Jenna's rectangular garden borders a wall. she buys 80 ft of fencing. what are the dimensions of the garden that will maximize its area?

The  dimensions are x =20 and y=20 of the garden that will maximize its area is 400

Step-by-step explanation:

Step 1:-

let 'x' be the length  and the 'y' be the width of the rectangle

given Jenna's buys 80ft of fencing of rectangle so the perimeter of the rectangle is    2(x +y) = 80

                         x + y =40

                               y = 40 -x

now the area of the rectangle A = length X width

                                                  A = x y

substitute 'y' value in above A = x (40 - x)

                                              A = 40 x - x^2 .....(1)

Step :2

now differentiating equation (1) with respective to 'x'

                                          ........(2)

Find the dimensions

40 - 2x =0

40 = 2x

x = 20

and y = 40 - x = 40 -20 =20

The dimensions are x =20 and y=20

length = 20 and breadth = 20

Step 3:-

we have to find maximum area

Again differentiating equation (2) with respective to 'x' we get

Now the maximum area A =  x y at x =20 and y=20

                                        A = 20 X 20 = 400

Conclusion:-

The  dimensions are x =20 and y=20 of the garden that will maximize its area is 400

verification:-

The perimeter = 2(x +y) =80

                           2(20 +20) =80

                              2(40) =80

                              80 =80

Given:

Number of orange balls = 3

Number of yellow balls = 3

Number of red balls = 4

To find:

The probability of:

1) 2 orange balls

2) 2 yellow balls

3) 1 red and 1 yellow ball

Solution:

We know that,

The total number of balls is

Using the above formula, we get

The ball drawn first is replaced before the second is drawn. So, the probabilities remains unchanged.

1) The probability of getting the 2 orange balls is

Therefore the probability of getting the 2 orange balls is 0.09.

2) The probability of getting the 2 yellow balls is

Therefore the probability of getting the 2 yellow balls is 0.09.

3) The probability of getting the 1 red and 1 yellow ball is

Therefore the probability of getting the 1 red and 1 yellow ball is 0.12.