At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
Hey there, not sure how far along you are in solving this problem, but the first step is to get an equation which relates the volume to the height. Once you have done that, rates of change usually involve differentiation. Since there are two rates of change, for volume and height, this problem lends itself well to implicit differentiation. Here is a very good video on implicit differentiation: http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/video-lectures/lecture-5-implicit-differentiation/
@datanewb the link you've given is not found..:(
I'm sorry the link is not working for you. I tested it in IE and Chrome and it is working on my computer. As an alternative to the above link, you can go to http://ocw.mit.edu and navigate to mathematics -> 18.01 -> lectures -> lecture 5. Or, simply do a Google search for "18.01 lec 5". The lecture video is the first result returned by Google. It's a 45 minute lecture, and the explanation builds off of the chain rule, so you should be familiar with that before watching the video. (The chain rule is explained in lecture 4).
@datanewb someone like you here at openstudy...gave me that answer too....however, he told me that the given V' is negative 2000 cm^3/min. for the problem stated above that its leaking a volume of 2000 right? so his answer is -5/2 cm/min.. which is which?? thank you!!
Well, yes, it would be negative. Generally speaking you can set the isosceles trapezoid in any reference frame, and thus the answer could be negative or positive depending on how you framed the answer. The only thing that is imperative is that you be consistent. That said, as I drew the figure and framed my answer, the correct answer is certainly negative. -5/21 cm/s! Thank you for pointing out my error!
the negative in this case represents a direction as opposed to a decrease of speed. thats understood right?