The farmer wants to use the 500 m to an enclosure divided into two equal areas, What is the total maximum area that can is achieved with the 500 m fence. using differential calculus to the solution.

Answer 1

Enclosure is divide into two equal parts.

Thats why you hawe width 3 times.

Two times of end of fence and one time in midle.

You hawe length 2 times both times of end of fence.

So:

3 W + 2 L = 500

3 W = 500 - 2 L = 2 ( 250 - L )

3 W = 2 ( 250 - L ) Divide both sides by 3

W = ( 2 / 3 ) ( 250 - L )

A = W * L

A = ( 2 / 3 ) ( 250 - L ) * L

A = ( 2 / 3 ) ( 250 L - L ^ 2 )

dA / dL = 250 - 2 L = o

250 - 2 L = 0

250 = 2 L Divide both sides by 2

125 = L

L = 125 m

W = ( 2 / 3 ) ( 250 - L )

W = ( 2 / 3 ) ( 250 - 125 )

W = ( 2 / 3 ) * 125

W = 250 / 3 m

A = W * L

A = 125 * 250 / 3 = 31250 / 3 =
10416.66667 m ^ 2

P.S.

Izvini zbog mog lošeg engleskog.

Answer 2

hvala ti puuuuuuuno, I tvoj engleski je suoper