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In a design for the Tower of Babel with an infinite height in order to...

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Calculus

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In a design for the Tower of Babel with an infinite height in order to reach the heavens the horizontal cross sections are circles with the radius as a function of height given by the equation r f h frac h left h 3 a right a If there is 4 cubic kilometres of material available for the construction of the tower find the value that the parameter a must take b The number of days per kilometre of height d that it takes to build a section of the tower depends on the cross sectional area and the steepness of the sides according to the function d g h frac pi f h 2 f prime h Find an explicit expression for this function c Use the function d g h to find the time it would take to build the entire tower if it exists

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