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anonymousgirl2002
03.07.2019 •
Mathematics
Jacob wants to build a rectangular enclosure for his animals. one side of the pen will be against the barn, so he needs no fence on that side. the other three sides will be enclosed with wire fencing. if jacob has 400 feet of fencing, you can find the dimensions that maximize the area of the enclosure. a) let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure (parallel to the barn). write an function for the area a of the enclosure in terms of w . (hint first write two equations with w and l and a . solve for l in one equation and substitute for l in the other). a(w) = b) what width w would maximize the area? w = ft c) what is the maximum area? a = feet
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Ответ:
Jacob wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn,so he needs no fence on that side.
Let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure (parallel to the barn).
one side of the length is not counted for perimeter because one side of length will be against the barn.
Perimeter = 400 ft
Perimeter of rectangle = L + W + W
400 = L + 2W
L = 400 - 2W
Area = L * W
Replace L by 400 - 2W
A(W) = (400 - 2W) * W
Now we find out x coordinate of vertex to find the width that maximize the area
a= -2 and b = 400
The width w would maximize the area is w = 100ft
To find maximum area we plug in 100 for W in A(W)
the maximum area is 20,000 square feet
Ответ:
Yes
Step-by-step explanation: