Applied Mathematics For The Managerial, Life, And Social Sciences, 6th Edition Solution Manual

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CONTENTSCHAPTER 1Fundamentals of Algebra11.1Real Numbers11.2Polynomials31.3Factoring Polynomials61.4Rational Expressions81.5Integral Exponents121.6Solving Equations141.7Rational Exponents and Radicals211.8Quadratic Equations251.9Inequalities and Absolute Value35Chapter 1 Review41Chapter 1 Before Moving On47CHAPTER 2Functions and Their Graphs492.1The Cartesian Coordinate System and Straight Lines492.2Equations of Lines512.3Functions and Their Graphs612.4The Algebra of Functions712.5Linear Functions782.6Quadratic Functions842.7Functions and Mathematical Models93Chapter 2 Review101Chapter 2 Before Moving On107CHAPTER 3Exponential and Logarithmic Functions1113.1Exponential Functions1113.2Logarithmic Functions1173.3Exponential Functions as Mathematical Models122Chapter 3 Review127Chapter 3 Before Moving On130v

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viCONTENTSCHAPTER 4Mathematics of Finance1334.1Compound Interest1334.2Annuities1394.3Amortization and Sinking Funds1444.4Arithmetic and Geometric Progressions155Chapter 4 Review158Chapter 4 Before Moving On162CHAPTER 5Systems of Linear Equations and Matrices1675.1Systems of Linear Equations: An Introduction1675.2Systems of Linear Equations: Unique Solutions1725.3Systems of Linear Equations: Underdetermined and Overdetermined Systems1865.4Matrices1965.5Multiplication of Matrices2025.6The Inverse of a Square Matrix213Chapter 5 Review231Chapter 5 Before Moving On240CHAPTER 6Linear Programming2456.1Graphing Systems of Linear Inequalities in Two Variables2456.2Linear Programming Problems2516.3Graphical Solutions of Linear Programming Problems2606.4The Simplex Method: Standard Maximization Problems2806.5The Simplex Method: Standard Minimization Problems309Chapter 6 Review330Chapter 6 Before Moving On343CHAPTER 7Sets and Counting3497.1Sets and Set Operations3497.2The Number of Elements in a Finite Set3547.3The Multiplication Principle3607.4Permutations and Combinations3637.5Experiments, Sample Spaces, and Events369

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CONTENTSvii7.6Probability3727.7Rules of Probability376Chapter 7 Review382Chapter 7 Before Moving On386CHAPTER 8Additional Topics in Probability3898.1Use of Counting Techniques in Probability3898.2Conditional Probability and Independent Events3938.3Bayes’Theorem4018.4Distributions of Random Variables4108.5Expected Value4138.6Variance and Standard Deviation418Chapter 8 Review425Chapter 8 Before Moving On428CHAPTER 9The Derivative4319.1Limits4319.2One-Sided Limits and Continuity4399.3The Derivative4489.4Basic Rules of Differentiation4619.5The Product and Quotient Rules; Higher-Order Derivatives4699.6The Chain Rule4809.7Differentiation of Exponential and Logarithmic Functions4929.8Marginal Functions in Economics499Chapter 9 Review503Chapter 9 Before Moving On514CHAPTER 10Applications of the Derivative52310.1Applications of the First Derivative52310.2Applications of the Second Derivative53710.3Curve Sketching55010.4Optimization I57110.5Optimization II586Chapter 10 Review594Chapter 10 Before Moving On609

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viiiCONTENTSCHAPTER 11Integration61511.1Antiderivatives and the Rules of Integration61511.2Integration by Substitution62311.3Area and the Definite Integral63011.4The Fundamental Theorem of Calculus63311.5Evaluating Definite Integrals63811.6Area Between Two Curves64511.7Applications of the Definite Integral to Business and Economics655Chapter 11 Review659Chapter 11 Before Moving On667CHAPTER 12Calculus of Several Variables67312.1Functions of Several Variables67312.2Partial Derivatives67812.3Maxima and Minima of Functions of Several Variables684Chapter 12 Review693Chapter 12 Before Moving On698

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1FUNDAMENTALS OF ALGEBRA1.1Real NumbersConcept Questionspage 61.The set of natural numbers isN= {1,2,3, . . .}; the set of whole numbers isW= {0,1,2,3, . . .}; the set of integersisI= {. . .,−3,−2,−1,0,1,2,3, . . .}; the set of rational numbers isQ= {a/b|aandbare integers andb/=0}(example: 1/2), and the set of irrational numbers contains all real numbers that cannot be expressed in the forma/b, whereaandbare integers andb/=0 (example:π). The set of real numbers contains all irrational and rationalnumbers.2. a.The associative law of addition states thata+(b+c)=(a+b)+c.b.The distributive law states thatab+ac=a(b+c).3.Ifab/=0, then neitheranorbis equal to zero. Ifabc/=0, then none ofa,b, andcis equal to zero.Exercisespage 61.The number−3 is an integer, a rational number, and a real number.2.The number−420 is an integer, a rational number, and a real number.3.The number38is a rational real number.4.The number−4125is a rational real number.5.The number√11 is an irrational real number.6.The number−√5 is an irrational real number.7.The numberπ2is an irrational real number.8.The number2πis an irrational real number.9.The number 2.421 is a rational real number.10.The number 2.71828. . .is an irrational real number.11.False.−2 is not a whole number.12.True.13.True.14.True.15.False. No natural number is irrational.16.True.17.(2x+y)+z=z+(2x+y): The Commutative Law of Addition.18.3x+(2y+z)=(3x+2y)+z: The Associative Law of Addition.19.u(3v+w)=(3v+w)u: The Commutative Law of Multiplication.20.a2bb2cc=ba2b2cc: The Associative Law of Multiplication.1

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21FUNDAMENTALS OF ALGEBRA21.u(2v+w)=2uv+uw: The Distributive Law.22.(2u+v) w=2uw+vw: The Distributive Law.23.(2x+3y)+(x+4y)=2x+d3y+(x+4y)e: The Associative Law of Addition.24.(a+2b) (a−3b)=a(a−3b)+2b(a−3b): The Distributive Law.25.a−[−(c+d)]=a+(c+d): Property 1 of negatives.26.−(2x+y)d−(3x+2y)e=(2x+y) (3x+2y): Property 3 of negatives.27.0(2a+3b)=0: Property 1 involving zero.28.If(x−y) (x+y)=0, thenx=yorx= −y. Property 2 involving zero.29.If(x−2) (2x+5)=0, thenx=2, orx= −52. Property 2 involving zero.30.Ifx(2x−9)=0, thenx=0 orx=92. Property 2 involving zero.31.(x+1) (x−3)(2x+1) (x−3)=x+12x+1 . Property 2 of quotients.32.(2x+1) (x+3)(2x−1) (x+3)=2x+12x−1 . Property 2 of quotients.33.a+bb÷a−bab=a(a+b)a−b. Properties 2 and 5 of quotients.34.x+2y3x+y÷x6x+2y=x+2y3x+y·2(3x+y)x=2(x+2y)x. Properties 2 and 5 of quotients and the Distributive Law.35.ab+c+cb=ab+bc+c2b(b+c). Property 6 of quotients and the Distributive Law.36.x+yx+1−yx=x2−yx(x+1). Property 7 of quotients and the Distributive Law.37.False. Considera=2 andb=12. Thenab=1, buta/=1 andb/=1.38.True. Multiplying both sides of the equation by 1a(which exists becausea/=0), we have 1a(ab)=1a(0), orb=0.39.False. Considera=3 andb=2. Thena−b=3−2/=b−a=2−3= −1.40.False. Considera=3 andb=2. Thenab=32/=ba=23 .41.False. Considera=1,b=2, andc=3. Then(a−b)−c=(1−2)−3= −4/=a−(b−c)=1−(2−3)=2.42.False. Considera=1,b=2, andc=3. Thenab/c=12/3=32/=a/bc=1/23=16 .

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1.2POLYNOMIALS31.2PolynomialsConcept Questionspage 131.A polynomial of degreeninxis an expression of the formanxn+an−1xn−1+ · · · +a1x+a0, wherenisa nonnegative integer anda0,a1, . . . ,anare real numbers withan/=0. One polynomial of degree 4 inxisx4+2x3−2x2−5x−7.2. (a)1+2b+b2b.a2−2ab+b2c.a2−b2Exercisespage 131.34=3·3·3·3=81.2.(−2)5=(−2) (−2) (−2) (−2) (−2)= −32.3.r23s3=r23s r23s r23s=8274.r−34s2=r−34s r−34s=916.5.−34= −3·3·3·3= −81.6.−r−45s3= −r−45s r−45s r−45s=64125.7.−3r35s3=(−3)r35s r35s r35s= −81125.8.r−23s2r−34s3=r49s r−2764s= −316.9.23·25=28=256.10.(−3)2·(−3)3=(−3)5= −243.11.(3y)2(3y)3=(3y)5=243y5.12.(−2x)3(−2x)2=(−2x)5= −32x5.13.(2x+3)+(4x−6)=2x+3+4x−6=6x−3.14.(−3x+2)−(4x−3)= −3x+2−4x+3= −7x+5.15.b7x2−2x+5c+b2x2+5x−4c=7x2−2x+5+2x2+5x−4=7x2+2x2−2x+5x+5−4=9x2+3x+1.16.b3x2+5x y+2yc+b4−3x y−2x2c=x2+2x y+2y+4.17.b5y2−2y+1c−by2−4y−8c=5y2−2y+1−y2+4y+8=5y2−y2−2y+4y+1+8=4y2+2y+9.18.b2x2−3x+4c−b−x2+2x−6c=2x2−3x+4+x2−2x+6=3x2−5x+10.19.b2.4x3−3x2+1.7x−6.2c−b1.2x3+1.2x2−0.8x+2c=2.4x3−3x2+1.7x−6.2−1.2x3−1.2x2+0.8x−2=1.2x3−4.2x2+2.5x−8.2.20.b1.4x3−1.2x2+3.2c−b−0.8x3−2.1x−1.8c=1.4x3−1.2x2+3.2+0.8x3+2.1x+1.8=2.2x3−1.2x2+2.1x+5.21.b3x2c b2x3c=6x5.22.b−2rs2c b4r2s2c(2s)= −16r3s5.23.−2xbx2−2c+4x3= −2x3+4x+4x3=2x3+4x.

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41FUNDAMENTALS OF ALGEBRA24.x y(2y−3x)=2x y2−3x2y.25.2m(3m−4)+m(m−1)=6m2−8m+m2−m=7m2−9m.26.−3xb2x2+3x−5c+2xbx2−3c= −6x3−9x2+15x+2x3−6x= −4x3−9x2+9x.27.3(2a−b)−4(b−2a)=6a−3b−4b+8a=6a+8a−3b−4b=14a−7b.28.2(3m−1)−3(−4m+2n)=6m−2+12m−6n=18m−6n−2.29.(2x+3) (3x−2)=2x(3x−2)+3(3x−2)=6x2−4x+9x−6=6x2+5x−6.30.(3r−1) (2r+5)=3r(2r+5)−(2r+5)=6r2+15r−2r−5=6r2+13r−5.31.(2x−3y) (3x+2y)=2x(3x+2y)−3y(3x+2y)=6x2+4x y−9x y−6y2=6x2−5x y−6y2.32.(5m−2n) (5m+3n)=5m(5m+3n)−2n(5m+3n)=25m2+15mn−10mn−6n2=25m2+5mn−6n2.33.(3r+2s) (4r−3s)=3r(4r−3s)+2s(4r−3s)=12r2−9rs+8rs−6s2=12r2−rs−6s2.34.(2m+3n) (3m−2n)=2m(3m−2n)+3n(3m−2n)=6m2−4mn+9mn−6n2=6m2+5mn−6n2.35.(0.2x+1.2y) (0.3x−2.1y)=0.2x(0.3x−2.1y)+1.2y(0.3x−2.1y)=0.06x2−0.42x y+0.36x y−2.52y2=0.06x2−0.06x y−2.52y2.36.(3.2m−1.7n) (4.2m+1.3n)=3.2m(4.2m+1.3n)−1.7n(4.2m+1.3n)=13.44m2+4.16mn−7.14mn−2.21n2=13.44m2−2.98mn−2.21n2.37.(2x−y)b3x2+2yc=2xb3x2+2yc−yb3x2+2yc=6x3−3x2y+4x y−2y2.38.b3m−2n2c b2m2+3nc=3mb2m2+3nc−2n2b2m2+3nc=6m3+9mn−4m2n2−6n3.39.(2x+3y)2=(2x)2+2(2x) (3y)+(3y)2=4x2+12x y+9y2.40.(3m−2n)2=(3m)2−2(3m) (2n)+(2n)2=9m2−12mn+4n2.41.(2u−v) (2u+v)=(2u)2−v2=4u2−v2.42.(3r+4s) (3r−4s)=(3r)2−(4s)2=9r2−16s2.43.(2x−1)2+3x−2bx2+1c+3=4x2−4x+1+3x−2x2−2+3=2x2−x+2.44.(3m+2)2−2m(1−m)−4=9m2+12m+4−2m+2m2−4=11m2+10m.45.(2x+3y)2−(2y+1) (3x−2)+2(x−y)=4x2+12x y+9y2−6x y−3x+4y+2+2x−2y=4x2+6x y+9y2−x+2y+2.46.(x−2y) (y+3x)−2x y+3(x+y−1)=x y+3x2−2y2−6x y−2x y+3x+3y−3=3x2−7x y−2y2+3x+3y−3.

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1.2POLYNOMIALS547.bt2−2t+4c b2t2+1c=bt2−2t+4c b2t2c+bt2−2t+4c(1)=2t4−4t3+8t2+t2−2t+4=2t4−4t3+9t2−2t+4.48.b3m2−1c b2m2+3m−4c=3m2b2m2+3m−4c−b2m2+3m−4c=6m4+9m3−12m2−2m2−3m+4=6m4+9m3−14m2−3m+4.49.2x− {3x−[x−(2x−1)]} =2x− {3x−[x−2x+1]} =2x−[3x−(−x+1)]=2x−(3x+x−1)=2x−(4x−1)=2x−4x+1= −2x+1.50.3m−2{m−3 [2m−(m−5)]+4} =3m−2 [m−3(2m−m+5)+4]=3m−2 [m−3(m+5)+4]=3m−2(m−3m−15+4)=3m−2(−2m−11)=3m+4m+22=7m+22.51.x− {2x−[−x−(1+x)]} =x−[2x−(−x−1−x)]=x−[2x−(−2x−1)]=x−(2x+2x+1)=x−4x−1= −3x−1.52.3x2−jx2+1−x[x−(2x−1)]k+2=3x2−dx2+1−x(x−2x+1)e+2=3x2−dx2+1−x(−x+1)e+2=3x2−bx2+1+x2−xc+2=3x2−2x2−1+x+2=x2+x+1.53.(2x−3)2−3(x+4) (x−4)+2(x−4)+1=(2x)2−2(2x) (3)+32−3bx2−16c+2x−8+1=4x2−12x+9−3x2+48+2x−7=x2−10x+50.54.(x−2y)2+2(x+y) (x−3y)+x(2x+3y+2)=x2−2x(2y)+(2y)2+2bx2−3x y+x y−3y2c+2x2+3x y+2x=x2−4x y+4y2+2x2−4x y−6y2+2x2+3x y+2x=5x2−5x y−2y2+2x.55.2x{3x[2x−(3−x)]+(x+1) (2x−3)} =2xd3x(2x−3+x)+2x2−3x+2x−3e=2xd3x(3x−3)+2x2−x−3e=2xb9x2−9x+2x2−x−3c=2xb11x2−10x−3c=22x3−20x2−6x.56.−3d(x+2y)2−(3x−2y)2+(2x−y) (2x+y)e= −3dx2+4x y+4y2−b9x2−12x y+4y2c+b4x2−y2ce= −3bx2+4x y+4y2−9x2+12x y−4y2+4x2−y2c= −3b−4x2+16x y−y2c=12x2−48x y+3y2.57.The total weekly profit is given by the revenue minus the cost:b−0.04x2+2000xc−b0.000002x3−0.02x2+1000x+120,000c= −0.04x2+2000x−0.000002x3+0.02x2−1000x−120,000= −0.000002x3−0.02x2+1000x−120,000.58.The total revenue is given byx p=x(−0.0004x+10)= −0.0004x2+10x. Therefore, the total profit is given bythe revenue minus the cost:−0.0004x2+10x−b0.0001x2+4x+400c= −0.0005x2+6x−400.59.The total revenue is given byb0.2t2+150tc+b0.5t2+200tc=0.7t2+350tthousand dollarstmonths from now,where 0≤t≤12.

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61FUNDAMENTALS OF ALGEBRA60.In montht, the revenue of the second gas station will exceed that of thefirst gas station byb0.5t2+200tc−b0.2t2+150tc=0.3t2+50tthousand dollars, where 0<t≤12.61.The gap is given byb3.5t2+26.7t+436.2c−(24.3t+365)=3.5t2+2.4t+71.2.62.The difference is given byb2.5t2+18.5t+509c−b−1.1t2+29.1t+429c=3.6t2−10.6t+80 dollars. Thedifference at the beginning of 1998 is obtained by replacingtwith 4, giving 3.6(4)2−10.6(4)+80=95.2, or$95.20. The difference at the beginning of 2000 is given by 3.6(6)2−10.6(6)+80=146, or $146.63.False. Leta=2,b=3,m=3, andn=2. Then 23·32=8·9=72/=(2·3)3+2=65.64.True.65.False. For example,x2+1 is a polynomial of degree 2 andxis a polynomial of degree 1, butbx2+1cx=x3+xis a polynomial of degree 3, not 2.66.False. For example,p=x3+x+1 is a polynomial of degree 3 andq= −x3+2 is a polynomial of degree 3, butp+q=x3+x+1+b−x3+2c=x+3 is a polynomial of degree 1.67.The degree ofp−qism. To see this, suppose thatp=amxm+ · · · +anxn+ · · · +a0andq=bnxn+ · · · +b0.Becausem>n,p−q=amxm+ · · · +(an−bn)xn+ · · · +(a0−b0)has degreem.1.3Factoring PolynomialsConcept Questionspage 191.A polynomial is completely factored over the set of integers if it is expressed as a product of prime polynomialswith integral coefficients. An example is 4x2−9y2=(2x−3y) (2x+3y).2. a.(a+b)ba2−ab+b2cb.(a−b)ba2+ab+b2cExercisespage 191.6m2−4m=2m(3m−2).2.4t4−12t3=4t3(t−3).3.9ab2−6a2b=3ab(3b−2a).4.12x3y5+16x2y3=4x2y3b3x y2+4c.5.10m2n−15mn2+20mn=5mn(2m−3n+4).6.6x4y−4x2y2+2x2y3=2x2yb3x2−2y+y2c.7.3x(2x+1)−5(2x+1)=(2x+1) (3x−5).8.2ub3v2+wc+5vb3v2+wc=b3v2+wc(2u+5v).9.(3a+b) (2c−d)+2a(2c−d)2=(2c−d)[3a+b+2a(2c−d)]=(2c−d) (3a+b+4ac−2ad).10.4uv2(2u−v)+6u2v (v−2u)=b4uv2−6u2vc(2u−v)=2uv (2u−v) (2v−3u).11.2m2−11m−6=(2m+1) (m−6).12.6x2−x−1=(3x+1) (2x−1).13.x2−x y−6y2=(x−3y) (x+2y).14.2u2+5uv−12v2=(2u−3v) (u+4v).

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1.3FACTORING POLYNOMIALS715.x2−3x−1 is prime.16.m2+2m+3 is prime.17.4a2−b2=(2a−b) (2a+b).18.12x2−3y2=3b4x2−y2c=3(2x−y) (2x+y).19.u2v2−w2=(uv)2−w2=(uv−w) (uv+w).20.4a2b2−25c2=(2ab)2−(5c)2=(2ab−5c) (2ab+5c).21.z2+4 is prime.22.u2+25v2is prime.23.x2+6x y+y2is prime.24.4u2−12uv+9v2=(2u−3v)2.25.x2+3x−4=(x+4) (x−1).26.3m3+3m2−18m=3mbm2+m−6c=3m(m+3) (m−2).27.12x2y−10x y−12y=2yb6x2−5x−6c=2y(3x+2) (2x−3).28.12x2y−2x y−24y=2yb6x2−x−12c=2y(3x+4) (2x−3).29.35r2+r−12=(7r−4) (5r+3).30.6uv2+9uv−6v=3v (2uv+3u−2).31.9x3y−4x y3=x yb9x2−4y2c=x yd(3x)2−(2y)2e=x y(3x−2y) (3x+2y).32.4u4v−9u2v3=u2vb4u2−9v2c=u2vd(2u)2−(3v)2e=u2v (2u−3v) (2u+3v).33.x4−16y2=bx2c2−(4y)2=bx2−4yc bx2+4yc.34.16u4v−9v3=vb16u4−9v2c=vKb4u2c2−(3v)2L=vb4u2−3vc b4u2+3vc.35.(a−2b)2−(a+2b)2=[(a−2b)−(a+2b)] [(a−2b)+(a+2b)]=(−4b) (2a)= −8ab.36.2x(x+y)2−8xbx+y2c2=2xK(x+y)2−4bx+y2c2L=2xd(x+y)−2bx+y2ce d(x+y)+2bx+y2ce=2xby−x−2y2c b3x+y+2y2c.37.8m3+1=(2m)3+1=(2m+1)b4m2−2m+1c.38.27m3−8=(3m)3−23=(3m−2)b9m2+6m+4c.39.8r3−27s3=(2r)3−(3s)3=(2r−3s)b4r2+6rs+9s2c.40.x3+64y3=x3+(4y)3=(x+4y)bx2−4x y+16y2c.41.u2v6−8u2=u2bv6−8c=u2bv2−2c bv4+2v2+4c.

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Applied Mathematics For The Managerial, Life, And Social Sciences, 6th Edition Solution Manual - Page 13 preview image

81FUNDAMENTALS OF ALGEBRA42.r6s6+8s3=s3br6s3+8c=s3Kbr2sc3+23L=s3br2s+2c br4s2−2r2s+4c.43.2x3+6x+x2+3=2xbx2+3c+bx2+3c=bx2+3c(2x+1).44.2u4−4u2+2u2−4=2u4−2u2−4=2bu4−u2−2c=2bu2+1c bu2−2c.45.3ax+6ay+bx+2by=3a(x+2y)+b(x+2y)=(x+2y) (3a+b).46.6ux−4uy+3vx−2vy=2u(3x−2y)+v (3x−2y)=(3x−2y) (2u+v).47.u4−v4=bu2c2−bv2c2=bu2−v2c bu2+v2c=(u−v) (u+v)bu2+v2c.48.u4−u2v2−6v4=bu2−3v2c bu2+2v2c.49.4x3−9x y2+4x2y−9y3=xb4x2−9y2c+yb4x2−9y2c=d(2x)2−(3y)2e(x+y)=(2x−3y) (2x+3y) (x+y).50.4u4+11u2v2−3v4=b4u2−v2c bu2+3v2c=(2u−v) (2u+v)bu2+3v2c.51.x4+3x3−2x−6=x3(x+3)−2(x+3)=(x+3)bx3−2c.52.a2−b2+a+b=(a−b) (a+b)+(a+b)=(a+b) (a−b+1).53.au2+(a+c)u+c=au2+au+cu+c=au(u+1)+c(u+1)=(u+1) (au+c).54.ax2−(1+ab)x y+by2=ax2−x y−abx y+by2=ax(x−by)−y(x−by)=(x−by) (ax−y).55.P+Prt=P(1+rt).56.−t3+6t2+15t= −tbt2−6t−15c.57.8000x−100x2=100x(80−x).58.R=k Qx−kx2=kx(Q−x).59.k M x−kx2=kx(M−x).60.−0.1x2+500x= −0.1x(x−5000).61.V=V0+V0273T=V0273(273+T).62.k D22−D33=D2tk2−D3u.1.4Rational ExpressionsConcept Questionspage 251. a.Quotients of polynomials are rational expressions;2x2+13x2−3x+4 .b.Any polynomialPcan be written in the formP1 , but not all rational expressions can be written as a polynomial.2. a.P RQ S;P SR Q.b.P+QR;P−QR.

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Applied Mathematics For The Managerial, Life, And Social Sciences, 6th Edition Solution Manual - Page 14 preview image

1.4RATIONAL EXPRESSIONS9Exercisespage 251.28x27x3=4x.2.3y418y2=16y2.3.4x+125x+15=4(x+3)5(x+3)=45 .4.12m−618m−9=6(2m−1)9(2m−1)=23 .5.6x2−3x6x2=3x(2x−1)6x2=2x−12x.6.8y24y3−4y2+8y=8y24yby2−y+2c=2yy2−y+2 .7.x2+x−2x2+3x+2=(x+2) (x−1)(x+2) (x+1)=x−1x+1 .8.2y2−y−32y2+y−1=(2y−3) (y+1)(2y−1) (y+1)=2y−32y−1 .9.x2−92x2−5x−3=(x−3) (x+3)(2x+1) (x−3)=x+32x+1 .10.6y2+11y+34y2−9=(3y+1) (2y+3)(2y−3) (2y+3)=3y+12y−3 .11.x3+y3x2−x y+y2=(x+y)bx2−x y+y2cx2−x y+y2=x+y.12.8r3−s32r2+rs−s2=(2r−s)b4r2+2rs+s2c(2r−s) (r+s)=4r2+2rs+s2r+s.13.6x332·83x2=12x.14.25y412y·3y25y3=54y2.15.3x38x2÷15x416x5=3x38x2·16x515x4=2x85x6=25x216.6x521x2÷4x7x3=6x521x2·7x34x=12x5.17.3xx+2y·5x+10y6=(3x)5(x+2y)6(x+2y)=5x2 .18.4y+12y+2·3y+62y−1=4(y+3)3(y+2)(y+2) (2y−1)=12(y+3)2y−1.19.2m+63÷3m+96=2(m+3)3·63(m+3)=43 .20.3y−64y+6÷6y+248y+12=3(y−2)2(2y+3)·4(2y+3)6(y+4)=y−2y+4 .21.6r2−r−22r+4·6r+124r+2=(3r−2) (2r+1)6(r+2)2(r+2)2(2r+1)=3(3r−2)2.22.x2−x−62x2+7x+6·2x2−x−6x2+x−6=(x−3) (x+2) (2x+3) (x−2)(2x+3) (x+2) (x+3) (x−2)=x−3x+3 .23.k2−2k−3k2−k−6÷k2−6k+8k2−2k−8=(k−3) (k+1)(k−3) (k+2)·(k−4) (k+2)(k−4) (k−2)=k+1k−2 .24.6y2−5y−66y2+13y+6÷6y2−13y+69y2−12y+4=(3y+2) (2y−3)(3y+2) (2y+3)·(3y−2) (3y−2)(3y−2) (2y−3)=3y−22y+3 .25.22x+3+32x−1=2(2x−1)+3(2x+3)(2x+3) (2x−1)=4x−2+6x+9(2x+3) (2x−1)=10x+7(2x+3) (2x−1).26.2x−1x+2−x+3x−1=(2x−1) (x−1)−(x+3) (x+2)(x+2) (x−1)=2x2−3x+1−x2−5x−6(x+2) (x−1)=x2−8x−5(x+2) (x−1).

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Applied Mathematics For The Managerial, Life, And Social Sciences, 6th Edition Solution Manual - Page 15 preview image

101FUNDAMENTALS OF ALGEBRA27.3x2−x−6+2x2+x−2=3(x−3) (x+2)+2(x+2) (x−1)=3(x−1)+2(x−3)(x−3) (x+2) (x−1)=3x−3+2x−6(x−3) (x+2) (x−1)=5x−9(x−3) (x+2) (x−1).28.4x2−9−5x2−6x+9=4(x−3) (x+3)−5(x−3)2=4(x−3)−5(x+3)(x+3) (x−3)2=4x−12−5x−15(x+3) (x−3)2= −x+27(x+3) (x−3)2.29.2m2m2−2m−1+32m2−3m+3=2mb2m2−3m+3c+3b2m2−2m−1cb2m2−2m−1c b2m2−3m+3c=4m3−6m2+6m+6m2−6m−3b2m2−2m−1c b2m2−3m+3c=4m3−3b2m2−2m−1c b2m2−3m+3c.30.tt2+t−2−2t−12t2+3t−2=t(t+2) (t−1)−2t−1(t+2) (2t−1)=t(t+2) (t−1)−1t+2=t−1(t−1)(t+2) (t−1)=t−t+1(t+2) (t−1)=1(t+2) (t−1).31.x1−x+2x+3x2−1= −xx−1+2x+3(x+1) (x−1)= −x(x+1)+2x+3(x+1) (x−1)= −x2−x+2x+3(x+1) (x−1)= −x2−x−3(x+1) (x−1).32.2+1a+2−2aa−2=2(a+2) (a−2)+a−2−2a(a+2)(a+2) (a−2)=2a2−8+a−2−2a2−4a(a+2) (a−2)= −3a+10(a+2) (a−2).33.x−x2x+2+2x−2=x(x+2) (x−2)−x2(x−2)+2(x+2)(x+2) (x−2)=x3−4x−x3+2x2+2x+4(x+2) (x−2)=2x2−2x+4(x+2) (x−2)=2bx2−x+2c(x+2) (x−2).34.yy2−1+y−1y+1−2y1−y=y(y+1) (y−1)+y−1y+1+2yy−1=y+(y−1) (y−1)+2y(y+1)(y+1) (y−1)=y+y2−2y+1+2y2+2y(y+1) (y−1)=3y2+y+1(y+1) (y−1).35.xx2+5x+6+2x2−4−3x2+3x+2=x(x+3) (x+2)+2(x−2) (x+2)−3(x+1) (x+2)=x(x−2) (x+1)+2(x+3) (x+1)−3(x+3) (x−2)(x+3) (x+2) (x−2) (x+1)=x3−x2−2x+2x2+8x+6−3x2−3x+18(x+3) (x+2) (x−2) (x+1)=x3−2x2+3x+24(x+3) (x+2) (x−2) (x+1).36.2x+12x2−x−1−x+12x2+3x+1+4x2+2x−3=2x+1(2x+1) (x−1)−x+1(2x+1) (x+1)+4(x+3) (x−1)=1x−1−12x+1+4(x+3) (x−1)=(2x+1) (x+3)−(x−1) (x+3)+4(2x+1)(x−1) (2x+1) (x+3)=2x2+7x+3−x2−2x+3+8x+4(x−1) (2x+1) (x+3)=x2+13x+10(x−1) (2x+1) (x+3)

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Applied Mathematics For The Managerial, Life, And Social Sciences, 6th Edition Solution Manual - Page 16 preview image

1.4RATIONAL EXPRESSIONS1137.xax−ay+yby−bx=xa(x−y)−yb(x−y)=bx−ayab(x−y).38.ax+byax−bx+ay−bxby−ay=ax+byx(a−b)+ay−bx−y(a−b)= −y(ax+by)+x(ay−bx)−(a−b)x y= −by2−bx2−(a−b)x y= −bbx2+y2c−x y(a−b)=bbx2+y2c(a−b)x y.39.1+1x1−1x=x+1xx−1x=x+1x·xx−1=x+1x−1 .40.2+2xx−2x=2x+2xx2−2x=2(x+1)x·xx2−2=2(x+1)x2−2.41.1x+1y1−1x y=y+xx yx y−1x y=y+xx y·x yx y−1=y+xx y−1 .42.1+xy1−x2y2=y+xyy2−x2y2=x+yy·y2(y−x) (y+x)=yy−x.43.1x2−1y2x+y=y2−x2x2y2x+y=(y+x) (y−x)x2y2·1x+y=y−xx2y2.44.1x3−1y31x−1y=y3−x3x3y3y−xx y=y3−x3x3y3·x yy−x=(y−x)by2+x y+x2cx2y2(y−x)=y2+x y+x2x2y2.45.12(x+h)−12xh=x−(x+h)2x(x+h)h= −h2x(x+h)·1h= −12x(x+h).46.1(x+h)2−1x2h=x2−(x+h)2x2(x+h)2h=x2−x2−2xh−h2x2(x+h)2·1h= −2x+hx2(x+h)2.47. a.2.2+2500x=2.2x+2500x.b.The total cost isxt2.2x+2500xu=2.2x+2500.48.A=kmq+cm+hq2=2km+2cmq+hq22q.49.P=Ri−Ri(1+i)n=R(1+i)n−Ri(1+i)n=Rd(1+i)n−1ei(1+i)n.50.P=kTV−b+abV2(V−b)−aV(V−b)=kT V2+ab−aVV2(V−b).

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