Asked by saud
Suppose that 404 ft of fencing are used to enclose a corral in the shape of a rectangle with a semicircle whose diameter is a side of the rectangle.
Find the dimensions of the corral with maximum area.
x=........ft
Y=......ft
Find the dimensions of the corral with maximum area.
x=........ft
Y=......ft
Answers
Answered by
Steve
rectangle perimter = x + pi*x + 2h
h = (404 - x - pi*x)/2
area = xh + 1/2 pi*(x/2)^2
= x(404 - x - pi*x)/2 + 1/8 pi*x^2
= 202x - x^2/2 - pi*x^2/2 + pi*x^2/8
= -(3pi/8 + 1/2)x^2 + 202x
= x(202 - (3pi/8 + 1/2)x)
This has a maximum when x = 60.187
You can probably get the dimensions from this.
h = (404 - x - pi*x)/2
area = xh + 1/2 pi*(x/2)^2
= x(404 - x - pi*x)/2 + 1/8 pi*x^2
= 202x - x^2/2 - pi*x^2/2 + pi*x^2/8
= -(3pi/8 + 1/2)x^2 + 202x
= x(202 - (3pi/8 + 1/2)x)
This has a maximum when x = 60.187
You can probably get the dimensions from this.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.