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course Mth 271
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.
146 000 = a 4^3
146 000 = a 64
a = 2281.25
y = 2281.25 * 14^3 = 6 259 750 kg
y = 2281.25 * 4.03^3 = 149 309.6991
needs to increase by 149 309.6991 - 146 000 = 3309.699094
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@& You didn't use the idea of the differential to estimate the change in mass.
What is the derivative of your volume function
y = 2281.25 * x^3?
If x changes by .03 meters, at the rate given by your derivative, then by how much does y change (based on that rate and the change in x)?
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