Answered

Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 2 m/s, exactly how fast (in m2/s) is the area of the spill increasing when the radius is 39 m?

Sagot :

Trancescient

Explanation:

The area of a circle of radius r is given by

[tex]A = \pi r^2[/tex]

Taking the derivative of A with respect to time t, we get

[tex]\dfrac{dA}{dt} = 2\pi r \dfrac{dr}{dt}[/tex]

We also know that

[tex]\dfrac{dr}{dt} = 2\:\text{m/s}\:\text{at}\:r = 39\:\text{m}[/tex]

[tex]\dfrac{dA}{dt} = 2\pi (39\:\text{m})(2\:\text{m/s})= 490\:\text{m}^2\text{/s}[/tex]

We hope this was helpful. Please come back whenever you need more information or answers to your queries. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.