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course Mth 173
6/21/13~6:08PM
week 3 quiz 3 version 1Solve using proportionalities by stating the appropriate proportionality law and finding the proportionality constant:
If a sand pile 2.1 meters high has a mass of 5000.939 kg, then what would we expect to be the mass of a geometrically similar sand pile 6.1 meters high?
If there are 1.323 billion grains of sand exposed on the surface of the first sand pile, how many grains of sand we expect to be exposed on the surface of the second?
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use the perportionality of y=kx^3.
-the sand pile has a height of 2.1
-mass of 5000.939 kg
Y=kx^3
5000.939=k*2.1^3
--> solve for k = 539.999892
Y=kx^3
539.999892*6.1^3=122569.7155kg weight of second sand pile.
grains is dealing with surface area, the proportionality of this is y=kx^2
1.323 billion grains of sand on the surface of the first sand pile with a height of 2.1 meeters
-->
Y=kx^2
1.323=k*2.1^2
k=.3
plug in the k value
Y=kx^2
Y=.3*6.1^2=11.163
The second sand pile has around 11.163 billion sand grains
&#Very good work. Let me know if you have questions. &#