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All Textbook Solutions for College Algebra

For the following exercises, use the Rational Zero Theorem to find all real zeros. x4+2x34x210x5=0 For the following exercises, use the Rational Zero Theorem to find all real zeros. 4x33x+1=0 For the following exercises, use the Rational Zero Theorem to find all real zeros. 8x4+26x3+39x2+26x+6 For the following exercises, find all complex solutions (real and non-real). x3+x2+x+1=0 For the following exercises, find all complex solutions (real and non—real). x38x2+25x26=0 For the following exercises, find all complex solutions (real and non—real). x3+13x2+57x+85=0 For the following exercises, find all complex solutions (real and non—real). 3x34x2+11x+10=0 For the following exercises, find all complex solutions (real and non-real). x4+2x3+22x2+50x75=0 For the following exercises, find all complex solutions (real and non—real). 2x33x2+32x+17=0 Use Descartes’ Rule to determine the possible number of positive and negative solutions. Then graph to confirm whichof those possibilities is the actual combination. 46. f(x)=x31 Use Descartes’ Rule to determine the possible number of positive and negative solutions. Then graph to confirm whichof those possibilities is the actual combination. 47. f(x)=x4x21 Use Descartes’ Rule to determine the possible number of positive and negative solutions. Then graph to confirm whichof those possibilities is the actual combination. 48. f(x)=x32x25x+6 Use Descartes’ Rule to determine the possible number of positive and negative solutions. Then graph to confirm whichof those possibilities is the actual combination. 49. f(x)=x32x2+x1 Use Descartes’ Rule to determine the possible number of positive and negative solutions. Then graph to confirm whichof those possibilities is the actual combination. 50. f(x)=x4+2x312x2+14x5 Use Descartes’ Rule to determine the possible number of positive and negative solutions. Then graph to confirm whichof those possibilities is the actual combination. 51. f(x)=2x3+37x2+200x+300 Use Descartes’ Rule to determine the possible number of positive and negative solutions. Then graph to confirm whichof those possibilities is the actual combination. 52. f(x)=x32x216x+32 Use Descartes’ Rule to determine the possible number of positive and negative solutions. Then graph to confirm whichof those possibilities is the actual combination. 53. f(x)=2x45x35x2+5x+3 Use Descartes’ Rule to determine the possible number of positive and negative solutions. Then graph to confirm whichof those possibilities is the actual combination. 54. f(x)=2x45x314x2+20x+8 Use Descartes’ Rule to determine the possible number of positive and negative solutions. Then graph to confirm whichof those possibilities is the actual combination. 55. f(x)=10x421x2+11 For the following exercises, list all possible rational zeros for the functions. 56. f(x)=x4+3x34x+4 For the following exercises, list all possible rational zeros for the functions. 57. f(x)=2x3+3x28x+5 For the following exercises, list all possible rational zeros for the functions. 58. f(x)=3x3+5x25x+4 For the following exercises, list all possible rational zeros for the functions. 59. f(x)=6x410x2+13x+1 For the following exercises, list all possible rational zeros for the functions. 60. f(x)=4x510x4+8x3+x28 For the following exercises, use your calculator to graph the polynomial function. Based on the graph, find the rationalzeros. All real solutions are rational. 61. f(x)=6x37x2+1 For the following exercises, use your calculator to graph the polynomial function. Based on the graph, find the rationalzeros. All real solutions are rational. 62. f(x)=4x34x213x5 For the following exercises, use your calculator to graph the polynomial function. Based on the graph, find the rationalzeros. All real solutions are rational. 63. f(x)=8x36x223x+6 For the following exercises, use your calculator to graph the polynomial function. Based on the graph, find the rationalzeros. All real solutions are rational. 64. f(x)=12x4+55x3+12x2117x+54 For the following exercises, use your calculator to graph the polynomial function. Based on the graph, find the rationalzeros. All real solutions are rational. 65. f(x)=16x424x3+x215x+25 For the following exercises, construct a polynomial function of least degree possible using the given information. 66. Real roots: 1,1,3 and (2,f(2))=(2,4)For the following exercises, construct a polynomial function of least degree possible using the given information. 67. Real roots: 1,1 (with multiplicity 2 and l) and (2,f(2))=(2,4)For the following exercises, construct a polynomial function of least degree possible using the given information. 68. Real roots: 2,12 (with multiplicity 2) and (3,f(3))=(3,5)For the following exercises, construct a polynomial function of least degree possible using the given information. 69. Real roots: 12,0,12 and (2,f(2))=(2,6)For the following exercises, construct a polynomial function of least degree possible using the given information. 70. Real roots: 4,1,1,4 and (2,f(2))=(2,10)For the following exercises, find the dimensions of the box described. 71. The length is twice as long as the width. The heightis 2 inches greater than the width. The volume is192 cubic inches.For the following exercises, find the dimensions of the box described. 72. The length, width, and height are consecutive wholenumbers. The volume is 120 cubic inches.For the following exercises, find the dimensions of the box described. 73. The length is one inch more than the width, which isone inch more than the height. The volume is86.625 cubic inches.For the following exercises, find the dimensions of the box described. 74. The length is three times the height and the height isone inch less than the width. The volume is 108 cubic inches.For the following exercises, find the dimensions of the box described. 75. The length is 3 inches more than the width. Thewidth is 2 inches more than the height. The volumeis 120 cubic inches.For the following exercises, find the dimensions of the right circular cylinder described. The radius is 3 inches more than the height. The volume is 16 cubic meters.For the following exercises, find the dimensions of the right circular cylinder described. The height is one less than one half the radius. The volume is 72 cubic meters.For the following exercises, find the dimensions of the right circular cylinder described. The radius and height differ by one meter. The radius is larger and the volume is 48 cubic meters.For the following exercises, find the dimensions of the right circular cylinder described. The radius and height differ by two meters. The height is greater and the volume is 28.125 cubic meters.For the following exercises, find the dimensions of the right circular cylinder described. The radius is 13 meter greater than the height. The volume 989 Cubic meters.Use arrow notation to describe the end behavior and local behavior for the reciprocal squared function.Sketch the graph, and find the horizontal and vertical asymptotes of the reciprocal squared function that has beenshifted right 3 units and down 4 units.There are 1,200 freshmen and 1,500 sophomores at a prep rally at noon. After 12 p.m., 20 freshmen arrive at the rallyevery ?ve minutes while 15 sophomores leave the rally. Find the ratio of freshmen to sophomores at 1 p.m.Find the domain of f(x)=4x5(x1)(x5).Find the vertical asymptotes and removable discontinuitiesof the graph of f(x)=x225x36x2+5x.Find the vertical and horizontal asymptotes of the function:. f(x)=(2x1)(2x+1)(x2)(x+3)Given the reciprocal squared function that is shifted right 3 units and down 4 units. write this as a rational function.Then, find the x-and y-intercepts and the horizontal and vertical asymptotes.Given the function f(x)=(x+2)2(x2)2(x1)2(x3), use the characteristics of polynomials and rational functions to describeits behavior and sketch the function.What is the fundamental difference in the algebraicrepresentation ofa polynomial function and a rationalfunction?What is the fundamental difference in the graphsof polynomial functions and rational functions?If the graph of a rational function has a removablediscontinuity, what must be true of the functionalrule?Can a graph of a rational function have no verticalasymptote? If so, how?Can a graph of a rational function have nox-intercepts? If so, how?For the following exercises, find the domain of the rational functions. 6. f(x)=x1x+2 For the following exercises, find the domain of the rational functions. 7. f(x)=x+1x21 For the following exercises, find the domain of the rational functions. 8. f(x)=x2+4x22x8 For the following exercises, find the domain of the rational functions. 9. f(x)=x2+4x3x45x2+4 For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. 10. f(x)=4x1 For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. f(x)=25x+2 For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. f(x)=xx29 For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. f(x)=xx2+5x36 For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. f(x)=3+xx327 For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. f(x)=3x4x316x For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. f(x)=x21x3+9x2+14x For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. f(x)=x+5x225 For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. f(x)=x4x6 For the following exercises, find the domain, vertical asymptotes, and horizontal asymptotes of the functions. f(x)=42x3x1 For the following exercises, find the x- and y-intercepts for the functions. 20. f(x)=x+5x2+4 For the following exercises, find the x- and y-intercepts for the functions. f(x)=xx2x For the following exercises, find the x- and y-intercepts for the functions. f(x)=x2+8x+7x2+11x+30 For the following exercises, find the x- and y-intercepts for the functions. f(x)=x2+x+6x210x+24 For the following exercises, find the x- and y-intercepts for the functions. f(x)=942x23x212 For the following exercises, describe the local and end behavior of the functions. f(x)=x2x+1 For the following exercises, describe the local and end behavior of the functions. f(x)=2xx6 For the following exercises, describe the local and end behavior of the functions. f(x)=2xx6 For the following exercises, describe the local and end behavior of the functions. f(x)=x24x+3x24x5 For the following exercises, describe the local and end behavior of the functions. f(x)=2x2326x2+13x5 For the following exercises, find the slant asymptote of the functions. f(x)=24x2+6x2x+1 For the following exercises, find the slant asymptote of the functions. f(x)=4x2102x4 For the following exercises, find the slant asymptote of the functions. f(x)=81x2183x2 For the following exercises, find the slant asymptote of the functions. f(x)=6x35x3x2+4 For the following exercises, find the slant asymptote of the functions. f(x)=x2+5x+4x1 For the following exercises. use the given transformation to graph the function. Note the vertical and horizontalasymptotes. 35. The reciprocal function shifted up two units.For the following exercises. use the given transformation to graph the function. Note the vertical and horizontalasymptotes. 36. The reciprocal function shifted down one unit andleft three units.For the following exercises. use the given transformation to graph the function. Note the vertical and horizontalasymptotes. 37. The reciprocal squared function shifted to the right2 units.For the following exercises. use the given transformation to graph the function. Note the vertical and horizontalasymptotes. 38. The reciprocal squared function shifted down 2 unitsand right 1 unit.For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph. p(x)=2x3x+4 For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph. q(x)=x53x1 For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph. s(x)=4( x2)2 For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph. r(x)=5( x+1)2 For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph. f(x)=3x214x53x2+18x16 For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph. g(x)=2x2+7x153x214+15 For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph. a(x)=x2+2x3x21 For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph. b(x)=x2x6x24 For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph. h(x)=2x2+x1x4 For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph. k(x)=2x23x20x5 For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote 0f the functions. Use that information to sketch a graph. w(x)=(x1)(x+3)(x5)( x+2)2(x4)For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph. z(x)=( x+2)2(x5)(x3)(x+1)(x+4)For the following exercises, write an equation for a rational function with the given characteristics. Vertical asymptotes at x=5 and x=5 , x-intercepts at (2,0) and (1,0),y-intercept at (0,4)For the following exercises, write an equation for a rational function with the given characteristics. Vertical asymptotes at x=4 and x=1,x-intercepts at (1,0) and (5,0),y-intercept at (0,7)For the following exercises, write an equation for a rational function with the given characteristics. Vertical asymptotes at x=4 and x=5 , x-intercepts at (4,0) and (6,0) , horizontal asymptote at y=7 For the following exercises, write an equation for a rational function with the given characteristics. Vertical asymptotes at x=3 and x=6,x-intercepts at (2,0) and (1,0), horizontal asymptote at y=2 For the following exercises, write an equation for a rational function with the given characteristics. Vertical asymptote at x=1, double zero at x=2,y-intercept at (0,2)For the following exercises, write an equation for a rational function with the given characteristics. Vertical asymptote at x=3, double zero at x=1,y-intercept at (0,4)For the following exercises, use the graphs to write an equation for the function.For the following exercises, use the graphs to write an equation for the function.For the following exercises, use the graphs to write an equation for the function.For the following exercises, use the graphs to write an equation for the function.For the following exercises, use the graphs to write an equation for the function.For the following exercises, use the graphs to write an equation for the function.For the following exercises, use the graphs to write an equation for the function.For the following exercises, use the graphs to write an equation for the function.For the following exercises, make tables to show the behavior of the function near the vertical asymptote and reflectingthe horizontal asymptote 65. f(x)=1x2 For the following exercises, make tables to show the behavior of the function near the vertical asymptote and reflecting the horizontal asymptote 66. f(x)=xx3 For the following exercises, make tables to show the behavior of the function near the vertical asymptote and reflecting the horizontal asymptote 67. f(x)=2xx+4 For the following exercises, make tables to show the behavior of the function near the vertical asymptote and reflecting the horizontal asymptote 68. f(x)=2x(x3)2 For the following exercises, make tables to show the behavior of the function near the vertical asymptote and reflecting the horizontal asymptote 69. f(x)=x2x2+2x+1 For the following exercises, use a calculator to graph f(x). Use the graph to solve f(x)0. 70. f(x)=2x+1 For the following exercises, use a calculator to graph f(x). Use the graph to solve f(x)0. 71. f(x)=42x3 For the following exercises, use a calculator to graph f(x). Use the graph to solve f(x)0. 72. f(x)=2(x1)(x+2)For the following exercises, use a calculator to graph f(x). Use the graph to solve f(x)0. 73. f(x)=x+2(x1)(x4)For the following exercises, use a calculator to graph f(x). Use the graph to solve f(x)0. 74. f(x)=(x+3)2(x1)2(x+1)For the following exercises, identify the removal discontinuity. 75. f(x)=x24x2 For the following exercises, identify the removable discontinuity. 76. f(x)=x3+1x+1 For the following exercises, identify the removable discontinuity. 77. f(x)=x2+x6x2 For the following exercises, identify the removable discontinuity. 78. f(x)=2x2+5x3x+3 For the following exercises, identify the removable discontinuity. 79. f(x)=x3+x2x+1 For the following exercises, express a rational function that describes the situation. 80. A large mixing tank currently contains 200 gallons ofwater, into which 10 pounds of sugar have beenmixed. A tap will open, pouring 10 gallons of waterper minute into the tank at the same time sugaris poured into the tank at a rate of 3 pounds perminute. Find the concentration (pounds per gallon)of sugar in the tank after t minutes.For the following exercises, express a rational function that describes the situation. 81. A large mixing tank currently contains 300 gallonsof water, into which 8 pounds of sugar have beenmixed. A tap will open, pouring 20 gallons of waterper minute into the tank at the same time sugaris poured into the tank at a rate of 2 pounds perminute. Find the concentration (pounds per gallon)of sugar in the tank after tminutes.For the following exercises, use the given rational function to answer the question. 82. The concentration C of a drug in a patient’sbloodstream thours after injection in given by C(t)=2t3+t2. What happens to the concentration ofthe drug as tincreases?For the following exercises, use the given rational function to answer the question. 83. He concentration C of a drug in a patient’sbloodstream t hours after injection is given by C(t)=100t2t2+75. Use a calculator to approximate thetime when the concentration is highest.For the following exercises, construct a rational function that will help solve the problem. Then, usea calculator toanswer the question. 84. An open box with a square base is to have a volumeof 108 cubic inches. Find the dimensions of the boxthat will have minimum surface area. Let x = lengthof the side of the base.For the following exercises, construct a rational function that will help solve the problem. Then, usea calculator toanswer the question. 85. A rectangular box with a square base is to have avolume of 20 cubic feet. The material for the basecosts 30 cents/square foot. The material for the sidescosts 10 cents/square foot. The material for the topcosts 20 cents/square foot. Determine the dimensionsthat will yield minimum cost. Let x= length of theside of the base.For the following exercises, construct a rational function that will help solve the problem. Then, use a calculator toanswer the question. 86. A right circular cylinder has volume of 100 cubicinches. Find the radius and height that will yieldminimum surface area. Let x = radius.For the following exercises, construct a rational function that will help solve the problem. Then, use a calculator toanswer the question. 87. A right circular cylinder with no top has a volume of50 cubic meters. Find the radius that will yieldminimum surface area. Let x = radius.For the following exercises, construct a rational function that will help solve the problem. Then, use a calculator toanswer the question. 88. A right circular cylinder is to have a volume of40 cubic inches. It costs 4 cents/square inchto construct the top and bottom and 1 cents/square inch to construct the rest of the cylinder. Find theradius to yield minimum cost. Let x= radius.Show that f(x)=x+53 and f1(x)=3x5 are inverses.Find the inverse function of f(x)=x+43 Find the inverse of the function f(x)=x2+1, on the domain x0.Restrict the domain and then find the inverse of the function f(x)=2x+3.Find the inverse of the function f(x)=x+3x2.Explain why we cannot find inverse functions for allpolynomial functions.Why must we restrict the domain of a quadraticfunction when finding its inverse?When finding the inverse of a radical function, whatrestriction will we need to make?The inverse of a quadratic function will always take what form?For the following exercises, find the inverse of the function on the given domain. 5. f(x)=(x4)2,[4,)For the following exercises, find the inverse of the function on the given domain. 6. f(x)=(x+2)2,[2,)For the following exercises, find the inverse of the function on the given domain. 7. f(x)=(x+1)23,[1,)For the following exercises, find the inverse of the function on the given domain. 8. f(x)=3x2+5,(,0]For the following exercises, find the inverse of the function on the given domain. 9. f(x)=12x2,[0,)For the following exercises, find the inverse of the function on the given domain. 10. f(x)=9x2,[0,)For the following exercises, find the inverse of the function on the given domain. 11. f(x)=2x2+4,[0,)For the following exercises, find the inverse of the functions. f(x)=x3+5 For the following exercises, find the inverse of the functions. f(x)=3x3+1 For the following exercises, find the inverse of the functions. f(x)=4x3 For the following exercises, find the inverse of the functions. f(x)=42x3 For the following exercises, find the inverse of the functions. f(x)=2x+1 For the following exercises, find the inverse of the functions. f(x)=34x For the following exercises, find the inverse of the functions. f(x)=9+4x4 For the following exercises, find the inverse of the functions. f(x)=6x8+5 For the following exercises, find the inverse of the functions. f(x)=9+2x3 For the following exercises, find the inverse of the functions. f(x)=3x3 For the following exercises, find the inverse of the functions. f(x)=2x+8 For the following exercises, find the inverse of the functions. f(x)=3x4 For the following exercises, find the inverse of the functions. f(x)=x+3x+7 For the following exercises, find the inverse of the functions. f(x)=x2x+7 For the following exercises, find the inverse of the functions. f(x)=3x+454x For the following exercises, find the inverse of the functions. f(x)=5x+125x For the following exercises, find the inverse of the functions. f(x)=x2+2x,[1,)For the following exercises, find the inverse of the functions. f(x)=x2+4x+1,[2,)For the following exercises, find the inverse of the functions. f(x)=x26x+3,[3,)For the following exercises, find the inverse of the function and graph both the function and its inverse. 31. f(x)=x2+2,x0 For the following exercises, find the inverse of the function and graph both the function and its inverse. 32. f(x)=4x2,x0 For the following exercises, find the inverse of the function and graph both the function and its inverse. 33. f(x)=(x+3)2,x3 For the following exercises, find the inverse of the function and graph both the function and its inverse. 34. f(x)=(x4)2,x4 For the following exercises, find the inverse of the function and graph both the function and its inverse. 35. f(x)=x3+3 For the following exercises, find the inverse of the function and graph both the function and its inverse. 36. f(x)=1x3 For the following exercises, find the inverse of the function and graph both the function and its inverse. 37. f(x)=x2+4x,x2 For the following exercises, find the inverse of the function and graph both the function and its inverse. 38. f(x)=x26x+1,x3 For the following exercises, find the inverse of the function and graph both the function and its inverse. 39. f(x)=2x For the following exercises, find the inverse of the function and graph both the function and its inverse. 40. f(x)=1x2,x0 For the following exercises, use a graph to help determine the domain of the functions. f(x)=( x+1)( x1)x For the following exercises, use a graph to help determine the domain of the functions. f(x)=( x+2)( x3)x1 For the following exercises, use a graph to help determine the domain of the functions. f(x)=x( x+3)x4 For the following exercises, use a graph to help determine the domain of the functions. f(x)=x2x20x2 For the following exercises, use a graph to help determine the domain of the functions. f(x)=9x2x+4 For the following exercises, use a calculator to graph the function. Then, using the graph, give threepoints on thegraph of the inverse with y-coordinates given. 46. f(x)=x3x2,y=1,2,3 For the following exercises, use a calculator to graph the function. Then, using the graph, give three points on thegraph of the inverse with y-coordinates given. 47. f(x)=x3+x2,y=0,1,2 For the following exercises, use a calculator to graph the function. Then, using the graph, give three points on thegraph of the inverse with y-coordinates given. 48. f(x)=x3+3x4,y=0,1,2 For the following exercises, use a calculator to graph the function. Then, using the graph, give three points on thegraph of the inverse with y-coordinates given. 49. f(x)=x3+8x4,y=1,0,1 For the following exercises, use a calculator to graph the function. Then, using the graph, give three points on thegraph of the inverse with y-coordinates given. 50. f(x)=x4+5x+1,y=1,0,1 For the following exercises, find the inverse of the functions with a,b, c positive real numbers. 51. f(x)=ax3+b For the following exercises, find the inverse of the functions with a,b, c positive real numbers. 52. f(x)=x2+bx For the following exercises, find the inverse of the functions with a,b, c positive real numbers. 53. f(x)=ax2+b For the following exercises, find the inverse of the functions with a, b, c positive real numbers. 54. f(x)=ax+b3 For the following exercises, find the inverse of the functions with a,b, c positive real numbers. 55. f(x)=ax+bx+c For the following exercises, determine the function described and then use it to answer the question. 56. An object dropped from a height of 200 meters hasa height, h(t), in meters after tseconds have lapsed,such that h(t)=2004.9t2. Express tas a functionof height, h, and find the time to reach a height of50 meters.For the following exercises, determine the function described and then use it to answer the question. 57. An object dropped from a height of 600 feet hasa height, h(t), in feet after tseconds have elapsed,such that h(t)=60016t2. Express t as a functionof height h, and find the time to reach a height of400feet.For the following exercises, determine the function described and then use it to answer the question. 58. The volume, V, of a sphere in terms of its radius, r,is given by V(r)=43r3. Express r as a function ofV, and find the radius of a sphere with volume of 200cubic feet.For the following exercises, determine the function described and then use it to answer the question. 59. The surface area, A, of a sphere in terms of its radius,r, is given by A(r)=4r2. Express r as a function ofV, and find the radius of a sphere with a surface areaof 1000 square inches.For the following exercises, determine the function described and then use it to answer the question. 60. A container holds 100 ml of a solution that is25 ml acid. If nml of a solution that is 60% acid isadded, the function C(n)=25+0.6n100+n gives theconcentration, C, as a function of the number of ml added, n. Express n as a function of C and determinethe number of ml that need to be added to have asolution that is 50% acid.For the following exercises, determine the function described and then use T(l)=2l32.2. to answer the question. 61. The period T, in seconds, of a simple pendulumas a function of its length l, in feet, is given by Express l as a function of T anddetermine the length of a pendulum with periodof 2 seconds.For the following exercises, determine the function described and then use it to answer the question. 62. The volume of a cylinder, V, in terms of radius, r,and height, h, is given by V=r2h . If a cylinder hasa height of 6 meters, express the radius as a functionof Vand find the radius of a cylinder with volume of300 cubic meters.For the following exercises, determine the function described and then use it to answer the question. 63. The surface area, A, of a cylinder in terms of itsradius, r, and height, h, is given by A=2r2+2rh. If the height of the cylinder is 4 feet, express the radiusas a function of Vand find the radius if the surfacearea is 200 square feet.For the following exercises, determine the function described and then use it to answer the question. 64. The volume of a right circular cone, V, in terms of its radius, r, and its height, h, is given by V=13r2h. Express r in terms of h if the height of the cone is12 feet and find the radius of a cone with volume of50 cubic inches.For the following exercises, determine the function described and then use it to answer the question. 65. Consider a cone with height of 30 feet. Express theradius, r, in terms of the volume, V, and find theradius of a cone with volume of 1000 cubic feet.The quantity y varies directly with the square of x. If y=24whenx=3 , find y when x is 4.A quantity y varies inversely with the square of x. If y=8whenx=3 , find y when x is 4.A quantity x varies directly with the square of y and inversely with z. If x=40,wheny=4andz=2 . find x when y=10andz=25 .What is true of the appearance of graphs thatre?ect a direct variation between two variables?If two variables vary inversely what will an equationrepresenting their relationship look like?Is there a limit to the number of variables thatcan jointly vary? Explain.For the following exercises, write an equation describing the relationship of the given variables. 4. y varies directlyas x and when x=6,y=12 For the following exercises, write an equation describing the relationship of the given variables. 5. y varies directly as the square of x and when x=4,y=80 .For the following exercises, write an equation describing the relationship of the given variables. 6. y varies directly as the square root of x and when x=36,y=24 .For the following exercises, write an equation describing the relationship of the given variables. 7. y varies directly as the cube of x and when x=36,y=24 .For the following exercises, write an equation describing the relationship of the given variables. 8. y varies directly as the cube root ofx and when x=27,y=15 .For the following exercises, write an equation describing the relationship of the given variables. 9. y varies directly as the fourth power of x and when x=1,y=6 For the following exercises, write an equation describing the relationship of the given variables. 10. y varies inverselyas x and when x=4,y=2 .For the following exercises, write an equation describing the relationship of the given variables. 11. y varies inversely as the square of x and when x=3,y=2 .For the following exercises, write an equation describing the relationship of the given variables. 12. y varies inversely as the cube of x and when x=2,y=5 For the following exercises, write an equation describing the relationship of the given variables. 13. y varies inversely as the fourth power of x and when x=3,y=1 .For the following exercises, write an equation describing the relationship of the given variables. 14. y varies inversely as the square root of x andwhen x=25,y=3 .For the following exercises, write an equation describing the relationship of the given variables. 15. y varies inversely as the cube root of x and when x=64,y=5 .For the following exercises, write an equation describing the relationship of the given variables. 16. y varies jointly with x and z and when x=2andz=3,y=36 .For the following exercises, write an equation describing the relationship of the given variables. 17. y varies jointly as x, z, and w and when x=1,z=2,w=5,theny=100 .For the following exercises, write an equation describing the relationship of the given variables. 18. y varies jointly as the square of x and the squareofzandwhen x=3andz=4,theny=72 .For the following exercises, write an equation describing the relationship of the given variables. 19. y varies jointly as x and the square root of z and when x=2andz=25,theny=100 .For the following exercises, write an equation describing the relationship of the given variables. 20. y varies jointly as the square of x the cube of zand the square root of w. When x=1,z=2 , and w=36,theny=48 .For the following exercises, write an equation describing the relationship of the given variables. 21. y varies jointly as x and z and inversely asw. When x=3,z=5,andw=6,theny=10 .For the following exercises, write an equation describing the relationship of the given variables. 22. y varies jointly as the square of x and the squarerout of z and inversely as the cube of w. When x=3,z=4,andw=3,theny=6 .For the following exercises, write an equation describing the relationship of the given variables. 23. y varies jointly as x and z and inversely as the square rootof w and the square of t. When x=3,z=1,w=25,andt=2,theny=6 For the following exercises, use the given information to find the unknown value. 24. y varies directly as x. When x=3,theny=12.Findywhenx=20 .For the following exercises, use the given information to find the unknown value. 25. y varies directly as the square of x. When x=2,theny=16.Findywhenx=8 .For the following exercises, use the given information to find the unknown value. 26. y varies directly as the cube ofx. When x=3,theny=5.Findwhenx=4 .For the following exercises, use the given information to find the unknown value. 27. y varies directly as the square root of x. When x=16,theny=4.Findywhenx=36 .For the following exercises, use the given information to find the unknown value. 28. y varies directly as the cube root ofx. When x=125,theny=15.Findywhenx=1,000 .For the following exercises, use the given information to find the unknown value. 29. y varies inversely with x. When x=3,theny=2.Findywhenx=1 .For the following exercises, use the given information to find the unknown value. 30. y varies inversely with the square ofx. When x=4,theny=3.Findywhenx=2 .For the following exercises, use the given information to find the unknown value. 31. y varies inversely with the cube ofx. When x=3,theny=1.Findywhenx=l .For the following exercises, use the given information to find the unknown value. 32. y varies inversely with the square root ofx. When x=64,theny=12.Findywhenx=36 .For the following exercises, use the given information to find the unknown value. 33. y varies inverselywith the cube root ofx. When x=27,theny=5.Findywhenx=125 .For the following exercises, use the given information to find the unknown value. 34. y varies jointly as x and z. When x=4andz=2,theny=16.Findywhenx=3andz=3.For the following exercises, use the given information to find the unknown value. 35. y varies jointly as x, z, and w. When x=2,z=1,andw=12,theny=72.Findywhenx=1,z=2,andw=3 .For the following exercises, use the given information to find the unknown value. 36. y varies jointly as x and the square of z. When x=2andz=4,theny=144.Findywhenx=4andz=5 .For the following exercises, use the given information to find the unknown value. 37. y varies jointly as the square of x and the square rootof z. When x=2andz=9,theny=24.Findywhenx=3andz=25 For the following exercises, use the given information to find the unknown value. 38. y varies jointly as x and z and inversely as w. When x=5,z=2,andw=20,theny=4 . Findy when x=3andz=8,andw=48 .For the following exercises, use the given information to find the unknown value. 39. y varies jointly as the square of x and the cube of zand inversely as the square root of w. When x=2,z=2,andw=64,theny=12 . Findywhen x=1,z=3,andw=4 .For the following exercises, use the given information to find the unknown value. 40. y varies jointly as the square of x and of z and inversely as the square root of w and of t. When x=2,z=3,w=16,andt=3,theny=1 . Findywhen x=3,z=2.,w=36,andt=5 .For the following exercises, use a calculator to graph the equation implied by the given variation. 41. y varies directly with the square ofx and when x=2,y=3.For the following exercises, use a calculator to graph the equation implied by the given variation. 42. y varies directly as the cube of x and when x=2,y=4.For the following exercises, use a calculator to graph the equation implied by the given variation. 43. y varies directly as the square root ofx and when x=36,y=2.For the following exercises, use a calculator to graph the equation implied by the given variation. 44. y varies inversely with x and when x=6,y=2.For the following exercises, use a calculator to graph the equation implied by the given variation. 45. y varies inversely as the square of x and when x=1,y=4.For the following exercises, use Kepler’s Law, which states that the square of the time, T, required for a planet to orbitthe Sun varies directly with the cube of the mean distance. a. that the planet is from the Sun. 46. Using the Earth’s time of 1 year and mean distance of93 million miles, find the equation relating T and a.For the following exercises, use Kepler’s Law, which states that the square of the time, T, required for a planet to orbitthe Sun varies directly with the cube of the mean distance. a. that the planet is from the Sun. 47. Use the result from the previous exercise to determinethe time required for Mars to orbit the Sun if its meandistance is 142 million miles.For the following exercises, use Kepler’s Law, which states that the square of the time, T, required for a planet to orbitthe Sun varies directly with the cube of the mean distance,a, that the planet is from the Sun. 48. Using Earth’s distance of 150 million kilometers, findthe equation relating T and a.For the following exercises, use Kepler’s Law, which states that the square of the time, T, required for a planet to orbitthe Sun varies directly with the cube of the mean distance,a, that the planet is from the Sun. 49. Use the result from the previous exercise to determinethe time required for Venus to orbit the Sun if itsmean distance is 108 million kilometers.For the following exercises, use Kepler’s Law, which states that the square of the time, T, required for a planet to orbitthe Sun varies directly with the cube of the mean distance a that the planet is from the Sun. 50. Using Earth’s distance of l astronomical unit (A.U.),determine the time for Saturn to orbit the Sun if itsmean distance is 9.54 A.U.For the following exercises, use the given information to answer the questions. 51. The distance s that an object falls varies directly withthe square of the time, t, of the fall. If an object falls16 feet in one second, how long for it to fall 144 feet?For the following exercises, use the given information to answer the questions. 52. The velocity v ofa falling object varies directly to the time,t, of the fall. If after 2 seconds, the velocity of the object is64 feet per second. what is the velocity after 5 seconds?For the following exercises, use the given information to answer the questions. 53. The rate of vibration of a string under constant tensionvaries inversely with the length of the string. If a stringis 24 inches long and vibrates 128 times per second,what is the length of a string that vibrates 64 times persecond?For the following exercises, use the given information to answer the questions. 54. The volume of a gas held at constant temperaturevaries indirectly as the pressure of the gas. If thevolume of a gas is 1200 cubic centimeters whenthe pressure is 200 millimeters of mercury, what isthe volume when the pressure is 300 millimeters ofmercury?For the following exercises, use the given information to answer the questions. 55. The weight of an object above the surface of the Earthvaries inversely with the square of the distance fromthe center of the Earth. If a body weighs 50 poundswhen it is 3960 miles from Earth’s center, what would itweigh it were 3970 miles from Earth’s center?For the following exercises, use the given information to answer the questions. 56. The intensity of light measured in foot-candles variesinversely with the square of the distance from the lightsource. Suppose the intensity of a light bulb is 0.08 foot-candles at a distance of 3 meters. Find the intensity levelat 8 meters.For the following exercises, use the given information to answer the questions. 57. The current in a circuit varies inversely with itsresistance measured in ohms. When the current in acircuit is 40 amperes, the resistance is 10 ohms. Find thecurrent if the resistance is 12 ohms.For the following exercises, use the given information to answer the questions. 58. The force exerted by the wind on a plane surface varies jointly with the square of the velocity of the wind andwith the area of the plane surface. If the area of thesurface is 40 square feet surface and the wind velocity is20 miles per hour, the resulting force is 15 pounds. Findthe force on a surface of 65 square feet with a velocity of30 miles per hour.For the following exercises, use the given information to answer the questions. 59. The horsepower (hp) that a shaft can safer transmitvaries jointly with its speed (in revolutions per minute(rpm)) and the cube of the diameter. If the shaft of acertain material 3 inches indiameter can transmit 45hp at 100 rpm, what must the diameter be in order totransmit 60 hp at 150 rpm?For the following exercises, use the given information to answer the questions. 50. The kinetic energy K of a moving object varies jointlywith its mass m and the square of its velocity v. If anobject weighing 40 kilograms with a velocity of15 meters per second has a kinetic energy of 1000 joules,find the kinetic energy if the velocity is increased to 20meters per second.For the following exercises, write the quadratic function in standard form. Then, give the vertex and axes intercepts.Finally, graph the function. f(x)=x24x5 For the following exercises, write the quadratic function in standard form. Then, give the vertex and axes intercepts.Finally, graph the function. 2. f(x)=2x24x For the following problems, find the equation of the quadratic function using the given information. The vertex is (2,3) and a point on the graph is (3,6).For the following problems, find the equation of the quadratic function using the given information. The vertex is (3,6.5) and a point on the graph is (2,6).For the following exercises, complete the task. 5. A rectangular plot of land is to be enclosed byfencing. One side is along a river and so needs nofence. If the total fencing available is 600 meters,find the dimensions of the plot to have maximumarea.For the following exercises, complete the task. An object projected from the ground at a 45 degree angle with initial velocity of 120 feet per second has height, h, in terms of horizontal distance traveled, x, given by h(x)=32( 120)2x2+x. Find the maximum height the object attains.For the following exercises, determine if the function is a polynomial function and, if so, give the degree and leadingcoefficient. 7. f(x)=4x53x3+2x1 For the following exercises, determine if the function is a polynomial function and, if so, give the degree and leadingcoefficient. 8. f(x)=5x+1x2 For the following exercises, determine if the function is a polynomial function and, if so, give the degree and leadingcoefficient. 9. f(x)=x2(36x+x2)For the following exercises, determine end behavior of the polynomial function. f(x)=2x4+3x35x2+7 For the following exercises, determine end behavior of the polynomial function. f(x)=4x36x2+2 For the following exercises, determine end behavior of the polynomial function. f(x)=2x2(1+3xx2)For the following exercises, find all zeros of the polynomial function, noting multiplicities. 13. f(x)=(x+3)2(2x1)(x+1)3 For the following exercises, find all zeros of the polynomial function, noting multiplicities. 14. f(x)=x5+4x4+4x3 For the following exercises, find all zeros of the polynomial function, noting multiplicities. 15. f(x)=x34x2+x4 For the following exercises, based on the given graph, determine the zeros of the function and note multiplicity.For the following exercises, based on the given graph, determine the zeros of the function and note multiplicity.For the following exercises. based on the given graph, determine the zeros of the function and note multiplicity: Use the Intermediate Value Theorem to show that at least one zero lies between 2 and 3 for the function f(x)=x35x+1 For the following exercises, use long division to find the quotient and remainder. 19. x32x2+4x+4x2 For the following exercises, use long division to find the quotient and remainder. 20. 3x44x2+4x+8x+1 For the following exercises, use synthetic division to find the quotient. If the divisor is a factor, then write the factored form. x32x2+5x1x+3 For the following exercises, use synthetic division to find the quotient. If the divisor is a factor, then write the factored form. x3+4x+10x3 For the following exercises, use synthetic division to find the quotient. If the divisor is a factor, then write the factored form. 2x3+6x211x12x+4 For the following exercises, use synthetic division to find the quotient. if the divisor is a factor, then write the factored form. 3x4+3x3+2x+2x+1 For the following exercises, use the Rational Zero Theorem to help you solve the polynomial equation. 25. 2x33x218x8=0 For the following exercises, use the Rational Zero Theorem to help you solve the polynomialequation. 26. 3x3+11x2+8x4=0 For the following exercises, use the Rational Zero Theorem to help you solve the polynomial equation. 27. 2x417x3+46x243x+12=0

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