1. A rancher wants to build a rectangular pen, using one side of her barn for one side of the pen, and using 200m of fencing for the other three sides. What are the dimensions of the pen built this way that has the largest area?

100m by 50m.

Step-by-step explanation:

Let the dimension of the rectangular pen be x and y

Area, A(x,y)=xy

Let the side opposite her barn = x

Since she wants to fence only three side

Perimeter = x+2y

Length of Fencing Available = 200m

Therefore:

We want to maximize the area of the pen, A(x,y).

Substituting x=200-2y into A(x,y)=xy

To maximize A(y), we find its derivative and solve for the critical points.

To ensure that this is a maximum, we use the second derivative test.

This is negative and thus, y=50 is a maximum point.

Recall:

x=200-2y

x=200-2(50)

x=200-100

x=100m

Therefore, the dimensions of the pen that has the largest area are 100m by 50m.

these sign is used to tell weather the number is greater or less than the number   <   or >     but this sign means its equal =    

hope this you and

step-by-step explanation:

b. y = 4x - 2

step-by-step explanation:

to find a parallel equation to an equation, make sure both equations have the same slope but different y-intercepts.

y = 4x + 1

4 = slope

1 = y-intercept

y = 4x - 2

4 = slope

-2 = y-intercept

they both have the same slope but different y-intercepts, so, b. is the correct answer.

and to check your work, you can graph both equations. : )