Homework:Sections 4.3 and 4.4 Homework
1 answer:
Answer:
8,000,000 m²
Step-by-step explanation:
The largest rectangular area is enclosed when half the fence is used for sides in one direction, and the other half of the fence is used for sides perpendicular.
Here, no fence is needed on the river side, so 8000/2 = 4000 meters of fence will be used parallel to the river. The other 4000 m of fence will be split between the two ends of the enclosure, so its area will be ...
4000 m × 2000 m = 8,000,000 m² . . . largest enclosed area
<h3>More formal solution</h3>We can let x represent the length of fence perpendicular to the river. The amount of fence available for the side parallel to the river is ...
L = 8000 -2x . . . . . the rest of the 8000 m of fence after 2 sides are used
The area is ...
A = x(8000 -2x) = 2x(4000 -x) . . . . area is product of length and width
This equation for the area describes a parabola that opens downward and has zeros at x=0 and x=4000. Its maximum will be on the line of symmetry, halfway between these zeros. The value of x that gives maximum area is ...
(0 +4000)/2 = 2000
The plot will extend 2000 meters out from the river and will have a length of ...
8000 -2(2000) = 4000 . . . meters
The maximum area is (2000 m)(4000 m) = 8,000,000 m².
<h3>Graph</h3>The attached graph shows area as a function of the dimension perpendicular to the river.
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