Pre calculus 12 grade

Question

I would like know why my answers is not correct for this problem: Ryan has 3000 ft of fencing to enclose a rectangular field for his horses. One side of the field lies along river, so only 3 sides require fencing. Express the area of the field as a function of length (y) of the field. My answer is A(y)= 1500y-y^2/2 It say incorrect. Correct answers A(y)= 3000x-2x^2 Picture say 2 sides x and one side y. I do not understand why is my answer incorrect

Answer 1

Lesya, Your answer is the area IN TERMS OF Y. That is exactly what the question asked.

What you typed as the "correct answer" is really the area IN TERMS OF x. That is not what the question asked.

Both answers are correct but yours followed the instructions. The "correct answer" is really A(x), not A(y).

I hope this helps.

Answer 2

The length can be expressed as y = 3,000 -2x.

The area = x*y = xy.

Substituting for y,

A(x) = x*(3000-x) = 3000x - x²

This is a function of x, not y.

As a function of y, 2x = 3000 - y or x = 1500 -(y/2).

So, area = A(y) = y*(1500-(y/2)) = 1500y - ((y²)/2).

I used parentheses to make it absolutely clear how the operations were to be performed.

A(y) is a function of y, the length. It canot have the variable x on the right-hand side of the equation.

Your answer is correct. Presuming you have provided correct information above, I suspect you are entering your answer into a computer, and the answers must conform to a string of characters which have a typo in them. Thank you programmers....