Problema Solution
A model of carry-on luggage has a length that is 6 inches greater than depth. Airline regulations require that the sum of the length, width, and depth cannot exceed 32 inches. These conditions, with the assumption that this sum is 32 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 432 cubic inches, determine two possibilities for its depth.
Volume=(depth)(length)(width): 32-(depth +length)
V(x)= x (x+6) [32-(x+x+6]
V(x)=x(x+6)(26-2x)
Answer provided by our tutors
let depth = x
length = 6 + x
let width = y
=> x + x + 6+ y <= 32
Volume = 432
=> V(X) = X(X+6)(26-2x) = 2x(x+6)(13-x) =>
2x(x+6)(13-x) = 432 => x(x+6)(13-x) = 216 => (x^2+6x)(13-x) = 216
=> 13x^2 - x^3 +78x -6x^2 = 216 => x^3 - 7x^2 -78x + 216 = 0
On solving these equaiton we get
x=12.0000
-7.4244
2.4244
But negative value is not possible..
so x = 12.0000
2.4244