A rectangular beam is cut from a cylindrical log of radius 15 cm. A cross-section of the log is shown below. (b) Find S'(w) = h W The strength, S, of a beam of width w and height h is proportional to wh². (a) Express the strength of the beam as a function of w only. Use k as the proportionality constant and lower case w S(W) = Height = 15 (c) Find the exact width and height of the beam of maximum strength. Width =
A rectangular beam is cut from a cylindrical log of radius 15 cm. A cross-section of the log is shown below. (b) Find S'(w) = h W The strength, S, of a beam of width w and height h is proportional to wh². (a) Express the strength of the beam as a function of w only. Use k as the proportionality constant and lower case w S(W) = Height = 15 (c) Find the exact width and height of the beam of maximum strength. Width =
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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Transcribed Image Text:A rectangular beam is cut from a cylindrical log of radius 15 cm. A cross-section of the log is shown below.
=
(b) Find S'(w) =
h
The strength, S, of a beam of width w and height h is proportional to wh².
(a) Express the strength of the beam as a function of w only. Use k as the proportionality constant and lower case w.
S(w):
W
Height =
15
(c) Find the exact width and height of the beam of maximum strength.
Width =
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