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myanmar
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I'm really having trouble with these three problems. I'd post my attempts but most of it is in graph from.
3. David subjects a cylindrical can to a certain transformation. During this transformation the radius and height vary continuously with time. The radius is increasing at 4 in/min, while the height is decreasing at 10 in/min. Is the volume of the can increasing or decreasing, and at what rate, when the radius is 3 inches and the height is 5 inches?
4. A particle moves along a path described by [tex]y=x^{2}[/tex]. At what point along the curve are [tex]x[/tex] and [tex]y[/tex] changing at the same rate? Find this rate if at that time we have [tex]y = sin^{2} t[/tex] and [tex]x = sin t[/tex]
5. Two straight roads intersect at right angles near the Krupps factory at Baden-Baden. Fabio drives his scooter towards the intersection at a rate of 50 kph. Ilsa drives her scooter on the other road away from the intersection at a speed of 30 kph. When Fabio is 2 kilometers from the intersection and Ilsa is 4 kilometers from the intersection:
(a) How fast is the distance between them changing?
(b) Are Fabio and Ilsa getting closer together or farther apart?
3. David subjects a cylindrical can to a certain transformation. During this transformation the radius and height vary continuously with time. The radius is increasing at 4 in/min, while the height is decreasing at 10 in/min. Is the volume of the can increasing or decreasing, and at what rate, when the radius is 3 inches and the height is 5 inches?
4. A particle moves along a path described by [tex]y=x^{2}[/tex]. At what point along the curve are [tex]x[/tex] and [tex]y[/tex] changing at the same rate? Find this rate if at that time we have [tex]y = sin^{2} t[/tex] and [tex]x = sin t[/tex]
5. Two straight roads intersect at right angles near the Krupps factory at Baden-Baden. Fabio drives his scooter towards the intersection at a rate of 50 kph. Ilsa drives her scooter on the other road away from the intersection at a speed of 30 kph. When Fabio is 2 kilometers from the intersection and Ilsa is 4 kilometers from the intersection:
(a) How fast is the distance between them changing?
(b) Are Fabio and Ilsa getting closer together or farther apart?