A rectangular playground is surrounded by a chain link fence that costs $2 per linear foot on three sides and a fancier wooden fence that costs $6 per linear foot on the fourth side. The area of the playground is to be 500 square feet. Find the dimensions of the rectangle that minimize the total cost of the fencing

31.6 feet by 15.8 feet.

Step-by-step explanation:

Area of a Rectangle = Length X Breadth = LB

The area of the playground is to be 500 square feet

Therefore:

LB=500

Perimeter of the Rectangle = 2(L+B)

The Chain link fence that costs $2 per linear foot on three sides and a fancier wooden fence that costs $6 per linear foot on the fourth side.

Cost = ${2(L+2B)+6L}=2L+4B+6L=8L+4B

Cost= $(8L+4B)

From: LB=500, B=500/L

Substitute B into 8L+4B

C(L) =

C(L)=

The minimum cost of the fencing occurs when the dimensions are minimum.

If we take the derivative of C(L)

At

Recall: B=500/L

The dimensions that minimizes the total cost of the fencing are 31.6 feet by 15.8 feet.

1.4

2.3

step-by-step explanation:

the formula for the constant of variation is

y= kx

divide each side by x

y/x =kx/x

y/x =k

we know a and y

1.   y/x = k

4/1 =4

check the other values to make sure they are the same

8/2 = 4   12/3 =4   and 16/4 =4  

the constant of variation is 4

2.   y/x = k

3/1 =3

check the other values to make sure they are the same

6/2 = 3   9/3 =3   and 12/4 =3  

the constant of variation is 3

step-by-step explanation:

i have done this all on a piece of paper but idk how to put it on here cuz it needs to be drawn