Example: dental hygienist

01+%'2& - PUC

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Transcription of 01+%'2& - PUC

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m/+'01'q23-' *(!",4 !*,*,*-*&'56*,"7)0%+!(,0'(%!R+!*4'0,(,"* !+!*(-+&!0'"/"%*70%++%6*8$'"# !$%&'"",.-,9,*:'"&';-,,*$'4 !"%+%6* (, ,;-%$%#0%! ,"&<* ",4'0'('" 4 !0 -*' (%"&'*+%'R2 ,&, *, $'" +'01'" (, $'" # !$%&'"2)"$*+, '0''4$%+'0$'+!*(%+%6*(,,;-%$%#0%!,"*,+," '0%!)))))))))))

2 ;-,,"+0%#'.!"&! ('"$'"7-,05'""!#0,-*'(,$'"# !*,*&,"0,+&'*1-$'0,"+!.!?~N=Ncos( /3) i+Nsin( /3) j@'7-,05'~Fe,"$',A,0+%('4 !0$'# !$%&'(,$'(,0,+:'"!#0,$'# !$% -%,0('/,"?~Fe=kq2R2B !"#$%&'()&*+,* '%&'-.!"#$%&'(%(#&)'*$+%&, #$-#(, #.*./*&#0$*1%0 #12/%3*1%3*$*-"%4%,12-%(#&1%-#. **6'2120$2#78'*$+%*.97 XFX=Ncos( /3) kq2R2= 0(1)8'*$+%*.:7 XFY=Nsin( /3) mg= 0(2);*<=>?*(#&6'*N=mgsin( /3)cos( /3) kq2R2= 0;*&, *C%.3#qq= Rrmgcot( /3)k !"#$%&'(!"#$"%"%&'()*(*($+,*-"()&")$()*. */+*0,%$&*(*#/*12(&",%("+)"%#'1"/#$.*-34 '56*)*(*$%7"/$'/"(#834**-"9#/")'$%7"/$'/ &"-("+)"%#':-*)*(*(,; "/$'/(";,"&")'1"/-$</")"%#"5*=>%.,"%#/"-*; '($.$?%&""0,$-$</$'&"-*)*(*(,; "/$'/5<=>%.,"%#/"-*7/".,"%.$*&"; '/-'0,"-*7,"/B*"-2.#/$.*"%#/"*)<*("(/";, -($1*5C(DA-*)*(*(,; "/$'/"9; "/$)"%#*,%*7,"/B*"-2.#/$.*E*.$**//$<*:(, ; "('E*.$**<* 4'A"(#*%&'"%"0,$-$</$'.,*%&'*)<*(7,"/B*( ('%$+,*-"(5F'%($&"/*%&'"(#'#"%")'(Amg=kq 2x02.)))))))))))))))))))))))))))

3 '%x0; '($.$?%&""0,$-$</$'5= x0=q skmg(1)<=F'%($&"/")'(,%*.' '/&"%*&*9"%#'/%'-*; '($.$?%&""0,$-$</$'x05G"%")'(; '/H&*-":&"I"J#?%F=md2xdt2= mg+kq2(x0+x)2K*/*'(.$-*.$'%"(; "0,"@*(A|x|<<|x0|= |xx0|<<1A; '/-'0,"F=md2xdt2= mg+kq2(x0+x)2= mg+kq2x02 (1 +xx0) 2 = mg+kq2x02 (1 2xx0)K"/'&"LM=#"%")'(0,"mg=kq2x02= md2xdt2 = 2kq2xx03= d2xdt2+2kq2mx02 xx0= 0K"/'&"LM=Amx02=kq2g= d2xdt2+2gx0 x= 0K'/#*%#'A#"%")'(0,"-*7/".,"%.$*&"'(.$-* .$'%"(; "0,"@*("(w=r2gx0 !"#$%&'()&*+,* '%&'-. !"#$%&'(!"#$%&'()*+,%-,.")(*/"0.#$,1.*#/ ),($-,#2-$3425)(,%+2(02%",02)*&2%6178*%, 9 x#2-*(,++*D"-,#2+2(02*B1.*,(-2*"A,(*$(2# 2-,(,+42*"A,(*$(5 y#2-,#9.")$<,-*$-,##2-$*"A,(*$(2#2+2(02- ,#&'()*+,%.9 ,(*$(732%*).2+*D",%2"/#$02,"#$%)(,%&'()* +,%E+,")('<$"$%,"#2+2(02-,(,+42*"A,(*$(7 C,",<$%1.,#2%A.,(B2%,#'+)(*+2%1.,,F9 ,(*<,")2%$"~F1=kq2L2 (cos( 3) x sen( 3) y) =kq2L2 ( x2 32 y)~F2=kq2L2 x32A.,(B2(,%.#)2"),,%~F=~F1+~F2=32kq2L2 x 32kq2L2 y= 3 kq2L2 ( 32 x y2) = 3 kq2L2 (cos( 6) x sen( 6) y)G,#%,")*-$-,#2A.)))))))))))))))))))))) ))))

4 ,(B2;&,<$%1.,:-,= ,%,(9 $%*)* -,0,$<,)(I2,#,<,")2#6,%)$%,-,J22##,+)$(69 $ -,<$%&,(1.,#2A.,(B2,")(,:561)*,",-*(,++*D" 6(,%9 ,+)$ x;9 $(#$1.,#2A.,(B2%$=(,61-,=*-$2#2%$)(2%+2(02%",02)*&2%,%2")*92(2#,#2+$"#2A.,(B2,#'+)(*+2%$=(,61-,=*-$2%.*"),(2++*D"+$":7H%I;92(21.,61,%)',",1.*#*=(*$;"$%=2%)2* #2(#$%<D -.#$%-,#2%A.,(B2%732-*%)2"+*2,")(,615:#29 $ -,<$%,"+$")(2(.%2"-$#2#,5-,#$%%,"$%%$=(,,#)(*/"0.#$61:61-,=2%,#2=2%,-,#)(*/"0.#$,1.*#/),($7H%I;rsen( 6)=Lsen(2 3)= r=L 3K$()2")$;2#* #2(#$%<D -.#$%-,#2%A.,(B2%$=),",<$% 3 kq2L2=kqQ(L 3)2= Q=1 3 q !"#$%&'(!"#$%&'%#()*+)%,-#( "#.+./%#0-#+1*#-(%&%2%#( "&)*%2.#+%*$.%2a34"&-,()*+"5-2."2-,#-'5-*+"6)-,%#)*-#-+&%7%)*(,%*"( -&( -*2.$),%&%,5.#5"38,,)'%&2-,"#()*+"#-*6)-,%9)-&7%#":&-)*%$%&'%2-(&)-:%6-*-,(,%*"-#51;.5%-#( "&#.5-+&<%)*%$.&$)*9-&-*$.%38*$)-*+&--,&%2."2-2.$=%$.&$)*9-&-*$.%3)"$*+, !-,%#.5-+&<%2-,(&":,-5%>2-%*+-5%*"#%: -5"#6)-,%9)-&7%#":&-,%$%&'%2-(&)-:%-#+1# ":&--,(,%*"3?)))

5 -%+%,(,%*"-,(,%*";@2-$" "&2-*%2%#$%&+-#.%*%#@( "*'%5"#%5:%#$%&'%##":&--,-A-73!--#+%9"&5 %>+-*-5"#6)-~r=R (cos( ) x+sen( ) y)>~r1=a z@~r2= a z>2"*2-~r-#,%( "#.$.B*2-,%$%&'%2-(&)-:%@~r1, ~r2#"*,%#( "#.$."*-#2-,%#$%&'%#( "#.+./%#%*+-#5-*$."*%2%#3C2-51#>|~r ~r1|=|~r ~r2|= R2+a23D%9)-&7%-,E$+&.$%#":&-,%$%&'%2-(&) -:%-#~F=~F1+~F2=kqQ(R2+a2)32 (Rcos( ) x+Rsen( ) y a z+Rcos( ) x+Rsen( ) y+a z)=2kqQR(R2+a2)32 (cos( ) x+sen( ) y).!--#+"/-5"#6)-,%9)-&7%#":&-,%$%&'%2-( &)-:%-#+1#":&--,(,%*"3F,%&%5-*+-,"6)-2-: -5"#=%$- . ,5B "&,"#()*+"#2"*2--,5B 2),"2--#+%9)- .5%38#2-$.&>2-: -5"#5%;. ,%9)*$.B*|~F|=2kqQR(R2+a2)32= 2kqQ f(R)= df(R)dR=(R2+a2)32 3R2(R2+a2)12(R2+a2)3= 0= (R2+a2)12 ((R2+a2) 3R2)) = 0 = R=1 2 2 a ! !"#$%&'()&*+,* '%&'-. !"#$%&'("#$%&'%($)*+&,-.$.$(/$0$,-%#%1#$ 2$&$23&%.1%*/$0%1#4-*5$-&*$#,%0%*$(/5*6% #1#$(%/-7#05#0%%8-&,%1#.$2) 5%*9.,( ~E:;%(</1($=>?-*$@ 5*-,$) %(2$#%.))))

6 %%#%A1-*-@(-5%#1#+#/1*5 %#,(%*$;%(,-.$*3%*4-*5>:$=B$*.1*$(*$.$(/ $A0%*$@ 5*-,$>:@=?1) 5#/$A1%*$@ 5*-,$)-%(0%.$(/$$1#$,$&$0% (C seg 1)>B$*.1*%*$;%*5 .-0$0$#/1*$(A1%)(5 ,$0%&.$(/$)$($ 1>)"$*+, '0C5)(-2%(5A1%&%0%@ %4$.%(%&0%,%(2-#$(,5 0$&*$&'1%(D$&A1%%&,+#$.,1$#05&5@(%*$@ $) 5(%*.$2) i>H5(*5,$#,5~FE=qE 5#%#,%&(%.,$#/1*$(%&F~T= Tsin( ) i+Tcos( ) j !"#$%&'()'*'&)+%$,%&-)'$.%&( #$/#+( #0'01'2%(,3/%$,%/#0*3/340*''5)3,36$3#78) '$.%'097 XFX=qE Tsin( ) = 0(1)8)'$.%'0:7 XFY=Tcos( ) mg= 0(2);'<=>7T=mgcos( )?''+(,%.%0*#'0< >7qE mgcos( )sin( ) = 0;''&1#@$'&),1%5)'7q=mgtan( )E !;',$'&),1%*#%01'$3#$A'+#&1'0'+#&5)'q=mg tan( )EBC#+# 11'0'+#&5)'tan( ) BD#$,#1%01#@( # *'+#&'&/$363$,%/%$E%'0-)0/340*',13'+( #/#+#7q(t) =mg (t)E;'$3A%+#&/#0$'&( '/1#%,13'+( ##61'0'+#&7dqdt=mgEd dtF)'E#@/#+#dqdt= @*'&( 'G%0*#d dt$'&),1%7d dt= Emg ! !"#$%&'()&*+,* '%&'-. !"#$%&'("#$%&'(&$+Q$)*&+,-)+)+.)))))))))

7 /&$&0+&1-$,&+%-&d1)$)2&'&%-3+45+&2&',6%0 7&1)%&'(&+)(&,-8& q9*&$&m$)$-,:&)+)7%)+,'#1))77 ,'&$0+2 )<0)=#1)$27&>&*-)+,#2 )'2 )+1-%07&'&7&76+)&<0)7 $)1)/&)+7-? )'&14")*0)$,')<0)7&2&',6%07&1)$%'-? )0+*#8-*-)+,#&'*3+-%#$-*27)9)+%0)+,')$02 )'-# 1#1)#$%-7&%-3+4)"$*+, @&'&')$#78)')72'#?7)*&0,-7->&')7&$-(0-)+,)1-$2 #$-%-3+)$2&%-&7AB#2'-*)'#<0)C&%)*#$)$%&7%07&'7&D0)'>&')$07,&+,)$#?')7&%&'(& q4E#,&'<0)&7$)'7&$%&'(&$./&$1)$-(+##20)$,#&7&%&'(&1)2'0)?&7&$D0)'>&$$)'F+&,'&9)+,)$9$)'F)$,#7#<0)2'# 10%-'F7&#$%-7&%-3+40'$+*$"1%~F1/B&%&'(&<0)2'# 10%)7&D0)'>&~F1$))+%0)+,'&)+7&2 #$-%-3+~r1=d/2 j97&2&',6%07&1)2'0)?&)+x q)Q(x i+d/2 j)l30'$+*$"1%~F2/G+)$,)% 7&%&'(&<0)2'# 10%)~F2$))+%0)+,'&)+7&2 #$-%-3+~r2= d/2 j;2 #'7#,&+,#7&D0)'>&1)&,'&%%-3+)+,'))$,&%&'(&97&%&'(&1)2'0) ?&$)'FA~F2=k( q)Q(x i d/2 j)l3"))$, 7&D0)'>&')$07,&+,)$#?')7&%&'(& q$)'FA~F=~F1+~F2= 2kqQxl3 i(1) !"#$%&'(#) % *#$%&+#, +#,,-+1%.

8 %0,-&*/& #03( *#,501(,% /0*/.-*%#0,-61(+--02#+/%+) %+,-+#, +/1%0%$72+/.-8d/2 = cos( )= = (d/2) cos( )9%$%&#)+% *(.#(0) #'(#:%*# -$/#02%*#, +1-*#)+(#<-=#,501(,% #&2-$</70) #'(#:%8 1>9%0#&2%?#$%&'(#cos( ) 1@) %+,%2-02% (d/2)>A?-,(-0*%#0B C&#2/#0#'(#8~F= @) %+,%2-02%m~a=md2xdt2 iH##&2-$-0#+-&#2#0*+5'(# 16kqQxd3=md2xdt2= d2xdt2+16kqQxmd3= 09%0#&2%?#+ $%&'(#, +1-&/1(#(0$%?/$/#02%-+$40/.%&/$),#>I-3+# .(# (,-+&#+5#02%0.#&8w= 4rkqQmd3A,) #+/% *%*#%&./, #+5#02%0.#&T=2 w= 2smd3kqQ ! !"#$%&'()&*+,* '%&'-. !"#$%&'("#$%&'()(*+%&,-&($.('&%.)&/-0&1$ '(0+),+%2-$.-+*(%3')4"-+$.#5+*((*0+62 #(*70.)&0#($(*2-$.#P&$'&0+'#8#)95+*-+)(* 0+62 #(*70.)&0#($(**:6 -(P(%.+6-<+*(=+'#'(*%&%.(6+*"$+, ')>#)%&6(.):+(*0+62 #(*70.)&0#(%.+)?($'&)(00&1$ j@9*0+62 #(*70.)&0#2)# '-0&'#2 #)*+0+),+0($.)+*%#/)((*2-$.#P%()?%&62*(6 ($.(3~E1=2kqr2 j"#6#(%A?0&*5()B*+%'#%0+),+%*+.()+*(%2)# '-0&)?$-$0+62 #(*70.)&0#($(*2-$.)))))))))))))))))))))) ))

9 #P<*+%0#62 #$($.(($y'(0+'+0+62 #<'(%2-7%%-6+)*#C2 #)2)&$0&2&#'(%-2 ()2 #$($.(($y'(*0+62 #(*70.)&0#%()?Ey=Ecos( )@9*6# '-*#'(*0+62 #(*70.)&0#BEB(%2 #)'(E$&0&1$3E=kqd2+r2 !"#$%&'($')&*+,-$./0$cos( ) =r d2+r212$$'34%45$.43$5$%6'/0$Ey= (kqd2+r2 r d2+r2) j=kqr(d2+r2)3/270$86(#4#6/0$,4* $'5$843+-4(9 6 #$%6'$'*.+:+.-$*36.+4,%$53$$'3$*4%9 6$,$*3.+*6*6%6~Ey= kqr(d2+r2)3/2 j;'3$*4%9 6'$.&$, #0*+#69 6.*4#4* ,43$.4,1<6.,634536$,*4%9 6$,=*3.+*6.$'0,3453$$5$,90536P'$.&9 +5*+9+6#$'09 $.9 (2kqr2 2kqr(d2+r2)3/2) j !B045#6P$'34%0A4,$C4#6#$,'+'3$%4'$3+$5$/0$d r1;,*4%9 6$,=*3.+*6$5* #6$54D,69 6 #$%6'$'*.+:+.#$) '.$#0*+#4*6%6E~E= 2qk(1r2 r(r2+d2)32);'36,69 6 #$%6'$'*.+:+.#$) $/0+-4,$53$*6%6E~E= 2qk(1r2 1r2(1 +d2r2)32)=2qkr2(1 (1 +d2r2) 32);58$5$.4,(,4)05*+>5(1 +x) '$90$#$ +% ,6.(*045#6x 04E(1 +x) = 1 + xB6%6d r('$3+$5$/0$dr 0A9 6.,634536(dr)2 01<6.,634536($5,4$F9.$'+>5#$,*4%9 69 6 #$%6'G4*$.))))))))))))

10 ,4'+80+$53$ +%4*+>5E(1 +d2r2) 32 (1 32d2r2);-4,045#6$'3$.$'0,34#6$5,4$F9.$'+ >56:3$5+# $,*4%9 6('$3+$5$/0$E~E=3qkd2r4 j ! !"#$%&'()&*+,* '%&'-. !"#$%&'("#$%& '(')(*+,-%+')#.#+/0& ')(*+,-%+'.#%1'-0)2)$)2&(/3/(%4)-/0)#,)$ ) '2%+%5#$)) (%7-%'8+'0'2)0.)2,-/)#( $'#$) )2 <(0'0)#,'$)%#)-+%/$)($% =%)($%& '('2)(%7 )-/$)2$)(/& )-')2,B#)#2)#,%$'2' <2,/21.)-3/22'#4)#)-/$/2& '-)(+/0& ')(*+,-%+'~E?,%)#)#0/4#%,.$F=qE;<2,'2)&.)$)/&-)+%/-)#(/2% )#,) <(,'-6.)2'7-))($%& '('2)-B)#,'#+)2( $),'-6.)2&-' $.+%$'& '-+/$/1.)-3/8+'#D2%$)-/#$')()E)$)-',/+%5#2'7-))( <#,'#+)22),)#$-B6.))(,'-6.)2'7-))($%& '(')2C = F asin( ) + F asin( ) = 2F asin( ) = 2qEsin( )<(2%4#'#)4/,%>'2)'7,%)#)/&/-,%-$)(/-)4(/$)(/0/#'$)-)+F /?2)&.)$)+'0&-'7/-/(F/+)-(/'& )-/+%'#$)0'0)#,'2$)1'-0/>)+,'-%/(;=/7 )0'26.))(,'-6.)2'7-).#2%2,)0/2)-B% (/(0'0)#,'$)%#)-+%/I& '-(//+)()-/+%5#/#4.(/- G/07 '2-)2& )+,'/()E)2'7-)OH8)2$)+%- =I 2qEasin( ) =I I'0'2)&-' $.


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