Suppose a farmer has 120 feet of fencing to make a rectangular barnyard enclosure. If the enclosure is x feet long, express the area A of the enclosure as a function of the length x.
120 equals x + two ends=x+(120-x) so each end is (120-x)/2
area is then A=x(120-x)/2
So would the answer be
A(x) = 60x – x^2?
Or
A(x) = 120x – x2
I get 60x-x^2/2
Thanks that is what I got to, so therefore A(x) = 60x – x^2 is the answer! Thanks for your help! :-)
A PIECE OF TIN IS TWICE AS LONG AS IT IS WIDE. IT IS TO BE MADE INTO A BOX BY CUTTING 2 INCH SQUARES FROM EACH CORNER AND FOLDING UP THE SIDES . FIND THE DIMENSIONS OF THE PIECE OF TIN IF THE VOLUME OF THE BOX IS 320 CUBIC INCHES
To express the area of the enclosure as a function of the length, we first need to determine the width of the enclosure.
Since the enclosure is rectangular, it has two equal sides, which will be the width. Let's call the width y feet.
The perimeter of a rectangle is given by the formula: P = 2(x + y), where P is the perimeter, x is the length, and y is the width.
In this case, the perimeter is given as 120 feet, so we have: 120 = 2(x + y).
We can rearrange this equation to solve for y: 120/2 = x + y, which simplifies to 60 = x + y.
Now, we can express the width y in terms of the length x: y = 60 - x.
The area A of a rectangle is given by the formula: A = x * y.
Substituting the expression for y, we get: A = x * (60 - x).
Therefore, the area A of the enclosure is expressed as a function of the length x by the equation: A(x) = x * (60 - x).