time. Thank you so much You get the comment of the week Turkish churro and gosh I mean that's what it's all about stories inspiring stories stories Impacting stories and it's pretty neat that Darryl impacted your story so thank you for sharing about his life and his journey within this sport that we all love and Guys, I'm calling it. I'm biting the bullet. It pains me sometimes to publish blogs that are maybe not as entertaining to watch. Let's just put it that way I hope you learned something though with the runner's knots, you know, especially for all the maybe newer runners out there that have not Ever been told about the runners not and not been taught how to tie it So if you struggle with tying it, let me know down in the comments And I'll try and walk you through it, but I love you and I'm calling it And we're going to we're going to bed soon once the sun goes down because oh man I need that I need like at least 12 hours of sleep tonight. Oh my goodness seek beauty work hard Love each other. Thanks for being here


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Good day, folks, and thanks for joining us. We're gonna have a discussion here today of utilizing hydroponic growing systems in a high school greenhouse and partnering with food service systems in the high school to provide an opportunity for students to learn hydroponic production, possibly operate a school-based enterprise and provide a healthy, fresh product directly into the food service or cafeteria program in the high school. We're gonna be highlighting a program today that has been in place for about a year now at Sterling High School, and our presenter, and she'll be talking about what they're doing there at Sterling High School is Cassie Kinney, and I will turn it over to you, Casey. Okay, thank you. So as Mike said, I'm Casey Anderson. I'm married now, so it's Anderson now. And I'm gonna talk to you guys a little bit about what we've been doing here at our school and some of the challenges that we've had to face and some ways that we've had to go about fixing those challenges to make that happen and be able to get this project rolling and have a year of success with it. And so we'll move to the next slide. I'll go on ahead and start talking about how we got this up and running. So what inspired me to create this partnership between myself and my program as well as the food service within our school was my advisory board chairman, Dr. Brent Young. He, him and I had been having some conversations about how we could go about utilizing our greenhouse. As you guys will see here in upcoming slides, our greenhouse is not set up ideally. We don't have water to the houses themselves, only water that we have is a one stick it inside of our head house and the greenhouses were built completely backwards. And so the head house is on the same wall as our cooling systems. And so we're not able to pool air through the cooling systems and utilize those to keep the greenhouse up and running and cool enough for the plants. And so we started bouncing around some ideas and he was talking about hydroponic systems, which is something that was completely new to me. I've never really utilized them very much prior to this. And so we started, he said that he would kind of help coach me along if I decided I wanted to do this. And so first things first, we went to NJC and he showed me their hydroponic system and what they've been doing in their program there and how easy it was to get up and started and get kids involved with that. And so I started thinking about it a lot more and realized that that was going to be an optimal way to utilize our greenhouse because I wouldn't have to worry about having a sprinkler system or anything in the greenhouse because I'd be able to fill up our tank a couple of times a week and then utilize that to water where we only have the one spigot. And then also by doing this, I was able to get students involved, not only in the building process, but also in other areas of the hydroponic system. And then finally, once it was up and running, was able to utilize students to harvest and plant and manage the hydroponic system. And the neat thing about starting up this program was kids seeing that that's what they were eating was the lettuce that we grew in the cafeteria. It really brought a lot of pride into our program which was something that I was really hoping because right now in our school and our community, there hasn't been a whole lot of pride and so this was something that I was hoping to help out with that. And it ended up doing a lot of good for that aspect. All right, let's go ahead and switch to the next slide. So how my plan came together, as I mentioned before, I was inspired by the NJC project. NJC, they not only have the lettuce hydroponic system but they also have a hydroponic system for vine crops as well. And it was kind of neat to be able to see how they were able to put this together and utilize it within their schools. And I wanted to try to model that. As I mentioned before, Dr. Young played a major role in getting this started. He also helped me select which hydroponic system would be best for our greenhouse and what we were wanting to produce the amount of lettuce and stuff that we're needing to produce to meet the needs of our school system. And so we chose the Crop King NFT 8-25 system and we're able to produce enough lettuce for our school with that system and even have some extra that gets sent over to some of the other schools in our district as well. From there, I purchased the system through my Perkins grants. Here at RE1, how we divvy out our Perkins money is we have to write a grant for what we're wanting.  And so I was able to get the hydroponic system through the grant. And then my power structural and technical system students, they're the ones that actually built the hydroponic system and put it together instead of doing their normal plumbing activity through this past fall. Usually they do a sprinkler system and this year we changed up a little bit and they put the hydroponic system together. And then my food science class, they were the ones who created our food safety plan for harvesting and delivering the lettuce to the cafeteria to ensure that we are keeping a safe and clean product. And then my ag leadership and communications class, they created posters that we have all over our school and on our school website showing what we're doing with producing lunch for the school cafeteria. And so that played a big role in terms of boosting the pride of our school because students were coming into the cafeteria and seeing the posters and realizing that the lettuce that they were eating was being produced by some of their fellow students and those kids that had been growing and harvesting the lettuce and has been part of this, they took a lot of pride in their classmates knowing that they were the ones that were providing food for them. And then finally, I didn't put this on the slide but my ag science class, they are the ones that have been harvesting and planting and keeping track of what's been harvested and how much and all that good stuff. So it's been a community project within our program. It wasn't just one class that's been working on this. All right, let's go on ahead and move to the next slide. So major supporters, Dr. Young, as I mentioned already he was a major supporter. And then also Brian Caley who also works in the extension office here in town and he's the gentleman in the blue polo and the picture on the far left and on the center. Brian Caley played a big role in this project because he was in here in our classroom helping to get it set up correctly. He's the one that did a lot of the work at NJC and so he'd already had helped put together their system and so he helped us as well. And then also he helped us get started with growing the lettuce for the first few months while we were kind of getting our feet under us and learning how to take care of the hydroponic system. He took one of the steps out of our hands and helped kind of gradually get us going and him and the NJC kids, they started our lettuce plant for us for the first couple of months. And then once we got a system to start the seed then we started taking over that as well but it was kind of nice having that extra support so that we were only learning one new thing at a time and then gradually working our way into the whole process. And for me being a person who is not a, does not have a green thumb naturally, having this extra support and this guidance was really helpful for me as well as my students. And so that's one thing that I stress is if you don't have any experience in starting up a hydroponic system or starting anything new in a program is to seek out help. As you guys all know, ag teachers don't know every aspect of every part of the industry. And so it's hard to be an expert in everything. And so make sure that you guys are seeking out help if this is not an area of your expertise. Another thing I wanted to point out to you guys is in the picture in the middle, if you notice, as I mentioned before, our wall with the cooling system on it, there's the head house behind it. And so as I mentioned before, my situation was not ideal with our greenhouse. And so even if you don't have the perfect setup already, it don't let that scare you away from starting up a hydroponic system in your program. All right, let's go ahead and move to the next slide. So one of the challenges that we faced is food safety. So the first step that we started was we wanted to have a plan in place to make sure that we are harvesting and sending that food over to the cafeteria in a way that is going to minimize contaminants and make it a lot easier for the food service folks. And so I had my food science create a food safety plan, which my ag science class then had to follow pretty strictly. And then the next thing we did was we converted the head house into a sanitary harvesting room. So the nice thing about our head house that already had concrete floors, we had some tables and saw horses in there that were able to set the trays on and the kids were able to harvest the lettuce and then put them into these foldable crates that we purchased that the kitchen were able to put into their dishwasher and sanitize before bringing them back to us. And so being able to utilize that area and be able to harvest the lettuce in a place that is clean and is easy to keep clean because it was concreted floors made it a lot easier. The nice thing too about hydroponic systems is that the lettuce is being grown in a naturally clean space as well. You're not growing it on the ground. And so there's less opportunity for contamination and the fertilizer is in the water. You're not having to worry about using things like manure for fertilizer. So it just reduces a lot of potential for contamination anyways. And then once it's brought over to the cafeteria they do still wash it twice as per what their food service code, I guess is what you would call it required as well. All right, let's go ahead and move on to the next slide. So the lettuce use and costs. Right now we are harvesting, we were harvesting 24 heads of lettuce twice a week.  Now in JC, they do sell theirs for $2 a head but our food service they could not keep up with that price. And so they were actually wanting to buy it at 50 cents a head but I was able to talk them up to a dollar. And so that's what we've done cost wise. All right, go ahead and switch to the next slide. Another thing that probably a lot of people would have on their minds is what do we do for during the summer? We actually shut down for the summer. As I mentioned before, we do not have adequate cooling in our greenhouse. And so if you keep anything plastic in there which the majority of the system is it will start to melt and warp. And so we don't keep anything in there during the summer. And then also obviously if it's too hot to keep anything plastic in there it's too hot to keep the plants going. And so we actually shut it down two weeks ago with our last harvest and we won't start it up again until school starts. Another reason too is where our greenhouses are located it's in a fenced in Walden area. And so it would be difficult to get kids to be able to come in and harvest unless I'm here every day. And because somebody would have to let them into the building and let them in through the shop to get to where our greenhouse is. And so I would have to find another teacher or staff member to let them in because I'm gone for case conferences, CBATA conferences. Also I'd try to take a week of vacation to go and see family out of town and stuff. And so really it's not, it just makes things a lot easier if we just shut down for the summer. Also we obviously our school isn't running during the summer and so we would have to find another buyer for it whether it may be send them over to NJC or sell at the farmer's market here in town. And it's just more work than it's worth at this moment. And then, but however we will start planting seedlings about 40 days before school starts or start seeding 40 days before school starts and get those seedlings going. And we'll do that in my classroom because it'll still be too hot in the greenhouse. And then a couple of weeks before school starts usually it's finally cool enough that we should be able to get the lettuce into the greenhouse and get it really growing by then. All right, let's go ahead and move to the next slide. So future plans. I would like to after we get this really under our belt I would like to try some of the vine crop hydroponic systems and maybe grow some cucumbers and tomatoes. And so that's something that I foresee happening in the next couple of years I'll put in another grant for Perkins Fund for vine crop hydroponic systems once we really feel like we have a good handle on the lettuce. And then also this is something that will be happening next year. The majority of our work this year was done in the classroom. And next year my plan is to turn this into a school-based SAE by modeling it more like a business. So I'll have kids that will be in charge of the financial aspect of it keeping records on the income and expenses. I'll have students that their job is solely harvesting and management. I'll also have students that their job is to advertise and get information out on what we're doing within our program. And so I'll be creating this over the summer some different jobs, checklists and that kind of stuff. If anyone's interested in those just shoot me an email at Anderson with an O-N-K-R-E, the number one valley schools.org. And once I have those completed I'll be happy to share those with you guys. Also, if you guys have any questions for me feel free to email me with that same email address and I'd be glad to answer those for you guys as well. So some last minute tips that I have for you guys. So as I mentioned before, don't let not having the perfect setup stop you from trying to do this. As I mentioned, we did not have an ideal greenhouse setup but we're still able to make it run. As you can see in that picture in the middle this is when we had lettuce up and growing in that picture in the middle there's a hose that's running from our head house. That's how we get our water to our water tank that has all the water and nutrients in it. And so we've had to make things work. Also make sure you take advantage of grants whether it's Perkins or other grant opportunities. Utilize people with expertise in this area. As I mentioned before, I don't have a green thumb and animal science gal. So this has been a adventure for me and a learning opportunity for me as well as my students. And also be patient and understand that your first year you're going to make mistakes and you will have a learning curve. We've had lost lettuce due to temperature control issues. We've had water control issues. Had a lot of powdery mildew. And so had to learn how to adapt and take care of each of these issues. And then also really from the get go make sure you set up a good accounting system for just making sure you're keeping track of how much lettuce you're harvesting and sending over to your cafeterias. That's extremely important to make sure that you're not being taken advantage of or anything like that. All right, that's all that I have for you guys. Okay, Cassie, thank you very much. And I apologize. I was looking at the screen and it has your maiden name there. But yes, I knew you changed your last name. So let's talk a little bit. While you were talking there, I realized I had some pictures of the NJC system. I've pulled those up. And let's see if we can get those on the screen if you would tell me, are there pictures up, Cassie? Yes, there are. Okay, this is a shot of what NJC has. Now, their greenhouse is quite a bit larger than Sterling high schools. And so they do have some more space, but you can see here that they're not using the frame system that was put into the Sterling greenhouse. They're actually sitting on top of their greenhouse benches and they just build a two by four frame that covers those benches. The system that this operates off of is made up of 25 of these white trays. The trays are eight foot long and the whole system will handle about 300 plants capacity. And you can see in this area right close to us that these are very close to harvest. Back over here in the background, you can see there's some plants there that are a couple of weeks away. And so they stagger based on what the demand is going to be from the marketplace. And so they are not wasting any other or any product at harvest time. Couple other pictures here. This is an in shot of it. You can see how simple it is. It's just a supply system. The pump sets down in the reservoir there. The supply comes down. The drip tubes go into one end of the tray. It goes through the tray then drops back into this large return pipe. Variation of the water is just based on the drop of the water back into the reservoir. You mentioned the vine crops. NJC is doing some vine crops. You can see here that they, this is kind of a Dutch bucket system, also from the same company that the trays are from. And you can see they're doing some cherry tomatoes. On the other side there, they're just starting some cucumbers. And this was in January. So they're getting good quality growth out of that and a good harvest for that. So the program that we've put together is from a company called Crop King. And they have various sizes of systems that what we are using and what Sterling has there and what NJC has is this nutrient flow system of eight foot trays, 25 foot trays. You can see there are some smaller systems. So if a person wanted to get started in a smaller in a less space and less commitment, they could do that. The program we've put together and we've written the language for career tech education programs. Cassie talks about the Perkins Grant. That is available only to career tech programs that are approved through our office here at the community college system. And so we drafted some language and we've provided this to our high school instructors that if they wanna drop this into their Perkins Grant, you don't have to do all the work that Sterling had to do to write their own grant. This has been a pre-approved. The amount for the system, we have it at $2,500. This includes not only the system, but also the seed, the fertilizer, everything that's needed to get it up and operating the first year. I think the system itself is around $1,600 and there's additional costs for some of the testing, some of the seed trays, and the other materials as needed. So this is a turnkey right here for $1,500. In addition to that, we feel that, because Sterling sits right there down the road from NJC and Dr. Young sits on their advisory committee, they have very easy access to professional development with schools all over the state that might be implementing a system like this. What we're proposing and we're adding to that grant application is a day and a half intensive professional development workshop that we would host there at the NJC campus, utilizing the expertise of Dr. Young and also the gentleman, I can't remember his name, but the gentleman from Extension, talking about not only- Oh, Brian. Pardon? Brian? Yeah, Brian, yeah. But not only how do you operate the system, how do you work with your food service or other groups or entities in your community? What are your harvesting practices, your accounting system, but also looking at beyond the school if a student wanted to go into business into low startup costs, hoop greenhouses, producing lettuce like this or producing a fresh produce crop that could be marketed in a community. In a lot of our rural communities, we really don't have good access to fresh produce. Even the grocery store struggled with it because of the quantities they would need to buy and having a fresh market for it. One of the things, and you mentioned that the difficulty of having students access to school greenhouse in the summertime makes it tough to do, this system is just simple enough that it feasibly could be moved out of the school greenhouse and if a group of students wanted to operate it during the summertime as their own business and develop their own marketplace, like you mentioned, a farmer's market, that could feasible to be done. They could almost rip the system from the school's, this trigger from the ag program, operate it during the summer and then when school starts up, they bring it back in. You can put the whole thing in the back of a pickup pretty easy and they build their own stand for itself. And so in this grant proposal, we've got the cost of the equipment, we've got the cost of a professional development. If a school wants to, they can also include the travel and cost to go to the professional development and sterling and because it's a Perkins grant, they could also include a couple of days of substitute teacher costs for covering classes when they're gone to the professional development. This information is available to our ag instructors. It sets on our Moodle group in the state resources and it is titled Perkins Language for State Projects. And it sets right, there's the state level resources and it's right at the bottom project language for Perkins grants. And so that's the document we just had open there. You can copy and paste that right into your grant application and we have pre-approved this through our Perkins coordinator here. And so there shouldn't be any problems with getting this approved to utilize your Perkins dollars for it. It's a good project. It's a good utilization of the greenhouse, especially in the off season. A lot of our greenhouses do bedding plant crops and which ties up in springtime, but you can come in, like you say, starting seeds about a month early. You can have this system up and running almost for the first day of lunch. And with the school-based enterprise opportunities for students to run a business out of the school, you can really provide a high quality work-based learning experience there. So we are encouraged to work with, live well on this and their communications with our food service directors. And if any food service directors are watching this video and you don't have an agriculture program there, but you have a science program or something, obviously you can't access the grant funds, but we'll be glad to work with you and get you connected to the system, the equipment, where it's ordered from and you would be more than welcome to join the professional development sessions and having the fall as well. So that's kind of what we've got. We're encouraged by this. It's, like Cassie said, it's pretty easy to run. You learn a lot from it and you make some mistakes and that's part of it, but it's a neat opportunity to actually have a production system up and producing fresh produce for our schools, especially out there in the rural areas where we're looking with small quantities that's difficult to order. So we appreciate your time. Thank you very much for you folks there up in Sterling and your time and expertise on that and being the guinea pig on this. So we hope you have a lot more of in the future. With that, just real quick, my name is Michael Wommachal and I work with the Community College System Office. I'm the Ag Program Director. And so I think we can probably add some emails here to the notes on this. So if you have any questions, be glad to answer any emails that you have. So thank you very much for your time and we will shut her down for here. Bye.


The study aimed to determine the residence time of permafrost groundwater in eastern Siberia using tritium, chlorofluorocarbons, CFCs, and sulphur hexafluoride, SF underscore 6, as traces. Tritium analyses showed that the apparent age of groundwater ranged from around 1 to 55 years, with one spring water containing more than 90% water recharged by precipitation before the 1960s nuclear testing era. The study suggests that 3H and CFC, 12 are the most applicable traces for groundwater vulnerability assessments in this region, but further analysis is needed to assess the contribution ratio of superpermafrost and intrapermafrost groundwater. This article was authored by Tetsuya Hayama, Kozayoshiose, Alexander B. Kolesnikov, and others.


I'm actually trying to help both of you find a color back. Call her back, dude. Call her back. Today, we have my guy, Jason Pryor, right? Jason Pryor. What's up, bro? Hey, how's it going, Ricky? How's it going? Good, man. Good, man. So tell everybody how long you've been in the business, what market you're in, all that good stuff, man. Tell everybody a little something about you. I've been in the business, what, three and a half years. I'm over here in the Southeast Texas, over here in Beaumont. Cool, cool, cool. Who you calling today? I'm going to circle prospect around in local neighborhood. Actually, it's my neighborhood. You know, we're going to see how this goes. Hey, let's hear Jason on the phone, man. Let's get that circle dialing. I want to hear that phone ringing. I want to hear people saying hello.  And cussing you out. I want to hear all that stuff. I like to hear that sound. Come on. Hello? Hello. Is this Mr. Silva? Mr. Who? Mr. Silva. I'm looking for the owner of 1117 Wild Meadow over here in Beaumont. 1117 Wild Meadow. Yes. Oh, okay. Are you the owner? Yes. Yes, this is Jason Pryor with EXP Realty. How are you doing today? Pretty good. That's good. Me too, just enjoying this beautiful weather outside. Isn't it gorgeous? Oh, yeah. Oh, yeah, it's pretty good, ain't it? Well, look, I don't want to take up too much of your time, but they had a house that just listed in the neighborhood, and I was just reaching out to some of the neighbors to see what you think was views in the market itself. Oh, no, no, I sold that one a long time ago. Oh, you already sold the property. Congratulations. But did you steal an area? No, no, no. I live up Pinewood. Oh, Pinewood? Okay. Okay. Do you have an agent that you would work with if you did buy or sell in the future? Terrin Hebert. Terrin Hebert. Okay. You're in great hands. You're in great hands. Well, I appreciate you taking my call today. Okay? Yes, sir. Thank you. All right. Thank you very much. One down. Kaboom, dude. Kaboom. Did you say that was an LLC? Yeah, it was an LLC. I think that's who was the purchased it. What was Richard Pryor's famous tagline? You want me to say it on here? Yeah. Hello. Hello, Christina. Hello. Yeah, so I was looking for the owner of 1168 Briar Metal Drive in Beaumont. Oh, it used to be here, but not even more. We don't know that no longer. Oh, okay. Okay. I'll go. Oh, okay. Okay. So you sold that property already? Yes. Okay. Excellent. Excellent. Congratulations. Do you still live in the area? No. Oh, okay. Okay. Okay. Is there anything I can do for you today? No, thank you. All right. And again, my name is Jason Pryor with EXP Realty. And if you have any questions, feel free to give me a call. Okay? Sure will. Thanks. All right. Thank you. Dude, you have this. You have this. I don't know, man. You got something going on, bro. You got something going on, man. This is you got to like a superpower or something, man. I don't know. Like you got you got people like I heard both of those people heard in their voice. They were like, they're like, yeah. Like they have this little question mark on everything they're saying like, huh?  Like what happens most of the time? Yes, I see. It's just like they're right in the middle. They're just like, okay. They like, they don't know what to do. Like you got them froze. They're statues. I'm surprised I'm getting many pickups at this time of day. Hello. Hello. How are you doing today? Good. And you? I am awesome. I am awesome. Better to good and better than most. This is Jason Pryor with EXP Realty. I'll just give you a call because that a house did sold around the corner from the property at 1181 Broward Metal Drive. And I'll just reach out to you, see if there's anything I can do to help you. Not right now. We're planning on leasing it. Oh, really? Really? Just wanted to let you know, I am one of your neighbors as well. And I'll just reach it out to you. Is that right there at 1181, right? Yes, sir. 1181. Oh, you have it on the market right now? With A-Rite management to lease out. Oh, okay. Okay. You currently have it on the contract. Okay. Well, what I could do is I'm going to reach out to them and see if I can get you a renter up in there and help you out. Okay. Yeah. Like 20 years. Okay. That's great. Y'all got a great relationship and I know she's going to have you in great hands. But you know, there are some, you know, I can't assist you in that process as well if I can bring you a renter over there. I'm going to just reach out to her and just see what I can do to help y'all. Okay. I'd rather with her. I'm a buyer's agent as well I'll bring tenants to the properties as well. That's what I was saying. Yeah. No, we'll take a look for us. But thank you. All right. Thank you. Have a great day. Bye-bye. Bye-bye. I'd rather have her do it. I'm like, wow. Well, no, no, I would have had a break that down for her brand. I would have been like, listen to me. Okay. Let me tell you how this works. Okay. She is going to handle it for you. But I can actually represent the renter and her still represent you. And I can bring the renter there to help you get it rented. And Shirley still represent you, right? Hey, listen, I'm not trying to do anything. I would have had to really break that down, man. Yeah. I was going to break it down here more, but for the time being, I didn't want to press. No, dude, for the time being, you should have broke it down. That had been great content. Yes. I don't pay.  I'm actually trying to help both of you. Call her back, dude. Call her back. Explain this to her, bro. What she needs to understand. Hello. Please leave a message after the talk. Well, we tried. We tried. Yeah, we tried. Well, still can help her. At the end of the day, I can reach. I'm still going with agent. Exactly. Exactly. I'm going to bring her a tenant. Hello. How are you doing? Who is this? This is Jason Pryor with EXP Realty. How are you doing today? I don't guess I know you. I'm one of your neighbors. I was just reaching out to you, just enjoying the weather today. And I was just reaching out because that house did just sold around a corner from you. And I'll just reach you out to see if there's anything I can do for you today. No. And don't call me again. Oh, okay. No problem at all, ma'am. I'll put you on my personal. Do not call. Okay. Right there when she was like, oh, do I know you and all this?  And then you said, I'm enjoying the day, but look, a house around the corner, so I'll just call to see if there's something I could do for you. Right? At that point, bro, she is not identifying you as a real estate agent. Okay.  She thinks you're some wacko in her neighborhood stalking her and wondering if you can do anything for her. Right? She didn't know what you're talking about. So right there, it would have been like, I'm your neighbor and I'm also a local real estate agent. You know, like she did not identify you as an agent. That's why the whole thing was weird at the end.  Hello. Hello, Mr. Powell. I do, please. Um, great. I'm great. This is Jason Pryor with EXP Realty. How are you doing? Okay. What can I do for you, Jason? Oh, well, I'll just want to reach out to you to see if I can assist you today. I'm a real estate agent, and I was just seeing what I can do to help you. Because I did have a house sold around a corner from you, and I was just reaching out to see if there's anything I can do for you today. About what? About real estate. No, I'm good, Jason. Thank you. Oh, okay. No, I got you. Is there an agent that you will work with if you did? Doing a thing in the future? Right there. Okay. Here's two things. And like this, this video literally is like your homework. Go back and watch this video and listen to all this. Look at all the comments. Take it all in, man, this whole situation so that you can really try to get something out of this. But like, here's another one. When he said like what, you know, and you said real estate, right? It's like, come back and say, I don't know, like maybe buying or selling a piece of property. Yeah. Because real estate can mean so many different things, you know, so many different things. Hello, Mr. James. Oh, you had the wrong number. Oh, I had the wrong number? Okay. Do you live in the Southeast Texas? Yes, sir. Awesome, awesome. My name is Jason Pryor and I'm with EXP Realty. You know, you need a good realtor, my man? Oh, no, I mean, no, not right now. Not right now? You'd be looking in the future, won't you?  Hey, you know that time in college can count towards the house. You know that in the future, right? Yeah. Awesome, awesome. But what are you going to school for, if I may ask? Well, in the Supreme Court. Oh, that's awesome, man. What are you looking to do after that? I'll play football, so I'm going to play football right now. Oh, and the plan? Okay, okay. Then I'll see them prices coming back over down at all. So that might be a good thing right now. Okay, awesome, awesome, awesome. Is there, would it be okay if we could stay in touch? Yes, sir. Okay, great, great. Is this your cell phone number right here? Oh, okay. And will it be a good email address to send your information to? You know, if you have any questions, feel free to give me a call anytime, okay? No, no problem, you have a good day. Dude, listen, it's all practice, practice. Remember that, Alan Iverson? Yes, practice. Practice, this is practice. So, man, like everything, everything is practice. So like, you took that situation and you turned it into like, okay, this guy's in college, like whatever, most people would have been like, all right, see you later. You actually was like, what do you study in this and that and connected and came through with the data? Who knows? That guy could turn into some serious client for you down the road.  No, I just, I just like how like, most people wouldn't even have looked at that as an opportunity, but you went for it. That's what I like. That tells me you're not going to leave any stone unturned. No, no. No stone unturned, man. I would never do that. That's just leaving money on the table at the end of the day.