kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/m072/lecture notes/m72 29 7.1.pdf(i) h.,,j 0-h sq~....

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{. I f r..e <;<; ·, OV\..S A. '°FU.VLc+\OV\.S -C. '). 'Ra........ +io V\.C . .-J ( e.:'>C-f o vvevrl--S ':f;?> ::f-. 4 c9 ( Q,kc.c.... -h c:> nS OY\ ccJ 4 lf r..e S. S \ OV\.S (.5" ra_c.ll'c.a-1 {--. E°\ l,La..-h DY\ s v D t \( lvt.cr '?,a .. A.-to:J E,x fr-"'- s $ ( D'Y't s -:t-.-i. CoW\.f lex.

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Page 1: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo

{. I ~u~\ t:-~ f r..e <;<; ·, OV\..S A. '°FU.VLc+\OV\.S

-C. '). 'Ra........+io V\.C . .-J ( ~c-ho'Y'I) e.:'>C-f o vvevrl--S

':f;?> StW\.flt~ff ~\caJ ~Kfr-"'~<"~lc?YJS

::f-. 4 c9 ( Q,kc.c....-h c:> nS OY\ ~l ccJ 4 lf r..e S. S \ OV\.S

(.5" Kor~ ra_c.ll'c.a-1 ~-h~

{--. ~ E°\ l,La..-h DY\ s ~ v D t \( lvt.cr '?,a .. A.-to:J E,x fr-"'- s $ ( D'Y't s

-:t-.-i. CoW\.f lex. N\...l-~krs

Page 2: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo

06j.ec.h v~S

\J t=; nd- s9 LlAf.Q,, routs t..01.~ou..t ~, -c-o..d,~ ccJ S'-'\ VV\.loo l. ~ :fi~ Squ..cL-v--e- VO~ v..;~ ~ 11~1.caJ St}VV\.bo l · '3) l)V)~·s-\-a_v-iJ w'vt~t ~ rcu::l'tcoe\ sj~\oo\ do-e,s

~+~ ck-f~~A".-+.

1-f) l=\"'-J h\l)~v - I~ roo+s

" ~ c_vtlo e.-- root-

e-i-c..

?) Ll._s.e_ alosolut.e_ v~-e~ Co"(Ye.c+s lA.J-t<f';li\ s ~h%~ Vt_~ eve-vt-\ V\,d.e.x. ~teals.

G) t:v~t.e .q rcul(C&l\ ~c-hoVI -:f) :\=1V\,d.. -4e &ovvitt-'IV1 o+. ct squ...a.r-e- ro~ ~'-d-\VY'l ai1-J

~.e-- ve>c+ ~vtch trV\.

Page 3: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo

(i) H.,,J 0-H sq~. rook o-1' 2!>. (No r<>J1ceJ s,yv"'lool)

Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo v~k:l1 1 VV~'eVI 4!..4X...reJ/ ,51v-e ~

:So s 'is tl scr-<-ar-.e- root of 276°'.

5o -L? Is c:t.LSo

@ bf al,t,u.-,.;t-~ ~ 2 5 · ( r a.di c-A.\ sy VVl.-boi ')

4 ~e rc.t.Al ca..\ .sy vvil,...?o \ ~-e.a.41.s B>Yl~ -~-e ~ ncifo..I Cpos't-hve) sqUctr:e- ~.

J z'3 ==-l\3 \ o V\~ ,

j \Nkevt- vve. u.5,e.., ~ 1AJo-rc:ls '-\s4u_ctt-e..- ·n::;cl tr ~ bof-&. 5 ~d -5

\ \.AJ~_t.'L w-e_ LC~ e.. vc:t..cU~l ~ OYiL:l LO =-~ ----~--,----~-

(3) 'E" "\fcJ ~e.... +oc; ==-- ~5 : ...... __ ..•

c;t) f(?) d) +( ?-=l-- ~)

b) +c-1; e) +c. 004) c-) +co)

(A} +:c~J = ""'~ =-~

b) +c-1) -= tci ::=- GJ

-, fW.y \iJ -..; lo - y . "2. - - - u -. -., __ _

:=r-1000 10 G 5

Page 4: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo

(5) 'Ev C\,~\AC\.}· .e .\- C'f.) -~ '1 ~-z. ~ v.~?J

bJ x::: --g._ ~) )(-::::- D

CAJ ~(?;) ~ w =- ~ :::- m \;) t l~?1-=:- ~ (:-?-)1- ==- ~ =-\21 c} _(: C 0 ) ·.::- { o·-v ::::- fa =::.- "B

® SIMphry {Xi

Vl~ '4 o... rM\ co...\ S~w-. 'bo \ 1

vJe o-\w~'ls ~e-\- °" tosi\t'V~ res u..l-\- . \')D\1\-YH':Ja-h \{"~

-\HJ --6·-Z- u5iNJ o.. Y-aAI ~~ symbo \ > V\t:~a::h ue.s VV\~+­\oec.-0~ ros ~ \i.e. I .-the St:eW\e a.S a,h ~lJ-e_, Ya.-~.

® S\Mpli-l'y Jx'L-(;t..-1-"1

=- J (x-3)

~CEiJ

® EvoJAA.cd-0 G. [·~'\()"\-a r-ea\ V\uwd:::~?-/rJ

So ..... M -=- \f\-o·i- v---e.oJ

Page 5: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo

@ ~v~l\Accte-o.) ·~

b) zr.32 0) tf-~\

J) V-?J; e) $

0.J ~ ~@] 't)~LJ~>iASe 3L\::-3"1

\?) $). =- )2l beawse ~= 32

c.) % :::[0ot-~ v:eal -it] ~~Is w\\\ \oe you'l' CLLt15Vl/e,v- VUtTh.lyol/l 50 - - -+v ~rcuLuccl-..e. school as ?t \/Vt~ ~on

d) ~-3J. =- @] because (-2)' - -32.

CJ $ [ 01 be_ca..vtS0 d1::: 0

So"' ..

Vo 0

Page 6: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo

Q) + (-3)

b) + (-?-)

c0 f lo)

~) + c~) == ~ =- efSi :::: 0 b) -Pc -:i-) = ~( -70~ = 0T0 -=- [ d- (

<-) +co)= efCJ' == ':!:Jo =@]

@ Sfw\plt+y ~

-JE]

@ Sh~~f\·l~ ~

e>e. -~{'2--) -==-- -8 ~ = m =- 'l

·~ ( ..si.) ::;_ ~;. :::: ~ ~ =-- -')_ V\€Ja.t\ \J e.. ires uJ;+s o~ · · · ·

~JX3 ~~

@ Sivnpl r~ W -==- GJ 0 JJ ·i\l'\JexJ S4,W\e ClS ~X 3 ·

® s·,VV\fhr-y ~* ~[ED

So .... ~ = 'X It 111 \s oJJ '\ ~ V\ i s .. e:vt,vi

Page 7: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo

@ G-retf h { L$) ·::;;: {°i DV\. &c. C\.V\d, +, >0d ·c+s ~M~\ A 1 A ., 1\\-eyvo.J Y\o-\.-ct;,hO V\ •

~~

ho Ye~u\.-\-5 resu .. .l·b ~ x~o x~o

@ Gt--a~h ~L)l;.J:::. ~ \-X

V"\ 0 \---zt,-h OY)

"------...--___; ~ '\{ a. Lu..e-~J s~ ',(\ 0 V\.e. .+err X~\ X>I

\-~ > 0 \>X

~··ti·'~ v~·~.

D

X ::!::.. \ -4-l'c/'v/1"'4.-.A..,. .. vi.-" ... a 0

@ Fi V\,J -1\A.e..- do vV\V\.I. VI o-C· . ...(J~) ::::. I aljeb~·-t:\~lly, '1 ')_X-_..} \ I

w-e \<,V\,trv\i ~J ~e.. Y'C:l_J '1ec.t.V\d- (_ \V\S '1Je') c.a.V\V\a\- 6e V\e~@'v-e­avtd b) vV-e CAJl\V\ot dllJLJe. \o-y ·z_~.

So '2X.+\ >O

2...X '? -\ x > -l.. < "].._

0/1 II 4"' A u. ~;--.. .... -... J .$9>1'40'0? ~

.-\

c lie-.d.c:. ~s~~: \

Page 8: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo

oVV V9;;>V4.;)4 v o v v'"vcv~ 0

~.~~~~~-

al W ''-'f S ~e\- -r-.e S \kl-\- 'S

Page 9: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo
Page 10: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo
Page 11: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo
Page 12: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo
Page 13: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo
Page 14: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo
Page 15: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo
Page 16: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo
Page 17: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo
Page 18: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo
Page 19: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo
Page 20: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo
Page 21: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo
Page 22: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo
Page 23: Kor~ lvt - dept.swccd.edudept.swccd.edu/mcarey/M072/Lecture Notes/M72 29 7.1.pdf(i) H.,,J 0-H sq~. rook o-1' 2!>. (No rJ1ceJ s,yv"'lool) Ls..:. fl-tis Vvt-ea.l/15 aU lt1UvV\beo