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- Homework Statement
- The specifications for a storage container state that the length is 1 metre more than triple the width and the height is 5 metres less than double the width. Find the range of possible dimensions for a volume of at least 8436m^3
- Relevant Equations
- None
I understand how to get the dimensions that equal 8436m^3. What I don't understand is how to find the range of all possible dimensions.
I solved the inequality to get ##6w^{3}-13w^{2}-5w-8436##
Using systematic guessing I found the root is x=4, so the factor is x-4.
Dividing (x-4) into ##6w^{3}-13w^{2}-5w-8436## gives me ##6w^{2}+59w+703##
so, ##6w^3-13w^{2}-5w-8436 = (w-12)(6w^{2}+59w+703)##.
this means that
w=12
l=3(12)+1=37
h=2(12)-5=19
v=lwh
v=8436
This is as far as I get. I don't understand how to find the range of all possible dimensions.
I solved the inequality to get ##6w^{3}-13w^{2}-5w-8436##
Using systematic guessing I found the root is x=4, so the factor is x-4.
Dividing (x-4) into ##6w^{3}-13w^{2}-5w-8436## gives me ##6w^{2}+59w+703##
so, ##6w^3-13w^{2}-5w-8436 = (w-12)(6w^{2}+59w+703)##.
this means that
w=12
l=3(12)+1=37
h=2(12)-5=19
v=lwh
v=8436
This is as far as I get. I don't understand how to find the range of all possible dimensions.
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