FREE Trial

(a) If A is the area of a circle with radius r and the circle expands as...

Question:

(a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of dr/dt.

(b) 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 1 mys, how fast is the area of the spill increasing when the radius is 30 m?

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Answer rating: 75% (8 reviews)

a b A r ...View the full answer


answer-question-section
Answered By
tutor-profile-image
Abigael martinez
I have been a tutor for over 3 years and have had the opportunity to work with students of all ages and backgrounds. I have a strong belief that all students have the ability to learn and succeed if given the right tools and support. I am patient and adaptable, and I take the time to get to know each student's individual learning style in order to best support their needs. I am confident in my ability to help students improve their grades and reach their academic goals.
5.00+ 1+ Reviews 10+ Question Solved
Related Book For  book-img-for-question
Calculus Early Transcendentals

Calculus Early Transcendentals

ISBN: 978-1285741550

8th edition

Authors: James Stewart

See More Books
Question Posted:
See More Questions

Related Video

The area of a circle is given by the formula: A = ?r^2 Where A is the area, ? is a mathematical constant (approximately 3.14), and r is the radius of the circle. The radius is the distance from the center of the circle to the edge. So for example, if the radius of a circle is 5 units, the area would be: A = ?(5^2) = ?(25) = 78.5 square units Here three friends went out to a restaurant and decided to have pizza for lunch. While they were waiting for their order, one of them stepped out to take a call but promised to return in two minutes. The waiter came and presented them with the menu, and they decided to order two 10-inch pepperoni pizzas. The waiter took their order and left. Just then, the third friend returned and asked what they had ordered. They explained that they had ordered two small pepperoni pizzas as they were only three of them and it would be enough for them. However, the third friend suggested that for the same price, they could get a large pizza that would be much bigger than the two small ones. He asked the waiter for a pen and paper and proceeded to calculate the area of the two small pizzas and compared it to the area of one large pizza. The friends were amazed at how the circle measurements worked and decided to change their order from two small pizzas to one large pizza.

Students also viewed these Mathematics questions

Economics Demystified 1st Edition - ISBN: 0071782834 - Free Book