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A barnyard is to be fenced is as indicated in Figure $23 .$ If 4200 feet of fencing is to be used in its construction determine the dimension $x$ and $y$ that will maximize its total area? Hint: The area of an equilateral triangle with side $s$ is $\frac{s^{2}}{4} \sqrt{3}$

$$x=777.501 \mathrm{ft}, y=363.332 \mathrm{ft}$$

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

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01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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A barnyard is to be fenced…

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A rancher has 200 feet of …

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we know that the barnyard has to be fenced, so we're gonna use our equations from before. Um in this case though it will be 4200 ft of fencing. Um and we want to maximize the area, so uh the area of an equilateral triangle, we know we're given, so the fencing in this case is going to be um s squared over four. Andrew three, essentially. What we want to do is relate the side and the X. And Y. We can solve for one of these variables and plug it into the area and once we do that we can maximize the function because it will have um it will be an opening up problem when we do that, we end up getting the X. Is about 777.5 ft. And why is going to be 363? Mhm. Okay. And 3 3 ft.

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