Calculus

Precalculus: Graphical, Numerical, Algebraic | 8th Edition | ISBN: 9780321656933 | Authors: Franklin Demana, Bert K. Waits, Gregory D. Foley, Daniel Kennedy, Dave Bock
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Author: Franklin Demana, Bert K. Waits, Gregory D. Foley, Daniel Kennedy, Dave Bock
Publisher: Pearson
ISBN: 9780321656933
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Chapter 2 Problems

Chapter: 2 Problem: 69

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1 and 2, write an equation for the linear function satisfying the given conditions. Graph \(y=f(x)\). \f(-3)=-2\) and \(f(4)=-9\)

Chapter: 2 Problem: 70

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1 and 2, write an equation for the linear function satisfying the given conditions. Graph \(y=f(x)\). \(f(-3)=6\) and \(f(1)=-2\)

Chapter: 2 Problem: 71

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3 and 4, describe how to transform the graph of \(f(x)=x^{2}\) into the graph of the given function. Sketch the graph by hand and support your answer with a grapher. \(h(x)=3(x-2)^{2}+4\)

Chapter: 2 Problem: 72

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3 and 4, describe how to transform the graph of \(f(x)=x^{2}\) into the graph of the given function. Sketch the graph by hand and support your answer with a grapher. \(g(x)=-(x+3)^{2}+1\)

Chapter: 2 Problem: 73

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, find the vertex and axis of the graph of the function. Support your answer graphically. \(f(x)=-2(x+3)^{2}+5\)

Chapter: 2 Problem: 74

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, find the vertex and axis of the graph of the function. Support your answer graphically. \(g(x)=4(x-5)^{2}-7\)

Chapter: 2 Problem: 75

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, find the vertex and axis of the graph of the function. Support your answer graphically. \(f(x)=-2 x^{2}-16 x-31\)

Chapter: 2 Problem: 76

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 58, find the vertex and axis of the graph of the function. Support your answer graphically. \(g(x)=3 x^{2}-6 x+2\)

Chapter: 2 Problem: 77

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9 and 10, write an equation for the quadratic function whose graph contains the given vertex and point. Vertex \((-2,-3)\), point \((1,2)\)

Chapter: 2 Problem: 78

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 9 and 10, write an equation for the quadratic function whose graph contains the given vertex and point. Vertex \((-1,1)\), point \((3,-2)\)

Chapter: 2 Problem: 79

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11 and 12, write an equation for the quadratic function with graph shown, given one of the labeled points is the vertex of the parabola.

Chapter: 2 Problem: 80

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11 and 12, write an equation for the quadratic function with graph shown, given one of the labeled points is the vertex of the parabola.

Chapter: 2 Problem: 81

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, graph the function in a viewing window that shows all of its extrema and x-intercepts. \(f(x)=x^{2}+3 x-40\)

Chapter: 2 Problem: 82

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, graph the function in a viewing window that shows all of its extrema and x-intercepts. \(f(x)=-8 x^{2}+16 x-19\)

Chapter: 2 Problem: 83

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, graph the function in a viewing window that shows all of its extrema and x-intercepts. \(f(x)=x^{3}+x^{2}+x+5\)

Chapter: 2 Problem: 84

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1316, graph the function in a viewing window that shows all of its extrema and x-intercepts. \(f(x)=x^{3}-x^{2}-20 x-2\)

Chapter: 2 Problem: 85

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 17 and 18, write the statement as a power function equation. Let k be the constant of variation. The surface area S of a sphere varies directly as the square of the radius r.

Chapter: 2 Problem: 86

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 17 and 18, write the statement as a power function equation. Let k be the constant of variation. The force of gravity F acting on an object is inversely proportional to the square of the distance d from the object to the center of the earth.

Chapter: 2 Problem: 87

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 19 and 20, write a sentence that expresses the relationship in the formula, using the language of variation or proportion. F = kx ,where F is the force it takes to stretch a spring x units from its unstressed length and k is the springs force constant.

Chapter: 2 Problem: 88

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 19 and 20, write a sentence that expresses the relationship in the formula, using the language of variation or proportion. \(A=\pi \cdot r^{2}\), where A and r are the area and radius of a circle and is the usual mathematical constant.

Chapter: 2 Problem: 89

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2124, state the values of the constants k and a for the function \(f(x)=k \cdot x^{a}\). Describe the portion of the curve that lies in Quadrant I or IV. Determine whether is even, odd, or undefined for \(x<0\). Describe the rest of the curve if any. Graph the function to see whether it

Chapter: 2 Problem: 90

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2124, state the values of the constants k and a for the function \(f(x)=k \cdot x^{a}\). Describe the portion of the curve that lies in Quadrant I or IV. Determine whether is even, odd, or undefined for \(x<0\). Describe the rest of the curve if any. Graph the function to see whether it

Chapter: 2 Problem: 91

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2124, state the values of the constants k and a for the function \(f(x)=k \cdot x^{a}\). Describe the portion of the curve that lies in Quadrant I or IV. Determine whether is even, odd, or undefined for \(x<0\). Describe the rest of the curve if any. Graph the function to see whether it

Chapter: 2 Problem: 92

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2124, state the values of the constants k and a for the function \(f(x)=k \cdot x^{a}\). Describe the portion of the curve that lies in Quadrant I or IV. Determine whether is even, odd, or undefined for \(x<0\). Describe the rest of the curve if any. Graph the function to see whether it

Chapter: 2 Problem: 93

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2528, divide by \(f(x) \text { by } d(x)\), and write a summary statement in polynomial form. \(f(x)=2 x^{3}-7 x^{2}+4 x-5 ; d(x)=x-3\)

Chapter: 2 Problem: 94

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2528, divide by \(f(x) \text { by } d(x)\), and write a summary statement in polynomial form. \(f(x)=x^{4}+3 x^{3}+x^{2}-3 x+3 ; d(x)=x+2\)

Chapter: 2 Problem: 95

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2528, divide by \(f(x) \text { by } d(x)\), and write a summary statement in polynomial form. \(f(x)=2 x^{4}-3 x^{3}+9 x^{2}-14 x+7 ; d(x)=x^{2}+4\)

Chapter: 2 Problem: 96

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2528, divide by \(f(x) \text { by } d(x)\), and write a summary statement in polynomial form. \(f(x)=3 x^{4}-5 x^{3}-2 x^{2}+3 x-6 ; d(x)=3 x+1\)

Chapter: 2 Problem: 97

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 29 and 30, use the Remainder Theorem to find the remainder when f (x) is divided by \(x-k\). Check by using synthetic division. \(f(x)=3 x^{3}-2 x^{2}+x-5 ; k=-2\)

Chapter: 2 Problem: 98

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 29 and 30, use the Remainder Theorem to find the remainder when f (x) is divided by \(x-k\). Check by using synthetic division. \(f(x)=-x^{2}+4 x-5 ; k=3\)

Chapter: 2 Problem: 99

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 31 and 32, use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. \(x-2 ; x^{3}-4 x^{2}+8 x-8\)

Chapter: 2 Problem: 100

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 31 and 32, use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. \(x+3 ; x^{3}+2 x^{2}-4 x-2\)

Chapter: 2 Problem: 101

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 33 and 34, use synthetic division to prove that the number k is an upper bound for the real zeros of the function . \(k=5 ; f(x)=x^{3}-5 x^{2}+3 x+4\)

Chapter: 2 Problem: 102

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 33 and 34, use synthetic division to prove that the number k is an upper bound for the real zeros of the function . \(k=4 ; f(x)=4 x^{4}-16 x^{3}+8 x^{2}+16 x-12\)

Chapter: 2 Problem: 103

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 35 and 36, use synthetic division to prove that the number k is a lower bound for the real zeros of the function . \(k=-3 ; f(x)=4 x^{4}+4 x^{3}-15 x^{2}-17 x-2\)

Chapter: 2 Problem: 104

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 35 and 36, use synthetic division to prove that the number k is a lower bound for the real zeros of the function . \(k=-3 ; f(x)=2 x^{3}+6 x^{2}+x-6\)

Chapter: 2 Problem: 105

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 37 and 38, use the Rational Zeros Theorem to write a list of all potential rational zeros. Then determine which ones, if any, are zeros. \(f(x)=2 x^{4}-x^{3}-4 x^{2}-x-6\)

Chapter: 2 Problem: 106

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 37 and 38, use the Rational Zeros Theorem to write a list of all potential rational zeros. Then determine which ones, if any, are zeros. \(f(x)=6 x^{3}-20 x^{2}+11 x+7\)

Chapter: 2 Problem: 107

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3942, perform the indicated operation, and write the result in the form \(a+b i\). \((1+i)^{3}\)

Chapter: 2 Problem: 108

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3942, perform the indicated operation, and write the result in the form \(a+b i\). \((1+2 i)^{2}(1-2 i)^{2}\)

Chapter: 2 Problem: 109

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3942, perform the indicated operation, and write the result in the form \(a+b i\). \(i^{29}\)

Chapter: 2 Problem: 110

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3942, perform the indicated operation, and write the result in the form \(a+b i\). \(\sqrt{-16}\)

Chapter: 2 Problem: 111

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 43 and 44, solve the equation. \(x^{2}-6 x+13=0\)

Chapter: 2 Problem: 112

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 43 and 44, solve the equation. \(x^{2}-2 x+4=0\)

Chapter: 2 Problem: 113

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4548, match the polynomial function with its graph. Explain your choice. \(f(x)=(x-2)^{2}\)

Chapter: 2 Problem: 114

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4548, match the polynomial function with its graph. Explain your choice. \(f(x)=(x-2)^{3}\)

Chapter: 2 Problem: 115

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4548, match the polynomial function with its graph. Explain your choice. \(f(x)=(x-2)^{4}\)

Chapter: 2 Problem: 116

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4548, match the polynomial function with its graph. Explain your choice. \(f(x)=(x-2)^{5}\)

Chapter: 2 Problem: 117

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4952, find all of the real zeros of the function, finding exact values whenever possible. Identify each zero as rational or irrational. State the number of nonreal complex zeros. \(f(x)=x^{4}-10 x^{3}+23 x^{2}\)

Chapter: 2 Problem: 118

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4952, find all of the real zeros of the function, finding exact values whenever possible. Identify each zero as rational or irrational. State the number of nonreal complex zeros. \(k(t)=t^{4}-7 t^{2}+12\)

Chapter: 2 Problem: 119

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4952, find all of the real zeros of the function, finding exact values whenever possible. Identify each zero as rational or irrational. State the number of nonreal complex zeros. \(h(x)=x^{3}-2 x^{2}-8 x+5\)

Chapter: 2 Problem: 120

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4952, find all of the real zeros of the function, finding exact values whenever possible. Identify each zero as rational or irrational. State the number of nonreal complex zeros. \(k(x)=x^{4}-x^{3}-14 x^{2}+24 x+5\)

Chapter: 2 Problem: 121

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5356, find all of the zeros and write a linear factorization of the function. \(f(x)=2 x^{3}-9 x^{2}+2 x+30\)

Chapter: 2 Problem: 122

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5356, find all of the zeros and write a linear factorization of the function. \(f(x)=5 x^{3}-24 x^{2}+x+12\)

Chapter: 2 Problem: 123

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5356, find all of the zeros and write a linear factorization of the function. \(f(x)=6 x^{4}+11 x^{3}-16 x^{2}-11 x+10\)

Chapter: 2 Problem: 124

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5356, find all of the zeros and write a linear factorization of the function. \(f(x)=x^{4}-8 x^{3}+27 x^{2}-50 x+50\), given that \(1+2 i\) is a zero.

Chapter: 2 Problem: 125

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5760, write the function as a product of linear and irreducible quadratic factors all with real coefficients. \(f(x)=x^{3}-x^{2}-x-2\)

Chapter: 2 Problem: 126

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5760, write the function as a product of linear and irreducible quadratic factors all with real coefficients. \(f(x)=9 x^{3}-3 x^{2}-13 x-1\)

Chapter: 2 Problem: 127

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5760, write the function as a product of linear and irreducible quadratic factors all with real coefficients. \(f(x)=2 x^{4}-9 x^{3}+23 x^{2}-31 x+15\)

Chapter: 2 Problem: 128

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5760, write the function as a product of linear and irreducible quadratic factors all with real coefficients. \(f(x)=3 x^{4}-7 x^{3}-3 x^{2}+17 x+10\)

Chapter: 2 Problem: 129

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6166, write a polynomial function with real coefficients whose zeros and their multiplicities include those listed. Degree 3; zeros: \(\sqrt{5},-\sqrt{5}, 3\)

Chapter: 2 Problem: 130

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6166, write a polynomial function with real coefficients whose zeros and their multiplicities include those listed. Degree 2; -3 only real zero

Chapter: 2 Problem: 131

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6166, write a polynomial function with real coefficients whose zeros and their multiplicities include those listed. Degree 4; zeros: 3, \(-2,1 / 3,-1 / 2\)

Chapter: 2 Problem: 132

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6166, write a polynomial function with real coefficients whose zeros and their multiplicities include those listed. Degree 3; zeros: \(1+i, 2\)

Chapter: 2 Problem: 133

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6166, write a polynomial function with real coefficients whose zeros and their multiplicities include those listed. Degree 4; zeros: -2 (multiplicity 2), 4(multiplicity 2)

Chapter: 2 Problem: 134

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6166, write a polynomial function with real coefficients whose zeros and their multiplicities include those listed. Degree 3; zeros: \(2-i,-1 \text {, and } f(2)=6\)

Chapter: 2 Problem: 135

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 67 and 68, describe how the graph of the given function can be obtained by transforming the graph of the reciprocal function \(f(x)=1 / x\). Identify the horizontal and vertical asymptotes. \(f(x)=\frac{-x+7}{x-5}\)

Chapter: 2 Problem: 136

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 67 and 68, describe how the graph of the given function can be obtained by transforming the graph of the reciprocal function \(f(x)=1 / x\). Identify the horizontal and vertical asymptotes. \(f(x)=\frac{3 x+5}{x+2}\)

Chapter: 2 Problem: 137

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6972, find the asymptotes and intercepts of the function, and graph it. \(f(x)=\frac{x^{2}+x+1}{x^{2}-1}\)

Chapter: 2 Problem: 138

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6972, find the asymptotes and intercepts of the function, and graph it. \(f(x)=\frac{2 x^{2}+7}{x^{2}+x-6}\)

Chapter: 2 Problem: 139

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6972, find the asymptotes and intercepts of the function, and graph it. \(f(x)=\frac{x^{2}-4 x+5}{x+3}\)

Chapter: 2 Problem: 140

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 6972, find the asymptotes and intercepts of the function, and graph it. \(g(x)=\frac{x^{2}-3 x-7}{x+3}\)

Chapter: 2 Problem: 141

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7374, find the intercepts, analyze, and graph the given rational function. \(f(x)=\frac{x^{3}+x^{2}-2 x+5}{x+2}\)

Chapter: 2 Problem: 142

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7374, find the intercepts, analyze, and graph the given rational function. \(f(x)=\frac{-x^{4}+x^{2}+1}{x-1}\)

Chapter: 2 Problem: 143

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7582, solve the equation or inequality algebraically, and support graphically. \(2 x+\frac{12}{x}=11\)

Chapter: 2 Problem: 144

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7582, solve the equation or inequality algebraically, and support graphically. \(\frac{x}{x+2}+\frac{5}{x-3}=\frac{25}{x^{2}-x-6}\)

Chapter: 2 Problem: 145

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7582, solve the equation or inequality algebraically, and support graphically. \(2 x^{3}+3 x^{2}-17 x-30<0\)

Chapter: 2 Problem: 146

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7582, solve the equation or inequality algebraically, and support graphically. \(3 x^{4}+x^{3}-36 x^{2}+36 x+16 \geq 0\)

Chapter: 2 Problem: 147

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7582, solve the equation or inequality algebraically, and support graphically. \(\frac{x+3}{x^{2}-4} \geq 0\)

Chapter: 2 Problem: 148

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7582, solve the equation or inequality algebraically, and support graphically. \(\frac{x^{2}-7}{x^{2}-x-6}<1\)

Chapter: 2 Problem: 149

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7582, solve the equation or inequality algebraically, and support graphically. \((2 x-1)^{2}|x+3| \leq 0\)

Chapter: 2 Problem: 150

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 7582, solve the equation or inequality algebraically, and support graphically. \(\frac{(x-1)|x-4|}{\sqrt{x+3}}>0\)

Chapter: 2 Problem: 151

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Determine whether \(f(x)=x^{5}-10 x^{4}-3 x^{3}+28 x^{2}+20 x-2\) has a zero outside the viewing window. Explain. (See graph.)

Chapter: 2 Problem: 152

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Launching a Rock Larry uses a slingshot to launch a rock straight up from a point 6 ft above level ground with an initial velocity of 170 ft/sec. (a) Find an equation that models the height of the rock t seconds after it is launched and graph the equation. (See Example 8 in Section 2.1.) (b)

Chapter: 2 Problem: 153

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Volume of a Box Villareal Paper Co. has contracted to manufacture a box with no top that is to be made by removing squares of width x from the corners of a 30-in. by 70-in. Piece of cardboard. (a) Find an equation that models the volume of the box. (b) Determine x so that the box has a volume

Chapter: 2 Problem: 154

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Architectural Engineering DeShanna, an engineer at J. P. Cook, Inc., completes structural specifications for a 255-ft-long steel beam anchored between two pilings 50 ft above ground, as shown in the figure. She knows that when a 250-lb object is placed d feet from the west piling, the beam bends s fe

Chapter: 2 Problem: 155

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Storage Container A liquid storage container on a truck is in the shape of a cylinder with hemispheres on each end as shown in the figure. The cylinder and hemispheres have the same radius. The total length of the container is 140 ft. (a) Determine the volume V of the container as a function of t

Chapter: 2 Problem: 156

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Pell Grants The maximum loan permitted under the federal student-aid program is given in Table 2.24 for several years. Let x = 0 represent 1990, x = 1 represent 1991, and so forth. (a) Find a quadratic regression model for the Pell Grant amounts, and graph it together with a scatter plot

Chapter: 2 Problem: 157

Precalculus: Graphical, Numerical, Algebraic 8th Edition
National Institutes of Health Spending Table 2.25 shows the spending at the National Institutes of Health for several years. Let x = 0 represent 1990, x = 1 represent 1991, and so forth. (a) Find a linear regression model, and graph it together with a scatter plot of the data. (b) Fin

Chapter: 2 Problem: 158

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Breaking Even Midtown Sporting Goods has determined that it needs to sell its soccer shinguards for $5.25 a pair in order to be competitive. It costs $4.32 to produce each pair of shinguards, and the weekly overhead cost is $4000. (a) Express the average cost that includes the overhead of produci

Chapter: 2 Problem: 159

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Deer Population The number of deer P at any time t(in years) in a federal game reserve is given by \(P(t)=\frac{800+640 t}{20+0.8 t}\). (a) Find the number of deer when t is 15, 70, and 100. (b) Find the horizontal asymptote of the graph of \(y=P(t)\). (c) According to the model, what

Chapter: 2 Problem: 160

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Resistors The total electrical resistance R of two resistors connected in parallel with resistances \(R_{1} \text { and } R_{2}\) is given by \(\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}}\). The total resistance is 1.2 ohms. Let \(x=R_{1}\). (a) Express the second resistance \(R_{2}\) as

Chapter: 2 Problem: 161

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Acid Mixture Suppose that x ounces of distilled water are added to 50 oz of pure acid. (a) Express the concentration of the new mixture as a function of x. (b) Use a graph to determine how much distilled water should be added to the pure acid to produce a new solution that is less than 60% ac

Chapter: 2 Problem: 162

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Industrial Design Johnson Cannery will pack peaches in 1-L cylindrical cans. Let x be the radius of the base of the can in centimeters. (a) Express the surface area S of the can as a function of x. (b) Find the radius and height of the can if the surface area is \(900 \mathrm{cm}^{2}\). (

Chapter: 2 Problem: 163

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Industrial Design Gilman Construction is hired to build a rectangular tank with a square base and no top. The tank is to hold \(1000 \mathrm{ft}^{3}\) of water. Let x be a length of the base. (a) Express the outside surface area S of the tank as a function of x. (b) Find the length, width, an

Chapter: 2 Problem: 164

Precalculus: Graphical, Numerical, Algebraic 8th Edition
If you collected motion data using a \(\mathrm{CBL}^{\mathrm{TM}} \text { or } \mathrm{CBR}^{\mathrm{TM}}\), a plot of height versus time or distance versus time should be shown on your grapher or computer screen. Either plot will work for this project. If you do not have access to a CBL or CBR, ente

Chapter: 2 Problem: 165

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Find values for a, h, and k so that the equation \(y=a(x-h)^{2}+k\) fits one of the bounces contained in the data plot. Approximate the vertex 1h, k2 from your data plot and solve for the value of an algebraically.

Chapter: 2 Problem: 166

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Change the values of a, h, and k in the model found above and observe how the graph of the function is affected on your grapher or computer. Generalize how each of these changes affects the graph.

Chapter: 2 Problem: 167

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Expand the equation you found in #2 above so that it is in the standard quadratic form: \(y=a x^{2}+ bx+c\).

Chapter: 2 Problem: 168

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Use your grapher or computer to select the data from the bounce you modeled above and then use quadratic regression to find a model for this data set. (See your graphers guidebook for instructions on how to do this.) How does this model compare with the standard quadratic form found in #4?

Chapter: 2 Problem: 169

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Complete the square to transform the regression model to the vertex form of a quadratic, and compare it to the original vertex model found in #2. (Round the values of a, b, and c to the nearest 0.001 before completing the square if desired.)

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