Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

The answer of A herd of 575 deer is introduced...

Question 3

Find a polynomial with leading coefficient of , degree , and zeros: - . A)f ( x ) = x⁴ - 33x² + 50x + 200 B)f ( x ) = x⁴ - 2x³ - 33x² + 200 C)f ( x ) = x⁴ - 2x³ - 33x² + 33x + 200 D)f ( x ) = x⁴ - 2x³ - 33x² + 50x + 200 E)f ( x ) = x⁴ - 7x² - 18x + 40

Accepted Answer

The answer of Find a polynomial with leading coefficient of...

Question 4

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)

Accepted Answer

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

Question 5

Sketch the graph of  for the indicated value of  . 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Sketch the graph of  for the...

Question 6

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

Accepted Answer

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

Question 7

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)

Accepted Answer

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

Question 8

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

Accepted Answer

For a polynomial with real coefficients, complex roots must occur in conjugate pairs. Since i is a root, -i must also be a root, making it impossible for a degree 3 polynomial to have 7, -7, and i as its only roots.

Question 9

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

Accepted Answer

The answer of A meteorologist determines that the temperature T...

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

The answer of Use the remainder theorem to find ...

Question 12

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 )

Accepted Answer

The answer of Use synthetic division to decide whether ...

Question 13

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

Accepted Answer

The answer of For the following function, find a number...

Question 14

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)

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

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

Accepted Answer

The answer of Use the factor theorem to decide whether...

Question 17

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

Accepted Answer

The answer of An arch has the shape of the...

Question 18

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 9.90

Accepted Answer

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

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

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)

Accepted Answer

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

Quiz 4: Polynomial and Rational Functions

Find all values of such that

Find a polynomial with leading coefficient of , degree , and zeros: - .

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.

Sketch the graph of for the indicated value of .

Find all solutions of the equation.

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

Does there exist a polynomial of degree 3 with real coefficients that has zeros 7 , - 7, and i ?

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.

Sketch the graph of .

Use the remainder theorem to find ,

Use synthetic division to decide whether is a zero of ;

For the following function, find a number such that the graph of contains the point

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

Find all solutions of the equation.

Use the factor theorem to decide whether is a factor of the polynomial. ;

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 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

Find all solutions of the equation.

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) .

Quiz 4: Polynomial and Rational Functions

Find all values of such that

Find a polynomial with leading coefficient of , degree , and zeros: - .

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.

Sketch the graph of for the indicated value of .

Find all solutions of the equation.

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

Does there exist a polynomial of degree 3 with real coefficients that has zeros 7 , - 7, and i ?

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.

Sketch the graph of .

Use the remainder theorem to find ,

Use synthetic division to decide whether is a zero of ;

For the following function, find a number such that the graph of contains the point

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

Find all solutions of the equation.

Use the factor theorem to decide whether is a factor of the polynomial. ;

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 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

Find all solutions of the equation.

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 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