Question

Suppose you have 50 feet of fencing to enclose a rectangular dog pen. The function A=25x-x^2, where x=width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum are?

Answer 1

maximum is the second coordinate of the vertex
the first coordinate of the vertex is always \(-\frac{b}{2a}\) which in your case is \(-\frac{25}{2\times -1}=12.5\)

Answer 2

so your final answer is 12.5?

Answer 3

in other words, in plain english, build a square

Answer 4

your question has two parts:
a) find the width, and
b) find the area

Answer 5

huh? I got A=25-x^2 using -b/2a and got -50/2-1 and got width equaling 25

Answer 6

yes that is the question

Answer 7

the answer to the first part is the width and the length should both be \(12.5\)

Answer 8

\(b=25\) not \(50\)

Answer 9

so the maxium are would be.....

Answer 10

12.5x12.5?

Answer 11

whatever \(12.5\times 12.5\) is
or whatever \(25\times 12.5-12.5^2\) is
either way, it is the same number

Answer 12

thank you

Answer 13

yw

Answer 14

ok i have one more problem for you

Answer 15

it is fairly easy

Answer 16

ru up for it

Answer 17

What is it?