The inside lane of a school running track consists of two straight sections each of length x
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The inside lane of a school running track consists of two straight sections each of length x metres, and two semicircular sections each of radius r metres, as shown in the diagram. The straight sections are perpendicular to the diameters of the semicircular sections. The perimeter of the inside lane is 400 metres.
i. Show that the area, Am2, of the region enclosed by the inside lane is given by A = 400r − πr2.
ii. Given that x and r can vary, show that, when A has a stationary value, there are no straight sections in the track. Determine whether the stationary value is a maximum or a minimum.
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i The perimeter of the inside lane is the sum of the lengths of the two straight sections and the ci...View the full answer
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Related Book For 
Cambridge International AS And A Level Mathematics Pure Mathematics 1 Coursebook
ISBN: 9781108407144
1st Edition
Authors: Sue Pemberton, Julian Gilbey
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