As you know, the sides of a square are equal. Therefore, in Practice Problem 1 you can determine the length of any side by finding the square root of the area. In Practice Problem 3 the area of a circle is expressed by the formula A=TX2. Since A and are known, this becomes 3.89 =3.14\r2. Now if we divide both sides of this equation by 3.14, 3.89 this becomes =r2. Next, using the C and D scales, divide 3.89 3.14 by 3.14 to get 1.239. Set 1.239 on the left side of the A scale and find its square root on the D scale. The answer will be 1.113 inches. Since 1.239 is a little difficult to set on the A scale, your answer may be 1.114 inches. This general method can also be used in Practice Problem 5. The answer to this problem is 3.76 feet. Your answer to Practice Problem 13 should be 760 instead of 761 as shown at the back of your text. Page 118. As mentioned earlier, finding the square or square root of a number is usually only one part of a problem. Consequently, you are cautioned against using the A and B scales for the other parts of the problem. While it may seem quicker, using the A and B scales for multiplication and division will not give you as precise answers. This temptation might occur in a problem such as 6X42=? The 4 should be squared by locating it on the D scale and reading its square, 16, on the right half of the A scale. The number 16 should be set on the D scale and then multiplied by 6. As mentioned earlier, it may be simpler to multiply by the number twice, using the C and D scales, when the square is one part of a long series of operations. In this way you can avoid reading the answer on the A scale and resetting it on the D scale. Page 121. The answer to Practice Problem 6 is 27,800,000 instead of 28,800,000 as given at the back of your text. In Practice Problems 21-25 you will need to write down your results for each step. For example, in Practice Problem 21 first use the slide rule to square 24.5 and 33.1. This will give you 600 and 1,095, respectively. Using paper and pencil, add 600 and 1,095 to get 1,695. Now use the slide rule again to find the square root of 1,695. Your answer is 41.2. Pages 121-123. Answers to these Review Problems are given at the back of this study guide. In several places in these problems you will find the hypotenuse of a right triangle mentioned. A right triangle is a triangle containing one right angle, i.e., a triangle containing a 90° angle. The hypotenuse is the longest side of such a triangle and is found opposite the 90° angle. The other two sides are called the legs of a right triangle. Review Problem 1, which is solved below, involves these terms. In the above problem, the squares of 6 and 9 are found by means of the slide rule. These squares are added using pencil and paper. The square root of their sum is then found by means of the slide rule. When you see an expression such as 117√231, it means the square root of the number under the radical sign is to be multiplied by the number in front of the radical sign. In other words, 117X√231. Self-Examination Select the correct answer in each of the following exercises. 9. How many small boxes 2 inches square and 1%1⁄2 inches deep can be packed in a cardboard box 28 inches square and 6 inches deep? 8. 44 b. 75 c. 676 d. 784 e. None of the above 10. A large trunk is 49 inches long, 36 inches high, and 36 inches wide. How many square inches of exterior surface does this trunk have? a. 2,592 b. 7,056 c. 8,712 d. 9,648 e. None of the above 11. How long would the sides of a square be if the square is painted with 1.47 quarts of paint known to cover 187 square feet per quart? a. 11.3 ft. b. 13.7 ft. d. 275 ft. e. None of the above c. 16.6 ft. 12. The area of a circle is equal to 3.14 times the square of the radius. A circle of what radius would have an area of 10 square inches? a. 1.77 in. b. 1.787 in. d. 17.87 in. e. None of the above c. 5.60 in. Instructions for submitting written work to USAFI are given in the Introduction of this study guide. 1. Using Illustrative Example 1 on page 110 in your text as a guide, explain how you would find the square of 31.80. This explanation must include the method of locating the decimal point. 2. Using Illustrative Example 8 on page 116 in your text as a guide, explain how you would find the square root of 177. This explanation must include the method of locating the decimal point. 3. Square each of the following numbers: 4. Find the square root of each of the following numbers: 5. Calculate the results of the following expressions, writing the original expression, all steps, and the final answer on your lesson sheet. 6. Calculate the results of the following expressions, writing the original expression, all steps, and the final answer on your lesson sheet. a. 0.07462X349 b. 237 0.0446 c. √4.61X√4.61 d. √4.61X6X4212 e. 13.17X0.1112 7. The heat developed in an electric element can be calculated from 0.24XE2Xt the formula H= where H is the heat developed in Ꭱ calories, E is the potential difference in seconds, and R the resistance in ohms. heat would be developed in 1 second in elements? a. A 14.7 ohm element across 110 volts b. A 2.64 ohm element across 32 volts c. An 8.4 ohm element across 220 volts d. A 16.8 ohm element across 440 volts e. A 33.6 ohm element across 440 volts volts, t is the time in How many calories of each of the following 8. The kinetic energy of a moving body is expressed by the formula K.E.= = WX v2 where K.E. is the kinetic energy in foot-pounds, W the weight of the body in pounds, and v is the velocity in feet per second. Calculate the kinetic energy of the following objects: a. A 2,995 pound automobile moving 104 feet per second b. A 3 ounce bullet moving 3,700 feet per second c. A 17.4 ton truck moving 50 miles per hour d. A 185 pound man running 9.7 yards per second e. A 0.10 pound bullet moving 2,000 feet per second |