The vertex is not allowed
8 written marks
A sector has fixed perimeter \(40\) cm and must satisfy \(\displaystyle 0< \theta \le \frac{4}{3}\). No differentiation is to be used.
Part a · 2 marks
Find the feasible interval for its radius \(r\).
Part b · 3 marks
Express its area in completed-square form.
Part c · 3 marks
Find the greatest permitted area, giving the radius and angle. Explain why the value \(100\text{ cm}^2\) is not attainable.
Complete-answer checking, worked solutions and indicative written criteria.
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