Asked by Mathlete
A farmer wants to enclose a rectangular field with 180m of fencing. The side of the barn will act as one side of the enclosure, leaving 3 sides to be covered. The function that describes the area inside is f(x)=x(180-2x) what are the dimensions of the closure with the largest area?
Answers
Answered by
Damon
180 x - 2 x^2 = A
2 x^2 -180 x = -A
x^2 - 90 x = - A/2
x^2 - 90 x + 45^2 = -A/2 + 45^2
(x-45)^2 = -(1/2) (A- 4050)
vertex at x = 45
so 45. 45 , 90
area = 4050
2 x^2 -180 x = -A
x^2 - 90 x = - A/2
x^2 - 90 x + 45^2 = -A/2 + 45^2
(x-45)^2 = -(1/2) (A- 4050)
vertex at x = 45
so 45. 45 , 90
area = 4050
Answered by
Mathlete
Thanks Damon! We got it now. We were stuck after line three so this was helpful.
Answered by
Damon
Good, you are welcome
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.