Agardener has 440 feet of fencing to fence in a rectangular garden. one side of the garden is bordered by a river and so it does not need any fencing. what dimensions would guarantee that the garden has the greatest possible area?

Dimensions would guarantee that the garden has the greatest possible area = 220 feet x 110 feet

Step-by-step explanation:

Fencing available = 440 feet

Here 3 sided need to be considered

That is

             Perimeter = 2x Length + width = 2l +w

             440 = 2l +w

              w = 440 - 2l

We have area = length x width

               A = lw

               A = l x (440 - 2l) = 440l - 2l²

For area to be maximum we have

Substituting in  w = 440 - 2l        

             w = 440 - 2 x 110 = 220 feet

Dimensions would guarantee that the garden has the greatest possible area = 220 feet x 110 feet

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b