Question 1

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

Accepted Answer

The answer of Find the polynomial function of degree ...

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. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of An aspirin tablet is in the shape...

Question 3

Find all solutions of the equation. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find all solutions of the equation. 
A)...

Question 4

Find all solutions of the equation. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find all solutions of the equation. 
A)...

Question 5

Find all values of  such that  
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find all values of  such that...

Question 6

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)

Accepted Answer

The answer of A flat metal plate is positioned in...

Question 7

Find the quotient and remainder if  is divided by   
A)

B)

C)

D)

E)

Accepted Answer

The answer of Find the quotient and remainder if ...

Question 8

Find all solutions of the equation. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find all solutions of the equation. 
A)...

Question 9

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)

Accepted Answer

The answer of Show that the number is a zero...

Question 10

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 x² 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)

Accepted Answer

The answer of From a rectangular piece of cardboard having...

Question 11

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)

Accepted Answer

The answer of Express the statement as a formula that...

Question 12

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)

Accepted Answer

The answer of Find an equation of a rational function...

Question 13

Find all values of  such that  
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find all values of  such that...

Question 14

Find the quotient and remainder if  is divided by  .  , 
A)quotient:  , remainder:

B)quotient:  , remainder:

C)quotient :  , remainder :

D)quotient:  , remainder:

E)quotient:  , remainder:

Accepted Answer

The answer of Find the quotient and remainder if ...

Question 15

Sketch the graph of  . 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Sketch the graph of  . 
A)...

Question 16

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 4.24

Accepted Answer

The answer of A thin flat plate is situated in...

Question 17

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)

Accepted Answer

The answer of The period P of a simple pendulum...

Question 18

Find all values of  such that   .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find all values of  such that...

Question 19

Find all solutions of the equation. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find all solutions of the equation. 
A)...

Question 20

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

Accepted Answer

A polynomial with real coefficients must have complex roots in conjugate pairs. Since i is a root, -i must also be a root for the polynomial to have real coefficients. Therefore, a polynomial of degree 3 with real coefficients cannot have 5, -5, and i as its roots.

Quiz 4: Polynomial and Rational Functions

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

Find all solutions of the equation.

Find all solutions of the equation.

Find all values of such that

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 the quotient and remainder if is divided by

Find all solutions of the equation.

Show that the number is a zero of of the given multiplicity, and express as a product of linear factors.

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

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

Find all values of such that

Find the quotient and remainder if is divided by . ,

Sketch the graph of .

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

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.

Find all values of such that .

Find all solutions of the equation.

Does there exist a polynomial of degree 3 with real coefficients that has zeros 5 , - 5, and i ?

Quiz 4: Polynomial and Rational Functions

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

Find all solutions of the equation.

Find all solutions of the equation.

Find all values of such that

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 the quotient and remainder if is divided by

Find all solutions of the equation.

Show that the number is a zero of of the given multiplicity, and express as a product of linear factors.

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

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

Find all values of such that

Find the quotient and remainder if is divided by . ,

Sketch the graph of .

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

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.

Find all values of such that .

Find all solutions of the equation.

Does there exist a polynomial of degree 3 with real coefficients that has zeros 5 , - 5, and i ?

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