Explore a wide range of topics and get answers from experts on IDNLearn.com. Discover the information you need from our experienced professionals who provide accurate and reliable answers to all your questions.
Sagot :
If water is being pumped into the trough at 2 cubic feet per minute, then the water level rising (in feet per minute) when h is 1.6 foot deep is 0.1 feet cubic per minute.
Suppose that we have a function y = f(x), and wish to find the rate of change of y with respect to a third variable t, where we do not have y expressed explicitly in terms of t. We use the chain rule in differentiation to find this rate of change in a process called implicit differentiation.
dy/dt = dy/dx × dx/dt
If base is equal to the height, by similar triangles:
Volume v = base x height x length/2
= bhl/2
= h²12/2
= 6h².
Therefore,
dv/dt = 12hdh/dt
= 2 ft³/min
Now,
dh/dt = 2/(12h)
when h = 1.6,
dh/dt = 2/(12 × 1.6) ≈ 0.1 ft³/min
Learn more about Volume :
https://brainly.com/question/1578538
#SPJ4
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Discover the answers you need at IDNLearn.com. Thanks for visiting, and come back soon for more valuable insights.
