anonymous
  • anonymous
calc help
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
A circle is growing so that each side is increasing at the rate of 2cm/min. How fast is the area of the circle changing at the instant the radius is 10cm? Include units in your answer.
anonymous
  • anonymous
@Zale101
Zale101
  • Zale101
|dw:1450393944381:dw|

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Zale101
  • Zale101
We know that the circle keeps increasing at a rate of 2cm/min. Meaning, the area of a circle keeps increasing.
Zale101
  • Zale101
What is the area of a circle?
anonymous
  • anonymous
pir^2
Zale101
  • Zale101
\(A(r) =\pi r^2\) How fast is the area of a circle changing? To answer this, we need to take the derivative of the area to obtain the instantaneous value for the rate of change of the area.
anonymous
  • anonymous
2piR(dr/dt)
Zale101
  • Zale101
Your question is asking you to find the area's rate of change.
Zale101
  • Zale101
\(\Large \frac{d(A(r))}{dt}=\frac{dA}{dt}=\frac{d}{dt}[\pi r^2]\) \(\Large \frac{dA}{dt}=2\pi r \frac{dr}{dt}\)
anonymous
  • anonymous
ok so whats next?
Zale101
  • Zale101
You are giving the radius (r) and dr/dt (the rate of change of the radius). Plug them in the dervative of the area to get dA/dt.
anonymous
  • anonymous
dA/dt= 2pi (10)(2)
Zale101
  • Zale101
Yes.
anonymous
  • anonymous
So the answer is 40pi?
Zale101
  • Zale101
Yes.
anonymous
  • anonymous
ok thanks. i have one more if you don't mind

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