Hello, and welcome to Road Gear Reviews. I'm Josh from The Freedom Theory, and today I'm going to be showing you one of my favorite apps for travel, which is overnightRVparking.com. If you were to ask me which tools or resources any RVer or traveler must have, I would say overnightRVparking.com. I use this app literally every single trip that we go on. If it's going to be more than one day of travel, I use this app to find a place for us to sleep, and just as importantly to find places that we can't sleep because not every Walmart and not every Cracker Barrel and not every Sam's Club will allow you to do it. So this is the app that I use a lot. So today I want to give you a demo of the Android app as well as their web interface. So first I want to show you guys the website. This is the front page when you're not logged in, and as you can see, they really have a feel for what RVers need. Right here it says, if you're wondering where you can park overnight to sleep or if you can sleep without an eviction or a ticket, et cetera, this is a site for you. So they really have a good feel of what RVers need. And I wanted to show you guys this in particular because if you haven't subscribed, this is where you'll do it. You'll just hit the subscribe now button. Now the cost to subscribe is $25 a year. So let's go ahead and go to Google Maps and we'll take a look at what our annual pilgrimage might look like. Pretty much every year we end up in the state of Washington and then we end up down in New Orleans for Thanksgiving. So let's go ahead and put in New Orleans here. I'm gonna hit directions and I'm gonna start in, oh, let's just start in Seattle. So as you can see here, we've got quite the route. It looks like it's gonna bring us down here through Oregon, through Colorado and so on. So let's go ahead and just look for a spot. I don't know and let's say Salt Lake City, Utah for us to spend the night. So we're gonna be coming through. We wanna stop in Salt Lake City. So we're gonna go ahead and just search for that. All of the addresses are based on Google Maps. So we'll put in Salt Lake City and in a second here. Okay, there we go. You're gonna see all the locations populate. So there is a legend and you can look through that. It's your convenience. It'll show you what all the different colors mean. But what we're mostly looking for is green and red. Red means that you're not allowed to sleep there and green means that you are allowed to sleep. Always wanna check with a proprietor. Of course, if it's a business to make sure that the information here is up to date because this information is submitted by users. But let's just go ahead and click on one of these and I haven't planned this demo. This is as new to me as you. So we'll see what kind of places are in the area. So I'm gonna click on this one right here and it's a Walmart store. And you can see that RVers have reported that it is okay to spend the night. They've also reported that it's well-lighted, appears to be level and that there's a Taco Bell and McDonald's within walking distance. That's the sort of information that you're likely to see. RVers like to submit that information and when you submit sites, which you can do, I hope you'll include that information as well. The other thing to pay attention to is up here people have given the phone number, they've given directions. And then GPS coordinates here as well. So you can go ahead and put those directly into your GPS. There are two other things that I wanna show you really quickly. One is that you can submit new sites by clicking this info button right here. And there's a whole host of different options here. And if you go through these, you'll see how to submit new sites. That is worth doing because you'll get free weeks or even months added to your membership for doing so. So I highly recommend that you take the time to submit new sites and help other RVers out. The big advantages of overnight RV parking is that it doesn't just have Walmart's and other commonly known stops. It just so happened that the first location I chose was a Walmart, but I was clicking through some of these other ones. And if you look at, there's a cracker barrel. Another cracker barrel, there's one over here. There we go, Rocky Mountain Cummins. So Rocky Mountain Cummins allows RVers to park overnight. So that's just a sort of information that you'll find all across the nation, everywhere from dirt lots to closed lots, you know, closed businesses where you can sleep in the lot to Cummins dealerships. You just, you're gonna find all kinds of places here that you won't find on a lot of other apps. The other things that I wanted to show you real briefly, if you click this info button, you can submit a new location here. You can submit a new location here where it says add a new location. You can also click over to satellite view. And you can do this in the app as well. And satellite view is really handy because, as you can see, I'm zooming in here. And we're looking in this case at this Walmart and we can get a really good look and see, okay, here's the Walmart, this is what it looks like. Here are the roads coming into it.  The final thing I wanna show you on the website is this tab that says files. If you click on this tab, it will present you with the form that you can fill out that will allow you to get a PDF file containing all of the locations for the area that you're going to be in. That's obviously really helpful if you're going to be in a place without internet access or cell service. So now let's go ahead and take a look at the Android app. Here in the Android app, and as you can see the interface or the map itself is very similar to what's on the website. Let's just use a different example here and let's look at Albuquerque, New Mexico. This is a place that we come through quite a bit, along I-40 just as we're traveling from east to west and so on. So let's say we're traveling through Albuquerque and we're looking for a place to spend the night. I'm just going to choose, I would butcher the name if I said it, Cedillo, Cedillo, I don't know. I'm gonna hit the green dot here and this is actually a parking ride plot. So you can see that users have said there's no signage there, restricting time or duration of parking. There is a space for trucks and other large vehicles and apparently you can stay the night there. There is a clickable address up here at the top that will open up the default mapping application on your phone. The GPS coordinates are here. And then another thing is this last update time. This is the last time that a user submitted information about this location. I find that handy because sometimes users haven't submitted information in a long time. If the place hasn't been updated in several years, you may want to call ahead just to make sure that circumstances haven't changed. However, you also can get free time added to your membership by updating existing sites. So you can get free time by referring friends, by updating existing sites and also by updating locations. So that concludes my review of overnightRVparking.com. I highly encourage you, sign up, try it out. It's a tool that should always be in your tool chest, so to speak. Every traveler should have it in my opinion. And I'd also love to hear from you. What apps do you like? Are there any apps that you would like to see reviewed? If so, please leave it down in the comments below. And also don't forget to subscribe. And until next time, we'll see you on the road.


So frankly. I'm so excited I don't want to drag out this intro any longer if you're new to the channel We cover FNAF news all the gosh dang time So if you want to stay up to date with what's going on with not only FNAF plus But also the entirety of the FNAF franchise subscribing to this channel is the best way to guarantee You'll stay up to date and if you're excited about FNAF plus hit the like button tell me your theories for the game in the Comments down below. What are you hoping to see in the game? What characters mechanics, etc? And let's just hop into the video. So Phil felt bored one day and he's like, you know what you guys have been patient Let's give y'all some footage of FNAF plus to be fair. His exact wording was just a bit different more professional He said fixing the AI for a hashtag FNAF plus is taking too long So I'm gonna put up a small showcase for what I've been doing the past few weeks on at FNAF plus as a thank you For how patient people have been a lot still left to be done But everything is coming together very nicely also updated the FNAF plus FAQ saying what is the current state of the game? Update 2 as of June 5th 2022 the game's final visuals have been implemented all UI styles have been added and are fully Customizable if you want more info on all the UI options for FNAF plus We did do a video on that already on the channel that'll be linked down below and the game's AI is still in the process of being Tested and balanced at the moment. There are lots of crashes and unintended behavior after the AI is polished up and balanced Development will move forward with adding sound effects and atmosphere menus and the endings Interesting tidbit there. He said endings plural now that could be the typical you get to night 5 you beat it You get a paycheck night 6 you beat it a overtime paycheck night 7 you beat that You know, whatever the max mode is you get fired or it could be something different a small showcase of the game's visuals Has also been uploaded today and that's exactly what we're moving on to next so without further ado This is our showcase. This is the office. Wow. I mean already just looks absolutely insane Now we did see a bit of this office in the breaking and entering short But this is what it's gonna look like in the game You got the celebrate poster of course the signature fan You got a figure of mr. Cupcake You got a figure of Freddy got a whole bunch of drawings party hats cobwebs speakers monitors You know, you also have a speaker right here or a intercom Maybe this is where that you know phone guy stand in is gonna instruct us But also take note of what's missing here no puppet mask and also keep track of this Freddy figure So there's not actually any sound before this video. So if you're like, hey, where's the sound? There's no sound effects for the video. There's no sound. I promise but actually pressing play on the video This is our look at some gameplay. Look. You got a spinning fan on the desk. Oh What's over here? Huh moving my cam so you can see the clock So it looks like not only do you have a clock in the top right at all times You can also see the exact minute you're at in the night by turning to the left and looking at this clock You got some office rules from Freddy. Don't waste power. Don't lays around. Don't take the pens Don't let customers inside. Don't make weird noises. Don't stain the carpets a yo And also don't allow refunds and it looks like this office Actually works as an office. It looks like someone you know a customer could come up on this side of the windows speak through the Speaker and also be able to pass things in and out through this little hole You can see the clock taking down in real time taking a look at the right side of the office now safety first Zero nights since last incident. Hey, I'm back It's gonna be interesting to see if that number actually Changes depending on how many times you die in the game some more drawings of Chica and the cupcake absolutely terrifying Bonnie Freddy Chica and also Foxy peeking out from the curtains looks like trying to give this kid a present another booth right here Looks a bit different looks like this one's chained off and it also doesn't have a speaker or an opening But I think we do see so that's how you close the doors So you physically have to pull your cursor down. Let's go back and take a look at that You have to pull it down and pull it back up to open and close the door.  Maybe we're gonna talk about that a bit more Later on in the video, but that's a look at the doors and I think do we go into the cameras next? Yes So these are the cameras and see right now. We're looking at the dining hall a.k.a. Cam one B This just looks absolutely insane. We're gonna see what this meter does in a little bit But right now we'll go into cam 5 the restrooms again looking absolutely amazing Look at this. So this is what this meter does. I say meter. It's not really a meter But you click on this and it looks like you have to physically pull this arrow to pan over the camera feed Looks like on this side of the restroom feed You can see a camera TV a poster visit the fun-filled prize corner some light switches But yeah, you have to physically pull in arrow, which is certainly interesting Usually in FNAF, you know the cameras will pan themselves, but this time it's manual the player has to you know Again click on the arrow click and drag. But anyways moving on to cam 1a. This is the entrance Now we did see this camera in breaking and entering I do believe this lever gets pulled down and you can open and close the gate I don't know if you can do that, you know Actually in the game as a mechanic, but you can see a flashing exit sign Creepy and now this is one of the most interesting rooms in the game cam 10 the electrical room This is not a this is not a location a room in the original FNAF 1 This is brand new to plus it also looks like you can't pan in here So maybe some cameras you can't pan and it's just a static location where the feed is But keep track of what this room looks like a closed fuse box and Five yellow lights on this panel also help be saying warning high voltage. Yeah, look see it's blinking That can't be good But now let's move on to cam 9a the West Hall a very very creepy hallway Pan a little bit. We did see this shot once again in the breaking and entering teaser video Just a whole bunch of drawings. You can see you know Bonnie Freddy Bonnie again Chica It looks like lonely Freddy from the Fazbear Fright story and a bit more healthy safety tips. Don't run Don't yell don't scream. We still can't poop on the floor at Freddy's absolutely disgraceful stay close to mom Don't touch Freddy don't hit leave before dark and you got help you saying thank you Let's look at the hallway and Then we're back into the office and that concludes the video We're not done just yet because we also got a few still images from FNAF plus his Twitter account showing off a bit more The game most of which we did see in that video But there's also a few smaller details that I want to point out first up This is the office now remember what I said about the puppet mask and the Freddy figure It looks like the puppet mask has appeared again in this image in the video. It wasn't there But now in this image it's there could it be like a entered scenario from sister location where a character takes that mask I definitely do think that this mask has some importance in the game, you know, it's been teased too much There's definitely something going on with that mask and also the Freddy figure has suddenly turned into a balloon boy figure Maybe that's just a small Easter egg where the figure, you know switches different characters depending on you know Just a random number generator or maybe it's another customizable feature where you get to pick and choose different You know figures maybe even plushies and other toys you can have on your desk This is a look at the left side of the office and the lights turned on you can see a light button That wasn't there in the video So it looks like to flash the lights in the hallway outside of the outside of your door in the blind spot You have to press a physical light button and the panel on that button has three lights green Orangey yellow and I'm assuming red once again Maybe if you use it too much or maybe if you're using too many electrical themed You know mechanics at the same time, maybe one gets like short circuit or something I am not entirely sure moving on. This is a look at a different UI This might be the classic UI if I'm remembering the name correctly So you can see all of the elements of the UI now feature a theme similar to the classic FNAF one style the cameras the Time the night the power meter the power percent all very similar to the UI We see in classic FNAF one and it looks like the UI not only affects the cameras But also some of the mechanical elements in the office You can see this is still the classic UI and the door and light buttons have you know matched that classic UI feel that FNAF one had Also once again the figure on the shelf has changed It's now DD from FNAF world coming back an ultimate custom night. So that's a third figure It seems like we can have on the shelf Yeah, just that small touch of the UI of the office changing as well to match the the theme that the player set That is such a nice touch. I freaking love that This is the old-school UI and you can see once again Just how much changes when you select a different UI not only does everything have that super old like Windows aesthetic to it, but also the camera feed is now in black and white such such nice Attention to details Phil you're doing a freaking amazing job with these UIs next image We take a look at cam 2 which looks to be some sort of storage area behind the main stage You can see a bunch of cleaning products a lost and found box and also poster a ripped missing person Poster as well as some of the trash in the gang members. You can see mr. Hugs you can see mr. Can do I think's the name of the balloon bucket Bob is on the shelf number one crate is also on the shelf and I think Where's pan stand? We're missing pan stand. I can't see him, but I'm hoping and I'm praying that Pan stand is in that camera feed somewhere next image is another look at the West Hall and Interestingly enough the icon for cam 9a that we've selected is purple so once again more customizable options for the color of Certain things like the camera feed, you know icons now. This is the final image This is one of those camera feeds that I said hey pay attention to this We're gonna need some info on this camera later on in the video that now have you noticed what's changed the fuse Box is open the panel only has two lights on now It also has another bar on the right side that has three yellows and a red so clearly something's going on that either the animatronics are malfunctioning our power system or the player themselves is able to Maybe interact with the panel and fuse box through the camera feed I think it's gonna be interesting if some of the characters You know some of the animatronics can go into the electrical room and mess around with our power supply And I'm assuming some of the borers and lights we saw on like the doors and the lights in the office Affect what goes on in the electrical room with the lights with the fuse box You know with the panel all that stuff, but that was our update on FNAF plus. Oh my god, dude It looks so so good Phil also briefly mentioned that a steam page Maybe is a possibility sometime soon basically Phil was on this huge break from social media for like I want to say two months I don't know exactly the length, but it was a pretty long time and he came back on the last day may saying anything happened Well, I was gone wanted to come back with a surprise steam page for FNAF plus But you know some opportunities are too good to pass up So maybe sometime in the near future, we can actually see a steam page for FNAF plus That'd be super exciting to see and speaking of steam pages I feel like a fanverse game just recently came out with the steam page now I am probably gonna do a whole separate video dedicated to the steam page for pop goes arcade Just because it released a whole bunch of new info and footage for the game But I'm gonna throw it in quickly at the end of this video pop goes arcade a official fanverse game now Has a steam page like I said a whole bunch of new footage and content and right now It has a release date of July at some point, but if you want to go wish list it I'll leave it as a link down in the description below. Let's gonna do it for this update on FNAF plus Thank you so much for watching and I'll see you all on the flip side. Goodbye


Welcome to our review for exam 2 for math 1050 college algebra. As usual, I'll be your instructor today, Dr. Andrew Misseldine. With exam 2 now upon us, let's talk about the types of questions we're going to see in this exam. Just like exam 1, this question or this exam will have two types of questions. There'll be actually nine multiple choice questions, which are worth five points and then there will be six response questions that range from five to 12 points each and we'll talk about the specifics of them in just a moment. There are some specific, well I should say semester specific details about this test like time, place of manner and such. I refer to you to Canvas for that information as you won't find it in this video. The basic structure and the resources available to you for this test are essentially identical to what you had on exam 1, so again refer to Canvas for those. In this review video, I mostly just want to focus on what are the types of questions that you're going to see for exam 2. Now as you're preparing for exam 2, I want you to be aware that this exam is going to cover lectures 9 through 21. So for our lecture series, this covers what we're calling chapters 2 and chapters 3. Chapter 2 was about linear functions and their applications. Chapter 3 was about quadratic functions and their applications, so lectures 9 through 21 will be covered in this exam. So without further ado, let's get to some of the specific question types you should be prepared for as you prepare for exam 2. So starting with the multiple choice section, of course, we'll do question number 1. You see question 1 here, it's asking you to calculate the slope of the line that passes through 2 specific points right here. In particular, question number 1 is going to ask you a question involving the very first lecture of this unit, lecture 9. Lecture 9 was a was a introduction review of linear functions, some things that we found in that section in that lecture. We learned how to solve linear equations, we learned how to solve linear inequalities, we learned how to graph lines and come up with linear equations to graph those lines. And therefore the slope was a very important ingredient there. To answer question like number 1, you probably do need to know the slope formula m equals y2 minus y1 over x2 minus x1 that rise over 1. But you should also be familiar with the important equations of a line, right? So we have the slope intercept form of a line y equals mx plus b, right? m is the slope that we get from this formula, v is the y-intercept. You probably also want to know the point slope form y minus y1 equals m times x minus x1, where x1 comma y1 is a specific point on the line, m is the slope that's computed right here, like I mentioned before. And oftentimes we use the point slope form to then transition into the y-intercept form. So those are some important formulas we got from lecture 9, but also the ability to solve linear equations, to solve linear inequalities, that's an important thing as well. And so again, for question number 1, it will cover lecture 9, something from lecture 9 about linear functions. It could be like what you see on the screen, what you have to then just compute the slope of a line from the formula or maybe given the equation you're asked to identify the slope. You could be asked to build the equation of a line, put in slope intercept form, but like I said, you'll probably start with the point slope form. Can you solve a very simple linear equation? Can you solve a simple linear inequality? Can you find the intercepts of a line? That's an interesting question. Of course, the y-intercept is right there in the formula. If you want to find the x-intercept, you plug in y equals 0 and then solve for x. And so those are some variants you could see for question number 1. Question number 2 will be a lot more specific than say question number 1 was. Question number 2, you are going to be given an absolute value equation. It'll be an equation involving absolute value, and that's absolutely true. I know horrible pun there. Absolute value we covered at the very end of chapter 2, specifically lecture 15. So you should be able to be prepared to solve an equation involving absolute value. Really the things to review for absolute value is essentially the following observation. If absolute value is equal to some positive number like say 7, then you're going to get two solutions to that equation. You're going to get x equals plus 7 and minus 7. So you have to consider the two cases because absolute value forgets the sign. If you take the absolute value of some variable x, you don't know if it's positive or negative. So when solving it, you have to consider the two possibilities plus 7 or minus 7 in the situation. Now of course if the absolute value is equal to 0, that same strategy works there as well. You're going to get x equals plus or minus 0. But there is no difference between plus or minus 0. It's just a 0. So if absolute value does equal 0, you get a unique solution. Be prepared for that. But it is also possible that absolute value equations have no solution. If the absolute value is equal to something negative like negative 2, well absolute value is always non-negative. The absolute value of x is always greater than or equal to 0. So if the absolute value equals a negative, we would actually have to then do no solution in that situation.  All right. One other variant I do need to point out on this problem right here.  In that situation, when you have two absolute values equal to each other, it really doesn't fundamentally change the problem. And it's actually similar to this one right here. You would proceed to look at x plus 1 is equal to plus or minus x plus 3. Now in this example, I should mention that one of those choices will lead to no solution, but the others will lead to a solution. So you might only get one solution. Absolute value equations can have no solution, one solution, or two solutions. So be prepared for these possible variations. Question number three is going to be a question about complex numbers, in particular doing arithmetic with complex numbers. Complex numbers were reviewed in section, I should say lecture 16. That was our first section for chapter three, our introduction to quadratic equations, quadratic functions. And that's because sometimes quadratic equations have non real solutions. You might have to have a proper complex number. In this exercise right here, it's asking us to take the quotient of two complex numbers, three plus five i over one minus two i. So some things to remember there is that when you divide by a complex number, you should times the numerator and denominator by its complex conjugate, you switch the sign. Then you got the FOIL, something that's things out there. So you definitely have to be able to add, subtract, multiply, and potentially divide complex numbers. One of the beautiful things about asking you a division problem with complex numbers is that in order to do division, you have to also do multiplication. You have to also be able to add and subtract complex numbers. And so it really is the whole enchilada. So if you understand how to do a question like number three here, from this practice test, you're probably fine from the type of stuff we saw from lecture 16 there. The things to remember, of course, is when you add and subtract complex numbers, treat it like combining like terms, all right? You add the real parts, you add the imaginary parts. When it comes to multiplying complex numbers, it's basically the FOIL method because each complex number has the two parts, the real part, the imaginary part. The, of course, the important thing to remember is that when you FOIL at some point, you might get something like i squared. Well, since i is the square root of negative one, i squared is itself negative one. That also allows us to do things like i cubed, which is negative i, i to the fourth, which is positive one, and other higher powers of i as well. So be comfortable with doing these arithmetic calculations, the four arithmetic functions, addition, subtraction, multiplication, division with complex numbers. Moving on to question number four, as you can see here on the screen, question number four is going to be something about solving quadratic equations. So you see on this one right here, you're asked to solve the quadratic equation, 3x squared plus 5x plus 2 equals 0. When solving quadratic equations, I guess the first thing to mention is that these topics were covered in particularly lecture 17 and 18. That's where we talk about solving quadratic equations. So some basic principles we want is that when you have a quadratic equation, we like the right hand side to be 0. I mean, it could be the left hand side, doesn't make much of a difference, but you want to make one of the sides of the equations, we'll just say the right hand side for the sake of it, to be 0. And then you want to combine all the like terms on the left hand side. So that is to say we're looking for something of the form ax squared plus bx plus c equals 0. Once the quadratic equation is in the standard quadratic form, it's then prime for solving it. We could solve it by factoring, right? We could take three times two to get six and look for factors of six that add up or subtract maybe to be five. Won't say much more about that. We did talk about how to factor a quadratic polynomial in lecture 17 and how that when combined with the zero product property helps us solve quadratic equations. That'd be useful. Another approach is you could try to solve the quadratic equation by completing the square. That's what we talked about in lecture 18. That method is admittedly not as popular as perhaps the two other methods that we're talking about right here, but it is a legitimate method. So you should know how to complete the square. There actually will be some questions that mandate it, but we'll talk about that in just a second. You can also use the quadratic formula, right? So think of pop goes to B's on your head there, right? X equals negative B plus or minus the square root of B squared minus four AC all over two A. So you could solve this using the quadratic formula. This thing is in the quadratic form already. You could just plug in the numbers A, B, and C. Now, admittedly, when it comes to actually doing the number crunching, generally speaking, factoring is easier than the quadratic formula. But of course, you can use whichever of these three methods you feel most comfortable with. Sometimes factoring doesn't quite work because it could be that the solutions are irrational. But admittedly, if I'm looking at this question, I don't see any solutions with square roots or with the I, the symbol I, right? Complex I here, which itself is a square root, square root of a negative. And as such, that actually suggests to me that I probably could solve this one using factoring because if the answers are rational numbers, whole numbers are fractions, that actually means we can solve it by factoring. So just a little bit of a tip there. The quadratic formula is perfectly fine, but I think you might actually find factoring to be easier on this one. So how do we solve quadratic equations? We can also solve quadratic equations again by these three methods. I'll just leave it at that. One other thing you should be prepared for on this question. You don't see it in this variant, but one possibility here coming from section 19, could we identify the vertex of a quadratic function? So let's say we have something like f of x equals 3x squared plus 5x plus 2. Could we find the coordinates of the vertex of that function, whether it's in the standard form, or maybe it's in the vertex form? One has to be cautious about that because when you're in vertex form, you might have to switch the sign of something. So it's probably useful to know the formula for the vertex h, which is the x-coordinate of the vertex. This is going to be negative b over 2a. Notice this is just the part of the quadratic formula if you forget the discriminant. And then to find k, there's a formula for it, but my suggestion is just do f of h. Just plug this formula into the function and simplify to get the y-coordinate. That's probably going to be your best bet. You probably want to know the vertex form. f of x is equal to a times x minus h plus k. Don't forget the square, so it's a quadratic function there. Where this a here is the same a as was here. This should be the leading coefficient. The h and k can be found using these formulas, or you can do it by completing the square. And so if the quadratic function is given to you in vertex form, then you don't have to compute the vertex.  You do have to change the sign on the horizontal coordinate because it's in the horizontal zone. You don't have to change the sign on the k though. So those are some versions of question 4 you should be prepared for. Coming on to question 5, then question 5 is going to be our second and final question about absolute value. So remember absolute value is covered in lecture 15. I mentioned that, but I'll just say it again. This time you have to solve an inequality that involves absolute value. That does change things a little bit. It's very similar to solving equations, right? If you have the absolute value of x, it's greater than or equal to say some positive number like 3. That will then tell you that okay x is greater than or equal to 3, or x is less than or equal to negative 3. You have to consider both the positive and the negative case, but the sign switches on the negative case because we need times an inequality by negative sign. It switches the sign. So we have to consider that. You have those two possibilities. If x is greater than or equal to 0, in that situation, well, you would get all real numbers in that situation because absolute value is always greater than or equal to 0. So it doesn't matter what you choose for x. You get all real numbers. If you get something like the absolute value of x is less than or equal to 0, you get some negative in that situation. That does change things, right? In that situation, you'd only get the x-intercepts as your solutions, right? I guess I should have mentioned this before. If you have the absolute values less than 3, same basic idea. You have to consider x is less than 3, and you're going to have x is greater than negative 3. So put those things together. So the direction of the inequality does matter. My recommendation, of course, is just to just to consider your markers. You have negative 3 and 3 and use test points. Which one satisfies the original inequality? Is it the beak or is it the wings of your bird, right? Because this is going to be absolute value, something like that. That'll take care of all of them. But of course, there are situations where there are no markers, maybe. If you have to take the absolute value of x is less than 0, there's no solution to that. There's no markers. And that's because in that situation, your absolute value sits entirely above the x-axis. So you might get either everything or nothing, depending on the direction. So there are a few special cases you have to consider. But generally, you're going to be seeing something like this on question number 5. So be prepared for that. I'm going to erase a little bit on the screen here so that we can do question number 6. Question number 6 is going to be a question about discriminants, all right? So remember, the discriminant is the radicand inside of the quadratic formula, right? It's this number right here, d equals b squared minus 4ac. And so by just knowing the discriminant of a quadratic equation, we can determine are there real solutions, are there non-real solutions, how many solutions are there. So remember, when the discriminant is a positive number, you're going to get two real solutions, all right? When your discriminant is 0, you're going to get one real solution. Because when your discriminant is 0, it turns out your quadratic equation is actually a perfect square. And the one solution is the vertex. If your discriminant is less than 0, you're going to get two non-real solutions. They're complex numbers. All of them are complex numbers. Real numbers are complex numbers, right? Just like a tree is a plant, but not all plants are trees. If your discriminant is less than 0, you'll get two non-real solutions. So with this one right here, if it's asking which of the following quadratic equations has one real solution, at least one real solution, that means the discriminant is either positive or zero. That would count as well. So we mostly just need to throw out which of these have negative discriminant. You don't have to solve the quadratic equation. You just have to determine how many solutions there are. And so the discriminant is a very nice shortcut in that regard. So we spent four lectures on systems of equations. In particular, lectures 11 through 14 in our lecture series are about systems of equations. So there's going to be quite a few questions about systems of linear equations on this test. In terms of the method used to solve them, you really want to be familiar with all of them. Like question number seven, the way it's phrased is it's with augmented matrices. You do have to have fluency with these augmented matrices in order to or answer this version of question seven. But there are alternate versions of question number seven, which have you solving systems through elimination, through substitution. So you should be familiar with all these of these techniques on this one and asked which of the following augmented matrices are consistent. So we should know this vocabulary here. Consistent means that the system has a solution. It could have one solution or it could have infinitely many solutions. Inconsistent means that it has no solution. So really, we want to figure out which of these things have no solution and throw it out. We could also ask things like when are the equations in a linear system? When are they dependent? That would suggest that we have infinitely many solutions. When are the equations independent? Or that would mean that we have a unique solution in that situation. So we should be familiar with those cases. Again, but we also should know the basics of how does elimination work. Like if I gave you a linear system and was like, okay, what elimination would sort of be the best choice right now? Could you answer that? Or if you were trying to solve a system by substitution, could you answer the question, what would be the best substitution to do right now? That is kind of like do the next step of a problem. That's really what question seven is about. It's not about solving a system of linear equations. It's basically like we're in the middle of solving a linear system. What's the next step using these, one of these techniques? That's what you should be prepared to do. And so again, these topics were covered in lectures 11 through 14. We had four lectures about solving systems of equations. Question number eight is going to be an application of linear functions. So a linear model. And this is the type of stuff we did, of course, in lecture 10. There were lots of different linear models that we learned about in that lecture. There are two that are extremely important. One of them is manifest here on the screen right now. That's simple interest. You should know the formula for simple interest and be able to do some simple interest calculations. It's just a linear model, right? The amount is equal to the principle times one plus RT, where R is your interest rate. Typically, that will be an interest rate for years. So like APR is annual percentage rate there. T is a measurement of time. That measurement of time needs to reflect the measurement of time that's in the rate. So for talking about APR, annual percentage rate, then T is a measurement of years. So like on this one, we have four years. P is the principle. That's the amount of the original loan. And then A is the amount that one pays back. The principle plus the interest. So that's why there's one plus RT.  P times RT gives you the interest on the principle that one gives back. So be able to calculate and solve some problems using simple interest here. Another important application you should be aware of. Very simple but still very powerful. The idea of direct variation, right? So we have two variables that are directly related to each other. So like say Y equals KX. That is, some constant K, your constant of variation there is the K.  And so be able to do some very basic variation problems involving direct variation, X and Y. Or they could have other names. Now that's not to say that simple interest in direct variation are the only linear models you should know. But these ones are ones you should memorize, the formulas are put them on your notes as you prepare for the test of course. But we have some other story problems we did in lecture 10 about linear growth. And so if we just have some information about, oh, this quantity is increasing or decreasing over time, like maybe the population or some commodity is growing over time, or perhaps an infectious disease is decreasing over time, things like that. It'll tell you that the spread or decay of the quantity is growing or decaying linearly. And so use the linear equation in that situation. Question nine brings us to the end of the multiple choice section of this test, in which case we're asked to solve a quadratic inequality. Solving these is very similar to how we solve absolute inequalities. My, my suggestion is actually to solve the underlying quadratic equation. So x minus one times x plus four is equal to zero. You can solve that by factoring, which this one's will be factored for you. So that's pretty great. You can complete the square, you can, you could use the quadratic formula. I can promise you that nearly all of them, you could probably solve by factoring just for the sake of convenience. You have to solve the equation, this gives you your markers. So you have your two solutions. And then we think of what's the basic shape of the graph, let's say just for simplicity, a concave upward like this. And so then like absolute value, are we looking for the beak? Are we looking for the wings of the bird? And that depends on which direction inequality is going. Are we trying to be above the x-axis, below the x-axis, or something like that? Are we allowed to be on the x-axis? So try to solve these inequalities using this idea. Lecture 21, the very last lecture of this unit is where we talked about quadratic inequalities, the very last unit, less section I should say in chapter three. So be prepared to answer that one. Question number 10 is the first question in the free response section. It's only worth five points. So each of the free response questions is, excuse me, each of the multiple choice questions is worth five points. This one really is on par with a multiple choice question. It's just by the nature of the question. It doesn't really make sense to ask it as a multiple choice question. So on question number 10, you'll get another question from lecture nine about linear functions, linear equations. You can be asked to solve a linear equation. So this, you could argue, is a hard linear equation. There's really no such thing as a hard linear equation, frankly speaking, but it's very, there's more involved, let's say that. It's more involved than what you might see in question number one. Solve this one. It could be that there's no solution. Maybe the x's cancel out. Maybe every number is a solution, all real numbers because it's an identity, but most likely you should get a unique solution when you solve this linear equation. So maybe you have to distribute some things. Maybe you have to combine some like terms because there's x's on both sides of the equations. It has all of the possible ingredients you could see here. But another possibility is you're asked to graph a linear function. So maybe you're given a function like Michael's mx plus b. How do you graph that thing? Again, it's not too difficult of a question, which is why it's only worth five points. But these graphing questions don't really make sense to be multiple choice. I actually want you to graph it. To graph a linear function, I would definitely recommend you should label two points and then do the best you can to connect the dots. If you have a straight edge, that's great, but don't worry too much about it. If your line is too wiggly because you're so nervous, I suppose I could live with that. Just maybe label your points so that it's very clear exactly what the points that you're trying to draw were. Moving on to the next page, where the heat will turn up a little bit on these free response questions. Question number 11 is worth eight points. This will be a story problem involving systems of equations for the most part, right? You actually might just give you the system of equation. You're asked to solve it. It'll be a two by two system. There's a three by three system that's coming up. But most likely on question number 11, you'll be given a story problem of some kind. This will most likely be a mixture problem. And by most likely, if it's a story problem, it will definitely be a mixture problem. Those were the types of questions. The story problems I should say we saw with when it came to these systems of equations. Again, I promise you this question 11 will be a two by two. There'll be two equations, two unknowns. For a story problem, you can decide what they're called. For this one, where Alexi has some number of coins here, quarters and dimes. You might call your variables Q and D, something like that. So you have one equation involving Q and D. You have a second equation involving Q and D and you have to solve it. If you don't have to set up this system of equations, if it's given to you, I can promise you it'll be a little bit on the harder side to justify why you get the same amount of points without having to set it up. Though these mixture problems in terms of solving them will be pretty easy. But it will be a two by two problem. That's the case. In terms of solving systems of equations on question 11, you can use whatever method you want. Substitution elimination, Gaussian elimination. Heck, if you want to use Kramer's rule and you feel pretty good about it, you can do that. I personally think that the matrix approach is pretty good. But for a two by two system substitution or elimination also works out pretty good. Heck, even Kramer's rule works pretty well in that situation. It's really in the three by three systems where the matrix method really starts to shine above the other methods. So I'll make that recommendation when we get there. Of course, there's lots of lectures that cover systems of equations. It's lectures 11 through 14. But if you're specifically looking for some of these mixture problems, you want some extra practice on those, those were covered in lecture 12. So be prepared for those. Question number 12. This one's worth also eight points. This is a question which you might actually be mandated to solve the equation by completing the square or some other method. Maybe you're told to do it by factoring. Maybe you're told to do it by the quadratic formula. Question number 12 will ask us to solve a quadratic equation. So some of the principles I said earlier because you have to solve the quadratic equation in the multiple choice section as well. Those same principles apply right here, but you do have to show your work. And generally speaking, this might be a little bit harder to do. So if you're going to solve it by factoring, finding the magic pair might not be so obvious. Maybe you have to use the quadratic formula or completing the square because maybe factoring is impossible. But the important thing to be aware of here is that if it tells you to do it by a certain method, you have to do it by that method for following the instructions, right? If I were to solve this by using the quadratic formula, even if I do everything correct, you're going to get no points because the instructions do say complete the square. And any of the methods we've learned is possible. So you should be prepared to do any of them. You should know the quadratic formula. You should know how to do it by completing the square. You should know how to do it by factoring. Of course, if factoring is possible. And so solving quadratic equations as a reminder, this was covered in sections 17 and 18. 18 mostly talked about fact, excuse me, 17 mostly talked about factoring. 18 was about completing the square and the quadratic formula. But like I said, you do have to be prepared with both, not just both. I should say both lecturers, all three techniques you should be aware of. Question number 13. This one has the highest point total for the entire exam. In this case, you will be given a three by three system of linear equations. You won't have to set it up. It will just be given to you. And you have to solve it and show all of the steps. Now, which method do you want to use? Do you want to do it by substitution elimination, some hybrid of substitution elimination? Do you want to use matrices and use row reductions to simplify it into echelon form? That is up to you. Unlike the previous question, which mandated a method, on this one, number 13, you can use any method you want. And as such, you might want to reference all of lectures 11 through 14. Now, admittedly, lecture 11 only focuses on two by two systems. Lecture 12 started showing us how to solve three by three systems. And then lectures 13 and 14 did it with matrices. So that's a pretty good approach. But still, I'll include 11 in there for reference. There's a lot of steps to do here. Do try to fit it in here. If come the actual test, you can't fit it all in here. Just see something like C attached. Actually, say it's on a scratch paper, but actually make a marker it continues on if you can't fit it all in there. You probably can though. So don't worry about it too much. And like I said, there is no mandated method. Elimination substitution, matrices or some combinations are available. You can even try Kramer's rule if you feel comfortable with it. But I should warn you, no student has ever gotten full credit on this question trying to use Kramer's rule for a three by three system. It doesn't work out super great. So I don't recommend it. It can be done. But many of the 1050 students has failed in that attempt. So I don't recommend it. Question number 14. This is going to be a story problem involving quadratic functions. So this was the main topic of lecture 20. That is quadratic modeling quadratic story problems. This will be a situation very likely you might be given the quadratic equation. Because you're not physics students necessarily. This is in a physics class. I don't need you to set up a projectile motion type problem. But I do need you to analyze it. If it was given to you, important things to know here is finding the vertex. Because if we're launching a rocket, like in this example, we want to find its maximum height. That's information we glean from the vertex of the parabola. But we might also need to find the x intercepts or the y intercepts as well. So the important thing is given a quadratic function. Can you find its vertex? Can you find its intercepts? That's stuff you really need to know how to do. And then the story problem will ask us to apply it. All right. Now while this one actually gives you the formula, there are some examples where you will be asked to set it up. So in particular, a question that we've seen the area of a rectangle that has come up a couple times where there's some type of stipulation about the perimeter. So like we've seen situations where like the perimeter is some constraint or maybe because there's a river here and you only have three sides. Or we've done situations where we're like a chicken coop and we have to separate the roosters from the hens or maybe there's also something else has to be separated. So we've done some problems like this where we have some constraint about the perimeter. And the perimeter might be more than just twice the length, twice the width. Like in this situation, you'd get two times the length, but four times the width. That's your perimeter. Anyways, in that situation, the area is still going to be length times width. But you have to substitute out one of the variables using this perimeter constraint. You solve for like say maybe L and then you plug it in there. We've done some equations like that. What would be then be the maximum area we could form for such a rectangle? Well, once you substitute the perimeter in for like say length, because there's a linear relationship between width and length, when you substitute it in there, you're going to get a quadratic relationship on the width and then you can maximize that by looking at the vertex. So that's a problem you should be able to set up and solve. Another problem that we've done was about revenue. The revenue problem is basically the following. Revenue equals P times X, where P is the price of some commodity that's being sold and X is the number of those commodities that got sold. So price times the number of sales gives you revenue. It's a financial problem. And so if the price function, so price or demand, you can call it the same way, right? If we treat price as some function of X, right? Because if we increase the price, you'll sell fewer commodities. If you lower the price, you'll sell more commodities. And so price and sales are typically going to be inversely proportional to each other. One goes up, the other goes down. We can often describe that with a linear relationship. If we have that linear relationship, we can substitute that in for P. And therefore, the revenue then becomes a quadratic relationship on the number of things you want to sell. And thus maximizing revenue would be finding the vertex of that parabola. These are two examples where you're asked to set up and solve it. And in particular, to solve the quadratic, that is, to set up the quadratic, it's just the variable time, some linear function. But you might have to set up that linear function, right? Some information about the perimeter is given.  Therefore, you set up the linear demand. So setting up the quadratic is pretty easy, but setting up the linear relationship is probably the hardest part about this. But as this test also includes linear models, that's a very appropriate question. So be prepared to do those ones. Those are some of the harder questions for number 14. Be prepared how to do them. And so that then brings us to the last question on this exam, question number 15. This is a graphing question, in which case you are asked to graph a quadratic function. That quadratic function will be given to you in the standard form, ax squared plus bx plus c. One of the instructions will tell you that this quadratic form needs to be put into the vertex form. That is, we have to rewrite this as f of x equals a times x minus h squared plus k. That is necessary. If you do not include the vertex form, you do not get full credit. You basically lost half the points. You're going to have to draw the parabola, yes, but that's only about half the points, five out of 10. The other five come from getting this vertex form. You do have to show your work. Probably the easiest way to get the vertex form is just to complete the square, to switch it from one form to the other. But another possibility, of course, is you can use the formula h equals negative b over 2a. You can compute that. That then plugs in for h. Once you have h, you can compute f of h using the original formula. That's going to give you a k for which you can plug in there. Then the leading coefficient doesn't change, so 3 and 3. You can actually calculate the vertex formula without completing the square, so to speak. These formulas came from completing the square, but there does need to be some work to show you how you transition from the standard form to the vertex form. That's necessary for full credit. Once you have the vertex form, you then have the transformations. This a value, this tells you if there's some type of vertical stretch. You have a vertical stretch by a factor of a. This would tell you if you reflected or not. If a is a negative number, it means you reflected across the x-axis, your parabola would be concave down now versus concave up. Those are some things there. The h value, this is going to give you a horizontal shift. So a shift to the right or left, depending on what the sign of h is. The k value tells you whether there's a vertical shift to shift up or down. So this vertex form is not just some annoying thing. It actually gives you the transformations. And then from there, we can graph our parabola. So we end up something like, to graph it, I would start off with the, I would start off with the vertex. You have to label the vertex of your graph that's mandatory. So you have to find it. You have to also label the x and y intercepts. The y intercepts generally pretty easy because you plug in x equals 0. It's going to be, in this case, you get like a negative 2. So do something like that. In which case, then from there, you can use like the axis of symmetry to try to graph the rest of it, something like that. You can use the x intercepts. You can also use the vertical stretch. Like, if you stretch it by a factor of 3, the idea is you're going to go down 3 over 1, something like that. So there's a lot of things you can do to graph this parabola. But what you do need to have is you do need to have the correct parabola, and you must label where's the vertex with its coordinates, where are the x and y intercepts with their coordinates. The x intercepts could be irrational, mind you. You can either approximate them. Like, if your x intercept turned out to be like 1 plus the square root of 2, you can approximate it using your calculator. If you don't have a calculator, just write it as exact. Like, oh, the x intercept is 1 plus square root of 2. And do your best to estimate how that is. You can use other information like y intercepts or the stretching factor to get that. So you don't necessarily have to have the calculator to do this one, not at all necessary. And so that brings us to the end of exam 2, which remember covers chapters 2 and 3 about linear and quadratic functions. If you have some other questions that weren't answered in this video, please reach out to me and I'd be glad to help you. Best of luck in your studies and I'll see you next time.


arted with these very personal reference, the kind of end product also, the sense of the way that it sort of deconstructs the house into a series of objects or moments or rooms, also strangely is sort of like really getting us away from, you know, kind of a traditional humanist conception of the house as a kind of, you know, cozy space or, you know, adapted to particular subjects. And of course with the teacherless micro school that, you know, and the opening question of like, can machines replace humans, can we be around kind of learning and teaching, which is a problem that is kind of confronting all of us right now. You know, I think there's something interesting about the way that all of these projects, like sort of make us really rethink these kind of type of, these, you know, very old typologies.  At this point it's fascinating to see so many different projects and studios all at once. It's my first time seeing this kind of, this format and supercrit, I'm finding it really, it's actually really wonderful to see these through lines between the different studios, but also sort of take as a, a given this like many, many different ways of exploring a project, right, and finding your way. I'm still really thinking across all these projects to David's question earlier about modes of research. And I think what that had made me think, take it a little bit of a different direction was how we, what are the ways in which we really explore a site. And I don't mean the literal, you know, territory of this site, but a site if it's most expanded sense of site, which is physical, social, cultural, ecological, and economic, all of those different layers. I think I would, I wish I could talk to all of the students right now and hear from you how, you know, being in a studio, I know my students right now at Penn are really struggling with this question of how to continue to explore a site when you can't go there or where some, when some of the traditional methods in which we are maybe accustomed to accessing information have been taken away from us. Right. And I think it's a, an interesting time to really think about those tools because hopefully they won't be taken. We will not be isolated forever. But it really also makes me think of how different types of information are always actually mediated or have varied accessibility at different times. So it really strikes me that a lot of the projects feel very, very grounded in architectural history, and precedent buildings. Some are really delving into, as we've talked about already, cultural context or historical events. Some are grounded in literature.  And I'm also really interested in the projects that are trying to also move into these spaces that might feel a little more distant. Industrial ecology, behavioral ecology, thinking about non-human species, thinking about material flows, chemistry, racial theory, social justice. So I think it's, it's just kind of an overarching comment. Not very many projects have really looked at microclimate or the actual physicality of experience in the site in that way. And I don't think all those layers should be present in every project. But I think it's an interesting moment looking across all of those studio, all of these different studios to think about, you know, what techniques we have at our disposals and what sorts of information is more or less accessible, whether it's a specific version of history, right, rather than all of the other versions of, of these sites that we could be looking at, or other disciplinary lenses. And when is there benefit to kind of opening up those different spaces of inquiry? Yeah, I mean, I think this, this general line of discussion is, is really interesting and relevant, especially at this moment, because I think as, as all the comments have, have touched on the work is like a kind of tour de force in, you know, research and design and representation and different levels of taking on, you know, architecture, but more broadly the city and more broadly, even the countryside and the world. And as we've talked about at different times, flows of materials of information, layers of culture and history. And, you know, one way of, of re, of looking back at all of the presentations over the afternoon is to just be kind of in awe of the, not only the diversity of projects, but of the diversity of skills that each single author must have had in order to execute this, you know, really clear and concise presentation, you know, using a whole range of, you know, skills and expertise. And I think like what you're saying, Stephanie, there are some that may have been a little underrepresented today as a whole. There are some probably that each author has that they didn't use in that single project. But as a whole, it's, it's kind of hard not to be impressed by the, the range collectively and individually of, of the kind of skills we saw. I know we've gone over time and I feel responsible for that because I was probably not as strict a timekeeper as I intended to be. So I did want to give, you know, one quick opportunity if there are other professors on the line. I know that, you know, everyone can, if they want to see the list of presenters. I'm very happy to see that many faculty have joined today and a lot of students. I know some people had to drop off a little bit early. But let's see, is there any, is there anyone who wants to make a kind of question or a comment before we start to wrap it up? I can say one thing very quickly. I was pretty impressed that, I mean, with the quality of the work, I mean, after, I mean, everything that we've go, going through and especially, I mean, the fact that most of the students, they didn't travel and they had to engage with such broad context, which are entirely alien to their background. I mean, it's pretty impressive how research was well conducted and how people were able to really dig into other realities and produce such amount of, such amount in such quality of work. That's it. Yeah, I think, I think that's great to hear, Pedro. And it's a great point. I mean, there's, there's a whole like list of things that people have had to go through this semester and still to be at a point where we're having, you know, this level of presentations and this level of discussions. It's really great to see. I'll just read a note from Gallia, who I think had wanted to join in, but she had to leave for another meeting and she said that this, she found that this year's supercrit was stronger and more cohesive than even in past years. So despite our new format, all the challenges of the semester, you know, the glitches of dealing with a webinar for the first time, all the boxes of faces on the screen, you know, I think it's, I think that's a kind of shared sentiment that this was a really great moment to see the work together and to kind of celebrate the work, even though, you know, it should be noted that it's still two weeks away from most final reviews. So it's, it's only, you know, I really was saying, yes, 13 weeks is not enough. This is really, in essence, only been 11 weeks. Plus maybe you subtract some of the weeks of lost time of moving and stuff. So. Are there any, yeah, the work looks quite complete to me. I think all the students should just take the next couple of weeks off and rest on their laurels. Yeah. Yeah. Tremendous. Tremend. I mean, when I just look across my notes and think about the range of really important and meaty issues that you guys are delving into and with such depth and, you know, sophistication of thought and care. I'm just kind of overwhelmed and, you know, very, very impressed. So congratulations to everyone. Yeah, agreed. I just wanted to again, also echo that the work is really, really incredible that I, you know, I hope that for all the things we're all, you know, missing in terms of being in studio and being together, you know, I hope we can find a little bit of a few ways in which some of this digital communication actually helps us share our work and feel comfortable and letting things not have to be perfect or totally polished all the time, but really peek in on each other's crits, talk about work in process, share some of these story or issues because, you know, a really good project is never built. Right. There's no perfect conclusion to a studio. And I think the ideas that's been, it's been a real privilege and a pleasure to see all of this work and all this incredible thinking that's going on in your ideas. Okay, I think that's, that's a perfect way to end it. I do want to thank, you know, all of the, all of the students, even the ones who didn't present for kind of producing this, you know, great body of work for engaging the discussion for being here on this kind of session, even though it's, you know, late on a Friday, many of you are different parts of the world. I want to thank everyone for bearing with us during some of our technical difficulties of this new format for the supercrit. I want to send a big thanks to all of the presenters for staying cool, going with this format that we kind of imposed on you of having to say next for most of you and submitting your file in a way that was a little bit thrown upon you. And especially to Irene, Stephanie and Tim for really engaging with such kind of clarity and insightfulness, these projects and all the kind of diverse worlds. So it's really a mind bender to kind of jump into all of those different worlds. And it was great to see the threads of topics that you raised, you know, kind of connecting the dots a little bit between the projects, but also giving some very specific and relevant comments to individual people. So. And last but not least, I want to thank very much Lila and Skylar for running this show in, you know, a very complicated way, probably, you know, as we were saying at the first webinar of the school, but also probably one of the biggest Zoom sessions we've hosted with certainly the most in a row presentations we've probably ever done on Zoom. So thank you all to be continued in the final reviews and hope everyone is able to find some moment of rest and peace over the weekend before getting back to work. Thank you everyone.


Hello and welcome to the session that has discussed the following question. It says, annual income from salary of Mrs. Usha, who is a senior citizen, is Rs. 3,5,000. She donates Rs. 10,000 to Prime Minister's Relief Fund, 100% Exumption, and Rs. 10,000 to the Charitable Society, 50% Exumption. She contributes Rs. 70,000 towards PPF and PENI, and she pays quarterly premium of Rs. 3,500 towards life insurance. She also purchases NSC for Rs. 20,000. She pays Rs. 1,600 per month towards the income tax for 11 months. What is her liability for last month of the financial year? Choose the following for calculating the income tax, and we get 100% exemption for saving up to Rs. 1,000,000. And this is the slap for the rate of income tax for senior citizens. Let's now move on to the solution, and let's see the first step for calculating the income tax. The first step is find the gross income of the SSC. Now the annual income is Rs. 3,85,000. Now the second step is to find the amount of donation if any eligible for reduction. Now the rebate on donations, she donates Rs. 10,000 to Prime Minister's Relief Fund, and gets 100% exemption. She also donates Rs. 10,000 to Charitable Society, and gets 50% exemption is equal to Rs. 10,000 plus 5,000, that is 15,000. Now the third step is find the amount of total savings, maximum up to Rs. 1,000,000. Now we find the savings made by Mrs. Usha. We are given that she contributes Rs. 70,000 towards PPF annually. She pays quarterly premium of Rs. 3,500 towards life insurance, and she also purchases NSE for Rs. 20,000. So the savings are PPF Rs. 70,000 annually. She pays Rs. 3,500 quarterly premium. So the annual premium is Rs. 3,500 into 4, that is 14,000, and she purchases NSE for Rs. 20,000. Rs. 70,000 plus 14,000 plus 20,000 is Rs. 1,400,000. Now the fourth step is subtract the amount, subtract the sum of the amounts obtained in step 2 and 3 from the step 1. So we have to subtract the sum of the amounts obtained in step 2 and 3 from the amount we got in step 1, step 4. The sum of the amounts obtained in second and the third step Rs. 15,000, Rs. 1,400,000. Now we are given that savings can be maximum up to Rs. 1,000,000. So we have to make it Rs. 1,00,000 is Rs. 3,085,000, Rs. 1,15,000 and this is equal to Rs. 50,000. Now we will compute the income tax using this lab and here the taxable income is Rs. 270,000. So the rate of tax will be given by this, that is Rs. 13,000 plus 30% of the amount by which taxable income exceeds Rs. 250,000. So the income tax will be Rs. 13,000 plus 30% of the amount by which Rs. 50,000 would be Rs. 13,000 plus 30% that is Rs. 30,500 into, now the taxable income is Rs. 270,000 minus Rs. 250,000 by which taxable income exceeds Rs. 250,000 is Rs. 270,000 minus Rs. 250,000. So that gives us Rs. 13,000 plus 30% 100 into Rs. 20,000 that gives us Rs. 13,000 plus Rs. 6,000 that is Rs. 19,000. So this is the income tax. Now we also have to find the education says which is 2% of the amount of the taxable. Now the education says equal to amount of taxable. So it is 2% of Rs. 19,000 because taxable is 19,000. So this would be 2 by 100 into 19,000 and that gives us education says as Rs. 380. Now we are given that she pays Rs. 1600 per month towards the income tax for 11 months. But before that we need to find the total taxable which is obtained by adding the education says to the taxable which is Rs. 19,000 plus 380 and that becomes Rs. 19,380. Now tax deducted sources at this TDS for 11 months is given by Rs. 1600 into 11 becomes Rs. 17,600. Now we have to find the taxable for the last financial year. So she has paid Rs. 17,600 for 11 months as income tax and total taxable is Rs. 19,380. So the net payable is Rs. 1,708.


This lecture is entitled Rachel Royche and Dutch Baroque still life painting or sometimes a flower is just a flower. Now on the screen here, we see a portrait of Rachel Royche here in the center of the screen and she's flanked by two of her still life paintings and these are representative examples of the kinds of still life she was famous for and as you can immediately see she's famous for her flower still life paintings and they tend to be compositions like this where a bouquet of flowers fills the entire composition and maybe you'll have the inclusion of fruit or something like that as you do over here on the left. Now this image on the left dates to 1704 and the image on the right dates to let's write it up here 1716 and these dates are a little bit later than what we've been looking at so far in the Baroque. We're into the 18th century now and in that way Rachel Royche is an interesting figure because she's one of these transitional figures again. And she kind of bridges the gap between the Baroque which we've been looking at for a long time now and the Rococo which is a style associated with the 18th century that we're going to be looking at in a couple of units. Now before we move on and take a closer look at one of her paintings, I just wanted to say a few words about her and first, you know, one of the things I always point out when we look at a woman artist is of course that she is a woman artist. You need to think about that. You need to focus on that because that in itself is a remarkable thing in this day and age. So remember that she's a woman and she was extremely successful. She wasn't just you know a mediocre artist. She was very successful and in fact she was so successful that she became the court painter in Düsseldorf. So that gives you a sense of the degree of her success and it's also interesting that her father was a botanist. A lot of scholars like to talk about the fact that her father was a botanist and she certainly would have been around images of plant life growing up and a lot of people speculate that that may have had a big influence on her development as a painter. So a few things to keep in mind as we now move on and look at one of her paintings. So the image on the left here is the image we saw just a minute ago on the right. It's the painting that dates to 1716 and over here on the right, hopefully this is familiar to you. We've looked at this before and it's by Clara Peters who was a Flemish still life painter and remember she was famous for her breakfast pieces and I have this comparison on the screen for you here because I think it shows a what's so unique about Rachel Royish and her flower still lifes and also it shows the changes that have occurred in still life painting over the course of about a century. Now Clara Peters included a bouquet of flowers in her still life here, right? We see the whole left third of this painting is a beautiful and artfully arranged bouquet and it's very naturalistic with little leaves that have fallen off and it's it's very relaxed and free and naturalistic. What's interesting to me is the way a still life that is only made up of flowers, flowers that fill the whole composition really give us a kind of gravity and importance to those flowers. You know, all of our attention is focused on the flowers because that's the only thing in this painting but there's a sort of seriousness and almost grandier in this simple flower bouquet. Especially notice the way the light catches the front of these flowers and the flowers sort of emerge from the darkness. So we're seeing some of these things that we've been talking about in the Baroque that are so typical of the Baroque and that is that use of light and shade. Light and shade. We have a kind of theatricality, which is a part of that. Theatricality. We also have a really dynamic composition and you can see, you know, the the stems of the flowers create diagonals and the way the flowers fall out from the center of this bouquet creates almost this spiraling beautiful, elegant and very moving composition. And I think if you compare the flowers in Rachel Royce's painting to the flowers in Clara Peters, you see flowers that are much more animated. It's almost as though they seem to be moving in this composition, whereas Clara Peters flowers are part of a bigger composition and they're not as animated. They're not as come to life as Rachel Royce's. And again, it's important to keep in mind, as I said earlier, she's Rachel Royce is this transitional figure and now that we're into the 18th century, she's kind of foreshadowing styles that will come. And that's something you should also keep in mind with this. She's kind of foreshadowing the Rococo, as I mentioned, Rococo and we'll talk a lot more about that in the next in a couple of units. And just back to what I said at the beginning, sometimes a flower is just a flower. When I say that I don't mean just a flower in a negative way that, you know, we're just looking at a flower and there's no meaning there. Certainly there can be a lot of meaning imbued in this beautiful and simple composition of flowers, but it's not a part of something else. It's not a part of a Vanitas still life. It's not a part of a landscape.  It's self contained and it speaks for itself. So Rachel Royce is yet another example of the many different faces of still life painting in the Baroque. And I think she's a wonderful example to end The Dutch Baroque with as we look forward to some some new styles as well as some new places


This is another video brought to you by the Open Group Healthcare Forum. Please visit us at www.opengroup.org. FIM, the Federated Health Information Model, advancing healthcare interoperability by harmonizing standards. Thanks to rapid 21st century technology developments. Today we use all kinds of digital products that transfer key information to help us do things we value, like managing our finances, shopping online, finding a flight, booking a place to stay, reserving transit, keeping up with family and friends, and last but not least, managing our health and healthcare. Unfortunately, transferring healthcare information among all of those who need it often feels like being stuck in a time warp. Consider, for example, Mr. John Smith. John is a 70-year-old retired veteran who lives on a modest pension with his wife, Mary. He suffers from multiple health problems, heart disease, chronic low back pain, obesity, borderline diabetes, and bouts of depression. When John begins to experience moderate chest pain, his internist refers him to a cardiologist. When John and Mary arrive at the office, they are given page after page of forms to fill out about John's health, insurance, and basic demographics. They complete them while knowing the same information already exists in the EHR at its primary care physician's office. Imagine their frustration. Why couldn't this information be sent electronically to the new cardiologists? Of course, the answer is that most EHRs don't easily talk to one another. They don't interoperate. Everyone is handicapped by poor interoperability in healthcare. Most healthcare stakeholders experience information sharing challenges every day. For example, clinical staff know they don't always have the most up-to-date patient information. Yet they need to make decisions in real time. Not having information needed to provide high-value care is frustrating and costly. Sometimes the source of frustration is too much information. Providers often have to scour through detailed clinical narratives, looking for key information to gain an accurate picture of their patient's health care needs. As a result, clinicians often lack confidence in the information they use to make vital decisions with their patients. We need better solutions to help information flow securely and timely so patients can receive the highest value healthcare possible. At the heart of this problem is lack of standards agreement. Consider a real-life example of what can happen in the absence of agreed-on standards. Our story goes back over 100 years ago to Baltimore, Maryland, the fifth largest U.S. city at the time.  Naturally, neighboring firefighters responded. They came with fire trucks and hoses ready to extinguish the flames and limit the damage. However, their hoses did not fit the fire plugs in Baltimore. With no standard size for couplings, water could not be transported to the flames. Firefighters stood by helplessly as the fire burned out of control and much of central Baltimore burned down in what became the third largest fire disaster in American history. Unlike the Baltimore example, the primary barrier to gaining standards agreement in healthcare today is not physical or technical, rather, it's economic and social. Alas, it's easier to create new standards than to build consensus on making existing standards work. Fortunately, compatibility among healthcare standards does not mean that everyone needs to use the same standard. As long as standards are mapped to a common logical information model, they can work together and information can flow. This is the purpose and promise of the Federated Health Information Model. The FEM is an expandable health information model and different standards can be mapped to it. By providing a common map for different standards, the FEM can harmonize standards developed by different organizations. The FEM provides a detailed map of healthcare information put into distinct groupings or domains. This map of health information and associated standards can be used to increase interoperability so health information is available when and where it is needed. The result is more efficient healthcare systems, better care and improved patient outcomes, and much less frustration for providers and for patients and caregivers like John and Mary Smith.