Calculus related rates

Calculus
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a fish is reeled in at a rate of 2m/min from a point 12m above the water. There is a total of 15m of line out. At what rate is the fish moving at the same point?

Apr 9th, 2015

let the distance between the fish and the fisher is x then we have x^2+12^2 = s^2, where s is the length of the line out

take derivative from both sides, 2x*dx/dt = = 2s*ds/dt

x*dx/dt = s*ds/dt 

dx/dt = s/x*ds/dt = 15/x *2  =30/x 

x = sqrt(15^2-12^2) = sqrt(225-144) = 9 

dx/dt = 30/9 = 10/3 m/minutes  

Apr 9th, 2015

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