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Volume formula to write polynomial function?
Origional dimentions of a retangular prism are;
Length: 1cm
Width: 2cm
Height: 3cm
origional volume is 6cm^3
I need the volume to be 120cm^3, while increasing the length, width, and height by the same amount.
So the new dimentions are;
Length: 4cm
Width: 5cm
Height: 6cm
New volume is 120cm^3
Length can be represented by (x+1), width by (x+2), height by (x+3)
so x = 3
But how do I use the volume formula to write a polynomial function to model the situation? And what are the restrictions on x?
1 Answer
- Anonymous7 years agoFavorite Answer
You pretty much have the polynomial function already:
(x + 1)(x + 2)(x + 3) = 120
More generally, A(x) = (x + 1)(x + 2)(x + 3)
The restriction is x > -1. Anything less than or equal to -1 would give a negative length or 0 to at least on of the sides, which cannot happen.