Question: A wire is bent into the plane shape ABCDE as shown. Shape ABDE is a rectangle and BCD is a semicircle with diameter BD. The

A wire is bent into the plane shape ABCDE as shown. Shape ABDE is a rectangle and BCD is a semicircle with diameter BD. The area of the region enclosed by the wire is R m², AE = x metres, and AB = ED = y metres. The total length of the wire is 2 m.

a. Find an expression for y in terms of x.

b. Prove that R = x/8(8 − 4x − πx).

Given that x can vary, using calculus and showing your working:

c. Find the maximum value of R.

A E B D C

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a To find an expression for y in terms of x we can use the fact that the total length of the wire is 2 meters Lets analyze the wires components The re... View full answer

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