Question 211668: A cubic shipping container had a volume of v^3 cubic meters. The height of the container was decreased by a whole number of meters and the width was increased by a whole number of meters so that the volume of the container is now v^3+2v^2-3v. Find out the following:
a. By how many meters the height was decreased?
b. By how many meters the width was increased
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! If it was a cubic shipping container, then it was a perfect cube making the dimensions of each side = v.
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original volume = v*v*v = v^3
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The height was decreased by an integer called a.
The width was increased by an integer called b.
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new volume =
(v-a)*(v-b)*v = v^3 + 2v^2 - 3v
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If we divide both sides of this equation by v, we get:
(v-a)*(v+b) = v^2 + 2v - 3
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if we factor the equation on the right side, we get:
(v-a)*(v+b) = (v-1)*(v+3)
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This means that a = 1 and b = 3 will satisfy the equation.
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The height is reduced by 1 and the width is increased by 2.
v*v*v = v^3
(v-1)*(v+3)*v = v^3 + 2v^2 - 3v
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Answer is:
height is reduced by 1 and width is increased by 3 meters.
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