Noah has 50 feet of fencing to completely enclose a rectangular garden in the backyard. Find the length and width of a rectangle that would produce the largest possible area

Length = 12.5 feet

Width = 12.5 feet

Step-by-step explanation:

We can set two equations to solve this problem.

First equation:

The perimeter of a rectangle is 2*L + 2*W, where L is the lenght and W is the width, and Noah has 50 feet of fencing to use, so:

2*L + 2*W = 50

Second equation:

The area of the rectangle (A) is calculated mutiplying the lenght by the width:

A = L * W

Dividing the first equation by 2 and isolating L, we have:

L + W = 25 -> L = 25 - W

Using this equation in the second one, we have:

A = (25 - W)*W = 25W - W^2

The formula to calculate the point that gives the maximum value is:

x = –b/2a

So, the value of W that gives the maximum area will be:

W = -25/2*(-1) = -25/(-2) = 12.5 feet

Using this value in the first equation W + L = 25, we have:

12.5 + L = 25

L = 12.5 feet

So, the length and width that produce the largest possible area are 12.5 feet and 12.5 feet.

32

step-by-step explanation:

part a

x     y

0     8

1     7.5

2     7

3     6.5

4     6

5     5.5  

for every hour i deducted .5 inches from the length of the candle

part b

it is a function because for every x value there is only one y value

part   c

for every x value there is only one y value

x       y

0       8

1       7.6

2       7.2

3       6.8

step-by-step explanation: