Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
[tex] \frac{dr}{dt} = 6.79 \: \frac{m}{s} [/tex]
Step by Step Explanation:
The area a is defined as
[tex]a = \pi {r}^{2} [/tex]
Now take derivative of the above expression with respect to time:
[tex] \frac{da}{dt} = 2\pi r \frac{dr}{dt} [/tex]
Solving for dr/dt, we then get
[tex] \frac{dr}{dt} = \frac{1}{2\pi r} \frac{da}{dt} [/tex]
Note that da/dt = 900 m^2/s and when the area of the oil slick is 1400 m^2, the radius r is r = √(1400/π) = 21.1 m. Therefore,the rate at which the radius is increasing dr/dt is
[tex] \frac{dr}{dt} = \frac{1}{2\pi(21.1 \: m)}(900 \frac{ {m}^{2} }{s} ) = 6.79 \frac{m}{s} [/tex]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.