A company that sells prefabricated homes ships the frames for each home in large shipping containers. Each shipping container is in the shape of a rectangular prism and its volume can be represented by the polynomial expression 5x3 + 7.5x2, where x is the width of the shipping container. If the length of the shipping container is five times the width, write the expression that represents the height of the shipping container in terms of its width, x.
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Answer:
h = x + 1.5
Step-by-step explanation:
Volume of container = Length * Width * Height
Width = x
Length = 5 * width = 5x
height = h
Volume = 5x * x * h = 5x²h
Volume is given as 5x³ + 7.5x²
5x²h = 5x³ + 7.5x²
dividing by 5x² both sides
=> h = x + 1.5
the expression that represents the height of the shipping container in terms of its width is h = x + 1.5
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