Finding (dA)/(dt) in terms of (dr/dt) and finding velocity
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Finding (dA)/(dt) in terms of (dr/dt) and finding velocity

[From: ] [author: ] [Date: 11-11-07] [Hit: ]
the derivative of A,pi is a constant.d/dt (A) = d/dt (pi r^2), can you do it now?Hint: I wrote down everything except one step.Recall chain rule and that r is a function of t.......
Here are the questions I need help with:

(a) If A is the area of a circle with radius r and the circle expands as time passes, find (dA)/(dt) in terms of (dr/dt).

(b) Bunker oil split from a sunken ferry and spread in a circular pattern. If the radius of the oil spill increased at a constant rate of 1 m/s, how fast was the area of the spill increasing after the initial sinking when the radius was 30m?


Can someone explain how to solve these?

-
(a) A = πr^2
dA/dt = 2πr dr/dt

(b) A = πr^2
dA/dt = 2πr dr/dt = 2π(30 m) (1 m/sec) = 60π m^2/sec

-
dA/dt means d/dt (A), i.e. the derivative of A, where

A = pi r^2

pi is a constant.

d/dt (A) = d/dt (pi r^2), can you do it now?

Hint: I wrote down everything except one step. Recall chain rule and that r is a function of t.
1
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