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course MTH 173
7/21/10 9:21 p..m.
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.4m=a(146000)^3
4m=a(3112136000000000)
a=1.28529 * 10^-15
14m=1.28529*10^-15((x)^3)
x^3= 14/1.28529 *10^-15
x^3= 1.08925 * 10^16
x=(1.08925*10^16)^1/3
x= 221671 kg when the sandpile is 14 meters high
the differential is y=1.28529*10^-15)(x)^3 = y'= 3(1.28529*10^-15)(x)^2
y'(4)=6.16939 * 10^-14
y'(4.03)=6.26228 * 10^-14
y'(4.03)-y'(4)
you would have to increase the mass .09289 *10^-14 kg
That is the change in y ' , which is the change in the rate of change, not the change in y.
The differential is y ' multiplied by `dx, the rate of change of y with respect to x multiplied by the change in x.
The rate of change is calculated at the x = 4 point, and the differential extrapolates to the x = 4.03 point by multiplying the rate y ' by the change `dx = .03.
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