ang4elali8zzsalli
Answered

If a rancher plans to fence a rectangular pasture adjacent to a river. The rancher has 100 meters of fencing, and no fencing is needed along the river.

How do you write an area of A as a function of x? Then I would have to find domain afterwards

Verified Answer :

taskmasters

The perimeter of the area is the length of the fence.

Perimeter = x + y + y. This can be simplified to
Perimeter = x + 2y. You're told that the rancher has 100 m of fence, so the perimeter is 100 m:
100 = x + 2y (1)

The area of a rectangle is given by the formula A = length * width. The length in this case is x, and the width is y.

So, A = xy.

Solve equation (1) for y. Once you find the expression to which y equals, plug that for y into A = xy.

100 = x + 2y. Solve for y by subtracting both sides by x:
100 - x = 2y. Divide both sides by 2:
(100 - x)/2 = y

Substitute (100 - x)/2 for y into A = xy:

A = x[(100 - x)/2]
A = [x(100 - x)]/2

You can rewrite this as (100x - x²)/2 or 50x - (x²/2) or 50x - (1/2x²).

Hope that helped!

meerkat18

he perimeter of the area is the length of the fence.

Perimeter = x + y + y. This can be simplified to
Perimeter = x + 2y. You're told that the rancher has 100 m of fence, so the perimeter is 100 m:
100 = x + 2y (1)

The area of a rectangle is given by the formula A = length * width. The length in this case is x, and the width is y.

So, A = xy.

Solve equation (1) for y. Once you find the expression to which y equals, plug that for y into A = xy.

100 = x + 2y. Solve for y by subtracting both sides by x:
100 - x = 2y. Divide both sides by 2:
(100 - x)/2 = y

Substitute (100 - x)/2 for y into A = xy:

A = x[(100 - x)/2]
A = [x(100 - x)]/2

You can rewrite this as (100x - x²)/2 or 50x - (x²/2) or 50x - (1/2x²).

Related Questions