#$&*
course mth 173
7/18 8
If a sand pile 4 meters high has a mass of 146000 kg, then what would we expect to be the mass of a geometrically similar sand pile 14 meters high? Q(x) = kx^3
146000 = k(4^3)
k = 2281.25
Q(x) = 2281.25(x^3)
Q(14) = 2281.25(14^3) = 6259750 kg
Using the differential estimate the mass of sand required to increase the height of the pile from 4 meters to 4.03 meters.
Q(x) = 2281.25(x^3)
Q'(x) = 3(2281.25)x^2 = 6843.75(x^2)
dx = .03
avg. rate = dy/dx
6843.75(4^2) = 109500
6843.75(4.03^2) = 111148.65
avg rate = (109500 + 111148.65)/ 2 = 110324.33
110324.33 * dx = 110324.33 * .03 = 3309.73 kg
`gr41
#$&*
course mth 173
7/18 8
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? Q(x) = kx^3
146000 = k(4^3)
k = 2281.25
Q(x) = 2281.25(x^3)
Q(14) = 2281.25(14^3) = 6259750 kg
Using the differential estimate the mass of sand required to increase the height of the pile from 4 meters to 4.03 meters.
Q(x) = 2281.25(x^3)
Q'(x) = 3(2281.25)x^2 = 6843.75(x^2)
dx = .03
avg. rate = dy/dx
6843.75(4^2) = 109500
6843.75(4.03^2) = 111148.65
avg rate = (109500 + 111148.65)/ 2 = 110324.33
110324.33 * dx = 110324.33 * .03 = 3309.73 kg
This looks very good. Let me know if you have any questions.