A72 APPENDIX Review Constructing a Box From each corner of a square piece of sheet metal, remove a square with sides of length 9 centimeters.Turn up the edges to form an open box. If the box is to hold 144 cubic centimeters ( ) cm , 3 what should be the dimensions of the piece of sheet metal? Solution EXAMPLE 8 Use Figure 31 as a guide. We have labeled by x the length of a side of the square piece of sheet metal. The box will be of height 9 centimeters, and its square base will measure −x 18 on each side. The volume V ( ) × × Length Width Height of the box is therefore ( )( ) ( ) = − − ⋅ = − V x x x 18 18 9 9 18 2 Hours to Do Job Part of Job Done in 1 Hour Danny 4 1 4 Mike 6 1 6 Together t t 1 Table 2 Solution Set up Table 2. In 1 hour, Danny does 1 4 of the job, and in 1 hour, Mike does 1 6 of the job. Let t be the time (in hours) that it takes them to do the job together. In 1 hour, then, t 1 of the job is completed. Reason as follows: + = Part done by Danny in 1 hour Part done by Mike in 1 hour Part done together in 1 hour From Table 2, Now Work problem 35 + = + = = = = t t t t t 1 4 1 6 1 3 12 2 12 1 5 12 1 5 12 12 5 The model = LCD 12 on the left Simplify. Multiply both sides by t 12 . Divide both sides by 5. Working together, Mike and Danny can do the job in 12 5 hours, or 2 hours, 24 minutes. They should make the golf date, since they will finish at 12:24 pm. The next example is one that you will probably see again in a slightly different form if you study calculus. Figure 31 Volume = 9(x - 18)(x - 18) x cm x - 18 x - 18 x - 18 x - 18 x cm 9 cm 9 cm 9 cm 9 cm 9 cm 9 cm 9 cm 9 cm 9 cm
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