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Let A be the area of a circle with radius r. If dr/dt=3, find dA/dt when r=2.

User Virus
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area=pir^2
take deritivive
dA/dt=2pir (dr/dt)
given dr/dt=3
dA/dt=2pi(2)(3)
dA/dt=12pi

User Swapnil Nakade
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\bf \textit{area of a circle}=A=\pi r^2 \\\\\\ \cfrac{dA}{dt}=\pi \cdot 2r^1\cdot \cfrac{dr}{dt}\implies \cfrac{dA}{dt}=\pi \cdot 2r\cdot \cfrac{dr}{dt}\quad \begin{cases} r=2\\ (dr)/(dt)=3 \end{cases} \\\\\\ \cfrac{dA}{dt}=\pi \cdot 2(2)(3)
User Varogen
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