HP 33s 7–8, 40 40_2H, 7–8 Solving Equations, Example: Using Guesses to Find a Root

„If an equation does not allow certain values for the unknown, guesses can prevent these values from occurring. For example,

y = t + log x

results in an error if x ≤ 0 (message !).

In the following example, the equation has more than one root, but guesses help find the desired root.

Example: Using Guesses to Find a Root.

Using a rectangular piece of sheet metal 40 cm by 80 cm, form an open–top box having a volume of 7500 cm3. 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. A taller box is preferred to a shorter one.

H

40 40_2H

H

H 80_2H H

80

If H is the height, then the length of the box is (80 – 2H) and the width is (40 – 2H). The volume V is:

V = ( 80 – 2H ) ⋅ (40 – 2H ) ⋅ H

which you can simplify and enter as

V= ( 40 – H ) ⋅ ( 20 – H ) ⋅ 4 ⋅ H

7–8Solving Equations