Pam has 90 m of fencing to enclose an area in a petting zoo with two dividers to separate three types of young animals. The three pens are to have the same area. Express the area function for the three pens in terms of x. Determine the domain and range for the area function

The area function is

.

The domain and range of A is and .

Step-by-step explanation:

The given length of fencing is .

Let the length and width of each pen be and respectively as shown in the figure.

As there are 3 pens, so, the total area,

From the figure the total length of fencing is .

Here, for a significant area for the animals, as well as as and are the sides of ben.

From the given value:

Now, from equation (i)

This is the required area function in the terms of variable .

For the domain of area function, from equation (ii)

[as y>0]

So, the domain of area function is .

For the range of area function:

As or , then [from equation (i)]

Now, differentiate the area function with respect to .

Equate  to zero to get the extremum point.

Check this point by double differentiation

As,  , so, point is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

Hence, the range of area function is .

step-by-step explanation:

∆abc has the points a(1, 7), b(-2, 2), and c(4, 2) as its vertices. formed with the point d(1, 2) as its third vertex, then ∆abd is triangle.