Question

A rectangular pen is made with 100 m of fencing in three sides. The fourth is a stone wall. Find the greatest possible area of such an enclosure.

Answer 1

here's a pic:

http://img207.imageshack.us/img207/335/fenceoj2um1.jpg

First find an equation for what it is you want to maximize (or minimize). We need to maximize the area. Area "a" = length X width. If we let the short sides of the fence be of length "x" then we can let the long side be of length 100-2x since there's only 100m of material to use. So our length X width would be x(100 - 2x).

Once you get your equation for what it is you want to maximize you need to differentiate it, set its derivative equal to zero, and solve for x. So first multiply the x through to get 100x - 2x^2. Then its derivative would be 100 - 4x. Setting that equal to zero and solving for x gives us x = 25. So the 100 - 2x side equals 50. Thus our max area = 25 X 50 = 1250m^2.

Answer 2

\[100x-2x^{2}\] how do you get 100-4x

Answer 3

Are you looking for x?

Answer 4

yes i am

Answer 5

Im sorry I have to eat but like a said the answer=max area = 25 X 50 = 1250m^2. You can bump the question and ask for more of an explination. Im sorry

Answer 6

ok thanks

Answer 7

Take derivative of 100x - 2x²
-> 100 - 4x

Answer 8

@jclyne any more questions?

Answer 9

@Chloropyll yes. A ball is thrown vertically upward with an initial speed of 80 f/s. Its height after t seconds is given by \[h=80t-16t^{2}\]

Answer 10

a) how high does the ball go and b)when does the ball hit the ground

Answer 11

No, I mean question for the same post?
Pls open new post for new question?

Answer 12

how do you open a new post ive been trying to figure that out

Answer 13

If you complete with this post, close it first; then click on "Ask a question" to open new one!

Answer 14

ok thanks