A rectangular package sent by a delivery service can have a maximum combined length and
Chapter 3, Problem 107(choose chapter or problem)
Geometry
A rectangular package sent by a delivery service can have a maximum combined length and girth (perimeter of a cross section) of 120 inches (see figure).
(a) Show that the volume of the package is given by the function \(V(x) = 4x^2(30 - x)\).
(b) Use a graphing utility to graph the function and approximate the dimensions of the package that yield a maximum volume.
(c) Find values of x such that V = 13,500. Which of these values is a physical impossibility in the construction of the package? Explain.
Text Transcription:
V(x)=4x^2(30-x)
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