Answer
(a) $S=13.8x(100-x^2)$
(b) $x\in[0,10]$
(c) see graph
(d) $x=5.8in$
Work Step by Step
The strength S of a wooden beam of width x and depth y is given by the formula $S=13.8xy^2$
(a) Express the strength S of this beam as a function of x only.
Refer to the figure in the book, $y^2=10^2-x^2$ (Pythagorean Theorem).
$S=13.8xy^2=13.8x(100-x^2)$
(b) What is the domain of the function S?
$x\in[0,10]$
(c) Draw a graph of S.
see graph
(d) What width will make the beam the strongest?
Maximum of S happens at $x=5.8in$
