Here, we are required to find the equation, in terms of w, that could be used to find the dimensions of the storage unit in feet.
The polynomial is;. 3w³ + 22w + 24w = 5440ft³.
From the question;
The volume of a rectangular prism is given by the product of its length, width and height. Thus;
Volume = l × w × h
Therefore, Volume, V = (3w +4) × w × (w +6)
To obtain the required polynomial, we expand the expression for Volume above;
V = (3w² + 4w) × (w + 6)
V = (3w² + 4w) × (w + 6)V = 3w³ + 22w² + 24w.
However, the volume of the rectangular prism has been given to be 5440 cubic feet.
Therefore, the polynomial is;
3w³ + 22w + 24w = 5440ft³.
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Answer:
3w^3+22w^2+24w=5440
Step-by-step explanation:
The length and height are given in terms of the width. Width =w; Length =(3w+4); Height =(w+6); and the Volume is equal to the product of the three. Therefore, we can set up the equation as follows:
w×(3w+4)×(w+6)=5440
To finish, we distribute and combine like terms:
(3w2+4w)×(w+6)=54403w3+18w2+4w2+24w=54402w3−9w2+10w=528
Therefore, 3w3+22w2+24w=5440 is our equation for the dimensions of the storage unit in terms of w.
