Modeling Data The hydiauhc cylinder on a woodsplitter hasa 4-inch bote (diameter) and a

Chapter 6, Problem 42

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Modeling Data The hydiauhc cylinder on a woodsplitter hasa 4-inch bote (diameter) and a stroke of 2 feet. The hydiaulicpump creates a ma\imnni pressure of 2001) pounds per square inch. Therefore, the maximum force created by the cylinder is 20001 7t2-) = 800077 pounds.(a) Find the work done through one extension ol the cylmdei"given that the maxnnum force is required.(hi The force exerted in splitting a piece of wood is \ariable.Measurements of the force obtained when a piece of woodwas split are shown in the table. The variable .v measuresthe extension of the c\linder in leel, and / is the force inpounds. L'se .Simpson's Rule to approximate the work donein splitting the piece of wood(c) Use the regression capabilities of a graphing utility to finda fourth-degree polynomial model for the data. Plot the dataand graph the model.(d) L'se the model in part (e) to approximate the extension ofthe cylinder when the force is maximum.(e) Use the model m part (c) to approximate the work done msplitting the piece of wood.