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Item 1
Given the information provided:
- Set A: Rectangular prism with height (2x-1) meters and volume (6x³- 13x² + x + 2) cubic meters
- Set B: Rectangular prism with height (2x-1) meters and base area (3x² -7x-6) square meters
- Set C: Rectangular prism with height (3x-2) meters and base area (2x²+x-3) square meters
Determine the length and width of each set of storage spaces.
Solution for Item 1
To find the length and width of each set of storage spaces, we can use the formula for the volume and base area of a rectangular prism.
For Set A:
Volume = length × width × height
(6x³- 13x² + x + 2) = length × width × (2x-1)
Solving for the length and width:
Length × Width = (6x³- 13x² + x + 2) / (2x-1)
For Set B:
Base Area = length × width
(3x² -7x-6) = length × (2x-1)
Solving for the length and width:
Length = (3x² -7x-6) / (2x-1)
Width = (2x-1)
For Set C:
Base Area = length × width
(2x²+x-3) = length × (3x-2)
Solving for the length and width:
Length = (2x²+x-3) / (3x-2)
Width = (3x-2)
Therefore, the length and width of each set of storage spaces can be determined using the given information.