Please show all work and be as thorough as possible. Thanks! A wire of length 10

Question

Please show all work and be as thorough as possible. Thanks!

A wire of length 10 meters is cut into two parts. One piece is bent into a circle and the other piece is bent into a square The goal is to determine how to cut the wire in order to obtain the maximum area. To this end, set up a mathematical function (also specify its domain) whose maximum value in its domain corresponds to the maximum area obtained. PLEASE NOTE: You don't have to find the maximum value of the function. Your job is to just get the right function.

Explanation / Answer

2) If you cut it into lengths of x and 10-x, and turn the x into a circle and the y into the square, then the circumference of the circle is x, so its radius is x/2pi. Then its area is pi(x/2pi)^2 = x^2/4pi. A side of the square has length (10-x)/4, so it's area is (10-x)^2/16. Therefore, the total area is f(x) = x^2/4pi + (10-x)^2/16. The domain is 0 < x < 10, since it is cut into two parts.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.