Question 1

Find a factored form with integer coefficients of the polynomial f shown in the figure.

Accepted Answer

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Question 2

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.

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Question 3

Sketch the graph of   for the indicated value of   .

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Question 4

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

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Question 5

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).

Accepted Answer

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Question 6

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.

Accepted Answer

A) 6.66 
B) 6.74 
C) 5.74 
D) 4.74 
E) 6.1 
A) 6.66 
B) 6.74 
C) 5.74 
D) 4.74 
E) 6.1

Question 7

Find all solutions of the equation.

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Question 8

Find the fourth-degree polynomial function whose graph is shown in the figure.

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Question 9

Find all solutions of the equation.

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Question 10

Find the quotient and remainder if   is divided by

Accepted Answer

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D)   
  
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Question 11

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.

Accepted Answer

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B)    
C)    
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B)    
C)    
D)    
E)

Question 12

Find all solutions of the equation.

Accepted Answer

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Question 13

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.

Accepted Answer

A) -8 < t < -24 
B) 0 < t < 24 
C) 0 < t < 16 
D) 8 < t < 24 
E) 0 < t < 8 
A) -8 < t < -24 
B) 0 < t < 24 
C) 0 < t < 16 
D) 8 < t < 24 
E) 0 < t < 8

Question 14

Find all solutions of the equation.

Accepted Answer

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Question 15

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?

Accepted Answer

A) t = 8 
B) t = 10 
C) t = 4 
D) t = 5 
E) t = 6 
A) t = 8 
B) t = 10 
C) t = 4 
D) t = 5 
E) t = 6

Question 16

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

Accepted Answer

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Question 17

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).

Accepted Answer

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A)    
B)    
C)    
D)    
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Question 18

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.

Accepted Answer

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Question 19

Find all solutions of the equation.

Accepted Answer

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Question 20

Find all solutions of the equation.

Accepted Answer

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Find a factored form with integer coefficients of the polynomial f shown in the figure.

Sketch the graph of for the indicated value of .

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 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).

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.

Find all solutions of the equation.

Find the fourth-degree polynomial function whose graph is shown in the figure.

Find all solutions of the equation.

Find the quotient and remainder if is divided by

Find all solutions of the equation.

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.

Find all solutions of the equation.

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 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).

Find all solutions of the equation.

Find all solutions of the equation.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

Topics From Analytic Geometry

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Exam 4: Polynomial and Rational Functions

Find a factored form with integer coefficients of the polynomial f shown in the figure.

Sketch the graph of for the indicated value of .

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 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).

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.

Find all solutions of the equation.

Find the fourth-degree polynomial function whose graph is shown in the figure.

Find all solutions of the equation.

Find the quotient and remainder if is divided by

Find all solutions of the equation.

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.

Find all solutions of the equation.

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 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).

Find all solutions of the equation.

Find all solutions of the equation.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

Topics From Analytic Geometry

Filters