someone please help. "the radius of a circle is increasing at a constant rate of 0.2 meters per second. in terms of (pie) what is the rate of increase in the area of the circle at the instant when the circumference of the circle is 20(pie) meters?
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You have the change in radius over time, dr/dt. You want the change in area over time, dA/dt. Think in terms of multiplying fractions: dr/dt = dA/dt times what? Well, the "what" must cancel the dA we don't want and introduce the dr we need.
Thus we have dr/dt = dA/dt times dr/dA. Your task now is to find a formula that relates r and A (that should be easy). Solve for r and take the derivative with respect to A; that's dr/dA. Then just muliply as indicated at the top of this paragraph, using the value of r implied in the problem. Okay?
i'm still a little confused with this
You'll have to tell me where you're confused and why if you want more. This is several pages in your textbook and I can't type that much. :)
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i understand the dr/dt. and the da/dt. i know i'm looking for da/dt. but the multiplying paRt confused me. A=(pie) R(squared) and the derivative of that isDa/Dt= 2(pie) Dr/Dt right? can i just plug in 0.2 which is Dr/Dt?
that way i get Da/Dt?
Okay, I think I typed something backwards. Sorry. You want da/dt, right? So my equation should have said da/dt = dr/dt (known) times da/dr. If we can find da/dr, we're home free.
Begin with a = pi r^2 and take the d/dr of both sides to get da/dr = 2 pi r (not quite what you have -- I'm applying d/dr, not d/dt). The 0.2 is dr/dt, as you said, and yes, you can plug that in. So multiply dr/dt (0.2) by 2 pi r (you'll need to calculate the correct r from the circumference given) and you're done. Good?
ok cool. i had that in mind but wasn't quite sure thanks for the reassurance. :)