A fixed boundary and an area target
8 written marks
A proper sector has fixed perimeter \(44\) cm and variable radius \(r\).
Part a · 3 marks
Express its angle and area in terms of \(r\), and state the full feasible interval for \(r\).
Part b · 3 marks
Use completing the square to find the greatest area and the corresponding angle.
Part c · 2 marks
Find all radii for which the area is at least \(112\text{ cm}^2\).
Complete-answer checking, worked solutions and indicative written criteria.
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