SOLUTION: Beth has 3,000 feet of fencing available to enclose a rectangular field. One side of the field lies along a river, so only three sides require fencing. (a) Express the area A of t

Question 59545: Beth has 3,000 feet of fencing available to enclose a rectangular field. One side of the field lies along a river, so only three sides require fencing.
(a) Express the area A of the rectangle as a function of x, where x is the length of the side parallel to the river.
(b) Graph A = A(x) using a graphing utility. For what value of x is the area largest?
A wire of length x is bent into the shape of a circle.
(a) Express the circumberence of the circle as a function of x.
(b) Express the area of the circle as a function of x.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
If the side parallel to the river is x,
the remaining 2 sides are equal and each
equals

From the graph, it looks like A is maximum when x = 1500
A would be (1500)^2 / 2 then or 1,125,000 sqare feet
------------
answer
to find the area in terms of x, first find the area in terms of the
circumference
where r is the radius

,so

Another way to express A is

multiply both sides by 2

but

answer
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