Question

The area of a circle is increasing at a rate of 87 square meters per hour. At a certain instant, the area is 367 square meters. What is the rate of change of the circumference of the circle at that instant (in meters per hour)? Choose 1 answer: ® 4v2 © 127 E10

Answer 1

Let a(t) rachios att Alt) - Area at t C (t) - Circunference at t Civen. A'(t)=85 Also, A (bol = 367 for a We need to find c'lt) = ? particular to we know, c(t) = 22 r(t). for Differentiating both sides: c' (t) = 250 ri(t). - ;) But A(+) = a[°ct]]? tii) Again differenbuting: Allt - (259 (t)) si (t) j) using the A' (t) = 87 85= (25 & ()) r' (t) 'Lt) o Using this in it 8T nrlt rt)) rit using: Alto) & in egen. ) 3680 2t [x (to)] & using 3600 r (to) = 1836=6

In eam cili ci (to) 28th or oto en tu option A,

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