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;SPMlt;BR;SPMgt;
Exercises
;SPMlt;/H1;SPMgt;
;SPMlt;P;SPMgt;
;SPMlt;DL class=;SPMquot;COMPACT;SPMquot;;SPMgt;
;SPMlt;DT;SPMgt;1.;SPMlt;/DT;SPMgt;
;SPMlt;DD;SPMgt;;SPMlt;A ID=;SPMquot;q1;SPMquot;;SPMgt;;SPMlt;/A;SPMgt;Find all the primes between 100 and 120.
BITMAPSETAnswer0.2214in0.205in0ina1
;SPMlt;P;SPMgt;
;SPMlt;/DD;SPMgt;
;SPMlt;DT;SPMgt;2.;SPMlt;/DT;SPMgt;
;SPMlt;DD;SPMgt;;SPMlt;A ID=;SPMquot;q2;SPMquot;;SPMgt;;SPMlt;/A;SPMgt;Find two positive integers between 1000 and 1100
whose greatest common divisor is 23.BITMAPSETAnswer0.2214in0.205in0ina2
;SPMlt;P;SPMgt;
;SPMlt;/DD;SPMgt;
;SPMlt;DT;SPMgt;1.;SPMlt;/DT;SPMgt;
;SPMlt;DD;SPMgt;;SPMlt;A ID=;SPMquot;q3;SPMquot;;SPMgt;;SPMlt;/A;SPMgt;Compare the prime factorizations of 19!, 20!, 21!, !, 23!, 24!, and 25! with the number of zeros at the end of the
evaluated factorials. Use these results to predict how many zeros will
appear at the end of 100!. Check your prediction by direct evaluation.
Revise your method of prediction, if necessary, and predict the number of
zeros for each of 125!, 200!, 500!, 625!, and 1000!.
BITMAPSETAnswer0.2214in0.205in0ina3
;SPMlt;P;SPMgt;
;SPMlt;/DD;SPMgt;
;SPMlt;DT;SPMgt;2.;SPMlt;/DT;SPMgt;
;SPMlt;DD;SPMgt;;SPMlt;A ID=;SPMquot;q4;SPMquot;;SPMgt;;SPMlt;/A;SPMgt;Evaluate numerically the power
;SPMlt;P;SPMgt;;SPMlt;!-- MATH
#math2#
#tex2html_wrap_indisplay181#1 + #tex2html_wrap_indisplay182##tex2html_wrap_indisplay183#
--;SPMgt;
;SPMlt;/P;SPMgt;
;SPMlt;DIV ALIGN=;SPMquot;CENTER;SPMquot;;SPMgt;
;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img1.png;SPMquot;
ALT=;SPMquot;#math3##tex2html_wrap_indisplay185##tex2html_wrap_indisplay186#1+#tex2html_wrap_indisplay187#;SPMquot;;SPMgt;1 + ;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img2.png;SPMquot;
ALT=;SPMquot;#math4##tex2html_wrap_indisplay189#;SPMquot;;SPMgt;;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img3.png;SPMquot;
ALT=;SPMquot;#math5##tex2html_wrap_indisplay191##tex2html_wrap_indisplay192#1+#tex2html_wrap_indisplay193##tex2html_wrap_indisplay194#;SPMquot;;SPMgt;
;SPMlt;/DIV;SPMgt;;SPMlt;P;SPMgt;;SPMlt;/P;SPMgt;
for ;SPMlt;I;SPMgt;n;SPMlt;/I;SPMgt; = 2, 4, 8, 16, 32, 64, 128 and 256. What well-known
number is starting to emerge?BITMAPSETAnswer0.2214in0.205in0ina4
;SPMlt;P;SPMgt;
;SPMlt;/DD;SPMgt;
;SPMlt;DT;SPMgt;3.;SPMlt;/DT;SPMgt;
;SPMlt;DD;SPMgt;;SPMlt;A ID=;SPMquot;q5;SPMquot;;SPMgt;;SPMlt;/A;SPMgt;Experiment with numbers to test the potential identities
;SPMlt;P;SPMgt;;SPMlt;!-- MATH
#math6#
a∧#tex2html_wrap_indisplay196#b∨c#tex2html_wrap_indisplay197# = #tex2html_wrap_indisplay198#a∧b#tex2html_wrap_indisplay199#∨#tex2html_wrap_indisplay200#a∧c#tex2html_wrap_indisplay201#
--;SPMgt;
;SPMlt;/P;SPMgt;
;SPMlt;DIV ALIGN=;SPMquot;CENTER;SPMquot;;SPMgt;
;SPMlt;I;SPMgt;a;SPMlt;/I;SPMgt;;SPMamp;#8743;;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img4.png;SPMquot;
ALT=;SPMquot;#math7##tex2html_wrap_indisplay203##tex2html_wrap_indisplay204#b∨c;SPMquot;;SPMgt;;SPMlt;I;SPMgt;b;SPMlt;/I;SPMgt;;SPMamp;#8744;;SPMlt;I;SPMgt;c;SPMlt;/I;SPMgt;;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img5.png;SPMquot;
ALT=;SPMquot;#math8##tex2html_wrap_indisplay206##tex2html_wrap_indisplay207#b∨c#tex2html_wrap_indisplay208#;SPMquot;;SPMgt; = ;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img6.png;SPMquot;
ALT=;SPMquot;#math9##tex2html_wrap_indisplay210##tex2html_wrap_indisplay211#a∧b;SPMquot;;SPMgt;;SPMlt;I;SPMgt;a;SPMlt;/I;SPMgt;;SPMamp;#8743;;SPMlt;I;SPMgt;b;SPMlt;/I;SPMgt;;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img7.png;SPMquot;
ALT=;SPMquot;#math10##tex2html_wrap_indisplay213##tex2html_wrap_indisplay214#a∧b#tex2html_wrap_indisplay215#;SPMquot;;SPMgt;;SPMamp;#8744;;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img8.png;SPMquot;
ALT=;SPMquot;#math11##tex2html_wrap_indisplay217##tex2html_wrap_indisplay218#a∧c;SPMquot;;SPMgt;;SPMlt;I;SPMgt;a;SPMlt;/I;SPMgt;;SPMamp;#8743;;SPMlt;I;SPMgt;c;SPMlt;/I;SPMgt;;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img9.png;SPMquot;
ALT=;SPMquot;#math12##tex2html_wrap_indisplay220##tex2html_wrap_indisplay221#a∧c#tex2html_wrap_indisplay222#;SPMquot;;SPMgt;
;SPMlt;/DIV;SPMgt;;SPMlt;P;SPMgt;;SPMlt;/P;SPMgt;
and BITMAPSETAnswer0.2214in0.205in0ina5
;SPMlt;P;SPMgt;;SPMlt;!-- MATH
#math13#
a∨#tex2html_wrap_indisplay224#b∧c#tex2html_wrap_indisplay225# = #tex2html_wrap_indisplay226#a∨b#tex2html_wrap_indisplay227#∧#tex2html_wrap_indisplay228#a∨c#tex2html_wrap_indisplay229#
--;SPMgt;
;SPMlt;/P;SPMgt;
;SPMlt;DIV ALIGN=;SPMquot;CENTER;SPMquot;;SPMgt;
;SPMlt;I;SPMgt;a;SPMlt;/I;SPMgt;;SPMamp;#8744;;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img10.png;SPMquot;
ALT=;SPMquot;#math14##tex2html_wrap_indisplay231##tex2html_wrap_indisplay232#b∧c;SPMquot;;SPMgt;;SPMlt;I;SPMgt;b;SPMlt;/I;SPMgt;;SPMamp;#8743;;SPMlt;I;SPMgt;c;SPMlt;/I;SPMgt;;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img11.png;SPMquot;
ALT=;SPMquot;#math15##tex2html_wrap_indisplay234##tex2html_wrap_indisplay235#b∧c#tex2html_wrap_indisplay236#;SPMquot;;SPMgt; = ;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img12.png;SPMquot;
ALT=;SPMquot;#math16##tex2html_wrap_indisplay238##tex2html_wrap_indisplay239#a∨b;SPMquot;;SPMgt;;SPMlt;I;SPMgt;a;SPMlt;/I;SPMgt;;SPMamp;#8744;;SPMlt;I;SPMgt;b;SPMlt;/I;SPMgt;;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img13.png;SPMquot;
ALT=;SPMquot;#math17##tex2html_wrap_indisplay241##tex2html_wrap_indisplay242#a∨b#tex2html_wrap_indisplay243#;SPMquot;;SPMgt;;SPMamp;#8743;;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img14.png;SPMquot;
ALT=;SPMquot;#math18##tex2html_wrap_indisplay245##tex2html_wrap_indisplay246#a∨c;SPMquot;;SPMgt;;SPMlt;I;SPMgt;a;SPMlt;/I;SPMgt;;SPMamp;#8744;;SPMlt;I;SPMgt;c;SPMlt;/I;SPMgt;;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img15.png;SPMquot;
ALT=;SPMquot;#math19##tex2html_wrap_indisplay248##tex2html_wrap_indisplay249#a∨c#tex2html_wrap_indisplay250#;SPMquot;;SPMgt;
;SPMlt;/DIV;SPMgt;;SPMlt;P;SPMgt;;SPMlt;/P;SPMgt;
;SPMlt;P;SPMgt;
;SPMlt;/DD;SPMgt;
;SPMlt;DT;SPMgt;4.;SPMlt;/DT;SPMgt;
;SPMlt;DD;SPMgt;;SPMlt;A ID=;SPMquot;q6;SPMquot;;SPMgt;;SPMlt;/A;SPMgt;Test the potential identity
;SPMlt;P;SPMgt;;SPMlt;!-- MATH
#math20#
A∩#tex2html_wrap_indisplay252#B∪C#tex2html_wrap_indisplay253# = #tex2html_wrap_indisplay254#A∩B#tex2html_wrap_indisplay255#∪#tex2html_wrap_indisplay256#A∩C#tex2html_wrap_indisplay257#
--;SPMgt;
;SPMlt;/P;SPMgt;
;SPMlt;DIV ALIGN=;SPMquot;CENTER;SPMquot;;SPMgt;
;SPMlt;I;SPMgt;A;SPMlt;/I;SPMgt;;SPMamp;#8745;;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img16.png;SPMquot;
ALT=;SPMquot;#math21##tex2html_wrap_indisplay259##tex2html_wrap_indisplay260#B∪C;SPMquot;;SPMgt;;SPMlt;I;SPMgt;B;SPMlt;/I;SPMgt;;SPMamp;#8746;;SPMlt;I;SPMgt;C;SPMlt;/I;SPMgt;;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img17.png;SPMquot;
ALT=;SPMquot;#math22##tex2html_wrap_indisplay262##tex2html_wrap_indisplay263#B∪C#tex2html_wrap_indisplay264#;SPMquot;;SPMgt; = ;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img18.png;SPMquot;
ALT=;SPMquot;#math23##tex2html_wrap_indisplay266##tex2html_wrap_indisplay267#A∩B;SPMquot;;SPMgt;;SPMlt;I;SPMgt;A;SPMlt;/I;SPMgt;;SPMamp;#8745;;SPMlt;I;SPMgt;B;SPMlt;/I;SPMgt;;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img19.png;SPMquot;
ALT=;SPMquot;#math24##tex2html_wrap_indisplay269##tex2html_wrap_indisplay270#A∩B#tex2html_wrap_indisplay271#;SPMquot;;SPMgt;;SPMamp;#8746;;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img20.png;SPMquot;
ALT=;SPMquot;#math25##tex2html_wrap_indisplay273##tex2html_wrap_indisplay274#A∩C;SPMquot;;SPMgt;;SPMlt;I;SPMgt;A;SPMlt;/I;SPMgt;;SPMamp;#8745;;SPMlt;I;SPMgt;C;SPMlt;/I;SPMgt;;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img21.png;SPMquot;
ALT=;SPMquot;#math26##tex2html_wrap_indisplay276##tex2html_wrap_indisplay277#A∩C#tex2html_wrap_indisplay278#;SPMquot;;SPMgt;
;SPMlt;/DIV;SPMgt;;SPMlt;P;SPMgt;;SPMlt;/P;SPMgt;
using the sets ;SPMlt;!-- MATH
#math27#A = #tex2html_wrap_inline280#1, 3, 5, 7, 9#tex2html_wrap_inline281#
--;SPMgt;
;SPMlt;I;SPMgt;A;SPMlt;/I;SPMgt; = ;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img22.png;SPMquot;
ALT=;SPMquot;#math28##tex2html_wrap_inline283##tex2html_wrap_inline284#1, 3, 5, 7, 9;SPMquot;;SPMgt;1, 3, 5, 7, 9;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img23.png;SPMquot;
ALT=;SPMquot;#math29##tex2html_wrap_inline286##tex2html_wrap_inline287#1, 3, 5, 7, 9#tex2html_wrap_inline288#;SPMquot;;SPMgt;, ;SPMlt;!-- MATH
#math30#B = #tex2html_wrap_inline290#1, 4, 9, 16#tex2html_wrap_inline291#
--;SPMgt;
;SPMlt;I;SPMgt;B;SPMlt;/I;SPMgt; = ;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img24.png;SPMquot;
ALT=;SPMquot;#math31##tex2html_wrap_inline293##tex2html_wrap_inline294#1, 4, 9, 16;SPMquot;;SPMgt;1, 4, 9, 16;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img25.png;SPMquot;
ALT=;SPMquot;#math32##tex2html_wrap_inline296##tex2html_wrap_inline297#1, 4, 9, 16#tex2html_wrap_inline298#;SPMquot;;SPMgt;, and ;SPMlt;!-- MATH
#math33#C = #tex2html_wrap_inline300#2, 3, 5, 7, 11#tex2html_wrap_inline301#
--;SPMgt;
;SPMlt;I;SPMgt;C;SPMlt;/I;SPMgt; = ;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img26.png;SPMquot;
ALT=;SPMquot;#math34##tex2html_wrap_inline303##tex2html_wrap_inline304#2, 3, 5, 7, 11;SPMquot;;SPMgt;2, 3, 5, 7, 11;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img27.png;SPMquot;
ALT=;SPMquot;#math35##tex2html_wrap_inline306##tex2html_wrap_inline307#2, 3, 5, 7, 11#tex2html_wrap_inline308#;SPMquot;;SPMgt;.BITMAPSETAnswer0.2214in0.205in0ina6
;SPMlt;P;SPMgt;
;SPMlt;/DD;SPMgt;
;SPMlt;DT;SPMgt;5.;SPMlt;/DT;SPMgt;
;SPMlt;DD;SPMgt;;SPMlt;A ID=;SPMquot;q7;SPMquot;;SPMgt;;SPMlt;/A;SPMgt;;SPMlt;A ID=;SPMquot;Volume__question;SPMquot;;SPMgt;;SPMlt;/A;SPMgt;The mass of a block of aluminum is ;SPMlt;!-- MATH
#math36#1403.2 #tex2html_wrap_inline310#lb
--;SPMgt;
.2;SPMamp;nbsp;;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img28.png;SPMquot;
ALT=;SPMquot;#tex2html_wrap_inline312#;SPMquot;;SPMgt;;SPMlt;I;SPMgt;lb;SPMlt;/I;SPMgt; and the density is ;SPMlt;!-- MATH
#math37#168#tex2html_wrap_inline314#
--;SPMgt;
168;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img29.png;SPMquot;
ALT=;SPMquot;#math38##tex2html_wrap_inline316#;SPMquot;;SPMgt;.
What is its volume?BITMAPSETAnswer0.2214in0.205in0inVolume
;SPMlt;P;SPMgt;
;SPMlt;/DD;SPMgt;
;SPMlt;DT;SPMgt;6.;SPMlt;/DT;SPMgt;
;SPMlt;DD;SPMgt;;SPMlt;A ID=;SPMquot;q8;SPMquot;;SPMgt;;SPMlt;/A;SPMgt;;SPMlt;A ID=;SPMquot;Rocket__question;SPMquot;;SPMgt;;SPMlt;/A;SPMgt;If a toy rocket shoots vertically
upward with an initial velocity of 80 ;SPMlt;!-- MATH
#math39##tex2html_wrap_inline318#m/#tex2html_wrap_inline319#s
--;SPMgt;
;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img28.png;SPMquot;
ALT=;SPMquot;#tex2html_wrap_inline321#;SPMquot;;SPMgt;;SPMlt;I;SPMgt;m;SPMlt;/I;SPMgt;/;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img28.png;SPMquot;
ALT=;SPMquot;#tex2html_wrap_inline323#;SPMquot;;SPMgt;;SPMlt;I;SPMgt;s;SPMlt;/I;SPMgt;, at ;SPMlt;I;SPMgt;t;SPMlt;/I;SPMgt; seconds
after the rocket takes off, until it returns to the ground, it is at the
height ;SPMlt;!-- MATH
#math40#80t - 16t2#tex2html_wrap_inline325#m
--;SPMgt;
80;SPMlt;I;SPMgt;t;SPMlt;/I;SPMgt; - 16;SPMlt;I;SPMgt;t;SPMlt;/I;SPMgt;;SPMlt;SUP;SPMgt;2;SPMlt;/SUP;SPMgt;;SPMlt;IMG
STYLE=;SPMquot;;SPMquot; SRC=;SPMquot;img28.png;SPMquot;
ALT=;SPMquot;#tex2html_wrap_inline327#;SPMquot;;SPMgt;;SPMlt;I;SPMgt;m;SPMlt;/I;SPMgt;. Find the time it takes for the rocket to
return to the ground. When does it reach its highest point?BITMAPSETAnswer0.2214in0.205in0inRocket
;SPMlt;/DD;SPMgt;
;SPMlt;/DL;SPMgt;
;SPMlt;P;SPMgt;
;SPMlt;HR;SPMgt;
;SPMlt;/BODY;SPMgt;
;SPMlt;/HTML;SPMgt;