Solution Manual for Calculus and Its Applications: Brief Version, 12th Edition

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Solution Manual for Calculus and Its Applications: Brief Version, 12th Edition - Page 1 preview image

A-1ANSWERS: CHAPTER RTechnology Connection, p. 71.Left to the studentExercise Set R.1, p. 101.1−1−1−2−3−4−5−2−3−4−5234554321xyy=x− 12.1−1−1−2−3−4−5−2−3−4−5234554321xyy=x+ 43.1−1−1−2−3−4−5−2−3−4−5234554321xyy= −x144.yx–1–2122341–1–2–3–4–3–4–53455–5y= –3x5.1−1−1−2−3−4−5−2−3−4−5234554321xyy= −x+ 3536.yx–1–2122341–1–2–3–4–3–4–53455–52–3y=x– 47.1−1−1−2−3−4−5−2−3−4−5234554321xyx+y= 58.1−1−1−2−3−4−5−2−3−4−5234554321xyx−y= 49.1−1−1−2−3−4−5−2−3−4−5234554321xy6x+ 3y= −910.yx–1–2122341–1–2–3–4–3–4–53455–58y– 2x= 411.1−1−1−2−3−4−5−2−3−4−5234554321xy2x+ 5y= 1012.1−1−1−2−3−4−5−2−3−4−5234554321xy5x− 6y= 1213.1−1−1−2−3−4−5−2−3−4−5234554321xyy=x2− 514.1−1−1−2−3−4−5−2−3−4−5234554321xyy=x2− 315.1−1−1−2−3−4−5−2−3−4−5234554321xyx=y2+ 216.yx–1–2122341–1–2–3–4–3–4–53455–5x= 2 –y217.y=5y-1-2-1-3-4-5x12345-2234118.y= -2y-1-2-1-3-4-5x12345-3234119.1−1−1−2−3−2−3−4−523455476321xyy= 7 −x220.1−1−1−2−3−4−5−2−3−4−5234554321xyy= 5 −x221.1−1−1−2−3−4−52345543298761xyy− 7 =x322.1−1−1−2−3−4−5−2−3−4−5234554321xyy+ 1 =x3Answers

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Solution Manual for Calculus and Its Applications: Brief Version, 12th Edition - Page 2 preview image

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A-2A N S W E R S29. (a)f1x2=4x+2;(b)1−1−123455476321xyf(x) = 4x+ 230. (a)g1x2=-3x-4;(b)1−1−1−2−3−4−5−2−3−4−5234554321xyg(x) = −3x− 431. (a)h1x2=x2+x;(b)1−1−1−2−3−4−5234554321xyh(x) =x2+x32. (a)k1x2=x2-3x;(b)1−1−1−2−3−2−3−4−5234554321xyk(x) =x2− 3x33.1−1−1−2−3−4−5−2−3−4−5234554321xyf(x) = 2x− 534.1−1−1−2−3−4−5−2−3−4−5234554321xyf(x) = 3x− 135.yx–1–2122341g(x) = –4x–1–2–3–436.g(x) = −2x1−1−1−2−3−4−5−2−3−4−5234554321xy37.1−1−1−2−3−4−5−2−3−4−5234554321xyf(x) =x2− 238.1−1−1−2−3−4−52345543298761xyf(x) =x2+ 423.344.4 mg24.1954: 3.99 min, 2000: 3.71 min, 2025: 3.56 min25. (a)18.62°;(b)32.92°;(c)43.56°26. (a)35.5 mm;(b)93.5 mm;(c)in 202227. (a)3.50 million;(b)202428. (a)3.38 million;(b)3.28 million;(c)answers may vary.29.About 27.25 mi/hr30.About 1.32 sec31. (a)$102,800;(b)$102,819.60;(c)$102,829.54;(d)$102,839.46;(e)$102,839.5632. (a)$306,600;(b)$306,636.30;(c)$306,654.65;(d)$306,672.93;(e)$306,673.1333. (a)$33,745.92;(b)$33,784.87;(c)$33,804.75;(d)$33,824.68;(e)$33,824.9034. (a)$1215.51;(b)$1218.40;(c)$1219.89;(d)$1221.39;(e)$1221.4035.$536.2536.$389.9437.$70,561.0138.$1635.9939. (a)2008–2014;(b)2006–2008 and2014–2016;(c)2010, 9.6%;(d)2006–2007, 4.6%40.Answers may vary.41. (a)$88,382.67;(b)$42,000, $46,382.6742. (a)$653.76;(b)$117,676.80, $42,000, $75,676.8043.5.43%44.4.16%45.3.82%46.4.08%47. (a)Western 2.5%, Commonwealth 2.46%;(b)Western’s account48. (a)Sierra 3%, Foothill 3.01%;(b)Foothill’s account49.2.179%50.3.699%51.–10–1010100–2–2220The window3-2, 2,-2, 24shows better detail around the origin.52.–10–1010100The graph appears to touch thex-axis, but using a smaller windowreveals that it does not actually do so.Technology Connection, p. 161.951; 42,7012.21,813Exercise Set R.2, p. 201.Yes2.Yes3.Yes4.No5.Yes6.Yes7.Yes8.Yes9.Yes10.Yes11.No12.No13.Yes14.Yes15.Yes16.Yes17.No18.No19.Yes20.Yes21.No22.No23. (a)17.4, 17.04, 17.004, 17;(b)13, 9,-11, 4k-3,4x+4h-324. (a)14.3, 14.03, 14.003, 14;(b)17,-1, 3k+2,3x+3h+225.-2,-3,-2, 22,a2+2ah+h2-3, 2x+h, forh?026.13, 4, 5, 53,a2+2ah+h2+4, 2x+h, forh?027.149, 19,11a+322,11x+h+322,-2x-h-61x+h+3221x+32228.14, 136,11k-522,11x+h-522

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A N S W E R SA-367.1−1−1−2−3−4−52345543298761xyy=f(x)68.1−1−1−2−3−4−5−2−3−4−5234554321xyy=f(x)69.1−1−1−2−3−2−3−4−523455476321xyy=f(x)70.1−1−1−2−3−4−5−2−3−4−5234554321xyy=g(x)71.1−1−1−2−3−4−5−2−3−4−5234554321xyy=g(x)72.1−1−1−2−3−4−5−2−3−4−5234554321xyy=g(x)73.1−1−1−2−3−4−5−6−7−2−3−4−52345321xyy=f(x)74.1−1−1−2−3−4−5−6−2−3−4−5234554321xyy=f(x)75.$530.8076.$875.0577.(a)1.818 m2;(b)2.173 m2;(c)1.537 m278. (a)1.708 m2;(b)1.871 m279. (a)Yes;(b)yes;(c)no;(d)yes80. (a)Yes, a unique number that rates the scale of impact isassigned to each event.(b)The inputs are the events, the outputsare the scale-of-impact numbers.81.y=5; yes82.y={Ax+52; no83.y={2x; no84.y=223x; yes85.Answers may vary.86.2, 0,-2, 287.XX = −3Y1−10−8−1420142400842−3−11357988.XX = −3Y1.6ERROR−1−.75−1ERROR.6−3−2−1012389.Left to the student90.Left to the student91. (a)f1x2=51x+22,g1x2=5x+2;39.1−1−1−2−3−2−3−4−523455476321xyf(x) = 6 −x240.1−1−1−2−3−4−5−2−3−4−5234554321xyg(x) = −x2+ 141.yx128–84–41–1–1–2g(x) =x342.1−1−1−2−3−4−5−2−3−4−5234554321xyg(x) =x31243.Yes44.Yes45.No46.Yes47.Yes48.No49.Yes50.No51.Yes52.Yes53.Yes54.Yes55.No56.No57. (a)1−1−1−2−3−4−5−2−3−4−5234554321xyx=y2− 2(b)No, the graph fails the vertical-line test.58. (a)1−1−1−2−3−4−5−2−3−4−5234554321xyx=y2− 3(b)No, the graph fails the vertical-line test.59.2x+h-3, forh?060.2x+h+4, forh?061.3,-262.7, 663.17, 664.11, 3.565.yx–1–2122341–1–2–3–4–3–4–53455–5y=f(x)66.1−1−1−2−3−4−5−2−3−4−5234554321xyy=f(x)

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A- 4A N S W E R S36.32,`2[2,q)237.R(-q,q)38.R(-q,q)39.1-`, 22<12,`2(-q, 2)´(2,q)240.1-`, 22<12,`2(-q, 2)´(2,q)241.R(-q,q)42.R(-q,q)43.¢-`, 72≤<¢72,`≤72q,´,q7272-()()44.¢-`, 92≤<¢92,`≤92q,´,q9292-()()45.J-45,`≤45-45-[,q)46.¢-`, 23R2323(-q,]47.R(-q,q)48.R(-q,q)49.1-`,-52<1-5, 52<15,`2(-q,-5)´(-5, 5)´(5,q)-5550.1-`,-62<1-6, 62<16,`2(-q,-6)´(-6, 6)´(6,q)-6651.R(-q,q)52.R(-q,q)53.3-1, 34-13[-1, 3]54.J-32, 125R32-321251253-,455.3-1, 2456.5-5,-4,-3,-2,-1, 0, 1, 2, 3, 4, 5657.158.3-4, 2259.5-3, 4660.3-6, 4461.Domain: [0, 80], range: [0, 3200]62.Domain: [0, 200], range: [0, 10]63. (a)[25, 102];(b)[0, 455];(c)answers may vary.64. (a)[0, 92.3];(b)[0, 6,000,000];(c)answers may vary.65.(a)f142=15.5; the charge for the first mile is $5, andthen the charge for the next 3 mi is $3.50 each, giving a fare of$15.50 for a 4-mi trip;(b)f14.252=$19; the 0.25 mi is consid-ered part of a fourth additional mile after the first mile ischarged at the $5 rate, so the total fare is $19.00 for a trip of atleast 4 mi up to and including 5 mi.(c)The fares will be $5,$8.50, $12, and so on, in increments of $3.50, up to $36.50. Thus,the range is55, 8.5, 12, 15.5, 19, 22.5, 26, 29.5, 33, 36.56.66. (a)S1952=20; it costs $20 to ship an order totaling$95;(b)S11022=$15; it costs $151$20-$52to ship anorder totaling $102, since $2 is considered a part of an extra$20.(c)Orders totaling up to and including $120 will be shippedfor $15; those totaling up to and including $140 will be shipped for$10; those totaling up to and including $160 will be shipped for$5. Thus, any order totaling $160.01 or more will be shipped forfree.(d)The shipping charges are reduced in increments of $5.Thus, the range ofSis50, 5, 10, 15, 206(the ordering of theelements does not matter).67.30, 5268.1-`, 02<10, 3469.1-`,-32<1-3, 02<10, 32<13,`270.1-`,-32<1-3, 02<10, 42<14,`2(b)1−1−2−4−6−2−3−4234101214168642xyfg(c)no92. (a)f1x2=1x-422,g1x2=x2-4;(b)1−1−1−2−3−4−5−2−3−4−5234554321xygf(c)no93.h=294.h=9Exercise Set R.3, p. 311.1-1, 322.3-2, 443.(0, 5)4.3-1, 245.1-9,-546.3-9,-427.3x,x+h48.1x,x+h49.3-4,-12<12, 3410.1-`, 02<33,`211.3-2, 2410−1−2−3−4−5234512.1-5, 5210−1−2−3−4−5234513.(6, 20]1202468 1014 16 18 2014.3-4,-1210−1−2−3−4−5234515.1-3,`210−1−2−3−4−5234516.1-`,-2410−1−2−3−4−5234517.1-2, 3410−1−2−3−4−5234518.3-10, 4220−2−4−6−8−10468 1019.3-4,-32<10, 54[-4,-3)´(0, 5]10-1-2-3-4-5234520.1-`,-22<31, 42(-q,-2)´[1, 4)10-1-2-3-4-5234521. (a)3;(b)5-3,-1, 1, 3, 56;(c)3;(d)5-2, 0, 2, 3, 4622. (a)-1;(b)5-4,-3,-2,-1, 0, 1, 26;(c)-2;(d)5-2,-1, 0, 1, 2, 3, 4623. (a)4;(b)5-5,-3, 1, 2, 3, 4, 56;(c)-5,-3, 4;(d)5-3, 2, 4, 5624. (a)2;(b)5-6,-4,-2, 0, 1, 3, 46;(c)1, 3;(d)5-5,-2, 0, 2, 5625. (a)-1;(b)3-2, 44(c)3;(d)3-3, 3426. (a)2.5;(b)3-3, 54;(c)2;(d)[1, 4]27. (a)-2;(b)3-4, 24;(c)-2;(d)3-3, 3428. (a)About 2.3;(b)3-4, 34;(c)0;(d)3-5, 4429. (a)3;(b)3-3, 34;(c)at about-1.4and 1.4;(d)3-5, 4430. (a)2;(b)3-5, 44;(c)[1, 4];(d)3-3, 2431. (a)1;(b)3-5, 52;(c)33, 52;(d)5-2,-1, 0, 1, 2632. (a)2;(b)3-4, 44;(c)10, 24;(d)51, 2, 3, 4633.1-`, 22<12,`2(-q, 2)´(2,q)234.1-`,-32<1-3,`2(-q,-3)´(-3,q)-335.30,`2[0,q)0

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A N S W E R SA-571.Answers may vary. One example isf1x2=1x1x2-42.72.Answers may vary. One example isf1x2=1x1x+121x-72.73.Answers may vary.74.1-`,-54<35,`275.1-`,-14<34,`276.Answers may vary.Technology Connection, p. 401.Graphs are left to the student. The two lines are parallel;y=x-5is shifted down 5 units fromy=x.2.Left to the studentExercise Set R.4, p. 4411.m=4,y@intercept=10, 1212.m=3,y@intercept=10, 6213.m=-2,y@intercept=10, 3214.m=2,y@intercept=10, 3215.m=1,y@intercept=10, 2216.m=-1,y@intercept=10,-4217.m=13,y@intercept=a0,-73b18.m=-14,y@intercept=a0, 34b19. (a)y-7=71x-12;(b)y=7x20. (a)y+3=-51x+22;(b)y=-5x-1321. (a)y-3=-21x-22;(b)y=-2x+722. (a)y+2=-31x-52;(b)y=-3x+1323. (a)y-0=-51x-52;(b)y=-5x+2524. (a)y-0=21x-32;(b)y=2x-625. (a)y+6=121x-02;(b)y=12x-626. (a)y-7=431x-02;(b)y=43x+727. (a)y-8=0#1x-42;(b)y=828. (a)y-3=0#1x-22;(b)y=329. (a)m=2;(b)y=2x+3;(c)(0, 3)30. (a)m=4;(b)y=4x-19;(c)10,-19231. (a)m=1;(b)y=x+4;(c)(0, 4)32. (a)m=-4;(b)y=-4x+21;(c)(0, 21)33. (a)m=25;(b)y=25x-195(c)¢0,-195≤34. (a)m=16;(b)y=16x+236 ;(c)¢0,236≤35. (a)m=-95;(b)y=-95x-875 ;(c)¢0,-875≤36. (a)m=-193 ;(b)y=-193x-563 ;(c)¢0,-563≤37. (a)m=0;(b)y=6;(c)(0, 6); horizontal line38. (a)m=0;(b)y=-1;(c)10,-12; horizontal line39. (a)m=0;(b)y=0;(c)(0, 0); horizontal line40. (a)m=0;(b)y=0;(c)(0, 0); horizontal line41. (a)Undefined;(b)x=4;(c)noy-intercept; vertical line42. (a)Undefined;(b)x=-6;(c)noy-intercept; vertical line43. (a)Undefined;(b)x=0;(c)all points on they-axis are onthis line, which is vertical.44. (a)Undefined;(b)x=0;(c)all points on they-axis are onthis line, which is vertical.45. (a)m=13;(b)y=13x-1;(c)10,-1246. (a)m=154 ;(b)y=154x+6516;(c)¢0, 6516≤47. (a)m=815;(b)y=815x+115;(c)¢0, 115≤48. (a)m=-103 ;(b)y=-103x-76;(c)¢0, 76≤49. (a)m=32;(b)y=32x+k-32h;(c)¢0,k-32h≤50. (a)m=1;(b)y=x+v-u+3;(c)10,v-u+3251.0.45=0.08, or 8%52.25=0.4, or 40%9.1−1−1−2−2−3−4−5234554387621xyy= 7m= 0y-intercept: (0, 7)m=0,y@intercept=10, 7210.1−1−1−2−3−4−5−2−3−4−5234554321xyy= −5m= 0y-intercept: (0, −5)m=0,y@intercept=10,-521.1−1−1−2−3−4−5−2−3−4−5234554321xyy= −2xm= −2y-intercept: (0, 0)m=-2,y@intercept=10, 022.m= −3y-intercept: (0, 0)1−1−1−2−3−4−5−2−3−4−5234554321xyy= −3xm=-3,y@intercept=10, 023.1−1−1−2−3−4−5−2−3−4−5234554321xyf(x) = −0.5xm= −0.5y-intercept: (0, 0)m=-0.5,y@intercept=10, 024.1−1−1−2−3−4−5−2−3−4−5234554321xyf(x) = 0.5xm= 0.5y-intercept: (0, 0)m=0.5,y@intercept=10, 025.m= 3y-intercept: (0, −4)1−1−1−2−3−4−5−2−3−4−5234554321xyy= 3x− 4m=3,y@intercept=10,-426.1−1−1−2−3−4−5−2−3−4−5234554321xyy= 2x− 5m= 2y-intercept: (0, −5)m=2,y@intercept=10,-527.m= 1y-intercept: (0, −2.5)1−1−1−2−3−4−5−2−3−4−5234554321xyg(x) =x− 2.5m=1,y@intercept=10,-2.528.m= −1y-intercept: (0, 3)1−1−1−2−3−4−5−2−3−4−5234554321xyg(x) = −x+ 3m=-1,y@intercept=10, 32

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A-6A N S W E R S5.−2−4−6−8−10−12−14−16−1−21242xyy= −3x2y= −3x2+ 2Domain:1-`,`2, orR, forboth6.−1−2−3−4−5−6−7−8−1−21221xyy= −2x2y= −2x2+ 1Domain:1-`,`2, orR, forboth(b)4882;(c)answers may vary.82. (a)N=1.02P;(b)204,000 people;(c)360,000 people83. (a)19.7, 19.78,20.5, 23.7, 24.5;(b)25.3;(c)tA(t)102030405020212223Age (in years)Number of years after 1950242560A(t) = 0.08t+ 19.784.2585.Answers may vary.86. (a)III;(b)IV;(c)I;(d)II87.[0, 15]88.Left to the studentTechnology Connection, p. 511. (a)2, 4;(b)left to the studentTechnology Connection, p. 531.-2, 12.0,-1.414, 1.4143.0, 7004.-2.079, 0.463,3.1165.-0.387, 1.7216.-1.414, 1.414, 1,-2Technology Connection, p. 551.Left to the student2.Left to the studentExercise Set R.5, p. 6053.43.331238=0.035, or 3.5%54.69=0.666c, or about 66.7%55.55100=0.55, or 55%56.87100=0.87, or 87%57. (a)T1w2=0.000806w;(b)$2.9858. (a)I1s2=0.0057s;(b)18 cartridges59. (a)C1x2=3x+1,000,000;(b)R1x2=75x;(c)P1x2=72x-1,000,000;(d)profit of $9,800,000;(e)13,889 calculators-1063*1062*1061060y10,00020,000R(x)C(x)P(x)x60. (a)C1x2=80x+45,000;(b)R1x2=450x;(c)P1x2=370x-45,000;(d)profit of $1,065,000;(e)122 pairsR(x)C(x)P(x)$70,000xy$35,000−$35,00010020030040050061. (a)C1x2=4x+250;(b)R1x2=20x; $20(c)16 lawns62. (a)C1x2=5x+25,000;(b)R1x2=25x, $25;(c)1250 tickets63. (a)V1t2=5200-512.5t;(b)V102=$5200,V112=$4687.50,V122=$4175,V132=$3662.50,V142=$3150,V172=$1612.50,V182=$110064.About $743,59065.$25,20066. (a)The number-700 indicates that the value of the photo-copier decreases by $700 per year, and the number 3500 indicatesthat the original value of the copier was $3500.(b)5 yr;(c)[0, 5], which means that after 5 yr, the value is 067.About 91% (don’t round up for legal reasons!)68.About 33.3%69.$682.7570.$240.3871.$161.89/yr72.$2.56 billion/yr73. (a)R=4.17T;(b)2574.0.02 sec75. (a)M=0.4W;(b)M=40%W,which indicates that muscle weight is 40% of body weight;(c)48 lb76. (a)B=0.025W;(b)B=2.5%W, which indicates that brainweight is 2.5% of body weight;(c)4 lb77. (a)115 ft,75 ft, 135 ft, 179 ft.(b)For every increase of 1°F in the airtemperature, the stopping distance increases by 2 ft.(c)Answersmay vary.78. (a)6 ft, 11.5 ft, 22.5 ft, 55.5 ft, 72 ft;(b)rD(r)101020302030D(r) = 11r+ 510(c)For every 1-mph increasein speed, the braking distanceincreases by 1.1 ft.(d)Answers may vary.79. (a)145.78 cm;(b)142.98 cm80. (a)y=263.5x-530,129.5;(b)2140.5 million;(c)answers may vary.81. (a)y=289.75x+3143;1.1−1−1−2−3−4−5−2−3−4−5234554321xyy=x214y= −x214Domain:1-`,`2, orR, forboth2.xyy=x21–2y= −x21–2–2–112–2–112Domain:1-`,`2, orR, forboth3.y=x2y=x2− 11−1−1−2−3−2−3−4−523455476321xyDomain:1-`,`2, orR, forboth4.y=x2y=x2− 31−1−1−2−3−2−3−4−523455476321xyDomain:1-`,`2, orR, forboth

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Solution Manual for Calculus and Its Applications: Brief Version, 12th Edition - Page 8 preview image

A N S W E R SA-77.2−2−2−4−6−8−10−4−6−8−10468 10108642xyy= |x− 3|y= |x|Domain:1-`,`2, orR, forboth8.1−1−1−2−3−4−5−2−3−4−5234554321xyy=x− 1y=xDomain:1-`,`2, orR, forboth9.y=|x|0-5-5-105xy5y=|x+2|+11010Domain:1-`,`2, orR, forboth10.0-55xy5-5y=|x-3|-4y=|x|-101010Domain:1-`,`2, orR, forboth11.xyy=x3+ 1–2–112–8–4–1148y=x3Domain:1-`,`2, orR, forboth12.−2−4−6−8−10−1−212108642xyy=x3y=x3+ 2Domain:1-`,`2, orR, forboth13.12345123xyx− 1y=xy=Domains:30,`2and31,`214.y123456123xx−2y=xy=Domains:30,`2and32,`215.x+2-1y=xy=xy-2-112-11Domains:30,`2and3-2,`216.y05x510x-3+4y=xy=Domains:30,`2and33,`217. (a)1-2,-12,x=-2;(b)opens upward;(c)1-3, 02,1-1, 0218. (a)13,-42,x=3;(b)opens upward;(c)(1, 0), (5, 0)19. (a)1-4,-162,t=-4;(b)opens upward;(c)1-8, 02, (0, 0)20. (a)1-6, 362,t=-6;(b)opensdownward;(c)1-12, 02, (0, 0)21. (a)¢14, 338≤,s=14;(b)opens downward;(c)¢1-2334, 0≤,¢1+2334, 0≤22. (a)¢13, 73≤,r=13;(b)opens downward;25.1−1−1−2−3−4−5−2−3−4−5234554321xy3xy=Domain:1-`, 02<10,`226.–4 –3–2 –11 2 3 4–4–3–2–11234y= 2–xxyDomain:1-`, 02<10,`227.–4 –3–2–112 34–4–3–2–11234y= – 2–xxyDomain:1-`, 02<10,`228.1−1−1−2−3−4−5−2−3−4−5234554321xy3xy= −Domain:1-`, 02<10,`2(c)¢1-273, 0≤,¢1+273, 0≤23.(a)¢-65,-12150≤,x=-65;(b)opens upward;(c)¢-175 , 0≤,11, 0224. (a)¢-35,-6475≤,x=-35;(b)opens upward;(c)¢-115 , 0≤,11, 0229.1−1−1−2−3−4−5−2−3−4−5234554321xyy=1x− 1Domain:1-`, 12<11,`230.–2 –1121234xyy= 1—x2Domain:1-`, 02<10,`231.–4 –3–2 –11234–212–1xy3xy=Domain:1-`,`2, orR32.1−1−1−2−3−4−5−2−3−4−5234554321xyy=1xDomain:1-`, 02<10,`233.1−1−1−2−3−2−3−4−5−6−7−825476321xyg(x) =x2+ 7x+ 10x+ 2Domain:1-`,-22<1-2,`234.1−1−1−2−3−4−5−2−3−4−5−6−72354321xyf(x)=x2+ 5x+ 6x+ 3Domain:1-`,-32<1-3,`2

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Solution Manual for Calculus and Its Applications: Brief Version, 12th Edition - Page 9 preview image

A-8A N S W E R S90. (a)1.93 m2;(b)1.88 m2;(c)hf(h)10020012f(h) = 0.144h1/291.26, 5192.Answers may vary.93.Answers may vary.94.0, 1,-195.-1.831,-0.856, 3.18896.1.5, 9.597.1.489, 5.67398.-2.449, 2.44999.-2, 3100.No zeros101.3-1, 24102.-10.153,-1.871,-0.821,-0.303, 0.098, 0.535, 1.219, 3.297103.1+252104.1+252105.1+252106.All three problems translate into the same equation:x2-x-1=0.Exercise Set R.6, p. 721. (a)x-3-2-10123f1x2=4x0.01560.06250.25141664(b)300%;(c)(0, 1);(d)xy1614121086421-1-22y=4x2. (a)x-3-2-10123g1x2=5x0.0080.040.21525125(b)400%;(c)(0, 1);(d)y3024272118151296321x-2-1y=5x3. (a)x-3-2-10123h1x2=2#1.5x0.59260.88891.3333234.56.75(b)50%;(c)(0, 2);(d)y=2–1.5x1.02.0-2.0-1.021435xy35.x=1{2336.x=1{2537.x=-3{21038.x=-2{2739.x=1{22240.x=-1{22241.y=-4{210342.p=5{233443.x=-7{213244.w=1{25245.25x46.27t47.23y248.25t249.125t250.123y251.123b52.125b53.12x2+354.124y2+755.x3/2,xÚ056.x5/2,xÚ057.a3/558.b1/2,bÚ059.x3,xÚ060.t261.t-5/2,t?062.m-2,m?063.1x2+72-1/264.1x3+421/265.2766.102467.1668.469.1-`, 52<15,`270.1-`,-22<1-2,`271.1-`, 22<12, 32<13,`272.1-`,-52<1-5,-12<1-1,`273.J-45,`≤74.33,`275.1-`, 7476.1-`, 5477.(50, 500); quantity=50, price=$50078.(40, 7600); quantity=40, price=$760079.(5, 1); quantity=5000, price=$10080.(4, 1); quantity=4000, price=$10081.(1, 4); quantity=100, price=$482.(1, 9); quantity=100, price=$983.(2, 3); quantity=2000, price=$300084.(3, 4); quantity=3000, price=$400085.140 tickets86.120,00087. (a)166 mi, 176 mi, 184 mi;(b)xR(x)R(x) = 11.74x0.2540,00080,0002040608010012014016018020088.64.2, 93.3, 121.6, 149.3,176.5, 203.4;wH(w)H(w) = 0.059w0.9240008000200060005010015020025089. (a)10.43og/m3; 10.20og/m3; 10.03og/m3;(b)t1020304050p(t)2468101214p(t) = 12.85t−0.077

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Solution Manual for Calculus and Its Applications: Brief Version, 12th Edition - Page 10 preview image

A N S W E R SA-94. (a)x-3-2-10123k1x2=6#1.2x3.47224.1667567.28.6410.368(b)20%;(c)(0, 6);(d)y=6–1.2x5-54681012216142018xy1234-4-3-2-15. (a)xm1x2=-3#2.15x-3-0.3019-2-0.649-1-1.39530-31-6.452-13.86753-29.8151(b)115%;(c)10,-32;(d)y=-3–2.15x12-2-1-14-12-6-8-10-2-4xy6. (a)xn1x2=-2#3.04x-3-0.0712-2-0.2164-1-0.65790-21-6.082-18.48323-56.1889(b)204%;(c)10,-22;(d)y=-2–3.04x12-2-1-15-5-10xy7. (a)xp1x2=12,00010.952x-313,996.2094-213,296.3989-112,631.579012,000111,400210,830310,288.5(b)-5%;(c)(0, 12,000);(d)y=12,000(0.95)x43215-5-1-2-3-410,000500015,00020,000xy08. (a)xq1x2=75,000,00010.8752x-3111,953,352.8-297,959,183.7-185,714,285.7075,000,000165,625,000257,421,875350,244,140.6(b)-12.5%;(c)(0, 75,000,000);(d)y=75,000,000(0.875)x100,000,000150,000,000200,000,000y51234-5-4-3-2-1x50,000,0009. (a)xr1x2=r010.2332x-379.0555r0-218.4199r0-14.2918r00r010.233r020.0543r030.0126r0(b)-76.7%;(c)10,r02;(d)y=r0(0.233)xr012-2-1xy

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Solution Manual for Calculus and Its Applications: Brief Version, 12th Edition - Page 11 preview image

A-10A N S W E R S77. (a)A1t2=90011.0452t;(b)A152=1121.56, which meansthat in 2020 the student population will be about 1122;(c)after 6.54 yr (or in 2021)78. (a)P1t2=12,50011.02752t;(b)P182=15,529.76, which means that in 2023 the populationof Parker Valley will be about 15,530;(c)after 17.3 yr, or in 203279. (a)M1t2=5010.98752t;(b)M1152=41.4, which meansthat after 15 days the mass of the sample is 41.4 mg;(c)after 72.8days80. (a)q1t2=250010.9762t;(b)q1112=1913.76,which means that in 2022 the population of Tonopah Acreswill be 1914;(c)after 28.5 yr, or in 203981. (a)E1t2=55011.4712t;(b)E1102=26,090.92,which means that in 10 years there will be about 26,091 studentsenrolled in the online program;(c)after 5.72 yr (in the 6thyear)82. (a)G1t2=1511.2222t;(b)G1122=166.3,which means that after 12 months the company will have about166 employees;(c)after 14 months83.In 28.1 yr84.In 37.2 yr85.After 10.5 weeks86.After 6 months87.Left to the student88.Left to the student89.Left to the student90.Left to the student91.80907908092.125200720012593.1-`,-12<11,`2Technology Connection, p. 791. (a)Left to the student;(b)93.5;(c)left to the studentTechnology Connection, p. 811.y=0.0016278847x4-0.1814259451x3+6.716198092x2-91.87760958x+397.9916923;the fit of this equation is slightly better.2.Graphs are left to the student.(a)y=-58.21428571x2+5258.214286x-45,399.19643;(b)y=-0.305555555x3-17.42261905x2+3597.290675x-25,339.89435;(c)y=0.00416666666x4-1.047222222x3+29.25625x2+2380.242163x-14,388.75272;(d)quartic;(e)$48,667, $73,624Exercise Set R.7, p. 821.Linear2.Quadratic witha70or exponential with06a613.Quadratic witha604.Polynomial, neitherquadratic nor linear5.Quadratic witha706.Linear,possibly polynomial7.Linear8.Quadratic witha709.Exponential with 06a6110. (a)y=0.1167x+5.1;(b)$6.03 million, $6.62 million;(c)in 202811. (a)y=0.933x+63.2;(b)$71.6 billion12. (a)y=-44.333x2+188.667x;(b)45.3 mg;(c)answersmay vary.13. (a)y=237.5x2-1400x+54,762.5(b)$64,512.5014. (a)y=0.144x2-4.63x+60;(b)about 188.5 ft;(c)answers may vary.10. (a)xs1x2=s010.7522x-32.3515s0-21.7683s0-11.3298s00s010.752s020.5655s030.4253s0(b)-24.8%;(c)10,s02;(d)y=s0(0.752)xs012-2-1xy11.log464=312.log5625=413.log100.01=-2, orlog 0.01=-214.log7¢149≤=-215.log255=1216.log366=1217.log2166=1318.log322=1519.logPQ=n20.logrz=v21.27=12822.45=102423.107=10,000,00024.105=100,00025.161/2=426.1001/2=1027.71/3=23728.151/4=241529.90=130.p0=131.25632.102433.534.835.136.137.-238.-239.p40.2241.2.8073542.1.2920343.2.5237244.1.3562145.2.3219346.1.6356347.1.7324948.3.1699349.0.6131550.0.3154651.1.7124152.1.4581653.2.4306854.1.8856255.10.7696156.39.1696057.1.8962058.3.7887859.1.0301860.1.0936961.1.44962.1.53263.1.73264.2.01565.0.28366.1.04967.1.96668.2.24969.-0.48370.-0.76673.y=log4(x-3)y-1x1 247231109865-2-35xux73674.1-1-1-2-3-2-3-4-62346531xy2y=log3(x+5)5xux7 -5671.2012 14 16 182468 10xy-1231y=log3x-25xux70672.2012 14 16 182468 10xy-1231-2y=log5x5xux70675.123456789 10-1-22xy1y=log(2x-1)bxux712r76.23415-5-4-3-1-2-1-22xy1y=log2(2-3x)bxux623r

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Solution Manual for Calculus and Its Applications: Brief Version, 12th Edition - Page 12 preview image

A N S W E R SA-1115. (a)y=1.491x-33.549;(b)41%;(c)the estimate ishigher than the actual value.16. (a)y=1.274x-25.309;(b)about 26%;(c)the estimate is slightly higher than the actual value.17. (a)y=11.4211.022x;(b)33.9 million18. (a)y=1.46710.9832x;(b)0.57 million19. (a)y=108.70811.032x;(b)$354.62;(c)answers may vary.20. (a)y=26.24611.1892x;(b)$148.21;(c)answers may vary.21.Answers may vary.22.Answers may vary.23.(a)2, 32 , 1, so the average slope is 1.5;(b)y=1.5x-1.166666 . . . ;(c)they are the same.24.Answers may vary.25. (a)y=0.00648x2-0.884x+33.217;(b)5.2;(c)y=24.06810.9752x, which gives an estimate of about 6.9;(d)answers may vary.26. (a)y=-0.278x4+4.929x3-30.271x2+73.18x+15.757(b)-$127.5 million;(c)answers may vary.27. (a)Equation (4) is-24a-2b=495;(b)equation (5) is32a+2b=341;(c)a=8368=104.5;(d)b=-30032=-1501.5;(e)c=6016Chapter R Review Exercises, p. 931.(d)2.(b)3.(f)4.(a)5.(e)6.(g)7.(h)8.(c)9.True10.False11.True12.True13.False14.False15.True16. (a)4.1 million;(b)32 and 85;(c)[0, 92.3]17.$4177.9418.$13,402.4319.No. Elizabeth (input) hasthree outputs.20. (a)-6;(b)-30;(c)-a2+a;(d)-x2-2xh-h2+x+h21.f(x) = (x− 2)21−1−1−2−3−4−52345547698321xy22.1−1−1−2−3−4−5−2−3−4−5234554321xyy= |x−1|23.-10103-xx+4f(x)=yx-20-10102024.x+ 1g(x) =1−1−1−2−3−4−52345678954321xy25.No26.Yes27.Yes28.No29. (a)1;(b)3-4, 44;(c)-3;(d)3-1, 3430.(a)1, 4, 3;(b)1−1−1−2−3−4−5−2−3−4−5234554321xyy=f(x)31. (a)3-2, 54;(b)1-1, 34;(c)1-`,a2;(d)1-`,-14<33, 4232. (a)3-4, 5210−1−2−3−4−52345(b)(2,`)10−1−2−3−4−5234533. (a)-2;(b)5-3,-2,-1, 0, 1, 2, 36;(c)5-1, 36;(d)5-2, 1, 2, 3, 4634. (a)1-`, 52<15,`2;(b)3-6,`2;(c)12,`2;(d)[0, 5]35.Slope:-3,y-intercept: (0, 2)36.y=14x-737.-338.-$350>yr39.75 pages/day40.A=0.1V(c)1−1−1−2−3−4−5−2−3−4−5234554321xy1xy= −(d)1−1−1−2−3−4−5−2−3−4−5234554321xyy=x2+x− 6x− 244. (a)x=1,x=3;(b)x=2{210245. (a)x4/5;(b)t4;(c)m-2/3;(d)1x2-92-1/246. (a)25x2;(b)125m3;(c)2x2-5;(d)23t47.J92,`≤48. (a)1−1−1−2−3−42345x54321yy=•(4)x120,)(12(b)1−1−1−22345x54321yy= 3•x))14(0, 3)49. (a)2.3%;(b)25,209, which means that in 2023 the popula-tion of Arvon Hill will be 25,209;(c)after 19.4 yr, or in 203750. (a)M1t2=12510.9862t;(b)-1.4%/week;(c)after 65 weeks51. (a)1.256;(b)0.183;(c)1.49752.4, which is thepower to which 3 must be raised to give 8153.(3, 16);quantity=300, price=$1654.About 3.3 hr41. (a)C1x2=0.5x+4000;xyR(x)C(x)P(x)40006000$80002000−4000−2000200400600(b)R1x2=10x;(c)P1x2=9.5x-4000;(d)422 CDs42. (a)x− 3y=xy=1−1−1−2−3−4−52345678954321xy(b)1−1−1−2−3−4−5−2−3−4−5234554321xyy=x3y= (x− 1)343. (a)1−1−1−22345678xyf(x)=x2−6x+8547896321vertex:13,-12(b)2−2−1−2−3−4−5−4−6−8−10468 1054321xyx+ 23g(x)=

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Solution Manual for Calculus and Its Applications: Brief Version, 12th Edition - Page 13 preview image

A-12A N S W E R S14.4812–8–4–12–4–8–121284xyf(x) = 8x15.t-1/216.125t317.-1218.201030-10462xyx-4+1f(x)=19.3c,d220.1-2,`221.1-`,-72<1-7, 22<12,`222.–3 –2–1123–3–2–112345x2+ 2, forx≥ 0ex2–2, forx< 0f(x) =23.1−1−1−2−32345x54321yf(x)=•(3)x120,)(12¢0, 12≤24. (a)4.1%/yr;(b)after 10.09 yr25. (a)x10203040y1700180019002000210022002300240025002600(b)Yes;(c)y=-1.94x2+102.74x+1253.49;(d)About 2590 calories;(e)answers may vary.26.11627.Domain:¢-`, 53R,x-intercept:¢-79823, 0≤28.One possible equation isy=1x+321x-121x-42.29.51730.|9 –x2| – 13y=–101012–12Zeros:{28,{210;domain:1-`,`2;range:3-1,`231. (a)y=-1.51x2+79.98x+1436.93;(b)about 2480 calories;(c)answers may vary.55. (a)M=0.2r+160(b)r50607080M= 0.2r+ 160M170171172173174175176177(c)173.4 beats/min56. (a)Left to the student;(b)yes;(c)P=1.9975x2-89.8444x+870;(d)about-$27.56;(e)answers may vary.57. (a)525,375 lb;(b)$4.31/lb58.3-5, 5459.[1, 2]60.a=-1261.−1010400−400y=x3− 9x2+ 27x+ 50x=-1.25; domain andrange:1-`,`262.|4 −x2| + 13y=−10106−1no zeros; domain:1-`,`2,range:31,`263.1-1.21, 2.36264. (a)P=1.86x2-84.18x+943.86;(b)$95.46;(c)answers may vary.65. (a)Linear:A=-9.190819894x+697.05481; quadratic:A=0.0757317559x2-15.51100944x+801.4311225; cubic:A=0.0052352573x3-0.5849501976x2+9.082584281x+545.8186828;exponential:A=1014.88304610.96776035972x;(b)8000800y1=29.190819894x+697.05481y2=0.0757317559x2−15.51100944x+801.4311225y3=0.0052352573x3−0.5849501976x2+9.082584281x+545.8186828y4=1014.883046(0.9677603597)xy1y2y3y4(c)Answers may vary.Chapter R Test, p. 971.$7502. (a)-4;(b)-x2-2xh-h2+53.m=45;y@intercept:¢0,-23≤4.y=14x+3145.-126.-$700/yr;7.12lb/bag8.F=23W9.(a)C1x2=0.08x+8000;(b)R1x2=0.50x;(c)P1x2=0.42x-8000;(d)19,048 cards10.(3, 25);quantity=3000, price=$2511.Yes12.No13. (a)-4;(b)1-`,`2;(c)5-3, 36;(d)3-5,`2

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Solution Manual for Calculus and Its Applications: Brief Version, 12th Edition - Page 14 preview image

A N S W E R SA-13Extended Technology Application, p. 991. (a)P1t2=0.1267032967t-0.5842857143;(b)y1070100(c)$8.28, $8.92, answersmay vary;(d)2112, which seems too farinto the future.2. (a)P1t2=0.0014796703t2+0.0305247253t+0.3775;(b)y2070100(c)$9.76, $10.99,answersmay vary;(d)2055, which is plausible.3. (a)P1t2=-0.00000183t3+0.0016588147t2+0.0260369288t+0.3972058824;(b)y3070100(c)$9.72, $10.91,answersmay vary;(d)2057, which is alsoplausible.4. (a)P1t2=0.00000046249829t4-0.00006196216t3+0.004115011t2-0.006602236t+0.4680672269;(b)y4070100(c)$10.02, $11.61,answersmay vary;(d)2042, which is plausible,but may be too soon.5. (a)P1t2=0.543038902411.0473325332t;(b)y5070100(c)$13.83, $17.43,answersmay vary;(d)2028, which is probably toosoon.6.Answers may vary.

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Solution Manual for Calculus and Its Applications: Brief Version, 12th Edition - Page 15 preview image

A N S W E R SA-63ANSWERS: DIAGNOSTICTEST, p. xviiPart AThe red bracketed references indicate where worked-out solutionscan be found in Appendix A: Review of Basic Algebra. Forexample, [Ex. 1] means that the problem is worked out inExample 1 of the appendix.1.64 [Ex. 1]2.-32 [Ex. 1]3.18[Ex. 1]4.-2x[Ex. 2]5.1 [Ex. 2]6.1x5[Ex. 3]7.16 [Ex. 3]8.1t[Ex. 3]9.x11[Ex. 4]10.x7[Ex. 4]11.40x3[Ex. 4]12.a[Ex. 5]13.b8[Ex. 5]14.1x6[Ex. 6]15.y158x12z9[Ex. 6]16.3x-15 [Ex. 7]17.x2-2x-15 [Ex. 7]18.a2+2ab+b2[Ex. 7]19.4x2-4xt+t2[Ex. 8]20.9c2-d2[Ex. 8]21.h12x+h2[Ex. 9]22.1x-3y22[Ex. 9]23.1x+221x-72[Ex. 9]24.12x-1213x+52[Ex. 9]25.1x-721x+221x-22[Ex. 10]26.x=6 [Ex. 11]27.x=0, 2,-45[Ex. 12]28.x=0,12,-12[Ex. 13]29.No solution [Ex. 15]30.x…2113or1-`,21134[Ex. 17]31.660 lb [Ex. 19]32.199 suits [Ex. 20]Part BThe red bracketed references indicate where worked-out solutionscan be found in Chapter R. For example, [Ex. R.2.5] means thatthe problem is worked out in Example 5 of Section R.2.1.242224222424xyy52x11[Ex. R.1.1]2.24222422426xy3x15y510[Ex. R.1.2]3.y5x221242224224268xy[Ex. R.1.3]4.6482222424xyx5y2[Ex. R.1.4]5.g102=8;g1-52=143;g17a2=147a2-14a+8[Ex. R.2.4]6.x=4 [Ex. R.2.4]7.213213212242221xyf(x)54,32x2,2x26,forx$0,for 0,x#2,forx.2.[Ex. R.2.8]8.1-4, 52[Ex. R.3.1a]9.5xuxis any real numberandx?526or1-`,522h152,`2[Ex. R.3.5]10.Slopem=12;y-intercept:10,-742[Ex. R.4.6]11.y=3x-2 [Ex. R.4.7]12.m=-32[Ex. R.4.1]13.x=5 [Ex. R.6.7]14.x=-2 [Ex. R.6.7]15.24622242242xyf(x)5x222x2324[Ex. R.5.1]16.242224222424xyg(x)5x3[Ex. R.5.4]17.242224222424xyf(x)51x[Ex. R.5.5]18.f(x)5|x|24222422426xy[Ex. R.5.7]19.f(x)5 2√x64822224262xy[Ex. R.5.8]20.$1102.50 [Ex. R.1.6]

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Solution Manual for Calculus and Its Applications: Brief Version, 12th Edition - Page 16 preview image

A-14A N S W E R S69.1-1-1-2-3-223456785476321xyg(x)=2x-5x-32, does not exist70.1-1-1-2-3-4-5-6-723543298761xyg(x)=4x+9x+24, does not existANSWERS: CHAPTER 1Exercise Set 1.1, p. 1121.0.3,xS0.3-2.1.7,xS1.7+3.-3,xS -3-4.-4.9,xS -4.9+5.23,xS1232-6.43,xS1432-7.0.3,xS0.3-8.1.2,xS1.2-9.1,xS1+10.0,xS0-11.-212.713.limxS2+14.limxS3-15.limxS516.limxS1217.“the limit,asxapproaches 4, off1x2” or “the limit off1x2asxapproaches 4”18.“the limit, asxapproaches 1, ofg1x2” or “the limit ofg1x2asxapproaches 1”19.“the limit, asxapproaches 5 from the left, ofF1x2” or “the limit ofF1x2asxapproaches 5 from the left”20.“the limit, asxapproaches 4 from the right, ofG1x2” or “thelimit ofG1x2asxapproaches 4 from the right”21. (a)-3;(b)-3;(c)-322. (a)1;(b)2;(c)does not exist23. (a)-1;(b)-1;(c)-124. (a)4;(b)2;(c)does notexist25.526.427.Does not exist28.029.230.031.232.433.134.335.436.-137.038.Does not exist39.040.041.042.143.144.145.446.247.148.Does not exist49.150.151.-152.153.254.Does not exist55.Does not exist56.057.058.359.260.161.1-1-1-2-3-4-5-2-3-4-5234554321xyf(x)=ƒxƒ0, 262.f(x)=x21-1-1-2-3-4-52345543298761xy1, 077.H12345-1-2-3-4-5-5-4-3-2-112345xydoes not exist, 278.G24-2-42468xy1, 979.$3.50, $3.50, $3.5080.$3.00, $3.50, does not exist81.$4.00, $4.50, does not exist82.$1.00, $1.21, does not exist83.$1.21, $1.42, does not exist84.$1.42, $1.42, $1.4285.Does not exist86.$1.6387.10%, 12%, does not exist88.12%, 12%, 12%89.22%, does not exist90.10%, 10%, 10%91.12%, 22%, does not exist92.22%, does not exist93.394.-395.-196. (a)0;(b)2;(c)answers may vary.97. (a)4;(b)4,(c)4;(d)4;(e)4;(f)no;(g)yes98.Does not exist, 299.0, 0100.Does not exist,1663.g(x)=x2-51-1-1-2-3-4-5-2-3-4-5234554321xy-5,-464.1-1-1-2-3-4-2-3-4-52345546321xyg(x)=ƒxƒ+14, 165.1-1-5-4-3-2-1-2-3-4-5-6-72354321xyG(x)=4x+24, does not exist66.1-1-5-4-3-2-1-2234567854321xyF(x)=2x-3does not exist, 267.1-1-1-2-3-4-5-6-7-2-3-4-52345321xyf(x)=1-2xx-2, does not exist68.1-1-1-2-2-3-4-5234554678321xyf(x)=1+3xx3, does not exist71.1-1-1-2-3-4-5-2-3-4-5234554321xFy3, 1, does not exist72.1-1-1-2-2-323456754786321xGy1, 3, does not exist73.1-1-1-2-3-223456785476321xyg1, 0, does not exist74.12345-1-2-3-4-5-5-4-3-2-112345xyf-1,-1,-175.F12-1-2-3-1123xy-176.G12-1-2-11234xy1

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