Giving brainliest
a rectangular area is to be enclosed with 12m of fencing.

a) what is the maximum area that can be enclosed if the fencing is used on all four sides. what are the dimensions of this optimal shape?

b) suppose an existing hedge is used to enclose one side. determine the maximum area that can be enclosed. what are the dimensions in this shape?

c) suppose two perpendicular hedges enclose the area on two sides. what are the dimensions of the maximum area that can be enclosed?

The dimensions of the region which enclose the maximal area will be:  Length = 162 feet and Width = 108 feet.

Explanation

According to the below diagram, the total rectangular area is divided into two separate regions by a vertical segment.

Suppose, the length and width of the rectangular area are  L and W respectively.

So, the length of that vertical segment will be equal to the width, W.

If the four walls of the rectangular area and the vertical segment are made up of fencing, then the total fence required  feet.

Given that, the farmer has 648 feet of fencing. So, the equation will be

Now, the area of the rectangular area:  

Substituting equation (1) into equation (2) , we will get

Taking derivative on the both sides of the above equation with respect to W, we will get

Now, A will be maximum when. So

Plugging this  into equation (1)

So, the dimensions of the region which enclose the maximal area will be:  Length = 162 feet and Width = 108 feet.

Step-by-step explanation:

the correct answer is 5 6 and 7

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for