week4quiz1

#$&*

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

week4quiz1

#$&*

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

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