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7-12 Solving Equations
The dimensions of the desired box are 50 × 10 × 15 cm. If you ignored the upper
limit on the height (20 cm) and used initial estimates of 30 and 40 cm, you would
obtain a height of 42.0256 cm — a root that is physically meaningless. If you used
small initial estimates such as 0 and 10 cm, you would obtain a height of 2.9774
cm — producing an undesirably short, flat box.
If you don't know what guesses to use, you can use a graph to help understand the
behavior of the equation. Evaluate your equation for several values of the unknown.
For each point on the graph, display the equation and press
— at the
prompt for x enter the x–coordinate, and then obtain the corresponding value of the
equation, the y–coordinate. For the problem above, you would always set V = 7500
and vary the value of H to produce different values for the equation. Remember that
the value for this equation is the difference between the left and right sides of the
equation. The plot of the value of this equation looks like this.
For More Information
This chapter gives you instructions for solving for unknowns or roots over a wide
range of applications. Appendix D contains more detailed information about how
the algorithm for SOLVE works, how to interpret results, what happens when no
solution is found, and conditions that can cause incorrect results.
7500
_
(40
_
) (20
_
) 4HHH
20,000
_
10,000
50
H
_
10