Week4Quiz1

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course Mth173

5/12 3pm

If a sand pile 4 meters high has a mass of 146000 kg, then what would we expect to be the mass of a geometrically similar sand pile 14 meters high? Using the differential estimate the mass of sand required to increase the height of the pile from 4 meters to 4.03 meters.Since the mass of the sand pile in kg is directly proportional to the height in meters, we have 146000= k4 where k is some nonzero constant. Solving for k, we have k = 146000 / 4 = 36500. Therefore, the function for the mass of the sand pile in kg with respect to the height in meters is M(x) = 36500x. The mass of a geometrically similar sand pile 14 meters high is 36500 * 14 = 511000 kg. Using the differential to estimate the mass of sand required to increase the height of the pile from 4 meters to 4.03 meters we have `dy = 36500 * .03 = 1095 kg.

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You'll want to review the associated modeling project.

The masses of geometrically similar sandpiles are not directly proportional to their heights.

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