Okay, so welcome back. Just a quick thought from Hosea chapter 10 and verse 12, okay. Hosea 10 verse 12, let me read it. It says, So for yourself righteousness reap in mercy, break up your fallow ground for it is time to seek the Lord till he comes and reigns righteousness on you. And if you see a lot of reference to agriculture, plowing, reaping, etc. In the verses following that also, I just want to turn our attention to that particular phrase, break up your fallow ground. So fallow ground is ground that is uncultivated, fallow ground is a ground which has a lot of potential, but it's lying uncultivated. It's not been touched for whatever purpose. It's got potential, but it's not cultivated. So that kind of a thing. So here comes the instruction, break up your fallow ground, break up meaning, fill it, prepare the land so that it can be used. So we see that it says, So for yourself righteousness reap in mercy and so on. So the question is, what is our fallow ground? Maybe there are certain aspects of our life where we have, maybe it's an area of gifting, maybe it's an area of ability, maybe it's an undiscovered place, undiscovered potential. But you know that, hey, that's not been used. It's lying waste. And the large instruction is break up that fallow ground, prepare it, it is hardened. No seed can actually fall and take root. It needs to be prepared. So whatever that we need to do in order to prepare that aspect of our life, in context of whatever we are doing with learning about life skills, what aspect of these things do we need to kind of prepare ourselves for so that there can be the sowing of the Lord, there can be a reaping and so on. So as we pray, let's ask the Lord, Lord, what is my fallow ground? What is it that's lying unused and neglected and it has potential? People have said, God, you have said, but it's still lying unused, it's still lying. So yeah, let's ask the Lord, right? Okay, let's pray. Father, we come before you Lord and we have this question, Lord, that you would show what is our fallow ground? Something that's so much potential below the surface, but it needs to be prepared. There needs to be some work on it. And Lord, we pray that you would show us what it is, what it is that we need to do, God, in order to prepare that, in order to break up that fallow ground. And I just pray, Lord, that you would, Lord, enable us, Lord, by your word and by the work of your spirit, that our hearts will be prepared, Lord, that this aspect or area of our lives will be prepared, Lord, to receive the word of God, to receive the reign of the Holy Spirit. And we do not want it to be fallow or God. We want to, Lord, receive your seed, the seed of your word to really bear fruit, 30, 60 and 100 fold or God. Yes, Master, we come at ourselves into your mighty hands. We pray that you'll continue to, Lord, lead us into this truth and so that everything that is hardened, everything that is lying unused, Lord, will be turned, prepared for your touch and for your glory. In Jesus' matchless name, we pray. Amen. Okay, so we are continuing with the life skills. Yeah, hello to those who joined us during the prayer. Okay, I'm just going to share the notes now. And yeah, okay. Okay, so today we're going to look at money management. So we might say, okay, I wish I had more of it so I could manage it. But the thing is to manage it even when it's in short supply. Or maybe it's not as much money as we would wish and as we would want. But to be able to have a strategy for managing money, to be able to have some information on what I can do with it. So money is, again, money is not evil. Money is not something that is, you know, that's a curse. In order to have money is not something that you need to feel guilty about. We need money to function, to work in this world. And the Bible has a lot to talk about finances. We know that. We've learned in that other course, financial stewardship. So we know what God's heart is towards money and we should have the same thing as well. So in this chapter, we're going to look at a few practical aspects of managing money. Some things that we can put in place. Maybe you're already doing it. It'll be a reiteration of that. So the first thing is budgeting. So budgeting, simply put, it is how we plan, it is a plan where we say, okay, this is how I'm going to spend my money. Okay, even if it's, let's say, 500 rupees or whatever, you know, you're deciding, okay, this is how I'm going to spend it. So it's a plan. So we plan ahead and say, these are, this is my income. These are my expenses. And therefore, here's the plan. This is how I'm going to spend it. Okay. So what is our income? Okay. Income to a person whose salary would be the monthly salary. Income to a businessman would be, you know, whatever he or she comes or gets through the business and it can be a regular flow coming in, you know, maybe daily as in when payments come in from clients to the services rendered or products sold. And it could be that income in terms of people who are in ministry could be tides and offerings coming in and where you decide, okay, this is my salary. Okay. This is coming into the church, the church account and then the board decides or you decide that this is, this amount is going to be my salary to take care of my expenses. Right. So that's the income. Now, maybe you're not a working person.  And it could be your income would be what is being given to you through parents or guardians or whoever's sponsoring your studies. So income is what you receive. Right. So that is the income that we get. So it could be, there could be a duration of frequency through which we get our income. Right. It could be weekly. It could be, you know, okay, one lump sum which we get for managing our expenses for the next six months. Right. Like if you're a student, maybe, you know, the parents or guardians say, okay, this you take care of this for the next semester. This is amount. It could be that or it could be coming at various frequency. So it's important to know the frequency with which you get. And so you can decide how you're going to plan for it. Right. Okay. So when we are planning, it is good to be meticulous. So just want to say that the plan can be time consuming. Right. It will involve certain thinking through and maybe we have, you know, some of us enjoy that. Most of us don't. Right. Spending that time. But once we do it, it will be, it can be a template. It can be something that we can follow through. It doesn't have to change drastically every time. Right. So, okay. So we need to work now having worked on the income. The next thing is to work on or list down what is our essential expenditure and essentially sorry, essential expenditure on certain things that have a fixed price on it. Okay. So essential expenditure for for us. What are some things? Could be our accommodation, right, or rent. These are essential. These don't fluctuate. The price doesn't fluctuate. It's a fixed thing. Right. Whether you're staying in it or not, if you're actually, you know, planned out your accommodation, you need there's so much amount that goes out every month as rental or maybe as a lease. You know, and if it is, if you're repaying loan or EMI or mortgage, whatever, you know, so all this, it could be there. Then there are some bills like electricity, water, the bill for your internet, your phone, you know, all these are bills. And these also most cases, these are fixed. Right. So these are fixed. Along with that expenditures also could be something like insurance, like insurance for the vehicle. Maybe there's a life insurance that policy that you've taken. So these are fixed price. What we would call as a fixed overhead, right, rentals and payments and so on. Right. So these are something. So it's good to list these out and say, okay, these are my fixed overheads. These are my expenses. The next one is to list down what are factor in what are non fixed. Right. What could be actually varying month on month. Maybe it could be, you know, on a certain month there's a food expenses go up because the food cost is more or you're eating out more. Right. The food cost goes up and then maybe travel. Sometimes maybe you have to travel more and therefore that goes up. That's a variable again. Right. So things like that. So the best thing to do whenever we are listing down these expenses is to take and, you know, take the history. Okay. So we're not actually saying projecting, okay, this is how it will be. But you look at the history. You look at the last six months, the last one year. And you look at, okay, what has been my expenses? So that will actually give a clear picture. We can even arrive at an average. And so it's good to look at the history. So there's no guesswork. Right. Because this is what you've actually spent on. And the thing is, this is what you will in the future also if you're continuing in the same place, same lifestyle. So it's more or less, it's going to be the same. There could be variations, but most likely it's going to remain the same. Right. So it's good to look at the history. So whenever we look at budgets, we look at the past and then we factor in what could be some changes. What could be certain things that we are new things, new ventures that we could be going into and because of which we factor in those costs also. Okay. So it's good to look at the past. So the thing is, okay, I've not really kept track. You know, I just spent, as money came, I spent, I lived for the day, sufficient under the days, the trouble thereof, you know, and all those verses I miscoated. And so I don't know. Okay. So no problem. In that case, we need to actually look at what, you know, take a month, maybe the just the previous month, what is it? Just look back and see what is it that I spent. Okay. Maybe it will, it more or less, it could be fresh in our memory. We might miss out on a few things, but that will help us. Okay. So, so make that list that down as the expenses. The other thing to do, next thing to do is to, so actually delete our expenditure from the income. Okay. So this is the income that I'm getting. This is the expenditure. So I subtract the expenditure from the income and hopefully it is, there's some amount, you know, left behind. If not, also it's okay, right? Because it's not, you're not going to remain in the same place. You're not going to be remaining in the same place of income. Okay. So as long as you are faithful, as long as you are, you know, working faithfully, the Lord will bring increase. Okay. The Lord will bring increase, you know, so, so not to worry about that. Right. So subtract that from the income. So you get what is called as a, you know, as a discretionary amount, miscellaneous. Right. So this can go into savings. This can be set aside for maybe emergencies or, you know, unplanned expenses. We can use for that. Right. So this is a very simple, simple formula or simple template that we can use. Okay. So that miscellaneous, you can decide, okay, am I going to save it? If so, how? Okay. How can I save it?  And where the return is more or if my, you know, discretionary in amount is more. Right. My salary levels are high. Well, where can I invest in? Right. Do I invest in land? Do I invest in maybe some shares? All these are possible. Right. So I just wanted to, you know, just remind us that we are being good stewards of it so that our needs are taken care of, your personal needs are taken care of, so that you can take care of others' needs also. And you can use it for Kingdom purposes as the Lord will lead, you know, for each person, the Lord has, you know, lead in a certain way personally and so you can use for that. So no need, there's no need to feel guilty when you think of saving. Right. So many people think, you know, maybe I should not be thinking about it. So it's a, it's a worldly thing to think about, you know, saving and all that. But the Lord, you know, we see in problems, go to the ants, go to the ants and learn what are they doing? They're working hard. But they're also saving for the winter months when they will no longer be able to go and find food like how it is in summer. So which means that there's a change in environment, there's a change in situation, there's a change in season. And so you're preparing beforehand for that season. So there's nothing wrong in preparing. So it's scriptural. Right. So when we read through problems, there's so much wisdom on how the simple, you know, how the simple just pass on and then they bear the consequences of it. But the prudent, weigh the matter, weigh their decisions. Right. So we can use wisdom. We can, you know, see what is, what is ethical? Right. What is gambling or anything, but what is ethical in order to save? What is ethical in order to multiply what the Lord has put in our money? What does the Lord has put in our hands? Right. Okay. Most important thing, let's learn to live with what we have. In that particular season. Okay. In that particular season, how can I use this, this X amount of money that I have? How can my lifestyle, you know, adapt to this? Or, you know, I don't want to, I want my expenditure to be extravagant when there is no income coming in. There's no money coming in. Right. So if that is the case, what would happen is that I will, I will most likely end up borrowing, taking a loan, right, to take care of the essential expenditure. And that's not a situation we want to be in. Right. Because at the same time we know that whatever we borrow, it has to be paid back. It has to be paid back with interest. And if it is like loan that is taken like a cash loan from money lenders, it is with very high interest. Right. So it has its consequences. Yes, there are certain cases where we take a loan, where we borrow, maybe for certain big expenditures, like maybe you're buying a house, or maybe there's a vehicle that needs to be bought, or things like that or land or whatever, where you make a plan and say, okay, monthly so much is required to pay back. Can I afford it? Can the essential expenditures, the fixed and the variable, can that be taken care of? Right. Very important. Because if that cannot be managed, then it's going to be a spiral, a never ending spiral of chasing money in order to pay the creditor. Right. So that's not a situation we need to be in. We don't have to put ourselves in that place. So the simple rule of thumb is, okay, this is how much I'm getting. What changes can I make? Now, we need to understand that it's not going to be forever. It could be for a season. It could be for a time, but you understand that with that in mind, I know that season is going to change. I know that the income levels will change. But with this what I'm getting, can I live my life? Can I change, suitably change my lifestyle so that I can live within the means, so that I don't have to go borrow by the end of the month for what are essential. Right. Okay. Now, there will always be inducements. There will always be a sale. There will always be an easy payback method. But don't be swayed by it unless it's a necessity. Especially when you go online, Amazon has a sale. There's an independent sale, whatever. There's always a sale. There's always some, just think about it. Do I need this gadget? Do I need this phone? What's wrong with the one that I have? Right. Does it serve the purpose? And so, you know, do that. Right. Any questions? No questions. Anything from the online students? Any questions at all? Because we're not going into the details, the specifics, like we did in financial management. But you know the, you know, the broad premise or the foundation based on which, you know, we say, we share this, right? When it comes to money. Okay. Yeah.  It'll be a good idea to do that. Right. To learn more, to see what are the avenues that are possible because many times we are, we are ignorant of the avenues for even saving, for even making our money work. Right. So these are some things that we can learn when we attend the workshop, when we do a course online. So we open to do that. And yeah, so don't think of it as worldly. It is not, right? As long as our intentions are clear, right? As long as our, you know, our, we are not putting our trust in uncertain riches, right? But we are trusting in the living God who gives us all richly all things to enjoy. Right. We see that in Timothy. So that's the guiding principle. Right. Okay. Okay. So let's look at another aspect which is management of people. Okay. So people management is also a skill. Okay. As managing time, managing money. So also when it comes to dealing or interacting with people, managing people, right? That is also a skill to be learned. So we see that money, time and people are resources, right? So if we use people, like we use things, well, they are resources, they are precious. But when it comes to, you know, ministry, when it comes to the workplace, we need to have the skill in order to work alongside and also to lead. Right. A lot of it we saw in Christian leadership. This will be some of those key things that we learned there we can look at. So we see that none of us are an island. We need to interact with people, especially when it comes to ministry, people are whom we are reaching out. Right. And when we reach out, we don't do that solo.  Right. There are others whom God sends alongside who's talking to our lives, whose lives we speak into and we work together as a team. We see that the Lord Jesus, when he sent out people, he sent them out two by two. Right. And we see the teams becoming even more complex as we go through the episodes. We see Paul's team, Paul and Silas.  Sorry, Paul and Barnabas. But then we see that there's John Mark who comes in, there's Timothy who's there. And then when we read Romans, the last chapter, we see the whole lot of people whom Paul was connected with, whom Paul was interacting with. And so, you know, so we see that, yes, people, there's no running away from people. Right. And we need to be able to work alongside and work, lead people as well. Right. So when we, when we study teams, we saw that when it comes to people, when we have more people, there are more resources. Right. When we consider people as resources, yes. Because each person brings fresh ideas, fresh set of skills. Okay. Now I might be strong in certain areas. I might not be able to do everything. Okay. But here comes someone who's strong in certain areas where I may not have that necessary expertise nor the skill. Right. What happens is there's synergy. Right. So their skill along with my calling, gifting abilities put together, there's major impact. There's great impact. The things that, you know, that was a challenge, it was a struggle to get things done now becomes a little more easier. It's more streamlined because of certain people in the team. Right. So, so there's always, you know, there's always benefits. It's always fruitful when we work together as a team. So there's, there's beauty and there's impact, high impact when it comes to ministering in teams. Right. At the same time, if not done well, right, it can actually pull down and end up in a big mess because there are people involved. Right. So that is something that we need to keep in mind. So in order to have high impact, it's good to work with teams and that we see as a blueprint in scripture as well. So maybe there's certain skills we have naturally, but what are those skills that we need to have? Okay. The first thing is, let's just list down a few things like organizing, organizing people, delegating to people. Right. Motivating people, motivating the team, then evaluating or assessing the effectiveness, the impact, everything. Okay. So first one is organizing. Okay. So how do we organize people around the common goal? I think we've learned it earlier, but also to have a clear vision. Okay. To have a clear vision, to make sure that okay, let me just put it on the chat to have that vision that is clear. Okay. To make sure that the vision is clear, the vision is communicated, the vision is reiterated and everyone is moving towards the same vision. Okay. So everybody knows, okay, this is what we are going after. Right. This is what we are going after. This is what we are called to achieve. So when the vision is clear, when the direction is clear, when the tasks that we need to do are clear, then everybody is able to focus, everybody is able to put their energy and effort after that particular task. Okay. If there is no clarity, then there is no, then the task, there's no effort or enough effort is not put in because you're not sure. Do I do this or do I do that? You run two minds. Is it good? Am I supposed to do it? There's no clarity. Right. But if there is clarity, when you know for sure, you're doing the right thing. This is the right thing. I need to put in effort. I need to put in energy into this. It's okay to do this. Then you will go all out and put wholehearted effort. Okay. So imagine having a team that's really working hard and putting in wholehearted effort towards the same thing. Right. That results in movement towards the whatever destination you have, whatever thing you need to achieve. Right. So organizing. So organizing, one is the vision. The second thing is how do we get these people? Right. How do we get the people? So several ways. If there are people already in the system or in the environment that you are, environment, we can say ministry. We can say it's a workplace. Right. We can say it's maybe a church. Right. If the people are already there, so the thing is to envision them. Right.  In other words, we're saying they are buying in. Saying, yeah, I want to. God told me the same thing. This is what we are going after. And I'm in. I'm signing up for it. I'm in. Just like the mighty men of David. They said, are you here? David asked them, are you here? Are you for me? They said, yes, we will do this for you. So when there is buy in. When there is loyalty, when there is commitment, then everything starts moving. That's the first. That I would say will be the second step. So vision is clear. There is commitment to move in. What happens if people are not there, then there has to be a method or process to get, to invite, right? Invite people towards the cost. Invite people towards the mission, whatever it is, towards the assignment, right? So, in practical terms, it would be, if it's a job, it would be a job interview. And you call for an interview and say, this is what we are. This is who we are. This is our vision. And so, are you interested? If you have these skills, if you have these abilities, then we'd like you to sign up. Why don't you sign up? Why don't you, you know, we can do this together. So, it's a invitation for an interview where we talk, find out, maybe test the abilities. The interview is also a right thing, right time to, you know, see what the motivations are, right? Because people could sign up for the interview for various things. You know, it's okay. You know, I don't really agree with it, but I need something. I need to do something with my time. I need some money. I don't really agree with it, but let me just sign up anyway, right? So, interview with the opportunity to check the motivation, to find out if it's real, to find out what the, what the heart's passions are, find out what the call is, to find out what whatever is there on the resume, whether it's true, whether it's, so an interview, you know, whether you're doing it on the phone, whether you're doing it online or in person, it helps to really reaffirm or reassure yourself that this is, these things are true, these things are, this is the right person for the job and so on, right? So, organize, right? Get people in, envision them, them committed. There is also an aspect of equipping, okay? So, people come with basic skills and abilities. Okay, I'll probably add this to the notes and put it up later. So, I think I'll do that. Yeah. So, there's also this aspect of equipping. So, people come in with basic skill sets, basic abilities and maybe the job that is required, job that is required to be done needs an upgrade in skills. But the skills which they have at the moment is maybe enough for them to learn, right? And you have the, you have the privilege of giving some time so that they can learn, they can be skilled, they can be trained in order to take that out. So, that is also another aspect of organizing people around tasks around a common goal, right? So, you're training them, equipping them and as part of the equipping, you're also giving them the equipment that is required. What are the tools that are required to get the job done? Okay, so that's another aspect of organizing. So, here are some people, maybe they are in the Department of Finance, do they have the skills? Do they need an upgrade in skills with these basic skills with regard to technology, with regard to whatever software package that they will be using for accounting and also, do they have the necessary equipment? Do they know, do they need a laptop? Do they need a whatever accounting software package to be installed in that? Do they have the know-how to operate it?  Do I have the stove? Do I have the microwave? Do I have the things like that? Do I have the enough dishes? Do I have enough spoons? Do I have the ingredients? So, think in those terms, how can I get these people organized? Because we want them, the expectation is wanting them to do a good job, but unless we organize people around the task, around the common goal and give them the necessary things required to finish the task and do it well, it's going to result in frustration. You are frustrated, they are frustrated and it's not a good start, so organizing people. So, think through and say, what is it? What kind of people do I need to have? Where can I look for them? Do I look internally? Do I look outside? If it's outside, how do I invite them to be part of this mission? And then, what do I assist them on? Skills, abilities, qualities, characteristics, and then, do they have the same heart for the division and so on? And then, the equipping part. So, that is how we organize and organize around tasks. So, organize around, let's say, departments or certain core areas. So, it could be, like we said, finances, it could be maybe outreach, it could be media, it could be maybe creative work, like design. So, organize people around that. There could be some who are multi-skilled. And maybe for a season of time, they can actually take care of multiple things. But when the workload grows, you cannot expect the same kind of efficiency or the same kind of results. Why? Because the workload is more, the time taken is more, and they need to deliver within that same time. The quality differs. So, that is the thing. If people are multi-skilled, then for a season, they can take care of multiple things. But as, be mindful, as things grow, then maybe we need to add another person to that particular thing so that it's done well. So, organizing people. The second one is delegation. Delegating of tasks. So, these are things that you have on your plate. You have on your list. Now, how do you delegate it? How do you give it and ask the person to do it? So, any thoughts? How to delegate or how not to delegate? Paul delegated. We're doing a book study on Thessalonians in church. So, we see that Paul delegates some responsibility to Timothy. He asks them to go to Thessalonica, find out how they're doing, come back with information. He delegates while he himself goes to Athens. So, when we look at delegating, we look at capability of the person. Is that person the right job, right person for this, for this task? Because what are you, when you delegate, you're handing over. You're handing over a particular task, a particular responsibility and you're saying, do this. So, I want this to be done. So, the first thing is, do they have the, do they have the ability? Do they have the ability to do it? For example, like when Paul writes to Timothy about certain responsibilities. So, he says, you know, these are something that you need to look for, right? He says, talking about characteristics. He talks about ability, right? Like, testimony chapter three, a lot of characteristics there, character, a lot of emphasis on character and even about deacons, a lot of emphasis on character and also about ability. So, considering all that, considering the task at hand, is the person, the right person for this job? Very important question. Because if you're delegating to the wrong person and if it's a very critical job, critical task, then they're going to be consequences, right? Paul also talks about how he says, first Timothy three and verse six, he says, not a novice, less being puffed up with pride, he fall into the same condemnation as the devil. Okay. So, this is a spiritual delegation or spiritual leader whom they are appointing. So, he says, among all the things he said, not a novice means, not someone who is new to the faith, maybe, who's got very less experience, right? For this particular task.  It cannot be a novice. Now, yes, novices can be given certain tasks with the training and everything, but it could not, it cannot be this task, right? Which requires certain capabilities. So, which means that we assess and see is the person, yes, is the task, yes, is the person and then say, is the right person for the task and he asks them to do it. Okay. We can also start by giving delegating tasks that are not too mission critical. Okay. So, what do we mean by that? Which means that if they fail, it's going to have disastrous consequences, right? It's going to have big impact, the failure of that. So, when you're delegating, maybe for the first time, to someone, for that person, it's the first time that they're handling these things, always delegate certain things which are not so critical, find out the strength, find out how they do it, right? So, there may be the critical things, the things which are of most importance, which have a lot of, you know, if things don't go well, it's going to have a bad consequence, you can handle it yourself. Okay. But maybe certain things to find out the strength, find out the ability with which they do it and then we can entrust them with more. Okay. So, the temptation is to do that task yourself. Okay.  We need to monitor. We need to see how they are doing, give some kind of a course correction, which means it's double the work now. Now, you're doing it, you're doing some other tasks, you've handed over this task, but then you need to monitor, initially at least, monitor to see how they're doing it. Do they need some more input, some direction, some correction, right? And then monitor that as well. So, it's going to take a lot out of us initially when we delegate. So, that's why many people say, okay, I don't want to delegate, I'll just do it myself, forget it. I'll just do it myself, you know, and then we end up not delegating, we end up carrying a lot of things ourselves and not giving it to others. So, other people can grow, other people can definitely make use of opportunities, they can grow, they can thrive, they can be an asset, they can be a great help, a great encouragement, a great support if we delegate it well. So, we delegate, we also assess or evaluate and monitor and see how well are they doing. Example, you know, when we have, like let's say, a worship team or somebody's preaching, we always give feedback and say, okay, here are some good things, you did well, okay, you came on time, you prepared, and you did these things, here are some things that can be done better, okay? Next time, just make sure you also cover these things, you know, this could be done better. And hey, these areas, maybe you didn't even think about it, but these are pretty important areas, you need to get that right. You know, these were wrong, this didn't come at the right time, so we need to do it, right? So, some feedback like that will always help. So, how am I able to give feedback only when I monitor? Only when I see, okay, how is that person doing it, what is them? So, we're not micromanaging and say, okay, every step, you know, but we delegate, we do monitor, okay? So, then it becomes, so that person, when what happens is when the person is sincere, they don't have any problem with the ability, they don't have every problem with the aptitude, okay? They're most likely to succeed, okay? When we give valuable feedback after delegating, they are more likely to succeed and they will do well, they will be a source of strength, okay? Third thing, motivating, okay? Motivating people towards the common ground. So, people being people, people not being machines have limited energy, also susceptible to certain distractions and also have life challenges, right? We need to understand that. They have ups and downs, right? They are people with emotions, they have ups and downs, they have families, they face challenges and all that happens. So, which means that when we are working towards a particular thing, if people are not really contributing, there's a reason, okay? The reason could be they don't know how to do it. The reason could be they don't want to do it. Now, that's a matter of attitude, okay? It's not a matter of learning. I don't want to do it. The other things could be I'm unable to do it even though I have the skill, I have the ability, right now I'm not able to do it because some things are challenging me. Emotionally, I'm being challenged. I'm being discouraged. So, many times we see Paul writing to the church to encourage, Peter writing to encourage, right? For example, I think it was Peter who says, you know, don't consider it strange that you're going through these fiery trials, right? Is that Peter? Or is it James? Yeah, so, yeah. So, Peter says, yeah, sorry. Yeah, so, so he says, yeah, don't think it's strange. No, this is actually about verse five, is it? No, verse four. Yeah. So, he says another place where he says that 412 first. Okay. Yeah, don't think it's strange concerning the fiery trial, which is to try you as though some strange thing happened to you but rejoice to the extent that you partake of Christ's sufferings and so on. So, he's really, thank you for that. So, he's really encouraging. He's, you know, so he does that. So, there is that place of motivation, motivating, encouraging, inspiring, right? Just put all that together in order to go after the thing. So, people get tired, people get distracted, people get, you know, challenged and they want to give up because of various things happening in their lives. So, be aware of that. Okay. So, as a leader or as a person who needs to improve on people's skills, who needs to build people's skills, this is another one thing to take care of. So, things won't be automatic just because we have taken a highly skilled person, highly motivated person maybe, person with great attitude. We cannot take it for granted that they will always be firing, I mean, you know, doing really well and just going full speed. No, because they are people, right? So, there is that place where we need to find out why things are not happening and then motivate them, encourage them, right? And you will be very surprised when they know that, hey, the person whom I am working with understands, so he is on my side and he is willing to, you know, go with me on this, willing to understand why I am doing this, then they will actually do even better, right? A couple of other things, evaluation, okay, we looked at that. The last thing is the letting go part, you know, there are times when people have to be let go, many reasons, why? Because maybe the scope of their call has increased, God wants them to go beyond the boundaries of what they are operating on right now. Maybe it's not just the local church, but God has it for them to go beyond the local church, go to the nations, maybe it's a night netting thing. God was equipping them, now he is launching them into that, so be aware of that, right? Sometimes we let go because despite repeated corrections, despite being patient, they are not able to or they don't want to, okay? So, they are not able to, we provide opportunities to learn, opportunities to increase the skills, etc. Then they come to a place where they don't want to, I don't want to contribute, I don't want to do that, then there needs to come to a place of, you know, you being faithful to the task, faithful to the organization, the right thing to do then it's to let go. Okay, so we look at a little bit of that in the next class and also look at the next one, which is conflict resolution. So, I think you just kind of flow into that. Okay, so we'll stop here for today. God bless, bye-bye. Thank you very much. All right, God bless, bye-bye.


Application of derivatives right so much awaited chapter for us so we'll start with application of derivatives. Application of derivatives. Okay. In this particular concept you are going to see various applications of derivatives so whatever concept of differentiation you have learned. Mostly those same concepts will now be coming in an application format. So what are the applications that we are going to study. Let me give a coverage of the chapter.  So, the first, let me write coverage. The first chapter that we are going to study under application of derivatives is d y by dx as rate measure, d y by dx as a rate measure. Okay. This chapter was actually skipped in last year's syllabus of CVSE. Maybe I'm not very sure whether your teacher has covered this concept with you in the in the school or she has kept it as well. But we are not going to skip it. They have done it or they have skipped it. Okay, great. Because I think last year they skipped it because they give a reason that it was already covered in physics. So there was no need to cover it again in mathematics. Okay. Next concept that we are going to talk about is errors in approximations errors. Approximations. And we also include differentials and differentials. Differentials. What are differentials? dx. dx is a differential of x. Okay. So how errors approximations and differentials could be, you know, figured out by the application of derivatives is what we are going to learn under this particular sub topic. Third sub topic that we are going to talk about is tangents and normals. Tangents and normals. Okay. Basically this comes from your geometrical interpretation of d y by dx. So that is what we are going to cover under tangents and normals. The next concept that we are going to talk about is mean value theorems. Mean value theorems. Mean value theorems would have a several sub concepts under it. So we are going to talk about three types of mean value theorems. The first one being called the roles theorem. The second one is your lang ranges mean value theorem. Lang ranges mean value theorem. Okay. And the third one is less than one to most of the students who she mean value theorem. Who she mean value theorem. Okay, it is pronounced as cushy, not couchy. Okay, so we are going to talk about RT, LMVT and CMVT under mean value theorems. Oh, did I. Okay. Okay, so we will cover up the concept of these three mean value theorems under the fourth sub chapter. The fifth sub chapter that we are going to talk about is your concept of monotonicity. So monotonicity is a part of calculus where we learned about the increasing and decreasing nature of functions. Okay, so how does calculus help us to know in which interval a function is increasing which interval the function is decreasing. So we'll be covering that concept and then monotonicity. And the last but not the least, we are going to talk about the concept of maxima and minima, maxima and minima. Okay, along with the application maxima minima minima minima minima minima. Okay, and it's practical application. Okay, and it's application. So we'll be trying to solve some questions based on optimization using maxima and minima and also be also giving you some extra applications like trying to know the nature of the roots of cubic equation. And also how calculus helps us in sketching the graphs. Okay, so a lot of concepts related to sketching are also dependent upon calculus or differentials or you can say derivatives so we'll talk about that as well in the application part. So overall this chapter has got six subchapters under it. Normally I take four classes to finish it. So you can expect at least 14 hours, 14 hours, 15 hours of lecture to happen on this entire chapter. Okay, so let's get started with our very first chapter, dy by dx as rate measure now theory wise, there is nothing special in this chapter. So based on your basic understanding of what is the process of differentiation, right, some is based on chain rules, some of them is based on first principles, some of them is based on geometrical interpretations, like some of them is based on continuity and differentiability, some of them is based on the nature of the slope at different points of the function, some is based on stationary points. So all these concepts that you are basically studying theory part is not very much in it. Of course, some of these concepts are very heavy in theory like fourth concept, mean value theorems, it is slightly theory heavy. But rest all the concepts are like, you know, you already know it, we just have to learn it as an application. So let's get started. Without much waste of time, we have four classes to cover up this. So today I'll start with dy by dx as rate measure as rate measure as rate measure. Now what are the meaning of rate of change. What are the meaning of rate of change, I would like to know from you people you have done it in school, what are the many of rate of change, change with respect to time, isn't it. Rate of change of displacement, ds by dt. Okay, that is your velocity rate of change of velocity, acceleration, rate of change of acceleration. What is it of change of acceleration. Check, right, all those kind of thing, not a nice word to use by the way. So dy by dx as a rate measure, basically what are we trying to learn is that when there is a function which relates to variables x and y with each other. So x and y are variables which are interconnected by this particular, you can say function or relation whatever you have it. Then how do you then how do you link dy by dt. What is it related to dx by dt. Okay, that means if there is a change happening with respect to time in x. How does it influence the change in y with respect to time or vice versa if there is a change in y happening with respect to time. How does it change the value of x with respect to time. So in order to find that you will say sir simple we already know this process, you just have to perform the derivative on both the sides with respect to time. Right, exactly. So when you differentiate both sides with respect to time. Remember, you are going to use chain rule here. So first you are going to differentiate f of x with respect to x and then into dx by dt. So guys and girls I would like to recall this particular thing this is just chain rule. Right, so this entire concept is based on chain rule that's it nothing new is basically learned here. Okay, so when you figure it out, you basically end up getting the rate of change of y. As f dash x times the rate of change of x. But mind you one very, very important thing I would like to tell you these all are instantaneous changes these all are instantaneous changes. These all are instantaneous changes means they are calculated at a given instant. Okay, so dy by dt f dash x dx by dt they all are calculated for a given instant. Okay, maybe some x value will be known to you. Okay, maybe some you know another parameter which is helping you to find out this instances is known to you. Let me give you an example to make this part clear what do I mean by instantaneous changes. See, all of you have celebrated birthdays, correct. And all of you have blown air into a balloon, right, everybody has done it. Have you experienced that when you're blowing air into the in the in the balloon, initially the radius becomes larger at a very, you know, less amount of time so the increase of the radius with respect to time is very high.  So you realize that the rate of change of the radius is not uniform throughout. Right, let's say when it was small it was DR by dt was fast, slightly bigger it became DR by dt became slightly lesser. More your radius became it became more less right so what happens is that your DR by dt itself is basically dependent upon what is the radius at that instant of time. Maybe the volume the rate at which you are putting blowing air inside the machine into the balloon that is fixed because of course our lung capacity is fixed right we cannot blow like machines right. So let's say we are blowing at a rate of 100 centimeter cube per second, but the radius initially will go very fast and later on it will just slow down. Okay, so that is what is meant by when we are trying to find out these rate of changes we are basically looking at at some instant of x or some instant of time. Okay, let us do problems based on that and then you will understand it in more detail. Let's take a question, very small question to begin with very simple one. Let's say I have this question. Yeah, let's let's take this question. Yeah, the question says if the radius of a circle is increasing at a uniform rate of two centimeters per second, find the rate of increase of area of the circle at the instant, read the word at the instant. So they're asking you for an instantaneous rate of change of the area when the radius is 20 centimeter. Now before you start solving this question, there are few steps that you should keep in mind. First, identify the two quantities which are changing. Okay, number one, number one, what is the step identify the two quantities which are changing or identify the quantities which are changing. Okay, so in this case, radius and area are changing. Second, write a relation between the two changing quantities. So you know in a circle, what is the relationship between area and the radius, everybody knows the formula of the area of a circle. Second is differentiate both sides with respect to time. Okay, third step differentiate both sides with respect to time. Once you have done this now start putting the instantaneous values provided to you in the question. Now why I'm making a step out of it because in past I have seen people. They normally put the values and then start differentiating it. Please do not do that. You will end up getting zero, not as marks, but as values. Okay, both in fact, so don't do that. So first, identify the quantities which are changing here identified area and radius are changing. Second, write down the relationship between them, which is a is equal to pi r squared differentiate both sides with respect to time. So this will be differentiated with respect to r because this is in terms of r into dr by dt. What rule we use here, chain rule. What rule we use here, chain rule, simple as that. Next, once you have done this, of course, write it down completely dA by dt as this is 2 pi r dr by dt. Now this is the time where you start putting the instantaneous values. So what are the instantaneous values? Now see radius is increasing at a uniform rate of 2 centimeter per second. So dr by dt is plus 2 centimeters per second. Now many people ask me, sir, why do you categorically write a plus there? Because if the radius is increasing, right, you have to write a plus radius is decreasing. That means dr is reducing with respect to time. That means you have to write a negative. So that positive negative sign is very important because if you don't put that, you will end up getting, you can say, you will not get an idea of whether the thing is increasing with respect to time or decreasing with respect to time. So it's very important to follow this sign convention. Something increasing with respect to time, it's a positive thing. Something decreasing with respect to time, it's a negative thing. So what I'm going to do, dA by dt, I don't know. 2 pi radius, I know instantaneously, 20 centimeter radius is there. Dr by dt, I know it is 2 centimeters per second. So overall, if you see, it becomes 80 pi centimeter square per second. Please ensure you are writing the units properly. R has a unit of centimeter. Dr by dt has a unit of centimeter per second. So overall, it becomes centimeter square per second. Now it is a positive quantity means your area is increasing at the rate of 80 pi centimeter square per second. Is this fine? Easy. Nothing difficult about it. Right. Now in this chapter, you will feel as if you are sitting in a physics class. Okay. So those who are very close to physics or physics is very close to their heart. They will really enjoy this sub topic of application of derivatives. So let us take more questions. Good to know that. Let's take another one. So read this question. The question says a man who is 6.1.6 meter tall walks away from a lamp, which is four meters above ground at a rate of 30 meters per minute. How fast is the man's shadow rendering? How fast is the man's shadow rendering? I want everybody to try this out and give me a response on the chat box. We have to use string. Yes. Whatever helps you to solve the question whether it is coming from trigonometry, coordinate geometry, or any part of mathematics. Let's use it to solve our purpose. Okay. Again, remember my steps. First identify the two things which are changing. Then write the relationship between the two things which are changing. Differentiate with respect to time throughout. And then put the instantaneous values. Simple as that. No brainer. This is no brainer actually. There is no need to think. Okay, Gayatri. Very good. Very good. Adwik Sinha. Good going guys. Aditya. Okay. Aditya has a different opinion than others. Okay, Pranav. Pranav, let's keep the unit as the same unit of time, minute. Okay. Guys, one more minute. This is not a difficult question. I'm sure in your school also you would have done a similar question. Okay. So I'm getting almost three to four types of answers. I don't know why. Okay, let's say this is a lamp. Okay. And there's a man who is walking away from the lamp. So let me make a man. Okay, let's say the man is this. Okay. Let me make head. Small arms. Small legs. Okay. This man is moving away from the lamp. Okay. Now lamp is four meters long. And this man is moving away at a rate of 30 meters per minute. And because of that, his shadow is rendering. Okay. So let me first cast the shadow of this man. So the shadow of this man on the ground will be this length. Okay. So let me make in blue color. So this is the shadow of the man. Correct. Now what are the two quantities which are changing? You'll say obviously said the distance of the man from the lamp. Okay. Let's call that as X. And of course the length of the shadow. So this is your distance of the man from the lamp. And this is your length of the shadow. Let me call it as Y. Okay. Now if the man is walking away from the lamp, you realize that DX by DT is given to you as how much? How much? Plus 30 meters per minute. Now Y plus, because when the man is walking away from the lamp, X is increasing with respect to time. Had the man been walking towards the lamp, I would have written minus 30 meters per minute. Get this point clear. Okay. Now second thing is I need to relate these two quantities X and Y with each other. So you'll say sir simple use your similarity. Right. Can we use similar triangles? Can I say triangle? Let me write it down. Lamp post man shadow. So can I say triangle MNS is similar to triangle LPS. Okay. So I can say LP upon MN.  Right.  Correct. Any questions, any concerns? Okay. So this is as good as saying 40 by 16 is equal to one plus X by Y. In other words, 24 by 16 is equal to X by Y. And if I just simplify this X by Y is equal to three upon two. That means Y is two-third of X. Correct. So I have now struck a relationship between the two quantities which are changing. Now, once I have done that, let me differentiate both sides with respect to time. So it'll become two by three DX by DT. Now, after we have achieved it, fit the instantaneous values given to you. What are the instantaneous values? Nothing but 30 meters per minute. That is DX by DT. So I'll put that down. So two by three into 30 meters per minute. That actually gives me 20 meters per minute. That is the rate at which the shadow is lengthening. So the positive sign automatically implies that the shadow is lengthening with respect to time. Okay. Lending shadow. Is this fine? Any questions, any concerns? So those who gave 20 meters per minute. Okay. Please do not change the unit. Some of you have started giving me answers in per second, but keep the unit as the same unit as given in that question. Is it fine? Easy. Some of you did make mistakes. I was quite surprised. Okay. All right. Now, let's take another question. Let's take this question. I hope everybody can read the question. It is everybody is able to see this question clearly. So there is a horse which runs along a circle with a speed of 20 kilometers per hour. A lantern is at the center of the circle. A fence is along the tangent to the circle at the point at which the horse starts. Find the speed with which the shadow of the horse moves along the fence at the moment. At the moment means at the instant. When it has covered one eighth of the circle, your answer should be in kilometers per hour. Please do it. Please try it out. And let me know your response in the chat box. Question is clear to everybody. Is the question clear to everybody? See, the question is, let's say there is a horse which is running on a circular path. Okay. It has been tied by some rope to the center of the circle and there is a light source being kept over it. Okay. So this horse when it is running, it is casting its image on a fence, which is let's say like this. Okay. So this is the fence. F E N C E. Okay. Now let's say the horse is at this position. Okay. So as you can see, because of this light source, it will cast a shadow over here. So this will be the shadow of the horse. No. So let's say it was at this position because of this light source, there will be a shadow cast here. So my question here is, as the horse is galloping along this circular path, the shadow will also be running along the fence. Correct. So shadow will seem to gallop on the fence or along the fence. Correct. So at the instant when this horse has covered one eighth of the circle, what is the rate at which the shadow is basically moving along this fence? This horse is galloping at the rate of 20 kilometers per hour. They have not provided us with the radius of the circular path. R is not known to us. Okay, Aditya. Okay, Gaurav. Anusha, you have answered with its R only. I didn't get that point. You mean to say the rate of the rate at which the shadow is running on the fences are the radius of the circle. I think four of you have answered so far. And your answer is, I think so. It is correct. We will check it out. Shritya also has answered very good. Shritya Pratik. One more minute I can give for the people who are trying hard so that all of you are satisfied with your attempt. And then we can discuss it. Okay, Anusha. Okay, Anusha. Anybody else? All right. So let's solve this question. Let's say I call this angle as theta. Let's say I call this angle as theta. Okay. Now, what has been given to us as our information? We have been given provided that the horse is running at a speed of 20 kilometers per hour. That means the rate at which it is covering R theta that is given to us as plus 20 kilometers per hour. Okay. Now, R is fixed. So that means R d theta by dt is given to you as 20. Correct? Yes or no? Now, what are the two things which are changing here? Of course, theta is changing. And this length, let me call it as X. X is changing. So theta is changing and X is changing. Radius is not going to change, right? So can I link these two quantities? Can I relate X and theta to each other? You will say, sir, yes, very easy. Write X as R tan theta. Okay. Now, having got that, let us differentiate both sides with respect to time. When I differentiate this, this will become secant square theta d theta by dt. Okay. Now, what are the quantities that we need over here? I need R, I need theta, I need d theta by dt. Okay. And dx by dt can be obtained after I plug in those values. But there is no separate R, no separate d theta by dt given, but we have been given a combined R into d theta by dt, which is actually 20. So can I say this into this is actually a 20. So it is secant square theta into 20. And what is theta? Now look at this information. When the horse has covered one eighth of the circle, one eighth of the circle means he has covered 45 degrees. That means theta at this instant of time. So let me write it down. Theta at the instant of time is 5 by 4, which is 45 degrees. So put it over here. So secant square 45 degrees into 20. Secant square 45 degrees is 2, 2 into 20. Answer is going to be 40 kilometers per hour. That means the shadow of the horse is running at twice the speed, 40 kilometers per hour. Is it fine? Correct. And if you realize as theta approaches 90 degrees, the speed of the shadow will become infinitely big. Right? Of course we are not going to calculate for that theta equal to 90. So you won't be able to see the shadow to be so fast. And if it crosses 90 degrees, your shadow will not be visible at all. Okay. Shadow cannot be seen. Yeah. Maybe that relation will now be true if the fence was on this side. Okay. Aditya. So this is one of the questions that comes normally, shadow-based questions. So we are going to take different varieties of questions. Let's take the next one. Yeah. I hope you all can read this question. Yeah. The question is, sand is pouring into, sorry, from a pipe at the rate of 12 centimeter cube per second. The falling sand forms a cone on the ground in such a way that the height of the cone is always one sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is four centimeter? So I hope the scenario is clear to you all. So the situation is something like this. So there is a pipe. Let me make the pipe in white. And through this pipe, sand is being poured. Okay. Sand has been poured. And the sand forms a cone like this. And the cone is also like that. At whatever instant you look at the height is always, the height is always one sixth of the radius. Okay. Oh, too fast. Very good. Oh, okay. Don't worry. We are just doing the basics question first and then we'll slightly complicate scenarios. Okay. Okay, Pranav Burman. Very good. Who else? Gaurav Burman Pranav so far. Guy three. Very good. Very good. Okay. Prka Thake Be Gav. Okay, guys tell, we'll discuss it. Now. First of all, what are the two things which are changing? You'll say said, the volume is changing of course, because the sand is constantly being poured. And because of that radius and height is also getting changed. And so can we write a relationship between the three quantities, which are actually changing yes there ideas. height and volume are related to each other by volume is equal to 1 third pi r square h. The good thing is we know what is the relationship between height and the radius and now look at the question. The question is basically trying to ask you what is the rate at which the height is changing at the instant when the height is 4. So at this instant when the height is 4 centimeter, how far is the height is changing? So it will be advisable that we convert everything in terms of h on the right side. So I will remove my radius and write 6 h in place of that. So volume is going to be 36 by 6 which is 12 pi h cube. Now once you have got that you can start differentiating both sides with respect to t. So this will be 12 pi 3 h square dh by dt. Now start plugging in values. So what are the values? dv by dt. dv by dt is already provided to you in the question. dv by dt is already provided to you in the question and that is 12 plus 12 centimeter cube per second. So this is 12, 12 pi 3 into 4 square into dh by dt I have to find out. So 12, 12 gone. So dh by dt comes out to be dh by dt comes out to be 1 by 16 into 3 is 48 pi. Please write down the proper units. It's centimeter per second. So this is going to be your answer for this question. dh by dt is 1 by 48 pi centimeter per second. Most of you have got it right. People who have got it wrong Pradyun and others Hariharan please have a look at your working. Alright next question. Next question is two men PNQs start with velocities you at the same time from a junction of two roads. Excuse me inclined at 45 degrees to each other. If they travel by different roads find the rate at which they are being separated. Find the rate at which they are being separated. Some of you would like to use vectors over okay Aditya. Right Hariharan. So most of the concepts that you have already done in physics we are learning it right now in mathematics. Okay Shatish very good. Okay Gaurav we'll resolve that. We'll resolve that. Let me give one minute for those who are trying hard. Okay let's discuss it. Let's discuss it. Okay Hariharan did you use a calculator or something for that? Okay since both are moving at the same we can say velocity u you can say let after a time t they would have covered a distance of x and let's say this distance let me first connect them. Let's say this distance is y. Let's say this distance is a y. Of course you have been provided that dx by dt is u okay and this is 45 degree. So because of changing x y is also changing right. So they have been getting separated as x you know they're getting separated more and more as x increases correct. So first of all what is the relationship between x y. So you can use your cosine rule for this and you can say cos 45 degrees is nothing but x square plus x square minus y square by 2x into x correct. That means 2x square by root 2 is equal to 2x square minus y square okay. Yes that is what I was saying most of you would have used vectors over here but not required you can basically solve without that also. So y square is nothing but 2x square minus root 2x square or you can say 2 minus root 2x square okay. Now this is a simple relation which says y is equal to under root of no plus minus business because you're dealing with distances y is equal to under root of 2 minus root 2x. So just differentiate this with respect to time right and just put your dx by dt as u over. So the rate at which they are getting separated will be this. So this is the rate at which rate at which separation is happening okay. So this is your answer. Any questions? Where did that cos 45 come from? The fact that the roads are inclined at 45 degree got it got it. Yes have the relationship been different then basically what would happen you have to use three variables x y and z write a relationship between them and now when you're differentiating both sides you would need instantaneous values of x instantaneous values of y and dx by dt and dy by dt got it. So dz by dt will come from there clear Aditya okay next. Now I have a very special question for you I will not be writing too many things here just listen to this question okay the question is there is a could you guys go to the previous question okay sure yes anything that you would like to ask me done okay thank you yeah so now this is a wall okay this is a wall and this is the ground this is the ground and this is a wall there is a ladder there is a ladder which is actually taller than this you know wall and it is basically like this okay so it is it is having some part protruding over the wall it is having some what part protruding over the wall I'll give you the dimensions this wall is seven meter long this wall is seven meter long and the length of the ladder the length of the ladder is 15 meters okay this ladder length is 15 meters okay now this ladder is slipping against this wall this ladder is slipping against this wall in this way okay and this rate of slipping is two meters per second so I let it down over here another important information is the ladder is slipping the ladder is slipping against the wall against the wall two meters per second okay question is find the rate at which find the rate at which the foot of the ladder is slipping is slipping away from the wall from the wall at the instant at the instant at the instant the projection of the protruded part of the ladder along the vertical ladder along the vertical is three meters okay the question is slightly lengthy so what are they asking you they're asking you what is the rate at which the foot of the ladder is slipping away this is moving down constantly at a rate of two meters per second so what is the rate at which this slipping is happening when when the projection of the protruded part along the vertical at the instant when this guy is three meters so at the instant when this length is three meters okay I'm not writing anything over there because you start thinking that that is a fixed value no that is changing so at the instant when this guy becomes three meters what is the rate at which the foot of the ladder is slipping away from the wall is the question clear to everybody if not I can explain you once again seven meter long wall 15 meter long ladder ladder is basically protruding over the wall and it is slipping like this okay it is slipping like this this contact is never broken okay this contact is never broken so this is slipping against it at the rate of two meters per second and because it is slipping this ladder is slipping from the ground as well the rate at which it is slipping against the wall is two meters per second find the rate at which the foot of the ladder the foot of the ladder is slipping from the wall at the instant the projection of the protruded part is three meters along the ladder Harir the slipping is along the ladder that's why I've shown it categorically the ladder is going down like this at a rate of two meters per second no vectors this is not a vector chapter you have to use derivatives how do you use a vector unnecessarily the process is the same guys the problem may look a bit complicated but the process is well defined just follow the process anybody any success anybody okay enough time has gone okay so first let us identify what are the quantities which are changing so can I say since the ladder is slipping against this wall this length is changing let me call this length as y that length is changing let me write properly yeah let me write on this side okay since the wall the ladder is slipping on the ground as well can I say this length is also changing let me call this as x okay so x and y are changing correct now the question says dy by dt is negative two meters per second because y is reducing with respect to time because the ladder is climbing down and down and down isn't it now how do I strike a relationship between x and y okay now one thing I can do here is I have to also relate this projection so what I'm going to do I'm going to take this angle as theta that means that that means this angle is also theta okay so can I first write down a relation between x theta and y theta and try to see what kind of a connection can happen between them so from this figure I can say x is equal to or x by seven is equal to tan of theta so x is equal to seven tan theta okay now what I want I want to know what is dx by dt at this instant where theta is something now what is that theta which we don't know right now okay at theta equal to something right we'll have to figure it out we'll have to figure it out now what I need here is dx by dt so that means I indirectly need seven six square theta d theta by dt so without knowing theta and without knowing d theta by dt I will not be able to solve this question correct okay now let's apply some more information given to us in the question if this is why this length this length is going to be 15 minus y and can I say can I say 15 minus y 15 minus y 15 minus y is seven seek theta right in other words y is equal to y is equal to 15 minus seven seek theta correct yes or no now I'm looking at that instant where where this length becomes three now if you look at the upper triangle let me name it for your sake of convenience let me call it as p q r s t if you look at the triangle p q r you are looking for that instant where y actually becomes three seek theta isn't it because of the basis three why will actually become seek three theta correct so at least by comparing these two I will get the instant of theta I will get the value at which or theta at which I'm trying to calculate dx by dt so when I relate these two I will get this is equal to seek three seek theta which means 15 is equal to 10 seek theta in short I get cos theta is equal to two by three if I'm not mistaken okay so this theta that I'm looking for this question mark is basically achieved that is actually cos inverse of two by three okay let me just segregate it from the question yeah now I need d theta by dt how will I find that out very simple let's come back to the same expression over here differentiate it with respect to time you will end up getting minus seven seek theta tan theta d theta by dt so for this d theta by dt I can use my this expression because I know dy by dt minus two I know seek of theta which is three by two by the way if cos theta is two by three what do you get as tan theta if I'm not mistaken this will give you a under root of five by two am I right if cos theta is two by three and theta is under root five by two so this will be under root of five by two d theta by dt okay so minus minus gone so d theta by dt will become eight upon 21 root five radians per second sorry I missed out I think the correct so now I have all the wherewithal with me I know the theta I know d theta by dt so what are we waiting for let's do the honors let's complete this so dx by dt will become seven seek square theta seek square theta will be three by two the whole square into d theta by dt is eight by 21 root five okay let's simplify I think 21 will get cancelled straight away here this will cancel two and I will end up getting six by root five meters per second so this is your answer to this question how many of you got it does it come out to be the same I think roughly yes I think your answer is roughly correct is it understood any questions any concerns any questions any concerns now one question that I would like to ask you to find d theta by dt to find d theta by dt why didn't I differentiate this guy it is recommended that you can use that you can if you want to use a parameter to make your life easy you can directly you can use that instead of directly relating x and y basically you are introducing a parameter to link them all right now my question to you is everybody why didn't I differentiate y equal to 3 c theta to get my to get my dy d theta by dt we cannot differentiate with respect to ty so Hariran if we could why didn't we do that why did I chose 15 minus 7 c theta think think answer is very simple we are not concerned after that point in time see this is an instantaneous value 3 is a fixed cost theta is also fixed so this is actually a constant for us because we are calculating it at an instant this is an instantaneous value of y this is a generic value of y get the point exactly front of are you getting my point this is a generic y value that means if your theta keeps on changing this guy will change your y as well but this is an instantaneous value so at the instant when that projection was 3 that is the y value at that time so you cannot differentiate this you should not be differentiating this are you getting my point because you'll get faulty results are you getting my are you getting my explanation why didn't I differentiate this to get my d theta by dt because the projection will not be 3 always so this I use only to get what is my instantaneous theta because I needed it in my in my expression here secant square theta right so this is only useful for finding your instantaneous theta but when you're differentiating why you have to take this because this is a generic y and theta relation no matter wherever is the wherever is the ladder rather point clear everybody okay next question next question is there is a lamp okay there is a lamp which is 50 feet high this is a lamp which is 50 feet high okay this is 50 feet high okay there is a ball which is at the same level as the lamp and place 30 meters away from it 30 feet away from it okay so this is a ball okay now this ball when it is dropped it covers a distance of 16 t square okay so when it is dropped at a time t let's say after a time t it would have covered 16 t square after time t okay my question here to you is my question to you is okay let me not draw anything here my question to you is find the speed of the shadow of the ball on the ground at the instant at the instant t is equal to half a second okay so what has happened this ball is released right at the instant when t is half at that instant of time what is the speed at which the shadow of the ball is moving this distance is 16 t square distance it has dropped distance it has dropped in time t that is 16 t square this distance so let's say in one second it would have dropped 16 meters 16 feet so this is the distance it basically drops in one second okay two second it would have dropped 64 feet by the way before two second it would have hit the ground actually clear Siddish is my question clear to everybody so it is not half gt square like the way you would have thought it to be okay let's say it is a different planet altogether where on free fall it covers 16 t square yes any success it's a big number how big in thousands okay so yeah that could be the answer why not that could be the answer anybody else okay Pranav see t equal to half is for the last okay don't use it initially see what are the quantities which are changing relate them first of all that is the very first step once you've related it then differentiate both sides with respect to time and once you have done with that then start putting the instantaneous values okay before that instantaneous values out of no use okay Pranav okay Pradyum yeah yeah I got it minus means it is coming towards the lamp post okay Aditya all the dimensions are in terms of feet only so I think Pradyum you meant to say that many feet per second right okay anybody else okay let's discuss it out let's discuss it out see if you see the image the image of this ball on the ground will be here correct this would be the image of the ball on the ground so what is changing you say this is changing let's say I call this as X okay and of course this is also changing let me call this as Y so as the ball is falling on the ground the height of the ball from the ground that is changing and the distance X is changing okay now how do I relate Y or X again can I use my similar triangles over here I can say this length I'll just name it P and I just drop a perpendicular from here P Q let me call it as L M N so can I say triangle triangle P Q N is similar to triangle L M N okay so P Q over Q N is equal to L M over M N could you show it with trig so am I not using trigonometry here triangle only no correct so P Q by Q N is equal to L M by M N right so let us try to write down P Q is Y okay and Q N is all of you please note down Q N will be X minus 30 right because this whole thing is X I have taken so this is this is 30 so I've subtracted 30 from X to get Q N okay this is equal to 50 divided by M N M N is X in other words what do we see is that Y is equal to 50 X minus 30 upon X okay that's nothing but 50 minus 1500 by X this is your Y correct now having got this relation let us differentiate both sides with respect to T that gives you minus 15 plus 15 X square DX by dt yes or no now do you know dy by dt so first of all what is Y Y is nothing but it is 50 minus 16 T square so dy by dt will be nothing but negative 32 T and you have to find the instantaneous value of this at T equal to half that means minus 16 feet per second so this is known minus 16 what is X what is X so for that you have to again find your X from this relation itself so Y is equal to 50 minus 1500 by X right now Y at that instant of time let us find out instantaneous Y Y at that instant of time will be 50 minus 50 minus 16 times half square that is actually 46 if I'm not mistaken isn't it so we have got from here let me just put a barricade 46 is equal to 50 minus 1500 by X so X is going to be 1500 by 4 1500 by 4 is 375 so let us try to put here so this is minus 16 this is 1500 this is 375 square 375 square I will write it as 375 375 DX by dt I don't know okay let's try to simplify so this will go by a factor of 4 and this also goes by a factor of 4 so you'll have minus 4 over n so dx by dt is anyways minus 4 into 375 that comes out to be minus 1500 feet per second so the shadow is traveling towards the lamppost or the speed of the shadow on the ground is minus 1500 that means it is moving towards the lamppost so you can say 1500 feet per second towards the lamppost is it fine now most of you could not solve this question I could get answers only from I think Pradyum Shatish and later on Pradam sir is there any easier way than dealing with X square dealing with X square in that case you have to in that case you may take an angle theta and deal with it that is another way to do it but there you have to strike a parametric relationship between X and theta and Y and theta it will it will come with a cost of increasing more variables okay so you can try it out you can try different methods to solve the same problem okay so there you have to find d theta by dt and then you have to relate dx by dt with d theta by dt that's all you need to do okay it's coming like that okay okay should this try it out you should be getting the answer Hariharan I substituted Y is equal to before differentiating and got stuck it's fine you can you can put your Y's here also right and then you can put TS half throughout that is also fine Hariharan you should not be ideally getting stuck okay that should have given you the same result oh okay okay maybe calculation error maybe calculation error okay next question next question okay the question says uh there is a comprehension okay it says that there is a lamp of length 10 meters placed at the end of a ladder AB maybe it is not too scale because as per the question this lamp should be of length 10 meters so this is 10 meters okay it's not too scale by the way and the ladders of length 13 meters which is leaning against a vertical wall as shown in the figure and its base slide away from the wall okay at the instant base is 12 meters from the vertical wall at the instant this is an instantaneous condition the base is moving at the rate of 5 meters per second okay and there's a man of height 1.5 meters standing at 15 meters from the vertical wall so this gap is 15 meters this gap is 15 meters there are two parts to the question there are two parts to the question find the rate at which theta decreases when the base is 12 meters from the vertical wall okay second is the rate at which the length of the shadow of the man increases when the base is 12 meters from the vertical wall so let us solve the ninth part of the question first give me a response for the ninth part very good Shatish anybody else with the first part first part is easy I believe okay Aditya okay last 30 seconds for covering the ninth one and then we can start with the tenth one okay all right so first part ninth part let's look into this see in the ninth question just focus on the ladder part because they're asking you how is the angle theta changing with respect to time when this ladder is slipping away right so what are the two things which are changing here that is the foot of the ladder let me call it as let me write it in green this is x okay yes I know correct and theta and theta correct so how is your x and theta related to each other so we'll say simple x is going to be 13 cos theta correct so dx by dx by dt is going to be negative 13 sin theta d theta by dt now they're asking you for that instant when this x becomes 12 when this x becomes 12 when x becomes 12 this guy is 5 isn't it so dx by dt which is 5 plus 5 because it is slipping away from the foot of the wall minus 13 sin theta in this case will be 5 upon 13 and d theta by dt I don't know okay so automatically from here you can get d theta by dt as negative 1 radians per second now this basically means theta is decreasing at a rate of 1 radian per second since the question is already asking you what is the rate at which theta decreases so your answer will be 1 radian per second option number 8 is it fine so there is no problem with question number 9 anybody having any issue with question number 9 let's work out 10th part the rate at which the length of the shadow of the man increases when the base is 12 meter from the vertical okay Shrutish let's let's draw the situation once again so let's say this is your ladder this is your lamp this is the man okay and there is an image cast by this lamp on the ground okay and this is your ground this is 10 meters this is 13 meters man I think is 1.5 meters okay and this is the shadow length so what are the two things changing x is changing and y is changing right so as the ladder is slipping away this guy x is changing and the length of the shadow of the man is changing correct so we want what is the rate at which the length of the shadow of the man is changing at the instant x is 12 meters okay at the instant x is 12 meters I think this distance was already mentioned to us as 15 this distance is already mentioned to us as 15 meters so what is happening the ladder is slipping because of that the lamp is coming down so you can imagine that the lamp is actually reducing its height so the lamp is coming down and because the man is stationary man is not going moving anywhere man is stationary and lamp is moving down because of that the shadow length is increasing so we have to find the rate at which the shadow length is increasing so I have got only one response so far which is from Shatij so far anybody else okay Pranav okay Aditya okay let's discuss it out this is not a difficult problem so let's say I call this this particular length as z okay so the reason for your x to change is because your z is changing and because of that your y is also getting changing so x is changing that creates a change in z and because of that z there is a change in y correct so let us first try to understand what relation connects x and z and that's a simple Pythagorean relation x square plus z square is equal to 13 square correct in other words if you differentiate both sides with respect to t by the way this is slipping if I'm not mistaken the slipping is happening at a rate of how much 5 meters per second yeah so dx by dt is 5 meters per second given to us plus 5 meters per second so when you differentiate both sides with respect to t you get 2x dx by dt plus 2z dz by dt is equal to 0 in other words dz by dt is negative x by z dx by dt correct now at the instant when x is 12 we know z was 5 and this guy was plus 5 again so it is going to be minus 12 meters per second so the foot of the lamppost is coming down at a rate of minus 12 meters per second at the instant when your dimensions of x is 12 of course z will become 5 by that time and of course dx by dt is also 5 okay now let us try to relate let us try to relate z with y but that is simple you can use the fact that let me name the triangle abc and apq so abc triangle is similar to is similar to triangle apq so I can say ab by bc y by 1.5 is equal to this whole length which is y plus 15 upon upon 10 plus z so 10 plus z is nothing but 1.5 times 1 plus 15 by y correct me if I am wrong okay so 1.5 10 z this is going to be I think 2.25 by y or 10 plus z my my so z is going to be z is going to be 2.25 y minus 8.5 any questions here anybody now differentiate both sides with respect to t 22.5 so this will be minus 22.5 by y squared dy by dt so let's try to put the values so here I know what is my dz by dt dz by dt is minus 12 minus 22.5 y square I do not know that I have to figure it out okay so you can use this fact that at the instant when you're looking for the slipping z was actually 5 okay so y will become correct me if I'm wrong 22.5 divided by 13.5 okay so this will become minus 22.5 divided by 22.5 square and 13.5 square okay this is equal to minus 12 sometimes we'll get cancelled off so your answer oh sorry dy by dt I forgot minus minus will also get cancelled off so your dy by dt will become 12 into 22.5 divided by 13.5 square correct me if I'm wrong I think this will go by a factor of you can write it as 120 into 22.5 by 135 into 135 so this thing will go by a factor of 25 times okay this is I think 9 and this will be I believe 6 no 5 we'll go by 25 or you can cancel off by 5 at least so this will be 45 and this will be 27 okay again let's cancel off by a 5 this will be 24 this will be this will be 27 again okay let's cancel off by 9 no I can cancel off by 315 and this is going to be 9 okay so this will be 3 this will be 8 this will be 5 oh 40 by 27 a bit of calculation towards the end 40 by 27 meters per second this is the rate at which the shadow is going to grow which is option number b which is option number okay so only three of only two of you about this correct shittish and aditya is there any question related to the solving of this part any question any concerns be do let me know if there was any and I knew about that I would have I would have used that but yes this is not the only way to solve it you may use parameters to solve it okay okay so I think we have done enough you know question on dy by dx as rate measure so now we can go on to our next concept


Hi welcome to today's tutorial. In this video you'll learn about how to sync Rhino with D5 render, and how to make an exterior scene of commercial complex from scratch. We'll start with D5 converter for Rhino live sync tutorial. To get started, please install D5 converter from workflow section in D5, or from D5 render official website. After installation, we can see the D5 converter tab in Rhino, which contains seven buttons. Start sync, stop sync, sync changes, view sync on, view sync off, send scenes, and send light. Before you start the live sync please separate different surfaces of the objects by materials. From the material panel on the right, you can see that in this project we used different colors to tell the materials apart. Now click on start sync to launch D5 render and sync the Rhino model into D5. When there's addition deletion or change to the objects in Rhino, you can use the sync button to quickly update the material and model changes in D5. At the same time, it will not replace materials or scene settings that have been adjusted in D5. When syncing, the viewports of D5 and Rhino are consistent, so when you rotate the viewport in Rhino, in D5 it rotates as well. Click on view off to turn off the live sync of viewports. By clicking on send scenes button, the view set in Rhino can be synchronized to the scene list of D5 render. The last feature is send light. To demonstrate it clearly, let's switch to wireframe view, and now you can see that there is already a group of lights in Rhino. Click send lights, and this set of lights will be synchronized to D5 and appear in the resource list as a group. You can adjust the light parameters either individually or in batch, such as attenuation radius, intensity, color temperature, color, visibility in reflection, and size. We've now covered the features and basics of D5 converter for Rhino. Other than live sync, D5 render support directly importing 3Dm files as well. In this case, we divide the project into three part, building ground and light. Step 1. Import the three files into D5, then select the building model and place it. Set the location to 000 and press Z to focus on it. Step 2. Import the ground model. To align it with the building, hold control to multi-select them, and then click on align button. Remember to select the building first because we'll take the first one as reference. Step 3. Import the lights just like in step 2. Select the building model, then hold control and select the lights. Click on align again. After importing the models into D5 and syncing coordinates for them, you can start to edit materials. Use the shortcut key eye to select the texture you need, and change its template to transparent. For now, the glass refraction seems a bit strange as it's single-sided without thickness. Switch on thickness option under refraction and it will produce the correct refraction effect as double-sided glasses do. Use the shortcut eye again to copy the adjusted glass texture, and paste it to other part of the model with the shortcut key O. To create a metal look or the frame of glass windows, increase the metallic parameter, and brighten the color tone, then turn on round corner to create rounded edges that look softer in the scene. You can also use the materials in D5 material library or import custom material maps for the road, lawn, ground and textures in interior spaces. After editing the textures, let's adjust the overall environment. First import custom HDRI for the general lighting effect. Then turn on fog effect with a tint of blue, making the scene more atmospheric. When making post-processing in the effect panel, it's recommended to turn off auto exposure first. Adjust exposure and white balance properly, make sure the scene won't be too bright or too warm. If used wisely, bloom. Vignette and chromatic aberration will make the scene much more realistic yet artistic. Luts can help you create different vibes for the scene. You can also adjust other parameters like contrast and saturation as you like. The final step is to turn on precipitation in environment, weather. Adjust the strength of rain to zero, and the level of puddle to 0.3. This will create an after rain ponding effect on the road. After finishing the environment and effect settings, don't forget to save the changes by clicking on the update scene button. Moving on to more details and decoration of the scene, you can use buildings and plants from D5 model library. Brush tool comes in handy for it quickly places the plants in the scene. Remember to set a proper brush size before painting. For lawns, you can set the radius of brush to maximum so as to activate scatter tool. Press shift and click on a model to add plants. Repeat this step if you need more grass for the lawn. Before placing a plant into the scene, you can use smart placement to rotate and resize its model by pressing the shortcuts R and C, while dragging the mouse. To place trees along a street, it would be more convenient to draw with the path tool. Path tool also works well with character models. Density, width of path parameters are adjustable, and you can also decide the direction, and whether or not the path is located on the ground. Apart from plants and characters, there are a lot of landscape assets from D5 for you to enrich the scene. An even easier way here is to add a sphere model from D5 model library, basic model. You can adjust its size and texture, turn on emissive, and it turns into a simple but beautiful landscape light. To add vehicles into the scene, you can use the path tool with adjustable parameters like density, width, random color, and light. As a finishing touch, choose from the decal assets in D5 like manhole covers and fallen leaves, to make the scene more realistic. If the decal overlaps with other plants, just scale it down a little. This is it. It's time to render. For image rendering, channel export including material ID, ambient occlusion are supported. For animation making, click the video button on the upper right. Set camera shots, add keyframes for the characters, and adjust the easy ease. There are several options for resolution and format of the clips. With your preferred settings, you're now all set to render. Click add to render queue for batch render, or render for direct output. That completes our tutorial for Rhino D5 workflow. Thanks for watching.