Q A 
 300 
 
 IN 
 
Answers to Exercises 
 
 IN 
 
 AN INTRODUCTION TO 
 
 MATHEMATICAL 
 ANALYSIS 
 
 BY 
 FRANK LOXLEY GRIFFIN 
 
 PROFESSOR OP MATHEMATICS, REED COLLEGE, PORTLAND, OREGON 
 
 HOUGHTON MIFFLIN COMPANY 
 
 Boston New York Chicago San Francisco 
 
COPYRIGHT, 1922, BY FRANK LOXLEY GRIFFIN 
 ALL RIGHTS RESERVED 
 
 CAMBRIDGE • MASSACHUSETTS 
 PRINTED IN THE U. S. A. 
 
QA300 
 
 ANSWERS TO EXERCISES 
 N.B. Very slight inaccuracies in graphical results are to be ignored. 
 
 Pages 8-10 
 
 I. 37.2 gm., 15.3 gm., -6.5°. 2. 13.6 in., 10,900 ft., 6.8 in. 
 
 3. 81,800, 64.7 yr., 9600. 5. 12.7 kg., 3.17 lb. 
 6. $24. 7. 12.3 mi. 
 
 Pages 12-13 
 I. $3990, 23.8 yr. 2. 13.5 yr., 49.7 yr. 3. $680 per yr. 
 
 4. -2.4 min., April 20, etc. 5. 1.8 larger. 6. 23 d., 81 d. 
 
 Pages 16-18 
 
 I. < = 1.39, 300 per hr., 820 per hr. " 2. 46.3°, 5.7 deg./min. 
 
 3. 825 mg., T = 1800, . . . , 4- 5200 ft., 1040 ft./min., 610 
 
 .26 mg./yr. (deer.). ft./min. 
 
 5. 21.5mi./hr., . . .,2.4mi./hr. per 6. .86 sq. cm./day. 
 
 ton/hr. 
 
 Pages 20-21 
 
 2. 11°. 3- 75615. 4. 25.87 in. 5. 11.72 yr. 
 
 7. 101.43,839.2. 8. 13.5296, 28.8. 10. .7052. 
 
 II. 1.03, .00075 H.P./R.P.M., y = 1950 gives p = 1.17. 
 
 Pages 22-24 
 
 4. 76.56,9.3541;... 5- ...,49046. 7.10:30. 
 
 8. $6550, 132 ft. ; $12.80 per ft. 9- . . . , 33 ft./min. gained per min. 
 
 10. 39600 ft. 
 
 , Pages 27-29 
 
 I. 343000 ft., 36 ft. /min. lost per min. 2. 193 ft. /min., 10.1ft. 
 
 3. 78400 ft. 4. 502.5 ft. 
 
 5. 3500 million mi., 14.5 million mi./yr. lost per yr. 
 7. 171 ton-sec, 23 tons/sec. 8. 16 in.-lb. 
 
 9. 38900 ft.-lb. 10. 12900 ft.-lb. 
 
 11. 14500 amp. /sec, .34 coulombs. 12. 2570 kw.-hrs. 
 
 m55;5509 
 
ii MATHEMATICAL ANALYSIS 
 
 Pages 30-31 
 
 I. 2730 sq. yd. 2. 20700 sq. ft. 3. 223000 cu. ft. 
 4. 1,640,000 cu. ft.; deer. 2370 sq.ft. /ft. 5. 320 cc. 
 
 6. 416,000 cu. ft. 
 
 Pages 33-35 
 
 2. 6.25 in. 3. 3.33 in., 592.6 cu. in. 4. 7.75 yd., 15.49 yd. 
 
 5. 3:12 P.M., 48 mi. 6. 8.66 in. 7. 11.55 in., 16.33in. 
 
 8. 8.32 in. X 12.49 in. 9. 14 X 14 X 28 cu. in. 10. 20 yd., 30 yd., 
 
 $240. 
 
 II. 6.21 ft. X 3.11 ft. 12. 4.54 yd. X 3.63 yd. 13. 3.92 in., 1056 
 
 cu. in. 
 Pages 39-40 
 
 9='= V57 10 5=^V"^. 1 1 J — 
 
 '• 4 V 3' ' 12 ' "5' "5' -2=^3 V-1; 
 
 -3±6V3 _ ^ ,, / ;= 1 
 
 ■; =*=2, =tl; =ty2V-5±Vii3; ^(-7=*= V49-12c); 
 
 l(-b±V62_j-i4o). 
 
 2. 3.24 in.; 9.26 in. 3. .658 in. 4. 10=fcV20. 
 
 5. -2.21, .54, 1.68; -2.19,3.19; -2.67; -3.97, -.49, .52,2.95. 
 7. 2.38. 8. 2.82, 12.5, 22.18. 11. 6, only. 
 
 Pages 41-42 
 
 1. -1.68, 1.61, 4.07; -2.95, .78, 2.17; -1.85, -.70, .58, 3.97; 
 3.18 only; -4.03, 5.02 only; -2.04 only; 
 
 a;2 = -3.56, .56; T' - -3.97, .90, 3.07. 
 
 2. 10.17 ft. 3. 4.11 in. 4. No imaginaries. 
 
 Pages 44-45 
 4. 96.32 ft. /sec. 5. 196 ft., V2(7± V29). 6. 47.84 ft. /sec. 
 
 7. .244 ft. per ft. 9. 15800 cu. ft. 10. 25.3, . . . , 35.8. 
 
 Pages 49-50 
 4. Four break, one twice. 5. -25,37.5. 7. 11.86,9.65. 
 
 ^. E = .08 W) 2.8. ID. V = 4500/p. 11. R = .072 V\ 
 
 12. A = 512,000,000/i22. 
 
 Page 53 
 1. TF = 54+.5 T, 3. F = 182 + % T. 
 
 5. L = 605 -.69 T. ' 6. M = 4.19&-132. 
 
ANSWERS TO EXERCISES iii 
 
 Pages 55-57 
 3. deer. .84 sq. cm. /day. 4. $365, $52peryr. 
 
 6. 1835 yd., .062 mils/yd. 7. 29200 sq. ft. 
 
 8. 19400°. 9. 1380 deg./min. gained per min. 
 
 10. 4.70, -20 per sec, 2.54 in. 12. -5.34; -2.91, -.68, .64, 3.95. 
 15. 44f^. 16. 16.2 cal, 3.33 ft. from A. 17. 8.91 in., 28 in. 
 
 Pages 62-63 
 _3. 140 ft./sec. 4. 40 ft./sec. 5. 320 ft./sec. 
 
 6. 10 sq. in. /in. 7. 12 x sq. in./in. 8. —500/441 units. 
 
 9. 180 units. 10. —500 units. 
 
 Page 65 
 
 2. 18.85 in., 28.27 sq. in. 3. 1100 mi., 2100 mi. 
 
 Pages 68-69 
 I. .75, etc. 2. 16%, etc. 4. .24. 5. 2. 
 
 6. 4. 8. .3. 9. -¥9; av. slope = -1/(9+3 Ax). 
 
 Pages 73-74 
 5. 100, etc. 7. . . . , -18.75; . . . , 32+27 Aa:+9 Aa:2+Ax'. 
 
 8. 12, . . . 9. 2. 10. -2.5 dynes/cm. 
 
 11. 2 ft./sec. gained per sec. 
 
 Page 77 
 
 I. 360 - 32 < ft./sec, .. .,2025 ft. 2. 3x2-6,±V2. 
 
 3. ^600/p2 cu. in. per Ib./sq. in. 6. 4 Trr^ cu. ft. per ft. 
 
 Page SI 
 
 1. 2 X, 3 a:2, 4 a^J, . . . , 2 x-9, -7/x2, 70-10 t, etc 
 
 2. . . . , 245 ft. 3. -10.25, X = 4.5. 
 5. 4 —.4 i ft./sec gained per sec. 6. —.6. 
 
 7. 180 units per in. 8. — 40/x^ dynes per cm. 
 
 Page 84 
 
 3. 48 ft. per ft./sec. 5. 1200 cu. in. /in. 6. 3.68 ft. per mi./hr. 
 
 Pages 86-87 
 I. . . . , 14 x^+Vs x\ 2. . . . , 10 ax5+8 3^/h, etc 
 
 3. 360x-60x2, 5a^+8x3+15x2-2x-2, 36x3-60x. 
 
 4. 2.4 ft./sec. per sec 5. .028. 
 
iv MATHEMATICAL ANALYSIS 
 
 6. 15000 cu. ft. per ft. 7. 3000 units/min. ; incr., deer. 
 8. 18; incr. ' 12. -.6819, -1.0899; etc. 
 
 13. 2a:+5-3M 14. 2x-22/x3. 
 
 16. A lb., approx. 
 
 Page 89 
 
 3. 78.54%. 3. 52.36%. 
 
 Pages 90-92 
 I. 7; 7.0035. 2. .215. 3. .00093. 4. .6 cu. in., .24 sq. in. 
 5. .0015 in., .0025 in. 6. .85 sq. in., .126 ft., 
 
 7. .00199 ft., 8. 7.54 sq. in., . . . , 3.77 sq. in. 9. .0125 cm., . . . 
 
 10. .6%, .0125%. II. 35.2 ft. 12. .0123 ton, ... . 
 
 13. .0138. 14. 7.2^ per hr., .... 
 
 Pages 95-96 
 
 1. X = 3, y = —4; x = —l,y= —1; max. y = 17, min. y = —15; 
 none; max. y = 10, min. y = —6 (twice); min. y = —332. 
 
 2. .04. 3. 538.2+. 4. 16000/2^ cu. in. 
 5. t = 80/3^ 6. X = V2. 
 
 Pages 97-98 
 
 I. 400 sq. in. 3. 7.5, 7.5. 4. -V2. 
 
 5. 78V8sq. in. 6. 20 V3/3, 20 V6/3. 7. 14 X l^X 28 cu. in. 
 
 8. 48 mi. 9. 44^, approx. 10. x=4 Vl5, L=8 Vl5. 
 
 12. radius = vertical side = 4.20 ft., approx. 
 
 Page 100 
 
 4. .3, 10/9, ., ., 6, 14-, -, ^9, %. 5. 1.6,145.5. 
 >/. X = 5. S. y = 40/x\ 10. -2M 
 
 Pages 102-103 
 
 I. (a) -4M -,-,-, 180/0:41^ etc. 2. -.411. 
 
 3. -.016. 4. -3. 5. -1.28. 
 
 6. -2.5. 7. $240. 8.- 7.83* ft., 6.52* ft. 
 
 9. 9.28* ft., 4.64* ft. 10. r = 5in.,;i = 5in. 12. r = 3.97* in., 
 
 _ _ h = 15.87* in. 
 
 13. V20. 14. 40 in, 15. 66+6V40sq.in. 16. 65.98* sq. in. 
 
 17. r = /i= V231/7r in. 18. 270 sq. in. 19. 600 sq. in. 
 
 Page 106 
 I. . . . , 550/X12, . . . , _6 /. 3. 12096 x3-5040M 
 
 * Approximately. 
 
ANSWERS TO EXERCISES v 
 
 4. 80-32^, 48ft./sec., -32ft./sec.2. 6. 12,12. 7. .008, .004. 
 10. 20 ft./sec, 8 ft./sec.2. 12. 0, 1600 ft./min. 
 
 Page 109 
 2. t = 12. 4. 18, 6. 5. 20; 8,800,000 units/min. 
 
 7. ...,-15. 
 
 Pafiie 112 
 I. 6x(m2-2), etc. 3. 36x2^3^ etc. 4. 24cu. in./hr. 
 
 5. (a) 400 x3(x4+25)99;(d) -4 7r(l -a:)2,(e) -420 ty{t^-l)Mg) 3/4 (8-0-. 
 
 6. incr. 1.058*. 7. 16.2. 
 
 Pa^es 115-116 
 
 1. -,-,{-mSMdx/dt, ..., (l+168/L3)dLM. 
 
 2. 32 TT cu. ft./min. 4. .5 in./min. 5. .7957* in./hr. 
 
 6. .00159* ft./min. 8. .000707* in./hr. 9. .00955* in., 2.4 sq. in. 
 10. -.3 units/min. 11. .0087* cc./min. 12. .02188* ft. /deg. 
 
 Pages 118-119 
 2. .225 ft./sec. 3. 64 ft./sec. 4. 7.5 ft./min. 
 
 5. -40 V5 ft./sec; t = 30, 1000 ft. 6. -92 ft./sec. 
 
 7. %VllO. 8. 21.69* ft./sec. 9. 32.49* ft./sec. 
 10. incr., 14 mi./hr. 11. 1.44; 96 mi. 12. .533* in./min. 
 
 2. 
 
 9 
 
 _ Posfel21 _ 
 
 4 Vx/3, . . . , -5/2 Vx^ 3. . • . , -40/3 Vx^. 
 
 4. .0053 sec. 5. .037 yr. 6. 756. 
 
 7. .122 mi. 8. .4 ft./sec. per ft. 9. (a) 7 x^ ^^+1)*. 
 
 (f) 8(x-5)/ V(x2-10x+7)3, {i) 400 <V9 ^(25-1^)^ 10. 3 hr. 
 
 Po^e 123 
 I. dy =^2 xdx, etc. 4. dx/df, etc. 
 
 Pages 124-125 
 3. ..., -20/x5 -28x/(10-a;2)3. " 4. $12.48, 2.88, 7.21 ft., approx. 
 S. 110 yd. each. 6. 144 tt cu. in./hr. 7. 2.4 sq. in./min. 
 
 8. 24cu. in. 9. .0318 in. 10. 12; 4. 
 
 12. 5; 300. 13. . . . , 30 V2 ft./sec. 14. 45i%3 im./hv, 
 
 15. i'^%6o. 16. -500 per in.; 625; -^^728 in.perft. 
 
 17. ...,i = 100; -1600 ft./sec. 
 
 * Appro2dmately. 
 
VI 
 
 MATHEMATICAL ANALYSIS 
 
 Pages 130-131 
 
 I. (b)..., S^'i-2x+C, (c)..., ¥2x'-\-kx+C. 
 
 3. . . . ; 2/=% V^+25 x-% x4+25%. 5. 671 lb. 
 
 8. 10,000. 9. 1100, 8400, etc. n. 83.3 lb., approx. 
 
 Pages 133-134 
 2. 60+80^-16 «2;%+VlO. 4. ..., 4200Oft.,50±20V5. 
 
 ^.-80 V30 ft. /sec. 6. t =12.22; -441 ft./sec, approx. 
 
 8. < = 15; 450 in. 9. 468.75ft. 10. -98.71 ft./sec. 
 
 II. 1600 ft. 12. 45 ft./sec, 675 ft. 16. 2.67; ysa;^. 
 
 
 
 Page 137 
 
 
 I. 150. 2. 114. 
 
 3- 
 
 19375. 4. 40,89/11, 
 
 3%, 11.25, .105,2. 
 
 5. 1248.75. 
 
 6. 
 
 32. 7. 256/3 ft,..ib. 
 
 
 
 Pages 140-141 
 
 
 I. 7741b.-ft. 
 
 
 2. 7500, 380, -, 328. 
 
 3. 250 in.-lb. 
 
 4. 30000 in.-lb. 
 
 
 5. 2 dyne-cm. 
 
 6. 3933^3 mi.-lb. 
 
 7. 1.4(10-20) dyne-cm. 
 
 8. 992 TT. 
 
 9. 486eu. ft. 
 
 16. 972 cu. in. 
 
 
 II. .3 X cu. ft. 
 
 12. 533V3CU. in. 
 
 14. 5236 cu. in. 
 
 - 
 
 15. 5333y3cu. in. 
 Page 145 
 
 
 4. 20000 TT. 
 
 
 5. 309 X. 
 
 6. ...; 3485.1 cu. 
 
 7. 11670 cu. ft. 
 
 
 8. 11666% cu. ft. 
 
 9. 66%cu. in. 
 
 10. %hr^. 
 
 
 11. 144 cu. in. 
 
 12. 5333^/^ cu. in. 
 
 13. 85V3CU. in. 
 
 
 14. 2666% cu. in. 
 Pages 149-150 
 
 
 I. 8437501b. 3. 
 
 1,406,250 1b. 4. 9375001b. 5. 3751b. 
 
 in. 
 
 6. (c)-(e) -V3(25 -x2)t+C, i%Vx5+9+C, -VssiS-j^y^+C. 
 8. 2666% lb. 9. 5208V3lb. 11. Final value, 36000 lb. 
 
 Pages 152-153 
 I. .000 000 000 693+. 2. .000 000 01354+. 3. 51b. 
 5. 50000 1b. 6. .4. 7. 1333y3cu. in. 
 
 4. 22501b. 
 8. 60001b. 
 
 II. 72 cu. in. 13. 6000 in.-lb. 
 
 15. 1000 ft.; approaching, 128 ft. /sec. 16. « = Vl25. 
 
 17. 12.5(1+ V5); 12.5. 19. 254.68. 20. 61.42 sq. in. 
 
ANSWERS TO EXERCISES 
 
 vn 
 
 
 
 Page 159 
 
 
 4. 
 
 607 ft. 
 
 5. 614 ft. 
 
 6. 2101b., 22^ 
 
 7. 
 
 700 lb., 38°. 
 
 8. 200 lb., 37°. 
 
 9. 550 lb., 53°. 
 
 10. 
 
 429 lb., 473 lb. 
 
 II. 115 lb., 231 lb. 
 
 12. 1000 lb., 866 lb. 
 
 13. 
 
 13100 lb., 10700 lb. 14. 311 tons, 238 tons. 
 
 15. 180000 lb. 156000 lb. 
 
 4- 
 
 5 V63 
 13' 63' 
 
 Pages 16&-166 
 5. .09,5°. 
 
 6. 548 ft. 
 
 7. 
 
 9". 
 
 8. 63.7 lb., 186 lb. 
 
 9. 22°. 
 
 10. 
 
 1410 ft. 
 
 II. 1.38 mi. 
 
 12. 12.3 mi., 49.5 mi. 
 
 13- 
 
 62° N. of E. 14 
 
 . 5.2%, etc. 16. 5°, etc. 
 
 17. 76°. 
 
 18. 
 
 22°. 
 
 19. 14400 lb., etc. 
 
 20. 10.5 ft. 
 
 21. 
 
 4830 sq. cm. 
 
 22. 23°, etc. 
 
 2S. 391 lb., etc. 
 
 26. 
 
 60°. 
 
 28. 31°, etc. 
 
 29. 4.79 mi./hr., etc. 
 
 30. 
 
 24.7 ft./sec. 
 
 31. 58° N. of E., etc. 
 Page 168 
 
 33. 24000 ft. 
 
 2. 
 
 944 ft., etc. 
 
 3. 31°, etc. 
 
 6. .918, etc. 
 
 7. 
 
 8506 ft. 
 
 8. 2250 1b., etc. 
 
 9. 123 in., 1170 sq. in. 
 
 10. 
 
 1580 mi. 
 
 II. 3630 mi. 
 Pages 170-171 
 
 15. 17900 cu. in. 
 
 I. 
 
 9.21 ft., etc. 
 
 2. 30.3 in. 
 
 3. 6.05 in. 
 
 4. 
 
 107 sq. in. 
 
 6. 122 sq. in., etc. 
 
 7. 559 cu. in. 
 
 8. 
 
 205 sq. in. 
 
 9. 308 lb., 948 lb. 
 
 II. 337 1b. 
 
 12. 
 
 N. 5.37 mi./hr., 
 
 etc. 13. S. 15.8 mi./hr. 
 
 14. 13.8, 10.8, ft./sec. 
 
 15. 
 
 3.03 m./s., etc. 
 
 16. 9481b. 
 
 17. 95100 ft.-lb. 
 
 18. 
 
 .866 sq. ft., .342 
 
 sq. ft. 
 
 Pages 173-174 
 
 
 I. 
 
 350 1b. 3. 185001b., etc. 4. 30001b 
 
 ., etc. 6. 6531b., etc. 
 
 7. 
 
 1331b. 8. 65001b. 9- 43600 lb., 35700 lb. 10. 2301b. 
 
 
 
 Page 175 
 
 
 2. 
 
 .08985, . . . , 1.0735. 3- 955.36 ft., 2°.87. 
 
 5- 
 
 111.07 sq. in. 
 
 6. 628.32 sq. in., 362.76 sq. in. 
 
 7- 
 
 1.0515 in. 
 
 9. 311.761b. [w) = 6 -2.6864 x]. 
 
 TO. 
 
 1.6782 ft. /min. 
 
 II. .00187 in. /min. 
 
 Page 177 
 (I) 79°22', 213.22, 695.68. (II) 623.01, 71°1'.5, 55°41'.5. 
 
 (Ill) 69°53'.4, 72°0M, 392.97; or, 110°6'.6, 31°46'.9, 217.62. 
 
viii MATHEMATICAL ANALYSIS 
 
 Pages 179-180 
 2. 439.20, 315.68, etc. 3. 482.77, 53n'.4, etc. 
 
 5. 5115.8 yd. 6. 3177.5 yd. 
 
 7. 91,570,000 mi. 8. 701b., 38°12'.8 from 2nd. 
 9. Incr. 58.06 ft. /sec. 
 
 Page 183 
 I. ..., .77875, .62733. 3- 13 tons. 4- 75°31'.4. 
 
 5. 108 mi. 6. 1014 ft. 7. 683.78 ft. 
 
 8. (i) 99°28'.4; 41°4'.8, etc. (iii) 4.493; 97°1', etc. (v) 9784.5; 
 34°57'.5; etc. (vi) 76.880; 49°2r.9, etc.; or 26.212; 130°38M, etc. 
 (vii) 11189; 5023.1, etc. 
 
 9. (i) 111240. (iii) 14.517. (v) 19,188,000. (vi) 1134.7; 386.89. 
 (vii) 24,609,000. 
 
 Page 184 
 I. 1821.1ft. 2. 1809.5 ft. 3. 2867.5 ft. 
 
 
 Pages 186-188 
 
 
 4. 47°11'.4. 
 
 5. 12078 yd., 6°27'.9 N. of E 
 
 
 7. 743.37 sq. ft., ( 
 
 or 346.63 sq. ft., etc. 
 
 9 
 
 126.42 ft. 
 
 II. 82*'5'.8. 
 
 12. 223,200,000 mi. 
 
 13. 
 
 21.048 ch. 
 
 16. 1683.9 cu. ft. 
 
 17. 10 ft. 
 
 19. 
 
 8.16 in. 
 
 20. 4 in., 3.3282 in 
 
 . 21. 9234; 11877. 
 
 23- 
 
 204.021b., 22°0'.4. 
 
 24. 2865.3 ft. 
 
 25. 3104.9 ft. 
 
 26. 
 
 182.49 ft. 
 
 27. 224.45 ft. 
 
 28. 73°18'. 
 
 29. 
 
 3.775 X 10^5 mi. 
 
 30. 10r32'.2. 
 
 31. .375ft./sec. 
 
 32. 
 
 233.4 cu. in. 
 
 33. 32235 1b. 
 
 34. ...,50°ir.7. 
 
 35- 
 
 17°39'.4. 
 
 36. .0031215 ft./min. 
 
 37. 
 
 .2 Ib./min. 
 
 
 Pages 191-192 
 
 
 3. 2.73 X 109. 
 
 4. 50.9. 6. 
 Page 198 * 
 
 4670 yr. 
 
 9. 9.44. 
 
 4. (a)-(e) 3432; 
 
 965,200; 7,260,000; 
 
 2.438; 
 
 979.9. 
 
 ifUj) 7.235; 
 
 1.796; 3.347; 
 
 26.22; 
 
 10,210,000. 
 
 7. 41.52; .00191. 
 
 9. 
 
 3.78. 
 
 
 Pof^es 200-201 * 
 
 2. (a)'ic) 1.288; .04756; .0004569. {d)-{f) .001947; .0007791; .002025. 
 (g)-(i) 1.262;. 2892; .001913. (j)-(O 4.168X10-6; .01545; .0002235. 
 
 3. .02129; 13.81; 7.706; .7171. 4- 2.015X10^2. 5 io.91. 
 
 * The answers given in groups are not always in order. 
 
ANSWERS TO EXERCISES ix 
 
 Page 202 * 
 3. -.-211, .---989. 4. -.-093 sec. 5- S20530. 
 
 6. $3768.80. 7. .--822 ft. 8. 10.552. 
 
 Page 206 
 
 3. {o,y{c) --.403, .---868, .--902. 
 (d)-(/) .---8872, -.-068, --.212. 
 
 4. -.-344. 5. -.-988X1011. 6. 2361.5 cu. ft., etc. 
 
 Pages 208-209 
 I. --4.15; -.-390. 3- -11.938. 4. 134,220 sq. cm. 
 
 5. 384.86 ft. 6. 19°44'. 7. (±?) .16057, etc. 
 
 Page 212 f 
 I. $10,421,000,000. 2. $3979.60. 3. 5.7%. 
 
 7. 4.64'o. 9- $1104.20. 11. C3359.10. 
 
 Page 214 
 I. 2?3219; 2.1827, etc. 2. 9.45+, 28.08, 13.13, etc. 3. $30072. 
 
 Page 217 
 3. 42''27'.7; 54.707 in.; etc. 5. 982.92; 816.70; etc. 6. 980.57. 
 
 7. (i)-(iii) 415.42, 169.65, etc.; .67640, .70432, etc.; 11.007, 20.497, etc. 
 (iv)-(v) 1134.2, 999.9; etc.; 46.289, 4.2878, etc. 
 
 8. 44.088 ft. 9. 20°21'.9. 
 
 Page 220 
 I. 27'*31'.2, 91°18', 6in0'.9. 3. (i) 38°41'.2, 86°37', etc. 
 
 3. (iii) 113°4'.2, 36°56M, etc. (v) 64°41'.8, 33°47'.8, etc. 
 
 4. S0°31'.3. . 5. 88°42'. 
 
 Page 222 
 I. 38°14'.9, ..., 70.233. 2. ..., 48°31 '.7, 50.938. 3- 547.84; 929.72. 
 4. (i) . . ., 110°45'.4, 1944.4; 1,169,000. (iv). . ., 38°14'.3, 7.8946; 10.172. 
 (vi) . . . , 40°3'.5, 167.40; 5186.6. 
 
 Pages 226-227 
 
 1. (c)-(f7) 421.33; -.13764; 54.708; 1.0931; -.25546. 
 {h)'{l) -7.1470; .0012565; 9965.5; 2.4304; 626.69. 
 
 2. $5306.70. 3. $3494.20. 4. 4.52%. 5. 22.5. 
 
 * Ea«h dash stands for a figure, perhaps zero, in the answer. 
 
 t These answers were obtained from five-place tables and are consequently somewhat inac- 
 
MATHEMATICAL ANALYSIS 
 
 6. .19708. 7. 88.191ft. 8. 369.17 ft. 9. 173.13 ft. 
 10. 389.79 ft. II. 154.03. 12. 380.76 ft. or 452 ft. 13. 1650.7 ft. 
 
 Review Set, pages 228-235 
 * Chapter I 
 
 2. -4^ sq. ft. /ft.; 160 cu. ft. 
 3. (19=b V249)-T-14; -2.33, .20+, 2.13. 
 
 Chapter III 
 
 7. $792.35. 8. « = 4; 80.5 cu. ft. 
 12. 14417 units /min.; .14716 units/min. 
 
 II. X = 2, Ax = .005. 
 
 2. ...,42000ft.; 
 5. 218,750 1b. 
 
 Chapter IV 
 
 ., 1639.52 ft. /sec. 3. 
 7. 9 TT CU. in. 
 
 50.4. 
 
 24°!' 
 
 Chapter V 
 4. 13584 lb., 18376 lb. 6. 297.6 ft. 
 
 4. 37500. 
 8. 1.08 TT lb. 
 
 7. 102331b. 
 
 Chapter VI 
 I. 73.42; 1.5416; (=«=?) .17394. 2. 26,017,000,000 mi. 
 
 3. 13.51. 4. 99.53 ft. 5. .35158 mi. 
 
 Miscellaneous, pages 232-235 
 i. 141.03 ft. 2. .01749 ft. /min. 3. 50000 ft.; < =6; 10935 ft./min. 
 
 f2^00 7rxdx. 6. 27000 tt cu. ft. 
 
 Bytrial, « = 13-. 11. 1875. 
 
 -8.2571 Ib./in., 1330.9 in'.-lb. 
 18. 45°; etc. 20. 4.1669 cu. in.; etc. 
 23. 300 Ib./sec. (Constant). 
 
 189,5901b. 27. 78.446. 
 
 5. 
 
 8. 
 
 14. 
 
 26 
 
 7. 
 
 2000 ft., -208 ft. /sec. 
 
 12. 
 
 2.87+. 
 
 16. 
 
 8.75%.* 17. 21.6-.* 
 
 21. 
 
 2098.1 ft. 22. 98.33 lb, 
 
 24. 
 
 $2636.20. 25. 85in.-lb. 
 
 28. 
 
 118,150 cu. in., approx. 
 
 29. 1.869 ft./sec. 30. .0129. 
 
 Pages 240-241 
 I. $2473.10. 2. 5.13%. 3. t = 24.08. 4- $41161. 
 
 5. 5.824%. 6. 91492; 203610;.... 7. 448. 
 
 8. t = 2.31. 9. 68.387 mg. 10. 82.088, t = 9.21. 
 II. 9.902. 12. 3.922%. 
 
 Page 243 
 I. 10008686<^ _ _ 2. . . ., 12.5353, 7.3132-10, 3.0088-10. 
 
 ♦ Substituting x for an expression gives a cubic equation. 
 
ANSWERS TO EXERCISES 
 
 3. 1.8379, . . . , 4.7574-10. 4- -, 202, -, .457, .0454. 
 
 5. 1.597, ...,.002813, .1247. 6. 2.305,7652,6.419. 
 
 7. .09119; 10.9-. 8. e-esau g.2332»^ 
 
 3. t = 4.48-. 
 
 I. / = 36/x2. 
 S- R = 3000 e--' 
 8. p = 2000/fI 
 
 2. .69330. 
 
 Page 247 # 
 
 5. . . . , Q = 50 e-50^. 6. 21.972%. 
 
 Pa^es 254-255 
 
 2. One C. /. L., one Power L. 3. D = 29.4 e" "i. 
 
 6. F = .25e0693ir 7. AT = 100 e-!^*. 
 
 9. r = Vz>3. 
 
 .^x 3 -28 
 
 Pa^es 259-260 
 7. (aHc) —,..., ^^; -, 
 
 X XX 
 
 8. 2.3026. 
 
 11. 5.056. 12. +260.6 ft. 
 
 ,,, .86858 X -2. 17145 .r^ 
 14. (b) 
 
 16 
 
 a:2-25 l-x' 
 
 l-x2 2(1 -x^) 2a;2-l 
 
 3 -5 1 
 
 10. 486.6. 
 
 13. 465.3 ft. /min. 
 4 
 
 15- ...;-. 
 
 2a; 
 
 x{x^+l)' x{x*+l)' x(x2-l)' (x2-l)(a:2+l)* 
 2a;» 1 ^ 1 dy 
 
 x^-\-l jjlogx 
 a:2+l 
 
 y dx 
 
 Page 2Q1 
 ;...; 14a;(7x3-l)(a:3-i)3; 5x2(5x4+3)/ V^^+l. 
 
 Pages 263-264 
 . ; -56 x/e*-^; Q(e^' -e-^'). 2. (a) 2.1972 x 3*\ 
 
 (x2-l)2 
 
 I. 1.2e-o«*; .. 
 
 9. i = 30 e-«o^ 13. 995°.* 15. 23.6 in. 17. n = ATeK 
 
 Pages 266-267 
 
 ^_^^^_ 2x(3x»+4.^+io) ^ (c) 4xlogx; (d) 2xe-(2:.+l); 
 
 (x^— 5)2 
 
 2x(25-2x^) l-61ogx -2x(x^+l) 
 
 C/) — , ; (^) :; — ; (h) 
 
 V25-X* 
 
 X' (X4-1)2 ' 
 
 * By five-place tables. 
 
xii MATHEMATICAL ANALYSIS 
 
 3 ,- 1 
 
 2. (a) X = V«, ?/ = — (max.). (6) x = %, n = ... (max.). 
 o e 
 
 (d) min. at — > 50, max. at VoO. 
 
 4. 30 cu. in. /min. 5. inc. 50 ttcu. in./min. 6. .2424 deg. /min. 
 
 7. dec. 2.1875 per min. 8. dec. .1 per rain. 9. inc. .00170 per min. 
 
 II. S = 1/2 e, when x = Ve. 12. x = 2 V2. 
 
 Pages 268-270 
 
 2. 10/x, 10(logx)Va:, (1-log a-)/x2, 2 xe^^ 3e'{e'+iy. 
 
 3. (a)-(c) 1.30287 (logio x^/x, (3 x+4)/2 .r(.r + l), . (1 -5 log x)/x«. 
 
 2x(2x-' + l) '—4 
 
 (e), (/), (/i). \-— ; 2x3e-io-(2-5x); 
 
 (i), 0'). 2x(loga:)2; 2x^62^ 
 
 5. X = ±V2/2. 6. inc. 4.375 per min. 7. x = 200(1 -e'^^. 
 
 8. 8.664%. 9. 13.86. 10. 32.894. 
 
 12. Only .3%. 16. / = 600/x2. ^ 17. / = 100 e'-^. 
 
 18. 5 = 6.2e-'i5«, approx. 19. / = 18400/d*, approx. 
 
 20. JS = 29.2e-*626f; Hess. 
 
 Po^es 273-274 
 2. FC = 4.919mi.,26°34'N.of E. 3- 13892 m., 30^5 '.4 N. of E. 
 5. . . . , 49.729 mi. 6. 18.4 ft. 7- 422 sq. ft. & 814 sq. ft. 
 
 10. 1494 ft. II. t = 5; X = 1200. 
 
 Pages 276-277 
 2. 913ft./sec.,28°49'up;etc. 3- ^^ = 30000; v = 1000; 7 = -36'*52'. 
 5. 3+3^2. 76. 8. 2(17^-1); 24; 224 
 
 Pages 278-279 
 I. X = 1399.4 f, 7j = 540 t-mtK 2. t = 33.75, x = 47230, . . . 
 3. f =1%6; (135.32, 39.06). 4- •••; 580.9ft. 
 
 Pages 281-282 
 
 I. 1 0,..., 201.91. 5- -54°28',^. 11. 750. 
 
 ,12. V2873, V3793. 14. VIoO, Vl57, etc. 15. Yes, no, yes. 
 
 18. 31°16'. 19. 74°30' (if prolonged). 20. 16.35 mi. 
 
ANSWERS TO EXERCISES xiii 
 
 Pages 285-286 
 2. No. (Test?) 8. (4, 4); also 12. The inscribed circle 
 
 13. a;*+2/' = 100. 14- x'^-y' = 16. 15. x'^+y'' = 64. 
 
 Page 288 
 
 7. No; no. (Test?) 10. Unlimited line, or sides of a square, accord- 
 
 5. 2 x—y = 9. ing to interpretation of " distance." 
 
 Pages 290-291 
 2, (6)(j--5)2 + (2/-4)2=25. (c) (x+2)2 + (?/-3)2 = 37. 
 4. (-8, 15), r = 17; etc. 5. ...;(-%, 0), r = %. 
 
 8. (.r +4)2 +7/ =64. 9. (1.5,7). 
 
 II. ...,16; etc. 13. 200; 150; . . . ; 32. 
 
 14. ...; 22 77, lOir. 
 
 Page 293 
 
 6. Straight line. 7. Circle, or straight line. 
 
 8. Circle. (What center?) 9. y^ = 12 x, simplified. 
 
 Pa^es 296-297 
 2. F (0, 1/4), Dir., y = -M] etc. 3. If in doubt, read § 198. 
 
 5. x2 = 25 ?/. 6. . . . ; 2. 7- • • • ; (ie., y = .000142 a:^); etc. 
 
 8. X'- = 1600?/; etc. 9. 6ft., etc. 13. x^ = lOOy',% in. 
 
 
 Pages 298-299 
 
 
 I. 
 
 \0, -10), etc. 4. a:2 =-4 2/. 
 
 5. x"^ = -400?/; 3 in. 
 
 6. 
 
 7.4 in.; -.0463. 8. 24.8 ft., 63.2 ft. 
 Pages 302-303 
 
 .t2 ?/2 
 
 '^ 400 144 
 
 z. 
 
 (±15,0);...,(0, =^2V5). 4. (c)§ + 
 
 l-^<<o+i£- 
 
 7. 
 10. 
 
 b = 92,986,000;^etc. . 8. (a) 38.4; 
 5.508ft.;etc. 11. ^+| = 
 
 Pages 305-306 
 
 (6) 40, when re = 5/ V2. 
 x"^ y- 
 '■ "■ 405 + 144=^- 
 
 I. 
 
 500 IT sq. in. 4. 250p tt cu. in. 6. 8 ft.; etc. 9. % = cos C; 
 ^ - SeO^^''^- "■ 2500 +900 = '• lU,e similar triangles.) 
 
 13- 
 
 400 225 
 
 
xiv MATHEMATICAL ANALYSIS 
 
 Page 309 
 
 I. . . ., c = 5, VlS^ 2V2. 2. c = 10, a = 6, /. 6=8; etc. 
 
 4. Two parabolas, and . . .? 5. Two hyperbolas (4 branchies). 
 
 6. Two parabolas. (Why?) 7. -^^ - ■—: = 1. 
 
 400 22o 
 
 Page 311 
 
 1. (0, =t3 Vu); etc. 2. G(6780, 5480). 3. G(7970, 6930). 4. ^V = 50. 
 
 Page 314 
 3. 3 parabolip^ 4 hyper.; 1 straight. 4. xy = V2k\ 7. 69.315. 
 
 Page 317 
 
 2. (a), (6)'. Foci: (18, -6), (-2, -6); (-10, ±5). 
 
 (y-6)^ (x+l)2 , . . , , ,w 1 11^ 
 
 (c) ,^ — = 1; foci, (-1,1), (-1,11). 
 
 16 9 
 
 fx— 4)2 (v— 4)2 
 4. -^TT^ + -^1^ = 1. 5. Vertex, (8, 1); p = 3; etc. 
 
 lb 25 
 
 (x-6y (2/ -2)2 
 6. -— - + ~~- = ,1. 8. {x - 15000)2 = -22500 (1/ - 10000). 
 
 25 16 '^ 
 
 10. (25-48000)2=: -4802(7/ -10000) ; i5'(48000, -47600); Dir.,y=Q7,mO. 
 
 12. x2(l-e2)_20x+?/2 + 100=0; ...; hyperbola. 
 
 Page 321 
 I- (d)'{f),ih) a:-62/+48=0,6x-7/ = 41,x+?/ = 7,3x-2i/+25=0. 
 
 2. 2x-?/ = 16,3x+7 2/ = 109,etc. 3. 3 J-IO ?/+ 61 = 0, 
 
 15x+2/ = 103, etc. 
 6. (V4, 2), 4x-2/+l=0. 
 
 Pages 322-323 
 I. (7%i, 23Ai). 3. 2x+i,' = 15,2x-5!/+19=0, (^%,i%). 
 
 4. Meet at (%, %). 5. (%, -^^Z^). 
 
 6. (2;-2)2 + (?/+l)2 = 100. 7. Center (^^.-i,^ 29/23)^ 
 8. (,-1,1)- 9- (15,30). 
 
 10. (5; 10). II. lOx+j/ = 19. 
 
 Pages 324-325 
 4. 16X-2/2+18 7/-65 =0. 6. 16x2+257/2+192x-200?/+576=0. 
 
 7. 32 x-y^-25Q = 0. 8. (x +9)2/225 -z/2/400 = 1. 
 
ANSWERS TO EXERCISES xv 
 
 9. Same as in Ex. 8. 12. (3, 6), (0, 6). 
 
 13. 9x'-my^-lUx-\-l2Sy-\-176 = 0. 
 
 14. x2- 120000 a: + 1600001/ =0; (60000, -17500). 
 
 15. y= -.00092098 a;2. 16. 3.8%. 
 
 17. About 48° S. of W. i8. y = V20 x^+C. 
 
 19. Y'- = SX. 21. Hyperbola (Why?); 85.836 in.-lb. 
 
 22. P = .05 F2; 1. 
 
 Page 328 
 
 3. =*=3, ±1; 3,%(-l± V^);etc. 4. 13.49. 5. 10.39. 
 6. .5193 I 7. E, P, //, pair of lines. 
 
 Pages 329-330 
 2. y, not X (Why?) 3. (a), (6) Yes. 4. k=%; x=%, ¥3. 
 5. (-4; -2, -2); etc. 6. -%, etc. 7. A: = 50, or .. .(Why two?). 
 
 Pages 333-334* 
 
 1. (a)-(e) 2,3,(-7± V37)/2; 1,-4,...; -2,-4,...; 
 -1,-2,5,.^ 1,-1, ...; (/)-(i) 5, -4,-1,...; 1/2,-3, ...; 
 
 %,-%, =^V-i; ^^,%, ...; -^^, -%,.... 
 
 2. (a)-(c) (2x-l)(3a;+l) (6x2+j;+l); (2 a:-5) . . . ; (x+1) . . . ; 
 (d)-(/) (2a:-l)(3a;+l) ...; (2x+l)(2x-3) ...; {x-iy (x^+l). 
 
 3. (8x3_^g^2 + i) ._. 4. ...^ (2x-3+9x2-4). 
 
 5. (5+5V33)-^8. 6. 10. 7. « = 5. 
 
 Pfli/es 338-339 t ' ' 
 
 2. 4. --6838. 3-. --33, -4. --01. 4- 2. -- 84, . - -16, -2. - -00. 
 
 6. -.-34579. 8. .6180, -1.6180. 10. .22. 11. .66. 
 
 12. X = 2.65. 13. X = 5.23. 14. 2.480, 2.510. 
 
 15. 47.82, .09 --8. 
 
 Page 341 (top) 
 3. One step, from 2.3: 2.3099. ■ 4. Three real. 
 
 Pages 341-342 
 I. 2.166013. 3- 2.92. 4. V2, 1.10; -V2, -2, -.62, .73, 4.40. 
 
 5. (x + l)...(4x2+8x+5); (.u-1) (2j:+5) ...(4x2-2^ + 1); 
 (x-iy ...• (.r2+4.c + l). 
 
 6. (3, 2), (3.6, -1.8), (-2.8, 3.2), ... 8. 32.23. 
 
 * The answers given in groups are not in order. '"" 
 
 t Here long dashes denote minus signs; short dashes, missing figures. 
 
xvi MATHEMATICAL ANALYSIS 
 
 9. 6.4%. (One step from a: = 1.03.) 11. .6931; 1.6094. 
 
 12. VlO. 13. 3.059. 14. 6.179. 15. 1.843. 
 Pages 344-345 
 
 1. 47.03 mi. 3- • . . ; 2.64, etc. 4. 15.8. 5. 30. 
 
 Page 347 
 
 2. 139.6 in. 4. 50; 187.5; 5890.4 ft. 5. 471.24. 
 
 Pages 348-349 
 
 3. 20in./min.; 4m./mm.2 4. 10.8in./sec. 5. .54 iu./sec.^ 
 6. At«=30,81ft. 12. .10472. 13. 7.27X10-6. 
 
 14. .288mi./sec. 15. .202 mi. /sec. 
 
 Page 350 
 I. 17900mi. 2. 116 mi. 3. 4.64X108mi. 4. 2.51X10i3mi. 
 
 5. 0".81. 6. 19.2 mi. 8. 9 mi., approx. 9- Vao^"). 
 
 Pages 358-359 
 
 6. .... 117°29'.2; 115^24', . . . ; . . ., 199°24'.8. 
 
 8. -.83898; -.54416; 1.5417. 
 
 9. 3.8877<''>, 5.5371(^^ .7671^^), 5.5161<^^ 3.0787('>, 6.2203<'>. 
 
 Page 360 
 I. 0, .0628, .1257, etc. ; .0314, .0942, etc. 3. Max. at t = .00196; ~- sec. 
 
 Page 363 
 
 5. (6) -4.8 sin 8 1, (e) 10 tt cos f ^ n , (/) - .21 «= sin {i^). 
 
 6. (o) 5.2359 cos (3 < +20). 7. .000964. 8. 168; 54000. 
 
 10. V— —1.40 cm. /sec. 11. <•= — 8in./sec. 12. w = .6283('"V«ec. 
 
 Pages 364-365 
 I. 1.05(^), . . . ; l-e^*"), ...; % TT (»•>,.. . 2. 44.73. 
 3. .8097, 1.4903. 4- • • . , -105 cos2(5 sin (5 0- 
 
 Pa^e 365 
 
 7. 273perrad. 8. -.00597, .0267. 
 
 Page 367 
 .3. . . . ; (-18.794, -6.840). 4. • • • ; (25, 323^*8'), or (-25,143°8'). . 
 
 8. (%, -Vs, -%, ...) or (-%, %, -%, . . .). 9. 3530 mi. 
 
0)ctn0). (/)-2cs.g)ctng). 
 
 ANSWERS TO EXERCISES xvii 
 
 10. 6000 in./mm.; 300 in./mm.2 12. ...; -.389. 
 13. 73.89; 2.5. 14. 1.0027(''>. 
 
 Pages 371-372 
 2. cos d, — sin ^, . . . , cos d — smd, cos d. 4. (a) [Factor]. 
 
 4. (6)-(c) sec0+tan0; sec0. (/) — 2sin0. 
 
 5. d+C; 2 0+C. 6. sec2 0; -csc9ctn0. 
 
 7. (a) 53°8', 306^52'. (6) 45°, 225°, 7r34', etc. 
 (c) 8°43'.7, 81°16'.3; and two in Q III. 
 
 8. (a) 30°; also II, III, IV. (6) 120°, 240°. 9. 2°45'.3; 87°14'.7. 
 
 10. 50000. II. 8°31'.8. 12. 45°. 
 
 13. 50°21'.4. 14. 14°2'.2[tan0=.25.] 
 
 Pages 373-374 
 
 1. (C) -10 t CSC2 (5 «2). {d) - CSC 
 
 (g) ctn e. (h) 3 ctn^ 6. (j) e' sec t (1 +tan t). 
 
 2. secx; — csc0ctn0; —esc 6; sec^^. 
 
 3. cos2 0— sin2^; ...; csc^e — csc^ctn^; sec2 — csc^d; 
 
 4. 1.6. 5. 1; -2. 
 
 Pof^e 375 
 
 2. 80 TT. 4. 320. 6. 10V2(l-cosf). 7. x = 10cos (2«+0- 
 9. 30 sin < cos 2; 15; 15. 
 
 Page 378 
 
 I. x=50i.2t -sin .2t),y= . . . ; etc. 2. 6 Vi in./sec. ; 12 in./sec. 
 
 3. -2ft./sec. ,..., .3328ft./sec.2 4. -44.82 in./sec. 
 
 5. a; =20 cos (2«-x/3), . . ., -9.787 in. /sec. 
 
 Pages 380-381 
 I. (a) Min. at t = .0067, max. at t = .0145. 2. -.1 cos 10 1 +C, 
 (c) Max. at t = .2487, min. at t = .7487. 3. Q = .0159+. 
 
 5. (6) (. . ) tanS e+C, (c) (. . ) sin-3 0+C. 
 
 6. (a) log sin ^+C, (6) 2^-2 cos 0+C. 
 
 7. (c) -COS0+C, (/)sin0+C, 
 (^)sin&— COS0+C, (/i) — COS0+C. 
 
 Po^es 384-385 
 
 7. 4cos3 0-3cos9. 8. (d) (cos A + V3 sin A) /2. 
 
 9. ^%5, ^%5. 10. ^%5, — ^%5. 
 
 11. (6) tan 5 d, (c) cos A. 12. 5 V3 sin 3 «+6 cos 3 1, 
 
 14. c = 10, A = 36°52'.2 = .6435^'^. 
 
xviii MATHEMATICAL ANALYSIS 
 
 Pages 386-387 
 
 1. {b)V2d-VL2smQd+C; etc. 2. 34'.3. 
 
 6. (tan A +tan B) -r- (1 —tan A tan B). 
 
 7. 8°7'.8, 19°26'.4, etc. 8. (=»= 2, 4), 77°28'.3. 
 9. (6, 2), 52°7'.5; (-3, -4), 86°49'.2. 
 
 Page 388 
 
 2. -ctn 4 6, tan 6 5, ctn 30° tan 20°, -tan 25° tan 5°. 
 
 3. V2 (sin 10 0+ sin 2(9), etc. 
 
 Pa^e 389 
 
 1. (6) y2 [xVa;2-25 -25 log {x+^x^-25)]. Use (41) with m = 0; etc 
 (e) % tan5 d -Vs tan^ 0+tan -d-\-C. 
 
 (/) Vs sin sec2 d (2 sec^ +3) +% log (sec +tan d) +C. 
 
 (h) V9J^{S\ogx-l)+C. (i) -VL3e-^\2 sin St+3co8 3 t)+C. 
 
 2. 6 TT. (Cf. § 214.) 3. 7rV2. 
 
 Pages 390-391 
 2. 2^221,220/231^2^220, etc. 5- 3 sin -4 sin^ 0. 6. 45°. 
 
 7. sin-M.005F). 8. .141 deg./deg. 
 9. c = .97985; 75°49'.3. 10. 38.114 ft. 
 
 II. 45°N. E. 12. A/2. 13. 45°. 
 
 14. 1.2113, .2218, 41°42'.9. 16. 75°49'.3, or ...; 165°49'.3. 
 
 Page 394 
 
 I. 248; 97.2; 134.14; 1. 2. 2. 3- 2. 
 
 4. 1318.3. 5. 102,500. 6. 238 7r/3 cu. ft 
 7. 7r-7rV4. 8. 750 7rcu. in. 9. 50001b. 
 
 Page 398 
 5. 20%. 6. Vs. 7- 180001b. 
 
 8. 270000 Ib.-ft. 9. 4000/3 Ib.-ft. 10. 250 7r/3 lb. 
 
 II. 8001b. 12. 752680 ft.-lb. 13. 3333V3. 
 
 Pages 401-402 
 
 1. (a) 5%. (c) 20/^+3 log 3.* 2. (a) (Vl000-l)7r/27. 
 
 2. (6)416 7r/3. (d)48V5. _ 4. (a) 18.33.* 
 4. (6) k [( x2 +4)t -8] -7- 3. (c) V2 (e^-1). (d) 10 tt. 
 
 6. 2133y3 Ib.-ft. 7. 128000 TT ft.-lb. 
 
 * Use formula (41), p. 497, with m = 0. 
 
ANSWERS TO EXERCISES 
 
 XIX 
 
 90. 
 819.2. 
 
 16^%i. 
 (d)-3, 6. 
 id) 2, 12. 
 
 125%05. 
 
 171%. 
 
 Page 405 
 3. 78. 
 7. 
 
 11.25. 
 
 (e) 5, 4. 
 
 Pafifes 407-408 
 
 3. (a) 4, 4. (6) -12, - 
 
 4. (a) 2, 4. (6) 2, 1. 
 
 6. (a) (3, -1, 17), min. 
 
 16. 
 
 10%. 
 170%. 
 
 (c) (0, 1, 17), neither, (d) four max., one min. 
 Page 411 
 2. y = 
 
 lOSVs. 
 
 .0795 (=5%) 
 170%;%;... 
 
 70 cu. ft. 
 672 -If cu. in. 
 
 1%). 
 
 I. 10 Vs. 
 
 4. ^%. 
 
 7. 16000 Ib.-ft. 
 
 leVs. 
 .0349 ( = 
 
 40/7r. 
 
 Pages 412^13 
 5940 IT cu. in. 
 1200 TT cu. in. 
 
 Fa^e 414 
 
 2. 12iy27. 
 
 5. 360 tt; 720 tt. 
 
 8. 800 7r/31b. 
 
 2l 
 
 10. 2400 7r2 Us comes out 48 ttV 100 
 
 11. 76800 lb. Iw comes out : 3 Vx]. 
 
 2. 
 
 5. 
 8. 
 
 13. 
 16. 
 
 900; 2500. 3- 
 
 $1252.50. 6. 
 
 ..., 16(1.530-1), 10. 
 
 $12080. 14. 
 
 $285.75 (=$22.50+*S) 
 
 Pages 417-418 
 420; 7656. 
 $4350. 
 .003171 W. 
 
 $642. 
 
 $22607. 
 $1188.90. 
 Life, by $3.53. 
 (6) $8.47-. 
 (e) $21.47+. 
 
 Pages 421-422 f 
 s. $8480.20. 
 ;. $37934. 
 
 ;. $8.84+. 
 
 (c) $16.06-. 
 K $187.66. 
 
 (c) 5, 10. 
 
 (c) 6, 4. 
 (6) (0, 0, 40), max. 
 7. (6,5). 
 
 2/= 80. 
 
 17.26; 370.67; .7072. 
 
 1280 TT cu. in. 
 304 7r/3 cu. in. 
 
 3.1 in. 
 1.00003. 
 
 12. 30%cu.ft. 
 
 4. 31360; 99500. 
 
 7. $615. 
 
 12. 3435.6a* 
 
 15. $1027.50. 
 17. V2, V2. 
 
 3. $1639.20. 
 6. $1685.54. 
 9. (a) $14.99-. 
 (d) $74.30+. 
 
 * Using six-place logarithmic tables. 
 
 t Five-place tables will not give some of these results very closely. 
 
XX 
 
 MATHEMATICAL ANALYSIS 
 
 
 Pages 424-425 
 
 I. $7494.03. 
 
 3. $3618.33. 4- $3419.16. 
 
 5. $1971.16. 
 
 6. $58.96. 7. $55.85-. 
 
 8. $6682.20. 
 
 10. (a) $63.91. (6) $56.03. 
 
 10. (c) $234.96. 
 
 II. $6065+. 12. $672.97. 
 
 
 Po^e 426 
 
 I. $372.43 +$564.81. 
 
 3- (a) $853. (6) $512.81, 
 
 3. (c) $4805.13. 
 
 id) $10127.30. (e) $34.25. 
 
 4. $173.23+. 
 
 5. $334.59. 
 
 
 Pfl^e430 
 
 x^ re* a^ 
 
 , X2 X3 , X* 
 
 etc. 4. X+-+-+-. 
 
 5. .09967. 
 
 6. x-x3/3!+x6/5!. 
 
 II. .493108; .049986. 
 
 12. a»+5a%+10a3x2,etc. 
 
 13. a"+na"-ix+p^^a»-2x2.... 
 
 
 Pages 432-433 
 
 
 ^...M"- 
 
 (sr) 1+X+X2, etc. 
 
 1 2x' x« 4x« 
 ^ •^ 9 27 27 243 ■ 
 
 2. -(x+xV2+x3/3, etc.). 3. -.05129, -.05033. 
 
 4. x+Vs x4- ^56 x^+i^eo xi°. 
 
 5. .5032. 
 
 Page 435 
 
 I. (a) log V^Y = l.5708J\^^, 4.7124 V^, etc. 
 
 (6) log (.5+.86603 V-l) = 1.0472 V-1, 4.I888 V-1, etc. 
 
 Pages 437-438 
 
 3. y = 10x+3x2; y = -7+.2x2; y == -5 -2x+.lx2. 
 
 y = ll+x2-V4x3; y = 2.47 +. 0515 x+. 00165x2 -.00005 x». 
 A = 1.4x2 -.1x3; etc. 
 
 4. 2/ = 125-.5x; y = 20x-x2. 
 
 6. 1.003984. 
 
 Page 439 
 i/ = 28-5x+^x«. 
 
 10. $1022.50. 
 
ANSWERS TO EXERCISES 
 
 XXI 
 
 
 Pages 441-442 
 
 I. 120; 15600. 2, 
 
 , 5040. 3. 6720. 5. 10,0001^9500!. 
 
 6. 64. 
 
 7. 504. 8. 20! X28!-i- 8!. 
 
 9. 8. 
 
 10. 1,814,400. 11. 48. 
 
 12. 64,48. 
 
 
 
 Po^es 445-446 
 
 * I. (a)-(d) 252; 5005; 
 
 38760 ; 12650. (Z) 47 ! -^ (36 ! 6 ! 5 !). 
 
 (n) 8,778,000. 
 
 3. 45. 4. 895440. 
 
 6. 288. 
 
 8. 30240. 9. 16800 X 181 -M3!. 
 
 10. 3696. 
 
 II. 2880X13! 12. 11760. 
 
 13. 5040. 
 
 14. 56. 15. ..., 220. 
 
 
 Pages 449-450 
 
 2 240 
 ^* 1001 1001' 
 
 3. .34-. 4. .004917, .1598. 
 
 5. (c) .007128. 
 
 6. .0401. 7. f^. 
 
 1 
 
 1 36 
 
 8. 
 
 11050 
 
 «^*N024- '"•*'343; "•«'>-°«l 
 
 
 Page 451 
 
 I. %6, .05427, .2257. 
 
 2. .288. 3. .512. 
 
 4. .3501. 
 
 5. %58e. 6. .000404. 
 
 7. .0108. 
 
 
 
 Pages 455-456 
 
 I. 9%, 91%. 
 
 2. ..., 28m. closer. 4- ^• 
 
 5. ...,98%. 
 
 6. .4724, .3829. 7. 5.529. 
 
 
 Page 458 
 
 I. 88/105; 7.53. 
 
 2. .0000462; etc. $- (fl)%^Vso. 
 
 3. (6) .8, -1, approx. 
 
 4. W = 35.33+. 04175 r. 
 
 
 Page 459 
 
 I. 7.6185 X 101°, approx 
 
 :. 2. .278, approx. 3. .0225. 
 
 4. TF = 6.9823 T+105.16. 5. .00811. 
 
 6. y = 3.95 X +52; x = 
 
 = .0805 y -2.82; i = .318. 
 
 
 Page 463 
 
 2. 92+34i,i7A3+%3i, 
 
 -, 13+z, 8+2i, -, 2-lli, %6-%3i. 
 
 3. =h[(3^-^)/V2,-,(l + 3^)/V2,l-2^,3-2^,(l-5^)/V2,4+^, 
 
 (3-5i)/V2, -, (9-7i)/V2, 2+5t, 5-6i. 
 
xxii MATHEMATICAL ANALYSIS 
 
 Page4QQ 
 
 3. (6) 2 V2 cis 225°. (e) 8 cis 150°^ (9-) 3 cis 180**. 
 
 4. (6) 3.2140- 3.8302 i. {e)-Q-Q^ISi. (/)4 V2(-l+i). 
 
 5. cis280<';-; 7.2812 cis 208°!'. 
 
 Pages 467-468 
 
 1. (d) 30 cis 220° = . . . . (^) 250 cis 150° = . . .. (h) — i. 
 
 2. -.75i. 3. 2.1426-2.55351. 
 
 Page 469 
 
 2. (6) 2 cis 75°, 2 cis 165°, etc. (e) 3 cis 140°, etc. 
 
 3. .80902 +. 58779 i; -.30902+.95106 ^, etc. 
 
 Page 470 
 I. (5) cis 22°30', cis 67°30', etc. (c) ( ^ls+i) /2, (l + V3 i) /2, i, etc. 
 (h) i, - ( V3 +i) /2, etc. (i) cis 22°30', cis 112°30', etc. 
 
 General Review, pages 475-484 
 Chapters I-VI 
 I. 150. 3. 45000 lb. 4- 11984 lb., etc. 
 
 5. 146.45 sq. in. ; . . . ; 277.02 cu. in. 6. 320000; . . . ; 13500. 
 8. $197.72. 9. -3permin. 10. 2298 yd. 12. 3.2282. 
 13. 62.5; 127.93 sec. 14. 2560 lb. 
 
 15. 26.67 deg./sec2; 291600°. 
 
 Chapter Vn 
 
 1. 2a-/(a;2+l); 2.17145/x; --; a:(l+21oga;); eV(e*+l)2. 
 
 2. . . . ; log a:2o+C; V2 {e^^ -e-^') -2 x +C. 
 
 3. 1/5 e. 4- 22.14%. 5. F=20e-o6«r. 8. 1/ = 7.44/Va:. 
 
 Chapter VIU 
 
 .Vh,...59»2'. 4. <-^ + '-^^=1,x--20(.-2), 
 
 «% 16 
 
 5. (x -38400)2 = -102400 (?/- 14400); .... 
 
 8. ...; 3.75ft.; (0,^00/3); etc. 9. (a;-3)2+(?/-4)2 = 25. 
 
 Chapter IX 
 I. ±2.3142, ±.55786. 3. Two linear, one quadratic. 
 
 4. -1.6751, -.5392, 2.2143. 
 
ANSWERS TO EXERCISES xxiii 
 
 
 Chapter X 
 
 5. 
 
 40in./sec. 6. -5.878, -1525 per sec; ^ = ^120, etc. 
 
 
 Chapter XI 
 
 I. 
 
 COS0. 2. —% eosQ t+C; ...; — logcos0+C. 
 
 3. 
 
 -i/2[csc(9ctn0+log(csc0+ctn9)]+C; ...; - 1^2 cos 6 0-1.4 cos 2 0. 
 
 4. 
 
 10°33', 79°27', 190°33', 259°27'. 
 
 5. 
 
 56 33 56 16 63 16 
 ^+^^ -^' ^' -^'^'"' ^-^^ -i^' ^' -S' — 
 
 6. 
 
 .1 VlO; 2y25. 7. -2 sec. ; 8; -239.03 units per sec. 
 
 9 
 
 10.63, 5792; t = .003678; 127 times per sec. 
 
 Chapter XII 
 
 3. 16.5 7r M7-V8 7rloge(4+Vl7). [Use (44), (41), p. 497.] 4. 16. 
 
 Chapter Xin 
 2. $104, nearly. 3. $18.74+. 4. $65.90. 5. $4180, nearly. 
 
 Chapter XIV 
 I. 358800. 2. 15504. 3. 302,400. 
 
 4. 1.71 X 10-«. 5- -1285. 7. 36 meters nearer. 
 
 8. y = .90lx. 9- 2/ = 33.41+.52a:,x = 25.72+.61?/;i = .3172. 
 
 Chapter XV 
 I. . . . ; -2%7 + i%7 i. 2. cis 18°, i, . . . ; -; 1.3797 cis 10°37'.6, etc. 
 
 Miscellaneous 
 
 I. F = 9e-»«93ir. 50.9. 2. (x+iy+y^ = 4. 
 
 4. .342. 5. 45°, 90°, 210°, 225°, 270°, 330°. 
 
 6. 59°2'; 239°2'. 9. -2,V3,2.12. 10. .2 in. /sec; 5 in. 
 
 12. (6) 62500 TT lb. 13. 1,014,500 ft.-lb. 14. (a)xyix+l)K 
 
 14. (6)-(d) sec d tan 9] sec^ x; [x sin .t+ 2 (cos a: — 1)] -^ a:^^ 
 
 15. (a)-(c) -Vs csc3 «+C; Va {x^-100)^+C; .01 a:/ VlOO-x^+C. 
 
 16. 2.1752; .3466. 17. (?/ -9)7225 -xV400 = 1. 
 18. 5.8%. 19. Ellipse; ?/=±2VlO, x==i=2. 
 20. ...; .10256. 21. +$6.08. 23. 79°41'.7or36°52'.2. 
 
 24. ^260. 25. .26; .94. 26. ^ = 100 e-»o% Q = . 1986 +. 
 
 27.6.53ft. 29. 165. 30. 49.6; (10.85, -16.56);.... 
 
 31. 5 VlO, left and up 63 °26'; hyperbola; 69.31. 34. 80 ft. 
 
UNIVERSITY OF CALIFORNIA LIBRARY 
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 SEP 10 1956 
 
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