\fdO'^ - Old Forge Coal Mines

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72 ARITHMETIC. in the root. Write in the root, as shown, and also add it to the trial divisor, 600, and annex a cipher, thereby making the next trial divisor 6,000. Bring down the next period, 99. The trial divisor 6,000 is contained in 000099, times, so we place as the next figure in the root, as shown, and also add it to the trial divisor 6,000, and annex a cipher, thereby making the next trial divisor 60,000. Bring down the next period, 40, and annex it to the dividend already obtained to form the new dividend, 00009940, and divide it by the trial divisor 60,000. 60,000 is contained in 00009940, times, so we place another cipher in the root, as shown, and also add it to the trial divisor 60,000, and annex one cipher, thereby making the next trial divisor 600,000. Bring down the next period, 09, and annex it to the dividend already obtained to form the new dividend, 0000994009, and divide it by the trial divisor 600,000. 600,000 is contained in 0000994009 once, we place 1 as the next figure in the root, and also add it so to the trial divisor 600,000, thereby making the complete divisor 600,001. Multiply the complete divisor, 600,001, by 1, the sixth figure in the root, and subtract the result obtained from the dividend. The remainder is 394,008, to which we annex the next period, 00, to form the next new dividend, or 39,400,800. Add the sixth figure of the root, or 1, to the divisor 600,001, and annex a cipher, thus obtaining 6,000,020 as the next trial divisor. Dividing 39,400,800 by 6,000,020, we find 6 to be the next figure of the root. Adding this last figure, 6, to the trial divisor, we obtain 6,000,026 for our next complete divisor, which, multiplied by the last figure of the root, or 6, gives 36,000,156, which write under 39,400,800 and subtract. Since there is a remainder, it is clearly evident that the given power îs not a perfect square, so we place -\- after the root. Since the next figure is 5, the answer is — . 3,000.017 In this problem there are seven periods—four in the whole number and three in the decimal— hence, there will be seven figures in the root, /our figures constituting the whole number, and three figures the decimal of the root. 4/9,000,099.4009 = 3,000.017 -. Hence,
(^) ^ ARITHMETIC. 73 |/.00'12'2 5 = .035. Ans. i_ 00 60 J 12 9 6 6 3 25 32 5 Pointing off periods, we find that the first period is com^ posed of ciphers; hence, the first figure of the root will be a cipher. No further explanation is necessary, since this problem is solved in a manner exactly similar to the problem solved in Art. 264. Since there are fAree decimal periods in the power, there will be three decimal figures in the root. (131) (a) 1 (^) 1 20 3 203 3 206 9 20 6 9 |/1'0 7'9 5.21 = 103.9 1 2 t/7'3 0'0 8.04 = 270.2 Ans 2 4
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( W v. 5 Copyright, 1897, by The Co
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Arithmetic, - CONTENTS Algebra, Log
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i ARITHMETIC. of tens. 1 + 8 + 7 +
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4 ARITHMETIC. and the difference (4
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ARITHMETIC. (c) 217 Multiply any tw
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8 ARITHMETIC. 72 in the dividend an
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10 ARITHMETIC. (70 X 50 X 24 X 20).
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12 ARITHMETIC, The 5 in the dividen
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14 ARITHMETIC. (22) (a) 576) 589824
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16 ARITHMETIC. (33) To reduce a fra
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18 ARITHMETIC. 3 3 (e) 15-r-7-43-=
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20 ARITHMETIC. (41) ,9| + 50i + 41+
Page 34 and 35: 22 ARITHMETIC. (45) The man evident
Page 36 and 37: 24 ARITHMETIC. • u s o e 3 2 o 93
Page 38 and 39: 26 ARITHMETIC. {b) Here again the p
Page 40 and 41: 28 ARITHMETIC. 64) 1.000000(. 01562
Page 42 and 43: 30 ARITHMETIC. (66) In subtraction
Page 44 and 45: 38 ARITHMETIC. (6) .875 — 5-=? Re
Page 46 and 47: 84 ARITHMETIC. {c) First perform th
Page 48 and 49: 36 ARITHMETIC. Reducing 387 387 to
Page 50 and 51: 38 ARITHMETIC. nominator of the fra
Page 52 and 53: 40 ARITHMETIC. (d) Base = percentag
Page 54 and 55: 42 ARITHMETIC. Another method of so
Page 56 and 57: 44 ARITHMETIC. (89) Here we have gi
Page 58 and 59: 46 ARITHMETIC. 24 ) 13750 gr. 20 )
Page 60 and 61: 48 ARITHMETIC. (98) Reduce the grai
Page 62 and 63: 50 ARITHMETIC. contained times in 3
Page 64 and 65: gal.
Page 66 and 67: 54 ARITHMETIC. (108) In multiplicat
Page 68 and 69: 56 ARITHMETIC. Since there are 24 g
Page 70 and 71: 58 ARITHMETIC. There are 100 lb. in
Page 72 and 73: 60 ARITHMETIC. 62 is contained in 1
Page 74 and 75: 63 ARITHMETIC. (121) (a) 106' = 106
Page 76 and 77: 64 ARITHMETIC. (^) .4044* = .4044 X
Page 78 and 79: 6G ARITHMETIC. Since there are 2 de
Page 80 and 81: 68 ARITHMETIC. (128) {a) .0133' =.0
Page 82 and 83: 70 ARITHMETIC (130^ (a) 1 1 20 _8 2
Page 86 and 87: 74 ARITHMETIC. (^) 9 -/QO.OO'OO'OO
Page 88 and 89: 76 ARITHMETIC. correction. This, mu
Page 90 and 91: 78 ARITHMETIC. found by division sh
Page 92 and 93: 80 ARITHMETIC. (137) {a) 1 1 f .0 6
Page 94 and 95: 82 ARITHMETIC. (138^ {a) In this ex
Page 96 and 97: 84 ARITHMETIC. (^)
Page 98 and 99: 86 ARITHMETIC. {b) f 6 = VTa 2 4/G.
Page 100 and 101: 88 8 8 ARITHMETIC.
Page 102 and 103: 90 ARITHMETIC. 40,000 144)40000.0(2
Page 104 and 105: 92 ARITHMETIC. (163) 2 ft. 5 in. =
Page 106 and 107: 94 ARITHMETIC. (164) Taking the tim
Page 108 and 109: 96 ALGEBRA. (171) See Arts. 352 and
Page 110 and 111: 98 ALGEBRA. In this case, where we
Page 112 and 113: 100 ALGEBRA. By Art. 482, the signs
Page 114 and 115: 102 ALGEBRA. (189) Applying the met
Page 116 and 117: 104 ALGEBRA. (196) {a) ^+_;/ + ^-(^
Page 118 and 119: 106 ALGEBRA- (201 ) The subtraction
Page 120 and 121: 108 ALGEBRA. Canceling the factors
Page 122 and 123: 110 ALGEBRA. (208) (a) Writing the
Page 124 and 125: 112 ALGEBRA. 20j^(4^+5)-12.r(3:r-7)
Page 127 and 128: ALGEBRA. (QUESTIONS 218-257.) (218)
Page 129 and 130: ALGEBRA. 117 Clearing of fractions,
Page 131 and 132: ALGEBRA. 119 Transposing, — A:X*
Page 133 and 134: Completing the square, ALGEBRA. 131
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Extracting ALGEBRA. 123
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(d) Completing the square, Extracti
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ALGEBRA. 127 (238) (a) i/| by Art.
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(242) ALGEBRA. 139 Let X = the whol
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(246) Then,-^ X ALGEBRA. 131 Let X
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ALGEBRA. 133 y+5-{x-o) = 6. (1) But
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ALGEBRA. 136 (266) Let X — the nu
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LOGARITHMS. (QUESTIONS 258-272.) (2
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lÔGARITHMS. 139 .6602 -3 — 1.980
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LOGARITHMS. 141 {l>) .76'"._ Log .7
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LOGARITHMS. 143 (271) Substituting
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140 GEOMETRY AND TRIGONOMETRY. in t
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148 GEOMETRY AND TRIGONOMETRY. 3 (2
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150 GEOMETRY AND TRIGONOMETRY. (302
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154 GEOMETRY AND TRIGONOMETRY. draw
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158 GEOMETRY AND TRIGONOMETRY. {d)
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1G4 GEOMETRY AND TRIGONOMETRY. (354
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166 ELEMENTARY MECHANICS. per min.
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168 ELEMENTARY MECHANICS. replaced,
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170 ELEMENTARY MECHANICS. (384) (a)
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172 ELEMENTARY MECHANICS. (389) See
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174 ELEMENTARY MECHANICS. (398) 1 h
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176 ELEMENTARY MECHANICS (412) Use
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180 ELEMENTARY MECHANICS. a distanc
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184 ELEMENTARY MECHANICS. (d) Using
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186 ELEMENTARY MECHANICS. (452) (a)
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188 HYDROMECHANICS. (457) (a) Area
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190 HYDROMECHANICS. Pressure due to
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192 HYDROMECHANICS. (47 1 ) (a) 36
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194 HYDROMECHANICS. 5' X 7854 (479)
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196 HYDROMECHANICS. (d) See Art. 10
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198 HYDROMECHANICS. Pressure per sq
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aOO HYDROMECHANICS. For z;„ = 4,/
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202 PNEUMATICS. (509) Substituting
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204 PNEUMATICS. (519) 8.47 = origin
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206 PNEUMATICS. (537) (a) 30 — 17
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208 PNE-aMATlCS. (548) CO' — 50'
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210 STRENGTH OF MATERIALS. P- p-^^.
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212 STRENGTH OF MATERIALS. Since 40
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214 STRENGTH OF MATERIALS. drawn. P
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21G STRENGTH OF MATERIALS. c \d of
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218 STRENGTH OF MATERIALS. n o. I//
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220 STRENGTH OF MATERIALS. Substitu
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222 STRENGTH OF MATERIALS. (589) Su
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224 STRENGTH OF MATERIALS. (597) {a
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226 STRENGTH OF MATERIALS. (d) In t
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228 STRENGTH OF MATERIALS. (604) Us
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230 STRENGTH OP MATERIALS. (609) Th
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232 STRENGTH OF MATERIALS. moments
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234 SURVEYING. adjacent sides of th
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236 SURVEYING. (622) 1st. A B in Fi
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238 SURVEYING. true bearing IS the
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240 SURVEYING. A B, as the bearing
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Un SURVEYING. an angle of 15° 10'
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244 SURVEYING. in dotted lines. In
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246 SURVEYING. table of Radii and D
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248 SURVEYING. ^^^ = 1.875'. The de
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. (690) 250 SURVEYING. sight to the
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252 SURVEYING. and including that a
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254 SURVEYING. horizontal lines 1 f
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(706) LAND SURVEYING (QUESTIONS 706
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LAND SURVEYING. 259 ture of A B is
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LAND SURVEYING. 261 -{-, in the col
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LAND SURVEYING. 263 is +8.86 chains
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a a *• o « .i Q a V Q + • hJ *
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LAND SURVEYING. 2G7
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RAILROAD LOCATION. (756) (QUESTIONS
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RAILROAD LOCATION. 271 second curve
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RAILROAD LOCATION. 273 in which;!'
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RAILROAD LOCATION. 275 Whence, we h
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RAILROAD LOCATION. 277 4.0827 ft.,
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point so determined by RAILROAD LOC
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282 RAILROAD CONSTRUCTION. (818) Th
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884 RAILROAD CONSTRUCTION. (833) Ap
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286 RAILROAD CONSTRUCTION. (859) Fi
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288 RAILROAD CONSTRUCTION. (864) (8
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RAILROAD CONSTRUCTION. (QUESTIONS 8
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RAILROAD CONSTRUCTION. 293 (896) Se
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RAILROAD CONSTRUCTION. 295 (a) The
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RAILROAD CONSTRUCTION. 207 (939) Se
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300 TRACK WORK. (962) (963) (964) (
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302 TRACK WORK. (994) See Art. 1687
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304 TRACK WORK. (1008) 8 ft. G in.
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306 RAILROAD STRUCTURES. (1039) See
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308 RAILROAD STRUCTURES. (1060) Fro
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3," ^ >;> :3 3>32> ^ >:> J> Oi?^ :>
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UNIVERSrTY OF ILLINOIS-URBANA 3 011
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