Get expert advice and insights on any topic with IDNLearn.com. Find the solutions you need quickly and accurately with help from our knowledgeable community.
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 using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Thank you for visiting IDNLearn.com. We’re here to provide accurate and reliable answers, so visit us again soon.
