Asked by ShelbyA
a farmer wants to enclose a rectangle garden using the sides of her barn as one side of the rectangle. what is the maximum area which she can enclose with 60ft of fence? what should the dimensions of the garden be to give this area?
Max area which she can enclose with 60ft of fence in sq.ft?
dimensions to give area is 30ft by___ft?
Max area which she can enclose with 60ft of fence in sq.ft?
dimensions to give area is 30ft by___ft?
Answers
Answered by
Damon
2 w + L = 60 so L =60-2w
A = w L
A = w (60-2w)
A = -2w^2+60 w
2 w^2 -60 w = -A
w^2 - 30 w = -A/2
w^2 - 30 w + 225 = -A/2 + 450/2
(w-15)^2 =-(1/2)(A-450)
w = 15
L = 60-30 = 30
A = 450
A = w L
A = w (60-2w)
A = -2w^2+60 w
2 w^2 -60 w = -A
w^2 - 30 w = -A/2
w^2 - 30 w + 225 = -A/2 + 450/2
(w-15)^2 =-(1/2)(A-450)
w = 15
L = 60-30 = 30
A = 450
Answered by
Damon
If you know any calculus, you can do this much faster
A = -2w^2+60 w
dA/dw = 0 at extreme = -4 w + 60
so w = 60/4 = 15 at max
A = -2w^2+60 w
dA/dw = 0 at extreme = -4 w + 60
so w = 60/4 = 15 at max
Answered by
Aljaka
I can verify that answer as correct
Answered by
Anonymous
A batter hits a baseball. The ball's height (in feet) h(t) after t seconds is given by h(t)=-16t^2+160+5
Answered by
Nisreen Azam
A batter hits a baseball. The ball's height (in feet) h(t) after t seconds is given by h(t)=-16t^2+160+5
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