Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
Using implicit differentiation, it is found that the rate of change is of the width is of -3 feet/min.
What is the area of a rectangle?
The area of a rectangle of length l and height h is given by:
[tex]A = lh[/tex]
Applying implicit differentiation, the rate of change is given by:
[tex]\frac{dA}{dt} = l\frac{dh}{dt} + h\frac{dl}{dt}[/tex]
In this problem, we have that:
- The area is constant, hence [tex]\frac{dA}{dt} = 0[/tex].
- Area of 2 square feet, height of 2 feet, hence [tex]h = 2, lh = 2 \rightarrow l = 1[/tex].
- The height is changing at a rate of 6 feet/minute, hence [tex]\frac{dh}{dt} = 6[/tex].
Then:
[tex]\frac{dA}{dt} = l\frac{dh}{dt} + h\frac{dl}{dt}[/tex]
[tex]0 = 6 + 2\frac{dl}{dt}[/tex]
[tex]2\frac{dl}{dt} = -6[/tex]
[tex]\frac{dl}{dt} = -3[/tex]
The rate of change is of the width is of -3 feet/min.
To learn more about implicit differentiation, you can take a look at https://brainly.com/question/25608353
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.
