Alright, welcome back everyone. The recording has started. I hope those who may have accidentally been removed from the call can join back. Alright, so we were talking about the miracle that took place at Gainbeautiful where a lame man was very obviously healed. In this case, excuse me, it's great to note that the miracle was so very real that people took notice of it and they wondered if it was really the man whom they saw sitting at the gate and Rupita begins to preach. I just said that he made a connection between the God whom the Jews worship and the Lord Jesus but initially it sounds more like he's trying to blame them. However, he's really calling them to repentance because they did not accept this Jesus whom God sent and that is why he's calling them to repentance. Now to help them understand further he says, he refers to Moses.  Give you shall hear in all things whatever he says you do this to you and it shall be that every soul who will not hear the prophet shall be utterly destroyed from among the people. So what is Peter trying to do? This is all homiletics when we talk about preaching. There are so many points we can notice over here. Firstly, taking the opportunity, he sees the right moment to preach and he preaches. He looks at how he can talk about Jesus. So he's using the miracle as that subject through which he can initiate introducing the Lord Jesus. Then he goes on to explaining who Jesus is but look at the way in which he does it. He spoke of the familiar people that the Jews know about Abraham and Jacob. Now he's talking about Moses because they will get it in terms of what the early fathers had said and it's truly the Lord Jesus fulfilling those words that were spoken. So right now he had mentioned saying Moses talked about the prophet and we need to believe that prophet. Who is that prophet? It is the Lord Jesus Christ. So again he says all the prophets from Samuel you see in context because he's trying to get the attention of the Jews. So it's sounding very scriptural because that's when they are going to respond. It's like the various versions of the Bible as well that we may refer to. Like if the people are those who understand the old KJV version then we may use that version but if it's a crowd that understands the simpler version of the Bible, we may use that but then present the truth accurately just so the audience gets the understanding of what is being spoken. So it's contextualizing basically. So that's what he's trying to do in this case. He's bringing up all these names and he's saying the prophet that all these men of God were referring to is the Lord Jesus Christ and God has sent this Jesus. God has erased this Jesus and he has sent him to bless you and interning away every one of you from your inequities. Remember how he had mentioned about repentance earlier and he said times of refreshing will come from the presence of the Lord when you repent. So using that miracle using that incident to preach the Lord Jesus Christ. Now let's move on and see what really happens in Acts chapter 4. So we are expecting a good outcome out of this because you know this is a great miracle that has taken place but now the response of the people will be recorded for us. Let's see what happens. Can someone please go ahead and read from verse 1 to 4 and then another person can be ready so that they can read the next set of scriptures. So we'll start with verses 1 to 4. Now as they spoke to the people the priests the captain of the temple and the Sadducees came upon them being greatly disturbed that they taught the people and preached in Jesus the resurrection from the dead and they laid hands on them and put them in custody until the next day for it was already evening. However many of those who were the word believed and the number of the men came to be about 5000. Amen. Yes thank you Rosalind. So what we have seen now is the response of the authorities who heard about the miracle and the preaching of Peter. So there are some people listed out there the captain of the temple then there is the mention of priests there is the mention of Sadducees who are all these people and why are they together. It's almost like the police force of those times that is why it's like that team of vigilants they were upset by what was going on and quite likely so because they were threatened they knew that Peter was preaching the Lord Jesus and he preached resurrection in Jesus from the dead. Now part of the police force are the Sadducees we know that they don't really believe in the resurrection of the dead so it was problematic for them to theologically and politically to speak the message of Jesus which is why they were disturbed how disturbed were they they were disturbed to the point of it says they laid hands on them that is nothing but seizing them or catching them so they caught them and put them in custody until the next day. So basically what they are sort of anticipating is a rising rebellion of some sort through led by Peter, John and you know maybe the believers because they would have felt that here are the disciples of Jesus now we don't know where he his body disappeared but his men have come to cause trouble and with that in mind for their own safety they felt that it is good to just put them in custody so they could have arrested them the next day but they did not want this situation to escalate so they catch them put them in custody until the next day it says what is the meaning of that they had some procedures they had a process so they could not cry them in the evening and they just had to wait for the courts to open the next day morning so that they get go through the actual steps of convicting them now what is going on may not have been what Peter and John expected now we don't know what Peter and John were thinking in their minds that wow what a miracle God has done we give God the glory we talk about the Lord Jesus we invite people to repent the church now is going to thrive the work of God is going to expand and increase maybe they were just joyful in anticipation of the work of God but here comes opposition here comes persecution so we don't know if they've got of God or if they were mentally prepared to face persecution but unfortunately you know sometimes we may go from a place of ministering so powerfully and thinking that you know people are going to respond positively to this message straight into finding opposition and we are like what just happened we thought for a miracle like this everyone will fall on their knees and you know repent and there will be a revival in the land and here are the people starting an opposing Peter and John however the greatness of our God is in the book of Acts even when we see opposition the next thing that you will read is the church is growing the church is growing the church is thriving okay so this is not the only place even later you will notice that God's work could not be stopped they may be the opposers where successful it's stopping a few men here and there but the work by the spirit of God continued in the hearts of people and the church only kept thriving so notice that last section verse 4 it says however many of those who heard the word believed and the number of the men came to be about 5000 so since the first day that the church started now Luke doesn't give us you know how many days it has been or weeks it has been but at this point 5000 is the attendance okay so like church we usually say oh how big is the church now church is 5000 God's work is continuing even in the face of persecution and that's what we observe here the book of Acts is a period of great opposition even today we find opposition in places around us maybe the places where we are from but the lesson we learn from the book of Acts is that even these things cannot really stop you know what God wants to do here on the earth so yes Peter and John are in custody but the church has now grown to 5000 okay let's read further and see what else we have in store here let's read from verse 5 all the way till verse 12 and it quits another person to go ahead and read and it came to pass on the next day that their rulers elders and scribes as well as Annas the high priest Guy Fass John and Alexander and as many as where our family of the high priest were gathered together at Jerusalem and when they had set them in the midst they asked by what power or by what name have you done this then Peter filled with the Holy Spirit said to them rollers of the people and elders of Israel if this day are judged for a good deed done to a helpless man by what means he has been made well let it be known to you all and to all the people of Israel that by the name of Jesus Christ of Nazareth whom you crucified whom God raised from the dead by him this man stands here before you all this is the stone which was rejected by you builders which has become the chief corner stone nor is there salvation in any other for there is no other name under heaven given among men by which we must be saved amen thank you John so here we find the next day trial is taking place there are the rulers elders scribes as well as Annas the high priest Guy Fass John Alexander so these are all the names that they had in that council and what are they doing okay they are questioning Peter and John who is Peter what is his profession any idea what was Peter's profession was a fisherman right okay and he also saw how Galileans will look down upon so it's a very interesting scene you have the who's who of the of Jerusalem all gathered together and they are threatened by a fisherman and his friend why what is this big threat because they felt as I stated earlier a political threat a religious threat maybe even culturally they felt that these guys are trying to completely don the hearts of people towards the Jesus of Nazareth because of whom we already had a lot of problems some some time ago and here come his representatives to create more chaos and they were afraid that they may lose their positions of authority so it could have been a you know a community a reason a collective reason but it could have also been a personal reason because they did not want to let go of their authority so they questioned Peter and John and they asked them directly by what power or by what name have you done this in other words who gives you authority to heal this man and Peter is sure he is uh you know going ahead and giving a response to this question and think about this with me the scene is like all the big people of the city are there and Peter is uneducated uh you know he's standing before these big people we would imagine that as he is being intimidated he will be scared he would open his mouth or be uh eloquent about his thoughts but no he's so bold what made him bold Luke writes in the beginning of verse eight Peter filled with the Holy Spirit that made all the difference that boldness came because he was filled with the Holy Spirit and he speaks he gives an answer to the rulers and he kind of uh you know he asks them a very direct question he says uh if we this day are judged for a good deed done to a helpless man by what means he has been made well so he feels that it's so funny that they're even asking this question uh he did a good deed but he's arrested for it but he goes ahead and he explains to them without holding anything back he says by the name of Jesus Christ of Nazareth we can imagine the boldness now uh we don't know what the crowds these days like you know if you watch a movie or something there's always a response of the crowd whether they're already quiet or they go oh because he is saying the name which can get him into more trouble he's already been in jail overnight Peter don't you want to go back home why are you putting yourself into more trouble he's saying how can you even ask me about helping a you know a lame man I did a good deed okay if you want to know let me tell you I did it by the name of Jesus Christ of Nazareth and if that was not enough he's saying whom you crucified okay so it's just getting a little more uh you know sort of fiery who you crucified who God raised from the dead now these points that he's making would have challenged the rulers even more because what is he saying to them you have the priest the high priest all of them there he's trying to tell them that Jesus is the Messiah and then he says God raised from the dead that can create trouble because the Sadducees are listening and they don't like to hear about resurrection of the dead he's not worried about anything he's just speaking the truth of God's word and he's saying by him this man stands here before you hold who asked the question and give you the answer okay and he goes on this is the stone which you which was rejected by you builders which has become the chief cornerstone so he's quoting a scripture also by which they will understand that he is referring to the Lord Jesus as the Messiah and that he says nor is there salvation in any other but there is no other name under heaven given among men by which we must be same so he is not saying Jesus could be the way Jesus might be the way he's one of the ways very direct response Jesus is the only way salvation is founded no other name but there's no other name under heaven given to man by which he must be seen how could Peter be so good was it Luke said Peter filled with the Holy Spirit gives them a direct answer to their question now let us see what happens okay so this whole court scene is going on Peter and John are being intimidated but Peter is responding very boldly what happens next so could somebody help us read from verse 13 till 22 next chapter 4 verse 13 to 22 the members of the council were amazed when they saw the boldness of Peter and John for they could see that they were ordinary men with no special training in the scriptures they also recognize them as man who had been with Jesus but since they could see the man who who had been healed standing right there among them there was nothing the council could say so they ordered Peter and John out of the council chamber and conferred among themselves what should we do with these men they asked each other we can't deny that they have performed a miraculous sign and everybody in Jerusalem knows about it but to keep them from spreading their propaganda any further we must warn them not to speak to anyone in Jesus name again so they called our courses back in and commanded them never again to speak or teach in the name of Jesus but Peter and John replied do you think God wants us to obey you rather than him we can't stop telling about everything we have seen and heard the council then kept them further but they finally let them vote because they didn't know how to punish them without starting a riot for everyone was praising what for this miraculous sign the healing of a man who had been named for more than 40 years thank you thank Jefina so we see that after the response of Peter the council was very confused because there is definitely proof that a notable miracle has taken place this man whom they all knew who used to sit at the gate of beautiful is now able to walk and it's a definite miracle so they cannot speak any they cannot do anything to Peter and John because it'll upset one section of the people so they are wondering what do we do to these men and then they come up come to the conclusion that they will just warn them right so they warn them and they tell them okay do one thing don't ever speak in the name of Jesus go back but don't speak to any man in this name the name of Jesus Christ so when they commanded in this way what was the response that Peter and John had they say whether it is right in the sight of God to listen to you more than to God you judge so so now again another question arises the authorities are saying something we are supposed to respect the law of the land right but what is it that Peter and John are responding with they are saying that no what we are being asked to do is to deny God and God's power and to not speak in the name of Jesus which is not possible because that is who that is what their faith is all about and so when the authorities are telling them something against their faith they stand up for themselves and they say you decide whether it is right in the sight of God to listen to you or to listen to God or in other words they say that we'll have to do what God is calling us to we cannot you know do what you're telling us to do so that again is a very very bold way of responding and they say but we cannot speak the things which we have cannot but speak the things which we have seen and heard so we are clearly proclaiming to the council that you can't stop us we will continue to do what we are doing but these the council couldn't do anything because of the nature of the miracle and they had to let them go and notice how this passage also said that Peter and John were uneducated right and they were not any kind of trained men but what was the difference they were with Jesus they were filled with the Holy Spirit these are all the reasons why do they gain that bonus which they carry if they spoke to the council now let's go ahead and read the next section here let's read from verse 23 to 31 Acts chapter 4 verse 23 to 31 as soon as they were free Peter and John written to the other believers and told them what the leading priests and elders are there when they heard the report all the believers lifted their voice together in prayer to God oh sovereign Lord creator of heaven and earth the sea and everything in them you spoke long ago by the Holy Spirit through our ancestors David your servant saying why were the nation so angry why did they waste their time with few dead plants the kings of the earth prepared for battle the rulers gathered together against the Lord and against his messiah in fact this has happened here in this very city for Herod Antipas whom his pilot the governor the Gentiles and the people of Israel were all united against Jesus your holy servant whom you anointed but everything they did was determined beforehand according to your will and now oh Lord hear their threats and give us your servants great boldness in preaching your word stretch out your hand with healing power many may miraculous signs and wonders be done through the name of your holy servant Jesus after this prayer the meeting place shook and they were all filled with the Holy Spirit then they preached the word of God with boldness all right so as we continue in you know what is really happening Peter and John were let go and we imagine what exactly they would go back and tell their church congregation they go the report it says to their own companions all that the chief priests and elders have said to them so basically they present a report and then we started to pray remember we saw that this was a praying church the early church is a praying church so their first response is praying and praying together that's so beautiful when they're going through and they're waiting upon the promise of the Lord they're praying when they have to make a decision they pray and now when they're going through a rough situation they have chosen to pray so they raise their voice to God with one accord remember that term one accord it's one us of heart one us of purpose they come together and they start to pray what do they say but they just state some of the scriptures and they talk about who God is and how it is the Lord whose ultimate purpose will prevail even though there is opposition coming through leaders and nations and kings and rulers can anyone stand against our Lord so you know they go ahead and just proclaim the truth they declare the truth that they know that no one can rise above God and do that God is the ultimate authority and then they in their prayer they exalt Jesus they say your holy servant Jesus whom you anointed and then what happened to Jesus the way in which he was he was crucified okay they talk about all these things they just make declarations of these things and they make a declaration that God no matter what happens it is your purpose that prevails their confession at a difficult time is God's greatness and the truth of God's word which says that the purpose of God will prevail and along with the declarations what would they do they say that you know yes these council members are threatening us but make us bolder now this is the part where some of us may be surprised we expect the disciples to only pray of prayer of protection because that is how we think or at least I think if I'm going through some opposition the first thing I would say is God protect me protect my family protect my church which is not a long prayer it's a good prayer to pray but notice the points of the early church additionally maybe they even pray for protection but what Luke has chosen to mention here is he says God give us boldness and we also ask God that he would do more signs he would do more wonders and when you know hands are stretched out to heal that healings would take place so grant to your servants is more like you could say maybe the focus was on the apostles that now that John and Peter have faced this difficult situation that these people along with the other leaders should move with mighty signs and wonders and boldness no matter what one miracle has taken place and you know these hearts are still hard let many more miracles take place so that people will know who God is and his name will be glorified so it was a really bold church filled with the Holy Spirit where their response is so commendable they declared that even rulers or nations kings authorities cannot override the purposes of God that was their declaration and the second thing they say is God give us boldness increase your work not by stretching out your hand to heal that signs and wonders may be done through the name of your holy servant Jesus meaning they are saying God you do more okay so what will this lead to more trouble but they're not afraid and it's almost like you know God gave them a supernatural experience to reveal his pleasure I don't know you know what was the reason that verse 31 is recorded by Luke but Luke says and then they had prayed the place where they were assembled together was shaken and they were all filled with the Holy Spirit and they spoke the word of God with boldness so something tangible happened in those moments where they had prayed this prayer it says that the like the place where they stood shook so it it would have happened like you know natural occurrence no wonder this has been recorded now some commentaries have this reference to a particular earthquake that took place in the north ridge at 4 31 in the morning okay so and they say oh it it refers to act chapter 4 verse 31 where the scripture say that the earth or the place where they stood shook but it's God's doing you know when God wants to manifest his presence in a certain unique way it can happen and I have heard testimonies of when people are praying some physical manifestations of you know God's presence like in this case it's the earth shaking in some cases there's a mighty with so many things happen and it's up to the Lord we cannot expect such things to take place every time but there are times that these things can happen I don't know how many of you have watched there is a particular South African minister an elderly man quite respected and in one meeting where he was preaching about the power of the Holy Spirit and the anointing of the Holy Spirit he goes to Acts 2 and he starts preaching about that you know rushing mighty wind and suddenly the rush of rushing mighty wind and the atmosphere was so calm and suddenly there's a rushing mighty wind to the point where his mic is also not standing you know everything is shaking and somebody had recorded this and put it up on social media that only at the point when he starts speaking about the rushing mighty wind the atmosphere goes from calm to you know real powerful winds upon the meeting just in just when he's talking about the Holy Spirit so these are just manifestations sometimes where you know God shows his pleasure or his agreement to what his people are praying and it was one such time where you know they prayed for boldness and you know God gave them that boldness so what is the result of their prayer God answered their prayer so it also says that they were filled with the Holy Spirit they spoke the word of God with boldness now some of the features of the early church are listed out for us in the last section of this chapter I would really request all of us to be ready to read the scriptures because in this class I think a few of our students have repeatedly read and they're quite long passages so it's nice if we can share the responsibility and be prepared to read sections so I request someone to go ahead and read please from verse 32 to verse 37 now the multitude of those who believe fear of one heart and one soul neither did anyone say that any of these hip process was his own but they had all things in common and with great power the apostle gave fitness to to the resurrection of the Lord Jesus and great grace was upon them all nor was there any one among them who laid for all who were possessors of lands or houses sold them and brought the proceeds of the things that were sold and laid them at the Apostles field and they distributed to each as anyone has need has need and Joseph who was also named Barnabas by the Apostles which is translated son of encouragement levite of the country of Cyprus having land sold it and brought the money and laid it at the Apostles feet yes thank you Zellie we notice here that the church continued strong they were in one accord again because the instead of one accord we see words like one heart one soul that simply means wonders among them and we see similar features as we saw in Acts chapter 2 where the church is strong in spiritual matters so we see great grace was upon them all and you know great power the apostle gave witness to the resurrection of the Lord Jesus Christ so this is all the spiritual aspects there is great power there is great grace and we saw earlier that even in the natural aspects of caring taking care of people they were quite good and the same way they are continuing we see that nobody lacked among them which just goes to say that whatever needs people had the leadership was doing the best that they knew how to take care of those needs and again incredible generosity to the point where people were what does say they were even selling their things to provide for the needs of the people there were possessions that they sold to lay them at the Apostles feet what is the meaning of that the meaning is that they were ready to provide to the church to meet all the needs of the church so if it is something like a treasury of the church people are willing to give it to it so that the work of God can go on so we see both the aspects or the spiritual aspects being so strong in the church as well as the natural aspects so you know it's a wonderful church it's a strong church it's a growing church and it's revealing reflecting the very heart of God so somewhere there is this glorious image of the church that we have right now and it's also a very rosy picture that oh I wish I was a part of the early church that existed from acts two to acts four because nothing seems to be wrong in this church right everything seems to be so beautiful and so correct but please hold on we'll go to acts chapter six and you'll see where there are people there shall be problems right so there are problems that the apostles we do solves that there will arise challenges when we work with people in the church but it's it is the responsibility of the leadership to resolve it with the power of God and that is another wonderful testimony of leaders that we will see so yes there will be challenges when you have to grow the work of God but by the power of the spirit by the wisdom of the spirit we need to see how to address those matters how to bring solution to the problems that may occur because we are dealing with people and there are all kinds of needs all kinds of issues that crop up and nuke will start to present more and more people as we move ahead from here so so far the focus lights were on Peter suddenly you know spotlights on Peter then acts chapter three John also comes into the spotlight Peter and John as if they were the men that the church looked up to and now there's another introduction they talk about Luke talks about Barnabas okay Barnabas who's this there's a small description about Barnabas over here and Joseph who was also named Barnabas but commonly we will use the name Barnabas by the apostles he was a Levite and he hailed from Cyprus what is what is his personality like having land he sold it and brought the money and made it at the apostles feet so he was a generous Christian that's what we understand he was not just generous but saying that he's a Levite also shows us that he was you know sort of like educated and quite respected in the community so you can think about all that so here is Barnabas and the apostles are named named him Barnabas because he's the son of encouragement so maybe that personality he was a very positive individual then another thing that you can add to this description is he was rich having land it says he sold it so overall when we think about Barnabas we think oh you know a really respected man in that early church is who Barnabas was so there is an introduction about Barnabas but you don't see too much you know beyond this right now but as we carry on we will notice you know how Barnabas will come to the spotlight and then eventually you know the spotlight will move to Paul but we'll have to hold on till such time and we'll see what really happens in Acts chapter 5 so maybe what we can do is I'm thinking we can just have some thoughts and some sharing right now and wrap up with what we have learned so far we'll start with Acts chapter 5 in the next class so yes whatever has touched you impacted you you want to share please feel free and go ahead so in Acts chapter 4 we see I mean in 3 we see Peter using the name of Jesus and in Acts chapter 4 there's a verse where they ask them to stop speaking in the name of Jesus and it just surprised me that they don't want them to stop preaching actually but they want them to stop preaching in the name of Jesus that that really stood out to me like it's not like they're against preaching they are they're okay with preaching if you want to preach something if you want to do some miraculous signs maybe they I feel like they're okay with it but only when the name of Jesus comes in that's when they are not okay with it and it's it's quite scary to know like they didn't really want to ban it or like you just stop it so that makes me feel how important it is how powerful is the name of Jesus that there was one point that they really want to stop it and sometimes I feel like sometimes we should just look deeper into the Bible we got very used to this in the name of Jesus I pray amen it's it became a routine for us to say those words and but sometimes we should just pause and think what we are actually saying and what's the part behind it because we are being Christian for a long time and sometimes things just becomes a routine things it's become like it's normal to say that but there is a great part behind every words that we speak there is a history behind there's a reason and there's a there's a lot of struggles behind what we have got today in the name of Jesus through Jesus so that just made me stood in all with me pause and think okay I should be I should know what else we can I should understand the power behind it and I think it should apply for each and everything that we do the worship the praise the words everywhere we should really try to get deeper into the scripture understand the power behind it yes sir Jatina thank you so much for sharing as you rightly pointed out they were against that name because it's it's not just like as I said politically and you know religious terms it was a threat threat to them but we know in Ephesians chapter 6 and verse 12 it says that we wrestle not against flesh and blood but against you know principalities powers of rumors of wickedness and so it's enlisting to us spiritual warfare and enlisting the powers of who are opposing us so we know that satan will try to oppose the work of God no matter where we are and at what point we are he just doesn't want us to spread God's word he will come against the work of God and that's a given it's just that how the apostles and the early church sought God's strength and you know declared their dependence on God they declared the word of God and they asked for more boldness to continue with God's work in the same way I think we should depend so much on God that's the only way to move forward yeah thank you yeah anything else that others want to share in verse 13 they now when they saw the boldness of Peter and John perceived that they were uneducated and untrained men they marvel and they realized that they had been with Jesus that was something which stuck me because you know we become what we behold and people also notice that and you know the background check everything they would have done about Peter and John or they are from this background they are from that background but once they started speaking the boldness and also the way they handled the situation they knew that they were with Jesus which which stood out other than the the background of Peter and John yeah just wanted to add that yeah thanks God yeah thank you John yeah that's so beautiful so that what made a difference to them is the fact that they were with Jesus beyond any other credentials that they could have had the fact that they were with Jesus made them bold and made them so powerful before the council so that's that's amazing sure so yeah thank you John thank you Jafina thank you class please continue to think about these matters and let's pray and trust God to really impact us as we go through the rest of this book so at this point we are going to pray and close and I will request Jafina to please pray that's great J heavenly Father we come to under the name of Jesus we thank you for this day we thank you for the class that we had we thank you for the acts that you do through your people Jesus thank you for taking up the cross for us thank you for saving us thank you for giving us this authority to use your name Jesus but I just pray for all my classmates and pastor and say right now as we teach as we discuss as we keep reading the scriptures help us to apply it in our life Jesus above all not just listening to it but just putting every verse into practice so that we can move powerfully for you down here on this earth so that people will know that it's not the education it's because they're with Jesus it's not their talents but because Jesus is with them and they are with Jesus they have a relationship with him God help us to reflect you more in a better way through our actions as we read this acts let everything be done for your glory we give you all the glory and honor and Jesus name we pray amen amen thank you Jafina thank you everyone God bless you have a wonderful weekend we shall meet next week bye thank you


In this video, I want to solve an exponential equation, but one of the very different type than we saw previously. This equation is an example of what one often calls an equation of quadratic type. Or you could say it's like a quadratic-like equation. So what do you mean by that? What does it mean to be like quadratic-like? Well, the idea here is that a quadratic equation usually looks like something like ax squared plus bx plus c equals c, or it's something equivalent to that. But why not? It doesn't have to be the variable x, right? We could use any variable we want. So what if we call just, you know, let's pick a variable that we don't usually use.  Like I said, u is a variable we often don't use. We usually like to use things like x, y, and z. Also, it makes for some very interesting, grammatically correct, but awkward English statements when I say things like, oh, u is five. You know, that makes people go crazy. But a quadratic-like equation is gonna be the following idea that if you make the substitution, you're gonna make the substitution, let's say u equals f of x, and you put it into some equation, and you end up with something like the following. This is what we mean by a quadratic-like equation. And so what I claim here is that this equation you see on the screen is quadratic-like. But what's my u? It's gonna be a function of x right here. So I'm gonna make a substitution of the variables. Sometimes it's called the u-substitution, for which I'm gonna make the substitution u equals two to the x, okay? So if you do that, notice what you see is the following. We'll worry about the four to the x in just a second. But you see that negative two to the x, that just becomes a u. You have a minus 12, that's constant equals a zero. So how do you do with the four to the x? Well, this is the fun part here. When you take four to the x, four to the x by x one rule, notice that four is two squared. So this is really just two to the two to the x, which by x one of the rules, this is the same thing as two to the two x, like so. But on the other hand, if I were to take two to the x squared, this is equal to two to the two x. Notice the two things are equal to each other. So in general, right, this is a pretty neat little trick right here. If you have a to the x right here and you square it, this is the same thing as just a squared to the x, all right? So here we had two to the x as our u, then that means four to the x right here. Turns out that's just your u squared. If I took u to be three to the x, then u squared is gonna equal nine to the x. And so, you know, if u was four to the x, you'd end up with u squared being six to the x, something like that. And so that's a nice little recognition so that we can actually identify quadratic like equations when exponentials are involved very, very quickly. So coming back to our four to the x over here, we see that the four to the x is actually just u squared. And so with that perspective, you made this little u substitution over here. We see that, I'm gonna put a little different color so we can come back to it. This is something we wanna remember. By just changing the variables from x to u, you didn't see that this equation right here is essentially just a quadratic equation. We have a u squared minus u minus 12 equals zero. We can solve this like any other quadratic equation, which I'm just gonna do it by factors, factoring here. We need factors of negative 12 that have to be negative one. I can take u minus four and u plus three, right? Notice negative four times three is a negative 12, but negative four plus three is negative one. So we have the correct factorization there.  Now, sometimes we get so excited about solving the quadratic equation. We forget that we made a u substitution here. We have to go back to the original variable, right? We have to go back to this u statement right here. So what this tells us is that if u equals four, that means two to the x is four. And if u equals negative three, that means two to the x equals negative three. Now on the left-hand side, there's a couple of things you could do. You could solve this by using a logarithm if you wanted to. This was not too hard to see, right? What power of two gives you four? Well, that's the second power. So that would tell me that x equals two because again, x squared equals four. On the right, the second one though, two to the x equals negative three. Well, remember the domain of an exponential function like two to the x is actually gonna be all positive numbers. Excuse me, not the domain, I meant to say the range. The domain is all real numbers. The range of two to the x, this is gonna be all positive numbers. So in fact, you can't have an exponential equal a negative when your input is a real number. So it turns out there's no solution that comes from this situation right here. So we can just get one solution and thus it turns out to be x equals two. And so we showed you how to show in this video how to solve a quadratic equation when your u substitution is an exponential function. But this idea works in general that if you can find u equals some f of x, right? And you make that substitution, you get this quadratic equation. Solve the quadratic equation, you're gonna get two solutions and then you have to solve the equations f of x equals the first solution and then f of x equals the second solution, which we did that with exponentials in this case.


Hello everyone, myself Dr. Diwali Vittal Trimukhi, I am first year junior resident in department of radio diagnosis in BKL Malavalkar, rural medical college Pratnagiri.  My topic is a case report of radiological manifestation of testicular tumour with metastasis. So testicular tumour represents 1% of all cancer in men. It is most common malignancy affecting young men of 20 to 34 years age group. Various risk factors includes undecended testis, testicular atrophy, client-reader syndrome, family history, history of any radiation, previous history of contralateral testicular tumour. This presentation is weight discomfort or painless mass in scrotum. Testicular tumours are divided into germ cell and non germ cell tumours. So to begin with my case, 63 year old male presented to surgery OPD with chief complaint of painless swelling in left scrotum since 6 months. Swelling was initially small which gradually increased in size, patient also has history of weight loss and loss of appetite since 6 months. Patient also has complaint of curve with expectoration. Since 6 months there is no history of pain in scrotum. Patient is a tobacco chewer since 40 years. On local examination, swelling is present in left scrotum, measuring about 10 x 6 cm. Its consistency is hard, it is non reducible and curve impulse is absent. With this clinical background, patient was subjected to radiological investigation which included chest x-ray, city abdopelvis and city chest. So this is chest x-ray PA view where we can see multiple rounded soft tissue density radio opacities of varying sizes seen scattered in both lung fills. This is city abdomen pelvis, axial and coronal section where we can see a well defined large oval shaped soft tissue density mass seen arising in left testis on post contrast. It shows heterogeneous enhancement, it shows calcipic pokai within, it also shows few hypodense areas within which are suggestive of necrosis, collection is also seen surrounding this lesion, lymph nodes are noted in pre aortic and retrocaval region, findings are likely suggestive of neoplastic etiology of testis with metastatic mediastinal lymph adenopathy. This is axial section and coronal section of high resolution city, chest and plain city chest which reveals multiple well defined heterogeneous soft tissue nodules predominantly in right lower lobe of the lung, few of them shows cavitation within, features are most likely suggestive of metastasis to lung. So biopsy was done and on histopathological examination the mass lesion shows features of seminometous germ cell tumour, based on the clinical history integrated with radiological and histological findings my diagnosis is seminoma of left testis with metastasis to lung and metastatic mediastinal lymph adenopathy, patient underwent surgical procedure which included high orchidic tommy along with chemotherapy. So testicular tumour is uncommon accounting for less than 1% of all internal organ malignancy. The commonest histology of the tumours vary with age of the affected individual. In first ticket, predominantly we can see yokes at tumour and testicular teratoma. Second decade there is predominance of coriocasinoma, in third decade predominance of embryonal cell casinoma is seen, in fourth decade there is predominance of seminoma and in more than seventh decade lymphoma, usually non-Hodgkin's lymphoma and permatocytic seminoma are common. So testicular tumour are classified into primary tumours and secondary tumours, primary tumours are further classified into germ cell tumour and non-germ cell tumour, germ cell tumour includes seminometre's germ cell tumour and non-seminometre's germ cell tumour, amongst non-seminometre's germ cell tumour it includes embryonal cell casinoma, yokes at tumour, poriocasinoma, teratoma, mixed germ cell tumour. In normed germ cell tumour it includes sertoli cell tumour, leading cell tumour, granulose cell tumour, fibromathecoma of testis and amongst the secondary tumours it includes secondary testicular lymphoma, testicular leukemia and metastasis to testis. So the spread is to the regional lymph nodes which includes aotokaval, para-aotic, para-caval, pre-aotic, pre-caval, retro-aotic and retro-caval lymph node groups and metastasis of this testicular casinoma is via lymphatic system to lung, liver, bone and other visceral sides. So on conclusion, imaging techniques which in my case included chest radiograph, city chest, city abdomen and pelvis plays a crucial role not only in diagnosis but also in staging and response assessment. Thank you.


Hey everyone, welcome to Las Vegas. Lisa Martin here on the ground with the queue about Koopa Inspire 2022. And can you hear the buzz behind me? It is so great to be in person. Nick Bonich joins me, the Chief Revenue Officer and Global Partnership Manager for the Koopa Alliance at MiBot Consulting. Nick, it's great to have you on the program. Thanks for having me, Lisa. First time here at Inspire and it's exciting. Is it exciting? It's great to see this room packed. It is. It feels like the pandemic is finally maybe behind us. Right? Fingers crossed. Talk to us a little bit about MiBot Consulting and a little bit about the Koopa partnerships that the audience gets that understanding of what you guys do. Yeah, I guess we're kind of new to the Koopa ecosystem. You could say we came as part of the acquisition of Lamasoft. So MiBot is a supply chain focus advisory consultancy engineering firm. So we have three different business lines, supply chain strategy, where we do things like supply chain design in the Koopa platform planning inventory, engineering, automation studies and distribution centers with the labor crunch that we're facing right now, as well as we have a digital transformation group that works on getting the decision-making as a supply chain industry into the digital realm and away from Microsoft Excel. Let's talk about the digitization of the supply chain. You know, one of the things that we've seen in the last couple of years is this massive acceleration to digital because businesses in every industry had no choice. But where are, what are the current trends from a digital supply chain perspective? You know, I think the kind of the integration of the compression of the decision-making cycle has really gotten companies to not look at strategic decisions, then operational decisions and tactical decisions and execution. That all has to be compressed now with the volatility we've all been exposed to. I mean, basically for the past 20 years we took the supply chain and turned it into a Swiss watch. It was very long, but very well orchestrated. But with the volatility, with labor issues, with the land war in Europe, this volatility and change is requiring companies to be much more adaptive and they've had to compress that decision cycle down. And the Koopa platform, certainly from a supply chain standpoint, absolutely helps infuse that process to shorten time from question to answer and allow you to address strategic and tactical topics in parallel to one another and not kind of waterfall down over the decision-making process. That's important because these days there is no time for waterfalls. So let's unpack the Koopa supply chain design platform. Talk to me about it, what it does, and how it is helping that acceleration. Yeah, so it's incredibly powerful. And what it allows you to do is create that digital representation. We can take a three-dimensional world and put it into a two-dimensional linear program. And within the same platform we can optimize strategically and take a look at end-to-end type of supply chain decisions, near-shoring, on-shoring, supplier diversification and risk aspects. We can look at it more operationally. We're actually looking at which manufacturing plants should make what? What distribution centers should serve what customers? How do I segment my products? How do I segment my customers? Then within the same modules you can use and go to your inventory optimization. Not only optimize inventory but also simulate it, which gives you phenomenal power in a world where there is so much uncertainty, you can apply risk and those questions of what if, so you're ready. So that way when the thing happens you're not then scrambling to have analysts crunch excel files to see what do you do to normalize inventory levels or normalize your supplier base, you're able to be more proactive with the predictive and prescriptive analytics that the full suite provides for you. That is essential. If that's one of the lessons we've learned in the last couple of years. Not if, but when. Yes. Talk to me about customers that are using the platform. What are some of the, using it well? What are some of the things that they have in common? You know, I think the organizations that are implementing it well look for it. They view it as a real platform. You know, historically supply chain design, network optimization was seen as a tool and companies implemented it as a tool. You purchased licenses, you assigned a couple of people to work on it from your analytical department and you just went with it. This is a very powerful platform to completely revolutionize how you make decisions within your supply chain. And you need to approach it the same way you approach a new warehouse management system, a new planning platform, a new labor management system, the change management aspects, the organizational aspects, the education of stakeholders on what is this, demystifying it so it's not a black box and everybody knows what it can and should do and how best to utilize it. So those organizations that view it as more than a distribution network tool, hey, where do I put my new warehouse? Hey, this lease is coming up in Central Europe, it's coming up in Ohio. Do I extend the lease? Do I need to move? That's like a level zero maturity on our maturity graph. The very mature companies are using it and infusing it both strategically, operational technically and are using it for distribution decisions, transportation decisions around mode selection, production footprint decisions. You have the capability to have a digital twin and by having the other thing companies struggle with is they just build one model. I start out, I buy the product, I get it built in, I move everything to the cloud and then I do a distribution solve for the US. And then the European group says, hey, that was great, that was insightful, can we do the same thing in Europe? And you take that model and then you add Europe into it. And then the production group says, hey, you know, we're thinking about changing some of our make by decisions. Can you model what the effect would be on total cost if we did do some nearshoring? And all of a sudden you turn your one model that you had built for a specific purpose into this Christmas tree where everybody's hanging their ornaments. And what you really need to do is having modeling strategy. What type, you should have a volume, a portfolio of models you can pull from and say, hey, here's our strategic end model. Hey, here's our tactical Asian production models. Hey, here's our total ended cost for top 15% of our customers. And having that set of models, so you have right models to write questions, that's what the companies that are really scaling this and really excelling. And you'll notice a pattern. The companies that are excelling that have the Koopa platform, typically you'll find them on lists like Gartner's Top 25 and things along those lines because it is a very powerful platform when you unlock the art of the possible with it. Sounds like those are companies that are very innovative but where does a company that maybe isn't there yet, how did they start? Because it sounds like there's a tremendous wealth of potential and opportunities that the technology can deliver. Do they have to start with executive buy-in? What do you see as kind of like some of those early steps? This is a change management exercise from the very beginning. So creating that sense of urgency, creating your powerful coalition, you have to start with that. If you view this as, hey, we're going to have a tool, we're going to use this once and then our supply chain's fixed for the next 10 years. I mean, I think most leaders are realizing that those days are long gone that supply chain design has to be a continual topic at the top levels. Supply chain is on the lips of every politician and every board member right now. So this is a wonderful moment for those supply chain leaders that have wanted to infuse a greater level of digital decision making. This is the perfect opportunity. You can get buy-in like you've never had before. Your CFO is probably analyzing labor inflation, fuel inflation rates, disruptions on supply base and you're probably having to deal with the more pressure out of the CFO and his department than you ever had to in the past. We see it with our clients. The pressure is on with those leaders and this allows you to very quickly be much more holistic in that decision making. You're not relying on how good was the analyst that made this Excel file that told you to open up this plant, move this distribution center, serve this customer base in this way. It's not based on how that data looks and how good that analyst was. You're infusing an entire practice into your organization. That's critical because every company these days is a data company. If they're not, they're not going to be around. It's about the ability to have visibility, extract the value from the data to make those data driven decisions because we don't have time. We heard a lot about that from a real time perspective in the keynote this morning. That's table stakes for any organization. Yeah and with the move of the platform to the cloud, as part of the Coupa ecosystem, with the DDM, with the rapid model builder and all those things that come along with it, it will significantly quash the amount of time you have from question to answer. Because the first time you do this, it probably takes four months. And of that four months to ask that question and get an answer, build your model, replicate the 3D world in that 2D environment, over half of that time is spent on cleaning data, building the baseline model, aligning with finance. They peanut butter spread certain aspects of cost onto SKUs and really getting correct cost allocations for A, B, and C SKUs. You spend half your time just playing around with your data to get the model to work right now. Once you have that model, next time, question to answer infinitely quicker, but you have to have a good data strategy. You have to have the right data architecture. If you don't have that specific to supply chain, leaders really need to get on that. Because what we see a lot of times is, organizations will have an enterprise data strategy and they're going to build a data warehouse or a data lake, whatever, I'm a consultant so I'm also guilty of the buzzwords. But we kind of call it the supply chain data pun. You don't need to wait for the whole enterprise to get ready to have all of your data sorted out in a single instance, homogenized, start collecting that supply chain data, have a data strategy around it so that way you can start replicating these things. Then you can feed it back into the enterprise data strategy, but you have to get your data right.  It's still true to this day no matter how powerful the analytical tools are. We're infusing machine learning, artificial intelligence and some of the solves in the platform. But if you don't have that good data, you're going to struggle. So that's a key piece to it. Getting that executive buy-in and having that right data strategy will set you on a much smoother path to success than if you don't do those things. Right, the data strategy is critical. If not one of the biggest competitive differentiators these days. Where is the chief data officer, the chief digital officer, the chief information officer in these conversations that Mibach is having with customers? Too often not at the forefront enough. Really? Those clients that have that group, have that organization and they have influencing power, those programs go much quicker, much simpler. The rate of adoption, the scalability of the program. All of a sudden you're not thinking about what am I going to do with one or two analysts interacting with the product. You're now developing apps. You have your planners interfacing with it. You have capacity managers interacting with the digital model. Those that don't have that do have much more impetus because it's always the adage of well IT and what do we do and our data's a mess. We have this data program and our IT resources are super constrained. So you have to bring those people to the table. You have to have them part of the conversation because they can be an incredible enabler if you bring them and get them bought in. That's a great point of those enablers and especially given the fact that nobody has extra time to waste here. This is, everything is so fast moving. You mentioned supply chain being on the lips of every politician. Some, everybody's lips. Everybody's expecting some delivery that is delayed for whatever reason. I mean, 12 years ago when I started with the firm and people, oh what is the firm doing? I'm like, oh, we're a global supply chain consultancy and they're like, what? Yeah. Now everybody knows and they're like, oh, it's amazing that the revolution, I mean the pandemic has been incredibly unfortunate with all the hardships and deaths and everything and still dealing with hotspots and things. I think it did bring supply chain. Supply chain was struggling for a while to get a seat at the table. Organization started having chief supply chain officers. That was a new thing, not that long ago. This has brought table stakes to the supply chain organization. My challenge back to us is, what do we do with this now? For years as an industry, we've asked to be at the table. We're here now. Spotlight's on us. It's time for us to deliver. Things like the KUPA platform are an incredible enabler of that. But you got to get it right when you roll it out. The spotlight's on you, but there's also a skills shortage. Talk to me about that. I just saw you do a big sigh. How can Meebok and KUPA with this platform help to mitigate some of the supply chain skills gap that organizations in every industry are facing? You know, it really comes down to the human element and when people talk a lot about sustainability, they talk about environmental conditions. There's a human sustainability topic we have to cover.  No, that's not an enjoyable, fulfilling task for many people. There are special people that it is and God bless them. So with things like the apps, with things like building out so that way we can take the people that you do have and have them making decisions, driving discussions around the insights the platform's giving versus just crunching numbers and building models. You know, this is where you're going to have a much higher retainment. People are going to be excited about the job. They're going to have fun at the job because you do see a turnover of organizations that don't get the data strategy right that people don't like being in a supply chain center of excellence and perpetuity. Again, there are certain people that are, but a lot of times once people get this analytical insight to how strategically the design of the company is set up, business units will grab them and give them a significant role and then you're continually churning and replacing your COE talent. So having a talent strategy for your COE and having a strategy of how you're going to leverage, you know, we're in a world where my first graders learn in coding, right? Like you need to have a data strategy so that way that becomes your people strategy as well.  What are the projects we're going to do? And not often enough do they talk about the people element of it to really make this work. And it absolutely has to be part of the discussion as you're setting up your center of excellence. It's people, it's processes, and it's technology. Absolutely. You got to bring those three together or you will struggle a bit. You do. And change management is not an easy thing to do for anybody, but one of the things you talked about this is the pandemic as an accelerator of getting the supply chain folks to the table, being able to accelerate, getting data into the hands of people that can actually take in clean insights and make decisions based on that. So if you look into a crystal ball, what's the future of supply chain design? Where is it going? I believe we're going to see a lot more of movement towards applications and infusing of artificial intelligence and machine learning. It's there, it's ready to go. What a lot of companies are lacking, and it goes back to what we already talked about is the data piece of it. I mean, we have been developing algorithms in a machine learning environment for three, four years now.  So I think it's going to be a big element of supply chain talent, securing that, figuring out with robotic process automation and things like that. How do you take non-value added work so you can take the talent you do have and give them more fulfilling work? I think companies are going to need to have data strategies and all that unlocks applications and things so you can democratize, right? You have this digital twin in the cloud. How many people within the organization cross-functionally have questions about the supply chain? What if this happens? What if that happens? Hey, if we do this, what does it affect upstream downstream? So once you build that cloud to develop the applications that allow the entire enterprise to interface with this digital representation to play around and see what the effect is to then make better, more informed, more holistic decisions, drive more conversational cross-functionally amongst leaders, and even below the top leadership level. I think this is really where we're going to go and the companies that don't just survive but thrive in this new normal, whatever that's going to be, is going to be the companies that get that right. They have to embrace that. They have to embrace it. Nick, it's been great having you on the program, talking about supply chain, what's going on there, the accelerators, but also the opportunities. Thank you so much for sharing your insight. I appreciate the opportunity. So it's been a great conversation. I look forward to the rest of the event. I agree. For Nick Bonich, I'm Lisa Martin on the ground in Las Vegas at Coupa Inspire 2022. Stick around. I'll be back with my next guest shortly.


Nice little touch from Nezha, and here's Alhazan Turei, who's lost a boot, but managed to pick out a fantastic cross on the save. And Craig Noon, with a wonderful goal. MacArthur have the early lead and some home cheer as well. They're back at Campbelltown Stadium, and they're in front. Now Nezha gets it in, and Tratos floats it back post. It's well-played, Mochella with the... Time and space for Mochella at the back post,