Author Question: What is the maximum area for this question? (Quadratics)? (Read 1652 times)

Sandstorm

  • Sr. Member
  • ****
  • Posts: 268
So i got this math question, and I have a lousy teacher, so I don't know exactly how to find the maximum area for this question.
Question:
A farmer has a 200m of fencing material to enclose a rectangular feild adjacent to a river. No fencing is required along the river.
The image has a rectangle with the widths (smaller sides of rectangle) labeled with 'w' and the length is 200-w. The function I came up with is a=200w-2w^2. I did graph it on the calculator. Vertex is (50, 5000). X-intercepts are (0,0) and (100,0). Y intercept is (0,0).
That is all I can get from what I have self-learned and I still need to find the maximum area of the field and the dimensions of it.
If possible, please explain each step so that I can learn it. :)
Heres a picture of the diagram if my description didn't make sense:
http://tinypic.com/view.php?pic=2cntoig&s=6



Hawke

  • Hero Member
  • *****
  • Posts: 679
l = 200 - 2w

A = w * l
A = w * (200 - 2w)
A = 2 * (100w - w^2)
A = -2 * (w^2 - 100w)
A = -2 * (w^2 - 2 * 50w + 50^2 - 50^2)
A = -2 * (w - 50)^2 + 2 * 50^2
A = -2 * (w - 50)^2 + 2 * 2500
A = 5000 - 2 * (w - 50)^2

The vertex is at (50 , 5000)

w = 50
A = 5000
l = 100



Related Topics

Need homework help now?

Ask unlimited questions for free

Ask a Question
 

Did you know?

The training of an anesthesiologist typically requires four years of college, 4 years of medical school, 1 year of internship, and 3 years of residency.

Did you know?

Cytomegalovirus affects nearly the same amount of newborns every year as Down syndrome.

Did you know?

Studies show that systolic blood pressure can be significantly lowered by taking statins. In fact, the higher the patient's baseline blood pressure, the greater the effect of statins on his or her blood pressure.

Did you know?

Intradermal injections are somewhat difficult to correctly administer because the skin layers are so thin that it is easy to accidentally punch through to the deeper subcutaneous layer.

Did you know?

In 1886, William Bates reported on the discovery of a substance produced by the adrenal gland that turned out to be epinephrine (adrenaline). In 1904, this drug was first artificially synthesized by Friedrich Stolz.

For a complete list of videos, visit our video library