The dimensions in inches of a shipping box at You Bring It, We Ship It can be expressed as width x, length x + 5, and height 3x - 1. The volume is about 7.6 ft3. Find the dimensions of the box in inches. Round to the nearest inch.

Question

rogue · Answer

$$V = lwh = x(x+5)(3x-1) = 3x^3 + 14x^2 -5x$$7.6 ft^3  ---> 13100 in^3$$V = 13100 = 3x^3 + 14x^2 - 5x$$

rogue · Answer

You can bang this out with the rational zeroes theorem, Decartes rule of signs, etc. Or you can just graph y = 3x^3 + 14x^2 - 5x - 13100, which would be the easiest way.
When you graph it, you get the root to be$$x \approx 14.9589 inches$$Solve for the other 2 sides.$$x + 5 \approx 19.9589inches$$$$3x - 1 \approx 43.8767 inches$$

anonymous · Answer

Thank you!!!

anonymous · Answer

15, 20, 44