SOLUTION: N is a fixed point on the circumference of a circle, centre O, radius 12cm. A variable point moves round the circumference with a constant speed of 4cm/s. The angle PON is denot

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Question 1048413: N is a fixed point on the circumference of a circle, centre O, radius 12cm.
A variable point moves round the circumference with a constant speed of 4cm/s. The angle PON is denoted by θ.
Find
(i) the rate of increase of θ in radians per seconds.
(ii)the rate of increase of the area of the sector NOP.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
(i) s+=+r%2Atheta ===> s+=+12%2Atheta ===> ds%2Fdt+=+12%2Ad%28theta%29%2Fdt ===> 4+=+12%2Ad%28theta%29%2Fdt ===>d%28theta%29%2Fdt+=+1%2F3 rad/sec.

(ii) A+=+%281%2F2%29r%5E2%2Atheta+=+%281%2F2%2912%5E2%2Atheta
===> dA%2Fdt+=+72%2A%28d%28theta%29%2Fdt%29
===> dA%2Fdt+=+72%2F3+=+24 cm^2/sec.