#White rectangle scored pill plus#
How does the perimeter change so D l b d d d p d t is going to be So I take the derivative that's going to d l d t plus two d w d t So in this particular case to evaluate under the conditions And what was that we had? Ah, we had l equal to 12 w equal to five, and we were increasing. So if I have the same rectangle l and W, the perimeter is going to be to l plus two w so over time. But instead of area, let's focus on the perimeter. So Part B says let's do this same problem. I net effect is I'm changing the area, increasing the area 14 square centimeters per second. So I can see that if I shorten the length and increase the width Ah, at the is opposing speeds. Let me right here in crease, because is a positive number. So the area is changing 14 centimeters per second. So this turns out to be, um um 14 season 24 24 minus 10. And the change of the length is minus two. So under those conditions, I'm gonna find that d a d t is going to be equal to 12.Īnd then d w t t is going to be two plus, the width is five. So how is this happening at these points under under these conditions that you see here. So over time, the change in area is going to be l, uh D W D W D t plus w d l e t. We're gonna figure out how does this affect the area? The area of a rectangle is the length times the wit. Uh, tell us what is happening to the area, the perimeter and the length of the diagonal. Okay, they're asking us when when the length is 12 and the width is five. So we're lengthening the width and we're shortening. The width is increasing, so D W D t is increasing at a rate of two centimeters for a second. So keep in mind when they tell you something is changing decreases a negative. So the change D l d t of the land is gonna be minus two centimeters for a second. And what they're telling us is this is that length of the rectangle is decreasing two centimeters per second, so the the length is changing. So here we're dealing with changing dimensions of a rectangle, so you know that a rectangle is going to have a length times a with okay. Section 3.8 looking at problem number 21. The perimeter is actually not changing at all at that point, and then the area is increasing areas getting bigger, the perimeter staying the same at that incident time and the diagonals are decreasing. So the question in says which ones? Air decreasing, which are increasing in this particular case. These year, I'm gonna have 1/13 and then multiplied by and then minus 24 plus 10 So that's going to be minus 14/13 and that's gonna be in centimetres per second. And I'm actually gonna cancel these twos right now, because I can.
So this right here is actually gonna be the spirit of 169. So what we're gonna end up with and I'll just go to the next page to finish this, um is you'll have Wallace scored 144 plus five Squared is 25. L is 12 at this time, so 12 squared and w is five. So if we do the derivative of that e d by d t then is gonna be one over to room Anil squared plus times you l d l binding t and then plus two w he w by all right.Īnd then I just got my numbers in d D by D. So for part c, we'll do it different color distance for the diagonals is gonna be the spirit of al spared plus u squared. I think you'll probably notice that is square root of l squared plus w squared. Or if you go back here again, we have minus two, and that's to and the perimeter again is L l and W W So then it asks us the third thing and asked us about our these diagonals.
All right, so that's gonna be two times minus two plus two times to what we're actually gonna end up with is zero centimeters per second. So dp by t t is gonna be two times d l buddy t plus two times d w by the tea. Okay, So for part B, the political is going to be two l's and to W's, right, because it's just the length around the outside. The areas increasing it 14 centimeter 20 and it asks about the perimeter.
The fact is that 14 and it's centimeter squared per second. Nobody which is minus two and you end up with 24 minus in. Then we're gonna take W, which is five and well played by you. So the area is length times width, which means D A by T t is gonna be L d w by the tea plus W d L by d. It's his DW bloody t is increasing at two centimeters per second and then it says at the point we're talking, the length is 12 centimeters and the wind is five centimeters.Īt the instant in time that we're talking to find the rates of chains of First of all, part A is the area. Buddy T Surrey is negative because decreasing and its two centimeters per second and in the width is changing as well. Ah, the rate at which the length is changing its is decreasing. This question gives a rectangle, and it tells us that the length and the width are changing.
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