1. Cross-sectional Area

The cross-sectional area of a beam cut from a log with radius 1 foot is given by the function A(x) = (4x)(sqrt{1 - x^2}), where x represents the length, in feet, of half the base of the beam. Determine the cross-sectional area of the beam if the length of half the base of the beam is one-third of a foot.

Let me see.

There are 12 inches in one foot.

So, (1/3)(12) = 4 inches.

If x represents the length, in feet, of half the base of the beam, then I cannot let x = 4 inches. So, do I replace x with 1/3 in the given function and then simplify?

2. Re: Cross-sectional Area

Originally Posted by harpazo
The cross-sectional area of a beam cut from a log with radius 1 foot is given by the function A(x) = (4x)(sqrt{1 - x^2}), where x represents the length, in feet, of half the base of the beam. Determine the cross-sectional area of the beam if the length of half the base of the beam is one-third of a foot.

Let me see.

There are 12 inches in one foot.

So, (1/3)(12) = 4 inches.

If x represents the length, in feet, of half the base of the beam, then I cannot let x = 4 inches. So, do I replace x with 1/3 in the given function and then simplify?
Yes.

3. Re: Cross-sectional Area

Originally Posted by Debsta
Yes.
That's easy enough. I will work on this tomorrow.

4. Re: Cross-sectional Area

See picture for answer.

Yes!!

6. Re: Cross-sectional Area

Originally Posted by Debsta
Yes!!
It certainly feels good to be right.