What is up gamers real estate gaming here and it is Friday, so happy Friday to everybody and today We are back in sponge chapter 2, so let's begin with this. Oh my god. Where are we at? Oh, I think we're inside of the pineapple the giant marvelous pineapple. Oh, dude. He got stuck on the door Okay, so it appears like we're inside SpongeBob's house This should be awesome. All right. Oh my god. There's doors and locks already Okay, so we need to find all the hammer. Okay, we got that. Oh, we got the gun Not the hammer out the door. Just smack this in the face Okay, okay, so we need to the hammer. He needs a hammer there.  That looks so creepy. Oh My god, right? Uh, what what is he doing? Let's get closer to him. Oh He just moved And he left Whatever, let's not question mr. Sponge and let him be The sponge that he is. Oh look, there's a bullet Okay, so now we got a little surprise for mr. Sponge.  Let's leave the gun Let's let mr. Sponge live and we'll go open this purple lock or unlock this purple lock. Should I say? Okay, so let's go up here. Oh my god Never notice SpongeBob's house had so many rooms in it. Like where did all these rooms even come from? Oh, I'm hearing a heartbeat Okay, we got to be careful guys because sponge is scary and crusty and dry and he likes to creep a lot Okay, nice you got the green key now But go yeah, we have to look around for notes So let's keep our eyes open and make sure if there's any notes hidden around the map That we're left behind for clues as clues Okay, so we need the green lock Okay, let's go over here Gary's bull has blood in it dude. What it says Mao Gee, oh my god, Gary. What have you done to Gary and that really hit that? That was so inspirational what Gary said a mile. Oh my god All right, let's go over here. Oh, we have to look for the green key. I mean the green lock I'm hearing a lot of heartbeats, but I don't know where sponge is that Alright, so let's keep on moving over here. Dude, I keep hearing sponge, but I don't I can't find this guy Whenever he's at Oh, what's up on nephew? We got my nephew right here. Okay, so now we got the blue key So sponge oh sponge you where can you be? Where can we be at? I'm not so sure. Okay, so we got the teal lock over here. Nice What there's an upstairs All right, let's hear some sort of library. Hey, this looks familiar What is the game that we play that we just had to collect some bucks and we had to bring them down There's an empty book here. Okay, so we need the red green and blue bucks So he should go back and look for those downstairs and place them up here My god, okay. I think there were downstairs on the first floor. Oh look, this is SpongeBob's essay You guys remember that episode where he has to write like an essay and he spends like so many hours Trying to figure out what to write down on the piece of paper and this beauty This masterpiece is the only thing he gets down That episode is so hilarious Oh, I just heard something break But if it was sponge because he was so crusty he just snapped What if his leg just snapped off? All right, so we got a green buck Dude, I have not seen sponge like this whole entire match. Oh my god. All right. Oh, okay. Nice. We got a green one We place this one here. We need two more bucks. Oh, they really place the ladder up here Where did this ladder take us? What looks this we're outside where we're on top of the pineapple Well, we can't see the pineapple itself, but this is pretty cool Okay, so we need to unlock this giant lock. My god That is one giant fence. Oh, we need a hammer for that crate. Oh My god, okay, so let's look for the hammer But first we need those books Wherever those books are Okay, let's go look down here There's a gun That might be helpful I'm hearing the heartbeat closer. I think sponge is somewhere over here But yeah, we did need a hammer So let's hold on to this What? What is sponge doing? Hey sponge.  No, that's probably not a good idea.  Um, you know what? I'm just gonna grab this bucket. I'll be out of my way Okay Whatever Let's just pretend like that did not happen. Okay, so we got nine minutes left I'm pretty sure we got enough time to escape. Hopefully we do. Oh man Okay, let's grab this book right here. We place this. Oh, it's like a secret layer behind there And there's a golden key. Oh a lot of the key we need for upstairs. Okay. It says look behind you Look behind me There's nothing What does he mean? Okay, maybe sponge was supposed to be behind me chasing me or something. Oh look in this open up too You can drop down there. Oh nice Okay, so we got the golden key to open this My god, there's three bullets. We need a key card. Oh he has a key card. Oh nice Okay, what did you say? I have the squirrel. There is no escape. Oh my god So Sandy has been taken hostage From what we can read of see from this note here. Oh my god, SpongeBob. How can you do such a thing? Sandy's our homegirl man right, so we can escape through a Believe there's multiple scapes. We can escape through here. That's one. That's the window escape. Let's go have a look around To see if there's more escapes. I Think you can escape through the main door too. I Think there's actually three escapes. Why are there bubbles here?  So he's still there We can either escape through the main window or Through the I mean through the window or through the door, but as you can see, there's many traps on the door. I don't think oh Is he gonna get him? Oh He didn't get him. All right, so we can escape through here on the window Let's try the main door.  No Okay, you know what? Let's just run for the door Let's just run for it man. He's letting us escape Let's not test our luck and there we go.   We have no idea why If it was SpongeBob pretty sure was SpongeBob because I mean just look at this Darn evil by the likes of it so then the last no I mean the other one just said like behind you that one had no context behind it I guess SpongeBob was supposed to be chasing us the entire time. So that was pretty much it So for chapter 3 it might be it might be a Sandy's house. It might be working. Where else can it be? I don't know the prison I mean they can use the prison since it's punch Bob does have a prison They can either use bikini bottom it can be anywhere man because SpongeBob has many locations to it All right, man What if you guys have any theories or any ideas of where chapter 3 might be let me know in the comments below If you guys enjoyed the video make sure to slap the like button Do the channel make sure to subscribe and turn that notification bell on and I will see you guys in the next one


Good morning guys. I hope everyone is doing good. Welcome back to our channel. So today in this video We will be talking about new gen software interview questions and these questions were shared by one of our subscriber friend So recently he got an opportunity to have an interview with new gen software So the same questions what he have experienced Like what he have encountered in the interview he has shared with us and we are talking about those questions In this video so before getting into that questions part we can have a look at the mail what we have angular interview questions New Gen software technologies. So we have received this mail on 12th, July So high drunken engineer team you're doing a fantastic job. It's really Helps in interview preparation below the questions that I encountered at new gen software technologies interview so Coming to the topics. So these were the topics on which the interview has happened angular basic and advanced RxJS and NGRX. So if you are looking out for Interview questions on the UI part of so this video will definitely be helping you out Before getting further into the video, let us talk about the current job openings in India's 5 top unicorns credit reservoir urban company 1mg digit insurance if your dream job is to get into this Companies then this is the golden opportunity for you Usually it is tough to get into this company as they mainly hire from tier 1 campuses like IIT IMS and Even for few opening they receive a lot of resumes and so Chances are your resume will be missed But now there is a easier hack to getting a job at India's top five unicorns You will not require your resume to sit for any interview with these companies Instead these companies have started hiring through tests We where candidate can sit for the test and get a score based on your score You will become eligible for the interview with these companies So let us have a look at the current openings In the credit currently there are openings in the credit razor pray urban company 1mg and Digit insurance so coming to credit credit was founded by Kunal Shah credit is one of the fastest growing unicorns in India with a Valuation of 2.2 billion dollars credit is hiding for back-end and front-end developer rose CDC being offered is 14 to 26 Lacks per annum. I like ideal candidates are passing out in 2021 batch or zero to three years of experience preferred skills and competencies are given in the description and You can visit the real well certain to apply for the same. See this is a golden opportunity for two zero to three years and 2021 passing out batch 14 to 26 lakhs package coming to razor pack So razor pay was founded in 2014 Reservoir is a new age well-founded startup in the payments and finance industry Reservoir is hiring for back-end development roles CDC being offered is 20 to 24 lakhs package ideal candidates passing out in 2021 Zero to one years of experience preferred skills and competencies are given in the description Coming to next that is urban company It is most of you know like it is largest online services company with valuation of over two billion dollars Urban company is hiring for business development rose CDC offered is three to six lakhs per annum Ideal candidate zero to one years of experience in the field experience graduation any field is preferred preferred skills and Competencies are given in the description and next company is 1mg. This is India's leading integrated consumer health platform So one and you is hiring for back-end developer roles It is being offered is 10 to 30 lakhs per annum ideal candidate zero to one years of experience or one to three years of experience Prefer skills and competencies are given in the description and the final company that is digit insurance is India's first unicorn in 2021 valued over $1.9 billion. It is one of the largest insurance online insurance providers So this is insurance is hiring for a front-end and back-end developer rose CDC offered is zero to sorry two to seven lakhs per annum Ideal candidate zero to one years of experience or one two three Prefer skills and competencies are given in the description. So how to apply for this you can visit the Side which is being displayed on the scale that is a real level go to the job section view all the jobs and skills and the skills required Register for the test by paying rupees one triple line. You can use our coupon And available 10% discount at the time of registration Book the slot of your choice and take your test to get the real world score You should hurry because slots are getting really filled fast Once you receive your real-world score create your candidate profile real level will guide with the process Sit back and sit back and relax Companies will reach out to you based on your profile the better your real-world score The more companies will reach out. So what are you waiting for grab this golden opportunity to get a chance to work in India's top five Unicorns and all the best for that So coming to the questions part guys, this was the first question. Can you explain some important angular hooks? So these are the listed of Lifecycle hookups of Angler so in your on-genius and your on-init and you do check and you after content in it After content check and the after viewing it and the after view checked and you on this one And we have to explain in detail about the process or at least on those life cycle hookups Which we frequently use our at least what you have worked on so the questions were shared answers but I have added for just for the reference Coming to the next question. What is the difference between constructor and ng on in it? So the constructor is a default method of the class that is executed when the class is instantiated and ensures proper initialization of fields in the class and its subclasses coming to ng on it This is a life cycle hookup hook Called the angular to indicate that angular is done creating with the component. So this is a basic difference. We can say Can you explain the difference between component and directives using help of some example? So basically components have their own view Directive like doesn't have in in fact component is in indeed a directive So you can have your own differences that I have listed out one sample difference here components basically extends directive Coming to the next question. What is metadata in angular? So to keep it simple made metadata is used to declare a class so that it can configure the expected behavior of the class What is dependency injection in angular so dependency injection is a design pattern in which a class request Dependencies from external sources rather than creating them anglers dependency injection framework provides dependencies to the classes upon Instance creation you can use angular dependency injection to increase flexibility and modularity in your application Coming to the next question. What is the purpose of ng for directive? Can you write some code snippet for the same? So basically for iteration purpose we go for ng for so the ng for directive is used to repeat a portion of html template once per each item for an iterable list or collection The engine for is an angular structural directive and it is similar to ng repeat in angular and one more thing guys Please do have hands-on experience on this because lot of the questions have like can you write some code snippet for me? like they were expecting The code Maybe this was happened through a virtual because all the interviews are happening virtually these days So maybe we have to share our screen and write the code Coming to the next question. What happens if you see scripting tag in set template? So to be honest, I am not sure of this so you can search for it You can Google it for the answer or you can provide if you know the answer You can comment it out in the comment section so that even everyone come can be aware of it like at this At least we will learn from that What are the various security context in angular? So these are the few listed out security concepts You can go through it in detail afterwards But at short we can give a preventing cross-site scripting angular cross-site scripting security model Sanitization and security concept sanitization Example trusting safe values content security policy enforcing tested type direct use of DOM APIs and explicit Sanitization calls so here are the few that are listed out So it's up to your project to how to follow and how to implement which one to implement again that varies There can be extra things as well Coming to security especially in the banking domains. There are there is a huge security involved there So that can be different the answer can vary there again So that was about the security context in angular coming to the next question. How do you support server side? Production in angular application So server side access of production is supported in an angular application by using a Templating language that automatically escapes the value to prevent Excesses vulnerabilities on the servers, but don't use a templating language to generate Angler templates on the server side which creates a high risk of introducing template injection vulnerabilities to be honest Even I am not sure about this. What is server side access protection in angular? so Google the answer and So took help from one of the site and answering this I may be wrong on this How can we implement lazy loading in angular? Can you write code snippet for this? So you have to explain in detail like how if you have worked on it would be very easy for you to What I can say write the code snippet to for implementing the lazy loading process So how you load modules how you load classes based on what? So this is very interesting question Coming to the next question. What practices could you adopt to share data to another component elsewhere in the component stream? So basically how? Sharing data between angular components have four ways like all of us know parent to child child to parent child child to parent sharing way output and event emitter child to parent using view child or parent to child using data in like in that input unrelated components sharing with service What are the most outstanding features of RxJ? So here are few I have listed it out like observer observable subscription operators subject schedulers So coming to observer the observer is an object with next error and complete methods coming to observable in RxJs An observable function is used to create an observer and attaches to the source where values are expected Like for example clicks mouse events from a DOM element or hdb request, etc Subscription the role of subscription comes in the scene when the observable Observable is created to execute the observable. We need to subscribe to it It can be also be used to cancel the execution operators Operators are very important part of RxJs and operators a pure function that takes observable input and emits a result in the output form input and output both are observables your Subject a subject is observable again that can multicast that is talk to many observers Suppose we have a button with an event list and the function attached to that event using add list There is called every time the user clicks on the button similar functionality goes for the subject schedulers scheduler controls the execution of when the subscription has to start and Be notified. So these were the few of the outstanding features of RxJs I know there are many other features extraordinary features of RxJs You can mention out your own outstanding features what you feel which are outstanding next question what is the difference between behavior subject and Observable in RxJs. So here are the few differences that I have listed out you can wait for a moment and Go through those things if you are well aware of it or you can skip and go to the next question Coming to the next question How RxJs observable is different from promise.  You have to subscribe to Observable can be cancelled promises cannot be cancelled. So there are few differences here if you know others you can see that that that as well When we should use merge map switch map and concat mapping RxJs this again depends upon like the scenario Depending upon the scenario we go with either switch map of merge map or concat map. So It varies the answer varies from person to person here again What do you understand by reactive programming and what is the biggest disadvantage of reactive programming? So basically reactive program is a style of of micro micro architecture involving Intelligent routing and consumption of events. So and coming to like the disadvantages more memory intensive to store to stream of data Most of the times might feel unconventional to learn that certain needs everything to be a stream Most complexities have to be dealt with the time of declaration of new services Lack of good and simple resources to learn. This is one thing often confused to be equivalent to functional reactive programming So these are few disadvantages that I could found of reactive programming Coming to the next questions These are these were the questions like what is the flow or steps performed within the reducer method in Angular? What is the flow or steps performed within the luxury same question? What are the states of NGRX? What is the difference between NGRX and RXJS? So these were the questions that were asked asked in the Nugent software interview So this is the mail that we got from our subscriber friend Okay, one question that I missed was what is the flow or steps performed? Within the reducer method this was covered. Do we need to send a payload in reducer? So this was the question that we missed So this is the mail you can go this was for 4.2 years of experience candidate and We don't know about the outcome of the interview whether the candidate was selected or not because we haven't we have replied to this Mail, but we haven't got any reply on top of that So thought of sharing it might help for definitely for Angular developers like full stack developers These are very good questions To brish up before taking up an internet as a full stack developer So thought of sharing this with you all guys so that's it in this video and If you're wondering if you're watching our channel for the for on a video for the first time you might be wondering Who are we and what we do? So we are basically a bunch of software engineers who attend interviews and share our real-time interview experiences through these videos So even if you we share our subscriber friends who share their interview experiences with us And if you want to share your interview experience You can reach at the email ID that is given in the description and one more thing In the description we have given links to re-level and as a coupon course you can use it and get benefit out of it So these companies are you can visit our channel and get There are a lot of videos that we have already shared and you can get benefit out of it And if you haven't subscribed us, please do subscribe. Please like the video if you like the content Provide the feedback in the comment section share it to other technical platforms so that it might helpful to others and All the best for your interviews if you are preparing for I hope you are preparing that's the reason you're watching and Thank you for watching and thank you for your time


Hi everyone, Joe for jaspyscasebreaks.com coming at you with a two box break of 2020 Panini contenders football two box Pick your team number 14 if you follow the instructions here. You got a chance at winning the Chargers So we left that spot blank right there. Thanks everybody for getting in I appreciate it. So now let's just to make it easy Let's sort your Names my first name right here. So Adam you bought four. That's two entries Brian you bought To that's an entry Karen with to that ventric Kevin Smith to that's an entry Kurt with four. That's two entries Mario with to that's an entry Matthew shear with to that's an entry Sean Maddock ended up getting a lot got ten That's five entries Good luck. So let's grab those names. Let's put them into this list right here And let's roll it. Let's randomize it one and a three four times name on top I've four have the chargers in this little two box break one two three good luck for And it's Sean Maddock. He certainly had the odds with him And now you have the chargers With a little rooftop next to your name so you know you won that spot Let's sort back by by team doesn't want to print on it doesn't want to print there we go Good luck. I think we Had marked these. Yeah, there's there's some like Some sharpie scratch marks right there so you know, they're all from the same case Yeah, Jared. Yeah, that that that seems to be almost impossible to get those those MBA packs Miguel tried Jared tried Grizzled tried Grizzles saying waited for 30 minutes and Was 67 thousandth in line. So yeah, like winning the lottery basically Nice Joshua cherry, thank you very much for getting in we should be able to get that on the schedule a little bit later tonight Miguel was after grizzled Easy Rex. Let's not get Sean's hopes up too much under promise over deliver. Yeah, well Miguel Thankfully, we're still here to do group breaks Plenty of basketball plenty of football and other stuff on the site. Jasper's case breaks calm All right, so five autos per box first one is Darrell Williams For the oh For the chiefs, so there's the final printout right there chiefs are ride over The world I didn't print out the one that had it alphabetized by team Well, sometimes there's a cube But it's definitely but you're but it eventually always happens Eventually, it'll happen Always ended with something. All right, there's Kyle Dugger Patriots That'll be for Karen. Here is the printout alphabetized by team That's easier for me to spot teams like the chiefs right here Sean Karen. She has the Patriots right there There you go. That's more like it Rex under promise over deliver points We'll randomize that to one person in the group here winner take all on the points if we happen to see another one Hopefully not We'll do left right randomizer even though the same team will go left right randomizers for the different team ones That'll also be over here on the randomizing pile So those points unfortunately do take the place of an autograph. We got AJ Terrell Falcons that'll be for Sean you miss it already. No, I don't I don't think we do We don't actually because I remember I Remember actually talking about that on Saturday Night we had more contenders cases, but we didn't have more optic cases, which was the which was the thing We got Jake from State Farm That'll be for Buffalo Mark Miller with the bills the Buffalo Bills Next box We've got another quick little two box break in the store buy at least two teams. You got a chance to get the Chargers in a two box break, so imagine Imagine getting someone like a Justin Herbert for a fraction of the price. I'd be pretty nice I think Sam Strayer was saying earlier that that looks like big Ben is gonna stay. Is that right? I don't know if Sam still listening is that right, but they got a restructure that contract though, right? There's the first half Right there. Here's the second half There you go Karen She has the buccaneers Isaiah Simmons Rookie of the Year contenders car to $199 for the Cardinals Sean Maddock with the Cardinals And we got Carter Coughlin New York Giants Brian Crouch with the New York football Giants big blue the G men Rookie of the Year contenders to a tango by Lowe For the Dolphins that'll be for Matthew. We got Ezra Cleveland. This is for you Minnesota Vikings going to Jeremy S Doesn't go to Cleveland his name is Cleveland though Little tug-of-war happening here. It's fun Resistance training Rodrigo Blankenship nice rookie ticket autograph So be a good one to have if he turns out to be a Hall of Fame kick or Kurt disser. It's pretty good Kind of like the goggles that he has here for guys that wear glasses. I think that's pretty cool Has a little Joe Kelly look I think and we got clave on chasing 27 out of 49 little cat team mojo for the Jaguars going to Kurt We've got Jalen or a guy thought to be Jalen Hertz for a second Jalen Raguir on card autograph For the Fly Eagles fly Matthew Shira with that and there's the Justin Herbert that Rex predicted Rookie of the Year contenders card for the bolts Sean Maddock with the Chargers And there you go ladies jump let's put this away. Let's do some randomizing here. That was for the Charger So let's use a new dice roll Couple lists here. There you go. There's the new dice will do left right randomizer And everyone has a shot at the little consolation prize the points after three and a one four times one two Three and a one fourth and final time. So all the left side teams on those round number cards will get those Three and a one four times for everyone else one two Three and fourth and final time It's gonna be for Sean. There you go Sean. Congrats to you. Thanks for getting in everyone I'm Joe for jaspyscasebreaks.com. We'll see you next time for the next one There's more in the store too check it out jaspyscasebreaks.com. Bye. Bye


8. The Drug War After Frank Potts molested an 11-year-old girl in 1982, he was sentenced to 15 years in prison. In 1988, he was granted an early release, despite his parole reports warning that he was still dangerous. Sadly, the report proved prescient as Potts was arrested a second time, in 1994, after he molested another 11-year-old girl. Once Potts was back behind bars, authorities began searching his 40-acre property on Alabama's Garrett Mountain. Local rumors that there were bodies buried around the property had long circulated, and they were finally confirmed with the discovery of the remains of a 19-year-old man who had gone missing in 1989. The Ralph Mountain terrain impeded the search for more bodies, but authorities believed Potts had committed as many as 15 murders since his release from prison. Given that the parole report warned that Potts was high-risk, why was he freed? The Anti-Drug Abuse Act, passed in 1986, dramatically expanded mandatory minimum sentences for drug offenses, including marijuana possession. The act was a gift to violent criminals and sex offenders, who were often granted early release to make room for convicted drug users. Frank Potts was one such beneficiary, and his early release allowed him to enjoy a six-year killing spree. From education to nutrition to healthcare, this series has looked at how individuals are better positioned to make decisions regarding their well-being than bureaucrats and politicians. But this doesn't mean that people never make poor choices. Substance abuse certainly reflects poor personal choices, and many people look to the state to prevent it. But even policies meant to save people from their own reckless decisions, such as the war on drugs, often cause more harm than they prevent. For example, economist Mark Thornton has shown that by creating an incentive for smugglers to maximize the street value of their product, while minimizing its size, drug prohibition unintentionally causes an increase in drug potency. This phenomenon, known as the Iron Law of Prohibition, was seen during alcohol prohibition, as rum-runners found it more cost-effective to smuggle moonshine than beer. The Fentanyl Crisis is the most recent and most deadly manifestation of the Iron Law of Prohibition. Fentanyl, a cheap synthetic opioid, is now linked to nearly all overdose deaths, as drug dealers mix it with black market heroin, cocaine, and amphetamines. By contrast, legal intoxicants, such as alcohol and tobacco, though still dangerous, remain fentanyl-free. We all want our loved ones to make good choices, but when they don't, we hope they can recover and learn from their mistakes. The war on drugs has not only failed in its efforts to protect people from making bad decisions, but it has made those mistakes far deadlier, and it has allowed innocent bystanders to become collateral damage along the way.


Going on everyone Sam here with late in sports cards been 23 tops chrome black baseball hobby 12 box case number 34 random team style Look again at your random results as always you can find these on the website under the results tab as well as the link in chat So good luck here everybody Let's do it TC black everybody Anthony Volpe Rookie to 199 Ozzy albies refractor and Byron books in case the auto is Fernando Tate's junior going to the Padres nice That's on that That's cool Very nice start there Michael Harris rookie refractor to 199 Mookie bets for the doors and Logan Ohapi Angels Got auto Vichy row nice one there congrats Seattle very nice. Take that all day Tantes in each row first two waters Not bad not bad at all Grats on that One second I have to sign it Would you have to do this game really annoying? It's fine. Just do something really annoying. We can just do something else Hey, thank you John picking up a spot in One in one. Thank you mr. John s. We're down to 12 to go 12 to go in one and one Thank you John appreciate your brother. Here is your link everybody 12 to go on one and one Look at this That is pretty holy cow. That is like 2011 right now Francisco lindor to 99 Brian Rock you Dominic Fletcher that was crazy Detrain for the Marlins Don't show Willis to 99. I love that dude. I'm all in on detrain all in on detrain tiger legend true He does a broadcast I Was gonna say if that was Melvin Gordon who fumbled it again, I would have lost my mind Absolute loss of my mind. Yeah, that's fine unless there's like you could do like golden under I suppose But yeah, autos are fine autos are good Christopher Morel a rookie 299 is Matt Mervis green wave and kodaisenka and Then Javier Assad to 25 on the orange auto for the Cubs Congrats on that one as well. I said we're second-loss fumble really Come on, dude Does the Magnifico the ones with the probably yeah All right on the next one large No, psycho, right? That's fine Paul Goldschmidt Sandiel Contra 150 nice one there purple mini diamonds for the Marlins and Brayden Shoemake rookie Sam it just went to pine Street David Ortiz Congrats on that one at their Red Sox on the big poppy. Very cool. Love it man Love it get 12 to go on one and one now everybody 12 spots remain at tiered random team style Guaranteed one from the top guaranteed one from the bottom 100% chance of a top 15 teams Bobby Miller Trish and Kossus on the variation you to focus Congrats on that one there red sox stupid pizza says the stupid a 99 for the cubbies and then Mariano nice one that it's a great case man Yeah, it's a really good case every auto has been good so far congrats on that Yankees very nice Love me some Mariano obviously is a die-hard Yankee thing I Jose Ramirez the 199 Lou Bob Louise Robert for the white Sox and Randy Rosa Rainer Trevor Hoffman. I love it dude to 150 on their frac their auto congrats on that Padres Padres Awesome, I know really a man ran to finish the deal honestly though really ran then fought to 75 The D-backs gold mini diamonds Josh young to 50 rookie for the Rangers Congrats on that day house they have some angels and Hosea al-Tube and then Xavier Edwards rookie auto for the mayor of Marlins Congrats on that Marlins They super futures coming up starting off with an Asturian Ruiz rookie purple mini diamonds the 150 Aaron judge The inks and at Pete Alonzo super futures is Francisco Alvarez to 99 congrats Mets Walt. It's stuff there, buddy Good stuff there my friend Francisco Alvarez super futures refractor rookie Gold mini diamond auto coming up next To be good very good Salvy blue to 75 James Altman the Dodgers and Oscar Coloss It's a Dodger. It's Michael Bush rookie gold mini diamond on the 50 Congrats on that there Los Angeles Congrats doiers take it all day Excited for this deal case man. I see you in the fan It's gonna be fun. It's a good. That's a good little mixture of some stuff potential stuff little do okay, sir That's a hunter-brown rookie Blue to 75 is Mazataka Yoshida for the Red Sox and Logan Webb and Kenny Lofton the Giants that's cool. That's like an Oscar. Yeah, yeah, I'm Kenny Lofton I've seen that card a few so and on that I've seen that card a few times That and the Prince there the Prince the Prince is next level Oh That's Tanner, baby No, well and her baby gold Zack neto to 50 I think that stressed about it to be honest mookie bets on the base I'd also rather not have this like eight game winning streak going into the playoffs either. You know what I mean That is a Raleigh at fingers to 150 and it's Kyle a Kyle Grats on that one upland Land of oak land of oak is right Quick recap errone here everybody We've got golds to 50 our Josh young and Zack neto a couple of rookies Others we've got Raleigh fingers Kenny Lofton Mariano, David Ortiz Fernando Tatis Jr. Ichiro Xavier Edwards Got to 150 Trevor Hoffman to 99 detrain to 99 and Super Futures of Francisco Alvarez gold mini diamonds of Michael Bush and an orange Javier Assad 25 That will do it for the break everybody. Thanks again for the fill coming up next is mega dual case That's gonna be fun


Now it is time for member's statements. I recognize the member from Hamilton West and Caster Dundas. And I would remind all members that during member's statements that it is respectful to be able to hear them. Madam Speaker, this week we hosted McMaster University here at Queen's Park. And as the MPP for Hamilton West and Caster Dundas, I am extremely proud to represent McMaster. Their incredible work benefits not just our local Hamilton, but has true impact on the world stage. McMaster hosts a variety of archives including the works of Bertram Russell, Bruce Coburn and Stuart McClain. Celebrated musician Tom Wilson will join this group when he donates his archives this spring. As part of this celebration, Tom has established an Indigenous Scholarship Award to support Indigenous students from across Ontario secondary schools. This award was established, and I quote Tom, to help honor, love, respect and shine a light back on the culture I have been introduced to later in life and to honor the charitable nature that Bunny Wilson who raised me embodied throughout her life. To help raise funds and awareness for the scholarship, a concert will be held on May 1st at the R.L. Wilson Concert Hall at McMaster University. I don't think there's a connection there. We hear daily in this house the very real struggles facing Indigenous communities. We hear about murdered and missing Indigenous women. We hear tragic stories about youth suicide. And daily we hear about the lack of access to clean water, a fundamental human right. Tom's decision to establish this award is an important contribution that is dedicated to empowering the next generation of Indigenous people that will lead us into the future. Thank you. Members' statements. I recognize the member from Mississauga Streetsville. Thank you, Speaker. Well, so this coming Sunday, March 8th, is International Women's Day. The first International Women's Day was observed on March 9th, 1911 in Austria, Denmark, Germany and Switzerland when more than one million women and men showed their support by participating in public events. Other countries soon followed suit in the years after as the push for women to participate in society and labour grew. In 1975, the United Nations marked International Women's Year and passed a resolution designating March 8th of every year. And today, International Women's Day marks a day of unity, celebration, reflection, advocacy and action. Last Friday, the Solicitor General and Associate Minister of Women and Children's Issues visited my community of Mississauga Streetsville and met with our first responders, the female police officers at the headquarters. We met with Ingrid Berkeley Brown, the Deputy Chief, former Chief Jennifer Evans, who is such a wonderful inspiration and many, many civilian officers, amongst others, who told us about the difficulties they faced in becoming officers, the challenges of having babysitting at different times of the day. It was such an enlightening experience for all of us to learn so much from our wonderful female officers. So Speaker, if any female members of this House aren't already, I encourage you to try and get out there and join many people at the events coming up this year. Tomorrow, the City of Mississauga will be meeting with young women and girls to share my experiences. Thank you very much. Member Statements, the Member for Parkdale High Park. Thank you, Speaker. I rise today to share an initiative that moved me deeply. It's called the Love Lettering Project, founded by my constituent, Lindsay Zeer Vogel. It's a postcard writing project aimed at combating the hate that female and female politicians, female identifying politicians, receive by sending thank you letters. I know that all elected women have similar stories to mine. We have received emails, social media messages, phone messages and letters filled with expletives, discrimination and hatred. Messages that are very gendered in their abuse. Messages that are an attempt to stop women from running for office. I have received envelopes full of my own photos torn into pieces.  The unspoken rule now is that handing this kind of gendered hatred is just part of the job. But why should this be? Women already face barriers to holding elected positions and then we have to face the unspoken acceptance of abuse once elected as well. We are expected to have the grit and metal to rise above it and keep doing our jobs with grit and determination. But we shouldn't have to. As we mark International Women's Day, Speaker, I want to thank all women who are taking up the spaces to deserve, especially women who face additional barriers due to their intersecting identities. And I want to thank women who lived other women up. And finally, Speaker, to all women interested in running for office, I want to say you belong here. Thank you. There are continuing member statements, and I would ask all members to quieten down as much as they can and I look forward to hearing the next statement from the member from Mississauga Erin Mills. Thank you, Mr. Speaker. The Mississauga Erin Mills community had the tough week with two teens of the riding disappearance. I would like to thank the Beale Regional Police for their diligence and tireless work with me and the families of the teens around the clock for almost three days till we locate them. I appreciate the police efforts in locating the missing two teens. To our first responders, the families and the whole community of Mississauga Erin Mills appreciate your immediate response. We are all thrilled that the teens were located safe and sound. Police and first responders work day and night making sure that we feel safe whenever we leave our homes. Mississauga Erin Mills community stood in solidarity and conventionally supported the families of the teens. Now I would like to ask that we give the families and the teens the privacy they need to recover from this terrible event. Mr. Speaker, I want to thank the government for granting the Beale Regional Police $20.5 million this year to give police officers the tools and resources they need to keep our streets safe. Thank you, Mr. Speaker. Thank you very much. Member Statements. The member for York Southwest. Thank you, Mr. Speaker. This past Friday, our community lost a kind gentleman. Bill Hunter was like an older brother to me. He was always working hard to make things better for people and for our community. Bill volunteered on my campaign and was the best volunteer there was. As my sign captain, he would crisscross York Southwestern every day to put up signs. He was dedicated. I have known Bill for many years. He was a caring, compassionate and decent man. He was a respected community leader and will be missed by all of us. I'm sending my sincere condolences to the Hunter family and I ask all members of the House to keep them in your thoughts and prayers. Thank you, Mr. Speaker. Thank you. Next statement, the member for Ottawa South. Thank you very much, Speaker. Speaker, I rise today to talk about sexual assault crisis centers in Ontario. In the budget in 2018, these centers were set to receive an additional 30% in funding about 14.8 million over three years. Instead, they never saw this money and received $1 million annually one time, split among 42 sexual assault centers across this province. Now the government, we heard yesterday, is going to take that money away. And then today we hear reports that the government may be reversing the decision which I welcome. The reality is these centers need more than $1 million annually one time. The crisis centers have experienced a constant increase in the demand since the Me Too movement started. We encourage women and men to speak out about sexual assault, seek help and look to put measures in place to ensure their safety. How is this supposed to happen if the government cannot sufficiently supply the resources that are necessary to meet the demands in this critical sector? It's too late for the government to act like they're coming to their senses. These centers need more support. It's not enough, Mr. Speaker. It's unacceptable that these centers need more help now. On the eve of International Women's Day, it is time for the government to have serious consultations and sufficiently fund these programs that are already overcapacity. Thank you. Thank you very much. Member statements. The Member for Mississauga Mall. Thank you, Mr. Speaker. Mr. Speaker, SEVA Food Bank is a registered charity under six serving Canada in my writing of Mississauga Mallton, equipped with the mission of ending hunger by coordinating and delivering programs that improve the food security needs of the community while also supporting their clients on their journey to self-reliance. Mr. Speaker, SEVA in Punjabi and many other languages means an act of kindness without expectation of reward or personal benefit. SEVA, the selfless help is also an integral part of Sikhism. All six are encouraged by the living Guru, Shri Guru Granth Sahibji to perform SEVA. It is the highest duty that anyone can perform. Mr. Speaker, our society is becoming more and more divided. And these moments, we need more organizations and more people that do selfless service. We need more people that bring each other together and do not divide us apart. This is exactly SEVA Food Bank is doing. Their goal is to provide access to culturally appropriate and personally acceptable supply of good nutritious food to all, Mr. Speaker, the word all, people living in the communities. They have served 900 families. Beneficiaries are from all diverse backgrounds, often marginalized with less disposable income and larger family structure. This year, SEVA Food Bank celebrated their 10th year of operation since opening the doors in 2010. Thank you very much. Thank you very much. The next statement, the member for St. Catherine's. Thank you, Speaker. What do subways, public health, childcare, license plates, families with autism, and now class sizes forced e-learning have in common? They are all cuts this government had made then retracted. Why do they make these retractions? It's simple. They get embarrassed. The government hopes for a problem to go away unless it gets so embarrassing, then they have to act. If it is not embarrassing enough, their strategy is to remain silent and do nothing. That is what still is happening with Jared Whelan, an SMA patient being made to wait for approval for a life-saving drug. He was told he could find approval through this case by case exceptional access program in the Minister of Health. Except, he isn't getting approved, nor is he getting rejected. He just gets silence. This government just makes him wait and wait in silence, hoping the issue will just go away. You know, it's almost been a year making a family wait without a response is heartbreaking. It's heart-wrenching. How is it not embarrassing enough to act now? Giving hope to Jared and never giving him an answer, how is that not embarrassing? This government needs to act now, not because it's embarrassing, but because it's the right thing to do. Approve patients like Jared that are waiting in this program and do it. Not because it's embarrassing, but because it's the right thing to do. Member's statements. The member for Etopico Lakeshore. Thank you, Mr. Speaker, and good morning to you. I rise to bring attention to an important nonprofit organization in my riding of Etopico Lakeshore. Today, I am joined by Susan Carbone, who is in the gallery from Haven on the Queensway. Haven on the Queensway is dedicated to meet physical, emotions, and spiritual needs of people in the Greater Toronto Area. Haven on the Queensway provides services at lessens the effect of poverty and homelessness, addiction and recovery, distributing food and clothing, as well as providing support services for women, men, children, and seniors. Haven on the Queensway offers an atmosphere of respect, dignity and security, as they help people on their way to becoming more self-sufficient. Last week, I had the privilege of joining these amazing women to see firsthand what the volunteers and staff were doing. From providing food, clothing, children's books to various rehabilitation services, Haven on the Q is where hope starts. I want to congratulate Susan and the entire team of volunteers and staff on Haven on the Queensway for their amazing work that they do. And I would like to encourage all members of the House to check out what Haven on the Queensway does to support our community. Thank you and thank you to all the volunteers. Thank you very much, members.


We're doing, so I guess I should remind you that there's a web assign due Wednesday.  Okay, so what we're doing, we were talking about Euler's method. And this is a way to, if you have a differential equation. So this, so we have a differential equation and we have an initial condition then we can numerically construct a solution. So the way this works is we just pick, so our differential equation looks something like, I don't know, y prime is, I don't know, some function. That's y. So if we write our differential equation like that and we have some initial condition like y of zero is some number. So we have something like that. And what we do is we just follow the slope field. So we pick some ratio that we like. Sometimes this will be told to you. Sometimes you just pick something which is, so we pick a step size h, which is the fraction of the derivative that you're going to pay attention to. So you could take h equals one and this usually gives you a fairly bad solution because you're not following very closely. You could take h very small. The drawback of doing h small is it will be, it will follow closely, but it will be a lot of work because you have to do a lot of steps. And then you just start going. So you just take your initial x, I guess this should really be, it doesn't have to be zero to be x naught, but we'll just start with our initial x to be zero and our initial y is whatever it is. No, it's not a. And then we can look at what is y prime of x naught by plugging these guys in. And then that gives us, now we're going to move x ahead a little bit.  And then we just keep going in this way. So y2 will be what we calculate here, y prime of x prime. And y2 is what we got last time plus h times whatever the derivative was from last time and so on. We just keep going until we get as far as we want. So all we're doing here in terms of a picture, if we have our differential equation here, at our starting point we look at the derivative vector and we go some distance along it. This gives us our next y value at our next step size h. And then from that one we look at the derivative vector, we go some part along it to get our next y value. And then if that one we look at the derivative vector, maybe it goes this way, we go some distance along it and we just keep following where it tells us to go. We're just looking at the slow field, but just in the place we're going. We could just plug this into a little machine. Very easy to write a computer program to do others method if you know how to program it all. Okay, so let me do an example of this. I'm going to estimate a couple of things in this example. So suppose I have like a block of clay or something and it's at say 50 degrees Fahrenheit and I'm going to put it in a kiln at 100 degrees Fahrenheit and I'm going to bake it. And I want to know how hot will it be. So I suppose I know I check after one hour if the block is at 100 degrees. But now I don't want to keep checking it every hour and I want to go to sleep. So I want to know what will the temperature be in 6 hours. If you didn't think very hard, you might say, oh well it's going to go up 300 degrees because 6 hours goes up 50 degrees an hour. So 6 times 50 is 300 so it will be 400 degrees in 6 hours. Do you think that's right? No. So you have to know a little bit of let's say physics. So Newton's law of cooling says that the change, if I have something, if I have something at one temperature in an ambient area that's another temperature, then this is some constant which depends on the thing times the difference in temperatures. So in this case it's, let's do it this way, T of H minus the ambient temperature. So this differential equation, in this case I guess it's Newton's law of heating, but this is, and we can solve this differential equation and get an explicit formula for what the solutions look like but let's not do that yet. So now let's just use this and use Euler's method to estimate what the temperature will be in 6 hours. Okay? So is it clear what to do now? That's good. If it was clear to you then we could just leave since it's not clear. So let me go through this and just for simplicity I'm going to take a step size of 1. So we need to know a couple of things. We need to figure out what is this K and we need to figure out how to use this to go ahead 6 hours in time. Okay? So first we have to guess K. Well we have to use the information we have to estimate K. This estimate will be wrong but it won't be too bad. So this is not a very good solution but it's a solution. Sorry? So K depends on how quickly the thing absorbs heat. If it's a block of clay it will absorb heat less quickly than say a metal. So if it's something that heats very slowly K will be different than if it's something that heats fast. Right? So this depends on the material. It also I guess depends on the oven. Whether the oven is filled with air or filled with water well you can't have water at 500 degrees. It could be filled with superheated steam. You know. So it's something that depends on the situation. Okay so first how would we guess how would we estimate K? I claim that most of the information needed is not assumed that we solved it yet. You should be able to get an idea. Is K a tenth? Is it a hundred? Is it negative six? What would we use to figure it out? Yeah. Use the two temperatures. Right. So looking at the two temperatures what do they tell us? We know T of zero is 15 and T of one is 100. Why does that tell us anything about K? I'm sorry. Find the difference? So T prime of zero is just about 50. Maybe it's 60, maybe it's 49 but it's like 50. So this tells us that T prime of zero is kind of like T of one minus T of zero over one. I mean this is the difference quotient that you will take you to the limit of remember that back in the dark ages so this is 100 minus 50 over one which is 50. It went up about 50 degrees in an hour. So using that we should be able to figure out what K is because now we know everything here. We're saying that T prime of zero is about 50 which is K times there's too many 50s on the board but oh well T of zero minus 500 so T of zero is 50 so that means that 50 is K times negative 450 so K now it seems to be a ninth doesn't it? Huh negative K I don't know how I got an eighth before because I did T of one well whatever so K is about 50 over negative 450 which is a ninth which is 0.111111 it's negative so let's just use 0.1 because all of this is just slop K is actually negative is log eight over log nine I mean log eight nines but we don't know that yet okay so using K to be negative 0.11111111 we can now use Euler's method to estimate what happens after six hours, five hours I don't know some number of hours so now I'm going to use so now my differential equation is T prime 10 hours is negative 0.11 enough ones negative a ninth of T of H minus 500 and so now I'm going to use Euler's method to guess, to estimate what's going to happen by T of six so T of zero we already know it's 50 T of one we already know we're going to write it so right this is unfortunately I have two H's here I have my step size H and I have my H for hours so unfortunately I need the same letter for the same thing but here my step is one so instead of writing H I'm just going to write one because I'm being lazy I'm using one so to guess what T of two is it's going to be just about T of one plus my step size which is one times the derivative at one well what's the derivative at one it's negative a ninth of the temperature at one minus 500 which is well I'm going to use 0.1 for a ninth so it's about 40 this is negative I'm going to forget about the values so T of two what did I do wrong this should be 450 because whatever method usually you use the previous X and Y because you don't necessarily know the next step so I want T prime of one yeah so I'm sorry this is right this is right that's okay because I did the 50 step already yeah whatever the number is it's still 40 okay it's like it's actually 44 well a ninth is 0.111111 so it's 44.444444 okay so this is 100 plus 44 is 144 and then the next step the temperature at three is going to be the temperature at two plus however fraction I'm taking one of the last temperature that I had the derivative at the last time I had so the derivative at the last time I had here is lost my place 144 plus 1 times so the derivative at the last time is I take these two values that I had 144 and 2 I don't need to and I plug them in here so 500 minus 144 is 56 56 yeah okay so that's 356 times 0.111111 is so it's 356 times 0.11 which is 39 call it 39 144 plus 39 is 143 plus 40 is 183 maybe I don't want to go all the way to 6 maybe you get the idea by now so T of 4 is T of 3 plus my step size times T prime of 3 T of 3 is 183 my step size is still 1 and now my derivative last time is 500 minus 183 is 317 so 317 times 0.1 is 31 34 35 okay is 200 should I keep going or are we good enough yeah T prime of 3 means I know my H is 3 and T of H and that's all I need for this so I looked at T of 3 I plugged it into the formula I got it I don't know and I just keep going the answer is after maybe you get the idea I can keep going but okay so after 4 hours instead of going up 200 degrees it only went up 168 degrees and so on so Euler's method is really very straightforward it's the most simple numerical way of solving a differential equation there is it's not very accurate essentially if you use a big step size like 1 if the step size gets teeny tiny then it gets more and more accurate it's very analogous to doing a numerical integral remember this stuff where we take the what side is that this side is left where we take the left side left hand rule it's almost exactly the same as doing the left hand rule and the step size H is choosing the width of the rectangles if we take a tiny with a rectangles you get a good answer but you have to do a lot of work there are other numerical methods I think we may come back to them there are other numerical methods but first off Simpson's rule was much more accurate for the amount of work there is something that can be here that's like Simpson's rule which is called Runge-Kutta Chris H there anyway, it's named after Mr. Runge and Mr. Kutta who came up with it and it's like Simpson's rule very close analogy between Simpson's rule and Runge-Kutta it's just numerical things so like in an engineering class where they have to solve a differential equation probably those people have to put there or they might use a slightly improved version called Runge-Kutta-Fellberg so later so this is like from I don't know the 1940s and then this is from like the 70s where we figured out how to make it a little better so there's these variations on Runge-Kutta which are now about 30-40 years old that people use to solve differential equations in computer programs or in engineering simulation and there's all sorts of there's an entire branch of mathematics devoted to doing this kind of stuff called numerical analysis okay so fine this is all good actually work on solving some differential equations coming up with formula you can't always come up with formula so like when I took this class we had electricity but just barely and we focused a lot on actually writing down solutions rather than thinking about what the solutions are the problem with that is for most differential equations you can't really write down the solutions just the ones that come up in class but for those that you can it's a good thing so let's work on coming up with some solutions and let's start with very easy differential equations so the easiest kind of differential equations to solve is called the separable and we have something that looks like y prime equals some function of x over some function of y so for example y prime equals let's make the simplest thing we can think of x over y the function of x could be a constant like one the function of y could be a constant like one so something like this then instead of writing it as y prime we write it as dy over dx and then we do something which is actually can be justified mathematically and I will but you just forget that it doesn't make any sense and you treat these things like fractions and you cross multiply so I treated dy dx like a fraction and I cross multiply mathematically this is just total crap but it works and actually I will justify it a little bit but you can do it because you really can't and then you just integrate both sides assuming you can do the integral and this gives you some function of y plus a constant and this gives me some function of x plus a constant that I solve for y and I'm done so let me do that in this case so in this case I think of this as dy dx equals x over y I separate the variables so this becomes y dy equals x dx then I integrate both sides if I integrate I get y squared over 2 equals x squared over 2 and then there's a constant floating around I only have to write one constant because we don't know the value of this constant so if I wrote plus c1 here and c2 here then I can just take my constant to be the difference of c1 and c2 so I can just put one constant for the whole equation and then I can solve and constants are magical I can just forget about constants times constants y squared equals x squared plus 2c but 2c is really some other k so the equate I think this would be a hit so the the solution to this then y squared equals x squared plus a constant or y equals well something like that maybe it's the plus square root so minus square root it depends on which c you take what your initial condition gets so that gives us our solution if we had an initial condition like we knew when x was 0 y was negative 1 so let's just augment this a little bit so I knew that y 0 is negative 1 then what would the solution be nobody knows how to figure that out so we can use this in this equation to figure out which one it is so y of 0 is negative 1 so that means negative 1 equals well it's a plus or it's minus square root of 0 squared plus some constant well obviously because this thing is always positive it better be the minus 1 and so c is 1 so my equation in this initial value is y of x is negative square root of x squared plus 1 let me do another version of this so let me actually just do one more equation and then I'll do another application maybe I'll do this one so is everybody okay with this this is really pretty straightforward pretty easy stuff the only place where it gets hard is sometimes the integrals get hard and you have to solve you have to pay attention a little bit oh maybe I should justify that it's okay let me do another example and then I'll justify so let's just change this just a little bit let's let's say dy dx is x squared y so this is separable because I can get all the y's over here get all the x's over here so divide both sides pi y and multiply through y dx should I put an initial condition on this do you want one no it doesn't matter so yeah so yeah so right so if you think about this picture when I have an initial condition it's telling me where to start there's lots of so if I give an initial condition see this is not a single curve this is a whole family of curves that look like things like this and I have to know which one I want so when I said when x is zero y is negative one that said I'm here and then I take this curve so that tells me which curve I want if I said when y is zero x is zero then that would give me one of these guys so x is zero doesn't really give me enough information to know whether I want the plus or the minus but if I said when y is one x is one that would tell me I was not at this point and so on so the initial condition nails down the constant integration to a specific value just like when I did this heating problem I told you it started at 50 degrees I would have a different answer if it started at negative 10 so back to this we integrate both sides and so when I integrate this what's the integral of dy over y so this is the log y and the integral of x squared is x cubed over 3 plus some constant and now we want to solve for y so I exponentiate both sides I can also so e to the log of y is the absolute value of y I can clean this up a little bit when I have a plus in the exponent it's the same as multiplying c is just some constant so e to the c is just some constant it's positive now so I can call it actually a so I have absolute value of y is some constant a times e to the x cubed over 3 that means y is plus or minus some constant a times e to the x cubed over 3 but a is positive so plus or minus some positive number is a positive number or a negative number so this is just something times e to the x cubed over 3 so k is any number could be plus, could be minus a is only positive here but k could be a if we have an initial condition we can figure out the value of k I told you when x was 2 y was 3 then we could figure out what a was let me do these are very easy I don't know, is anybody baffled by this at all? so the only time this gets hard is when the integrals get hard if you have a nasty integral then sometimes integrals are hard to do so should I do another example with some words about it like voltage in a circuit or oh yeah, I was supposed to prove something so I want to show that this actually is a reasonable thing to do so why does this make sense so we have something like dy dx is f of x over g of x which is the same thing as saying oops I guess this was a y g of y dy dx is so that's just rewriting it there's nothing wrong here what was wrong is sort of putting the dx over here so suppose that we know that the integral of g of y ui is the same as the integral of f of x dx because that's what we got out of that this process here all right, we do the integrals and they're going to be equal well what if we take the derivative of both sides of this equation so if I take the derivative so I'm also knowing y is some function that depends on x because that was the whole set y is some function depending on x I don't know what it is but it depends on x and it satisfies this relationship so what if I take the derivative of both sides of this with respect to x so if I take the derivative of this thing g of y dy and better equal the derivative with respect to x of the integral of f of x dx because these two things were equal well this is just f of x and if I take the derivative of the integral of g of y with respect to x I mean this thing is going to be g of y but I have to use the chain rule y is a function of x so this is dx of y so g of y is the derivative of y g of y times the derivative of y is x in other words it solves the equation because that's what I started so even though this looks like cheating in fact this cheating gives you the right answer because of the chain rule sometimes cheating doesn't give you the right answer it's sitting behind somebody who's not so smart but this looks like we're doing something not okay but in fact it is okay I was going to do a problem with yeah I was going to do a problem with a circuit and finding the voltage in a circuit do you want me to do that? yes? so I'm not going to exactly derive the differential equation I'll wave my hands about it so if we have a circuit that looks like so we have a battery here and we have a resistor here and we have a capacitor here and we have a switch so this is the battery so this gives me a charge this has a resistor which slows stuff down this is a capacitor this is a switch so Ohm's law says that voltage incidence times resistance and also using Kirchhoff's law using Ohm's law so I'm sorry this gives me R this gives me voltage this gives me inductance so if I mess around and use Kirchhoff's law then wait where did L come from is inductance yeah so why did I call it I? I don't know well anyway L and I are related well so anyway if I get so I mess around and I get that in such a circuit L times change in inductance plus the resistance times the inductance is going to be equal something's wrong here so this is the differential equation that describes and I seem to have extra stuff this is the differential equation that describes the current in the circuit when I close this okay so when I have such a thing so suppose I had this where this is 12 and this is yeah why do I have it on then this is for one of these entries I put a 60 volt battery over here then I can figure out what's so I is in the amps and I want to figure out how this goes so using this I can plug this jump together with that differential equation to figure out what's going to happen to the voltage so this is E what's going to happen to the voltage in this system I mean to the amps in this system so it'll describe it'll describe the change so we can write this in this case so we know L, L is 4 I we don't know or the derivative of I we don't know R is well that equals 60 so we don't have to check that all of the units match up but of course they do because we always use the right minutes in math and so let me actually write this as di ft just to emphasize that it's a differential equation and in fact we can separate everything we can just put all of the I's here and we get a very easy differential equation so 60 over 4 is the number I should know 15 so we have I prime is 15 minus 3 I and so I have to swap it back so di over 15 minus 3 I equals dt because it's separable I have this equation so I can put the T's over here and the I's over there and it's a 1 there so that I can solve I just integrate both sides to get that T is the log of 15 minus 3 I except I have to divide by minus 1 third because I'm really making the substitution mu equals 15 minus 3 I so du is minus 3 di so I have to divide by minus 3 so that means that the log of 15 minus 3 I minus 3T plus a constant exponentiate 15 minus 3 I is some constant e to the minus 3T and so we're solving for I so minus 3 I A is now plus or minus equals 15 minus A e to the minus 3 T something's wrong if my side's wrong this is a plus so I is that I is 5 minus B e to the minus 3T so that means that if we let it run for a long time the voltage will tend to 5 and I didn't give an initial condition but if we had an initial condition where it was after 1 second then we would have an explicit solution without constant e there these things are relatively easy and straightforward another kind of problem that you can do in this which I don't really have time for right now I lost track is you have like a vat of stuff you have a big vat of margaritamins and people are still drinking it so you want to know how strong it is and you can calculate the concentration as it goes I'll do one of those and then we'll move on to the next part