Problema Solution
A model of carry on luggage has a length that is 6 inches greater than its depth airline regulations require that the sum of the live with in depth cannot exceed 28 inches these conditions with the assumption that this sum is 28 inches can be modeled by the function V(v) that gives the luggage volume in cubic inches in terms of its depthX in inches if it's volume is 540 cubic inches determines two possibilities for its depth
Answer provided by our tutors
Let
depth = x
length = x + 6
width = 28 - (x + x + 6)
V(x) = depth * length * width
V(x) = x * (x+6) * [28-(x+x+6)]
V(x) = x(x+6)(22-2x)
The volume is 540 cubic inches meaning
x(x+6)(22-2x) = 540 divide both sides by 2
x(x+6)(11-x) = 270
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click here to see the equation solved for x
........
x1 = 9 in
x2 = √34 - 2
x2 = 3.83 in
The two possibilities for the depth are 9 in and 4.83 in.