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Question 854558: The volume of a shipping container in the shape of a rectangular prism can be represented by the polynomial 6x^3+11x^2+4x, where the height is x.
a.) Find the length and width of the container
b.) Find the ratio if the three dimensions of the container when x=2
c.) Will the ratio of the three dimensions be the same for all values of x?
THANK YOU SO MUCH! ANY HELP IS GREATLY APPRECIATED!!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The volume of a shipping container in the shape of a rectangular prism can be represented by the polynomial 6x^3+11x^2+4x, where the height is x.
a.) Find the length and width of the container
:
Factor out x (height): x(6x^2 + 11x + 4)
then
6x^2 + 11x + 4 is the area, the product of the length and width
Factor this
(3x+4)(2x+1); the length and width
:
b.) Find the ratio if the three dimensions of the container when x=2
length (3x+4) when x=2
3(2) + 4 = 10
width (2x+1)
2(2) + 1 = 5
height x, = 2
10:5:2 is the rato
:
c.) Will the ratio of the three dimensions be the same for all values of x?
Let's see, let x = 7
3(7) + 4 = 25
2(7) + 1 = 15
7
25:15:7, the answer is NO!
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