Can someone help me out with the calculus chemistry...I don't even know how to go about it! plz!
The radius of a circle is increasing at a constant rate of 6 ft/sec, Express the rate at which the area of the circle is changing in terms of the circumference, C of the circle.
The radius of a circle is increasing at a constant rate of 6 ft/sec, Express the rate at which the area of the circle is changing in terms of the circumference, C of the circle.
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Let's do this in steps.
radius is increasing at a rate of 6 ft/s, so dr/dt = 6
The circumference C(r) = 2pi*r is changing at a rate dC/dt = 2pi*dr/dt = 12pi
The area of the circle, which is A(r) = pi r^2 = 4pi^2 r^2 / (4pi) = (2pi r)^2 / (4pi) = C%
radius is increasing at a rate of 6 ft/s, so dr/dt = 6
The circumference C(r) = 2pi*r is changing at a rate dC/dt = 2pi*dr/dt = 12pi
The area of the circle, which is A(r) = pi r^2 = 4pi^2 r^2 / (4pi) = (2pi r)^2 / (4pi) = C%
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