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