### Answer

Fencing a horse Corral Carol has 2400 $\mathrmft$ the fencing come fence in a rectangular equine corral.(a) uncover a duty that models the area the the corral in terms of the width $x$ that the corral.(b) uncover the dimensions of the rectangle that maximize the area that the corral.

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### Video Transcript

Okay, so for this question, we're told the fence and also a horse Coral Carol together 8400 feet the fencing defense in a rectangular horse Coral. And also it says discover a function models the area that the coral in terms of the wit x of the coral. Okay, therefore we're gonna speak to the area a and also it tells united state that, um, the broad of the coral is X. Every right, so because that the moment, since it's not, um, it's gonna it is in a rectangle wherein so one of the signs weaken labeling X. And for the moment, we deserve to live v the various other one. Why? but we don't want to various variables in ours question. We just want you all to it is in one burial. So we need to uncover a method to compose Why, in regards to X, and also the method we're gonna carry out is that we know the perimeter. For this reason x add to X, since that's both the sides there. Plus, why close? Why, that's both the peak on the bottom side that's gonna be referred to as 2400. For this reason we'll simply collect turns to professionals to Ike to be 2400. So climate 2400 minus 2 acts that calls to why we have actually a common factor of 2 here. Therefore why is gonna be referred to as 1200 minus X? So then we can replace this up below just one minute from change this. Okay, rather of having a why Oh, uh, rather of having a why we can have, um, a 1200 finest X may have an leave pairs off. All right, so we haven't quite uncovered an equation for the area to discover an equation because that the area. Um, well, simply times these 2 together since the area is just the length times width. So the area Oh, aye. So we have the right to say a X equals X times by 1200 minus x. For this reason that's gonna it is in 1200 x minus next. Glad? all right. That's partly doing We found an equation because that the area, and component be asked united state to find the size of rectangle the maximized the area off curl. Okay, therefore to discover the dimension of the rectangle that maximize the area of coral, we'll just have to discover a MME. We'll discover we have to maximize this function here and find the equivalent X the maximizes the function. So there's an equation for this on. So it's gonna be X amounts to minus B end to a, um, i m sorry is gonna same from ours equation minus 1200 over simply minus two. For this reason X is gonna equal 600. Therefore that's among our sides. You got X equates to 600 here. Yet the other side is in reality 1200 minus X. For this reason that's just how Why here? Why? because 1200 minus, we found out X. Now we just need to uncover out why. 1200 minus X. That's gonna be 1296 and also 600 sir, once we acquire 600 so it's actually a square. Therefore the dimensions of it, you're gonna it is in the why to be on the bottom. That will certainly be 600 on this side. And also it can be 600. Decide on that legend in feet yet, teacher. Okay, therefore the dimensions space 600 feet by 600 feet. Yeah. Okay, so the answers the question. You have any kind of questions about that? though he couldn't message me at Daniel at Daniel decided. J B hates Doc Nolan in ~ gmail period com.

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