Peter Alfeld WW Prob Lib1 Math course-section, …...$15 per month increase, there will be a vacancy with-out possibility of lling it. The corporation wants to receive a total of $5085

Peter Alfeld WW Prob Lib1 Math course-section, semester yearWeBWorK problems. WeBWorK assignment 1 due 9/13/06 at 11:58 PM.

1.(1 pt) Solve for x: 25 x+ 2

5 = −25 x+ 2

5Answer: x =2.(1 pt) Solve for x: 7(x+2) = 3x+4Answer: x =3.(1 pt) Solve for x: 4

x−5 = 7x−6

Answer: x =4.(1 pt) Solve for x: x+10

x+3 = x+7x+5

Answer: x =5.(1 pt) Solve for x:

√x2 +21 = 4+ x

Answer: x =6.(1 pt) Solve for x:

√x−20−√

x = −2Answer: x =7.(1 pt) Solve for x: x2 −4x−32 = 0

Answer: The smaller solution is x =and the bigger solution is x =

8.(1 pt) Solve for x: x3 −21x2 +104x = 0Instructions: enter your answers in the increasing

orderAnswer: x = , ,

9.(1 pt) Solve for x: 1x+4 + 1

x−4 = 1x+10

Please enter the smaller answer first.Answer: x = ,

10.(1 pt) Solve for x: x4 −9x2 +18 = 0Please enter your answers in the increasing order.Answer: x = , , ,

Prepared by the WeBWorK group, Dept. of Mathematics, University of Rochester, c©UR1

Peter AlfeldMath 1090-4, Fall 2006WeBWorK Assignment 2 due 9/20/06 at11:58 PM

1.(1 pt) You work in a lab. One day you need 320oz of a chemical solution consisting of three parts al-cohol and five parts acid. How much of each shouldbe used?

Answer: oz of alcohol andoz of acid

2.(1 pt) You wish to invest $1300 over one yearin two accounts paying 5% and 6% annually. Howmuch should you invest in each to earn $72?

Answer: in 5% and in 6%account

3.(1 pt) You work for a corporation that owns anoffice complex consisting of 12 units. At $520 permonth every unit can be rented. However, with each$15 per month increase, there will be a vacancy with-out possibility of filling it. The corporation wants toreceive a total of $5085 per month. Determine therent that should be charged for each unit.

Answer: $4.(1 pt) 59% or 590 employees in a company are

female. How many are male?Answer:5.(1 pt) A company produce snowboards. Fixed

costs are $1440 and variable costs are $220. An or-der has been placed for 8 snowboards. What shouldthe retail price be in order for the company to breakeven?

Answer: $6.(1 pt) The same company produces skies, too.

Fixed costs are $ 2000, and the cost of producing eachpair of skies is $100. The selling price is $200 (perpair). How many pairs should be sold to make a profitof $21000?

Answer:7.(1 pt) When the price of a product is $ p each, the

manufacturer will supply 15p−6 units, and the con-sumers will demand 124−11p units. Find the marketequilibrium point.

Answer: (q, p) = ( , )8.(1 pt) A rectangular plot, 20 ft by 19 ft is to be

used for a garden. It is decided to put a pavementinside the entire border so that 240 squre feet of the

plot is left for flowers. How wide should the pave-ment be?

Answer: feet9.(1 pt) Solve the inequality6x+5 < −3Answer: xInstructions: Enter either <, >, >= or <= in the

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

10.(1 pt) Solve the inequality3(x+3) ≤ 6x+4Answer: xInstructions: Enter either <, >, >= or <= in the


11.(1 pt) Solve the inequality8−8x > 11Answer: xInstructions: Enter either <, >, >= or <= in the


12.(1 pt) Solve the inequality5(x−2) > 8(x−4)Answer: xInstructions: Enter either <, >, >= or <= in the


13.(1 pt) Solve the inequality5x−2

7 ≤ 15

Answer: xInstructions: Enter either <, >, >= or <= in the


14.(1 pt) A company manufactures a product thathas a unit selling price of $19 and a unit cost of $14.If fixed costs are $55, determine the least number ofunits that must be sold in order for the company tohave a profit.

Answer: More than units15.(1 pt) A manufacturer has 3900 units in stock.

The product is now selling at $4 per unit. Next monththe unit price will increase by $ 0.50. The manufac-turer wants the total revenue received from the saleof the 3900 units to be no less than $16600. What isthe maximum number of units that can be sold thismonth?

1

Answer: At most units16.(1 pt) Suppose consumers will purchase q units

of a product at a price of 90q +6 dollars per unit. What

is the minimum number of units that must be sold inorder to obtain revenue at least $144 ?

Answer: At least units17.(1 pt) Suppose a company offers you a sales po-

sition with your choice of two methods of determin-ing your yearly salary. One method pays $1200 plus a

bonus of 3% of your yearly sales. The other methodpays a straight 6% commission on your sales. Forwhat yearly sales amount S is it better to choose thefirst method?

Instructions: Enter either <, >, >= or <= in thefirst answer box. Enter a number in the second an-swer box.

Answer: S units


Peter Alfeld WW Prob Lib1 Math course-section, semester yearWeBWorK problems. WeBWorK assignment 3 due 9/25/06 at 11:58 PM.

1.(1 pt) Solve for x: |26− x| = 33Please enter the smaller answer first.Answer: x = ,2.(1 pt) Solve for x: |6+6x| = 10Please enter the smaller answer first.Answer: x = ,3.(1 pt) Consider the inequality : |x| < 72The solution of this inequality consists of one or

more of the following intervals (−∞,A), (A,B) and(B,∞) where A < B.

Find AFind BFor each interval, answer YES or NO to whether

the interval is included in the solution.(−∞,A)(A,B)(B,∞)

4.(1 pt) Consider the inequality : |x| ≥ 10The solution of this inequality consists of one or

more of the following intervals (−∞,A], [A,B] and[B,∞) where A < B.


the interval is included in the solution.

(−∞,A][A,B][B,∞)

5.(1 pt) Consider the inequality : |x−2| > 40The solution of this inequality consists of one or




6.(1 pt) Consider the inequality : |8−9x| < 6The solution of this inequality consists of one or






1.(1 pt) Find the domain of the function f (x) =9x−102x+6

Instructions: Enter either <, >, <=, >=, <> or =in the first answer box. Enter a number in the secondanswer box. <> means ”not equal”.

Answer: x2.(1 pt) Find the domain of the function f (x) =5x+10

(x−9)(x−13)

Instructions: Enter either <, >, <=, >=, <> or= in the first and third answer boxes. Enter a num-ber in the second and fourth answer boxes. Enter thesmaller number first. <> means ”not equal”.

Answer: x and x

3.(1 pt) Find the domain of the function f (x) =√8x−9Instructions: Enter either <, >, <=, >=, <> or =

in the first answer box. Enter a number in the secondanswer box. <> means ”not equal”.

Answer: x and4.(1 pt) Find the domain of the function f (x) =√8−8xInstructions: Enter either <, >, <=, >=, <> or =

in the first answer box. Enter a number in the secondanswer box. <> means ”not equal”.

Answer: x and5.(1 pt) Let f (x) = 3x2 +3x+5Thenf (4) = andf (x+1)=6.(1 pt) Let f (x) = 3x−3

4x+5Thenf (2) = andf (x+2)=7.(1 pt) Let f (x) =

√4x+4

Thenf (3) = andf (x+5) =

8.(1 pt) Find the domain of the supply function p =√q+2


Answer: q9.(1 pt) Find the domain of the demand function

p = 6q +4


Answer: q10.(1 pt) Consider the polynomial p(x) = 7x +

8x7 −8Its degree is and the leading coefficient

is

11.(1 pt) Let f (x) =

{

5x+6 x < 108x2 x ≥ 10

f (8) =f (10) =f (15) =

12.(1 pt) Let f (x) =

6x2 +6 x < 26 2 ≤ x ≤ 48− x x > 4

f (−3) =f (2) =f (3) =f (4) =f (7) =

13.(1 pt) The width of the rectangle is 4 inchesshorter then the length. The perimeter of the rectan-gle can be written as a function of the length p(l) =

. The area of the rectangle can be writtenas a function of the length a(l) = .

14.(1 pt) The tourist agency charges two rates fora trip. For groups of 20 or more, te price per personis $145. For groups smaller than 20, the price is $170per person. The cost for group of n persons can berepresented by a piecewise defined function

C(n) =

{

An n < DBn n ≥ D

A =B =D =

15.(1 pt) 4!1!3!

=

16.(1 pt) Let f (x) = 5x+3 and g(x) = 2−4x2.1

Then( f +g)(x) =and( f −g)(x) =

17.(1 pt) Let f (x) = 2x2 +3 and g(x) = 5x+3.Then( f ·g)(x) =( f/g)(x) =and3 f (x) =

18.(1 pt) Let f (x) = x2 and g(x) = 3x+2.Then( f ◦g)(x) =(g◦ f )(x) =and(g◦g)(x) =

19.(1 pt) Let f (x) = 2x+2.Thenf−1(x) =

20.(1 pt) Let f (x) = 2x3 +2.Thenf−1(x) =

21.(1 pt) Let f (x) =3x+65−8x .

Thenf−1(x) =

22.(1 pt) Find the x− and y− intercepts of thegraph of y = 5x + 6. If some solution does not ex-ist, type N for both coordinates.

x−intercept is ( , )y−intercept is ( , )23.(1 pt) Find the x− and y− intercepts of the

graph of y = 7x2 +8. If some solution does not exist,type N for both coordinates.

x−intercept is ( , )y−intercept is ( , )24.(1 pt) Find the x− and y− intercepts of the

graph of y = 5x2 −3. If some solution does not exist,type N for both coordinates. Enter the x− interceptwith the smaller x− coordinate first.

x−intercepts are ( , ) and ( ,)

y−intercept is ( , )

25.(1 pt) Find the x− and y− intercepts of thegraph of y =

4x+9. If some solution does not exist,

type N for both coordinates.x−intercept is ( , )y−intercept is ( , )26.(1 pt) Find the x− and y− intercepts of the

graph of y =4x + 3. If some solution does not exist,

type N for both coordinates.x−intercept is ( , )y−intercept is ( , )27.(1 pt) Find the x− and y− intercepts of the

graph of y =√

5x+8. If some solution does not exist,type N for both coordinates.

x−intercept is ( , )y−intercept is ( , )28.(1 pt)28.(1 pt) For each of the following graphs, deter-

mine whether or not it represents y as a function of x.Type YES or NO under each graph.

a)

b)

2

c)

d)

e)

29.(1 pt)

29.(1 pt) Match each graph to its equation.Instructions: enter the letter only (A, B, etc.)

1

2

3

3

4

5

6A y =

{

1 x < 0x x ≥ 0

B y =√

xC y = |x|D y = 1− xE y = x3

F y = x2

30.(1 pt)

30.(1 pt) The graph of y =√

x is

Match each graph to its equation.Instructions: enter the letter only (A, B, etc.)

1

2

4

3

4

5

6

7

8A y =

√x+1

B y =√

x−1C y =

√x+1

D y =√

x−1E y =

√−x

F y = −√x

G y = 2√

xH y = 0.5

√x



This assignment will cover the material from Sec-tions 3.1 and 3.2.

1.(1 pt) Find an equation of a line with slope 10passing through the point (7, 9).

y =

2.(1 pt) Find an equation of a line passing throughthe points (1, 5) and (9, 2).

y =

3.(1 pt) Find an equation of the horizontal linepassing through the point (2, 0).

y =

4.(1 pt) Find an equation of the vertical line pass-ing through the point (3, 0).

x =5.(1 pt) Find an equation of a line with slope -6 and

y-intercept 3.y =

6.(1 pt) Find the slope and the y-intercept of theline y = 6(3x−7).

Slope: m =y-intercept:y-intercept: ( , )7.(1 pt) Find an equation of a line parallel to y =

2x+3 and passing through the point (2, 3).y =

8.(1 pt) Find an equation of a line perpendicular toy = 5x+2 and passing through the point (5, 3).

y =

9.(1 pt) Find an equation of a line parallel to y = 5and passing through the point (3, 4).

y =

10.(1 pt) Find an equation of a line perpendicularto y = 3 and passing through the point (5, 4).

x =11.(1 pt) Find an equation of a line parallel to x = 4

and passing through the point (5, 5).x =12.(1 pt) Find an equation of a line perpendicular

to x = 3 and passing through the point (5, 3).y =

13.(1 pt) The business opened with a debt of$3000. After 2 years, it accumulated profit of $3000.Find the profit as a function of time t, knowing theprofit function is linear.

P(t) =

14.(1 pt) The consumers will demand 23 unitswhen the price of a product is $65, and 33 units whenthe price is $45. Find the demand function (expressthr price p in terms of the quantity q), assuming it islinear.

p =

15.(1 pt) A new appartment building was sold for$180000 3 years after it was purchased. The orig-inal owners calculated that the building appreciated$6000 per year while they owned it. Find a linearfunction that describes the appreciation of the build-ing, if x is a number of years since the original pur-chase.

f (x) =

16.(1 pt) An advertiser goes to a printer and ischarged $35 for 70 copies of one flyer and $49 for180 copies of another flyer. The printer chargesa fixed setup cost plus a charge for every copy ofsingle-page flyers. Find a function that describes thecost of a printing job, if x is the number of copiesmade.

C(x) =

17.(1 pt) Determine the linear function f knowingthe slope is 6 and f (16) = 16.

f (x) =

18.(1 pt) Determine the linear function f knowingthe f (16) = 14 and f (6) = 8.

f (x) =

19.(1 pt)

19.(1 pt) Match each graph to its equation.1

1

2

3

4A x = 1B y = x−1C y = 1D y = 1− x

20.(1 pt)

20.(1 pt) Match each graph to its equation.

1

22

3

4

A y = 2−2xB y = 2x+1C y = −2−2xD y = 2x−1




1.(1 pt) Find the vertex of the parabola y = (x−16)2 + 15 and determine whether it is minimum ormaximum .

The vertex is the point ( , ) and it is(MIN or MAX)

2.(1 pt) Find the vertex of the parabola y = 3−(x+14)2 and determine whether it is minimum or maxi-mum .


3.(1 pt) Find the vertex of the parabola y = 9x2 +10x+4 and determine whether it is minimum or max-imum .


4.(1 pt) Find the vertex of the parabola y =−11x2 + 5x + 13 and determine whether it is mini-mum or maximum .


5.(1 pt) Find the intercepts and range of the func-tion f (x) = 20x2 −13.

Instructions: Type the x-intercept with the smallerx-coordinate first. Type +INF for infinity, and -INFfor negative infinity.

x-intercepts: ( , ) and ( , )y-intercept: ( , )

range: ( , )6.(1 pt) Find the intercepts and range of the func-

tion f (x) = 225− (7x+13)2.Instructions: Type the x-intercept with the smaller

x-coordinate first. Type +INF for infinity, and -INFfor negative infinity.


range: ( , )7.(1 pt) Find the intercepts and range of the func-

tion f (x) = x2 −15x+54.

Instructions: Type the x-intercept with the smallerx-coordinate first. Type +INF for infinity, and -INFfor negative infinity.


range: ( , )

8.(1 pt)

8.(1 pt) Match each graph to its equation.

1

2

31

4A y = −x2 −2x+1B y = x2 −2x+2C y = x2 −4x+3D y = −x2 +2x+19.(1 pt) The demand function for a product is p =

56− 7q where p is the price in dollars when q unitsare demanded. Find the level of production that max-imizes the total revenue and determine the revenue.

q = unitsR = $10.(1 pt) A farmer wants to fence a rectangular

field and then divide it in half with a fence down themiddle parallel to one side. If 1644 ft of fence is tobe used, what is the maximum area of the lot that hecan obtain?

A = square feet11.(1 pt) A toy rocket is launched straight up from

the roof of a garage with an initial velocity of 56feet per second. The height h of the rocket in feet,t seconds after it was launched is described by h(t) =−16t2 + 56t + 16. Find the maximum height of therocket.

h = feet

12.(1 pt) Solve the system{

6x − 6y = 67x + 6y = 46

x = y =

13.(1 pt) Solve the system{

2x + 2y = 268x + 16y = 160

x = y =

14.(1 pt) The following system has infinitely manysolutions. Express x in terms of y (we know y can beany real number).

{

27x + 9y = 645x + 15y = 10

x =

15.(1 pt) An airplane travels 1800 miles in 2.5hours with the aid of a tail wind. It takes 3 hours forthe return trip, flying against the same wind. Find thespeed of the airplane in the still wind, and the speedof the wind.

Airplane speed: miles per hourWind speed: miles per hour16.(1 pt) Find the general solutions to the system.

3x+2y+ z = 3x− y− z = 2

2x+ y−2z = 1Solution: (x,y,z) = ( , , )

17.(1 pt) A brokerage house offers three stock port-folios. Portfolio I consists of 2 blocks of commonstock and 1 municipal bond. Portfolio II consists of4 blocks of common stock, 2 municipal bonds, and3 blocks of preferred stock. Portfolios III consists of7 blocks of common stock, 3 municipal bonds, and3 blocks of preferred stock. A customer wants 21blocks of common stock, 10 municipal bonds, and 9blocks of preferred stock. How many of each portfo-lios should be offered ?

Portfolio I =Portfolio II =Portfolio III =


Peter AlfeldMath 1090-4, Spring 2006WeBWorK Assignment 7 due 11/10/06 at11:59 PM


1.(1 pt) $1935 is invested at the rate 8.5% for 8years. Find the compound amount.

S= $2.(1 pt) $6688 is invested at the rate 5% for 2

years, compounded semiannually. Find the com-pound amount.

S= $3.(1 pt) $5860 is invested at the rate 9.5% for 17

years, compounded quarterly. Find the compoundamount.

S= $4.(1 pt) $7745 is invested at the rate 9% for 19

years, compounded monthly. Find the compoundamount.

S= $5.(1 pt) The population of a town of 22700 grows

at the rate of 1.5% per year. Find the population 6years from now.

P=6.(1 pt) The population of a country of 3261738

declines at the rate of 4% per year. Find the popula-tion 20 years from now.

P=7.(1 pt) Initially, there were 155 milligrams of a ra-

dioctive substance. The substance decays so that after

t years the number of milligrams present N is givenby

N = 155∗ e−0.038t

How many milligrams are present after 11 years?mg

8.(1 pt) A certain medicine reduses the amount ofbacteria in the bloodstream by 9% each hour. Cur-rently, 43000 bacteria are present. Determine theamount of bacteria after 4 hours.

bacteria9.(1 pt) log1000=10.(1 pt) log0.001+ log100− log1=11.(1 pt) lne31=12.(1 pt) log2

√26=

13.(1 pt) log918√9=

14.(1 pt) Solve for x: log3 x = 3.x =15.(1 pt) Solve for x: log5 x+3 = 3.x =

16.(1 pt) Solve for x: e5x = 5.x =

17.(1 pt) Solve for x: 7e4x = 4.x=18.(1 pt) Solve for x: logx (20− x) = 2.x =

19.(1 pt) Solve for x: logx (2x2 +6x−72) = 2.x =20.(1 pt) The supply function for a product is given

by p = ln(3+q/6). At what price will the manufac-turer supply 21 units?

p =


Peter AlfeldMath 1090-4, Spring 2006WeBWorK Assignment 8 due 11/14/06 at11:59 PM


1.(1 pt) log10+ log 1015

10 =

2.(1 pt) log27 3+ log27 243=3.(1 pt) Rewrite the following in terms of p = logx,

q = logy and r = logz:

log x3y7

z2 =

4.(1 pt) Rewrite the following in terms of p = logx,q = logy and r = logz:

log z9

x3√

y4=

5.(1 pt) Rewrite as a single logarithm2logx+5log(x+6) =log6.(1 pt) Rewrite as a single logarithm5log(x−6)− 1

2 log(x+8) =log7.(1 pt) Simplifye4ln7 =8.(1 pt) Simplify644log8 3 =9.(1 pt) Solve for x: log6 6(x+4) = 4x =

10.(1 pt) Solve for x: log5 25(x2−8) = 4

Please enter the smaller answer first.x = ,11.(1 pt) Solve for x: 3log3 (x+3) = 3x =

12.(1 pt) Solve for x: eln (x2+x) = 20x = ,Please enter the smaller answer first13.(1 pt) Calculatelog20 16using the change of base formula

14.(1 pt) Rewrite the following in terms of p =logx and q = logy:

logx

√

x8/y2 =15.(1 pt) Solve for x: log4− logx = log8x =

16.(1 pt) Solve for x: 6 log8 x+ log8 x = log85xx =

17.(1 pt) Solve for x: logx+ log(x+2) = log8x =

18.(1 pt) Solve for x: e5x+5 = 5x =

19.(1 pt) Solve for x: 123x+6 = 5x =

20.(1 pt) Solve for x: 83x = 18

x =

21.(1 pt) Solve for x: 3(97x+4 −2) = 15x =



1.(1 pt) The number of milligrams of a radioactivesubstance present after t years is given by 120e−0.02t .After how many years will there be 37 milligramspresent?

After years.2.(1 pt) The population of a town of 19000 grows

at the rate of 5% per year. After how many years willthe population reach 27800?

After years.3.(1 pt) After t years, the number of units of a prod-

uct sold per year is given by q = 200 ∗ 0.40.8t . Af-ter how many years will the number of units sold peryear be 125?

After years.4.(1 pt) Over 8 years, the original principal of

$1128 accumulated to $2232 in an account in whichinterest was compounded monthly. Determine theAPR.

APR = %5.(1 pt) Ken put $1210 in his savings account 9

years ago. The money was compounded quarterly,and has amounted to $2025. Determine the nominalrate.

APR = %6.(1 pt) Andy saved $6500. The best interest rate

he can find is 2.5% compounded quarterly. For howlong should he deposit the money in order to have$9900 ?

years7.(1 pt) How long will it take for $4400 com-

pounded semiannually at an annual rate of 4% toamount to $6800 ?

years8.(1 pt) What effective rate is equivalent to a nom-

inal rate of 18% compounded quarterly?re = %9.(1 pt) What effective rate is equivalent to a nom-

inal rate of 11% compounded monthly?re = %10.(1 pt) What effective rate is equivalent to a nom-

inal rate of 15% compounded daily?re = %11.(1 pt) Dan has a choice of investing a sum of

money at 8% compounded monthly or at 7.5% com-pounded daily. Calculate the effective rate in eachcase to determine the better rate.

8% compounded monthly is equivalent to re of%

7.5% compounded daily is equivalent to re of%

12.(1 pt) Suppose attending a certain college cost35000 in the 2000-2001 school year. Assuming an ef-fective 7% inflation rate, determine what the collegecosts will be in the 2008-2009 school year.

$13.(1 pt) A credit-card company has finance charge

of 2.4% per month on the outstanding indebtedness.What is the effective rate?

re = %



1.(1 pt) Find the present value of $1219 due after 4years if the interest rate is 9% compounded quarterly.

P = $2.(1 pt) Find the present value of $1095 due after 2

years if the interest rate is 2% compounded weekly.P = $3.(1 pt) After child’s birth, an account has been

open, and a single payment has been made, so whatwhen the child is 18, it will receive $13000. Find outhow much the payment was, if the interest rate is 6%compounded annually.

Payment = $4.(1 pt) A debt of $1650 due in 4 years and $1650

due in 7 years is to be repaid by a single payment now.Find out how much the payment is, if the interest rateis 2% compounded monthly.

Payment = $5.(1 pt) A debt of $1460 due in 5 years is to be re-

paid by a payment of $500 now and a second paymentat the end of 5 years. How much should the secondpayment be, if the interest rate is 9% compoundedquarterly.

Payment = $6.(1 pt) Find the fifth term of the geometric se-

quence if the first term is a1 = 6and the common ratiois 2.

a5 =

7.(1 pt) Find the sixth term of the geometric se-quence if the first term is a1 = 8and the common ratiois -2.

a6 =

8.(1 pt) Find the sum of the first 8 terms of thegeometric sequence if the first term is a1 = 5and thecommon ratio is 3.

S8 =

9.(1 pt) Find the sum of the first 8 terms of thegeometric sequence if the first term is a1 = 9and thecommon ratio is -2.

S8 =

10.(1 pt) Find the present value of an annuity of$1190 per month at an interest rate 6% compoundedmonthly for 8 years.

A = $11.(1 pt) $1820 is used to purchase an annuity con-

sisting of equal payments at the end of each quarterfor the next 3 years. The interest rate is 3% com-pounded quarterly. Find the amount of each payment.

R = $12.(1 pt) Paul and Anne are buying a house. They

have $22000 for downpayment. The house priceis $161000. If the interest rate is 7% compoundedmonthly, determine the size of payments they mustmake over the next 24 years to pay off the house.

R = $13.(1 pt) A small airline company wishes to lease

an airplane during the 5 month long tourist season.The rental fee is $21000 a month, payable in advance.The company wishes to pay in advance at the begin-ning or the rental period to cover all the rental feesdue over the 5 month period. If the money is worth7% compounded monthly, determine the size of thepayment.

A = $14.(1 pt) Tommi decided to put $320 in his savings

account at the end of every month. Find the amounthe has at the end of 6 years, if the money is worth 5%compounded monthly.

S = $15.(1 pt) Math department purchased a copy ma-

chine for $12000. After 4 years, the machine willbe worthless. How much money should the depart-ment deposit at the end of each quarter, if the moneyis worth 3% compounded quarterly, in order to saveenough to buy a new copy machine at the end of 4years?

R = $16.(1 pt) Math department also purchased a printer.

After 4 years, it will have a salvage value of $200.A new printer is expected to cost $2000. The de-partment established a sinking fund in order to pro-vide money for the difference between the cost andthe salvage value. If the fund earns 6% compoundedsemiannually, determine the size of payments.

R = $1

17.(1 pt) Aaron borrowed $4500 from the bank inorder to buy a new piano. He will pay it off by equalpayments at the end of each week for 2 years. Theinterest rate is 7% compounded weekly. Determinethe size of payments, and the total interest paid.

R = $Total interest = $18.(1 pt) To open a restaurant, Andy borrowed

$14000 from the bank. The interest rate is 9% com-pounded monthly. Andy wants to pay off the loan in5 years. Determine the size of each payment.

R = $After 2 years, Andy earned enough money to pay

off the entire loan. Find the amount he must pay.$19.(1 pt) Paul is buying a new sailing boat. He

can afford $1300 monthly payments. If the store

charges 4% interest rate, compounded monthly, andPaul wants to pay off his loan in 5 years, what is themost expansive boat he can buy?

Boat price = $

20.(1 pt) Mary bought a new computer for $2000.She will pay it off by making annual payments of$150. The store charges 3% interest rate, com-pounded annually. How long will it take Mary to payoff the computer?

years.21.(1 pt) Meagan is buying a new appartment. She

can afford a mortgage payment of $1020 a month,and a downpayment of $13000. She obtained a 22year loan at 9% compounded monthly. What is themost expensive appartment she can buy?

Appartment price = $



This assignment will cover the material from Sec-tions 6.3, 6.4 and 6.5.

1.(1 pt) Let

A =

−4 74 −35 8

Then

−A =

a11 a12a21 a22a31 a32

where a11 = , a12 = , a21 = , a22 = ,a31 = , a32 =

4A =

b11 b12b21 b22b31 b32

where b11 = , b12 = , b21 = , b22 = ,b31 = , b32 =

and

AT =

(

c11 c12 c13c21 c22 c23

)

where c11 = , c12 = , c13 = , c21 = ,c22 = , c23 =

2.(1 pt) Let

A =

(

3 8 63 8 3

)

,B =

(

−3 7 63 −8 7

)

Then

A+B =

(

a11 a12 a13a21 a22 a23

)

where a11 = , a12 = , a13 = , a21 =a22 = , a23 =

and

A−B =

(

c11 c12 c13c21 c22 c23

)

where c11 = , c12 = , c13 = , c21 =c22 = , c23 =

3.(1 pt) Let

A =(

3 6 0 5)

,B =(

1 4 3 0)

Then

8A+B =(

a11 a12 a13 a14)

where a11 = , a12 = , a13 = , a14 =and

6A−5B =(

c11 c12 c13 c14)

where c11 = , c12 = , c13 = , c14 =

4.(1 pt) Let

A =

(

5 65 9

)

,B =

(

−5 5−8 9

)

,C =

(

4 85 9

)

Then

A+BT =

(

a11 a12a21 a22

)

where a11 = , a12 = , a21 = , a22 =and

A−B+CT =

(

c11 c12c21 c22

)

where c11 = , c12 = , c21 = , c22 =

5.(1 pt) Let A be a 2 by 6 , B be a 6 by 6 and C bea 6 by 2 matrix. Determine the size of the followingmatrices (if they do not exist, type N in both answerboxes):

• AB by• BA by• AT B by• BC by• ABC by• CA by• BT A by• BCT by

1

6.(1 pt) Let

A =

(

9 1 44 −1 9

)

,B =

4 06 −62 2

Then

AB =

(

a11 a12a21 a22

)

where a11 = , a12 = , a21 = , a22 =

BA =

b11 b12 b13b21 b22 b23b31 b32 b33

where b11 = , b12 = , b13 = , b21 = ,b22 = , b23 = , b31 = , b32 = , b33 =

and

BT AT =

(

c11 c12c21 c22

)

where c11 = , c12 = , c21 = , c22 =

7.(1 pt) Let

A =

(

2 5−5 3

)

,B =

(

5 −36 5

)

Then

AB =

(

a11 a12a21 a22

)

where a11 = , a12 = , a21 = , a22 =

BA =

(

b11 b12b21 b22

)

where b11 = , b12 = , b21 = , b22 =and

AT BT =

(

c11 c12c21 c22

)

where c11 = , c12 = , c21 = , c22 =

8.(1 pt) Let

A =

0 6 80 0 70 0 0

Then

A2 =

a11 a12 a13a21 a22 a23a31 a32 a33

where a11 = , a12 = , a13 = , a21 = ,a22 = a23 = a31 = , a32 = a33 =

and

A3 =

c11 c12 c13c21 c22 c23c31 c32 c33

where c11 = , c12 = , c13 = , c21 = ,c22 = c23 = c31 = , c32 = c33 =

9.(1 pt) Solve

5x − 6y + 2z = 2x − y + z = 2

3x − 2y = 1x = , y = , z =10.(1 pt) Solve

x − y + z − w = 3y + 2z + w = 1

−z + w = 4−x + 2y − 3z + 5w = 1

x = , y = , z = , w =11.(1 pt) Let

A =

(

7 9−4 2

)

Then

A−1 =

(

a11 a12a21 a22

)

where a11 = , a12 = , a21 = ,a22 =

12.(1 pt) Let

A =

1 2 01 2 81 −7 8

Then

A−1 =

a11 a12 a13a21 a22 a23a31 a32 a33

2

where a11 = , a12 = , a13 = , a21 = ,a22 = , a23 = , a31 = , a32 = , a33 =

13.(1 pt) Let

A =

(

5 −33 5

)

Find A−1 and use it to solveAX = B

where

B =

(

54

)

X =

(

x1x2

)

where x1 = and x2 =

14.(1 pt) Let

A =

1 5 01 5 41 −5 5

Find A−1 and use it to solveAX = B

where

B =

10−1

X =

x1x2x3

where x1 = , x2 = and x3 =


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Peter Alfeld WW Prob Lib1 Math course-section, …...$15 per month increase, there will be a vacancy with-out possibility of lling it. The corporation wants to receive a total of $5085