I promise you that this video isn't boring. I know, you may have seen this before, but maybe not this color combo. I'm telling you, it's gonna get better. Just wait for it. Just wait, okay? This is me just being really happy about making this piece. It has sold already, but you can find more on my website. And ooh, look at that, see? Now I gotta spin it. Let me spin it. Spinny spin, spin, spin, spin, spin, spin, spin and stop. And ooh, yes. Link in bio, bro.


with that said. Let's begin reading together here in the book of Acts and before we read, I'll say one more thing in preparation for our study. I've already mentioned this before, I'll mention it again. What I've chosen to do, at least for a while as we go through this this book, and again I don't even know that I'll take you through the entire book of Acts, I do know that I want to take you for a while through it, but what I've been doing is taking kind of a snapshot from a chapter. Today's snapshot is going to come out of chapter 6, but in order to get you to that portion so that we have an understanding of what is taking place in that chapter, what I'm doing is I'm summarizing some of the previous events and verses that lead up to chapter 6. That's how I'm going to begin this study, so that you have a background and you understand, you know, as we read through the Bible, why did this particular thing take place? How is it that these events were recorded and what's the reason for them? And so I'm going to summarize some of the verses in chapter 5, and then I'll take you into chapter 6, and we're going to be looking today at verses 1 through 7. And so that's how it's going to be, and hopefully you'll be able to see why I'm doing that as I go through the portion of Scripture. So let me begin reading to you here in Acts chapter 6 at verse 1, and I'll read to verse 7, and we'll get into our study. Acts chapter 6, beginning at verse 1, reading to verse 7. Luke writes, Now in those days, when the number of the disciples was multiplying, there arose a complaint against the Hebrews by the Hellenists, because their winnows were neglected in the daily distribution. Then the twelve summoned the multitude of the disciples and said, It is not desirable that we should leave the Word of God and serve tables, therefore brethren, seek out from among you seven men of good reputation, full of the Holy Spirit and wisdom, whom we may appoint over this business, but we will give ourselves continually to prayer and to the ministry of the Word.  And when they had prayed, they laid hands on them. Then the Word of God spread, and the number of the disciples multiplied greatly in Jerusalem, and a great many of the priests were obedient to the faith. And so we've already looked at a portion of Scripture that gave us a very clear insight into how Satan had attempted to infect the church with sin. Ananias and Sapphira, a husband and a wife, had joined with the group of believers. Now they had seen how believers were caring for those who were poor, those who were in need. You see, believers were selling properties. They were distributing to those who had need. So at that time a disciple named Barnabas was introduced to us. Now Luke mentioned that he had sold land and given the proceeds to the church. So it seems that the honor he had received for doing so exposed the hearts of Ananias and Sapphira. So they conspired together to give an amount to the church after they had sold a parcel of land, but they kept the rest for themselves. You see, as we saw Peter was given discernment by the Lord, and he confronted them. And as a result of that, both of them died, and great fear came upon the church and amongst all those who had heard. Now after that took place the purging of this, this sin that was attempted to infiltrate into the life of the church, after they died, God began moving again in amazing ways through the apostles. Acts 5 12 tells us that the apostles performed many signs and wonders, and those works were impacting people deeply. It says in chapter 5 verse 13 that none of the rest dared join them, but the people esteemed them highly. So those who weren't converted to Christ didn't dare pretend that they were, and the immediate judgment separated the hypocrites from those who were really followers of Christ. And so the genuine believers were drawn closer together, and the unbelievers didn't pretend to be saved, but they greatly respected those who were genuine in their faith. Now in chapter 5, again verses 14 through 16, those verses tell us that God began moving mightily through the hands of the apostles, and Luke stopped giving us the numbers of new believers. He simply began to use the word multitude, and he began speaking of the multitudes of those who were being saved. Now Acts 5 14 says believers were increasingly added to the Lord multitudes of both men and women. And so what happened is people began to bring the sick into the streets, and they were laying them on beds and couches. They knew the root that the apostle Peter and the rest would take, and they were hoping that that Peter especially would pass by them, that even if his shadow fell upon them, they might be healed.  Luke tells us they were all healed. Now that led to an angry response by the religious authorities because they had forbidden the apostles from preaching in the name of Jesus, and this command had not stopped them from continuing their ministry. So the high priest, being a Sadducee, was angered. They were saying that Jesus was resurrected. This exposed their error. He had undermined their standing and challenged their authority in the community. So he had the 12 apostles arrested, and he placed them in what is called a common prison. But at night an angel opened the prison doors and brought them out, and he told them, stand in the temple and preach the words of this life. Now the words of this life would speak of the gospel and the eternal life that comes to faith in Christ. So they weren't just released from jail to go on with their lives. They were released to preach others about eternal life so that they could be released from their spiritual jails.  So preach so that these who are under the wrath and the condemnation and ultimate judgment of God can be set free, and that's what they were doing. So they went to the temple as they had been commanded. They began to teach the people. Well when this happens the high priest calls the council together, but he didn't know what was going on yet, and when they heard what was happening and somehow they had gotten out of jail, he was bewildered. As he was wondering about it, he was told that they were there in the temple, and he ordered the captain of the temple to arrest them, but he did so without incident because he was afraid of the people's reaction if they were taken by force.  You also intend to bring this man's blood on us. Well their response lays a foundation for generations of followers of Jesus. You see, they had seen God move in marvelous ways. Miraculous healings had taken place. Demons had been cast out. People were lining their sick on the streets. They were being healed. An angel busted them out of jail. How many times did you shout what happened to you? I'll wait for a moment. You cons. So an angel broke us out, and you're saying we need to stop serving God. Well we all can learn something from their united response to the commands of the high priest in chapter 5 verse 29. Peter and the other apostles answered and said, we ought to obey God rather than men. So instead of remaining silent, Peter boldly spoke to the high priest. Look what it says in verse 30 in chapter 5.  Him God has exalted to his right hand to be prince and savior, to give repentance to Israel and forgiveness of sins. And we are his witnesses to these things. And so also is the Holy Spirit whom God has given to those who obey him. And so he makes it very, very clear. We ought to obey God rather than men. We are his witnesses. The works that have been performed proves it. We have obeyed him and through our hands he has demonstrated this clearly and therefore we will continue to obey him and we refuse to obey your command to stop preaching. Well that infuriated the council they wanted to execute the apostles. But there was a respected teacher, a man by the name of Gamaliel, and he cautioned them against doing this. Now this man, Gamaliel, is mentioned in Scripture, he was Paul's, he was Paul's teacher. He was very highly respected in the nation of Israel. One thing needs to be mentioned about him. He was a Pharisee. Now the Sadducees did not believe in resurrection or spirits, but Gamaliel was a Pharisee and he did. His reputation was so great that he was listened to.  What was their response? Well verse 41 and 42 says in chapter 5, they departed from the presence of the council rejoicing that they were counted worthy to suffer shame for his name. Daily in the temple and in every house they did not cease teaching and preaching Jesus as the Christ. You need to keep that in mind because as we get into chapter 6, I'm going to return to that thought and we'll be looking at that. But they rejoiced that they were worthy to suffer shame for Christ. They were prepared for this. Jesus had prepared for them for the coming persecution. He had made it clear that this would take place. They had been forewarned and were prepared for this treatment. And that's what gave them strength to endure the beating that they went through. And so all of this is taking place as we come up to chapter 6. And so in chapter 6, I'll begin here at verse 1 and it says, Now in those days when the number of the disciples was multiplying, there arose a complaint against the Hebrews by the Hellenists because their widows were neglected in the daily distribution. Let me share some things about that to set this up for you. Even though they had been threatened, they continued their ministry. They continued preaching, they continued teaching. Why? Because they obeyed God rather than men. And as a result of that, the church continued to grow. So they continued preaching, they continued teaching, and people continued getting saved. Now the church is busy growing now and as it's growing, strife surfaces. Now on the surface, it appears to be financial. There's a dispute going on, as it says in verse 1, a complaint against the Hebrews and the Hellenists because their widows were neglected in the daily distribution. On the surface, it appears to be financial in nature, but it's much deeper than that. Now at the time, many believers were suffering financial hardship. And as is true even in our day, with growth comes challenge. Thousands were being saved. Growing numbers had needs. And that's something, by the way, that didn't cease at the beginning of the church. It continued on for some time. When you read the book of Romans, which was written probably about 25 or so years after this particular chapter is in four minutes of what took place. So it's about 25 years. There are people who are poor in need. Well, when Paul was writing to the Romans in chapter 15, verses 25 and 26, he said this. He said, I'm going to Jerusalem to minister to the saints for it, please those from Macedonia and Achaia to make a certain contribution for the poor among the saints who are in Jerusalem. And so there was a continuance of this need, this financial need. And so it began then, but it continued on for many, many years. And so what had happened, and we've already seen this in chapters two and four, is there was what we today would refer to as a general fund that had been set up to care for the needs of the poor. In Acts two, 44 and 45, it said, all the believers were together and had everything in common, selling their possessions and goods they gave to anyone as he had need. Well, that developed to chapter four, verse 34 and 35, when it says, there were no needy persons among them. For from time to time, those who owned lands or houses sold them, brought the money from the sales and put at the apostles feet. It was distributed to anyone as he had need. So we saw that develop even at the point when Barnabas had sold parcel of land and given the proceeds. And that's what Ananias and Sapphira had tried to get in and get some honor from. The church is exploding. There are new believers. They stopped keeping records at 5,000, which didn't include women and children. So with the explosive growth, administrative situations to church needs began to exist. With a group of people, a church this size, it was inevitable that neglect would occur. And that's something Satan takes advantage of. He saw the growth. He'd already begun his attack. He'd already begun to move against them. He's seen what's happening. So he had instigated a sustained attack. And he began first by religion because persecution against the believers started really with religious people. It was from the outside. It started with the Sanhedrin. But then he began to attack through false believers and Ananias and Sapphira being a good example of that. That began from kind of like almost the inside. It was on fringe. They were pretending to be believers, but this new attack comes through dissension within the church. The problem is not with false believers. The problem is with genuine ones. You have the Hebrews and you have the Hellenists. They were genuine Christians. So what does he do? What does Satan do to destroy a work? He instigates division. That's what he does. He knows that with division, when people are not working in unity, that they can begin to quarrel amongst themselves and then he can undermine the work that God is doing. In Luke 11.17, Jesus said, any kingdom divided against itself will be ruined and a house divided against itself will fall. So division is one of the earliest tactics of Satan. When God is moving, the enemy tries to plant seeds of disunity so that he can undermine what's taking place. And that's what's taking place here. Notice verse 1, there arose a complaint against the Hebrews by the Hellenists. Now, Hellenists are Jews who were not born in Israel, but their language and their culture was Greek. Now, they're called in Scripture like in John 7.35, those who are of the dispersion. Or in James chapter 1 verse 1, they're spoken of as those who have been scattered abroad. They didn't necessarily speak Hebrew or Aramaic. They read their Scriptures not in the Hebrew, but in the Greek translation called the Septuagint. And so what's taking place is a cultural division. It's a cultural division between those who are believers in Christ. They were actually ethnically Jewish, if you will, but some were from different lands. And so those who are homegrown Hebrews had a problem with those of another culture. And so that's the division that Satan was trying to capitalize on. Now, how can I illustrate this? You may have, we'll say, an Irish background. You know, you have an Irish last name. You got red hair. You're Irish. You don't drink anymore, but you're Irish. So you go to Ireland and you expect to be welcomed with open arms by the Irish. And they look at you. They say, it's nice to see you. And you say, yeah, I'm home. And they say, no, you're an American. You're not Irish. You don't speak Gaelic. You're not Irish. You just call yourself that. And you get kind of like hurt like, no, I'm Irish and you do a little and or you may be French.   And in your mind, you're going to the motherland. Why? Because your last name is Garnier or whatever. And there you are. And they look at you and they say, you're an American. Or me, I'm a Mexican American. I go to Mexico and they don't say, you're Mexican. They say, you're an American because culturally, that's what I am. And so we have that kind of thing to this day where people will have their own culture and the way things are done here. And you show up and you do things differently. You don't speak our language. You don't know our culture. You don't know anything. Yeah, you celebrate Cinco de Mayo, but that doesn't count. And so they look at you in a different way, right? That's true. So in the United States, if you're like me, I'll use myself again as an example, Mexican heritage. But the Mexicans will say, no, you're American. But but the non Mexicans will say, you're Mexican. And well, that's that that doesn't stop. That was there. And the enemy, and this is the point I want to make. The enemy knows that if you can, if you can battle over these kinds of things, he can stop the work of God. That's why it is very important for us to say, I recognize my heritage. I love my ethnicity, if you will. I am who I am by the grace of God. I'm very pleased with that.  And as a child of God, I can have fellowship with anybody. That's the key. That's the key. And I believe right now, say this quickly, because you see it, if you watch the news at all, it's absolutely true. What I'm telling you, there is a division that is taking place right now where you are being pitted against other cultures and ethnicities. Right now, there's a word racism, racism, racism, which is very often just just actually watering down a word that at one time had real meaning. But it's being used as a tool to divide. If that enters a church, if people come in and sit down and look at that person next to him and say, that one's not like me, Satan is having his work performed by the body of Christ itself. And it's happened here. I'll say it quickly, but it has happened here where I've had people, I had a, years ago, I had a group come out, the Guchettas Brothers, and they had learned ministry here. They are part of our church. And we put them in our worship team. And I brought them up and I said, could you, I had told them before service, I said, could you sing a worship song in Spanish? Just because I think it's beautiful. Can you do that? Yeah, of course. And then I get a letter. This is the United States. This is America. Speak English.  Why'd you do that? It broke my heart. Be careful. That person who is seated next to you may not be part of your ethnic family, but they are your brother, your sister in Christ. Never forget that. Never forget that. And so that's what's taking place here. They're saying they're not like us. Now, what is the solution to this problem here? Well, these Hellenists had been converted, many of them, on Passover. They had remained in Jerusalem and they remained serving the church. And they wanted to learn about Christ. They wanted to learn from the apostles. Others were retirees from other lands. They were living out their last days in Israel. But because their widows were being neglected in the daily distribution, they were getting upset. Why is that? Well, caring for widows, rather, is part of the heritage of the Jew. It was expected by all. You can see in the Old Testament book of Deuteronomy in chapter 24 verses 19 through 21 that this is outlined about caring for widows. It's also seen in Deuteronomy 26-12 where it reads, When you've finished setting aside a tenth of all your produce in the third year, the year of the tithe, you shall give it to the Levite, the alien, the fatherless, and the widow, so that they may eat in your towns and be satisfied. You see, until this point, unity had been the norm in the body of Christ. They were united in Jesus and the Word of God. People were being saved. And with this growth, this rapid growth, neglect begins to occur. And that's why this complaint against the Hebrews came. Now, the word complaint is another way of saying murmuring. A complaint or murmuring is a secret displeasure that isn't openly spoken of. And it's always wrong because murmuring leads to division. And it seems that when God is blessing, the enemy does his best to destroy. And so he helps to provoke a division because it drains you of emotional and physical energy. It takes your eyes off of what is important and you lose your perspective. That's why Jesus would pray for unity. That's why when Peter, James, John, and others would have a bit of a debate about who's the greatest in the kingdom, that's why Jesus would shut that down and say, The greatest is a servant. It's not that you have special revelation or closer walk with me. You need to understand that the greatest is the one who serves all. So don't be putting yourself on some kind of pedestal. Why? Because division will divide. And God intends the church to be united, that we might love one another, that we might evangelize sharing. Because when you live in this unity, there's a blessing. When you promote love and care, God blesses you. That's why Psalm 133 verse 1 says how good and pleasant it is when brothers live together in unity. Be united in heart. Be united in vision. Be united in direction so you can reach the lost. Well, what happens is this comes to the apostle's attention. Notice verse 2. It says the 12 summoned the multitude of the disciples and said, This isn't, it is not desirable that we should leave the Word of God and serve tables. It is not desirable. This is unacceptable to leave the Word of God to deal in church business. When it says to wait on tables, he's not saying that service is to be disregarded. Waiting on tables is another way of speaking about church business. The word table, it speaks of a table or a stand that the money changers would use. And that's the point he's making. He used that word to say it's not right. It's not acceptable that we should stop praying and seeking God through His Word and begin to handle the financial situations here. Well, the need is legitimate, but it doesn't require an apostle to deal with it. You see, the apostle's time in the Word is now being jeopardized by church business and their ministry priority is to teach and to preach the Word of God. So they're not about to start stamping out church brush fires. Again, this is a typical temptation of the enemy. He distracts us with what we see as urgent and it takes our eyes off of what is necessary. I went to a conference many years ago now and the one who was teaching that I went to hear shared an illustration. And again, this has been over 35 years, but I brought it into my philosophy of ministry because I saw the biblical insight that he was attempting to give to us and it was this. He said, when Moses was leading the children of Israel out of Egyptian bondage, his father-in-law Jathro was watching him as Moses was seated and the people were coming to him hour after hour. And so finally, Jathro approached Moses and said to him, what is this that you're doing? And Moses is, well, when the people have a complaint or need a desire, they come to me and I judge between them. And Jathro said, this thing that you're doing is not good because what's going to happen is you're going to burn yourself out. You're going to be taking care of the mundane things. So this is what I would share with you. He said, find men who are filled with wisdom, et cetera, qualified men, put them over the smaller things and you handle the greater. And that's called the theory of monkeys and gorillas because in ministry what will happen is somebody will walk up to me and they'll kind of like put their hand on my shoulder and they got a monkey on theirs. And they say, you know, so and so didn't show up to help in children's ministry today.  And I'll say, Oh, is that right? What I learned to do is put my hand on their shoulder and let that monkey go back and say, what are you going to do? Because that's a monkey. If they come and say something that's serious, that's a gorilla. That's my responsibility. I'll work on that myself because a gorilla should be taken on by the leader. But the little monkeys, their distractions and the enemy uses distraction. Oh, this isn't good. I didn't like the lights today. Oh, their conditioning wasn't on enough. When are you going to change the pews? You know, the little monkeys.  Those are monkeys. You can deal with those things. And so this is what's taking place, guys. They say it is not desirable. It is not suitable. It's not right that we should leave God's word in prayer and handle this kind of business. And so this is what we're going to do. And given the study, you're getting a little insight into how things are done here, by the way. We're not going to leave the word of God. You see, the apostles knew their priority and the necessity of spiritual feeding. They were spiritually leading people and they needed feeding themselves. The word of God in prayer was necessary. Like it says in Job 2312, neither have I gone back from the commandment of his lips. I have esteemed the words of his mouth more than my necessary food. Or Jesus, when he said in Matthew 4 verse 4, man doesn't live by bread alone, but on every word that comes from the mouth of God. You see, from Pentecost the apostles had faithfully preached and taught the word. It was a preaching of the word that had produced the church. It was the mark of the church to remain steadfast in the apostles' doctrine. When that man had been lame and he was healed, Peter preached. And when he and John were put into custody, they preached to the authorities. They had been forbidden to speak, but after the release they boldly preached. And great grace and power was evident in them. After the death of Ananias and Sapphira, they continued preaching. And as we've already seen, they were arrested a second time, but they still preached. Even after being beaten and threatened, the word had to go out. So a problem in the church has arisen. It can be a distraction. Again, one of the temptations of the leadership, a pastor's temptation, is to neglect the word of God to handle the distractions. Oh, you have building needs and you have staff needs and non-emergency ministry and operational concerns and all of those things can distract. They can quench the spirit. It stifles the minister's ministry. They couldn't leave God's word. They needed a biblical solution. So what did they do? Notice they delegated the people to select seven to meet the need. In verses three and four, it says, Therefore, brethren, seek out from among you seven men of good reputation, full of the Holy Spirit and wisdom, whom we may appoint over this business, but we will give ourselves continually to prayer and to the ministry of the word. Now notice, select from yourselves. Remember, the apostles were all natives of Israel. So select from the Hellenists. That way, we avoid suspicion or the accusation of preferential treatment. The 12 would confirm the decision, but they were to select the men. And so they were delegated so that the apostles could remain in the word of God and prayer. Why? Because that's where inspiration and direction finds its origin. They were not to be distracted from the main priority of teaching God's word. And so what did they do? Well, first, he said, Seek out from among you. So they selected from within the church. Those who are already there select from among you. So leaders need to be known in the church as mature believers, mature Christians. Leaders should be raised up from among those in the congregation. Today, some neglect mentoring leaders and the result is ineffective ministry. We have, I've been mentoring men now for many, many, many, many years. I, to this day, every two weeks meet with a group of men who are leading in various capacities here. After this service and after the Israel meeting, I have a two hour meeting with men in this church. I've been doing it for many years every two weeks. So I can mentor them so that they can have the foundations of our ministry and understand these things. And so you select them from amongst yourself. Notice they were to seek out seven men. They didn't seek out women. The women have a wonderful and great place in the church. You see women like Tabitha and Lydia and Priscilla. They're all amazing women, but they were to seek out men to be leaders. We men have been called by God to do so. Now, third thing is they were to have good reputations. They were to be men of integrity. Why? Because they were entrusted with the word of God as well as great sums of money. So their characters had to be well known and respected. Another requirement was that they should be filled with the Holy Spirit, meaning that they're totally yielded to the leading of the Spirit of God. They're to be walking in the Spirit and led by the Spirit. And then he says they had to possess godly wisdom. They needed biblical understanding and the proper application of those things. That's what they're looking for. Then verse five says that they're to be filled with faith. And that's essential in leading, especially in matters of finance and provision. And as they brought that up, notice again in verse five, the same pleas the whole multitude. Now, these seven names that are mentioned have one thing in common. They're all Greek, more than likely from the Hellenists. Now, as you look at the names, three of those names stand out. You have the name of Stephen. He's the first Christian martyr. You have the name of Philip. He's later referred to as Philip the Evangelist. You might find this interesting. He's the only one in Scripture ever referred to as the Evangelist, Philip. In Acts chapter eight, it records that he had been preaching in the region of Samaria, but later he was used by God to bring a eunuch to faith in Christ. In Acts 21, 8, and 9, that tells us that he had four unmarried daughters who prophesied and he lived and labored in Caesarea. Now, there is another one named Nicholas. The others are not mentioned, but Nicholas is referred to as a Gentile, a Greek from Antioch. He'd been converted to Judaism to become a Jew and had been circumcised, which is the meaning of proselyte, and he had come to faith in Jesus. Finally, they set them before the apostles. They prayed, they laid hands on them, and the word of God spread. The number of the disciples multiplied greatly in Jerusalem, and a great many of the priests were obedient to the faith. The word of God spread. The number of the disciples multiplied. You see, the result of dealing with this problem was God moved. His word spread out. They refused to leave the word. They refused to stop praying, and God moved. If they would have ceased preaching, people would not have been saved. Even a great many of the priests who were enemies were saved, and that gives you insight into why, even though there may be distractions in our fellowship here, we stay centered on the word of God and prayer. Because as the word of God goes forth, people are being saved. People are being raised up. People are being trained. Families are being saved. Children are being saved. Marriages are being saved. Communities are being impacted. Families outside of your core are being touched. That's why we preach the word of God, and that's why we will not be distracted from doing that. It's always the word of God. It always is, because nothing else will save a soul. It's the word of God and the power of the Holy Spirit. The enemy wanted them to stop preaching. The enemy wanted to divert their attention, but they said, we will not be taken from the word of God and prayer. You appoint people to take care of your business while we wait on the service of the Lord, because we're going to feed your souls so you can do the work of ministry God provided for you. That's how churches ought to operate, and that's how this church has operated for 42 years. That's why we have 42 years because of Jesus. That's how it works.


Lesson 10. What we're going to look at today, Kirsten, is tangent a little bit, but really cotangent, cosecant, and secant. Really secant and cosecant. We're not going to spend as much time on tan. Then what I'm going to do next class is really let you know what I expect you to know about tangent and cotangent, and secant and cosecant. Probably won't really expect you to graph them. I might expect you to recognize one of the graphs, but I don't think I'll ask you to actually graph it. Well, secant and cosecant, cady and cotangent are reciprocal graphs. So it would be hubus. That means it would be wise to review what we remember about reciprocals. So you're ready? Reciprocals, when my original graph was zero, my reciprocal had a vertical asymptote. When my original graph was zero, my reciprocal had a vertical asymptote. What's this graph of? Sine. So here's y equals sine x. What's the reciprocal of sine? Which reciprocal trig function goes with sine, secant, cosecant, or cotangent? I'll do this in red. I already know that wherever sine has a zero is zero high, it's going to be asymptotes. We're going to try and we're going to graph this later on in our notes, but let's try and anticipate what it's going to look like. What else did we say? Well, when my original graph is positive, my reciprocal is also plus ve positive. In other words, if your original is above zero, the y-axis, your reciprocal is still above the y-axis. Don't suddenly go below the y-axis. Oh, and when its original was negative, my reciprocal was also negative minus ve is my abbreviation for negative. In other words, over here, I'm pretty sure there's going to be some red graph down here and some green graph here, but I don't think there's going to be any green graph here. I don't think there's going to be any red graph here. I don't think there's going to be any red graph here. There's no reciprocal there and there. Ah, then we said this. When my original was one high, my reciprocal was one high, right? When my original was negative one high, how high was my reciprocal? Also, So negative one. We said these were the fancy word, remember this word, Tyson, invariant points. We said anywhere plus or minus one high, which is really important because Amanda, what's the amplitude of sine and cosine? So you know what? There is always going to be a key point or two plus or minus one high that's invariant. Oh, by the way, that's pi, pi by two, three pi by two.  When your original gets bigger, the reciprocal gets smaller, decreases. When your original gets smaller, your reciprocal gets bigger. Oh, and then remember, remember, remember, remember, Nicole, when my graph got really small, got close to zero, my reciprocal got really big. It shot up to either positive or negative infinity, depending on whether you're getting closer to zero from below or closer to zero from above the x-axis, right? And the graph approaches a vertical asymptote. Now we have to add a tiny bit more because when we did transformations in unit one, I did not give you graphs with asymptotes on them. I gave you graphs that were fun that may have had asymptotes when you did the reciprocal, but I never gave you an asymptote and told you to take the reciprocal. But tangent, your cousin, does have our asymptotes already. Where tangent has asymptotes, where it shoots off to infinity, my original graph is going to get closer and closer and closer and closer to zero. So we're going to say if you have an asymptote already, you're going to approach zero. And in fact, you're going to start to level off just about. You're almost going to get very briefly a horizontal asymptote. You're not going to approach zero like you're going to kind of and hit zero and then you'll see in a second. By the way, we have to reemphasize. This means inverse doesn't mean reciprocal. Inverse is when you wanted to find the angle if you were given the decimal value or the radian value and you had to go shift side or shift closer, shift hand to find the angle. How are we going to sketch the reciprocal functions? Something like this. Watch. Let's see. Remember my little invisible bug? As I move to my left, Ryan, am I getting closer to zero or further away from zero as I move to the left, the green graph here? The green graph? I think he's getting, isn't it getting closer to zero? Hi. So my reciprocal is going to do what? Get further. Noink. How about as I move to the right, Ryan, my green graph, my original is getting closer to zero. What's my reciprocal going to do? Yoink. Oh, and you know what? Yoink. Yoink. That's what cosecant looks like. Cosecant looks like that. Honestly, I hardly have it memorized. You know what I know how to do, Matthias? A reciprocal and I can graph sine and cos in my sleep. So if they ever asked me to do secant or cosecant, I don't. I quickly sketch the sine or the cos sign that goes with it and anywhere one high stays invariant. Bigger becomes smaller, smaller becomes, and I do the reciprocal. So here's sine x and we've graphed it between negative two pi and positive two pi. It says graph the cosecant. Okay, first thing we would do is we would say anywhere zero high there's going to be an asymptote. We're on page 302. Home, we're here. Sorry, go get it. Invariant points, anywhere how high? One or, careful. Well, let's see. That's not going anywhere. That's not going anywhere. That's not going anywhere. That's not going anywhere. Bug. Getting closer to zero, yoink further from zero, shoot off to infinity. Closer to zero, yoink further from zero, shoot off to infinity. Closer to zero but negative, shoot off to infinity but negative. Closer to zero but negative, how about we shoot off to infinity, but negative. And then it repeats, looks like that. Hey, let's graph it on our graphing calculator, it's just a C. So, clear whatever graphs you got and make sure you're in radians. How would I graph cosecant? I don't have a cosecant button. How do I type in cosecant? No, not second function sign. All right, I gotta freak out on you. I gotta freak out on you and say, no, that does not mean that. That does not mean that. That does not mean don't do that. Thank you for letting me freak. I missed that. How do I graph? How do I graph cosecant? Oh, one divided by sign X. But don't hit graph yet. Let's change our view windows to match theirs. So once you've typed that in, hit window. How far left does their graph paper go? Oh, let's do that as our X min. How far right does their graph paper go? Two pi, we say. Let's type that as our X max. What's their scale? Count, figure it out. What's one square worth? Figure it out. The easiest way to figure it out, Nicole, is to count how many squares make up pi. How many squares make up pi? So what's one square worth? Oh, let's do that as well. How low does this graph go, Nicole? What's their scale? Actually, technically sort of one third, which is a yucky, is three squares make up one. You know what? Vertically, I'm never as fussy because I'm not that... Anyways, hit graph. What do you get? Do you get the same as me? It depends. Who's got the 84s? Who's got a TI 84? Anyone in this class? Do you get the same exactly as me? So you don't have that, is that right? Or is that a different issue? I have no idea what you said. One line missing. You don't have that one or that one? Look out. Do you want to go under that one? So yours has better software. Anybody else not get this at all, first of all? Let me come help you. So we've graphed it. We've double checked on our graphing calculator a little bit. Looked like that. What kind of questions might I ask you? One thing I might ask you is to tell me the equations of the asymptotes. Now there is an asymptote. There is an asymptote. There is an asymptote. There is an asymptote. There is an asymptote. What are the equations? Well I can't list them all because there's an infinite number because this graph keeps going forever and ever and ever. Instead I'm going to list one and then spot the pattern. First question. What is the equation of a vertical line? Math then. It's equation of vertical line and I also did it at the beginning of this year. No one knows, really. You need to know this. Okay. One, two, three. That's a vertical line that goes through right at x equals three. What's the equation? What? You mean when I say that's a vertical line that goes through right at x equals three I'm actually saying the equation? What's the equation folks? Cassandra, what's the equation? Ready Cassandra? Here we come now. Here we come now. What's the equation of this line right here? That's not an equation. It's not what you said to me. That's a number. What's the equation? Loud voice please. That's what I'm looking for. There's the first one, the most obvious one. X equals zero. Where's the next one Cassandra? Then after that are they pi apart? X equals zero plus multiples of pi. And then we have to add though where the number n is an integer to say, look don't multiply pi by 1.5. It's not every 1.5 pi. It's every one pi, two pi, three pi, four pi, five pi, six pi, negative one pi, negative two pi, negative three pi. Oh, and then there's one more thing. What's zero plus five? Five, what's zero plus six? What's zero plus pi n? They probably almost certainly won't write that in front. But I just wanted to show you how we got that. And if you're not starting at zero, phase shift, you might have to start at plusing with something. What are the invariant points? Anywhere plus or minus one high. By the way, really it's X equals pi by two and every two pi in either direction. Sorry, every pi and no, every two pi, 12 squares. Yeah, two pi and X equals, I don't know, three pi by two and every two pi in either direction. I'm not gonna worry about any invariant points. I'm not gonna really be fussy on that to ask you then. We're useful to graph though. What I will probably ask you is domain and range. First of all, for sine, what was the domain of sine? All reels, right? What was the range of sine? Remember it was nice, negative one, less than or equal to Y, less than or equal to one between negative one and positive one. Sadly, cosy can't, not so nice. Domain. Well, it's sort of all reels, except there's gaps. Like it does go forever. Where are the gaps where the asymptotes are? Where is the first asymptote, Cassandra? Then, then, okay, so the domain, now the asymptote, you're saying what's the actual equation of those vertical lines? The domain, you're saying X can't be. X can't be pi n, where n is an integer. That's your domain. What's your range? Well, your range, okay. Andrew, how high does this graph go? How low? But there's a gap, see it? In fact, the only way that you can do this easily, there's a yucky way to do this in one line, but the easiest way is to say, you know what? I'm gonna do the range of this one. Everything above and touching how high. Everything above and touching one, comma. And then I'm gonna do the range of this one. Shannon, everything below and touching how high. Don't say one, careful. Below, less than, touching. There is a way to write that in one combined yucky statement, but I'm not gonna do it that way. It's easier just to say, you know what? It's kind of two separate graphs with a gap between them. That's cosecant. What would secant look like? Good question. There's cosine. I guess secant would have an asymptote right there, an asymptote right there, because that's where cosine is zero high, right, Tyson? It would be invariant right there. It would be invariant right there. It would be invariant right there, because those are plus or minus one high, right? And getting smaller, you know, getting bigger, getting closer to zero, shoots off to negative infinity. In fact, it looks an awful lot, like this guy slid sideways, because this guy has its first vertical, its first invariant point at pi by two. This one has its first invariant point at zero, or it's over here depending on how you wanna think about it. They look similar. What if we muck around with the, well with this? Oh, let's add one more thing. What's the period of cosecant? Two pi. That hasn't changed. Amanda, what's the period of cosecant? Woo-hoo. What about here? What about here? What if we replace the x-width in this equation? Two x. Do you remember what that did to a graph when you replaced an x with a two x? First of all, horizontal or vertical? Horizontal, okay, okay, okay. Horizontal what? Let's see how that affects things. What was the domain of cosecant? Well, we just have it on the previous line. It was x can't be pi n, where n is an integer. You know what the domain of cosecant of two x is? It's, so read that to me. X can't be pi n over two, where n is an integer. What if they put a three there? That'd be a horizontal compression divide by three. What if they put a one half there? That'd be an expansion by two, times by two. That give us a, you can memorize this, but I think we can actually tie this into something we kind of know, and it's good review, Katie, of some of the unit one stuff from way back when. Katie, this word right here, read it out to me. Will that change a range ever? Because I think range is vertical. Okay, you know what? Range is still the same. Y greater than, or negative, not negative one, that's positive one. Everything above and touching one, comma. Everything below and touching negative one. Everything above and touching one, comma. Everything below and touching negative one. What if we say the period of cosecant was? Amanda, Amanda, joy of my heart, light of my love. Read this to me please, light of my love? Oh well, what do you think? Because period is a horizontal. Yes, yes, yes, yes, yes. You're right, what? All right, two pi over two, so you can see the math that you did in your, yeah, pi. All right, Amanda, let's expand that. Hey, what if there was a five right there? What would the period be? What if there was a one half? Now that would be an expansion by four pi, yeah. Okay? Oh, could you even holly handle something algebraic and just think about the math that we did of it? I put like a A there, it'd be two pi over A. Oh, or two pi over B, if I wanna tie it into what we've already memorized, the period as being two pi over B, that's really what it is. What about the asymptotes? Well, the original equations were the same as the domain except it was, that's where they equal pi n where n is an integer, not equal to pi n over two where n is an integer. What we did here is we said, you know what? The graph of cosecant of two x is a transformation of cosecant by a horizontal compression by a factor of, and you know what? I wrote by a factor of two up here. I should have said by a factor of a half, shouldn't I? Because that was our notation by a half which was the same as timesing by a half which was the same as dividing by two. And it is a compression about the y-axis but I never asked you to remember that I just, because that confused me. In fact, compared to the asymptotes of cosecant, cosecant two x, the asymptotes are twice as frequent. They happen way more often. I'll show you. One divided by sine of two x because that's cosecant of two x. And I'm gonna go back arrow and I'm gonna hit enter to make this line thicker so it stands out. Graph. Yeah, asymptotes are twice as frequent. Period's half as long. Turn the page. The absolute value transformation. Remember that one? When we did this, y equals the absolute value of whatever graph we were dealing with. Remember what that was? Because that was a fairly, we did that at the very end of transformations and the reason we said it for the antithesis that was one of the easier ones. Anything that was positive nefanyl remember stayed as is. What happened to anything that was negative? Clipped up. Okay. When my original is positive above the x-axis, the absolute value is identical. Fancy word invariant. Oh, and Sabrina, when my original was negative, the absolute value is a, I think what they want us to write here nefanyl is a vertical reflection. It flips up. I like your explanation better. It became positive, flips up. Okay. Here's cosex. What would this look like? Well, that would stay. That would stay. And that would stay. You know how I know? Because they're positive already and the absolute value of positive is positive invariant. But nefanyl, what would happen to this little guy right here? Right there, yoy. Right there, yoy.  But you can use that as a memory tool if you want. Stuff to try. Number one, Mr. Dewick, there's tangent.  We'll talk about this tomorrow. I haven't talked about a phase shift. This moves pi by four left. Nicole, pi by four what? Will that change the range? Will it change the period? No, because the period length won't change. But you know what it's gonna change? Move your domain left, move your asymptotes left. See if you can figure that out. If not, I'll talk about that next class. So did I circle three? Let's circle three. Let's circle four. Try five, try six, try seven, nine, 10. And we'll pause there, but I also think I have a take home quiz for you. Let me double check.


This is Dan here, and y'all are the creepiest human beings on the planet. Like a power we would like to be on the good back there. Nobody come past this line, all right? Sorry. Bruh! All right, that one. All right, so now, I want to talk about creating pressure. So, thought we'd cover it, and we're like, what do we want to work on? And he was like hand-fighting, getting to a leg, but the in-between. And that's what me and him and Roper spent two hours discussing. I think I was more of a little bit of a debate last night about what the in-between is. So the in-between from whatever tie-up I have, right, so if I have double-outside ties, and I'm ducking under, or shooting a high-crash, or a single leg, from the time I set my tie to the time I get to the leg, the in-between, how do we make that better, all right? Well, I got to get to the leg in good position, and I got to have a good set-up, all right? And I got to have good conditions for my leg attacks, right? So I create pressure, I get an angle, and then I got to get from tie to get that faster. Well, that's a long-term thing, right? How do you get faster? You work on your speed and agility. How do I get faster in a match like that? Okay? Can't build it, all right? Unless you've got some Russian potion that makes you super fast. So if they say you need some time. All right? So now, what I need to do is create a little bit of a condition that makes me faster. So I'm just going from me to Jake, that's my speed. But if I'm going from me to Jake, but Jake's coming to me, they'll get faster and slower. How much faster? Twice as fast. If it's just me going from point A to point B, versus me going point A to point B, but this guy's going point B to point A. Twice as fast. Who said two times? You make a difference? Yeah. All right, that's a two-nigh answer right there. What's the DBA? Like a three-nigh. Oh, you put it in a bag. All right, so now we're going to talk about creating pressure and releasing pressure. That's the in-between that we're going to focus on making super fast, all right? So we're going to get back to our close distance, head position, inside time. A couple of people asked me about what I consider elbow control. When I say elbow control, I'm armpit all day.  The further I get down his arm, the bit tougher it is for me to control some close distance. Pressure with my head. Now, whoever wins the pressure battle is usually the guy with the lowest hips. So this is the drill we're going to do, stay home, close distance, he reaches up, I go inside time.  Notice my lead leg's not changing, but I'm driving into him. Stay at home in a good position. Because the minute I create enough pressure for my attack and we're going to do all kinds of attacks from there, it's going to be twice as fast. Just like that. Okay? Just by creating pressure and then disappearing. Okay? Because when I drive into him and he starts driving back and then I've disappeared, okay? My speed gets twice as fast. Twice as fast. All right? A lot of people say it looks slick. I just had the other. We're going to do simple all the way to grandma's trying to understand because she's so proud. All right? So that's all we're doing. Close distance. Inside time. Pressure, pressure, pressure, pressure. Stay nice. Go!


This device is kept Mr. Craig Lewis, a 55-year-old man with cardiac amyloidosis who had his heart removed and replaced by these two pumps alive now for 12 days and continuing to do better. I recall 42 years ago when we attempted to use a total artificial heart for the first time in a human patient. And this initial success there was, I think, a milestone. For the first time, it demonstrated that human patients could be completely supported by a totally artificial device. While this is not the end of the story, it's a very important milestone paragraph in the story and my heartiest congratulations guys. They're much smaller, they're much more robust, and they work really beautifully to support a weak left heart, but no one had ever used one to replace a heart or used two of them to replace both sides of the heart. So we realized there was going to be some arts and crafts involved. We would actually take the Dacron, put it over the form, and then wrap it in fiberglass tape and silicone. And originally we were using stuff from Home Depot, you know, tile caulk from the bathroom department and drywall tape. And the beauty of these continuous flow pumps, there's really two things, the obvious size, but they don't wear out. We haven't had one to wear out, so they behave like the natural heart, which is one of the reasons why, to me, this is the only hope long term for a really totally implantable artificial heart that we can take off the shelf and spare patients like Mr. Lewis premature death. So this is a milestone in cardiovascular history, in our opinion. It's a great step forward, and it's a great tribute to Dr. Cooley and Dr. Frazier and Dr. Cone and their teams. Let me just read a statement from the family of Mr. Craig Lewis. This is the patient, and they asked that we read this here today. This is a quote, we feel very blessed that the doctors at the Texas Heart Institute at St. Luke's Episcopal Hospital, the whole team are able to use their God-given talents to continue to help people like Craig in this situation. We hope he continues to get better. Thank you.


The Hornbill Festival is held at Naga Heritage Village, Kisama that is about 12 km from Kohima. The festival is named after Hornbill, the globally respected bird and which is displayed mostly in tribal folklor, dances and songs. There are 16 tribes and sub-tribes in Nagaland and all these tribes participate in this festival. The aim of this festival is to revive and protect the rich culture of Nagaland and display its extravaganza and traditions. The week-long festival unites one and all in Nagaland and people enjoy the colorful performances, crafts, sports, food fairs, games and religious ceremonies. Traditional arts that include paintings, wood carvings and sculptures are also displayed. Festival highlights include traditional naga morongs, exhibition and sale of arts and crafts, food stalls, herbal medicine stalls, flower shows and sales, cultural medley of songs and dances, fashion shows, beauty contests, traditional archery, naga wrestling, indigenious games and musical concerts. Mialipu, the fish dance. This folk dance is performed by a group of men acting like a group of fishes swimming in the river. The dance is accompanied with a rhythmic song, sound and dance. For visitors, it means a closer understanding of the people and culture of Nagaland. If you are visiting Nagaland during the festival, you can enjoy the food, song, dance and custom of Nagaland. Ladies and gentlemen, what you are witnessing right now is the honey bee dance, each the dance of the honey bees with gay abandoned hive during the bee. Similarly, the free-spirited youngsters attire in their traditional, best, enthusiastically dance in celebration of the youth. This is a folk song sung during the Chakisong Sukran year festival. It is annually celebrated in the first month. This festival is specifically observed to purify the body and the spirit and embrace the new year with purity. It is believed that observing this purification ceremony helps the villagers to accomplish the goals they were set for the years in life. That was the pet village youth society, performing Sukran year and year.


Hi everybody Random number black randomizer had a little twist. We were given away $75 break credit for getting it done so tonight, so I didn't do the brand or the break credit giveaway So we're gonna do it right now. So this is for the Break credit giveaway for this random number block of spectra pick a team eight Here are the people in the break itself. So new dice roll and Name on top after four gets $75 in break credit. Just forget it in the break itself. So good luck and one two three and congratulations to Rashid Grant Got yourself 75 bucks and break credit just for getting into the break. Congrats, man That was the break credit randomizer for the 2020 Panini Spectra football pick a team eight random number block I'm Sean jaspyscasebreaks.com the break is coming up next


I remind members of the Covid-related measures that are in place and that face covering should be worn when moving around the chamber and across the Holyrood campus. The final item of business is a member's business debate on motion 1675, in the name of Graeme Simpson on East Kilbride rail line dualling. The debate will be concluded without any questions being put. I would ask those members who wish to speak in the debate to please press the request to speak with us now, and I call in Graeme Simpson to open the debate up to seven minutes, please, Mr Simpson. Many thanks, Deputy Presiding Officer. I'm going to start by thanking all the members from across the chamber who signed the motion that gets us this debate today. I'm going to start with a quote. The East Kilbride line is one of the areas that we've identified. I was there fairly recently and the investigation works had started. The work involves not only electrifying the line but dualling it, which will provide it with much greater resilience and capacity to help to support the people who make use of the services. It also involves enhancements to East Kilbride railway station, which, in my view, is unacceptable in its present form. That is why that work is one of the early actions that we intend to take forward. Those are the words of Cabinet Secretary Michael Matheson when questioned by me at the Wreck Committee in September last year. That is the same Michael Matheson who described the service to East Kilbride as inadequate and not up to scratch. While posing in a hard hat on the line, he said that the combination of projects at East Kilbride and Hairmayers will transform the services into Glasgow in the next four to five years and is part of a major investment by us. We want to make sure that the line is able to cope with ever-growing demand for rail services on this route. Those are ambitious plans to take forward for the benefit of those who make regular use of the service on this line. You would think all was well. It was until we had the announcement sneaked out by Transport Scotland in October that we were not going to get a dueled line between Busby and East Kilbride and that the line will be decarbonised, which may or may not mean electrified. The line from East Kilbride runs into Glasgow through part of East Remfrewshire and then through the south side of the city. Going from East Kilbride, it is a single line until you get to Busby, apart from a small loop at Hairmayers so trains can pass each other. Only diesel trains operate on the line. Clearly, if we want to get to net zero, we need to tackle lines like that. We also need to encourage people on to the trains. One of the problems with having a single track line is that if problems occur and they do, trains just stop. If they are coming from Glasgow, they usually go no further than Busby. That is why I, the former MSP for East Kilbride, Linda Fabiani and others have been pushing for years to get the line dueled and electrified. As you have heard, we had agreement for that. That has now been torn up with no consultation whatsoever. Paul Speedy is making an important point about the reliability and resilience. Surely that is a lesson that was learned the hard way on the border railway, which was curtailed with significant sections of a single track line, which now is presenting a huge problem for the reliability of the line with massive delays as a result of the single track sections, which were, as a result of Transport Scotland Valley engineering the project? Mr Sweeney is absolutely right that the border railway is in the same position. The minister and I have spoken about this. I thank him for that. He will say that there is a potential for the £40 million cost of dualling the line to spiral. There is that risk with any infrastructure project, and you have to factor that in. That does not mean that you do not do them. The new MSP for the town, Collette Stevenson, has been quoted as saying that £100 million is still being invested in the East Kilbride corridor. I assume that she means the entire line into Glasgow, which in her view is, quote, great news for the people of the town. Well, it is only great news for the town if there is a guarantee of more trains and no hold-ups caused by there being only one line, or if there is extra car parking at the new Hermize station, not the reduced number which is now being mooted. I am afraid that none of what is being delivered right now, none of that is being delivered, so it is not good news for the town at all, and it is not gesture politics to point that out. East Kilbride is growing at a fast rate of knots. Thousands of houses are being built on what was Greenbelt land to the south-west of the town. We should be doing all we can to encourage the people living in those houses to use the train so that we should be increasing capacity and the frequency of services, not taking the short-term view based on current usage because it will bounce back. The minister is shaking his head, but it is a short-term view. At one time, the line continued from East Kilbride to Hamilton. When East Kilbride became a new town in 1948, the line beyond the town was closed. In the mid-1950s, the dueled section from Busby became a single track. Diesel replaced steam in the 1960s, and in 2000 the Hermize loop was built, allowing for a half-hourly service. Of course, we are not the only place to have a single track line and diesel train. The borders line mentioned earlier is the same. The line from Perth to Inverness is a single track line, and, of course, so is the far north line. There will be others that members may wish to highlight. All those deserve investment, too. This should not be a case of divide and conquer. If we are serious about cutting carbon emissions from transport, then we need to persuade people that they are better off not driving. East Kilbride could be a great example of what can be done. The ambition should not end at dueling and electrifying the existing line in my view. Right now, if you want to get anywhere in Scotland from the country's biggest town, people from Paisley may disagree with that title, you have to go via Glasgow or drive. If we are to be truly radical, then we should be looking to go beyond dueling just to East Kilbride. Why not extend the line again, maybe even to Hamilton at some point in the future? I'll just end with the quote that I started with. The work involves not only electrifying the line but dueling it. That is a promise, and no amount of weasel words can wriggle out of that. I have been clear that I believe that electrification and dueling of the East Kilbride line would offer the best outcomes. I have been saying all along to those who have been in touch with me regarding the issue, and I am happy to have that on record. I welcome today's debate from Graham Simpson, and I look forward to hearing from other members as it progresses. On 8 October, I was made aware of the Scottish Government plans to electrify the East Kilbride railway line. The press release from Transport Scotland's website stated that, by progressing with a single track, that allows funds to be reallocated to other decarbonisation projects such as orders electrification. Other than confirmation that electrification was to take place, there was a lack of detail on what the improvements to station and passenger facilities along the two routes would be. I have had confirmation from the Transport Minister on what that work entails, with moving Hermeyr train station and the creation of more than hundreds of parking spaces to accommodate future demands, where more can be added if required. I welcome plans to encourage active travel, and the commitment for electrification to the line that will decarbonise our railway by 2035. However, I have had several constituents who feel that the town has been shortchanged, and that current plans to enhance the single track only do not go far enough to accommodate future demand. I would like to continue. Although we can all understand that the pandemic has hit revenue, if uncertainty over future usage of the line is cited as a reason for changing plans, surely it makes more sense to dual the line. My position as the Transport Minister will be aware that, if we are upgrading the line just now, then it makes sense to dual it rather than doing it years down the line, where additional costs and disruption could be avoided. Constituents have queried how much dualing will cost, and I appreciate a steer on that. The Scottish Government suggests geotechnical conditions between Busby and Hermeyr are challenging, and double tracking would require significant earthworks to be undertaken, carrying a high degree of risk. We can assume that that is true of any project that is size. However, I would appreciate confirmation of what survey work has been carried out to date and more details on what challenges have so far been found. Can the minister confirm if current plans can accommodate four trains per hour outside the peak period with the enhanced loop? I have not been swayed that longer trains are the solution to ease pressure, and network rail has not been able to give a direct answer to that point. I understand that I have asked a number of questions on that, and I would appreciate an update in the new year as developments progress. Ultimately, the enhancements are good for the town, and the plans will ensure a more reliable greener service, which I am sure will offer locals a real alternative to using the car. I simply want the best for the people of East Kilbride and for the right decisions to be made, which will foolproof the line. I want to be followed by Neil Bibby. Up to four minutes, please. I am contributing to the debate, because a large section of the line runs through my eastward constituency. I thought that I was doing quite well. I have eight stations in my eastward constituency. I have now discovered that Stuart McMillan has got 22 stations in his constituency, although quantity does not mean quality. Nonetheless, I have eight stations in my constituency, and that line runs directly through. It is important to look at some of the positives. First, I am delighted that the electrification of that line is a fundamental part of the decarbonisation and will make a significant difference to that in the years ahead. Secondly, I am also grateful that, in response to representations that I made, and I would make this point despite Collette Stevenson's remarks just a moment ago, a network rail increased the capacity on that line from four carriages to six carriages during peak times. I know that constituents in eastward—I am quite sure that East Kilbride as well—were quite happy to be able to get a seat in the train when many of them I know found themselves standing during peak periods. There has definitely been enhancement in the service that is on offer. However, the decision to remove the dualling or not to proceed with the dualling from Busby, the last point of civilisation in eastward, before one heads out towards Thornton Hall and East Kilbride, let me say that my constituency would quite happily annex Thornton Hall, where the residents there and the Boundary Commission willing so to consider. Nonetheless, as we move through Thornton Hall and to East Kilbride, we resort to a single track. I regret that, and I regret it because all those eight stations that I referred to in eastward are historical. They were all there in the 1930s, and they are at one point of my constituency. That is what one would regard as the north end of the constituency, not the south. Yet the population and expansion and development of eastward and east remfisher has massively been in a southwards direction, with virtually no public transport infrastructure at all, with first bus significantly reducing bus services that are available there, too. There is no option for many constituents, particularly those in new housing developments, but to use their car. I would have preferred and would hope that the dualling would continue, because I would very much like a future consideration to be given to a spur from a dual track to East Kilbride to swing round the back towards the new developments in Maidenhill, up towards Whiteley wind farm, which would afford public transport access to the whole of the south side of the expanding population in Newton-Merns and Maidenhill. As a long-term project, we should be looking to provide additional access to public transport options to people. That would be, I think, a long-term worthwhile project, but it makes it almost impossible to achieve if we only have a single track. I can see the minister sitting there shrinking in shame at this development, particularly when only a fortnight ago the UK Government announced a £10 million investment in the Whiteley wind farm, which will allow for a carbon capture, which will allow for some 250 bus journeys to be made between Glasgow and Edinburgh a day on a completely decarbonised basis. The UK investing in the future of decarbonised transport while the minister sits there and cuts the options himself. The only people who should be shrinking with shame on the issue of rail investment are the Tories. Given what is happening south of the border, while the Scottish Government is investing heavily in rail and rail infrastructure, the UK Government is imposing swinging cuts on rail. The minister knows that the UK Government would be only too delighted to assist in transport projects in Scotland if only Scottish Government ministers would get off their high horse and sit down and have those conversations. Nonetheless, I think that it is important that the commitments that were given are honoured in order to make available future additional rail transport options feasible. Although I know that many of the improvements that have been made are positive, I think that this decision is a retrograde one and one given the long-term population expansion that people will regret and the Government will come to regret as well. Upgrading the East Coast Bride line has been a long-standing objective of campaigners through the decades. As we have just heard from Jackson Carlaw, the line serves growing populations across the south side of Glasgow, East Renfrewshire and East Coast Bride, while those communities have changed dramatically through the years. The railway itself has not. Passengers have raised their frustrations with an increasingly dated railway with me. For example, I have met thawntly bank commuters on the station platform to hear first-hand concerns about the frequency of services, breakdowns and that time excessive overcrowding. The adoption of network rails electrification enhancement proposals was set to be a game changer. That included sections of double track or loops between Haymars and Busby stations that could facilitate more trains to East Coast Bride. The decision to take forward enhancements was welcomed across the communities served by this line. It was the flagship of the Government's rail decarbonisation plan. Transport Scotland and the Scotland's rail website were peppered with references to double tracking on the East Coast Bride line to facilitate a more frequent service and more double tracking at the single line section between East Coast Bride and Busby. Make no mistake, the working assumptions of the Scottish Government and its partners on the ground was that the electrification of the East Coast Bride line included dual tracking after Busby. The assumed dual track would make it possible to improve the frequency of services, not just securing four trains per hour services at peak times but beyond that too. It is astounding that Scotland's largest city and Scotland's second largest town are still connected by a two train per hour service for so much of the day. The failure to improve rail links between two of the largest settlements represents a failure to improve rail links for my constituents in East Renfrewshire and everyone in between. This project would also alleviate pressure on Glasgow central station as a whole by reducing platform occupancy times with benefits to the city region as a whole. The customer outcomes from upgrading the line set out by Network Rail include greater punctuality, quicker journeys, more seating capacity and crucially more trains. The Scottish Government has now chosen not to implement Network Rail's proposals in full. They are limiting the network's capacities to provide more trains and they have done so by their own emission on cost grounds. There is nothing too impossible or too difficult and there is certainly nothing unaffordable about double-tracking the East Kilbride line. They are choosing to divert funds elsewhere rather than future-proof this rail line. Those are short-term financial decisions to the long-term detriment of the suburban rail network. That will not deliver modal shift, that will further entrench car dependency. The Scottish National Party has to come clean. They have no plan to build back rail services to pre-pandemic levels, never mind improving them. That is why they will not disown the discredited docketary report and that is why they are reading the budget for the East Kilbride line. The Tory Government's decision to scrap the eastern leg of high-speed rail 2 was met with opposition from across the north of England. In the words of Andy Burnham, levelling up means bringing forward your best solution, not a cut-price solution. That is precisely what the SNP transport minister is doing in the west of Scotland. That is a cut-price solution for our communities, not the best solution. That is a betrayal of the passengers who have endured overcrowded and inadequate services for years. That is a betrayal of the local economies counting on rail improvements to boost their recovery. My constituents in East Renfisher, where the line is already due, need double-tracking after Busby as much as the people of East Kilbride or the people of Glasgow, because it is only by extending double-track that we can secure for the future the full benefits and networks rails original proposals. Proposals that would mean more trains, quieter, quicker, greener and more frequent. Proposals that could meet the aspirations of the passengers that I met in Thornydbank and many more like them in Busby, Clarkston, Giffnick and all along the line. The Parliament should stand united in telling the Scottish Government to get dueling back on track. That is why Labour is calling on the SNP Green Government to reverse the decision to drop dual-track. Upgrade the East Kilbride line and upgrade it in full. As has been mentioned, given that the East Kilbride line travels through East Renfisher, it is obviously of significant interest to those of us who represent the area as constituency or regional MSPs. Ensuring that public transport infrastructure is fit for the 21st century is key to encouraging modal shift and getting people to move away from cars, to meet the Scottish Government's targets to reduce car travel, to reduce car kilometres by 20 per cent, to cut our carbon emissions and to ensure greater access for those who do not have access to a car. On that point, I would highlight, particularly given my interest in the sections of the track that runs through East Renfisher, that comments are made in debates about improving the line around the comparatively high levels of car ownership in an area like East Renfisher that is relatively prosperous. However, 15 per cent of children in that community live in it. Those assumptions are to the significant disadvantage that the families who are left behind are further marginalised. I have campaigned for improvements on the line for a while now. In fact, two years ago, I managed to secure an additional £5 million fund for improvements to the MoGai and East Kilbride lines. Unfortunately for East Kilbride, that fund was then used entirely for a specific £5.5 million upgrade project on the MoGai line. That was entirely justifiable, given that it has consistently been the worst performing rail line in Scotland. In fact, before the pandemic, it regularly saw less than one in four trains arrive at MoGai station on time. Both lines share a need for much more substantial infrastructure improvement. They both require dualling if they are to see the frequency of service that we need to drive modal shift at the level of reliability that is required to make it a viable and attractive alternative to the car. As was noted earlier, we have seen that single track sections across the country consistently present obstacles to wider capacity and performance improvements. Some of those are historical legacies from a century or more ago. Many are the result of a deeply misguided programme in the late 1980s and early 1990s, whereby twin track lines had one track removed for financial reasons. Some are more recent decisions that have been made again, I believe, on a financial basis. I welcome the £100 million worth of improvements that have been and are being delivered on the line, including improvements to make Gifnick station more accessible to my constituents. That is a necessary step towards decarbonising Scotland's transport infrastructure. Given that transport is the one area in which emissions have consistently risen, electrification of the rail network is essential if we are to meet our emission reduction targets. That is why it is disappointing to hear that the long-proposed dualling between Busby and East Kilbride will now not go forward despite past commitments, a view that I know is shared by my green colleague for Central Scotland, Gillian Mackay. She wrote to the minister to highlight her dismay at those reports, rightly noting that protecting and improving services is key to restoring confidence in public transport as we come out of the pandemic. She also noted that regions across Scotland should not need to compete for funding for essential upgrades, with the money for dualling this line apparently having been reallocated to electrification of lines elsewhere. In response to Gillian Mackay's letter, the minister said that one of the reasons for scrapping the dualling is the level of anticipated demand after Covid. I find that a troubling rationale, because it suggests that government policymaking should be led by external forces rather than used as a tool to proactively drive up use of public transport. If the justification for reduced capacity is that fewer passengers are returning to the railways, then that outcome is being guaranteed by providing them with inadequate capacity to return to and failing to deliver the improvements that have long been needed. That is precisely why the co-operation agreement between the Greens and the Scottish Government includes £5 billion of investment in our railways across this parliamentary term. We should be making it easier, not harder to use public transport, as we are doing for buses with our under-22 free travel scheme. We should be investing the money that is needed to meet the scale of the challenge that we face in cutting our transport emissions. Scotland needs to deliver a more effective and more attractive transport network that draws more people onto our railways, and there is no reason to leave East Kilbride behind on that agenda. I now call Paul Sweeney to be followed by Richard Leonard up to four minutes. Thank you, Deputy Presiding Officer. Greater Glasgow has the second-largest urban railway network in the United Kingdom, but it is fair to say that it is less than the sum of its parts. If we are to seriously look at investing in it, we really need to commit to a vision of a 15-minute service in all parts of the city. That is the sort of shift of a turn-up-and-go frequency that unlocks true modal shift that moves people onto railways. I do not know how many people here travel by rail frequently, but I find the attempt of waking up in the morning and trying to figure out whether we are going to miss your connection from the subway to the railway service by one minute and then have to wait half an hour for the next train—a significant deterrent to deciding whether to take the car or the train, particularly if you are having to meet an appointment under time pressure. Those are decisions and calculations that are being made by Glasgow regions every day of every week. Because our transport system across the greater Glasgow region is so infrequent, it is not up to a metro-level standard. That is why it has not been fully utilised. That is why we are not reaping the full benefits of that great legacy of infrastructure that was built during the 19th and 20th centuries, despite the cuts of beaching in the 1960s. We need to seriously look at how we build that commitment. I know that the Scottish transport project review coming up, the strategic project review coming up, will be looking at the idea of a Glasgow metro. Surely a key critical component of that metro is connecting the sixth-largest settlement in Scotland in the greater Glasgow region, East Kilbride, to the urban centre of the city region, Glasgow city centre, in a way that will allow people to say, it does not matter, I do not have to look at my watch, I can turn up at the station and there will be a train arriving within 15 minutes to take me to where I need to go. I recognise the argument that he makes and that is why the proposals around a Clyde metro system take account of seven local authorities around it. Will he accept that rail is only a component of that and that there will be other component parts to achieve what he is looking for? I do not mean specific to East Kilbride, but it might be light rail, it might be enhanced bus, glider-type services, that a metro scheme will take in a raft of modes of transport. I recognise that point and, for example, there are proposals such as converting the Cathcart circle to light rail, which will unlock past its central station, etc. I recognise that potential East Kilbride in the future could be a candidate for light rail conversion, which could increase frequencies and unlock the potential of the line in full. To do that, we still need dual tracking, we still need that reliability, even tramways need dual track. Even if it is using light railway vehicles rather than heavy rail vehicles, the same principle applies. We need the dual tracking to provide the through ways to provide the reliability of the service. It is one thing to model for train for our frequency on a computer. We know from the bitter experience of the Borders Railway that, in reality, it is not as reliable as all that. Of course, as Ross Greer demonstrated with MoGuy, we have a similar constraint on that part of Greater Glasgow's network. We need that commitment to dual tracking. The risk is not just about the earthworks of building up the dual track system, it is about the risk to the reliability of the service, which then deters people from making that choice. Hard pressed at 8 o'clock in the morning, thinking that I will get to work on time. If I miss my connection by two minutes, I have to stand at a platform in the winter for half an hour, waiting on the next train, as opposed to turning up and getting it within seven or eight minutes, as you would in London, which is very much par for the course to turn up and be able to get a service across London at any point in the day within a few minutes. That is the sort of ambition that we need for Scotland's largest city. We are going to unleash the economic potential of the Greater Glasgow region. That is the sort of ambition that we need. The measly attempt to quietly downgrade the line after the great bombastic statements from the cabinet secretary about how it was not up to scratch when it needed to do the dual tracking, to try and do it surreptitiously in this way without any true scrutiny, without any clear publications or the justification. We are knowing how difficult it is to get those railway upgrades on business cases approved, as it is to then quietly downgrade them. It seems like a double standard. We need to have the same level of scrutiny applied to justifying the downgrade. I do not think that it has been presented. Please, cabinet secretary, have more ambition for Greater Glasgow. It is a one-way bet to let us dual-track East Kilbride and unlock the potential of the Greater Glasgow region. I thank Graham Simpson for raising this important debate. Here is a simple test. Is the Government prepared to improve the everyday lives of the people of Scotland to a level that matches its COP26 summit rhetoric? Is it prepared to speak through its actions, not just with its words? Or, with the banners now folded and the flags taken down and the sounds of protest that filled the streets of Glasgow now fading, is the Scottish Government going to make the climate catastrophe not better but worse? We were told at the weekend by the cabinet secretary for finance that tomorrow's budget will be, I quote, a stepping stone towards a fairer greener Scotland. And she did not just leave it there. She went on, that is our social, economic and environmental imperative. So the question this Parliament is asking of the Government this evening is this. Where is that imperative when the transport minister is happy to slash Scotland's rail services across the board by 10 per cent? Where is that imperative when the plan double-tracking on the line between Busby and East Kilbride, which is at the centre of Transport Scotland's decarbonisation action plan, is facing cancellation? Where is that imperative at the very point when we need ambition? We are given managed mediocrity at the very point when we need vision, long-term thinking and investment in public transport, the people are offered short-sighted cuts and government indifference. I read with interest the transport minister's recent interview in the Holyrood magazine and I say to him that he cannot tell us that he has seen the light about rail transport in Scotland and then close his eyes to it in South Lanarkshire. He cannot tell us one week, and I quote him, we should be very clear, rail is devolved. It is for us to decide what Scotland's railways will do and tell us the next that it is somehow out of his hands. So I say to him, we need the same toughness to resist these cuts and boldly invest in the railway as we see in the fight over where decision making power lies in the railway. This is about how we organise the future but it is also about what future it is we want to organise. Earlier this week I read an open letter to MSPs from Kevin Lindsay of the train drivers union Aslef. In it he called for action in tomorrow's budget to reduce passenger fare, to invest in freight and to reject the proposed cuts to services and he is right. In recent weeks we have seen a report supported by all four rail unions, the RMT, the TSSA, UNITE and Aslef, in which they argue for the expansion of Scotland's railways, not their contraction, in which they call for the transport minister to reject the dockety proposals and the abelio plans to act 300 trains a day. So their clear demand and my unflinching message to the minister and to the Government tonight, and I include the Scottish Green Party members of it too, is this, reinstate the dualling of the e-skill bride line, drop the plans to act ticket offices, ditch the proposals to cut jobs and to undermine workers' terms and conditions and once and for all do the right thing and reverse the cuts, these cuts, your cuts to Scotland's railways. It was remiss of me not to mention earlier, not to refer members to marriage service interests earlier on, specifically that I received a financial donation earlier this year from a rail union, the RMT. That is now on the record and could I now call on Minister Graham Day to respond to the debate? Excuse me, I haven't finished yet. Thank you, Minister, up to seven minutes. I genuinely welcome the opportunity to respond to the member's debate on the e-skill bride rail project, not least of all because it provides an opportunity to clear up one or two misunderstandings. Like thousands of rail passengers along the e-skill bride to Glasgow rail corridor, I'm sure that the Parliament welcomes. We've heard from members welcoming the commitment to the full electrification of the e-skill bride line. I hope that clears up the question that Graham Simpson asked earlier about full electrification. This is an exciting project that will not only further our ambitious decarbonisation plans for Scotland's railways by 2035, but it will deliver for rail passengers from e-skill bride and its surrounding communities a sustainable travel option using cleaner greener trains, which will meet anticipated future demand well into the foreseeable future. We all recognise the need for wider decisive action to make the future challenges of the climate emergency. The substantial overall investment, which will rise to at least £120 million that we've announced in the e-skill bride line, will not only deliver electrified services, but also significantly enhance station and interchange options for the travelling public. Those will make rail services more attractive and accessible, and they will encourage a step-changing moral shift from the pleting car to a fully decarbonised rail corridor. Let me address the issue of duelling. Yes, that was talked about, but it was never a specific requirement for the route. What was required for this was to deliver a project that would meet peak passenger capacity into the foreseeable future in a decarbonised way. Duelling was certainly an option that was considered as part of the business case development process. The cost was prohibitive and simply didn't offer value for money or represent the best use of scarce public finance resources. When it is possible to meet projected demand by the approach that is being taken, I want to be clear about something here, because there is a bit of a myth out there that Network Rail had a proposal that was vetoed by Transport Scotland. The proposal that came to Transport Scotland for approval was a joint proposal from Network Rail and ScotRail based on the evidence that it had before them. I give way to the member. Jackson Carlaw. It's a simple question, and I don't know what the minister can answer. Can he define what he means by the foreseeable future? Minister. I want to come on to that, if I may, about the modelling that's done. Of course we know that passenger usage has shrunk during the pandemic. We know that that will return to some extent, maybe to a greater extent, and what's going to be delivered in this line will encourage further usage. The modelling takes account of growth. That was the whole point of this. The plans that we've announced together with the significant benefits that will be delivered will cost less than it would have done with dueing. It will deliver value for money, it will deliver for passengers and it will deliver for the environment. I respect Richard Leonard's demands for all sorts of investment in rail, but if he's going to call for more services, more stations, investment in infrastructure, reduce fares, he has a duty to say where that money would come from. It's so typical, I'm afraid, of the Labour Party to do that in this chamber, or to not do that in this chamber. Thank you, the minister, for taking the intervention. I'm listening very carefully to what he's saying. Does he not accept that the duelling of the East Kilbride line was not just an idea, it was a promise, it was a promise that was made by Michael Matheson, and if you don't do it, how do you get the resilience that we don't have right now where trains sometimes stop at Busby? How are you going to get more trains if you do not dual the line? How can that be achieved? I'll come on to that in a moment, but I want to explain the process here that's undertaken, and it's being undertaken across Scotland's railways just now. We have identified projects in order that are going to be part of the decarbonisation agenda. There is groundwork carried out, that's currently being carried out in the Dunwayne to Aberdeen stretch at the moment. That gives us a better understanding of what lies underneath our railways and to the sides of the railways. When you have an elderly rail network as we do in Scotland, there is no record of what it was built upon. For example, on the Borders rail, there were far more mine workings discovered as the project unfolded. That's inevitably going to lead to an outcome in terms of the nature of the delivery that's perhaps odds with what was anticipated, but we still have to ensure that we deliver the outcome in terms of the passenger capacity that everybody is looking for, and that's what we're setting out to do. Right now, the peak-time demand on the East Kilbride route remains lower than the Scotwell national average. It sits at 34 per cent at pre-pandemic levels. Of course, passengers are going to return, but that's what we want. That's what we want to encourage. The joint industry passenger modelling for this route and the analysis of changing travel and patterns across Scotland give us the confidence that the capacity that will be provided on cleaner, greener trains that we expect to roll into service for late 2024 will be more than sufficient to meet both current and forecast peak demand, because, for one thing, the carriages on the electric trains are significantly bigger than are available on the current rolling stock. Of course, to address Graham Simpson's point about how to address some of the resilience issues, as Mr Simpson knows from our previous conversations, what is being worked through at the moment, in addition to the single tracking, is potential enhancements around signals, which is one of the issues around Busby, and further track infrastructure in the form of loops, which will allow us to address the very points that he rightly makes. That development works currently on-going, and Anticipate Network Rail will be reporting back before the next stage of the business case process early next year. Given the genuine interest and concern that is expressed tonight, I am happy to commit tonight to arranging a briefing for all interested MSPs at that point, which will have an opportunity to interrogate the detail of what will be in the final proposal in terms of the overall package. Our significant investment in this critical route demonstrates a continuing commitment to decarbonisation of Scotland's railway. East Kilbride is only a part of the proposals. We are already targeting barhead, the border railways are coming up, the Fife circle is next on the agenda, the Levenmouth rail development is being done with electrification in place for that connection. As I said earlier, as we speak, the teams are out on the rail link from Dunblane right up to Aberdeen doing that groundwork assessment, and I am pleased to say that the last report I had was that it had not identified any issues. It takes time to plan these major infrastructure projects, and it is important that we do that preparatory work, so that when we go in to do the work on the ground, we do not anticipate any problems. I will pick up a point that was asked about earlier. In addition to the cost associated that we knew about with dueing, there is a risk assessment done because of the nature of the work that has to be carried out. There is a stretch on that line that would involve about roughly 14 metres of earth and various other things to be removed. You take that out, you have to dispose of it, but it is then what you find at that point. The risk assessment provided a degree of concern, but I go back to the point that I made earlier, which of course is about the outcome here. It is to deliver the capacity on a clean green line, and that is what we intend to deliver. As I said earlier, more than happy to invite all interested MSPs to a briefing earlier in the new year to allow them the opportunity to ask any questions that they have and interrogate what the final proposals will be. Thank you minister. That concludes the debate, and I close this meeting.


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