Question

In this application, Patricia wishes to have a rectangular-shaped garden in her backyard, and we are looking for a function to describe the area of this garden in terms of x, the width of the garden. She has 82 ft of fencing with which to enclose her garden. Thus, the perimeter P (in ft) of the garden is P. letting x denote the width of the garden, find a function f in the variable x giving the area of the garden. what is its domain?

Answer 1

Domain(= 0,41)

Explanation:

As mention in the question

width of the garden= x

Consider length of the rectangular-shaped garden = y1

As we know that

`Perimeter = 2 (Length+width)`

Putting the value of length and width in the above equation we get

`\ 2(\ x\ + \ y1\ )\ =\ 82\\(\ x\ + \ y1\ )\ =41`

`y1=\ 41-\ x`

Now the area of function can be written as

`f(x)\ =x(41-x)\\f(x)=41x-41x^(2)`

Also we know that x >0 and y1 > 0

therefore domain=
`0<x<\ 41`

Domain=(0,41) is the answer