Open-top box form problem
Description
HP-15C Owner's Handbook - Pages 189-190
Exercise:
Using a rectangular piece of sheet metal 4 decimeters by 8 decimeters, an open-top box having a volume of 7.5 cubic decimeters is to be formed. How should the metal be folded? (A taller box is preferred to a shorter one.)
Solution:
You need to find the height of the box (that is, the amount to be folded up along each of the four sides) that gives the specified volume. If x is the height (or amount folded up), the length of the box is (8 – 2x) and the width is (4 – 2x). The volume V is given by
V = (8 – 2x)(4 – 2x)x.
By expanding the expression and then using Horner's method (page 79), this equation can be rewritten as
V = 4 ((x – 6)x + 8)x.
To get V=7.5, find the values of x for which
f(x) = 4((x – 6)x + 8)x – 7.5 = 0.
Program Resources
Labels
Program
| Line |
Display |
Key Sequence |
|
| 000 |
|
|
|
| 001 |
42,21, 3 |
f LBL 3 |
|
| 002 |
6 |
6 |
|
| 003 |
30 |
− |
|
| 004 |
20 |
× |
|
| 005 |
8 |
8 |
|
| 006 |
40 |
+ |
|
| 007 |
20 |
× |
|
| 008 |
4 |
4 |
|
| 009 |
20 |
× |
|
| 010 |
7 |
7 |
|
| 011 |
48 |
. |
|
| 012 |
5 |
5 |
|
| 013 |
30 |
− |
|
| 014 |
43 32 |
g RTN |
|