The volume of a rectangular solid, in cubic inches, is given by the expression \((x^3 - 7x + 6)\). If the length and width, in inches, are given by the expressions \((x - 2)\) and \((x + 3)\) respectively, find an expression in \(x\) which describes the height.

V=x³-7x+6, V=(x-2)(x+3)*h
(x-2)(x+3)*h=x³-7x+6
h{x²+x-6}=x³-7x+6
h=(x³-7x+6)/(x²+x-6)
Therefore h=x-1

Check answer:
V=(x-2)(x+3)(x-1)
=(x-1)(x²+x-6)
=x(x²+x-6)-1(x²+x-6)
=x³+x²-6x-x²-x+6
=x³-6x-x+6
=x³-7x+6

Answered by Anonymous | 2024-06-10

The height of the rectangular solid can be determined using the formula for volume. By substituting the expressions for length and width into the volume equation and simplifying, we find that the height is given by h = x − 1 .
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Answered by Anonymous | 2024-12-26