A farmer has 20 yards of fencing to build a pen for her chickens. She decides to use a side of her barn as one side of the fenced-in area. What is the maximum area she can achieve?

The farmer can achieve a maximum area of 50 square yards with 20 yards of fencing.

Step-by-step explanation:

Given that farmer shall construct a rectangular fenced-in area and a side of the barn is one side of such area, the needed length of fencing is represent by the following perimeter equation (), measured in square yards:

Where:

- Length of the rectangle, measured in yards.

- Width of the rectangule (side of the barn), measured in yards.

In addition, the equation of the fenced-in area () is:

If , equation of area is now simplified as follows:

The value of associated with the maximum area is obtained with the help of First and Second Derivative Tests. Firstly, first and second derivatives of the area function are determined:

Let equalize first equation to zero, second derivative indicates that critical value follows to an absolute maximum. Hence:

The width of the rectangle is: ( and )

And finally, the maximum area she can achieve is:

The farmer can achieve a maximum area of 50 square yards with 20 yards of fencing.

answer: given that the roller coaster can accommodate 1600 riders per hour, thus the roller coaster can accomodate 1600 / 60 = 26.67 riders per minute.

given that there are 345 people in the line, the number of minutes it will take for the 345 persons to get into the roller coaster is given by 345 / 26.67 = 12.94 minutes.

therefore, it will take you 12.94 minutes to get to the front of the line.

step-by-step explanation: