A polynomial consists of exponential variables which are non negative
Tank volume with hemisphere installed is 6·x³ - 300·x² + 6480·x - 32400
Reason:
The given parameter are;
The length, L of the new tank = (2·x - 30)
The width, W, of the new tank = (2·x - 20)
The height, H, of the new tank = (2·x - 60)
The volume of the hemisphere, Vₐ = x³ - 70·x² + 360·x - 1800
The answer to question 1. is; The volume of the new tank, V = L × W × H
- ∴ V = (2·x - 30)·(2·x - 20)·(2·x - 30)
The volume of the new tank with the hemispheres installed, V' = V - 2·Vₐ
∴ V' = (2·x - 30)·(2·x - 20)·(2·x - 30) - 2×(x³ - 70·x² + 360·x - 1800)
Which gives;
- V' = 6·x³ - 300·x² + 6480·x - 32400
Volume of the new tank with the hemispheres installed, V' = 6·x³ - 300·x² + 6480·x - 32400
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