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2 76

(3) Square 2 and place it under 521 5 92

the 6. Subtract. 1

(4) Bring down 81, the next 521 5 21

two digits.
5221
71 13

(5) Bring down the 2 above the

6 and double it for the trial 1 5221 52 21

divisor. Divide the 4 into 28, 1892

the remainder less the last digit

to the right; 7 is obtained. 26. 11

(6) Annex the 7 to the trial 26. 11

divisor and multiply by 7; 329 is 26 11

obtained. This is too large. 261 1 15666

Next annex 6 and try it. This is 5222

satisfactory. Subtract the 276 681. 7321

from the 281. Place the 6 above 1892

the 81 group. Bring down the 681. 9213

next group, 92.

(7) Obtain a new trial divisor by doubling the 26. Divide the 52 into the 59; 1 is obtained. Annex the 1 and multiply. Place the 1 above the 92. Subtract and bring down the next group, 13.

(8) Obtain a new trial divisor by doubling 261. Divide the 522 in the 711; 1 is obtained. Annex the 1 and multiply. Place the 1 above 13. Subtract. 1892 is obtained as the remainder.

(9) Multiply 26.11. 26.11 and

add 1892; 681.9213 is obtained. i. Exercises.—Find the square root of the following: (1) V625 (2) V289

17 Answer. (3) 125.44 (4) V167281

409 Answer. (5) 18.93 (6) V.4387

.66234 Answer. (7) 1983.431 (8) V10.6934

3.27008 Answer.

19. Miscellaneous exercises.—The following exercises are based on the topics in this section:

(1) If 1 cubic foot of water weighs 62.5 pounds, what is the weight of 4.18 cubic feet of water?

(2) How many cubic feet are there in 180 pounds of water? (See a above.)

2.88 cu. ft. Answer. (3) Change the following common fractions to decimal fractions:

3. 7. 51. 17
g' 16' 75' 32

(4) Change the following decimal fractions to mixed numbers: 1.25; 3.875; 14.375.

1/4; 37; 1436 Answer. (5) Bolts 3 inch in diameter and 6 inches long weigh 117 pounds per hundred bolts. What is the weight of 1,200 bolts?

(6) A certain bomber can carry a bomb load of 4,500 pounds. How many 250-pound bombs can be carried?

18 Answer. (7) Which is larger 135° or 2328°? (8) Divide 6% by 25%.

24 Answer. (9) At an altitude of 5,000 feet and at 10° C., the calibrated air speed is 190 mph. The true air speed is 206 mph. What is the percent of increase in the two readings?

(10) At an altitude of 11,000 feet and at 20° C., the calibrated air speed is 210 mph. The true air speed is 242 mph. What is the percent of increase in the two readings?

15.2 percent. Answer. (11) The top air speed of an aircraft at 10,000 feet is 325 mph. At 15,000 feet it is 335 mph. What is the percent of increase in the air speed?

(12) If 469 cadets are sent to primary schools in Georgia and this group represents 14 percent of the class, find the number of cadets in the class.

3,350 cadets. Answer. (13) If 28 cadets out of a squadron of 196 are on guard duty, what percent of the squadron is on guard duty?

(14) On a certain flight a bomber used 40.5 gallons of gasoline per hour. The time of the flight was 3 hours 48 minutes. Find the amount of gasoline used.

153.9 gal. Answer. (15) An aircraft flies a distance of 160 nautical miles. Find the distance in statute miles.

(16) The temperature reading on a centigrade thermometer was 3° C. The reading increased 2° the first hour and decreased 7° the second hour. What was the final temperature reading?

-2° C Answer. (17) On a certain day, 10 temperature readings were taken on a centigrade thermometer. They were 6o, -3°, -7°, -15°, -4°, 0°, 2°, 3°, 5°, 3°. Find the average temperature reading.

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per hour.

Hint: Find the sum and divide by the number of readings.
(18) Find the product in each of the following:
(-6).(-1/4). (1%)

12 Answer. (-2)2. (873). (-4)

-25 Answer. (19) The following numbers represent the diameters of the bores on different guns: 37 mm, 3 inches, 1 inch, 155 mm, 6 inches, 75 mm. Arrange them according to size beginning with the largest one. (20) Express a speed of 118 kilometers per hour in terms of miles

737 mph. Answer. (21) Calculate the number of square centimeters in 1 square foot.

(22) A photographic film is designed for a picture 6 by 9 centimeters; express this in inches to the nearest quarter inch.

274 by 3% in. Answer. (23) If 570 cadets are sent to primary schools in Florida, and this group represents 30 percent of the class, find the number of cadets in the class.

(24) If 24 cadets out of a squadron of 180 passed the high altitude test, what percent of the squadron passed the test?

13.3 percent. Answer. (25) At a certain airdrome there are 88 aircraft, consisting of bombers and interceptor aircraft. The ratio of bombers to interceptors is 3 to 8. Find the number of each kind of aircraft.

(26) What is the diameter in inches of the bore of a 75-mm. gun? (This means the bore is 75 mm, in diameter.) 2.95 in. Answer.

(27) The following numbers represent the ranges of different aircraft: 250 nautical miles; 262 statute miles; 480 kilometers; 298 statute miles; 275 nautical miles. Arrange these distances in order of magnitude starting with the largest one.

(28) A detail of 33 cadets represents 15 percent of the squadron. How many cadets are there in the squadron?

220 Answer. (29) Find the difference in temperature readings of +47° C. and -5° C.

(30) On a certain day the lowest temperature reading was -14° F. and the highest temperature reading was +19° F. Find the increase in readings.

33° Answer. (31) Find the values of the following:

(-3)
(-2) (-1)
3(-2) (-1)
2(12)2 (4)3

8(-1)2 (12) (32) A panel is made up of 5 plies which are 14 inch, 36 inch, inch, % inch, and 316 inch thick, respectively. How thick is the panel?

1724 in. Answer.

(33) Divide 1.5625 by 0.125. (34) Multiply 244 %6 245 136.

1% Answer. (35) Find the sum of 172+27-44+58.

(36) How many strips each 3:2 inch thick are in a laminated piece 17 inches thick?

20 Answer (37) In a squadron of 200 cadets there are 14 cadets sick. What percent of the squadron is sick?

(38) The chord of an airplane wing is 72 inches. If the center of pressure is at a point 28 percent of the distance along the chord from the leading edge, how many inches is it from the leading edge?

20.16 inches. Answer. L

L ratio for an airfoil section is Find the ratio when D

D Le=0.0018 and D.=0.00008.

(40) Find the ratio of the areas of two circles having radii of 3 inches and 4 inches. (The areas are to each other as the squares of their radii.)

% Answer. SECTION III

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20

ALGEBRA

Paragraph Purpose and scope--Algebraic symbols..

21 Addition and subtraction of polynomials

22 Multiplication and division of polynomials.

23 Evaluation of algebraic expressions -

24 Equations

25 Word problems

26 Miscellaneous exercises..

27 20. Purpose and scope.- Algebra is the basis for all work in formulas and trigonometry. In the solution of many problems of these types the first thing that is done is to write facts in the form of an equation. To be able to handle such work, equations must be understood and the necessary background of algebraic manipulation must be thoroughly mastered. The following paragraphs contain exercises with accompanying explanations designed to give the student a working knowledge of necessary fundamentals of algebra.

21. Algebraic symbols.a. In working with general formulas, it is convenient to let numbers be represented by letters. In the actual evaluation of the formulas, the specific values are substituted for the letters.

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The above formula is solved for d. If it became necessary to solve for some other letter in the formula, other operations would be required. To perform such operations, it is essential to learn some of the fundamental characteristics of algebra.

b. In algebra, because of the use of x as a letter, new signs are adopted to indicate multiplication.

(1) 4x means 4 times X. When no sign appears between letters and numbers, multiplication is indicated.

(2) 4 means 4 times x. When some sign of multiplication is necessary, a dot is used as indicated.

(3) In any product such as the foregoing, the coefficient of the x term is defined to be the rest of that term.

(4) When there is a product of the type X-X•X•x, it is written 24. The 4 is called the exponent of 2, and 3* is called a power of x. This is simply a shorthand method of writing a product. The x is termed the base. Example: What are the coefficients and exponents of 4.22?

4x? x? Solution:

4 is the coefficient and 2 is the exponent.
1 is the understood coefficient and 2 is the exponent.
4 is the coefficient and 1 the understood exponent.

1 is understood as the coefficient and exponent. c. Rules for use of exponents.

(1) When two powers with the same base are multiplied together, the exponents are added, as shown in the following illustrations:

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32.33=35=243

(9.27=243) 22.04=26

(2) When two powers with the same base are divided, the exponents are subtracted, as the following examples show:

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(3) When two products are multiplied together, the coefficients are multiplied and each power is multiplied separately, as in the following example:

(a) 2.-3x2=6x8.

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