The diagram shows a metal plate consisting of a rectangle with sides x cm and y cm and a quarter-circle of radius x cm. The perimeter of the plate is 60 cm.

i. Express y in terms of x.
ii. Show that the area of the plate, Acm², is given by A = 30x − x².
Given that x can vary,
iii. Find the value of x at which A is stationary,
iv. Find this stationary value of A, and determine whether it is a maximum or a minimum value.

Transcribed Image Text:

x cm y cm →→xcm