MATH SOLVE

4 months ago

Q:
# The volume of a box is 80 cubic feet with length x-3 and width x-1 and height x+5. What are the possible values of x? What are the possible dimensions?

Accepted Solution

A:

Answer:the only possible value of x is 5the dimensions are 2 × 4 × 10Step-by-step explanation:The cubic equation ... (x -3)(x -1)(x +5) = 80has one real root: x = 5. Using that value for x, the dimensions become ... length = 5 - 3 = 2 width = 5 - 1 = 4 height = 5 + 5 = 10The dimensions are (length, width, height) = (2, 4, 10)._____We cannot tell the thrust of the problem, since it has only one solution. Perhaps you're supposed to write the cubic in standard form and use the Rational Root theorem to find possible values of x. That form can be found to be ... (x -3)(x -1)(x +5) -80 = 0 x³ +x² -17x -65 = 0Descartes' rule of signs tells you there is one positive real root. The rational root theorem tells you possible rational roots are factors of 65: 1, 5, 13, 65We know that x must be greater than 3 (so all dimensions are positive). Thus possible values of x are 5, 13, 65, and we're pretty sure that 65 is way too large.