posted by Kathy
To make an enclosure for chickens, a rectangular area will be fenced next to a house. Only 3 sides will need to be fenced. There is 120 ft. of fencing material.
a. What quadratic function represents the area of the rectangular enclosure, where x is the distance from the house?
b. what dimensions will maximize the area of the enclosure?
Let the length parallel to the house be y
let each of the other two equal sides be x
2x + y = 120
y = 120 - 2x
Area = xy
= x(120 - 2x) or -2x^2 + 120x
b) you want the vertex.
x of the vertex is -120/(-4) = 30
when x = 30
y = 60
Maximum area = xy = 1800 ft^2
Roller coaster that has uphill climb of 255 feet at an angle of 38 degrees on its largest hill