A farmer has 400 yards of fencing to enclose a rectangular garden. Express the area A of the rectangle as a fu

A farmer has 400 yards of fencing to enclose a rectangular garden. Express the area A of the rectangle as a function of the width X of the rectangle. What is the domain of A?|||if width = x then


length = 200 - x





400 = 2x + 2(200 -x)





and area


A = x * (200 - x) = f(x)





%26quot;domain%26quot; of f(x) = the set of all number greater than 0 and less than or equal to 100





I would NOT include 0 in the domain, since the statement said %26quot;enclose%26quot; a garden





and I used 100 instead of 200 since, by convention, length %26gt; =width





these last few points border on %26quot;quibbling%26quot;|||the area of the rectangle is x * y


the perimeter of the rectangle is 2(x + y)= 400





to express the area in terms of x, lets convert all the y%26#039;s to x%26#039;s by substitution...


from perimeter ... x + y = 200 so, y = 200 -x





area = x * (200-x) = 200x - x^ .... [-x^2 + 200x]





area is the negative of x squared plus 400 times x


graphing this function yields the following ...





(-x) (x - 200) = 0 [zero%26#039;s exist at x= 0, 200]


since area can%26#039;t be negative, we accept the domain as (0, 200)


the maximum value of a occurs at vertex ... ( -b /2a)


(-200/ 2(-1) = 100





when x= 100, y=100 ... the area is 10,000


if x = 90 .. y= 110 ... the area is 9,900 (less than 100 x 100)|||cant be 20x20 since that would be a square


length could be 40 and width could be 10


A=LxW


400=40x10





i dont have a clue what the first guy said lol|||perimeter = 2L + 2 W


400 = 2 (L+W)


200 = L+W


200-W = L





Area = L * W


= (200-W) * W


= (200W - W)|||I%26#039;m not sure what the domain of A means but the rectangle is 20 x 20.