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 deno
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-> 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 deno
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Question 1048339: 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 rothauserc(4718) (Show Source):
You can put this solution on YOUR website! i) arc length(in radians) = theta * radus(r)
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theta = arc length / r
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use implicit differentiation
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d(theta)/ dt = d(arc length)/ dt * (1/12)
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note that d(arc length) /dt = 4 cm/sec
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d(theta/dt = 4 /12 = 1/3
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theta increases at the rate of (1/3) radians per second
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ii) area of sector (in radians) = (theta/2) * r^2
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use implicit differentiation
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d(area of sector)/dt = d(theta)/dt * (2r/2)
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d(area of sector)/dt = d(theta)/dt * r
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d(area of sector)/dt = (1/3) * 12 = 4
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area of sector in radians is increasing at 4 radians / second
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