\fdO'^ - Old Forge Coal Mines

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186 ALGEBRA. Substituting the value of y, found above, 18;r— 9^ = 18; whence, :r = 2. y=1x = ^. Hence, the number = \Q>x -|- j = 20 + 4 = 24. Ans. (257) Let X = greater number. y = less number. Thea, x-\-4: = diy, (1) and .r+8 = |. Cleanng of fractions, 4;r+ 16 = 13y, and 2y + 16 = x; whence, Idy — 4:X = 16. (2) (3) 2y- ;r = - 16. (4) Multiplying (4) by 4, and subtracting from (3) 5y = 80, or y = 16. Ans. Substituting in (4), 32 — ;r = — 16; whence, x = 48. Ans.
LOGARITHMS. (QUESTIONS 258-272.) (258) First raise^ to the . 29078 power. Since ??? = 2, •"•" ^ 2-"»", and log 2-"''" = .29078 x log (200\ ^\ 2 = .29078 X .30103 = .08753. Number corresponding = 1.2233. Then, ^j = 1 - 1.2233 = - .2233. We now find the product required by adding the logarithms of 351.36, 100, 24, and .2233, paying no attention to the negative sign of .2233 until the product is found. (Art. 647.) Log 351.36 = 2.54575 log 100 = 2 log 24=1.38021 log .2233=1.34889 j«w = 5.27485 = 1 - (/200\ Ij^j ••••^' \ ) Number corresponding = 188,300. The number is negative, since multiplying positive and negative signs gives negative; and the sign of .2233 is minus. Hence, ;tr= — 188,300. Ans. (269) («) Log 2,376 = 3.37585. Ans. (See Arts. 625 and 627.) (^) Log .6413=1.80706. Ans. (^) Log .0002507 = 4.39915. Ans.
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c c c tec C €
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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+
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22 ARITHMETIC. (45) The man evident
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24 ARITHMETIC. • u s o e 3 2 o 93
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26 ARITHMETIC. {b) Here again the p
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28 ARITHMETIC. 64) 1.000000(. 01562
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30 ARITHMETIC. (66) In subtraction
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38 ARITHMETIC. (6) .875 — 5-=? Re
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84 ARITHMETIC. {c) First perform th
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36 ARITHMETIC. Reducing 387 387 to
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38 ARITHMETIC. nominator of the fra
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40 ARITHMETIC. (d) Base = percentag
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42 ARITHMETIC. Another method of so
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44 ARITHMETIC. (89) Here we have gi
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46 ARITHMETIC. 24 ) 13750 gr. 20 )
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48 ARITHMETIC. (98) Reduce the grai
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50 ARITHMETIC. contained times in 3
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gal.
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54 ARITHMETIC. (108) In multiplicat
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56 ARITHMETIC. Since there are 24 g
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58 ARITHMETIC. There are 100 lb. in
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60 ARITHMETIC. 62 is contained in 1
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63 ARITHMETIC. (121) (a) 106' = 106
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64 ARITHMETIC. (^) .4044* = .4044 X
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6G ARITHMETIC. Since there are 2 de
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68 ARITHMETIC. (128) {a) .0133' =.0
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70 ARITHMETIC (130^ (a) 1 1 20 _8 2
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72 ARITHMETIC. in the root. Write i
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74 ARITHMETIC. (^) 9 -/QO.OO'OO'OO
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76 ARITHMETIC. correction. This, mu
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78 ARITHMETIC. found by division sh
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80 ARITHMETIC. (137) {a) 1 1 f .0 6
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82 ARITHMETIC. (138^ {a) In this ex
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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
Page 135 and 136: Extracting ALGEBRA. 123
Page 137 and 138: (d) Completing the square, Extracti
Page 139 and 140: ALGEBRA. 127 (238) (a) i/| by Art.
Page 141 and 142: (242) ALGEBRA. 139 Let X = the whol
Page 143 and 144: (246) Then,-^ X ALGEBRA. 131 Let X
Page 145 and 146: ALGEBRA. 133 y+5-{x-o) = 6. (1) But
Page 147: ALGEBRA. 136 (266) Let X — the nu
Page 151 and 152: l^OGARITHMS. 139 .6602 -3 — 1.980
Page 153 and 154: LOGARITHMS. 141 {l>) .76'"._ Log .7
Page 155: LOGARITHMS. 143 (271) Substituting
Page 158 and 159: 140 GEOMETRY AND TRIGONOMETRY. in t
Page 160 and 161: 148 GEOMETRY AND TRIGONOMETRY. 3 (2
Page 162 and 163: 150 GEOMETRY AND TRIGONOMETRY. (302
Page 166 and 167: 154 GEOMETRY AND TRIGONOMETRY. draw
Page 170 and 171: 158 GEOMETRY AND TRIGONOMETRY. {d)
Page 176 and 177: 1G4 GEOMETRY AND TRIGONOMETRY. (354
Page 178 and 179: 166 ELEMENTARY MECHANICS. per min.
Page 180 and 181: 168 ELEMENTARY MECHANICS. replaced,
Page 182 and 183: 170 ELEMENTARY MECHANICS. (384) (a)
Page 184 and 185: 172 ELEMENTARY MECHANICS. (389) See
Page 186 and 187: 174 ELEMENTARY MECHANICS. (398) 1 h
Page 188 and 189: 176 ELEMENTARY MECHANICS (412) Use
Page 192 and 193: 180 ELEMENTARY MECHANICS. a distanc
Page 196 and 197: 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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