A bang-bang theorem with a finite number of switchings for by Vakhrameev S.A.

By Vakhrameev S.A.

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1, too, if you want) when figuring out the answers. Take your time! The correct answers are in the back of the book. 1. Make the following subtractions by hand, and check your results by addition. (a) 69 Ϫ 46 (b) 123 Ϫ 81 (c) 543 Ϫ 37 (d) 762 Ϫ 371 (e) 509 Ϫ 410 (f) 263 Ϫ 74 (g) 4,321 Ϫ 1,234 (h) 6,532 Ϫ 2,356 (i) 11,507 Ϫ 8,618 26 Mastering Technical Mathematics 2. 95. A local discount store offers a $160 discount on this item. How much would you pay at this store? Check your result by addition.

This device is now considered an antique, but knowing how it worked can help you understand addition in a practical sense. The simplest grocer’s balance, like the thing you’ve seen the blindfolded “Lady of Justice” holding, had two pans supported from a beam pivoted across a point or fulcrum. The pans were equally far away from the fulcrum on opposite sides. When the weights in both pans were equal, the scales balanced and the pans were level with each other. When the weights were unequal, the pan with the heavier weight dropped and the other one rose.

How much does the cat weigh? 5. A recipe calls for 1 pound 12 ounces of rice. You have a grocer’s balance to measure it with. All the pound weights are there, but the only ounce weights that have not been lost are the 1-ounce and 4-ounce ones. How can you use this balance to be sure you have 1 pound 12 ounces of rice? Prove it by showing that the scale balances. 6. You are studying a map on which town B is between towns A and C on highway X. The map shows only selected distances. Between A and B, the map shows 147 miles along highway X.

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