SOLUTION: A company makes rectangular shaped bird cages with height b inches and square bottoms. The volume of these cages is given by the function V=b^3-6b^2+9b

Algebra ->  Expressions -> SOLUTION: A company makes rectangular shaped bird cages with height b inches and square bottoms. The volume of these cages is given by the function V=b^3-6b^2+9b       Log On


   

Question 588032: A company makes rectangular shaped bird cages with height b inches and square bottoms. The volume of these cages is given by the function
V=b^3-6b^2+9b
Find an expression for the length of each side of the square bottom by factoring the expression on the right side of the function.
Use the function to find the volume of a cage with a height of 18 inches.
Use the accompanying graph to estimate the height of a cage for which the volume is 20,000 cubic inches.
the line graph display cannot be displayed.
But the volume is 50 (in thousand of cubic inches)
the height of the cage 10 (in inches)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+V=b%5E3-6b%5E2%2B9b+
Factor out b
+V+=+b%2A%28+b%5E2+-+6b+%2B+9+%29++
+V+=+b%2A%28+b+-+3+%29%5E2++
+b+ is the height and
+b+-+3+ is the side of the square bottom
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given:
+b+=+18+ in
+b+-+3+=+15+ in
+V+=+18%2A15%5E2+
+V+=+4050+ in3
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+V+=+20000+ in3
Here's the graph:
+graph%28+500%2C+400%2C+-10%2C+50%2C+-1000%2C+25000%2C+x%5E3+-+6x%5E2+%2B+9x+%29+
It looks like +b+=+29+ That would be
+V+=+29%2A26%5E2+
+V+=+19604+ close
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