# Quiz 4: Polynomial and Rational Functions

Mathematics

Free

Multiple Choice

A

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Multiple Choice

C

Q 3Q 3

For the following function, find a number such that the graph of contains the point
A)
B)
C)
D)
E)

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B

Q 4Q 4

A meteorologist determines that the temperature T for a certain 24-hour period in winter was given by the following formula. is time in hours and corresponds to 6 A.M.
A)-16 < t < -24
B)0 < t < 8
C)0 < t < 24
D)16 < t < 24
E)0 < t < 16

Free

Multiple Choice

Q 5Q 5

A herd of 575 deer is introduced onto a small island. At first the herd increases rapidly, but eventually food resources dwindle and the population declines. Suppose that the number of deer after years is given by the following formula. where How many years does it take for the population to become extinct?
A)t = 8
B)t = 10
C)t = 4
D)t = 5
E)t = 6

Free

Multiple Choice

Q 6Q 6

Use the remainder theorem to find ,
A)f ( 8 ) = 4,576
B)f ( 8 ) = 4,620
C)f ( 8 ) = 4,572
D)f ( 8 ) = 4,580
E)f ( 8 ) = 4,548

Free

Multiple Choice

Q 7Q 7

Use the factor theorem to decide whether is a factor of the polynomial. ;
A)x - c is not a factor
B)x - c is a factor

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Q 8Q 8

Find a polynomial with leading coefficient of , degree , and zeros: - .
A)f ( x ) = x

^{ 4 }- 3x^{ 3 }- 26x^{ 2 }+ 26x + 160 B)f ( x ) = x^{ 4 }- 6x^{ 2 }- 22x + 40 C)f ( x ) = x^{ 4 }- 26x^{ 2 }+ 48x + 160 D)f ( x ) = x^{ 4 }- 3x^{ 3 }- 26x^{ 2 }+ 160 E)f ( x ) = x^{ 4 }- 3x^{ 3 }- 26x^{ 2 }+ 48x + 160Free

Multiple Choice

Q 9Q 9

Use synthetic division to decide whether is a zero of ;
A)c is a zero of f ( x )
B)c is not a zero of f ( x )

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Multiple Choice

Q 10Q 10

An arch has the shape of the parabola A rectangle is fit under the arch by selecting a point on the parabola (see the figure). If the rectangle has base and height . Find the base of a second rectangle that has the same area.
A)10.85
B)9.85
C)8.85
D)8.62
E)10.8

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Multiple Choice

Q 11Q 11

Find the quotient and remainder if is divided by . ,
A)quotient: , remainder:
B)quotient: , remainder:
C)quotient: , remainder:
D)quotient : , remainder :
E)quotient: , remainder:

Free

Multiple Choice

Q 12Q 12

An aspirin tablet is in the shape of a right circular cylinder. The manufacturer also wishes to market the aspirin in capsule form. The capsule is to be centimeters long, in the shape of a right circular cylinder with hemispheres attached at both ends (see the figure below). If denotes the radius of a hemisphere, find a formula for the volume of the capsule.
A)
B)
C)
D)
E)

Free

Multiple Choice

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Q 14Q 14

Show that the number is a zero of of the given multiplicity, and express as a product of linear factors.
A)
B)
C)
D)
E)

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Q 19Q 19

Does there exist a polynomial of degree 3 with real coefficients that has zeros 9 , - 9, and i ?
A)no
B)yes

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Q 21Q 21

Find an equation of a rational function that satisfies the conditions. vertical asymptote: x = - 8, x = 0
Horizontal asymptote: y = 0
X-intercept: 7; f (8) = 1
A)
B)
C)
D)
E)

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Multiple Choice

Q 22Q 22

Express the statement as a formula that involves the variables u, v and a constant of proportionality k, and determine the value of k from the condition : u is directly proportional to v and if v = 40, then u = 3
A)
B)
C)
D)
E)

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Multiple Choice

Q 23Q 23

The period P of a simple pendulum - that is, the time required for one complete oscillation - is directly proportional to the square root of its length l. Express P in terms of l and a constant of proportionality k. If a pendulum 3.8 feet long has a period of 2.3 seconds, find the value of k.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 24Q 24

A thin flat plate is situated in an xy-plane such that the density d ( in lb/ft

^{ 2 }) at the point is inversely proportional to the square of the distance from the origin. What is the effect on the density at P if the x- and y-coordinates are each multiplied by A)d is multiplied 2 B)d is multiplied 2.83 C)d is multiplied 0.25 D)d is multiplied 0.50 E)d is multiplied 4Free

Multiple Choice

Q 25Q 25

A flat metal plate is positioned in an xy-plane such that the temperature T (in C) at the point (x, y) is inversely proportional to the distance from the origin. If the temperature at the point P (3, 4) is 20 C, find the temperature at the point Q (6, 5).
A)
B)
C)
D)
E)

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Q 28Q 28

For the following function, find a number such that the graph of contains the point
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 29Q 29

A meteorologist determines that the temperature T for a certain 24-hour period in winter was given by the following formula. is time in hours and corresponds to 6 A.M.
A)-8 < t < -24
B)0 < t < 24
C)0 < t < 16
D)8 < t < 24
E)0 < t < 8

Free

Multiple Choice

Q 30Q 30

A herd of 575 deer is introduced onto a small island. At first the herd increases rapidly, but eventually food resources dwindle and the population declines. Suppose that the number of deer after years is given by the following formula. where How many years does it take for the population to become extinct?
A)t = 10
B)t = 8
C)t = 5
D)t = 6
E)t = 4

Free

Multiple Choice

Q 31Q 31

Use the remainder theorem to find ,
A)f ( 7 ) = 3,064
B)f ( 7 ) = 3,094
C)f ( 7 ) = 3,054
D)f ( 7 ) = 3,040
E)f ( 7 ) = 3,059

Free

Multiple Choice

Q 32Q 32

Use the factor theorem to decide whether is a factor of the polynomial. ;
A)x - c is not a factor
B)x - c is a factor

Free

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Q 33Q 33

Find a polynomial with leading coefficient of , degree , and zeros: - .
A)f ( x ) = x

^{ 4 }- 6x^{ 2 }- 13x + 15 B)f ( x ) = x^{ 4 }- 2x^{ 3 }- 28x^{ 2 }+ 50x + 75 C)f ( x ) = x^{ 4 }- 2x^{ 3 }- 28x^{ 2 }+ 75 D)f ( x ) = x^{ 4 }- 2x^{ 3 }- 28x^{ 2 }+ 28x + 75 E)f ( x ) = x^{ 4 }- 28x^{ 2 }+ 50x + 75Free

Multiple Choice

Q 34Q 34

Use synthetic division to decide whether is a zero of ;
A)c is a zero of f ( x )
B)c is not a zero of f ( x )

Free

Multiple Choice

Q 35Q 35

An arch has the shape of the parabola A rectangle is fit under the arch by selecting a point on the parabola (see the figure). If the rectangle has base and height . Find the base of a second rectangle that has the same area.
A)2.61
B)3.61
C)4.61
D)4.46
E)5

Free

Multiple Choice

Q 36Q 36

Find the quotient and remainder if is divided by . ,
A)quotient : , remainder :
B)quotient: , remainder:
C)quotient: , remainder:
D)quotient: , remainder:
E)quotient: , remainder:

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Multiple Choice

Q 37Q 37

An aspirin tablet is in the shape of a right circular cylinder. The manufacturer also wishes to market the aspirin in capsule form. The capsule is to be centimeters long, in the shape of a right circular cylinder with hemispheres attached at both ends (see the figure below). If denotes the radius of a hemisphere, find a formula for the volume of the capsule.
A)
B)
C)
D)
E)

Free

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Q 39Q 39

Show that the number is a zero of of the given multiplicity, and express as a product of linear factors.
A)
B)
C)
D)
E)

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Q 44Q 44

Does there exist a polynomial of degree 3 with real coefficients that has zeros 7 , - 7, and i ?
A)no
B)yes

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Q 46Q 46

Find an equation of a rational function that satisfies the conditions. vertical asymptote: x = - 2, x = 0
Horizontal asymptote: y = 0
X-intercept: 3; f (4) = 1
A)
B)
C)
D)
E)

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Multiple Choice

Q 47Q 47

Express the statement as a formula that involves the variables u, v and a constant of proportionality k, and determine the value of k from the condition : u is directly proportional to v and if v = 30, then u = 3
A)
B)
C)
D)
E)

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Multiple Choice

Q 48Q 48

The period P of a simple pendulum - that is, the time required for one complete oscillation - is directly proportional to the square root of its length l. Express P in terms of l and a constant of proportionality k. If a pendulum 3.5 feet long has a period of 1.3 seconds, find the value of k.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 49Q 49

A thin flat plate is situated in an xy-plane such that the density d ( in lb/ft

^{ 2 }) at the point is inversely proportional to the square of the distance from the origin. What is the effect on the density at P if the x- and y-coordinates are each multiplied by A)d is multiplied 0.14 B)d is multiplied 7 C)d is multiplied 49 D)d is multiplied 0.02 E)d is multiplied 9.90Free

Multiple Choice

Q 50Q 50

A flat metal plate is positioned in an xy-plane such that the temperature T (in C) at the point (x, y) is inversely proportional to the distance from the origin. If the temperature at the point P (3, 4) is 30 C, find the temperature at the point Q (6, 8).
A)
B)
C)
D)
E)

Free

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Q 53Q 53

For the following function, find a number such that the graph of contains the point
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 54Q 54

A meteorologist determines that the temperature T for a certain 24-hour period in winter was given by the following formula. is time in hours and corresponds to 6 A.M.
A)13 < t < 24
B)0 < t < 11
C)0 < t < 24
D)-13 < t < -24
E)0 < t < 13

Free

Multiple Choice

Q 55Q 55

A herd of 575 deer is introduced onto a small island. At first the herd increases rapidly, but eventually food resources dwindle and the population declines. Suppose that the number of deer after years is given by the following formula. where How many years does it take for the population to become extinct?
A)t = 4
B)t = 6
C)t = 10
D)t = 8
E)t = 5

Free

Multiple Choice

Q 56Q 56

Use the remainder theorem to find ,
A)f ( 3 ) = 228
B)f ( 3 ) = 181
C)f ( 3 ) = 221
D)f ( 3 ) = 235
E)f ( 3 ) = 203

Free

Multiple Choice

Q 57Q 57

Use the factor theorem to decide whether is a factor of the polynomial. ;
A)x - c is a factor
B)x - c is not a factor

Free

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Q 58Q 58

Find a polynomial with leading coefficient of , degree , and zeros: - .
A)f ( x ) = x

^{ 4 }- 33x^{ 2 }+ 50x + 200 B)f ( x ) = x^{ 4 }- 2x^{ 3 }- 33x^{ 2 }+ 200 C)f ( x ) = x^{ 4 }- 2x^{ 3 }- 33x^{ 2 }+ 33x + 200 D)f ( x ) = x^{ 4 }- 2x^{ 3 }- 33x^{ 2 }+ 50x + 200 E)f ( x ) = x^{ 4 }- 7x^{ 2 }- 18x + 40Free

Multiple Choice

Q 59Q 59

Use synthetic division to decide whether is a zero of ;
A)c is not a zero of f ( x )
B)c is a zero of f ( x )

Free

Multiple Choice

Q 60Q 60

An arch has the shape of the parabola A rectangle is fit under the arch by selecting a point on the parabola (see the figure). If the rectangle has base and height . Find the base of a second rectangle that has the same area.
A)6.66
B)6.74
C)5.74
D)4.74
E)6.1

Free

Multiple Choice

Q 61Q 61

Find the quotient and remainder if is divided by . ,
A)quotient: , remainder:
B)quotient: , remainder:
C)quotient : , remainder :
D)quotient: , remainder:
E)quotient: , remainder:

Free

Multiple Choice

Q 62Q 62

An aspirin tablet is in the shape of a right circular cylinder. The manufacturer also wishes to market the aspirin in capsule form. The capsule is to be centimeters long, in the shape of a right circular cylinder with hemispheres attached at both ends (see the figure below). If denotes the radius of a hemisphere, find a formula for the volume of the capsule.
A)
B)
C)
D)
E)

Free

Multiple Choice

Free

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Q 64Q 64

Show that the number is a zero of of the given multiplicity, and express as a product of linear factors.
A)
B)
C)
D)
E)

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Q 69Q 69

Does there exist a polynomial of degree 3 with real coefficients that has zeros 5 , - 5, and i ?
A)yes
B)no

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Q 71Q 71

Find an equation of a rational function that satisfies the conditions. vertical asymptote: x = - 1, x = 0
Horizontal asymptote: y = 0
X-intercept: 8; f (9) = 1
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 72Q 72

Express the statement as a formula that involves the variables u, v and a constant of proportionality k, and determine the value of k from the condition : u is directly proportional to v and if v = 40, then u = 3
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 73Q 73

The period P of a simple pendulum - that is, the time required for one complete oscillation - is directly proportional to the square root of its length l. Express P in terms of l and a constant of proportionality k. If a pendulum 2.7 feet long has a period of 2.3 seconds, find the value of k.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 74Q 74

A thin flat plate is situated in an xy-plane such that the density d ( in lb/ft

^{ 2 }) at the point is inversely proportional to the square of the distance from the origin. What is the effect on the density at P if the x- and y-coordinates are each multiplied by A)d is multiplied 0.11 B)d is multiplied 0.33 C)d is multiplied 3 D)d is multiplied 9 E)d is multiplied 4.24Free

Multiple Choice

Q 75Q 75

A flat metal plate is positioned in an xy-plane such that the temperature T (in C) at the point (x, y) is inversely proportional to the distance from the origin. If the temperature at the point P (3, 4) is 15 C, find the temperature at the point Q (9, 8).
A)
B)
C)
D)
E)

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Q 79Q 79

From a rectangular piece of cardboard having dimensions W = 16 and L = 30 an open box is to be made by cutting out identical squares of area x

^{ 2 }from each corner and turning up the sides (see Illustration). Find all positive values of x such that the volume of the box V ( x ) > 0. Include only allowable values of x in your answer. A) B) C) D) E)Free

Multiple Choice

Free

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Q 81Q 81

Use synthetic division to decide whether is a zero of . ;
A)x - c is a zero
B)x - c is not a zero

Free

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Q 82Q 82

Use synthetic division to find ;
A)f ( 5 ) = 515
B)f ( 5 ) = 525
C)f ( 5 ) = 6
D)f ( 5 ) = 221
E)f ( 5 ) = 521

Free

Multiple Choice

Q 83Q 83

Use synthetic division to decide whether is a zero of the equation. ;
A)c is not a zero
B)c is a zero

Free

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Q 84Q 84

Find a polynomial of degree that has the indicated zeros and satisfies the given condition.
A)
B)
C)
D)
E)

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Q 85Q 85

Find the fourth-degree polynomial function whose graph is shown in the figure.
A)
B)
C)
D)
E)

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Q 86Q 86

Applying the first theorem on bounds for real zeros of polynomials, determine the smallest and largest integers that are upper and lower bounds, respectively, for the real solutions of the equation. With the aid of a graphing utility, discuss the validity of the bounds.
A)The upper bound is , the lower bound is
.
B)The upper bound is , the lower bound is
.
C)The upper bound is , the lower bound is
.
D)The upper bound is , the lower bound is
.
E)The upper bound is , the lower bound is
.

Free

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Q 87Q 87

A polynomial f ( x ) with real coefficients and leading coefficient 1 has the given zero and degree. Express f ( x ) as a product of linear and quadratic polynomials with real coefficients that are irreducible over R.
A)
B)
C)
D)
E)

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Q 88Q 88

A polynomial f ( x ) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f ( x ) as a product of linear and quadratic polynomials with real coefficients that are irreducible over R.
A)
B)
C)
D)
E)

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Q 90Q 90

Find a factored form with integer coefficients of the polynomial f shown in the figure.
A)
B)
C)
D)
E)

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Q 91Q 91

A canvas camping tent is to be constructed in the shape of a pyramid with a square base. An 8-foot pole will form the center support, as illustrated in the figure. Find the length x of a side of the base so that the total amount of canvas needed for the sides and bottom is 384 ft

^{ 2 }. A)11 ft B)13 ft C)12 ft D)10 ft E)14 ftFree

Multiple Choice

Q 92Q 92

The density D(h) (in kg/m

^{ 3 }) of the earth's atmosphere at an altitude of h meters can be approximated by where and . Use a graphing utility to graph D and approximate the altitude h at which the density is 0.6. A)7,000 m B)7,200 m C)6,400 m D)6,800 m E)6,600 mFree

Multiple Choice

Free

Multiple Choice

Q 94Q 94

Salt water of concentration 0.1 pound of salt per gallon flows into a large tank that initially contains 40 gallons of pure water. If the flow rate of salt water into the tank is 5 gal/min, find a formula for the salt concentration (in lb/gal) after t minutes.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 95Q 95

Express the statement as a formula that involves the variables w, z, u and a constant of proportionality k, and then determine the value of k from the condition : w varies directly as z and inversely as the square root of u, if z = 2 and u = 36, then w = 12
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 96Q 96

Express the statement as a formula that involves the variables q, x, y and a constant of proportionality k, and then determine the value of k from the condition : q is inversely proportional to the sum of x and y, if x = 0.3 and y = 3.7, then q = 0.4
A)
B)
C)
D)
E)

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Multiple Choice

Q 97Q 97

The pressure P acting at a point in a liquid is directly proportional to the distance d from the surface of the liquid to the point. Express P as a function of d by means of a formula that involves a constant of proportionality k. In a certain oil tank, the pressure at a depth of 6 feet is 354. Find the value of k.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 98Q 98

Poiseuille's law states that the blood flow rate F ( in L/min ) through a major artery is directly proportional to the product of the fourth power of the radius r and the blood pressure P. During heavy exercise, normal blood flow rates sometimes triple. If the radius of a major artery increases by 5%, approximately how much harder must the heart pump?
A)about 2.47 times as hard
B)about 3.61 times as hard
C)about 1.22 times as hard
D)about 2.10 times as hard
E)about 2.22 times as hard

Free

Multiple Choice

Q 99Q 99

When uranium disintegrates into lead, one step in the process is the radioactive decay of radium into radon gas. Radon enters through the soil into home basements, where it presents a health hazard if inhaled. In the simplest case of radon detection, a sample of air with volume V is taken. After equilibrium has been established, the radioactive decay D of the radon gas is counted with efficiency E over time t. The radon concentration C present in the sample of air varies directly as the product of D and E and inversely as the product of V and t. For a fixed radon concentration C and time t, find the change in the radioactive decay count D if V is multiplied by 2 and E is reduced by 14%.
A)increases 255.81%
B)increases 281.40%
C)increases 175.44%
D)increases 232.56%
E)increases 1,428.57%

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Q 103Q 103

From a rectangular piece of cardboard having dimensions W = 30 and L = 32 an open box is to be made by cutting out identical squares of area x

^{ 2 }from each corner and turning up the sides (see Illustration). Find all positive values of x such that the volume of the box V ( x ) > 0. Include only allowable values of x in your answer. A) B) C) D) E)Free

Multiple Choice

Free

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Q 105Q 105

Use synthetic division to decide whether is a zero of . ;
A)x - c is not a zero
B)x - c is a zero

Free

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Q 106Q 106

Use synthetic division to find ;
A)f ( 3 ) = 135
B)f ( 3 ) = 3
C)f ( 3 ) = 48
D)f ( 3 ) = 138
E)f ( 3 ) = 153

Free

Multiple Choice

Q 107Q 107

Use synthetic division to decide whether is a zero of the equation. ;
A)c is not a zero
B)c is a zero

Free

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Q 108Q 108

Find a polynomial of degree that has the indicated zeros and satisfies the given condition.
A)
B)
C)
D)
E)

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Q 109Q 109

Find the fourth-degree polynomial function whose graph is shown in the figure.
A)
B)
C)
D)
E)

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Q 110Q 110

Applying the first theorem on bounds for real zeros of polynomials, determine the smallest and largest integers that are upper and lower bounds, respectively, for the real solutions of the equation. With the aid of a graphing utility, discuss the validity of the bounds.
A)The upper bound is , the lower bound is
.
B)The upper bound is , the lower bound is
.
C)The upper bound is , the lower bound is
.
D)The upper bound is , the lower bound is
.
E)The upper bound is , the lower bound is
.

Free

Multiple Choice

Q 111Q 111

A polynomial f ( x ) with real coefficients and leading coefficient 1 has the given zero and degree. Express f ( x ) as a product of linear and quadratic polynomials with real coefficients that are irreducible over R.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 112Q 112

A polynomial f ( x ) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f ( x ) as a product of linear and quadratic polynomials with real coefficients that are irreducible over R.
A)
B)
C)
D)
E)

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Q 114Q 114

Find a factored form with integer coefficients of the polynomial f shown in the figure.
A)
B)
C)
D)
E)

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Multiple Choice

Q 115Q 115

A canvas camping tent is to be constructed in the shape of a pyramid with a square base. An 8-foot pole will form the center support, as illustrated in the figure. Find the length x of a side of the base so that the total amount of canvas needed for the sides and bottom is 384 ft

^{ 2 }. A)14 ft B)13 ft C)12 ft D)11 ft E)10 ftFree

Multiple Choice

Q 116Q 116

The density D(h) (in kg/m

^{ 3 }) of the earth's atmosphere at an altitude of h meters can be approximated by where and . Use a graphing utility to graph D and approximate the altitude h at which the density is 0.1. A)19,000 m B)19,800 m C)19,400 m D)19,200 m E)19,600 mFree

Multiple Choice

Free

Multiple Choice

Q 118Q 118

Salt water of concentration 0.1 pound of salt per gallon flows into a large tank that initially contains 72 gallons of pure water. If the flow rate of salt water into the tank is 6 gal/min, find a formula for the salt concentration (in lb/gal) after t minutes.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 119Q 119

Express the statement as a formula that involves the variables w, z, u and a constant of proportionality k, and then determine the value of k from the condition : w varies directly as z and inversely as the square root of u, if z = 4 and u = 36, then w = 20
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 120Q 120

Express the statement as a formula that involves the variables q, x, y and a constant of proportionality k, and then determine the value of k from the condition : q is inversely proportional to the sum of x and y, if x = 1.9 and y = 3.7, then q = 0.7
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 121Q 121

The pressure P acting at a point in a liquid is directly proportional to the distance d from the surface of the liquid to the point. Express P as a function of d by means of a formula that involves a constant of proportionality k. In a certain oil tank, the pressure at a depth of 7 feet is 413. Find the value of k.
A)
B)
C)
D)
E)

Free

Multiple Choice

Q 122Q 122

Poiseuille's law states that the blood flow rate F ( in L/min ) through a major artery is directly proportional to the product of the fourth power of the radius r and the blood pressure P. During heavy exercise, normal blood flow rates sometimes triple. If the radius of a major artery increases by 10%, approximately how much harder must the heart pump?
A)about 3.19 times as hard
B)about 1.80 times as hard
C)about 2.05 times as hard
D)about 1.46 times as hard
E)about 1.68 times as hard

Free

Multiple Choice

Q 123Q 123

When uranium disintegrates into lead, one step in the process is the radioactive decay of radium into radon gas. Radon enters through the soil into home basements, where it presents a health hazard if inhaled. In the simplest case of radon detection, a sample of air with volume V is taken. After equilibrium has been established, the radioactive decay D of the radon gas is counted with efficiency E over time t. The radon concentration C present in the sample of air varies directly as the product of D and E and inversely as the product of V and t. For a fixed radon concentration C and time t, find the change in the radioactive decay count D if V is multiplied by 4 and E is reduced by 20%.
A)increases 605.00%
B)increases 500.00%
C)increases 333.33%
D)increases 550.00%
E)increases 2,000.00%

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Q 127Q 127

From a rectangular piece of cardboard having dimensions W = 18 and L = 40 an open box is to be made by cutting out identical squares of area x

^{ 2 }from each corner and turning up the sides (see Illustration). Find all positive values of x such that the volume of the box V ( x ) > 0. Include only allowable values of x in your answer. A) B) C) D) E)Free

Multiple Choice

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Multiple Choice

Q 129Q 129

Use synthetic division to decide whether is a zero of . ;
A)x - c is a zero
B)x - c is not a zero

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Multiple Choice

Q 130Q 130

Use synthetic division to find ;
A)f ( 3 ) = 80
B)f ( 3 ) = 165
C)f ( 3 ) = 189
D)f ( 3 ) = 170
E)f ( 3 ) = 5

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Multiple Choice

Q 131Q 131

Use synthetic division to decide whether is a zero of the equation. ;
A)c is not a zero
B)c is a zero

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Multiple Choice

Q 132Q 132

Find a polynomial of degree that has the indicated zeros and satisfies the given condition.
A)
B)
C)
D)
E)

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Multiple Choice

Q 133Q 133

Find the fourth-degree polynomial function whose graph is shown in the figure.
A)
B)
C)
D)
E)

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Multiple Choice

Q 134Q 134

Applying the first theorem on bounds for real zeros of polynomials, determine the smallest and largest integers that are upper and lower bounds, respectively, for the real solutions of the equation. With the aid of a graphing utility, discuss the validity of the bounds.
A)The upper bound is , the lower bound is
.
B)The upper bound is , the lower bound is
.
C)The upper bound is , the lower bound is
.
D)The upper bound is , the lower bound is
.
E)The upper bound is , the lower bound is
.

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Multiple Choice

Q 135Q 135

A polynomial f ( x ) with real coefficients and leading coefficient 1 has the given zero and degree. Express f ( x ) as a product of linear and quadratic polynomials with real coefficients that are irreducible over R.
A)
B)
C)
D)
E)

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Multiple Choice

Q 136Q 136

A polynomial f ( x ) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f ( x ) as a product of linear and quadratic polynomials with real coefficients that are irreducible over R.
A)
B)
C)
D)
E)

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Multiple Choice

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Multiple Choice

Q 138Q 138

Find a factored form with integer coefficients of the polynomial f shown in the figure.
A)
B)
C)
D)
E)

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Multiple Choice

Q 139Q 139

A canvas camping tent is to be constructed in the shape of a pyramid with a square base. An 8-foot pole will form the center support, as illustrated in the figure. Find the length x of a side of the base so that the total amount of canvas needed for the sides and bottom is 384 ft

^{ 2 }. A)13 ft B)10 ft C)12 ft D)11 ft E)14 ftFree

Multiple Choice

Q 140Q 140

The density D(h) (in kg/m

^{ 3 }) of the earth's atmosphere at an altitude of h meters can be approximated by where and . Use a graphing utility to graph D and approximate the altitude h at which the density is 0.3. A)12,400 m B)12,600 m C)12,000 m D)12,800 m E)12,200 mFree

Multiple Choice

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Multiple Choice

Q 142Q 142

Salt water of concentration 0.5 pound of salt per gallon flows into a large tank that initially contains 220 gallons of pure water. If the flow rate of salt water into the tank is 4 gal/min, find a formula for the salt concentration (in lb/gal) after t minutes.
A)
B)
C)
D)
E)

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Multiple Choice

Q 143Q 143

Express the statement as a formula that involves the variables w, z, u and a constant of proportionality k, and then determine the value of k from the condition : w varies directly as z and inversely as the square root of u, if z = 3 and u = 4, then w = 18
A)
B)
C)
D)
E)

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Multiple Choice

Q 144Q 144

Express the statement as a formula that involves the variables q, x, y and a constant of proportionality k, and then determine the value of k from the condition : q is inversely proportional to the sum of x and y, if x = 2.5 and y = 3.6, then q = 3.8
A)
B)
C)
D)
E)

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Multiple Choice

Q 145Q 145

The pressure P acting at a point in a liquid is directly proportional to the distance d from the surface of the liquid to the point. Express P as a function of d by means of a formula that involves a constant of proportionality k. In a certain oil tank, the pressure at a depth of 8 feet is 472. Find the value of k.
A)
B)
C)
D)
E)

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Multiple Choice

Q 146Q 146

Poiseuille's law states that the blood flow rate F ( in L/min ) through a major artery is directly proportional to the product of the fourth power of the radius r and the blood pressure P. During heavy exercise, normal blood flow rates sometimes triple. If the radius of a major artery increases by 7%, approximately how much harder must the heart pump?
A)about 1.31 times as hard
B)about 3.43 times as hard
C)about 2.29 times as hard
D)about 2.04 times as hard
E)about 1.92 times as hard

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Multiple Choice

Q 147Q 147

When uranium disintegrates into lead, one step in the process is the radioactive decay of radium into radon gas. Radon enters through the soil into home basements, where it presents a health hazard if inhaled. In the simplest case of radon detection, a sample of air with volume V is taken. After equilibrium has been established, the radioactive decay D of the radon gas is counted with efficiency E over time t. The radon concentration C present in the sample of air varies directly as the product of D and E and inversely as the product of V and t. For a fixed radon concentration C and time t, find the change in the radioactive decay count D if V is multiplied by 2 and E is reduced by 14%.
A)increases 1,428.57%
B)increases 281.40%
C)increases 255.81%
D)increases 175.44%
E)increases 232.56%

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Multiple Choice