enter here the expression 1 a b webwork demonstration ... · find out how to print a hard copy on...

WeBWorK demonstration assignmentThe main purpose of this WeBWorK set is to fa-

miliarize yourself with WeBWorK.Here are some hints on how to use WeBWorK ef-

fectively:� After first logging into WeBWorK changeyour password.� Find out how to print a hard copy on the com-puter system that you are going to use. Printa hard copy of this assignment.� Get to work on this set right away and answerthese questions well before the deadline. Notonly will this give you the chance to figureout what’s wrong if an answer is not accepted,you also will avoid the likely rush and con-gestion prior to the deadline.� The primary purpose of the WeBWorK as-signments in this class is to give you the op-portunity to learn by having instant feedbackon your active solution of relevant problems.Make the best of it!

1.(1 pt) setDemo/demo pr1.pg

Evaluate the expression8�7 � 5 � = .


Evaluate the expression8 � � 8 � 6 � = .Enter you answer as a decimal number listing at least4 decimal digits. (WeBWorK will reject your answerif it differs by more than one tenth of 1 percent fromwhat it thinks the answer is.)

3.(1 pt) setDemo/demo pr3.pgLet r � 5 �

Evaluate 4 � π � r � .Next, enter the expression 4 � � π � r �� and letWeBWorK compute the result.

4.(1 pt) setDemo/demo pr4.pgEnter here the expression 1

a � 1b .

Enter here the expression 1a b .

5.(1 pt) setDemo/demo pr5.pgEnter here the expression

a � 12 � b

Enter here the expressiona � bc � d

If WeBWorK rejects your answer use the previewbutton to see what it thinks you are trying to tell it.

6.(1 pt) setDemo/demo pr6.pgEnter here the expression�

a � b

Enter here the expressiona�

a � bEnter here the expression

a � b�a � b


Enter here the expression�x2 � y2

Enter here the expression

x�

x2 � y2

Enter here the expressionx � y�x2 � y2


Enter here the expression� b � � b2 � 4ac2a

Note: this is an expression that gives the solution ofa quadratic equation by the quadratic formula.

Prepared by the WeBWorK group, Dept. of Mathematics, University of Rochester, c

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WeBWorK demonstration assignmentThe main purpose of this WeBWorK set is to fa-

miliarize yourself with WeBWorK.Here are some hints on how to use WeBWorK ef-

fectively:� After first logging into WeBWorK changeyour password.� Find out how to print a hard copy on the com-puter system that you are going to use. Printa hard copy of this assignment.� Get to work on this set right away and answerthese questions well before the deadline. Notonly will this give you the chance to figureout what’s wrong if an answer is not accepted,you also will avoid the likely rush and con-gestion prior to the deadline.� The primary purpose of the WeBWorK as-signments in this class is to give you the op-portunity to learn by having instant feedbackon your active solution of relevant problems.Make the best of it!

1.(1 pt) set1/despotovich-math1090-fall2003-p1-1.pgSolve for x: 15x � 9 � 7x � 13

Answer: x =

2.(1 pt) set1/craw-math1090-spring2003-pr1-9.pg

The solution of the equation

xx � 4

� x � 7x � 9

is x � .(You may enter your answer as a decimal number oras a fraction.)

3.(1 pt) set1/craw-math1090-spring2003-pr1-11.pgLet F denote a certain temperature in degrees Fahren-heit, and C the same temperature in degrees Celsius.Then you can convert between F and C by the for-mula

F � 32 � 95

C �Suppose the temperature is 24 degrees Celsius.Enter here the corresponding temperature indegrees Fahrenheit.

4.(1 pt) set1/craw-math1090-spring2003-pr1-5.pgLet f

�x �� 2x3 � 3x2 � 2x � 4. Find f

�1 � � 2 � .

5.(1 pt) set1/craw-math1090-spring2003-pr1-6.pgThe domain of the function f

�x �� 28

10x � 27 is all realnumbers x except for x where x equals

6.(1 pt) set1/despotovich-math1090-fall2003-p1-6.pgThe domain of the function y �� 6x2 � 7 is an inter-val�A � B � , where A and B are some (possibly infinite)

numbers. Similarly, the range is an interval�C � D � .

Find A, B, C and D. Use +INF for ∞ and -INF for� ∞.Answer:A =

B =C =D =

7.(1 pt) set1/despotovich-math1090-fall2003-p1-7.pgThe domain of the function y � � x � 23 is an inter-val � A � B � ,where A and B are some (possibly infinite)numbers. Similarly, range is an interval �C � D � . FindA, B, C and D. Use +INF for ∞ and -INF for � ∞.

Answer:A =

B =C =D =

8.(1 pt) set1/despotovich-math1090-fall2003-p1-8.pgLet f

�x �� 18x � 7, g

�x �� 10

x . Find(a) f � g =

(b) f � g =(c) f � g =(d) f

g =(e) f � f =(f) g � f =

9.(1 pt) set1/despotovich-math1090-fall2003-p1-9.pgA swimming pool has an area of 1000 square feet. Ifthe pool is x feet long, express its length as a func-tion F

�x � of x. What restrictions must be placed on x

(domain) so that the problem makes physical sense?F�x � =

Domain:10.(1 pt) set1/craw-math1090-spring2003-pr1-1.pg

Answer all parts of the question. Given the equation14x � 2y � 16,

1

a) the x-intercept is ;b) the y-intercept is ;c) if x is -2, then y � ;d) if y is 4, then x � .

11.(1 pt) set1/craw-math1090-spring2003-pr1-12.pgSuppose a mining company will supply 120000 tonsof ore per month if the price is 100 dollars per tonbut will supply 71500 tons per month if the price is10 dollars per ton. Assuming the supply function is ofthe form y � mx � b, find the slope, m and y-intercept,bm :b:

12.(1 pt) set1/craw-math1090-spring2003-pr1-2.pgA road rises 7.1 feet for every 100 feet travelled. Howfar must one travel to rise a mile (5280 feet)?

Answer: mile(s).13.(1 pt) set1/craw-math1090-spring2003-pr1-10.pg

You are hiking along the California coast and wonderabout the height of a particular Giant Redwood tree.You are 5 feet and nine inches tall and your shadow is

13 feet long. The shadow of the tree is 481 feet long.How tall is the tree? Enter its height here: feet.

14.(1 pt) set1/craw-math1090-spring2003-pr1-3.pgWrite down the equation of the line through the point�17 � 167 � which is parallel to the line through the

points�11 � 12 � and

�12 � 21 � .

y � x � .

15.(1 pt) set1/despotovich-math1090-fall2003-p1-15.pgWrite down the equation of the line through the point�4 � 4 � which is orthogonal to the line

2x � 18y � 5 � 0Answer: y = x +

16.(1 pt) set1/despotovich-math1090-fall2003-p1-16.pgWrite down the equation of the line through the point�6 � 9 � which is (a) orthogonal and (b) parallel to the

line

x � 5(a) y =(b) x =


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Shawn Harrison WW Prob Lib1 Math 1090-3, Fall 2003WeBWorK problems. WeBWorK assignment 2 due 9/16/03 at 8:00 PM.

1.(1 pt) set2/craw math1090 spring2003 p2-3.pgSolve the system. �

2x � 6y � 218x � 51y � 13

x �y �2.(1 pt) set2/craw math1090 spring2003 p2-4.pg

Solve the following system.�x � 6

2 � y 83 � 4

x � 2y � 5x �y �3.(1 pt) set2/s3p36.pg

Suppose you go to an event where children’s ticketscost $5 and adults tickets cost $10. You buy 6 ticketsfor $40. There are adults and children inyour party.

4.(1 pt) set2/craw math1090 spring2003 p2-8.pgSolve the system�� 2x � 2y � z �� 18

x � 3y � z � 8� x � y � � 2x �y �z �5.(1 pt) set2/craw math1090 spring2003 p2-6.pg

Solve the system of linear equations�� x � 2y � 7z � 172x � y � z � 133x � 9y � 36z � 72

The solutions have the form x � a � bt � y � c �dt � z � t, where t is any real number.Find a � b � c � d.

a �b �

c �d �

6.(1 pt) set2/math1050 spring2003 bestvina set10 pr3.pgThe Aeros scored a total of 104 points in a basket-ball game. The scoring resulted from a combinationof 3-point baskets, 2-point baskets, and 1-point free-throws. There were twice as many 2-point basketsas free-throws scored and twice as many free-throwsas 3-point baskets. What combination of scoring ac-counted for the Aero’ 104 points?

Answer:Free-throws:

2-point baskets:3-point baskets:

7.(1 pt) set2/despotovich-math1090-fall2003-p2-7.pgA company produces swimsuits. Suppose fixed costsare $1000 and cost of producing each swimsuit is$16. Find the cost function and the marginal cost.

Cost Function: C�x � =

Marginal Cost:

8.(1 pt) set2/despotovich-math1090-fall2003-p2-8.pgSuppose the marginal profit for a pair of skies is $20,profit function is linear, and profit from producingand selling 34 pairs of skies is $75. Find the profitfunction.

Profit Function: P�x � =

9.(1 pt) set2/craw math1090 spring2003 p2-9.pg

A company manufactures and sells bookcases. Theselling price is $56.9 per bookcase. The total costfunction is linear, and costs amount to $37360 for2000 bookcases and $19480 for 800 bookcases.Find the break-even point.�

, �10.(1 pt) set2/despotovich-math1090-fall2003-p2-10.pg

Retailers will buy 13 cordless phones if the price is$33, and each will buy 17 if the price is $21. Thewholsaler will supply 14 phones at $26 each and 16at $28 each. Assuming the supply and demand func-tions are linear, find the market equilibrium point.

Equilibrium point:�q � p � = ( , )

11.(1 pt) set2/craw math1090 spring2003 p2-5.pgFind the point of equilibrium if the demand functionfor a product is

1

p � 30 � 6 � 0 � 1q

and the supply function is

p � 25 � 0 � 6q

Answer:�q � p � = ( , )

12.(1 pt) set2/despotovich-math1090-fall2003-p2-12.pgSuppose that certain product has the following de-mand and supply functions:

Demand: p �� 1q � 5Supply: p � 1q � 2If a $1 tax per item is levied on the supplier, who

passes it on to the consumer as a price increase, findthe market equilibrium point after the tax.

Equilibrium point:�q � p � = ( , )


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1.(1 pt) set3/math1090 fall2003 despotovic set3 pr1.pgThe expression x2 � 5x � 66 factors as

�x � A � � x � B �

where A � B, A = and B= . Therefore, thesolutions to the equation x2 � 5x � 66 � 0 are x1 =and x2 = . (Enter the smaller root first.)

2.(1 pt) set3/math1090 fall2003 despotovic set3 pr2.pgSolve by taking roots of both sides

�2x � 7 � 2 � 81.

Answer (please enter the smaller the root in thefirst answer box and the larger one in the second box):

x1 =x2 =

3.(1 pt) set3/math1090 fall2003 despotovic set3 pr3.pgSolve the fractional equation

32x � 4

� xx � 13

� 4 � 13x � 13

�Answer: x =

4.(1 pt) set3/math1090 spring2003 harrison set2 pr1.pgFind the standard form of the parabola equation,

y � a�x � h � 2 � k

with vertex (0,-4) and passing through the point(6,5).Then h is

and k is

and a is:

5.(1 pt) set3/math1090 spring2003 harrison set2 pr2.pg(a) Find two quadratic functions, one that opens up-ward

f�x �� x2 � b1x � c1 �

and one that opens downward,

g�x �� x2 � b2x � c2 �

whose graphs have x-intercepts (12,0), (14,0).b1 =

c1 =b2 =c2 =(b) Find the vertex of both parabolas in part (a).

The vertex�h1 � k1 � of the open upward quadratic

function ish1 =

k1 =and the vertex

�h2 � k2 � of the open downward qua-

dratic function ish2 =

k2 =6.(1 pt) set3/math1090 spring2003 harrison set2 pr3.pg

Find the turning point of the graph of

f�x �� x2 � 50x

The turning point�h � k � has the values

h =and k =7.(1 pt) set3/math1090 fall2003 despotovic set3 pr7.pg

The graph of a function y � 3�x � 7 � 2 � 5 was shifted� 7 units in the x-direction and 9 units in the y-

direction. Write down the equation of the new graph.Answery =

8.(1 pt) set3/math1090 spring2003 harrison set1 pr24.pgFind the number of units sold that produces a maxi-mum revenue from the total revenue function,

R � 560x � 0 � 4x2 �(in dollars) and x is the number of units sold.Answer =

9.(1 pt) set3/math1090 spring2003 harrison set1 pr25.pgSuppose the total cost in producing a product is givenby the following cost function. How many unitsshould be sold to minimize cost?

C � 0 � 6x2 � 360x � 900 �(in dollars) and x is the number of units sold.Answer =

10.(1 pt) set3/math1090 spring2003 harrison set1 pr27.pgFind the number of units sold that produces a maxi-mum profit from the profit function,

P � 720x � 0 � 9x2 � 25 �(in dollars) and x is the number of units sold.

1

Answer =

11.(1 pt) set3/math1090 fall2003 despotovic set3 pr11.pgA rancher wants to fence in a rectangular field andthen divide it in half with a fence down the middleparallel to one side. If 1308 ft of fence is to be used,what is the maximum area of the lot he can obtain?

AnswerMaximum Area =

12.(1 pt) set3/math1100 fall2002 despotovic set7 pr12.pgThe manager of a large apartment complex knowsfrom experience that 80 units will be occupied if therent is 416 dollars per month. A market survey sug-gests that, on the average, one additional unit willremain vacant for each 8 dollar increase in rent. Sim-ilarly, one additional unit will be occupied for each 8dollar decrease in rent. What rent should the managercharge to maximize revenue?


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1.(1 pt) set4/math1090 fall2003 despotovic set4 pr1.pgThe supply and demand functions for a certain prod-uct are

Demand: p �� 6�q � 3 � 2 � 1277

Supply: p � 4�q � 8 � 2 � 7

Find the market equilibrium point�q � p � = (

, ).


Supply: 5p � q � 18Demand: pq � 3540 � 19qFind the market equilibrium point

�q � p � = (

, ).


Supply:pq� 2

Demand: pq � 10�20 � 4 �

If the supplier is taxed $4 and passes tax to the con-sumer as a price increase,find the market equilibrium point

�q � p � = ( ,

).

4.(1 pt) set4/math1090 fall2003 despotovic set4 pr4.pgLet C

�x �� 0 � 6x2 � 10x � 588 and R

�x �� 0 � 9x2 �

73x.Find the break-even points. (Enter the smaller x

first.)�x1 � y1 � = ( , )�x2 � y2 � = ( , )


�x �!� 0 � 4x2 � 12 � 8x � 496 and R

�x �"�#� 0 � 4x2 �

53 � 6x. If production is restricted to fewer than 26units, find the break-even point.�

x � y � = ( , )

6.(1 pt) set4/math1090 fall2003 despotovic set4 pr6.pgIn a monopoly market, the demand for a product isp � 497 � 0 � 7x and the revenue function is R

�x �!� px.

What price will maximize the revenue?p =


�x �$� 0 � 7x2 � 27x � 502 and the price is p �

108 � 0 � 2x. Find the level of production that willyield maximum profit and the maximum profit.�

x � P � x �%� = ( , )

8.(1 pt) set4/math1090 spring2003 harrison set2 pr9.pg

The figureshows the graph of the function f

�x �&� x3. The fol-

lowing are graphs of quadratic functions in the formf�x �� a

�x � h � 3 � k where a is 1 or � 1. Write the

function that coresponds to the graph:

a) The figuref�x �'� .

1

b) The figureshows the graph of the function

f�x �� .


f�x �� .


f�x �'� .

9.(1 pt) set4/math1090 fall2003 despotovic set4 pr9.pgLet f

�x ��)( x � 4 ( . Then

(a) f� � 1 � =

(b) f�9 � =

(c) f�0 � =

10.(1 pt) set4/math1090 spring2003 harrison set2 pr10.pgBelow are two graphs. Indicate the number of turningpoints, x-intercepts, and the degree of the function.

a) The graphhas,

turning points,x-intercepts,

and is of degree .2

b) The graphhas,

turning points,x-intercepts,

and is of degree .


The function, y � 7x � 5

has a,

vertical asymptote at x � , and ahorizontal asymptote at y � .


The function, y � 5x � 14 � x

has a,

vertical asymptote at x � , and ahorizontal asymptote at y � .

13.(1 pt) set4/math1090 fall2003 despotovic set4 pr13.pgLet

f�x �'�

�� 2x2 � x * 555 � x � 5 � x * 149x � x + 14

Then(a) f�2 � =

(b) f�5 � =

(c) f�8 � =

(d) f�14 � =

(e) f�17 � =


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1.(1 pt) set5/math1090 fall2003 despotovic set5 pr1.pgIf A and B are 8 , 11 matrices, and C is an 11 , 8matrix, which of the following are defined? (Enter Yfor YES and N for No.)

(a) A � B(b) B � C(c) AT

(d) BT � C


A � -. 7 � 3 81 8 8� 5 8 � 3

/0Find � A.

� A � -. a b cd e fg h k

/0a =

b =c =d =e =f =g =h =k =


A �21 9 � 28 8 3

B � 1 9 2 0� 8 0 8 3C � 1 9 � 8� 2 8 3D � 1 9 � 2

8 8 3

Then matrices and are equal, andmatrices , and have the same order.(Please enter answers in alphabetical order.)


If

A � -. � 4 � 4 33 � 1 � 34 4 � 1

/0and B � -. 2 � 3 � 2

3 0 � 3� 1 � 3 � 3

/0Then

3A � B � -. d11 d12 d13d21 d22 d23d31 d32 d33

/0 �whered11 = , d12 = , d13 = ,

d21 = , d22 = , d23 = ,d31 = , d32 = , d33 = ,


If

A �546 � 1 � 3 4� 4 1 0� 4 1 0

78B �546 2 1 � 1� 2 � 4 � 3� 2 � 1 3

78Then

2A � B � 46 d11 d12 d13d21 d22 d23d31 d32 d33

78and

AT � 46 e11 e12 e13e21 e22 e23e31 e32 e33

78whered11 = , d12 = , d13 = ,

d21 = , d22 = , d23 = ,d31 = , d32 = , d33 = ,

ande11 = , e12 = , e13 = ,

e21 = , e22 = , e23 = ,e31 = , e32 = , e33 = ,

1


If

A �946 2 0 13 2 2� 2 1 0

78B �946 4 � 2 � 1

0 � 4 � 1� 2 2 0

78 �Then

5A � B �546 d11 d12 d13d21 d22 d23d31 d32 d33

78and

5AT �946 e11 e12 e13e21 e22 e23e31 e32 e33

78whered11 = , d12 = , d13 = ,

d21 = , d22 = , d23 = ,d31 = , d32 = , d33 = ,

ande11 = , e12 = , e13 = ,

e21 = , e22 = , e23 = ,e31 = , e32 = , e33 = ,


A � 1 3 0 11 5 0 3

B � -. � 3 11 50 � 5

/0C � 1 0 � 1 3� 1 5 5 3

Then

A � BT � C � 1 d11 d12 d13d21 d22 d23 3

d11 = , d12 = , d13 = ,d21 = , d22 = , d23 = ,

8.(1 pt) set5/math1090 fall2003 despotovic set5 pr8.pgIf 1 x 8

1 y 3 � 1 � 8 81 9 3 �

then x= and y= .

9.(1 pt) set5/math1090 fall2003 despotovic set5 pr9.pgIf 1 x � 5

z 3w 3 � 1 2x y9 2 3 � 1 21 5

0 � 1 3 �then x = , y = , z = , and w = .


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1.(1 pt) set6/math1090 spring2003 craw set5 pr4.pg

If A and B are 8 , 2 matrices, and C is a 5 , 8 matrix,which of the following are defined?� A. B � A� B. CA� C. AC� D. B � C� E. BTCT� F. BT

2.(1 pt) set6/math1090 spring2003 harrison set3 pr5.pgIf

A � 1 � 8 � 1� 6 � 3 3 and B � 1 6 5� 2 7 3then

AB � 1 c11 c12c21 c22 3 �

wherec11= , c12=

c21= , c22=


A � 46 � 1 2 0� 1 � 4 � 24 � 2 � 2

78B � 46 3 3 � 1� 1 � 3 � 1

0 � 3 � 1

78Then

AB �546 c11 c12 c13c21 c22 c23c31 c32 c33

78and

BA �946 d11 d12 d13d21 d22 d23d31 d32 d33

78wherec11 = , c12 = , c13 =

c21 = , c22 = , c23 =c31 = , c32 = , c33 =

andd11 = , d12 = , d13 =

d22 = , d22 = , d23 =

d33 = , d32 = , d33 =4.(1 pt) set6/math1090 spring2003 harrison set4 pr9.pg

A dietician is planning a meal that supplies certainquantities of vitamin C, calcium, and magnesium.Three foods will be used, their quantities measured inmillirams. The nutrients supplied by these foods andthe dietary requirements are given in the table below.

Nutrient Food 1 Food 2 Food 3 Total Required (mg)Vitamin C 20 10 20 2175Calcium 30 30 40 4105

Magnesium 20 25 40 3492 � 5Write the augmented matrix for this problem:-. a11 a12 a13 b1

a21 a22 a23 b2a31 a32 a33 b3

/0wherea11 = , a12 = , a13 = , b1 =

a21 = , a22 = , a23 = , b2 =a31 = , a32 = , a33 = , b3 =

What quantity (mg) of Food 1 is neccesary to meetthe dietary requirements?



5.(1 pt) set6/math1090 fall2003 despotovic set6 pr5.pgThe following system has an infinite number of so-lutions. Form an augmented matrix, then use Gauss-Jordan elimination to write the matrix in the reducedform. Write the reduced form of the matrix belowand then write the solution in terms of z.�� 4x � 4y � 3z � 4

8x � 8y � 2z � 212x � 4y � 5z � 6

AnswerThe required augmented matrix is:

1

-. a11 a12 a13 b1a21 a22 a23 b2a31 a32 a33 b3

/0 �wherea11 = , a12 = , a13 = , b1 =

a21 = , a22 = , a23 = , b2 =a31 = , a32 = , a33 = , b3 =

And,x =y =

6.(1 pt) set6/math1090 spring2003 craw set4 pr4.pgSolve the following matrix equation for X

2X � 2A � B

where

A � 1 � 2 � 7� 8 � 4 3 and B � 1 � 5 610 � 5 3

Then

X � 1 a bc d 3

a �b �c �d �7.(1 pt) set6/math1090 spring2003 harrison set3 pr9.pg

Solve the system using matrices (row operations)�4x � 9y �:� 77� 1x � 7y �:� 27

x �y �8.(1 pt) set6/math1090 spring2003 harrison set3 pr11.pg

Solve the system using matrices (row operations)�� 4x � 3y � 5z � 1� 3x � 2y � 2z �:� 16

6x � 5y � 6z � 26x �y �z �


A � -. 2 4 � 10 � 1 1� 1 � 2 1

/0then

A � 1 � -. b11 b12 b13b21 b22 b23b31 b32 b33

/0 �whereb11 = , b12 = , b13 =

b21 = , b22 = , b23 =b31 = , b32 = , b33 =


If

A �<; � 2 � 33 � 3 =

Thendet�A � = , and

A � 1 �<; b11 b12b21 b22 = �

whereb11 = , b12 =

b21 = , b22 =


A � 1 4 � 31 4 3

Then

A � 1 � 1 d11 d12d21 d22 3 �

whered11 = , d12 =

d12 = , d22 =Use this to solve the matrix equation AX � B where

B � 1 3 34 1 3 �

Answer2

X �21 x11 x12x21 x22 3 �

wherex11 = , x12 =

x12 = , x22 =12.(1 pt) set6/math1090 spring2003 harrison set4 pr8.pg

For each system, determine whether it has a uniquesolution (in this case, find the solution), infinitelymany solutions, or no solutions.

1.� � 5x � 10y � 65� 2x � 1y � 5� A. No solutions� B. Infinitely many solutions� C. Unique solution: x � 0 � y � 0� D. Unique solution: x � 1 � y �� 7� E. Unique solution: x �� 7 � y � 1� F. None of the above

2.�

1x � 1y � 4� 2x � 2y �:� 7� A. No solutions

� B. Unique solution: x � 0 � y � 0� C. Unique solution: x �� 7 � y � 4� D. Infinitely many solutions� E. Unique solution: x � 4 � y �� 7� F. None of the above3.

� � 1x � 2y � 8� 3x � 6y � 24� A. Unique solution: x � 8 � y � 24� B. No solutions� C. Unique solution:x � 8� 1 � y � 0� D. Infinitely many solutions� E. Unique solution: x � 0 � y � 0� F. None of the above4.

�7x � 6y � 0� 3x � 9y � 0� A. Unique solution: x � 0 � y � 0� B. Unique solution: x � 13 � y �� 12� C. No solutions� D. Infinitely many solutions� E. Unique solution: x �>� 9 � y � 7� F. None of the above


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1.(1 pt) set7/math1090 spring2003 harrison set5 pr1.pgMatch the statements defined below with the letterslabeling their equivalent intervals. The symbol ” ? ”means ” is an element of,” or ” is in the interval.”You must get all of the answers correct to receivecredit.

1. x ? � 4 � 9 �2. x ?@� 4 � 9 �3. x ? � 4 � 9 �4. x ?@� 4 � 9 �5. x ? � � ∞ � 4 �A. 4 * x � 9B. 4 * x * 9C. 4 � x � 9D. 4 � x * 9E. x * 4

2.(1 pt) set7/math1090 spring2003 harrison set5 pr2.pgConsider the inequality

3 � 3x * 2x � 2

The solution of this inequality consists one or moreof the following intervals:

� � ∞ � A � and�A � ∞ �

Find AFor each interval, answer YES or NO to whether

the interval is included in the solution.� � ∞ � A ��A � ∞ �

3.(1 pt) set7/math1090 spring2003 harrison set5 pr4.pgConsider the inequality

10 � 8x * 2x � 9

The solution of this inequality consists one or moreof the following intervals:

� � ∞ � A � and�A � ∞ �

Find AFor each interval, answer YES or NO to whether

the interval is included in the solution.� � ∞ � A ��A � ∞ �

4.(1 pt) set7/math1090 fall2003 despotovic set7 pr4.pg

Solve the inequality

6�x � 7 ��A x � 5

8�

Answer: x .Instruction: Enter either * , A , AB� or *C� in the

first answer box. Enter a number in the second an-swer box.


Solve the compound inequality

8 *D� 8x � 7 * 9 �Answer: x ? ( , ).


Two phone companies offer long distance phoneservices. The first company charges $0.25 perminute, and the second company charges $0.17 perminute plus $0.88 connection fee. For how longwould it be cheaper to talk using the second com-pany?

AnswerFor at least minutes.


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Find the minimum and maximum of the function

f�x � y �� 9y � 12x

subject to �EE� EE� y + 04x � 6y � 362x � 2y � 163y � 6x � 18

The maximum is attained at�x � y � = ( , )

and equals .The minimum is attained at

�x � y � = ( , )

and equals .


Maximize f�x � y �'� 51x � 108y subject to�EEEE� EEEE� x + 0

y + 08x � 18y � 1983x � 6y � 69

12x � 9y � 216AnswerThe maximum is attained at

�x � y � =( , )

and equals


Minimize f � 41x � 84y subject to�� 9x � 9y � 1355x � 6y � 811x � 7y � 22

AnswerThe minimum is attained at

�x � y � =( , ) and

equals


Find the minimum and maximum of f � 2x � 5ysubject to �EE� EE� y � 5

3y � 4x � 155y � 1x + 25x � 2y � 10

AnswerThe minimum is attained at

�x � y � =( , ) and

equals .The maximum is attained at

�x � y � =( , )

and equals .

5.(1 pt) set8/math1090 spring2003 harrison set5 pr7 modified.pgAn accounting firm has 810 hours of staff time and126 hours of reviewing time available each week.The firm charges $156 for an audit and $36 dollarsfor a tax return. Each audit requires 114 hours of stafftime and 14 hours of review time. Each tax return re-quires 18 hours of staff time and 6 hours of reviewtime.

a) What numbers of audits and tax returns willyield the maximum revenue ?Audit=Tax return =

b) What is the maximum revenue ?Maximum revenue=


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1.(1 pt) set9/math1090 spring2003 harrison set5 pr8.pgAfter t years,the value of a car that cost 47000 dollarsis modeled by

V�t �F� 47000 ; 4

8 = t

(a) What is the horizontal asymptote of this function?V =

(b) What is the value of the car 2 years after it waspurchased ?V�2 � =

2.(1 pt) set9/math1090 spring2003 harrison set5 pr9.pgLet Q represent a mass of radioactive radium with thehalf-life 1720. The quantity of radium present after tyears is

Q � 175 ; 12 = t G 1720

(a) Determine the initial quantity ( when t � 0 ).Q�0 � =(b) Determine the quantity present after 6000 years

Q�6000 � =


If $5000 is invested at 8%, compounded monthly,then the future value of the investment S after t yearsis given by:

S � 5000�1 � 0 � 08 � 12t �

Find the future value of the investment after 9years.

AnswerS =4.(1 pt) set9/math1090 fall2003 despotovic set9 pr4.pg

Find the domain, range, y-intercept and horizontalasymptote of

y � 2 � 69x �Type +INF for ∞ and -INF for � ∞.Answer

The domain is ( , ).The range is ( , ).The y-intercept is , ).The horizontal asymptote is y = .

5.(1 pt) set9/math1090 spring2003 harrison set6 pr1.pgStudents in a mathematics class were given an examand then retested monthly with an eqivalent exam.The average scores for the class are given by the hu-man memory model

f�t �F� 80 � 17log10

�t � 1 �H� 0 � t � 12

, where t is the time in months. ( round all answers tothe nearest whole number.)(a) What was the average score on the original exam,t � 0 ?

AV �(b) What was the average score after 4 months ?AV �(c) What was the average score after 10 months ?AV �6.(1 pt) set9/math1090 spring2003 harrison set5 pr10.pg

Find x such that

log16 x � 52

x �7.(1 pt) set9/math1090 spring2003 harrison set5 pr11.pg

Change 0.0001 into exponential from 10x then usethis to calculate

y � log10�0 � 0001 �

x �y �8.(1 pt) set9/math1090 spring2003 harrison set5 pr12.pg

Find the domain, x-intercept, and vertical asymp-tote of

y � log5�x � 3 �I� 4

Domain is x A a, where a �x-intercept is xint �

1

Vertical asymptote, xasy �9.(1 pt) set9/math1090 spring2003 harrison set6 pr2.pg

Find real numbers a and b so that

logx89� lna

lnba �

b �10.(1 pt) set9/math1090 spring2003 harrison set6 pr3.pg

Find the exact value of

x � log4 2 � log4 32

x �x � 3ln

�e4 �

x �ln� 4�

e3 �x �


Apply the inverse properties of lnx and ex to sim-plify

log9 93x � 1 � yy �12.(1 pt) set9/math1090 spring2003 harrison set5 pr13.pg

Find real numbers a and b so that

logx29� lna

lnba �

b �13.(1 pt) set9/math1090 spring2003 harrison set5 pr14.pg

Find numbers a and b so that

lnx8

y6 � a ln�x �I� b ln

�y �

a �b �


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1.(1 pt) set10/math1090 spring2003 harrison set5 pr16.pgThe population of a city is

P � 240059e0 J 018t

,where t � 0 represents the year 2000. According tothis model, when will the population reach 276461 ?

t �Instruction: Round to the nearest integer.


Solve for x exactly

10 � 2 � x � 100000x �3.(1 pt) set10/math1090 spring2003 harrison set6 pr6.pg

Solve for x exactly

13�913 � x �'� 3159


Solve for x exactly

7�10x � 10 �'� 700


Solve for x exactly

ln�x � 7 � 17 � 0


The half-life of radioactive radium is 1620 years.What percent of a present amount of radioactive ra-dium will remain after 870 years ?

% �Instruction: Round to the nearest integer.


Suppose the number of rabbits on a small island isgiven by

N � 400 � 0 � 10 J 2t

where t is the number of years after 2003.(a) How many rabbits are there on the island now?

(b) What is the expected upper limit on the numberof rabbits?


Suppose that the number y of otters t years afterotters were reintroduced into a wild and scenic riveris given by

y � 391 � 192e � 0 J 1t

(a) Find the population when the otters were rein-troduced.(b) How long will it be before otter population num-bers 234?


The number N�t � of people in a community who

are reached by a particular rumor at time t (in days)is given by

N�t �� 680

1 � 169e � 0 J 4t �(a) Find N

�0 � .

(b) What is the upper limit on the number of peopleaffected?(c) How long before 50% of the upper limit isreached? days


The demand function for a product is given by

p � 191 � 4 � q G 19 �(a) At what price per unit will the quantity de-

manded equal 2 units?(b) If the price is $122 per unit, how many units willbe demanded to the nearest unit? unit(s)

Instruction: Please round the price to the nearestcent.

1


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1.(1 pt) set11/math1090 spring2003 harrison set7 pr1.pg1800 dollars is invested for 37 years at a simple inter-est rate of 15%. Determine the interest earned, I andthe future value, S of the investment:I � dollarsS � dollars

Please give your answers accurate to the nearestdollar.

2.(1 pt) set11/math1090 spring2003 harrison set7 pr2.pgIf you borrow 5000 dollars for 12 years at 12% an-nual simple interest, how much must you repay at theend of 12 years? i.e. What is the future value of theloan, S?S � dollars

Please give your answer accurate to the nearestdollar.

3.(1 pt) set11/math1090 spring2003 harrison set7 pr4.pgFind the 23th term of the sequence that begins2 � 5 � 8 � 11 �%�K�L� .

a23 �Find the sum of the first 23 terms of the same se-quence.s23 �

4.(1 pt) set11/math1090 spring2003 harrison set7 pr6.pgConsider the Fibonacci Sequence, an arithmetic se-quence where any term can be found by addingthe previous two terms of the sequence, i.e. an �an � 1 � an � 2 .

Observe the pattern 1,1,2,3,5 (here a1 � 1, a2 � 1,a3 � 2, a4 � 3, �%�%� and find a11.

Answera11 =

5.(1 pt) set11/math1090 spring2003 harrison set7 pr7.pgFind the future value, S of a principal of 10,000 dol-lars invested for 30 years at 8% compounded annu-ally. Determine the interest earned, I � S � P.S �I �


6.(1 pt) set11/math1090 spring2003 harrison set7 pr8.pgFind the future value, S of a principal of 10000 dollars

invested for 35 years at 8% compounded monthly.Determine the interest earned, I � S � P.S �I �


7.(1 pt) set11/math1090 spring2003 harrison set7 pr9.pgFind the future value, S of a principal of 10000 dol-lars invested for 38 years at 8% compounded contin-uously. Determine the interest earned, I � S � P.S �I �


8.(1 pt) set11/math1090 spring2003 harrison set7 pr10.pgThe previous 3 problems dealt with investing 10 � 000dollars at 8%, each with a different number of com-poundings per year. Determine the Annual Percent-age Yield, APY as a decimal for the three cases:Case I, Annual Compounding: APY �Case II, Monthly Compounding: APY � CaseIII, Continuous Compounding: APY �

Please give your answers accurate to two decimalplaces.

9.(1 pt) set11/math1090 spring2003 harrison set6 pr10.pgDetermine the principal P that must be invested at arate of 12%, compounded monthly, so that 500 � 000dollars will be available for retirement in 29 years.

P �Please give your answer accurate to the nearest

dollar.10.(1 pt) set11/math1090 spring2003 harrison set8 pr1.pg

How much more interest will be earned if $5000 isinvested for 9 years at 4% compounded continuously,instead of at 4% compounded quarterly? (Please giveyour answer accurate to the nearest dollar.)

Difference in future values = dollars11.(1 pt) set11/math1090 spring2003 harrison set8 pr2.pg

Find the 7th term of the sequence that begins4 � 8 � 16 �M�%�%�

a7 �Find the sum of the first 7 terms of the same se-

quence.1

s7 �Please give your answers accurate to two decimal

places.

12.(1 pt) set11/math1090 spring2003 harrison set8 pr3.pgFind the sum of the first 5 terms of the geometric se-quence with first term 9 and common ratio, 1

3 .s5 �13.(1 pt) set11/math1090 spring2003 harrison set8 pr4.pg

Find the future value,S of an ordinary annuity of700dollars paid quarterly for 4years if the interestrate is 7 � 1%, compounded quarterly.S � dollars


14.(1 pt) set11/math1090 spring2003 harrison set8 pr5.pgWhat size payments,R must be put into an account atthe end of each month to establish an ordinary annu-ity that has future value of 45000dollars in 12years,if the investment pays 8 � 6%, compounded monthly?(This problem is taken from section 6.3 of the text)R � dollars per month



Find the future value S of an annuity due of $256paid semiannually for 3 years if the interest rate is3%, compounded semiannually.

AnswerS = dollars.Please give your answer to the nearest dollar.


Grandparents plan to open an account on theirgrandchild’s birthday and contribute at the begin-ning of each 2-month period until she goes to col-lege. How much must they contribute each time intoan investment that pays 13%, compounded every 2months, to have $70000 at the end of 18 years?

AnswerBimonthly contribution required: dollarsPlease give your answer accurate to the nearest

dollar.


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1.(1 pt) set12/math1090 spring2003 harrison set8 pr6.pgFind the present value An of an ordinary annuity of$1320 paid at the end of each year for 28 years if theinterest rate is 7.1%, compounded annually.

An � dollars

Please give your answer accurate to the cent.

2.(1 pt) set12/math1090 spring2003 harrison set8 pr7.pgExamine the difference in Ordinary Annuity and An-nuity Due investments

(1) Find the present value,An of an annuity of140dollars paid at the end of each monthfor 7years if the interest rate is 8 � 9%, com-pounded monthly.

(2) Find the present value,An of an annuity of140dollars paid at the beginning of eachmonth for 7years if the interest rate is 8 � 9%,compounded monthly.

An � dollarsAn N due � dollars

Please give your answers accurate to the cent.

3.(1 pt) set12/math1090 spring2003 harrison set8 pr8.pgFrank received a 620000dollar inheritance on his32th birthday and invested it into a fund that earns5 � 9%, compounded semiannually. If this amount isdeferred until Frank’s 60th birthday, how much willit provide at the end of each half-year for the next6years?R � dollars


4.(1 pt) set12/math1090 spring2003 harrison set8 pr9.pgA debt of 6000dollars is to be amortized by equalpayments at the end of each month for 9years. If theinterest charged is 8 � 6%, compounded monthly, findthe periodic payment, R.R � dollars per month


5.(1 pt) set12/math1090 spring2003 harrison set8 pr10.pgA young couple is ready to buy their first home. Theyhave 26000dollars for a down payment, and theirbudget can accomodate a monthly mortgage paymentof 950dollars. What is the most expensive home theycan buy if they can borrow money for 30 years at8%, compounded monthly? HINT: See example 3 onp.476 of the text for a similar problem.TotalPriceo f House � dollars


6.(1 pt) set12/math1090 spring2003 harrison set8 pr11.pgAnother couple already bought a home. Theyborrowed 100000dollars, at 7 � 8%, compoundedmonthly, for 30 years. What monthly payment dothey make, R? Also, suppose they want to move outafter 2 years. Find the unpaid balance immediatelyafter the 24th payment, An � k.R � dollars per monthAn � k � dollars

Please give your answers accurate to the cent.


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