The city park department is planning to enclose a play aea. one side of the area will be against an existing building, so no fence is needed there. find the dimensions ofthe maximum rectangular area that can be enclosed with 800m of fence

length = 200 m

width = 400 m

Step-by-step explanation:

Let the length of the plaing area is L and the width of the playing area is W.

Length of fencing around three sides = 2 L + W = 800

W = 800 - 2L (1)

Let A is the area of playing area

A = L x W

A = L (800 - 2L)

A = 800 L - 2L²

Differentiate with respect to L.

dA/dL = 800 - 4 L

It is equal to zero for maxima and minima

800 - 4 L = 0

L = 200 m

W = 800 - 2 x 200 = 400 m

So, the area is maximum if the length is 200 m and the width is 400 m.

Dimensions : Length = 400 , Width = 200

Step-by-step explanation:

Let length & width of rectangle park be = L , W . Also, let one side of length be supported by building wall, so not needing fencing.

So, the perimeter of rectangle park, including 2 width & 1 length :

2W + L = 800

L = 800 - 2W

Rectangle Area = Length x Width

A = L x W

A = (800 - 2W) W

A = 800W - 2W^2

To maximise area, it will have to be differentiated w.r.t dimension width

dA / dW = 800 - 4W

dA / dW = 800 - 4W  = 0

800 = 4W

W = 800 / 4

Width [W]  = 200

Length [L] = 800 - 2W

= 800 - 2(200)

= 800 - 400

Length [L] = 400

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

can you put the picture up?

step-by-step explanation: