A wire is bent into the plane shape ABCDE as shown. Shape ABDE is a rectangle and
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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.
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Related Book For
Edexcel AS And A Level Mathematics Pure Mathematics Year 1/AS
ISBN: 9781292183398
1st Edition
Authors: Greg Attwood
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