June 29, 2016

Homework Help: Algebra Word Problem Help

Posted by Jeanna on Thursday, August 6, 2009 at 11:23pm.

A gardener has 40 feet of fencing with which to enclose a garden adjacent to a long existing wall. The gardener will use the wall for one side and the available fencing for the remaining three sides.

If the sides perpendicular to the wall have length x feet, which of the following (A, B, C, or D) represents the area A of the garden?

A. A(x) = 2x^2 + 20x
B. A(x) = 2x^2 + 40x
C. A(x) = 2x^2 40x
D. A(x) = x^2 40x

I say it is B. A(x) = 2x^2 + 40x, any thoughts?

The area function is a quadratic function and so its graph is a parabola.

Does the parabola open up or down? I say down, am I correct?

Find the vertex of the quadratic function:

(-b/2a, f (-b/2a))

(0+20)/2 =10

-2x^2+40x = 200

Vertex = (10,200)

Is my vertex correct?

Use the work in the previous parts to help determine the dimensions of the garden which yield the maximum area, and state the maximum area. (Fill in the blanks below. Include the units of measurement.)

The maximum area is 2000 sqft. Is this accurate?

After differentiating and equating to 0
= -4x + 40=0
Putting this value in area function..
in the perimeter function.

Put x=10

200*10 = 2000 sqft

When the sides perpendicular to the wall have length x = 10ft

and the side parallel to the wall has length 200ft

Are these calculations correct based on my original answer of
B. A(x) = 2x^2 + 40x

Any feedback is very much appreciated! Thanks!

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