Area Word Problem + Graph Problem

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To determine the maximum area for a rectangular pen using 1200 ft of fencing, the equation for perimeter (P = 2L + 2W) can be used to express one dimension in terms of the other, leading to the area equation (A = L * W). The maximum area is found to be 90,000 sq ft when both length and width are 300 ft. For the second problem, the points provided indicate a set of coordinates, and the domain consists of the x-values while the range consists of the y-values. Understanding these concepts is crucial for solving the problems effectively. The discussion highlights the need for equations related to perimeter and area, as well as the identification of domain and range in a set of points.
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PROBLEM #24- A goat rancher is going to fence off a rectangular pen in the middle of a large open area. Build an equation to help determine the maximum area (to the nearest sq ft) that can be fenced off if 1200 ft of fencing is avilable. Include a diagram as a part of your solution.)

I have attached the two problems I need help with in picture format for number 24 and 25. I need to write an equation for 24 which I am having trouble with even though I know the answer is 90,000 sq ft
@ 300ft x 300ft.

On #25 I am not sure if this is a line, function, or if it even has a slope or pattern. How do I answer the questions beneath? Thanks.






 

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Someone please help here this is due tomorrow morning- thanks.
 
Ah, that is bad luck. They still haven't approved the image.
 
A goat rancher is going to fence off a rectangular pen in the middle of a large open area. Build an equation to help determine the maximum area (to the nearest sq ft) that can be fenced off if 1200 ft of fencing is avilable. Include a diagram as a part of your solution.
 
Ok so for #24 you need to build an equation to help find the maximum area. It says that perimeter is 1200ft. What kind of equations can you think of that would be helpful? How about the equation for perimeter and area? If you find those two equations you are finished.
 
For problem 25 you say you are "not sure if this is a line, function, or if it even has a slope or pattern". It is precisely the points shown: (-2, 5), (-1, 3), (1, 0), (3, -3), and (4, -5).

The "domain" is the set of all "x" values- all first numbers in the pairs.
The "range" is the set of all "y" values- all second numbers in the pairs.
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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