Problema Solution
A model of carry-on luggage has a length that is 11 inches greater than its depth. Airline regulations require that the sum of the length, width, and depth cannot exceed 23 inches. These conditions, with the assumption that this sum is 23 inches, can be modeled by the function V(x) that gives the luggage's volume, in cubic inches, in terms of its depth, x, in inches. If its volume is 240 cubic inches, determine two possibilities for its depth.
Answer provided by our tutors
depth = x
length = x + 11
width = 23 - (x + x + 11)
V(x) = depth * length * width
V(x) = x * (x+6) * [23-(x+x+11)]
V(x) = x(x+6)(12-2x)
the volume is 240 cubic inches meaning:
x(x+6)(12-2x) = 240 divide both sides by 2
x(x+6)(6-x) = 120
-x^3 + 36x - 120 = 0
by solving we find one real solution and 2 complex:
x1 = -7.25
Since the depth is always positive we conclude that there are no solution, that is, there is no such luggage.