For both of these cans, the volume would be 1000 cube centimeters for this one and for this one. Okay, so now what we have, we have a distance that depends both on time and wind, and another way to express it would be to draw this box in which we have a function, and then we would have two inputs now and then. Now, one thing that I want to mention is that look, you have this blue line and then you have this read the other line and they overlap. 73. And there is a constant, which is plus 300 because remember, the graph was shifted up. Only at time equals one second. Why and leave. 220 it would be 11 hi over nine radiance. Because instead of this, let's say if you have some kind of function, why equals, let's say three plus X and to plus X Now you would use the caution rule here. And the third function will describe your downward acceleration in other words, how fast your downward velocity changes. It does not care about specific situations. How would the graph look like so you can take time? Do you remember the very first example that we had the airplane example in the first lecture where we had an airplane flying in a certain direction and we found out that that the best way to represent that information was is a mathematical function and we represented we represented the distance of the aircraft like this D, which is distance equals 800 which was the speed 800 kilometers per hour times time. Then you see those posts from your car. Onley at time equals two Onley there. We could say, like delta H over built a time equals new miners old. So one way to look at functions is like this. So for example, if I say that it's a 1000 like 10 to the party tooth equals 1 100 then the the way I would denote it is like this log My base. You you have a physical situation that you have that you have established using experiments , and then you can have different functions describing this physical phenomena in different places. So not the center, but the left and right edges. Well, you you can already I guess that this access would be why, over our and then this access would be radiance. And that is, of course, if B is greater than zero. So So if you have a three dimensional function than than what you have, you would have a surface and here I am using screen cast to show you an example of it. You would have to know the context off your specific problem. So what would be the distance? He and you would add, Why squared And then you would get this quantity squared so radius would be square rude both x squared Plus why squared So that came also came from the from the triangle, right? It's the slope of the lines. Over the X equals and then either using the limits or or some kind off Z, in fact, that you would use a power rule and we're we're gonna talk about it just in a bit. And if you take sign two times pi over two, then even though your seat a spire or two, you lend that Because of the two you'll end with pie and pie is zero. In the previous example with sign theater, it was expressed implicitly, right, So sign feet equals something. And if the piston goes up that this being being number two will rotate like this and the situation is the following so suppose that you have some kind of fly, a small fly flying and then it smashes into the into this piston. At times it was 1.5 hours and the time equals two hours. 21. But the irrational number would be a number that you can express in a ratio for example, 0.333 And it would go in into infinity. Fool. Fair question! Do you remember? Another thing that I want to mention is that pi is an irrational number. What about science? Now. And we put X inside these parenthesis and we get why What if we want to go back? So I need to let's they find a mathematical way to represent how, first of all, I need to represent those two points. So you would get well, this would be zero. What happens with with this expression? Here should be velocity. Right, And on the function graph, the right age is the upper line. Mark Misin, Aerospace & Robotics Engineer. So now here I would have the zero line right t you won. So I had the line over here and then I had the line over here and then those lines they would go to infinity, right? Okay, so that's one way to look at it. SIM: Avoid the crash - solution 9: welcome back. So we have three main trigger metric functions that we have covered so far. So the center off this block moves along this dimension in a sign of soil way. If you look at it, then. And that's how you no whether whether the exes that you found on the first from the function of the first derivative when you equated it to zero in order to find the extreme points x one and x two and x three. The main function that we have been using so far in our previous lectures has been the straight line function. So really Sita equals two. So, in my view as a car driver, as I approach this position x eight Quiet, I I assume that as I approached this position, I expect to see post eight based on my previous experiences based on when I had seen before . Functions VS Non-functions 1: welcome back. All right, And that's why the line is negative now. But you see it never. Then why would also be one if X equals two? So you go from want to tend to 100 to 1000? So if you want to jump very high, then it's very few. Because you can't have You can't sell zero point 586 bags. Too big meter. It doesn't change. So in the end, we our goal was to find the the change of the angle off both beams with respect to with respect to the motion in the X direction. And then we divided the entire thing by the l T. And since we couldn't directly calculate the derivative because we cannot divide by zero, we simply said that. And so your function would be something like this and again. Why it? Now what can we do here, though? So I could say that. So cute. Because you're inverse. I need to start moving it closer and closer to this original point. Find INVERSE of a PARABOLA: So I have a parabola here. But we have time. Okay, so I'll just put one here. You would have a negative delta. So, in order to do that, where to take the second derivative of this one? And here is Well, yeah, So this is a tension function. One of the examples for logarithms is something called a logarithmic scale, because in the world there's some quantities that can be very small at the same time, very big. It it would be zero. SIM: 3 airplane race - who wins, and when? The airplane has covered this distance, which is, I don't know, one kilometer, then also this distance, which is four kilometers, for example. Then you can see from this equation that also whatever x I have and whatever why I have, they will be multiplied automatically by the same number. Minimize material used for can manufacturing 3: Okay, So back to our example then. You have one function that is like this, and then you have another function that can be like this. So you can also see two beams here that are connected to the walls and those two beams they can freely rotate along these points. How much is one squared? Not here, not here only at one second. And then on Mars, the slope is minus 3.7 and then on moon mines 1.6. And then why over our and the same thing with co sign and minus ec with coastline intentions, so would because signed miners one. How much why instantaneously changes with respect to X.
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