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A fire has started in a dry, open field and is spreading in the form of a circle. If the radius of the circle is increasing at the rate of 6 feet/min, find the rate at which the fire area is increasing when the radius is 150 feet.

Respuesta :

[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2\qquad \qquad \implies \cfrac{dA}{dt}=\pi \cdot \stackrel{chain~rule}{2r\cdot \cfrac{dr}{dt}}\quad \begin{cases} \frac{dr}{dt}=6\\ r=150 \end{cases} \\\\\\ \cfrac{dA}{dt}=\pi \cdot 2(150)(6)\implies \cfrac{dA}{dt}=1800\pi \frac{ft}{min}[/tex]

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