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1 Two congruent pieces of glass whose areas are described by the region bounded by...

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Geometry

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1 Two congruent pieces of glass whose areas are described by the region bounded by both axes y 4 and the graph of x g y see right are to be glued together Let A h be the area of the pieces of glass covered by glue when the glue is at height y h from the bottom of the pieces The glue is injected at a constant rate R that is R dA dt 3 1 0 ii iii iv A h a Intuitively for what approximate height hy is the glue level changing most rapidly What does this mean about Give reasons for your answer dt c We now want to mathematically find the heights hy and hm i x g y b Intuitively for what approximate height hm is the glue level changing most slowly Give reasons for your answer What integral describes the area A h when the glue is at a height y h How does the Fundamental Theorem of Calculus help you compute dA dh How can you computed in terms of What other term is involved Why can you conclude that is inversely proportional to g h For what approximate value of his g h minimal What does that say about Does this agree with your answer to part b What can you say when g h is maximal Estimate the values of h and hm

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