Question 1

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)

Accepted Answer

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

Question 2

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 )

Accepted Answer

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

Question 3

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)

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

Find a polynomial with leading coefficient of , degree , and zeros: - . A)f ( x ) = x⁴ - 6x² - 13x + 15 B)f ( x ) = x⁴ - 2x³ - 28x² + 50x + 75 C)f ( x ) = x⁴ - 2x³ - 28x² + 75 D)f ( x ) = x⁴ - 2x³ - 28x² + 28x + 75 E)f ( x ) = x⁴ - 28x² + 50x + 75

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

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 4

Accepted Answer

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

Question 8

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 9

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 10

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

Accepted Answer

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

Question 11

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 12

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

Accepted Answer

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

Question 13

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)

Accepted Answer

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

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

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 16

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 17

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 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

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

Accepted Answer

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

Quiz 4: Polynomial and Rational Functions

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) .

Use synthetic division to decide whether is a zero of ;

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

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

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

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

Find all values of such that

Sketch the graph of for the indicated value of .

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.

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.

Find the quotient and remainder if is divided by . ,

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

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

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

Use the remainder theorem to find ,

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

Find all solutions of the equation.