SOLUTION: Beth has 2200 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 th

Question 909053: Beth has 2200 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. For what value of x is the area largest?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Beth has 2200 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. For what value of x is the area largest?
***
x=length of side parallel to river
(2200-x)/2=width of rectangular area
Area=length*width
A(x)=x(2200-x)/2
A(x)=(2200x-x^2)/2
A(x)=-1/2(x^2-2200x)
complete the square:
A(x)=-1/2(x^2-2200x+(1100^2))+1100^2/2
A(x)=-1/2(x-1100)^2+605000
This is an equation of a parabola that opens down with vertex at (1100,605000)
For what value of x is the area largest? x=1100 ft
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