Analyzing The Pole-Corner Problem - Texas Instruments TI-89 Manual Book

Analyzing the Pole-Corner Problem

Maximum Length of
Pole in Hallway
Tip: When you want to
define a function, use
multiple character names as
you build the definition.
Note: The maximum length
of the pole is the minimum
value of c(w) .
384 Chapter 23: Activities
A ten-foot-wide hallway meets a five-foot-wide hallway in the
corner of a building. Find the maximum length pole that can be
moved around the corner without tilting the pole.
The maximum length of a pole
the interior corner and opposite sides of the two hallways as shown
in the diagram below.
Hint: Use proportional sides and the Pythagorean theorem to find
the length with respect to
c
derivative of . The minimum value of
c(w)
of the pole.
w
1. Define the expression for side
in terms of and store it in
a w
a(w) .
2. the expression for side
Define
b in terms of w and store it in
.
b(w)
3. the expression for side
Define
in terms of and store it in
w
c(w)
Enter: Define c(w)=
‡(a(w)^2+b(w)^2)
4. Use the function to
zeros()
compute the zeros of the first
derivative of to find the
c(w)
minimum value of
c(w)
is the shortest line segment touching
c
. Then find the zeros of the first
w
c(w)
10
a = w+5
b = 10a
w
a
c
5
b
c
.
is the maximum length