Organizers of an outdoor concert will use 320 feet of fencing to fence off a rectangular vip section. what is the maximum area that they can fence off

Answer-

The maximum area that they can fence off is 6400 ft²

Solution-

Organizers of an outdoor concert will use 320 feet of fencing to fence off a rectangular vip section.

i.e the perimeter of the rectangular section is 320 feet

Let us assume,

x = length of the rectangular section

y = breadth of the rectangular section

Hence,

Now, we have to find the maximum area for which they can fence that off.

The area of the rectangular section is,

So we have to maximize the area function.

Putting the value of y,

Finding the critical values,

∵ f"(x) is negative (i.e -2), so for the value of x=80, f(x) or area function will be maximum.

Therefore, the maximum area that they can fence off is 6400 ft²

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: