Lab 1: Parametric Curves (Adapted from Multivariable Calculus 5e, by Edwards and Penney.) Here we wish to investigate parametric curves like the ones that a spirograph makes. To make our life easier, we will first define a and b and then use them in the equation. This will allow us to go back and change a and b and hence our graph without having to retype the entire entry. For all of these we will assume a and b are integers. Investigation A: For our first investigation we will look at the trochoid, given by 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 and 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. This is the curve traced by a point P on a solid wheel of radius a as it rolls along the x-axis; the distance of P from the center of the wheel is b > 0. (Note: The graph is a cycloid if 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). Include two pictures, one when a>b and one when a<b. a:=4; b:=5; plot([a*t-b*sin(t),a-b*cos(t),t=0..8*Pi]);

IiIl

IiIm

-%%PLOTG6%-%'CURVESG6$7iy7$$""!!""$!#5!""7$$!0yioXq@I"!#:$!0OF&>L7k&*!#:7$$!0*['o)QuXB!#:$!0f?40h6[)!#:7$$!0QVAf/GK$!#:$!0*4h\^_*\'!#:7$$!0Y`18Di*R!#:$!0E@k%)43s$!#:7$$!0*Qh4s8fU!#:$!0OjzQ$o3A!#;7$$!0O=Pu0,1%!#:$"0Uxnvfvi$!#:7$$!0kZ.KGCL$!#:$"0-h9Y"zj")!#:7$$!0K4c)f#G&>!#:$"0<cG![9P8!#97$$"0rKtsO#z6!#;$"0#Hxk6-+>!#97$$"0'y)*R#=`-$!#:$"0^Koep[^#!#97$$"0C)R:dxri!#:$"0*G'zB]"yI!#97$$"0^G!4b%>2"!#9$"0ij(4guEP!#97$$"0d1-%yH/;!#9$"0.![aLo#Q%!#97$$"0f(\<I_)>#!#9$"0(\pUop3]!#97$$"/3V"*[-1G!#8$"0Wf*)ynMc&!#97$$"0`u^<'p4O!#9$"0ch?XGd>'!#97$$"09k]!RCcV!#9$"0$f2&)3x*p'!#97$$"0o+-(3?&H&!#9$"/f%>r2-C(!#87$$"0%*f<['4%='!#9$"0x&e>'\*pw!#97$$"0%3bi<`9s!#9$"/pU%y]83)!#87$$"0OM&firT#)!#9$"0jgW[N%3%)!#97$$"0<8:JvAN*!#9$"0N.>`'*on)!#97$$"0%>="*3')R5!#8$"0FUc)\4a))!#97$$"0-gyj^q4"!#8$"0E]!)3V6#*)!#97$$"0`*[s$3Y:"!#8$"0b'=Y'Gy'*)!#97$$"0&H'[#=g%="!#8$"0T![qQ(R)*)!#97$$"0f4I$*RY@"!#8$"0$47#4bX**)!#97$$"0/5S3/ZC"!#8$"0$oX)\g&***)!#97$$"0>rejvZF"!#8$"0re:]%)*)**)!#97$$"0_=ub#4F8!#8$"0TQu]pY)*)!#97$$"0KWM6x#z8!#8$"/>2!H!\`*)!#87$$"0v#y(Qw`V"!#8$"0U"38i*4!*)!#97$$"0Jg6'\3"\"!#8$"0*4@B=;H))!#97$$"0h%G:kV/;!#8$"0=')R6x2i)!#97$$"0Bf]1DAr"!#8$"0()>"Q<jT$)!#97$$"0\5^"Gs7=!#8$"0es'pJ#\+)!#97$$"0J!o0&))*=>!#8$"0#R<)ec0c(!#97$$"0Qqj9L*3?!#8$"0vyY(=c/r!#97$$"0*)QrEg%)4#!#8$"08^GtKkc'!#97$$"0;B)[$fK<#!#8$"0>'4n;iSg!#97$$"0$HR`PoZA!#8$"0-Q6KMKV&!#97$$"0vB-fr.J#!#8$"0okQ?l&R[!#97$$"0c\CIi!oB!#8$"0mWc%4"e?%!#97$$"0y')o5?mT#!#8$"0eI=p$*Ge$!#97$$"/jX#on"fC!#7$"0w&)*\y&y$H!#97$$"01-(4IG#\#!#8$"0YsK2tNL#!#97$$"0W$\YWX=D!#8$"0Y;/$R)Gu"!#97$$"0:)=,P8PD!#8$"0e"*>ZgQ>"!#97$$"0$4Z5(f$[D!#8$"/nQBtL$H(!#97$$"0H]"y2)[b#!#8$"/v/#pUW_#!#97$$"0wQ`QOcb#!#8$!0#41Prar6!#:7$$"0a[6%p&>b#!#8$!0$o5mcmdW!#:7$$"0)H&)eH"\a#!#8$!0PWK-t:#p!#:7$$"/)4$3D4MD!#7$!0R\1s'HJ))!#:7$$"0%G=Q(=(GD!#8$!.(H&po%z$*!#87$$"0%Q4xB2BD!#8$!0JvS,Miv*!#:7$$"0nX\P&y>D!#8$!0U(*3z)G$*)*!#:7$$"0LBc'=Y;D!#8$!0o'*zuaX(**!#:7$$"0X?@_?J^#!#8$!/E!o,T*****!#97$$"0:st.!y4D!#8$!0mL8@>%p**!#:7$$"04"zIXv.D!#8$!0w<S71,x*!#:7$$"0Eo9"p!z\#!#8$!.$R_-$fQ*!#87$$"07)=Z$zi[#!#8$!0F(yH#>)3z!#:7$$"0tSSAZ#yC!#8$!0p(3k%>$\f!#:7$$"0wT'yOJsC!#8$!09L-oF%zH!#:7$$"0e;-bJ2Z#!#8$"0V"e<^C(*e!#;7$$"0yMi")oSZ#!#8$"0r@v08ly%!#:7$$"0r_,#Q.$[#!#8$"0=T>rQv_*!#:7$$"0&*4^;hv\#!#8$"0#He`3%QX"!#97$$"0l$)3=l._#!#8$"0m-wMCs.#!#97$$"0$zkpXT\D!#8$"0dUs1KYi#!#97$$"0O(3;11)e#!#8$"/%4;DedE$!#87$$"0FFb["QIE!#8$"0c$e'3Nt&Q!#97$$"0Goh8c`o#!#8$"0OXtdPJ^%!#97$$"0D#H+y/YF!#8$"0xP2`TJ8&!#97$$"0jIpPhU"G!#8$"04@/t)zLd!#97$$"0nv"f8Q$*G!#8$"0rqaGB>L'!#97$$"0pI"e0)H(H!#8$"0'33(fZw%o!#97$$"0%3>*e)pgI!#8$"0DnD%))yKt!#97$$"0K+yTMT;$!#8$"0TMm2a!4y!#97$$"0k&)y[8IE$!#8$"0,Df5W$z")!#97$$"0Kim[h%oL!#8$"0sW0?L?\)!#97$$"0ysy9)GzM!#8$"0'))\d2[O()!#97$$"0(HUka^$e$!#8$"/b/&R%H#*))!#87$$"0X^Re1(RO!#8$"0@!HDJcZ*)!#97$$"0@PH6%='p$!#8$"0TYDs6K)*)!#97$$"0s^1&fFCP!#8$"/&)e;1d$**)!#87$$"0Q'eVDR_P!#8$"0ViEt_!***)!#97$$"0,,7k=0y$!#8$"0<ror_'***)!#97$$"0/tO)*Q'3Q!#8$"0JjK)*p`**)!#97$$"-Za!4(oQ!#5$"0y#Q@j$)p*)!#97$$"0BXT2M&GR!#8$"0G[w\%4A*)!#97$$"0n/Z^05)R!#8$"0'ev+koh))!#97$$"0'\&3^qI.%!#8$"0ypY4fVy)!#97$$"0>UB=C6:%!#8$"0YG5&)HHa)!#97$$"0%p#\(>PaU!#8$"0^b<&os_#)!#97$$"0Xza-JEN%!#8$"/9E#RiC!z!#87$$"0G9TnBJX%!#8$"0"Hy4Zqhu!#97$$"0<I)Hx#ya%!#8$"0x-E]V(fp!#97$$"0Vej'y)zi%!#8$"0`:r]_&ek!#97$$"0J3;T:jq%!#8$"0G@AaP"))e!#97$$"0e?s`)evZ!#8$"0jLwya@I&!#97$$"0'**RVFLU[!#8$"0p)z;RtWY!#97$$"0ig,<)*G*[!#8$"/^6si4mS!#87$$"0BWvorE%\!#8$"0a#e$R*)3S$!#97$$"0TUdEB9)\!#8$"0J)[zT/&y#!#97$$"0vz]A+B,&!#8$"0%fPKM!R>#!#97$$"0$fD1*=g.&!#8$"0v63k>,j"!#97$$"0l?f(RA`]!#8$"0(RHDrx#4"!#97$$"0/C:KaV1&!#8$"0n(>f7lUd!#:7$$"0iboeu(o]!#8$"0mfbmB&G:!#:7$$"0DZv5"Ro]!#8$!0XLnGg,1#!#:7$$"0`)3`%)ej]!#8$!0H_-u1)3_!#:7$$"0"egTg?b]!#8$!06I&4$Q3f(!#:7$$"01[Nzfa/&!#8$!02B3(QN\!*!#:7$$"0_n1a=!R]!#8$!0$y:*=47g*!#:7$$"0)4bqzFK]!#8$!076'y\\<**!#:7$$"0Dq&[h_E]!#8$!0A(Gz()******!#:7$$"0RCSpu2-&!#8$!0@%)H?@i"**!#:7$$"0**3\mwT,&!#8$!0Q))ybgwg*!#:7$$"0')>-,jy+&!#8$!/)>g4OM2*!#97$$"0&)pl?Zr*\!#8$!0pMnE[oV(!#:7$$"0D'4%Hg(*)\!#8$!0(y_qmr5`!#:7$$"0*f9Q9#[)\!#8$!00SS[.m?#!#:7$$"/8b(yrV)\!#7$"0p!**>dgH;!#:7$$"0yf\]2$*)\!#8$"0teosu@4'!#:7$$"/jI,(o$**\!#7$"0eW!f-*Q2"!#97$$"03ISXZf,&!#8$"0r:z0k$*f"!#97$$"0rg'HOAS]!#8$"0(*HYB1<=#!#97$$"0f8(pw2s]!#8$"06>V%*z?z#!#97$$"0Tp/V`J6&!#8$"0c#="z/0W$!#97$$"04R_fvk:&!#8$"0E\3))f+-%!#97$$"03Ti=1L@&!#8$"0y")H"fyrY!#97$$"0%4k91))y_!#8$"0_(p9Mj9`!#97$$"0(o^7S$*\`!#8$"0[`=v\G"f!#97$$".'fMl'3U&!#6$"/BO'HR)Hk!#87$$"0BQntzE^&!#8$"0eG5KcB+(!#97$$"0_jT#)=jf&!#8$"0^&>RX(RW(!#97$$"0"f^\^n*p&!#8$"0"y'yrL$**y!#97$$"0x6pv>fz&!#8$"0rv1#3wV#)!#97$$"0Ldie-e!f!#8$"0LdT(HC_&)!#97$$"/"eaoLP,'!#7$"0jV"\`#Qx)!#97$$"0))\1A852'!#8$"0_OgGi-'))!#97$$"0>#=*y(yGh!#8$"0"ec!4-i#*)!#97$$"0x"Q\S;#='!#8$"0<DUkh%o*)!#97$$"0M14tRdB'!#8$"0-@gC]I**)!#97$$"0'G(opzYE'!#8$"06Sl)H%*)**)!#97$$"0)\C+.j$H'!#8$"0MGNFj'***)!#97$$".#\**[dAj!#6$"0'zph.@&**)!#97$$"0x&Hfo\^j!#8$"0*)=&e))e&)*)!#97$$"0NW6%fV6k!#8$"0A'y)RG"\*)!#97$$"0nXHUd5Z'!#8$"0'p_*pt0*))!#97$$"0V!p,_mtl!#8$"0m'\MJuO()!#97$$"0TsasI?o'!#8$"0kT>UV()\)!#97$$"0%QWD"f.z'!#8$"0([rlsTy")!#97$$"0p+Eer=*o!#8$"0U=nO]pz(!#97$$"0KJh55^)p!#8$"0;"p1cdpt!#97$$"0Oe82$3#3(!#8$"08,g<>e$o!#97$$"0k>3&*3F;(!#8$".=>U]4J'!#77$$"0dg%*\P9C(!#8$"0:F+'eX7d!#97$$"0$49ab%eI(!#8$"09d'Q,aW^!#97$$"0"fUA'G%ot!#8$"0.m(3da0X!#97$$"0<0`g)o>u!#8$"06q()*[N'*Q!#97$$"0w$=fbKlu!#8$"0WWO]o8E$!#97$$"0CBPqw@](!#8$".#4%fz?l#!#77$$"0v9X[]F`(!#8$"0$f7'\"zO?!#97$$"/d]-Pzav!#7$"0s<B"4mv9!#97$$"0`wll$Hqv!#8$"0$G2BQ.J%*!#:7$$"0:xKY7#zv!#8$"0dK&["Gxk%!#:7$$"0PHO`GBe(!#8$"0%))4;;Hnv!#;7$$"0"HaXNr!e(!#8$!0>@!\B8QI!#:7$$"0z?-=b`d(!#8$!0w$3"\<vx&!#:7$$"0UlI&)pkc(!#8$!0DW"ou%4(z!#:7$$"0WB:@*ybv!#8$!00Ll8t[L*!#:7$$"0@a7pu#\v!#8$!0l!*yD"Rt(*!#:7$$"/&4&p+aUv!#7$!0Gbeh8:)**!#:7$$"0zO*pafRv!#8$!0#[U"Hr)****!#:7$$"/#)4b=lOv!#7$!08P!)\H[(**!#:7$$"0B*R4?sLv!#8$!0')e<(*4k!**!#:7$$"0%QH0(=3`(!#8$!.l,5sYz*!#87$$"/KebRRCv!#7$!0(yO'QC3Q*!#:7$$"0/E#f*>$=v!#8$!0dx%3_<Y()!#:7$$"0$fCZ/j3v!#8$!02c0!4EJq!#:7$$"0%>Son%4](!#8$!0")3JGirN%!#:7$$"0vT7qrv\(!#8$!0U6.a"z99!#:7$$"0*>)yqu#)\(!#8$"/7$eSU2g#!#97$$"0)fNHyM/v!#8$"0;m$Q_E*3(!#:7$$"06&paOV;v!#8$"0A^#zM457!#97$$"0)fpl!o]`(!#8$"0"\,gAw`<!#97$$"0Kkb*zjfv!#8$"0L.r9E(4B!#97$$"0Q5YYcRf(!#8$"0#)3Av<$QH!#97$$"0VP$*RSWj(!#8$"0Co)RVZaN!#97$$"0j"Q1xS&o(!#8$"/)oUDX-@%!#87$$"0O<?*>'*Qx!#8$"00m0Wi5![!#97$$"08&4yDC1y!#8$"0=O'pRaSa!#97$$"0>hn7C%yy!#8$"0/u")3H*Hg!#97$$"0*e]-lidz!#8$"0Bx]G=fe'!#97$$"0R)ePC`Z!)!#8$"0e,q;*3Br!#97$$"0@y!\KGO")!#8$"0d$pxZjqv!#97$$"0j_2e_CB)!#8$"0/Im#30vz!#97$$"0.OG\$)RM)!#8$"0a8Bf[3N)!#97$$"0,-v7^*[%)!#8$"0%3V,<U@')!#97$$"0`5Va0$f&)!#8$"0A"Q@n;D))!#97$$"0D5k+$G;')!#8$"0vL*z6R**))!#97$$"0CmOosOn)!#8$"0J)3Z(yL&*)!#97$$"0*3]!Gwms)!#8$"0(4I$)3'\)*)!#97$$"06[K7:)z()!#8$"0^Y-$\9***)!#97$$"0P8v+d"3))!#8$"0Cwwmx&***)!#97$$"0uquW#\O))!#8$"0TK`d_]**)!#97$$"0v6e$e!['))!#8$"0e@09ub)*)!#97$$"0U&4(e"3$*))!#8$"0"4`i<:r*)!#97$$"07%z6+.\*)!#8$"0TwYMVz#*)!#97$$"0LX26[Y+*!#8$"0KRW)))[l))!#97$$"02V)p_(>7*!#8$"0*Q])*>Zo')!#97$$"/$H]@#*GA*!#7$"0D&R>6BD%)!#97$$"0i,svh_L*!#8$"0%)ot!oOo!)!#97$$"/&Q"pn2K%*!#7$"0-O(obZ"o(!#97$$".Rb)>&G_*!#6$"0&[j2_,Ws!#97$$"0L6TF#=9'*!#8$"0:$)orr.s'!#97$$"/c:#yy')p*!#7$"0j&y$f=z9'!#97$$"0M`1S@)o(*!#8$"0tC2=(p%f&!#97$$"0"Q3%f8f$)*!#8$"0t,nQ9D)\!#97$$"0m0yK)z$*)*!#8$"0\Mj'3zpV!#97$$"0PV/`Gz%**!#8$"0&*R&Q9]*p$!#97$$"0rRojBv)**!#8$".T3qPM7$!#77$$"0px)>M[-5!#7$"0'\oFJ$oZ#!#97$$"0b^]B>_+"!#7$"0[CR9UM*=!#97$$"/jgJtA25!#6$"0LO]dI#[8!#97$$"0P%*R*Re35!#7$"/)3gy2WV)!#97$$"0/"*G^_$45!#7$"0(fBWi](y$!#:7$$"0>8jKl&45!#7$!0;3IN!=G]!#;7$$"0P@"**RH45!#7$!0h)3drA(z$!#:7$$"0@Kd`n'35!#7$!0y:dNh))R'!#:7$$"0ytg#fp25!#7$!0>LyQ\>U)!#:7$$"0vO_!p^15!#7$!07p2`doi*!#:7$$"0#f8\'4`+"!#7$!#5!""-%&COLORG6'%$RGBG$"#5!""$""!!""$""!!""-%+_ATTRIBUTEG6#/%'sourceG%,mathdefaultG-%+AXESLABELSG6$Q!6"Q!6"-%%ROOTG6'-%)BOUNDS_XG6#$"$g#!""-%)BOUNDS_YG6#$"#]!""-%-BOUNDS_WIDTHG6#$"%I7!""-%.BOUNDS_HEIGHTG6#$"%55!""-%)CHILDRENG6"

Investigation B: For this one we have 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 and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KVEhRicvJSdmYW1pbHlHUSxDb3VyaWVyfk5ld0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRKlsyNTUsMCwwXUYnLyUrZXhlY3V0YWJsZUdGNC8lMGZvbnRfc3R5bGVfbmFtZUdRLE1hcGxlfklucHV0RicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtRiw2JVEieUYnRjJGPS1JI21vR0YkNi1RIj1GJy9GPlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRk0vJSlzdHJldGNoeUdGTS8lKnN5bW1ldHJpY0dGTS8lKGxhcmdlb3BHRk0vJS5tb3ZhYmxlbGltaXRzR0ZNLyUnYWNjZW50R0ZNLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGZm4tRiM2J0YrLUYjNiYtSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUSJhRidGMkY9LUZGNi1RKCZtaW51cztGJ0ZJRktGTkZQRlJGVEZWRlgvRmVuUSwwLjIyMjIyMjJlbUYnL0ZobkZpby1GLDYlUSJiRidGMkY9RkktRkY2LVExJkludmlzaWJsZVRpbWVzO0YnRklGS0ZORlBGUkZURlZGWC9GZW5RJjAuMGVtRicvRmhuRmJwLUYjNiUtRiw2JVEkc2luRicvRjNGTUZJLUZGNi1RMCZBcHBseUZ1bmN0aW9uO0YnRklGS0ZORlBGUkZURlZGWEZhcEZjcC1GXm82JC1GIzYjLUYsNiVRInRGJ0YyRj1GSUYrRmVvLUYjNiZGW3BGXnAtRiM2JUZmcEZqcC1GXm82JC1GIzYjLUkmbWZyYWNHRiQ2KC1GIzYlRl1vRl5wRmFxLUYjNiNGW3AvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmhyLyUpYmV2ZWxsZWRHRk1GSUYrRitGK0Yr. This is a hypocycloid - the path of a point P on a circle of radius b>0 that rolls along the inside of a circle of radius a > b. Include two pictures, make sure that they look different, but a > b for both. Explain why I chose to graph from 0 to 2b*Pi. a:=8;b:=2;plot([(a-b)*cos(t)+b*cos((a-b)*t/b),(a-b)*sin(t)-b*sin((a-b)*t/b),t=0..2*b*Pi]);

IiIp

IiIj

-%%PLOTG6%-%'CURVESG6$7ex7$$"#!)!""$""!!""7$$"0f>j$=vZz!#9$"0^9+mf@I#!#<7$$"09J%\JV=y!#9$"0t5x3ou\"!#;7$$"0(*ewuSOe(!#9$"0%)*H?kQR_!#;7$$"0yE#[CXes!#9$"0fzVEn(e7!#:7$$"0@wxDzc&o!#9$"0,'p,IZYC!#:7$$".j"*yS<U'!#7$"/aTs"[X-%!#97$$"0/vF?VD#f!#9$"06az+")H>'!#:7$$"0uR3&>Jm`!#9$"0v6"[!f*Q!*!#:7$$"0@)fo;.'y%!#9$"0)>q8>P\7!#97$$"0)=Kkj*z<%!#9$"0D_X!*pqm"!#97$$"0mR*p"fck$!#9$"0/G2LeM3#!#97$$"0^tmUIM1$!#9$"0=4Xxg(*f#!#97$$"0jn6N/+^#!#9$"0f_w&3GfJ!#97$$"0_Y$\3E<?!#9$"/Am)z]hs$!#87$$"0[nHc\;h"!#9$"0Jz)>p#RD%!#97$$"0Z0"o*4!)="!#9$"0xogGtJ)[!#97$$"0K()4d[c#))!#:$"0ln6"o80a!#97$$"0k!yld%e!f!#:$"0L?ysxS)f!#97$$"02a)H'R0)Q!#:$"0;%*4$*\#ek!#97$$"0"4'ow$[FA!#:$"0%=fp+MBp!#97$$"/>.ls/^6!#9$"0"Rm;ps+t!#97$$"0**Q5F[ik%!#;$"0<o"*yCah(!#97$$"0<PYrA*49!#;$"0s2U>ab#y!#97$$"0Rb<3-)f9!#<$"/-zUaUhz!#87$$"0#eJ!)fU;5!#=$"07"Q+qY$*z!#97$$!0x#Q#e,n=)!#?$"0)flK9y)*z!#97$$!0,\xGA?![!#=$"0oZ3Y5;)z!#97$$!00EVY'\PD!#<$"/"4?H`U%z!#87$$!0$38>MN'y"!#;$"0Ho`Esez(!#97$$!0`&*H$=)y!f!#;$"0%f&o\u#\v!#97$$!0Tk&o#H9N"!#:$"0X!Qsy5Bs!#97$$!0>LD/j6^#!#:$"0#G$=9Dh$o!#97$$!0GGHQ)**oV!#:$"/&e#3fSOj!#87$$!/"**[0z;g'!#9$"0bn9^Fp$e!#97$$!09OeZjSg*!#:$"0tUH*RMl_!#97$$!0$o#[WDzG"!#9$"0^P=3Rhs%!#97$$!06$41m7/<!#9$"0%p!RKYz7%!#97$$!0O%pS?$o9#!#9$"0`?7mQ*pN!#97$$!0N26Q+cl#!#9$"0XwmX[[+$!#97$$!0CXmFN'*=$!#9$"0@zC!z)>[#!#97$$!0YzzWvfx$!#9$"0y(\q(yo(>!#97$$!/B!oa8WN%!#8$"/>'4"owR:!#87$$!0O%GxZzX\!#9$"0iBte9#\6!#97$$!0rm7"o_<b!#9$"0K6<[*f?#)!#:7$$!0hYV4(G<g!#9$"0%[k&>$=`d!#:7$$!0O78%p:Xl!#9$"0Pb')44fa$!#:7$$!06Q-6CV'p!#9$"08GOBQ&)4#!#:7$$!0=b,2AUM(!#9$"0PcjGGQ/"!#:7$$!0N8"RlWLw!#9$"0;&z8+*4K%!#;7$$!0lW9<m,'y!#9$"0jP&*3c2,"!#;7$$!0H\p"fwqz!#9$"0^(4&***HG'*!#=7$$!0$*oE2)>()z!#9$"0-g;c?()y#!#=7$$!04#[kn%p*z!#9$"0&zGrD8ZK!#>7$$!0J%*>#H****z!#9$!0.`c&*oRi$!#B7$$!0N-aeIj*z!#9$!0&R%R*)>#yU!#>7$$!/P'[fGC(z!#8$!0`_>(RA=))!#=7$$!/NVo[UEz!#8$!0-&3t%3'\Q!#<7$$!/j(G#[P]x!#8$!0Xgv8J#>C!#;7$$!/&Q/[u)=v!#8$!/Ym!)y,Al!#:7$$!/Nh#e&\sr!#8$!0l(zhq:)["!#:7$$!0l`uT%\jn!#9$!0Rl9Vuov#!#:7$$!/=VsS#HH'!#8$!/D8uTr[X!#97$$!0_ENn=^x&!#9$!0b?ggrL!p!#:7$$!0&pmMh>W_!#9$!/rbdvKC(*!#97$$!/(4e"H(zk%!#8$!0:MRAw!R8!#97$$!0&H))ofPsS!#9$!0Q78Sldu"!#97$$!0f9iP$ztM!#9$!0#yp(*z')GA!#97$$!0i;zvT.&H!#9$!0Cj>hR#3F!#97$$!0am(zbQ/C!#9$!0>sJ.E[F$!#97$$!04mr%flB>!#9$!0.<KC0D%Q!#97$$!0())*p@DL\"!#9$!037xZ*e?W!#97$$!0ActZAD5"!#9$!0GP'zUYA]!#97$$!0eP6e/%))z!#:$!0C))pH$fhb!#97$$!0*o3W"yfW&!#:$!0KR%e(4_3'!#97$$!0)=H(\rzG$!#:$!0,Zd>+Vh'!#97$$!0*fpuBv!)=!#:$!.6#QCqNq!#77$$!0x?)\E*)e"*!#;$!0OZVdZ#)R(!#97$$!0j4iJCAU$!#;$!0HI*G%peo(!#97$$!06B(GEEU*)!#<$!0()[2#>5ry!#97$$!0l`B@&*H]&!#=$!0aNm_i)zz!#97$$!0kB_!3ivt!#?$!0$=b1L'))*z!#97$$"0%R'\:.,(z!#>$!.0@iWW*z!#77$$"0Vt@*pID8!#<$!0aHB*3$Q'z!#97$$"0ayE?25]&!#<$!0-!H3dp1z!#97$$"0s"['e+L`#!#;$!0)Ho"*4jUx!#97$$"0$yyR^V<y!#;$!0B&z'yJyX(!#97$$"0.Cy]9Uj"!#:$!0vU^WR-7(!#97$$"0MoX:N)3H!#:$!0ajSO#y>n!#97$$"0^b3p"pE[!#:$!0f!>b,(pA'!#97$$"0"=^b,ast!#:$!0'QJ*f!="o&!#97$$"0XTtHr\-"!#9$!0H=.ZQJ:&!#97$$"0P+n$)Q()Q"!#9$!/fZ**pVtX!#87$$"0J_c5D*)z"!#9$!0\p(4&GC+%!#97$$"0Pc$znQ*H#!#9$!0D%ztgx#R$!#97$$"0lleNGDx#!#9$!0Pw`f'p%)G!#97$$"0.>lRE<N$!#9$!0')f!>=hNB!#97$$"046X"zk>R!#9$!/3Dp%HH'=!#87$$"0VwO7t>\%!#9$!0a**z:=SW"!#97$$"0agVO;:1&!#9$!0'Qs%**y!z5!#97$$"0"o;]W/Dc!#9$!0@aI*>/fw!#:7$$"0zx?52t='!#9$!0j#zv0(p*\!#:7$$"0WwF^]sl'!#9$!0mT+M'[JJ!#:7$$"0:Taf*Qmq!#9$!0;(3uE")*y"!#:7$$"0^V`[**>V(!#9$!0nEYJv)*Q)!#;7$$"0d;%z)[Er(!#9$!0em.>*\"*H!#;7$$"0^B(>S>')y!#9$!0o)*Ql@^T(!#<7$$"/jU[G>_z!#8$!0ewYI(o9?!#<7$$"0#>bT95!*z!#9$!0@hvDye*=!#=7$$"0%y]`)*****z!#9$"0T#p&*HAz5!#D7$$"00v&['[**)z!#9$"/)G1K`*R>!#<7$$"/"yCZlH&z!#8$"0c6:l(*f'>!#<7$$"/'Q5Gq!*)y!#8$"0h&yn'\^8(!#<7$$"/6137S%p(!#8$"0T%pXL&GG$!#;7$$"0a&y'GNRW(!#9$"0YB76AO7)!#;7$$"0:yQQdK3(!#9$".&epX_S<!#87$$"0L#=!\Wek'!#9$"0l$z4>wsJ!#:7$$"/H7]p%)[h!#8$"0"yWBwIk^!#:7$$"0l_+15_k&!#9$"0&f=oYfbv!#:7$$"0s0t,LK4&!#9$"00]a(p?g5!#97$$"0Z8bd`S]%!#9$"0'Q[]UvN9!#97$$"0l\#zP*H"R!#9$"0xQ-BE"o=!#97$$"0-@Gj<iJ$!#9$"0ku%o$>sO#!#97$$"0id8"GU6G!#9$"0)p$Hela%G!#97$$"0x-cm'*zF#!#9$"/$yHy%><M!#87$$"0-ql'o#)*y"!#9$"0swX*>K9S!#97$$"0J(>?"HAP"!#9$"0Tmq#42)f%!#97$$"0**=5R!RU5!#9$"0a`]45M7&!#97$$"0(=e"yvF9(!#:$"0<zHIjos&!#97$$"0l8J9z."\!#:$"/P$o**3u?'!#87$$"/m!>">G@H!#9$"0"R;=.C;n!#97$$"0)4IRUrj;!#:$"01a\b#*)4r!#97$$"0tWVKF(zv!#;$"0(z#*H=vou!#97$$"0;kI7r6s#!#;$"/Bd848Ix!#87$$"0s#ow)G<2&!#<$"0;i/51;"z!#97$$"0ym*)HIpT"!#<$"0/zH$Q=iz!#97$$"0cN"fipl9!#=$"0oMjuh;*z!#97$$!0&\C@8<j:!#?$"00+7$ff**z!#97$$!0E&ox"3mP%!#=$"06$HfGr#)z!#97$$!0-U/y3u:*!#<$"0#4(GJ[!py!#97$$!0*))o9[6<M!#;$"0M!G)3!='o(!#97$$!0F5**)4,y*)!#;$"08)H@S41u!#97$$!0)oy@&RR)=!#:$"0"G7RojMq!#97$$!0yBtxA#QL!#:$"/W$=ps1g'!#87$$!/u#QDHnE&!#9$"0#f(Rs]b7'!#97$$!/<IblMa!)!#9$"0a(onQ-\b!#97$$!0'[<iya:6!#9$"0*Qp>'H4+&!#97$$!0JO<D')z]"!#9$"0@"=7%*e*R%!#97$$!0*f)G^c^">!#9$"06=:FAK&Q!#97$$!0m"H41\5C!#9$"0'G<<R1oK!#97$$!/%yR8Fo"H!#8$"0`xblQ4u#!#97$$!0#)zm8$yxM!#9$"0>,\OGaA#!#97$$!/:%3Z0h/%!#8$"0O]BdKcw"!#97$$!0f!*4R1%[Y!#9$"08&4X**yQ8!#97$$!0[rj)oY@_!#9$"0Ju[I@V&)*!#:7$$!0l6EO5by&!#9$"0[894gA&o!#:7$$!0pfL//$3j!#9$"0*)oAxB[[%!#:7$$!0m&G_NbWn!#9$"06J`XYB#G!#:7$$!0PP1Y*Gzr!#9$"0caE`I&p9!#:7$$!/9$[<*o)\(!#8$"0M/i*\JTp!#;7$$!0DnP.`xv(!#9$"0N)3ARA7B!#;7$$!0[F#\wJ?z!#9$"0VHlip&RV!#<7$$!0yzkOAG(z!#9$"03y*\B))H')!#=7$$!/9lP<y(*z!#8$"0&H=NSz5?!#>7$$!0x3%G(zp*z!#9$!0G(e(\&o%>$!#>7$$!0'f7+LPvz!#9$!0L3hMSKW(!#=7$$!0NZ"GO,]y!#9$!0/2>_pJ7"!#;7$$!0#*)\Y&3kk(!#9$!0&RD.s6#4%!#;7$$!0R'eLP]Kt!#9$!0&Gu'[\B2"!#:7$$!03dvt8A*p!#9$!0J2;44C,#!#:7$$!0V0kM&fOl!#9$!0U$4,9OyN!#:7$$!0dx$[:dRg!#9$!0DI^sZ;l&!#:7$$!09#*Q-D.]&!#9$!0n)zq"3?J)!#:7$$!0m!))p$yY$\!#9$!0/X)*4eg:"!#97$$!0kWL3*zxV!#9$!0c)y(>uK_"!#97$$!0FifrXbx$!#9$!0Uln8Ds(>!#97$$!0FB\VoZ@$!#9$!06g!))o$*eC!#97$$!00Z*3o">l#!#9$!0-/8h)o3I!#97$$!0Vusk-n<#!#9$!0^y#f(*oMN!#97$$!0b:#f1*))p"!#9$!0/Ep#Q)\8%!#97$$!0pAL&="\H"!#9$!0"yp[oP:Z!#97$$!/6e_\%*)[*!#9$!0B)>$f'p&G&!#97$$!0Gon'=70l!#:$!06&p(4ap&e!#97$$!0OfKl%>BV!#:$!/B;X))fZj!#87$$!0d)Hrb3DE!#:$!0<09$o8-o!#97$$!0xTMm\JK"!#:$!0W.!z/!QB(!#97$$!0#>tG[#G*e!#;$!0Hy'GK.]v!#97$$!03`&[(z$\=!#;$!0W-"p(>6z(!#97$$!0^q5zHma#!#<$!0m*eg(>T%z!#97$$!0c\!*3qdm%!#=$!0Dl4&)f>)z!#97$$!/rS$z`aK'!#>$!0\+#RR(*)*z!#97$$"0bFs>uN!))!#>$!0sIC#Q1%*z!#97$$"0(pE'=k&R7!#<$!0[F!)32a'z!#97$$"0"p<Kl.[7!#;$!0:V%p18Ry!#97$$"0f&ong9H[!#;$!0MyM:#[0w!#97$$"0dm7LwB5"!#:$!0$4IW^G?t!#97$$"0l-AYu[F#!#:$!.MHZ(\3p!#77$$"0W98D2-$Q!#:$!0/.1qK6Z'!#97$$"/cd]%*o')e!#9$!/oV(pD#))f!#87$$"0=db-^tq)!#:$!07s]`VoU&!#97$$"0#4*4f?&=7!#9$!0bB%**peM[!#97$$"0`_0&3t*e"!#9$!0,#fOOK%G%!#97$$"0L&*o(G9P?!#9$!0%*[*fE#=q$!#97$$"/Ui"RC0_#!#8$!0k$=]q$z9$!#97$$"0NYT>-s3$!#9$!/%=i%fJxD!#87$$"0%3H(*)=Rg$!#9$!0L0zOf#=@!#97$$"0\(e2t![@%!#9$!0ZEaq#3S;!#97$$"0ioJa&o#z%!#9$!0y'p(yA^C"!#97$$"0j(GF6na`!#9$!0`aiqYL5*!#:7$$"0C)R20>$*e!#9$!01bsz&*=L'!#:7$$"0%)Qb>6RS'!#9$!0Z!y>'4c4%!#:7$$"0vZNYTy)o!#9$!0\M0+N9M#!#:7$$"0N/CzJtE(!#9$!0:&)3eeeB"!#:7$$"0cLa^x<d(!#9$!0btY43qY&!#;7$$"/O$4*HQ6y!#8$!0jENn$)ee"!#;7$$"04kvqk_&z!#9$!0pc@x$[B=!#<7$$"#!)!""$"0AC/!\W<m!#Q-%&COLORG6'%$RGBG$"#5!""$""!!""$""!!""-%+_ATTRIBUTEG6#/%'sourceG%,mathdefaultG-%+AXESLABELSG6$Q!6"Q!6"-%%ROOTG6'-%)BOUNDS_XG6#$"$S"!""-%)BOUNDS_YG6#$"$?"!""-%-BOUNDS_WIDTHG6#$"%q7!""-%.BOUNDS_HEIGHTG6#$"%I7!""-%)CHILDRENG6"

Investigation C: Given: 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 and 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. This is an epicycloid traced by a point P on a circle of radius b>0 that rolls along the outside of a circle of radius a > b. Include two pictures, make sure that they look different, but a > b for both. a:=8;b:=5;plot([(a+b)*cos(t)-b*cos((a+b)*t/b),(a+b)*sin(t)-b*sin((a+b)*t/b),t=0..2*b*Pi]);

IiIp

IiIm

-%%PLOTG6%-%'CURVESG6$7\^l7$$"#!)!""$""!!""7$$"0RfLi#4x#)!#9$"03E$QD^kb!#;7$$"0%[(z*RP7*)!#9$"/&)zt3,WN!#97$$"0/R!4?z%))*!#9$"0;vSAeA>"!#97$$"0@C?&)3d3"!#8$"0dVNM#y1F!#97$$"0i2`$HW[6!#8$"0"H;a0?&)[!#97$$"0;4x9Y([6!#8$"0sY.2!4zt!#97$$"0CuH3H%p5!#8$"0<^iN**3-"!#87$$"0<U&*y3m#**!#9$"0vQIUWr;"!#87$$"0G$eXZ**4*)!#9$"0Q&=5P;28!#87$$"0%H)*Hzrcw!#9$"0F4/f)zN9!#87$$"0eyduU6='!#9$"0QQaoo*[:!#87$$"0:M'Rm**eW!#9$"0Y8=3_[k"!#87$$"0`P>**Qmc#!#9$"0QlMYCgr"!#87$$"08pLMvQ%z!#:$"0d(fS'=dv"!#87$$!03f^ki2/"!#9$"0u1c!pAs<!#87$$!0Ed"*4ef8$!#9$"08nDP?>w"!#87$$!08vH_R(4_!#9$"0:Una.2s"!#87$$!0"))zm%oe@(!#9$"0l0=(*Q*[;!#87$$!0B&ycOC$4*!#9$"0tPm,:&[:!#87$$!0"p%\qpN2"!#8$"0</k:/sU"!#87$$!0:<jliw@"!#8$"0b#4Z&*4&G"!#87$$!0%*e!RS[G8!#8$"0ei>o!HT6!#87$$!0UqFDh%=9!#8$"0%y7S4'y')*!#97$$!0c^K,Bo\"!#8$"0:T(e4lRz!#97$$!0*o$>TTMa"!#8$"0;B7fo(pf!#97$$!00,R6b%e:!#8$"0L#3q#=HJ%!#97$$!0l.y7]?b"!#8$"06o#=)oQq#!#97$$!0nc=A]SY"!#8$!0,\)yOAJo!#:7$$!0k$\41%4K"!#8$!0,U0WvA2$!#97$$!0NfRwHi7"!#8$!0KJ(f$f6*[!#97$$!0bd&=;8o$*!#9$!0P.in[8%e!#97$$!0p"*HM0xl(!#9$!0#>)p?'Rah!#97$$!0MQ8b/[^'!#9$!0:%[mUNUg!#97$$!0Ols!RKFe!#9$!0xr2k8tx&!#97$$!0pS:?hNo&!#9$!0koY5h+o&!#97$$!0f(3-#y8m&!#9$!0l+WNg;m&!#97$$!0p-A%y^=d!#9$!0Fm2HA]t&!#97$$!/_^#*\EAe!#8$!0`!>6X&*3f!#97$$!0h%>(**ft2'!#9$!0*e,0/.tm!#97$$!0xC06c:8'!#9$!0<*[ySp@!)!#97$$!0"*HrPl=p&!#9$!/7)QTSdx*!#87$$!/:'e]P')f%!#8$!0`8_Ktj;"!#87$$!0:64phA]#!#9$!0bA:FAMO"!#87$$"0_b?&Hu"R"!#:$!0RrHn,e\"!#87$$"/>*pdt#oN!#8$!0o@VF)4e:!#87$$"0QqY**e'[_!#9$!0:"=d)\Eb"!#87$$"0Q%pF#\)ep!#9$!03V^8KS_"!#87$$"/-')of:<))!#8$!0^EU]LaY"!#87$$"0o-dtL81"!#8$!0AvVQ#Qy8!#87$$"095v\"4?7!#8$!00Y^*QWr7!#87$$"0(>S#3zZO"!#8$!0l)*eaf>9"!#87$$"0(***=3")p\"!#8$!0`$R.2\^)*!#97$$"0GAd,Uhg"!#8$!0O7eD"y)4)!#97$$"03e!f)*y(o"!#8$!/^;1(*fYi!#87$$"/#=w)\nU<!#7$!0/;">)[5I%!#97$$"0N??Th-x"!#8$!0e==jsW@#!#97$$"0uH'G/1n<!#8$!0;?8TZ[I"!#:7$$"04*pp<iN<!#8$"0MCgo>U#=!#97$$"0)['GA!*zn"!#8$"07m)\oh"o$!#97$$"0-)H"*R\%f"!#8$"0pov=ewV&!#97$$"0s#H))\\*["!#8$"0vA?%))>6q!#97$$"04$>!yY!o8!#8$"0[+wi.<O)!#97$$"0XF))z)oL7!#8$"0BEilU>[*!#97$$"0z(*)>+y-6!#8$"0Q$[*y%yH5!#87$$"0'=r-%\Yo*!#9$"0@se!*p14"!#87$$"0GQZW%Rlm!#9$"0vm<sya:"!#87$$"0H*[e^&pF%!#9$"0#>rS(=w8"!#87$$"0Q"pm<&*yA!#9$"0a&[7%*>k5!#87$$"0')=JZ1g"**!#:$"0o/9Xsxp*!#97$$"0E!p#)4b3C!#:$"0J"*p<&=:()!#97$$"0_VOC'*eL#!#;$"0OB3%o\c")!#97$$"0.Szf\Ny'!#<$".pI$z)*o!)!#77$$"0M%oS1,6z!#=$"0BtE6=l,)!#97$$!.N!>9QL))!#?$"/)))*Q$Q++)!#87$$!0ZB'4@?U5!#<$"/*y#[n%)>!)!#87$$!02`:[Q*R@!#;$"/R*[\&pZ")!#87$$!0CKa;uFF*!#;$"03&=Qd!oQ)!#97$$!0fx!eQ\hc!#:$"0(zQUy2=#*!#97$$!0Tv$=b!yY"!#9$"0Jw%yuE65!#87$$!0"=E9?2^J!#9$"0p@+8\V5"!#87$$!0@OLRm)3a!#9$"00#ywe=a6!#87$$!06WIq.;7)!#9$"0;*)4cOh8"!#87$$!0[8p"Gq+6!#8$"0>')>h#*3."!#87$$!0>NT^ffB"!#8$"//v\cfl%*!#87$$!0%f!*eXkj8!#8$"0d*\NK'QS)!#97$$!0l3qM@')["!#8$"0H*)\/<C-(!#97$$!0LEs!QZ&f"!#8$"0rBj3u.U&!#97$$!0(>f1Ffw;!#8$"0oeT*fI<P!#97$$!0$Q="4nVt"!#8$"0[Y1oYs(=!#97$$!0"R-r([tw"!#8$!0f)[2d_K;!#:7$$!0$*z#GB**p<!#8$!0\t;eP'fA!#97$$!0/^itGbu"!#8$!0G*=R]6gT!#97$$!0N*pKlp&p"!#8$!0LxxXo2-'!#97$$!/rcan?7;!#7$!0_lp#\^#)z!#97$$!0f<F1E5]"!#8$!09H0S$f&z*!#97$$!.#HjfYr8!#6$!0fXSl[]8"!#87$$!0GXY&o%GA"!#8$!0m^<^%Hp7!#87$$!0=y+Q4'f5!#8$!0HhA8x$z8!#87$$!0HFrFE"e))!#9$!0^boY)zj9!#87$$!0ez1+m-)p!#9$!0,5V"Q_B:!#87$$!0/oIuK64&!#9$!.tbZ7Tb"!#67$$!03hh#\#fQ$!#9$!0&ep:6Ld:!#87$$!0aFa_CIv"!#9$!0"p\1d:Q:!#87$$"0P%y9TgG7!#9$!/V'[ma'Q9!#77$$"/N7!\S*\P!#8$!0^VlEK6E"!#87$$"0V%4A!H-B&!#9$!/zT["GB2"!#77$$"0rP:oa6*f!#9$!0w:j0lf%))!#97$$"0h>VL^+:'!#9$!0L4tGM0F(!#97$$"0K$Qg_@uf!#9$!0xB)eY5wi!#97$$"09$)[V2Rs&!#9$!0YS))z:Gu&!#97$$"0m(f8P1%o&!#9$!/kd:Rb)o&!#87$$"0*z*[))y5m&!#9$!/,/(3L8m&!#87$$"0W%3n$y%ec!#9$!0)))QK>Uec!#97$$"0P>sKd%zc!#9$!0pyaO7nn&!#97$$"0U*pM74;e!#9$!0,6w#4nqd!#97$$"0'QD&f'H%4'!#9$!0:%p#y.v!f!#97$$"0G46u[0'p!#9$!0ESO_=K7'!#97$$"0rBqZ>D_)!#9$!00ws0n/1'!#97$$"06y*)3$GI5!#8$!0nXKhA`X&!#97$$"0y&y%fRu@"!#8$!08L"HKOrT!#97$$"0u>+!oG)R"!#8$!0pWqZjE'>!#97$$"0c/,UKD_"!#8$"0&[O'[n9/"!#97$$"02;QYW5b"!#8$"/sP5z-7E!#87$$"0KO&ehbe:!#8$"/ue')zQpU!#87$$"0ke]x!eT:!#8$"0Xh7sB`3'!#97$$"0b#H`%Rw\"!#8$"09bQorR"z!#97$$"0)>CA(p$G9!#8$"0T#=pA(\m*!#97$$"0)Gl6p^L8!#8$"0w]t>]P8"!#87$$"0uSc.bL?"!#8$"0QK^3J6I"!#87$$"/yP*[Yu/"!#7$"0`?=E3!\9!#87$$"0.))o,*GY*)!#9$"09v]04xb"!#87$$"07REx?FG(!#9$"0=:FEafk"!#87$$"0OGd*oF[_!#9$"00YTfK'><!#87$$"0'H<u^:MJ!#9$"0#y(>dU>w"!#87$$"/WE*3aa7"!#8$"/jnN$4Cx"!#77$$!0_d>?w%\&)!#:$"/[w\wva<!#77$$!0/%Q^L$Gu#!#9$"0PcW9=2r"!#87$$!0'p!)>Mx:X!#9$"0pH-C.Ak"!#87$$!0ojiI,z8'!#9$"0_lXD0=b"!#87$$!0"=GC]dwv!#9$"0eZl)R'GW"!#87$$!0FIK-w*H))!#9$"0V&yg1d;8!#87$$!0`s*f#e-&)*!#9$"0j<xq)Gz6!#87$$!0'Q9[Ok@6!#8$"0ER9`jes)!#97$$!07/@Q_p:"!#8$"0Pwe*GM=g!#97$$!0[9#*y'QB6!#8$"/wY"3%H<P!#87$$!0"y60+9R5!#8$"0lj!=V1g=!#97$$!07t$f%3"z$*!#9$"0f,nm$*o&p!#:7$$!0/R"RmV)e)!#9$"02Jr['[u<!#:7$$!0o`&R'**RD)!#9$"0d(\MB;t[!#;7$$!0JdMV/M0)!#9$"0)3-]r'Qh%!#<7$$!/$f.5$H8!)!#8$"0XW<CL'4d!#=7$$!0WqMz+++)!#9$!/'zC3)))HE!#B7$$!0*Q%*zjq8!)!#9$!0-"of^<yf!#=7$$!0lg$HaAa!)!#9$!0;dPt65s%!#<7$$!/)yyIt*\#)!#8$!0i_KC$)fv%!#;7$$!0"fCE>Du&)!#9$!0^dKM(G3<!#:7$$!0,XWk^[X*!#9$!/Qzy"37h(!#97$$!0z>pT#\N5!#8$!0f9.hqZ!=!#97$$!0e^l>^17"!#8$!0Nk]CAhi$!#97$$!0@pW62q:"!#8$!0"=%[&Q/%3'!#97$$!03e"pPX:6!#8$!0c!)*RWXW*)!#97$$!0(>Tg1p:**!#9$!0)yN09!*o6!#87$$!/oDosqL*)!#8$!0j,zwQVI"!#87$$!0D*ou[/Ex!#9$!0$QCL!*eH9!#87$$!0C)*p%[<ci!#9$!.rwW))Ra"!#67$$!0"HpcIW(e%!#9$!0L*f&\8)Q;!#87$$!0)R7!*)*4gF!#9$!0*)Q^H%=5<!#87$$!0x<sKUy4)!#:$!0H,W*oZb<!#87$$"0["*pFXhF"!#9$!0e&>J!4Ex"!#87$$"0'4GY7V*Q$!#9$!0;4y9o&e<!#87$$"0&=z*yP!H_!#9$!0*GV(oo,s"!#87$$"06(z0*Q&3q!#9$!03TW2Rzl"!#87$$"0\o#R+]%*))!#9$!0TG(44*3c"!#87$$"0=8zJ551"!#8$!0D%f'e=yV"!#87$$"0')*3]p">@"!#8$!0WwY]'f"H"!#87$$"0FAS:yzL"!#8$!0X&)3=wp7"!#87$$"0k0"QUeL9!#8$!04$p6rma&*!#97$$"0\uJ%))R-:!#8$!0X]\;c0w(!#97$$"0rKbC$GT:!#8$!02k"o'3K5'!#97$$"02(=$3<!e:!#8$!0t9TAWfX%!#97$$"0d:.`7/b"!#8$!0YX"=kQdD!#97$$"0d^nqMa^"!#8$!04PV*GRPx!#:7$$"0bA02HqY"!#8$"0$R[X!oe8'!#:7$$"0i)f:D=/9!#8$"0"fYz.kj=!#97$$"0G(omy%*=7!#8$"0<w(y@sdT!#97$$"0ADwp$\N5!#8$"0/KE'*=#Ha!#97$$"0FQ&yG&HY)!#9$"0aXx+_72'!#97$$"04aS<s&Gq!#9$"0x8NP858'!#97$$"0c:*QFjpg!#9$"0k(eG"zs*e!#97$$"0d9%plxBe!#9$"0`pN2H_x&!#97$$"0TB$4s?"p&!#9$"0#y)p\hho&!#97$$"0,*G-(f=m&!#9$"0#zgu+chc!#97$$"0V3cqu$ec!#9$"0sOoeG%ec!#97$$"09aA)4Pxc!#9$"0F*=A!f-o&!#97$$"0PX&fb3:d!#9$"/WDL08Id!#87$$"0Ph(Gvoxf!#9$"0ugbaOnG'!#97$$"0)[snH'*\h!#9$"-a[6$)os!#67$$"0#yzV[F,g!#9$"0/F&\!RN!))!#97$$"0hOx$HAF_!#9$"0Ra0C]G2"!#87$$"0,x$\\E$p$!#9$"0"y5')))em7!#87$$"0soC'fGT9!#9$"0=@0&ysF9!#87$$!0\'o!4R'G=!#9$"0rmXUZ&R:!#87$$!0>1))*em"\$!#9$"0*[*yz3yb"!#87$$!0KP`k#)oA&!#9$"0K?2vjGb"!#87$$!0#yo^dC9r!#9$"0aQF)zD?:!#87$$!0P))fABm)*)!#9$"0B"ox'p&e9!#87$$!0ztY0$ei5!#8$"03r&3'fwP"!#87$$!0uyBl)*p@"!#8$"0cCxYVQF"!#87$$!0Q_G\g0P"!#8$"0_sq$**)f8"!#87$$!0:Q?a-R]"!#8$"0*ezto\b(*!#97$$!0$y.S(*\2;!#8$"0V'fH_(H2)!#97$$!0.)*Hn.to"!#8$"0>+;v/,E'!#97$$!/kEyyJV<!#7$"0"QFhD#*pU!#97$$!0L#p*oj,x"!#8$"0EoNmb6B#!#97$$!0Qe:5!*zw"!#8$"08(y*o"=&R#!#:7$$!/b$ya(RQ<!#7$!0fP9K^Mq"!#97$$!0xY"oLrz;!#8$!0>+K`*>PO!#97$$!0&>`4_L&f"!#8$!0@zIjAGU&!#97$$!0#\Jws.$\"!#8$!0ruD**\a'p!#97$$!0_<3'e&QP"!#8$!0Z]uxKaI)!#97$$!0KFZ6C)Q7!#8$!0.6p(y&[W*!#97$$!0s%Rvo:&4"!#8$!0Bl'3O#Q."!#87$$!06q954K.)!#9$!0lrd>Pz8"!#87$$!0by(G$Gr^&!#9$!0#*GmLz\:"!#87$$!0%3NO+X:J!#9$!0/,+D")H5"!#87$$!0$444:wc:!#9$!0lpq'z,=5!#87$$!0"[/iUq<a!#:$!0k7")e$)e=*!#97$$!0u=A1jU/"!#:$!0*RB&GiyT)!#97$$!0><#*\mV4#!#;$!0hHzM4c9)!#97$$!0">?M'p&**[!#=$!0DdY!\+7!)!#97$$"0Z&*\yoKy(!#=$!0`mY)*Rj,)!#97$$"/$>xHCr!=!#:$!0E(p(Ry?8)!#97$$"0f&GY1)>n#!#:$!0e!z`(RQw)!#97$$"0"R@W`K6%*!#:$!0e<;<7uk*!#97$$"0A9G#HROB!#9$!0TjZ)3Jn5!#87$$"/%)3x1wAT!#8$!0o>-\BT8"!#87$$"0C*[h6!\r'!#9$!0$R5nK=b6!#87$$"0i&>]i=g&*!#9$!0nJ\rc_4"!#87$$"0HtL,KAC"!#8$!0W-'[%=+U*!#97$$"0#=Nq<Wu8!#8$!0WQ?_;(*H)!#97$$"0N]E;@Q\"!#8$!0J=y_o_&p!#97$$"0*[g&o^Df"!#8$!0-UMuV<Z&!#97$$"0M>ugwAn"!#8$!0Oox=1d#Q!#97$$"0eg,sFQt"!#8$!0()ejGh(**=!#97$$"0%4W[p3n<!#8$"0aDt#QiM8!#:7$$"0VHE"\vq<!#8$"0eDvZbW7#!#97$$"0P%[#H:ju"!#8$".3vzY*>T!#77$$"0CS[B</p"!#8$"0d#[`n(G<'!#97$$"0Mwx%[z/;!#8$"0#>%zGiU7)!#97$$"0.V"3O_.:!#8$"/dDeczg(*!#87$$"0nik0%3#Q"!#8$"0^&Q@-)Q7"!#87$$"0p)zg`"zA"!#8$"081'>=Jl7!#87$$"/by2e@d5!#7$"0fthY_2Q"!#87$$"0O&>cCpG))!#9$"0,!*=nu\Y"!#87$$"0n_UAVk-(!#9$"0p&oa\TA:!#87$$"0r-g\>q@&!#9$"0))pQRfHb"!#87$$"/<yD#=<W$!#8$"0%=JmWfd:!#87$$"0lso/P+n"!#9$"0to5!*pl`"!#87$$"0mW"zgFUD!#;$"0$pe7z%=\"!#87$$!0%[zN/-cD!#9$"0f8\&)y'f8!#87$$!0**Rl3p!yW!#9$"0,z!pHf"="!#87$$!0&*o%y>)Rr&!#9$"0-M9$G1?(*!#97$$!0)y:L%e>8'!#9$"0:&H'fBv,)!#97$$!0.QPR<B3'!#9$"0@7\"4_)p'!#97$$!0'[Jf&)fAe!#9$"0N@4C)f4f!#97$$!0..8'GV<d!#9$"/_$*>*pMt&!#87$$!06'>3Ongc!#9$"0M`,i"*3m&!#97$$!0*RahD0"o&!#9$"0uQCt?!yc!#97$$!0`$GU7w3e!#9$"0W1Looiw&!#97$$!0'\o'fsIW'!#9$"0Ti*fd$R-'!#97$$!0&[GGVV7x!#9$"0ZS)Gkd_h!#97$$!0_x"ykBk#*!#9$"0)*=JZu[(e!#97$$!0KThepJ8"!#8$"0&GJ.M8V[!#97$$!0@(p]!HiJ"!#8$"0P5z*R_IJ!#97$$!0>nVIlIY"!#8$"0_Y0zn#eq!#:7$$!0(GB3,!y^"!#8$!0)>%*z<P,')!#:7$$!/#[/")p0b"!#7$!0"=]1\yqD!#97$$!0#z6%=F#e:!#8$!0MHR#*eQR%!#97$$!0vzd+t#Q:!#8$!0K>!Qs>wi!#97$$!0DIl'R'\\"!#8$!0<>fWmu*z!#97$$!0&envUQF9!#8$!/HGOb`&o*!#87$$!0\22Ko&H8!#8$!0FwL5v'R6!#87$$!0uDc(3N17!#8$!0-sch9yH"!#87$$!0#)f^ZKQ1"!#8$!/"H_'\XN9!#77$$!0UBTJRB-*!#9$!0%)e[y")Hb"!#87$$!0J.e1Xh4(!#9$!0#GGPJ=a;!#87$$!0k'f`ZwQ]!#9$!0d'H(f;`s"!#87$$!0saF!)*)f>$!#9$!0t5$ez;h<!#87$$!0i.4K'4N8!#9$!01\4nVEx"!#87$$"0;+Lhj?v(!#:$!08)fat,c<!#87$$"0wi(*y0K!G!#9$!0o*f&oS)3<!#87$$"0L&))3WD)e%!#9$!.*4D[xQ;!#67$$"0/\[$["o@'!#9$!0#*oSA5ma"!#87$$"0[%)yQaUk(!#9$!0")[BE0pV"!#87$$"0\xj6AM'))!#9$!0Ov?7iEJ"!#87$$"0oG@W$Gi5!#8$!0fKOUsp."!#87$$"0T!3@xLZ6!#8$!0w=6M'4#[(!#97$$"/"fu**)pX6!#7$!/JL"e-Sq%!#87$$"0*)>&pvh$3"!#8$!0[sn:G<m#!#97$$"0)e#o.Dy#**!#9$!07V:&paT7!#97$$"0LRMu`\%*)!#9$!0/OIZ5*[P!#:7$$"0\(y8j(zB)!#9$!0px8*Q'GT%!#;7$$"#!)!""$"0AC/!\W<m!#Q-%&COLORG6'%$RGBG$"#5!""$""!!""$""!!""-%+_ATTRIBUTEG6#/%'sourceG%,mathdefaultG-%+AXESLABELSG6$Q!6"Q!6"-%%ROOTG6'-%)BOUNDS_XG6#$"#q!""-%)BOUNDS_YG6#$"#]!""-%-BOUNDS_WIDTHG6#$"%+8!""-%.BOUNDS_HEIGHTG6#$"%I8!""-%)CHILDRENG6"

Investigation D: Given: 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 and 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. This is an hypotrochoid. Note: a, b, and c are all greater than 0. Include two pictures, make sure that they look different. Note: if c=b, this is a the hypocycloid of part B. a:=10;b:=2;c:=4;plot([(a-b)*cos(t)+c*cos((a-b)*t/b),(a-b)*sin(t)-c*sin((a-b)*t/b),t=0..2*b*Pi]);

NiM+JSJhRyIjNQ== NiM+JSJiRyIiIw== NiM+JSJjRyIiJQ== -%%PLOTG6%-%'CURVESG6$7_z7$$"$?"!""$""!!""7$$"2oSO,i&y&>"!#:$!1:=y+n`AF!#;7$$"2#*y%>uJ@$="!#:$!0<0&)R5gM&!#:7$$"2x5a)GM\i6!#:$!1C3!)\'pKx(!#;7$$"2,B>cItR8"!#:$!1(HPeE]4"**!#;7$$"2z!*oHGfb0"!#:$!2'[o2,yP(H"!#;7$$"1-XNAklJ&*!#:$!2L)GyzD!HR"!#;7$$"0T$Q,)*p(\)!#9$!1R$QB='ep7!#:7$$"1=WNKA'QQ(!#:$!1%*)*)f;nuN*!#;7$$"2:o'*o\QTC'!#;$!1cvIoy`mQ!#;7$$"10mm5sfK^!#:$"2amOmm!y'p$!#<7$$"1Cy#RDE'zR!#:$"2r'oAJt,U9!#;7$$"2v;9[N30*H!#;$"2nr@CXQWq#!#;7$$"2U!GE6yC:A!#;$"1jR`IY8'4%!#:7$$"2bDPeRfmo"!#;$"1uPU[2iXb!#:7$$"2/>v`q4sT"!#;$"2&****[BJ&\)p!#;7$$"29lK<Q^TS"!#;$"1.B6<,hD$)!#:7$$"2&pN$*49??;!#;$"1<#4)*[eQ\*!#:7$$"2&H]6">'**>?!#;$"2AV;!y$[E/"!#:7$$"1s&=^wW#pA!#:$"2WBqTk8(y5!#:7$$"2Zd%Hpd$3a#!#;$"1#)o%o'4H26!#97$$"2tbH![E%e#G!#;$"2.=:wJr!G6!#:7$$"1\kF[2.:J!#:$"2[pdaLs39"!#:7$$"1JO2b"G!*R$!#:$"22U@JRTc9"!#:7$$"1"3Vu1*\oO!#:$"29.vSMcC9"!#:7$$"16p%))e;V"R!#:$"2o2ao$R_J6!#:7$$"1Bg%o"=tFT!#:$"2:^Tb#f<86!#:7$$"2vOF"pI[*G%!#;$"2d9tyEJ**3"!#:7$$"1F$*y9hI5W!#:$"2G!3p+I9h5!#:7$$"1kSgahz%[%!#:$"2s))*=,.LF5!#:7$$"1e=?TTC3X!#:$"1())H@h!z!*)*!#:7$$"1`I0sC5(Q%!#:$"1E#fPeC)=!*!#:7$$"1$[a-h<d-%!#:$"1%\KtOq?0)!#:7$$"1Qyg.gg"R$!#:$"1pR]$*ey:q!#:7$$"1_"QR2yI]#!#:$"16#GUj*R5g!#:7$$"2mqb/elqQ"!#;$"0C\V9r$*4&!#97$$"1*Q?C(Q/z&)!#<$"1Gz7!3%)yL%!#:7$$!2([)\Nn=kR"!#;$"2-"Hx0/d`P!#;7$$!1m3.Yu<ZH!#:$"1p)Q%Qfm1M!#:7$$!1dGlmU-!\%!#:$"1D00:#G%4L!#:7$$!1uiBvq;[f!#:$"2Qxj-=)HaM!#;7$$!1Rs*G.6fC(!#:$"2t`d3mTI"Q!#;7$$!1AMxm&GnK)!#:$"1G@f>)f@M%!#:7$$!1>t8p:=V"*!#:$"1>WMdO<%)\!#:7$$!13#))*3"y\m*!#:$"1f!ycyN=n&!#:7$$!1W:@_#yT")*!#:$"1plmbVx>g!#:7$$!1Q))))>'*p#))*!#:$"1)y`mjc2N'!#:7$$!1u9eY0Ys)*!#:$"1'R">\v0bm!#:7$$!1.I\Q]s'y*!#:$"1^!zx]UL#p!#:7$$!1;kK7$Q+j*!#:$"1`o.$yXo9(!#:7$$!0\?veQ"3%*!#9$"1xWtu$QvJ(!#:7$$!1,#f4yYy7*!#:$"1'))4(fAGGu!#:7$$!0s!>lh$pz)!#9$"1"R&oK"oHZ(!#:7$$!1A"oh>;u6)!#:$"1@4'**4$fwt!#:7$$!0FO!=B,ft!#9$"1;"=BZ")H/(!#:7$$!1lV`a`4wl!#:$"1u>\5Whnk!#:7$$!17<(*)[,I#e!#:$"1Tq%>;B$fc!#:7$$!1@![A/2W2&!#:$"1)oLMet#)\%!#:7$$!1;$Gdtk:\%!#:$"02*fUnl=J!#97$$!1a:3.&QK7%!#:$"1MPN&)Gk%e"!#:7$$!1-25K*R++%!#:$!2K?0!p&3h'G!#=7$$!1(ojf<PK8%!#:$!1=Fk[$Hqk"!#:7$$!1*4&ez"HF^%!#:$!2C^:"e[L#=$!#;7$$!1@nAB>r1^!#:$!1wU')[K!*eX!#:7$$!1x3BJG1le!#:$!1lO5$\&R7d!#:7$$!1frPvA*4p'!#:$!0'zLE/\nl!#97$$!1-+t%[**Ga(!#:$!2N,d;g%*Q9(!#;7$$!1$f]6-!fcz!#:$!0r`8L>VK(!#97$$!0mo2[7.N)!#9$!0e&Gt^]Lu!#97$$!1*\&GpeX:()!#:$!0w^`xrLZ(!#97$$!1#oS*flxV!*!#:$!1@m"3VmpW(!#:7$$!1.*pcG:NI*!#:$!1G09U8,pt!#:7$$!1<m5=6<@&*!#:$!1&*R@x$*eVs!#:7$$!1e\$H^F>p*!#:$!1A-.)e@^2(!#:7$$!1DH/dUb6)*!#:$!1efa\feoo!#:7$$!1Y'f1**ok()*!#:$!1/&\[bW%Hm!#:7$$!1;b(4i*y$))*!#:$!0*35-Scjj!#97$$!0JxL)oPJ)*!#9$!1"ytG5Ir2'!#:7$$!0j?fWmyr*!#9$!1<^">7elx&!#:7$$!1$*=c<Wy+#*!#:$!1-P(yxDM/&!#:7$$!1P)y)QuHZ$)!#:$!1hhSj81bV!#:7$$!1&z7"fq"G>(!#:$!1a8:vRC$z$!#:7$$!1F[[31"\z&!#:$!2mhW"*G)HFM!#;7$$!1&3*e4cyvW!#:$!2v7/?h(=4L!#;7$$!29EDKLt&)3$!#;$!2F'*pUKEvQ$!#;7$$!23t?V[e#*o"!#;$!2Q)pz!R>%oO!#;7$$!19)G16j#RL!#;$!1%[)\TI%\9%!#:7$$"1bNB<m@<6!#:$!2WS!z4Pw=\!#;7$$"1:lxAoJkB!#:$!1(f"=#=J+)e!#:7$$"1<Y&G&Hw]L!#:$!1:$[i`"=hp!#:7$$"1$[c?L!\SS!#:$!1E_Lowd#3)!#:7$$"1"eei,EDR%!#:$!12b$RGS,/*!#:7$$"1VJ3#zB$3X!#:$!1/>?@Q..**!#:7$$"1k*ojAaO[%!#:$!2E1h]&*\"G5!#:7$$"1GLlPd#)3W!#:$!2/=V!zDhh5!#:7$$"1vSimDX)G%!#:$!2W0h8**>,4"!#:7$$"1;*)p`A#y7%!#:$!2KLj/tlJ6"!#:7$$"1Q2PRiE7R!#:$!2`5s32a;8"!#:7$$"2mWkB$zxjO!#;$!2<X,8P%eU6!#:7$$"1:X'f_f8R$!#:$!20"HI=shX6!#:7$$"1YSYcBS/J!#:$!2<R.V-V09"!#:7$$"296C4m4D"G!#;$!2p#GDZgGF6!#:7$$"2XuIB^:`_#!#;$!2lh1J(f!f5"!#:7$$"2%R7#yD.BD#!#;$!2Yj/>.(fw5!#:7$$"2dK%o%zEE+#!#;$!1$e7Mm%oR5!#97$$"2N\^%3&pAi"!#;$!0MHtKe2]*!#97$$"2oYzN0;)49!#;$!1.`4d2k)Q)!#:7$$"29]#>v;T09!#;$!1p<l\Ma:r!#:7$$"2tb]?qmTj"!#;$!1T_)))RObu&!#:7$$"1A.`V^=I@!#:$!1h#R#z!HtG%!#:7$$"1;[X,!Q"yG!#:$!2w;W>"))HxG!#;7$$"21Xcq&eAZQ!#;$!27Mu0y))*)e"!#;7$$"1_TXS%p())\!#:$!2()=WIv#yc[!#<7$$"2N$fZ%R^]8'!#;$"1L2RG!)=EK!#;7$$"1;&o$4'QrJ(!#:$".dPRAW4*!#87$$"1A*><*R![Z)!#:$"2D.O!="[ZE"!#;7$$"1:9F[()pZ&*!#:$"2Zu4#y2D$R"!#;7$$"2Q)\()=&oW0"!#:$"2(\ONu>')*H"!#;7$$"2e3W(=1\J6!#:$"2$HE0Aq&f+"!#;7$$"1aC<h?#*f6!#9$"1JANb(=s+)!#;7$$"1Owb,r*4="!#9$"12^bW*\9n&!#;7$$"2Qr,f;"Q%>"!#:$"21su)H=(z8$!#<7$$"1x%y]]h)*>"!#9$"20")GR9:6'\!#=7$$"29Dj!yJ4(>"!#:$!2FUq*)\g[E#!#<7$$"2.bZwe^d="!#:$!2wm+89(fT\!#<7$$"2Y:>yFJg;"!#:$!1&oE(3)3JV(!#;7$$"2))f1n7q#Q6!#:$!1*zT*yK1U'*!#;7$$"2m@AwK_11"!#:$!2['>hJ(p_G"!#;7$$"1`DT:4g"e*!#:$!2uXeQw:QR"!#;7$$"1.3`'3a-a)!#:$!2'Ge@-nMy7!#;7$$"1x*Ht$)z\T(!#:$!1^0Okzqx%*!#;7$$"1d>'f[m;E'!#:$!1wKBIM[nR!#;7$$"1/rA%Qnj8&!#:$"1w9Z)3zpm$!#;7$$"1GI"R&o[8S!#:$"2$oyPxzL09!#;7$$"2Zg?C\<P/$!#;$"2'p$Gh%)f^i#!#;7$$"2uqH(RyitA!#;$"1%>8+El3(R!#:7$$"2*)GJ]x(fM<!#;$"1mZx7'ytP&!#:7$$"1(*f"H&>EN9!#:$"1'H7*RxN>o!#:7$$"2c&Gf+@*GR"!#;$"1*\bH(pCs")!#:7$$"2W4&4W[r#e"!#;$"1<\&f,x>O*!#:7$$"2xj=WrR<'>!#;$"2x+_(\*HC."!#:7$$"2ZYdbU(**)>#!#;$"23gL+>Y'p5!#:7$$"1ht@W/**fC!#:$"2(e'zn^l(*4"!#:7$$"2._a@k:kt#!#;$"2MBV"4RYA6!#:7$$"0/s)*3S'>I!#9$"2@`GJ<Lv8"!#:7$$"2-Q\0fa3I$!#;$"2V8**QM%)[9"!#:7$$"2NK)=F.BrN!#;$"2vJR!R!\X9"!#:7$$"2nGB"3f2AQ!#;$"1)4c&R(ym8"!#97$$"1Vw3*3#*\/%!#:$"2%3"[7,U:7"!#:7$$"0(y"[n$fEU!#9$"2WLEalP.5"!#:7$$"2NRf8a2zO%!#;$"2aX"H!)f7t5!#:7$$"1d&H3aoGY%!#:$"1#G$R*[J//"!#97$$"2lbHCkPh]%!#;$"2yx$)pVbG+"!#:7$$"1z@tOMS?W!#:$"1`H>MZ(y:*!#:7$$"0Mjf&zg&3%!#9$"16Z%G-*oy")!#:7$$"1f"[$pp\6M!#:$"10"Rc%\wUq!#:7$$"1n"[hE&*3V#!#:$"0:3M'z'=%f!#97$$"2`C@os)zz6!#;$"1:!z0v$[f\!#:7$$!1@&)GBc<RG!#;$"1V:Q!yHn;%!#:7$$!2:"G)*p\l=<!#;$"2$3`K0(*QgO!#;7$$!18-q=')R,K!#:$"28*f]*HFPP$!#;7$$!1$*)Rb\gam%!#:$"1.j*Qr"=9L!#:7$$!1.U3G#)fWg!#:$"2lbHz[7GZ$!#;7$$!1<3j6F$RN(!#:$"0ow_Kp[&Q!#97$$!1Ac*z'3+K%)!#:$"1YpOn-g4W!#:7$$!10nnn^.I#*!#:$"1$y")obpX2&!#:7$$!19(4N44#=(*!#:$"18#\"HPGxd!#:7$$!1L0'*yc@M)*!#:$"1j`0LEN(3'!#:7$$!1A4K8![^))*!#:$"1u()4ET6#Q'!#:7$$!1-Y)>1^D()*!#:$"140-H6_am!#:7$$!0-;()yZ))z*!#9$"1,zi7Tz(*o!#:7$$!1j06u/In'*!#:$"1-'**)[f_0r!#:7$$!1:ZoV%f>[*!#:$"1Tsh/7yrs!#:7$$!1m5U")**fZ#*!#:$"2bOGjP)="R(!#;7$$!1k![GQ['p*)!#:$"1XB$>nB!fu!#:7$$!18x$*R\&)R#)!#:$"13P`pWO4u!#:7$$!2ll8Cb(f+u!#;$"1R&=p67p1(!#:7$$!1'f*\Gi8Fl!#:$"10wobJLBk!#:7$$!1:BO[D%\p&!#:$"0)*3VU*)4\&!#97$$!1)=*o/Oc7]!#:$"1/AHQmtyV!#:7$$!1xz@RI=zW!#:$"1*4f*\Mo!3$!#:7$$!1$)Gxi#pO8%!#:$"2Me'p%)*p'\;!#;7$$!1it^to/,S!#:$"2))*\!o,XuY"!#<7$$!1#*[JmQ=+T!#:$!2Z*\#e=P+V"!#;7$$!1W*\p%GWMW!#:$!2mQ`JNw'QH!#;7$$!1m@)f`)Rx\!#:$!11n.yxh3V!#:7$$!0hFOgmeo&!#9$!1Jfr="e'ya!#:7$$!1y"QR_vR['!#:$!1MK3qRU$Q'!#:7$$!0*[![%RnBt!#9$!1J[K%zM@-(!#:7$$!1U#*Q*=")z8)!#:$!1x<_d)GDQ(!#:7$$!0B)Rs%y'f))!#9$!1B)\>!)\+Z(!#:7$$!1/dGA_7z"*!#:$!2&[E8tA,9u!#;7$$!1"[Ff)=hZ%*!#:$!164))\><%H(!#:7$$!1%egU$*Qxl*!#:$!1(4q)R*Gm6(!#:7$$!1j[jfF/.)*!#:$!1nBZV:X))o!#:7$$!1#yh,#o6y)*!#:$!1br]$oUvh'!#:7$$!1#Q**)3Ory)*!#:$!1mI\$="\7j!#:7$$!1\-X!eD=!)*!#:$!0;mwh5C)f!#97$$!1k*3?bVdk*!#:$!1_@2$oonj&!#:7$$!1f'H&G(f;7*!#:$!1(p@Yk(pi\!#:7$$!11%o2bYZJ)!#:$!18.6]TqMV!#:7$$!1ujcrA(RD(!#:$!18#[n(34;Q!#:7$$!1WE6y\9%)f!#:$!0V`bUm5Y$!#97$$!17#*QbmdHX!#:$!2t,EBe5-J$!#;7$$!0n2-E%Q))H!#9$!2%)4ma%f(3S$!#;7$$!29Yr5%pBP9!#;$!2x!=]#QM6u$!#;7$$"1KLwPKbQZ!#<$!1V>hO$f#>V!#:7$$"21h=zfJSQ"!#;$!1X9h7iE(4&!#:7$$"28[s**="3ED!#;$!13h\$4vD.'!#:7$$"2'46wK.>GM!#;$!19B#4<3c1(!#:7$$"0E*3Q?'>1%!#9$!1u,H!fWx7)!#:7$$"1;>WFA;*R%!#:$!1p(yRkeo1*!#:7$$"1EJcU3N3X!#:$!1i@&*zF#G"**!#:7$$"1NM%>OeK[%!#:$!29-UaCH%G5!#:7$$"1GK[<rq4W!#:$!2\:At`L81"!#:7$$"1jh2NF3#H%!#:$!2Q]cR6_%*3"!#:7$$"1"e%3n2SNT!#:$!27U!3HCI76!#:7$$"2Nyd]i&*\"R!#;$!2Yf[Vn![J6!#:7$$"28x_^0X(fO!#;$!2-xO[`"pU6!#:7$$"2`'G;4BSzL!#;$!1QP`ovcX6!#97$$"2%HlND1:%3$!#;$!2o$4jpe))R6!#:7$$"21RiP^+Wy#!#;$!0G&=#esb7"!#87$$"2'zq!)>Fe!\#!#;$!2`B()4b/F5"!#:7$$"1[nTx3%H@#!#:$!2&efVx!3:2"!#:7$$"2TZ,'oyKh>!#;$!2Jg!>/[NK5!#:7$$"2bq#pjv([g"!#;$!0>rA8m:W*!#97$$"2Cq-O6qsS"!#;$!1iSu$[]6O)!#:7$$"2_So7)o1/9!#;$!11$)y3'[@8(!#:7$$"1Yp>r:v<;!#:$!0b.xe\@"e!#97$$"2/Xi/POJ4#!#;$!1-08'yvTP%!#:7$$"2W2;g+"f9G!#;$!2W*Hn1n`yH!#;7$$"1G&yFBQQv$!#:$!2(fq=EQ>'p"!#;7$$"1M7(3M;b'[!#:$!196wv;a()e!#;7$$"1oETJ7MOg!#:$"1r%y.(oeGE!#;7$$"2XF,(G3<]s!#;$"1X&>J!fCB))!#;7$$"10,0FG'=W)!#:$"2u&*p'y\jd7!#;7$$"0*)oR,3fa*!#9$"2=L#zwW@$R"!#;7$$"2$y`+D&Hk0"!#:$"2<)p&=co`H"!#;7$$"2l1!RnGQM6!#:$"1&>[#z-(f))*!#;7$$"2Qol"4%GF;"!#:$"1[u.5aN^x!#;7$$"2Ga;y3>L="!#:$"1(y#3cq&)H`!#;7$$"1&eTCK7e>"!#9$"2`1>3n!*Rr#!#<7$$"$?"!""$!2aIns?iE^%!#C-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%+AXESLABELSG6$Q!6"Q!6"-%%ROOTG6'-%)BOUNDS_XG6#$"#q!""-%)BOUNDS_YG6#$"#]!""-%-BOUNDS_WIDTHG6#$"%+8!""-%.BOUNDS_HEIGHTG6#$"%!R"!""-%)CHILDRENG6"

Investigation E: Given: 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 and 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. This is an epitrochoid. Include two pictures, make sure that they look different. Again make sure a>0, b>0 and c>0. Note: if c=b, this is a the epicycloid of part C. a:=10;b:=2; c:=2; plot([(a+b)*cos(t)-c*cos((a+b)*t/b),(a+b)*sin(t)-c*sin((a+b)*t/b),t=0..2*b*Pi]);

NiM+JSJhRyIjNQ== NiM+JSJiRyIiIw== NiM+JSJjRyIiIw== -%%PLOTG6%-%'CURVESG6$7ev7$$"$+"!""$""!!""7$$"2^*[)GdKQ,"!#:$"1/#*4@SKGA!#<7$$"2elW]"Hd_5!#:$"1lK&[(HzO<!#;7$$"2P,QZ**4%36!#:$"1)=?4yv=h&!#;7$$"1#o/&ecyp6!#9$"1wKlhVE^7!#:7$$"1FEun$*G<7!#9$"2FE'4QXN5@!#;7$$"1j5PmGA]7!#9$"1jOizkN&=$!#:7$$"1'[S?!**Hh7!#9$"2Ng_0>jCU%!#;7$$"2:!z@2W^X7!#:$"14D*)[aOXd!#:7$$"1-MnNg?$>"!#9$"1P!QbWZTA(!#:7$$"1CCD_yD16!#9$"0e*Q[q#*o&)!#97$$"1U@sO#)p8**!#:$"1vec;$zrm*!#:7$$"1&G:8%3J!f)!#:$"18u3Hm1W5!#97$$"1>s:-U')4s!#:$"2[DTph1f3"!#:7$$"17rKMwK6f!#:$"21XL//vN4"!#:7$$"1[U&R-Xk![!#:$"2NS$GJZ"R2"!#:7$$"1\#z-<\/(R!#:$"2G3HMc/v."!#:7$$"1(G#p<*oE;$!#:$"1f**\*Gs)['*!#:7$$"2#ygq6_a4J!#;$"1R(zQ\rOi*!#:7$$"2$)\&H_/Z,J!#;$"1()eKAG*p'**!#:7$$"1y0#)4"f%pH!#:$"2#))p)om9:0"!#:7$$"2LSlKFJHj#!#;$"2Vv)e%>S37"!#:7$$"2<&*[!GPqQ?!#;$"20%ef7`3'>"!#:7$$"1yk,Wl%H8"!#:$"2/q!oq-ap7!#:7$$!2:&QEjsjRX!#=$"2$*QJ16BuK"!#:7$$!2i()f8*)3GV"!#;$"2E\*=>A:g8!#:7$$!29?)H'*)3S$H!#;$"2-!eWu2:h8!#:7$$!1zFhDo^&[%!#:$"2#o,*G.(3E8!#:7$$!1T]Nze:5f!#:$"2'G_&G@!Rc7!#:7$$!1Pc%)G-8)4(!#:$"1z#\tT,)e6!#97$$!1"*Gu)\(*Q(z!#:$"20y;]T1P/"!#:7$$!14vfg(=k])!#:$"1^oR15**Q#*!#:7$$!17b"=&\!)=()!#:$"1%>g&3(QU6)!#:7$$!1ariZNbw')!#:$"1\wJ%e9&or!#:7$$!1%HzHsz,[)!#:$"1=PorD0tk!#:7$$!1"Hs3LHJC)!#:$"20dcH!ftXg!#;7$$!1TLXVCg)4)!#:$"2mq&)fMoX)e!#;7$$!0$[@8$eP:)!#9$"1MueAHo8f!#:7$$!1tlf5fXv%)!#:$"2D#QGKyA?g!#;7$$!1Mzd!3AH**)!#:$"10x4r\Kug!#:7$$!1Exy4v![q*!#:$"2b0)Q&G5)**f!#;7$$!20nKx7Ac0"!#:$"1O+nHeiBd!#:7$$!1jWezJ#p9"!#9$"2Dbo_Pem>&!#;7$$!2Pf?]j8dC"!#:$"29s@aW`:G%!#;7$$!2"RSW'*\nF8!#:$"1\0_Cf/]I!#:7$$!2(pt-[<g"Q"!#:$"2u7<zd=fd"!#;7$$!2t/%>5S***R"!#:$!1a/kfM5mG!#<7$$!2&)*\nen6!Q"!#:$!2.3yAMDsj"!#;7$$!2eG1>WDYK"!#:$!2tr)\9?I4J!#;7$$!2Zs;$*>'HT7!#:$!1mSk2IkKV!#:7$$!2wP:kt,;9"!#:$!11#>V6mYB&!#:7$$!2jO`^boC/"!#:$!1n9l*)*o#zd!#:7$$!1z2SQe5@&*!#:$!06\Sw#HLg!#97$$!1#Q"*)GR!4!))!#:$!2vRh*Gzvmg!#;7$$!12myY%\YK)!#:$!2DP,=jo.)f!#;7$$!1Px2M:D=")!#:$!1_(z@?1^*e!#:7$$!1oOtCQE1")!#:$!1rj&G%=8"*e!#:7$$!1%Rg380*Q#)!#:$!1B&))zca+/'!#:7$$!0/.2$3*RW)!#9$!1D6Vaz*4R'!#:7$$!016)o3!Rm)!#9$!2bF)\UU5(4(!#;7$$!1j-XBNF?()!#:$!07an6$f"4)!#97$$!1%>%zQE***[)!#:$!1d![@h!="H*!#:7$$!1eAa+pc%*y!#:$!2s0bX'*)yc5!#:7$$!1"oXQ;B$)3(!#:$!2e4Wab>)f6!#:7$$!2lIxDIf!Hg!#;$!2fq.M3d&[7!#:7$$!1$[duz.3x%!#:$!27.2*R%=`J"!#:7$$!1aT(Q+;5R$!#:$!2nAf5qRZN"!#:7$$!2o:['eRSa<!#;$!2.ZWvSKKO"!#:7$$!2)=K.QK!3B#!#<$!2['HOYm^L8!#:7$$"2x-S$o7)p2"!#;$!2)o<@+-4t7!#:7$$"1x5uYg0h?!#:$!2VLb#)=$y$>"!#:7$$"2vE5-()4Mk#!#;$!29A-$o]9>6!#:7$$"2:b06jFG(H!#;$!2JNn<B_00"!#:7$$"2v+=\qx=5$!#;$!12I*3M1O'**!#:7$$"1mVCG3b4J!#:$!1#4g7.HPi*!#:7$$"2Pl>3Wsb;$!#;$!/fv<!3Ml*!#87$$"2wOTebng*R!#;$!1kv5(4.!R5!#97$$"1^aJB72+[!#:$!248O*G(=P2"!#:7$$"1Vx?bkt]e!#:$!2V'p&f;mJ4"!#:7$$"1d&QT6(=$3(!#:$!2&ee([\(*z3"!#:7$$"1h)z%\FG,%)!#:$!2p4(*4<P>0"!#:7$$"0%HMod/X(*!#9$!1(\$)\0U+z*!#:7$$"21Dm;!=)G4"!#:$!1UjrG)ods)!#:7$$"2KiUa&[B%="!#:$!2%3vA.wG+u!#;7$$"2([3*Qk87C"!#:$!1K>]&R&>Cf!#:7$$"22*HHNa+h7!#:$!1<Tq?EXZX!#:7$$"2VH'es"Q:D"!#:$!1BL$f+aTD$!#:7$$"2U-%ybY;=7!#:$!2V#)**eZy48#!#;7$$"2B)H%GEI*o6!#:$!2P#=')yX7R7!#;7$$"27"4%>AM"46!#:$!1B7d&\_an&!#;7$$"1HlKZDXa5!#9$!2CgL&*3*eN=!#<7$$"2GvA:;Nc,"!#:$!1W9))oQt$o#!#<7$$"1nv#=S:,+"!#9$!2jz6U[)Hq;!#@7$$"1Z*eN.h<,"!#9$"08h$\?eU<!#;7$$"2&*o*H4HI\5!#:$"2ENRDFe,d"!#<7$$"2%3]0b*3]5"!#:$"1'f%)RJy"=`!#;7$$"22P`i46r;"!#:$"2tJn7(zf87!#;7$$"2%\&[)o9k:7!#:$"/8[Mn>s?!#87$$"2D:Y8x#e\7!#:$"13us\NV`J!#:7$$"2A7I(pOKh7!#:$"1p$e0c#[-W!#:7$$"2N5*>]&>cC"!#:$"1DA.k.qSd!#:7$$"2)*>SPW)Q&>"!#:$"0d2bn+$zr!#97$$"1e32+:H76!#9$"0QpRwR\\)!#97$$"2<T)3H**H-5!#:$"14[rdC9$e*!#:7$$"0>sOU?%[()!#9$"2A5Xb5Dp."!#:7$$"1*4^t`N.P(!#:$"2#R5D<b%G3"!#:7$$"1.pNeh0fg!#:$"1#4L`ytU4"!#97$$"1WMxj7qG\!#:$"2C&3M.-Zx5!#:7$$"1y+2\X3fS!#:$"1D5aW[cU5!#97$$"1p@+<"o6>$!#:$"0rc%z]q"p*!#97$$"1."4"y47/J!#:$"12F$G_;)y&*!#:7$$"1M!)=*Gp*4J!#:$"1)y$fm(f<))*!#:7$$"2ExsL.d^+$!#;$"1P^j8ksS5!#97$$"2)4$)H4<E*p#!#;$"2wm4uGq(46!#:7$$"2.n&pk(=*H@!#;$"2)eT"o)4\'="!#:7$$"2B*)QPQz-;"!#;$"2TEq(=@xn7!#:7$$!2%=/tfe=!Q"!#<$"0-:TEv1L"!#87$$!2'yz1,nH!o"!#;$"29<"yMRmi8!#:7$$!1eil)QzsL$!#:$"1E'y[2ecN"!#97$$!1(pV-vP!*z%!#:$"27f0V*H<98!#:7$$!1r!ef$paAh!#:$"2-a)=(**R@C"!#:7$$!10oFF03<s!#:$"2=EM,n%3Y6!#:7$$!1;)p\kg@-)!#:$"2")*z)*)fe`."!#:7$$!1b'*)y?q#Q&)!#:$"1C@q"[f>8*!#:7$$!1,w;tU8D()!#:$"14*oBd)y(*z!#:7$$!1P"[Z;Hol)!#:$"1R,0`J]gq!#:7$$!1-zE4ttV%)!#:$"1Ro1.-X!R'!#:7$$!1is/&4JGB)!#:$"1JJ@7])>.'!#:7$$!1Pll*)>#>5)!#:$"0\4+')pt)e!#97$$!1'4Q9VT$H")!#:$"1Hb_O(*=,f!#:7$$!1th@=ZTn$)!#:$"1`9$\nLJ*f!#:7$$!1-;R7yB!*))!#:$"1F#)G^L#>2'!#:7$$!1l+4'p&oi'*!#:$"1LnD-BK3g!#:7$$!2<j&)*o?Hh5!#:$"1'>N.$o9)p&!#:7$$!2s1%*eFzK;"!#:$"1t#oZaAN2&!#:7$$!2Fh7Is2UD"!#:$"2&=@$>YY*zT!#;7$$!1;9<k:YH8!#9$"1N0u-)=Y,$!#:7$$!2Q!y#>h_+Q"!#:$"1U]T"R=)R;!#:7$$!2N5j_(H%)*R"!#:$"2'*eBZVwtY"!#<7$$!1nvY;-.&Q"!#9$!2<tovsPOU"!#;7$$!2W:;MbKfL"!#:$!2_l:T[_:)G!#;7$$!2Y)4gM%f!f7!#:$!1)G3tc?)>T!#:7$$!2&>NXQsWk6!#:$!1OgE2TNk]!#:7$$!2sQ)p6BKm5!#:$!1a;J%G"yuc!#:7$$!1%y:M^i3u*!#:$!1&4EXcL@*f!#:7$$!1o'R=@9a(*)!#:$!1FR,zP<ug!#:7$$!1&>rSX<\V)!#:$!2bS,"*yl3,'!#;7$$!1JC[#4h,9)!#:$!1">=V"R'o!f!#:7$$!1u[0V&\K5)!#:$!1:d8l*3&))e!#:7$$!1JcZby)eD)!#:$!1WlijLCjg!#:7$$!1s$[Bm'3#\)!#:$!1-!>$[-(=]'!#:7$$!1ND.%)p'3o)!#:$!11<1a>)\>(!#:7$$!18$=#R&)*yr)!#:$!1eeQloSF")!#:7$$!1(H.npo)3&)!#:$!0(=&H1V5B*!#97$$!1fAMZ]0#*z!#:$!2&e]2gBgS5!#:7$$!1%p7_n__7(!#:$!2Yb!*f<if:"!#:7$$!1^RO%[1]%f!#:$!2$**Qgq:8a7!#:7$$!2v"))pf#=d_%!#;$!2Q&)>0$olC8!#:7$$!1/Qij))QwH!#:$!1dCu&)))og8!#97$$!2_()3EMakV"!#;$!2=s$fAh>g8!#:7$$!2bg@C3;"z:!#=$!2GT!*fB[jK"!#:7$$"/&>zKeK="!#8$!2<L)z=yEm7!#:7$$"29\,z]6P4#!#;$!2=K$\%ej.>"!#:7$$"2:/a8f&QcE!#;$!2'GFJ[#>q6"!#:7$$"0XMTZ$\vH!#9$!1)RD!*>$y\5!#97$$"2xL0hUO;5$!#;$!0"G>'H=c'**!#97$$"2<@Fa0<+6$!#;$!0*=JJLiG'*!#97$$"2X]$*)3.HrJ!#;$!12V]et@i'*!#:7$$"1,R*p_R(fS!#:$!2%oP&>'4gU5!#:7$$"0T3[^C[&[!#9$!2%42`NxOv5!#:7$$"13jxuK:xe!#:$!1V9%pD`L4"!#97$$"1V*4*)ptq1(!#:$!2_`d%*)GC)3"!#:7$$"1rG(\\U!Q$)!#:$!2i%\;h;Ta5!#:7$$"1JVg![Xxm*!#:$!1)ys4&[rV)*!#:7$$"2A'yNXP"\3"!#:$!1'fL9'y"["))!#:7$$"2BU>L7su<"!#:$!1t&\=,o__(!#:7$$"2W'pmDy1P7!#:$!1d$=f0n(yg!#:7$$"2Q?#y#>=0E"!#:$!1N*[i"=\hY!#:7$$"2CbEB?zFD"!#:$!1yetNfnBL!#:7$$"2EeWF**4%>7!#:$!1%R%Q&Hl2;#!#:7$$"2CLx)>f-p6!#:$!24kF,wx/C"!#;7$$"2)=)R68Jy5"!#:$!1XS!\uA8c&!#;7$$"2D/"e\@E_5!#:$!1HZX/,n?<!#;7$$"2rulLGYP,"!#:$!2k+'p0BF2A!#=7$$"2-+++++++"!#:$"2')op,'z(pk#!#R-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%+AXESLABELSG6$Q!6"Q!6"-%%ROOTG6'-%)BOUNDS_XG6#$"#q!""-%)BOUNDS_YG6#$"#]!""-%-BOUNDS_WIDTHG6#$"%I9!""-%.BOUNDS_HEIGHTG6#$"%!\"!""-%)CHILDRENG6"

Investigation F: Given: 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 and 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 . These are Lissajous curves. Include your favorite two. a:=3;b:=4; plot([cos(a*t),sin(b*t),t=0..2*Pi]);

IiIk

IiIl

-%%PLOTG6%-%'CURVESG6$7fx7$$"#5!""$""!!""7$$"0Y>5kK4&**!#:$"0.lTIQvJ"!#:7$$"0*[,)[\(G)*!#:$"0U1MrLgW#!#:7$$"0bZzJ`Tg*!#:$"07?YZNen$!#:7$$"0P2P))GpG*!#:$"0pu#3ew^[!#:7$$"0BfO\5M)))!#:$"0\m%)eX1%f!#:7$$"0h6)GeNM%)!#:$"01itg>;'o!#:7$$"0J$[5[P(*y!#:$"0W]_[;4r(!#:7$$"0mk!RF))ps!#:$"0;g22`QY)!#:7$$"06wZ=Prd'!#:$"0G/Rjg_2*!#:7$$"0GTgQX7!e!#:$"0#o(3m$p[&*!#:7$$"0DM&))ehq]!#:$"04%4x"p&G)*!#:7$$"0:ox?!Q-U!#:$"/L?%Gb])**!#97$$"/GG[='**G$!#9$"0`j1nn1(**!#:7$$"0Zp)>eT!Q#!#:$"/$3;T#R%z*!#97$$"0'*)*fs$oN:!#:$"/'p&=1a)\*!#97$$"0KIehP!p^!#;$"0;NwieT)*)!#:7$$!0Yet$>23N!#;$"0Wg+9WpT)!#:7$$!0xw2="Rc8!#:$"0)QF*))\gh(!#:7$$!0oEp&)*HNA!#:$"0uhkd.;z'!#:7$$!0p(y_d")yJ!#:$"0UJ&yMqwd!#:7$$!0eqDU3!\S!#:$"0')RkrX$=Z!#:7$$!0faP;U#>\!#:$"/J_W3YON!#97$$!0j!p%e#[xc!#:$"0&4XkT8)R#!#:7$$!0pi=*HEWk!#:$"0mdmrpD8"!#:7$$!0`K<]Ur<(!#:$!0&)f0aO`,#!#;7$$!0')><u"pcx!#:$!0)R)4*\yg8!#:7$$!0kNQY*>;$)!#:$!0>hS(fn"f#!#:7$$!0m]"z-m;))!#:$!0VdG%p;?Q!#:7$$!0JZbxyaA*!#:$!02Jj+L*f\!#:7$$!0K^]Ha9a*!#:$!/VZe!\o)f!#97$$!06QD3@tz*!#:$!0YI1sl1-(!#:7$$!01Vw[c)R**!#:$!0n*[*z*zQy!#:7$$!0%p_G?L****!#:$!0"[\EH<#e)!#:7$$!0Ld0-h+(**!#:$!/w"\aj#H"*!#97$$!/EP"3!p?**!#9$!04AYv5XP*!#:7$$!0lgA)['y%)*!#:$!0/C;7j.e*!#:7$$!0K^()oy!e(*!#:$!/WtI]IP(*!#97$$!0HD<`nyk*!#:$!0tc96=!e)*!#:7$$!0^G>`#36&*!#:$!0_lWI&)\%**!#:7$$!03Z]*ea_$*!#:$!0U:'zZ_"***!#:7$$!08$42h'o<*!#:$!0YYFwex***!#:7$$!0Rq=;D6)*)!#:$!0D(><P9l**!#:7$$!0np-)R<b()!#:$!0M:&*R8&*))*!#:7$$!0,B9>Y#3&)!#:$!0AJ#yiwr(*!#:7$$!0'\N!y4d(z!#:$!0C,D#*f#G%*!#:7$$!0o'f1h'yN(!#:$!0vSYp*4B*)!#:7$$!03l]6-wn'!#:$!0x'zgIhw#)!#:7$$!0Xw)o@b)*f!#:$!0>F#pKzjv!#:7$$!0**omr$oj^!#:$!0wz,B<*>m!#:7$$!0TA4FmBP%!#:$!0&*=#z\;uc!#:7$$!0"RFGMw*[$!#:$!/o2TU4wX!#97$$!0@+VxfZh#!#:$!0Ax'RZlaM!#:7$$!0/T#oZj<;!#:$!0h'*e-g%\@!#:7$$!0l?8FN@S(!#;$!0K/p%)*[i)*!#;7$$"0#)RnWPHi#!#;$"0t;w&z$p\$!#;7$$"0f#ph@$R<"!#:$"0Tj`jKCc"!#:7$$"0/,Zu>'f@!#:$"0p?e%HyhG!#:7$$"0b50h7J*H!#:$"0ao6b#*G%R!#:7$$"0*z0%)4*["R!#:$"0;i,4o)4^!#:7$$"02Sb.-&pZ!#:$"0HU%z67ah!#:7$$"0;GTQZ1e&!#:$"/M"e'[K*4(!#97$$"0z@gi.*Qj!#:$"0"yG;5DGz!#:7$$"/Zc6<89q!#9$"0&H>')QH1')!#:7$$"0Y-z%G!*yw!#:$"0te@w%G(>*!#:7$$"0u3VJ_PC)!#:$"0eUXvJUh*!#:7$$"/,kf*p-w)!#9$"0*HRx,f"*)*!#:7$$"0)4@_'Gk'*)!#:$"0xh&G4Mh**!#:7$$"/#)zu7ya"*!#9$"0UCe^Gf***!#:7$$"/(>`!HyT$*!#9$"0\$oSa5$***!#:7$$"0c04)e71&*!#:$"0d?^c)>Z**!#:7$$"0lRBQB>k*!#:$"0y;YO7I')*!#:7$$"0$G!p!\Ec(*!#:$"0sYT>8)R(*!#:7$$"0*G1!3(p[)*!#:$"0,0UHG&y&*!#:7$$"0i]jo>$>**!#:$"0f(\])R&z$*!#:7$$"0&G*y>`e***!#:$"03'\0-#e%))!#:7$$"0sG_;S4)**!#:$"0._(*y3(>#)!#:7$$"0ppn$e!4))*!#:$"0bl>zLXX(!#:7$$"0#RcOm(=n*!#:$"0cL^o&*zZ'!#:7$$"0;O?TX^R*!#:$"0GkOU#H*[&!#:7$$".=:t,(G!*!#8$"0">ktbk"R%!#:7$$"0fto,&)Gd)!#:$"0_d&[<f.K!#:7$$"0MLOITN3)!#:$"0_877=W1#!#:7$$"0Ekw0Z@\(!#:$"0mzmR=y=)!#;7$$"0^gy9z"Ro!#:$!0NdPV)\-V!#;7$$"0z;[2lV2'!#:$!0p4z<#Re<!#:7$$"/H$44"[[`!#9$!/aA<X50H!#97$$"0-?H%GKfW!#:$!0%[7'**yp<%!#:7$$"03Qu)*ynh$!#:$!0oC#on,f_!#:7$$"0"y1U[*Gv#!#:$!/nl;<l^i!#97$$"0u<"H$H')z"!#:$!0k.'Q_q:s!#:7$$"0u(y3nNJ#)!#;$!00-xUc(f!)!#:7$$!0aR9VO#fr!#<$!0O_7S(e2()!#:7$$!0>j*GJ'4-"!#:$!/'zw$fdf#*!#97$$!0[G$GOiQ>!#:$!/G5PZ#\l*!#97$$!0lJY#oF9H!#:$!.1/::l"**!#87$$!.(4#eZ]t$!#8$!0J.&=i7****!#:7$$!0v^e2^Ck%!#:$!0>%=iP&z#**!#:7$$!0Yat2@LX&!#:$!0_C^,&G+(*!#:7$$!0jq="G#*3i!#:$!0tqB))3[K*!#:7$$!0*Q`,xG6p!#:$!0$eJNsP0))!#:7$$!0>T=`hec(!#:$!0#=zf,'e8)!#:7$$!0%4`$yX]=)!#:$!0"\sv%[SG(!#:7$$!/ULCp**z')!#9$!0:![SrJ(Q'!#:7$$!0QZ'H*Hg4*!#:$!0$fI">">2a!#:7$$!0[AfWRrX*!#:$!03&za#)frU!#:7$$!0*)zJT1!G(*!#:$!0mB`;tm1$!#:7$$!/A"RR.H*)*!#9$!0DdWiI2%>!#:7$$!0^1#oqr!***!#:$!/0PHqOUd!#:7$$!09IItt0***!#:$"0PU.4)['y&!#;7$$!0uOr5?c*)*!#:$"0/vn5Ci">!#:7$$!0VVwra0r*!#:$"03Xd>n1;$!#:7$$!0&o-*=o(o%*!#:$"0D=!oh=GU!#:7$$!.0xh/H6*!#8$"/"=l!HNh`!#97$$!0l*)RS2#o')!#:$"0<)eV@f6k!#:7$$!0,!)pXpO9)!#:$"/<*)e^<\t!#97$$!0TK%>Ii)e(!#:$"0"42V:t3")!#:7$$!0;/piH"\p!#:$"0*o1])))>x)!#:7$$!/bp@"*HCi!#9$"0Z.()QA`J*!#:7$$!0P:h))*>Wa!#:$"0[$>"3*z.(*!#:7$$!0tqH')z$*e%!#:$"0he^!e>P**!#:7$$!0a'4*e<!*z$!#:$"01n)>&>*****!#:7$$!0o]h+&4vG!#:$"0\q0oH$4**!#:7$$!0&G?#=%f>>!#:$"0Eo+;e"['*!#:7$$!0(ea8<)3")*!#;$"09^oHl#R#*!#:7$$!0t%*\/5'47!#;$"0OT!4owR()!#:7$$"0'H-m4dC!*!#;$"0'zeTLY'*z!#:7$$"0H$*Q#eWi<!#:$"0j'RkDc\s!#:7$$"0LKP!=oXF!#:$"0oDftb%fi!#:7$$"0ONL_!*Hf$!#:$"0uNw\3zG&!#:7$$"0$R[c$z$*[%!#:$"0<zPPAi8%!#:7$$"0/!flP)HI&!#:$"0aC7i6O(H!#:7$$"00&H$GND5'!#:$"0,=&yFw6<!#:7$$"0'*Rx#R'fy'!#:$"0pd[kW1F&!#;7$$"0.#\!QG@Y(!#:$!0kN([#Hpe(!#;7$$"0a0yQm34)!#:$!00'p+Bm!3#!#:7$$"0&))QBBDs&)!#:$!0y&og'R??$!#:7$$"0*Q*[d$z=!*!#:$!0nLX;%3kV!#:7$$"0u3xN7gR*!#:$!0__&\S6#\&!#:7$$"01r>vV*y'*!#:$!0vF)fiN1l!#:7$$"0">nr=>p)*!#:$!0`D1y(3)Q(!#:7$$"0QF<rZA)**!#:$!0"GxM*\gB)!#:7$$"03ZvKnZ***!#:$!/@$zy3y'))!#97$$"/RVh'Q\"**!#9$!0<96Z5_R*!#:7$$"0'4&\>gs%)*!#:$!09&pj2p"e*!#:7$$"0'y0qI5g(*!#:$!0"4E[0[M(*!#:7$$".r`SLFk*!#8$!0MiVSRB')*!#:7$$"0LI$>mc-&*!#:$!/N$zR`([**!#97$$"0Z02$)f,N*!#:$!0*Gxu.*=***!#:7$$"0[zs!>=y"*!#:$!0#*ouI^y***!#:7$$"0*y64e)y(*)!#:$!0Jte@?V'**!#:7$$"0")yI[dqv)!#:$!0Cut!GG!*)*!#:7$$"0M)Gwp*yE)!#:$!0&evX&o(H'*!#:7$$"0#))>&f]%yw!#:$!/W)*4_"p>*!#97$$"01#3)*p9Tq!#:$!0(e.om'>j)!#:7$$"0v1UIeZK'!#:$!0a8ZywL"z!#:7$$"0CUUGVib&!#:$!0/g+>"orq!#:7$$"04"[<n60[!#:$!0%39>Em'>'!#:7$$"0mv!)4(**)*Q!#:$!0'*ySYl+4&!#:7$$"0k/t)>zaI!#:$!/hUiP.AS!#97$$"0tHtaxv7#!#:$!0NFYOX)>G!#:7$$"0Vh%z1j@7!#:$!08>"yEnD;!#:7$$"0)4+")4RR?!#;$!/,4\8/>F!#:7$$!0h&*e$)eSz'!#;$"0_g9m:L0*!#;7$$!0C#G4(3_n"!#:$"0x!=tCSDA!#:7$$!0[7$*yc$oD!#:$"0ESQ.pWR$!#:7$$!0=A)yp[?N!#:$"0W,\jT\h%!#:7$$!0=FDIzSJ%!#:$"0v'z>,"Hg&!#:7$$!0$\%y?i%y^!#:$"0>oqharj'!#:7$$!0G![0j/mf!#:$"0yStq-$Gv!#:7$$!08m1eV%*p'!#:$"0-rh?N&)H)!#:7$$!0$\Qt-Bqt!#:$"0Z)y8K2M*)!#:7$$!0nRilXF&z!#:$"/OE%Qk7T*!#97$$!0V3R7<'3&)!#:$"0iMM>m>x*!#:7$$!0n<It()\u)!#:$"0LV%)e:`))*!#:7$$!0#))[bgAi*)!#:$"0of_EA-'**!#:7$$!0k*\cNnp"*!#:$"0&ek4)>s***!#:7$$!03M]K+\N*!#:$"0'fkua:"***!#:7$$!.jy:PI]*!#8$"0`!f'[\&[**!#:7$$!/@Y"H-Bj*!#9$"0dWz[D3()*!#:7$$!0A4Y(G!Hv*!#:$"0xTV%pSW(*!#:7$$!0(=FCw%)\)*!#:$"0M3s#o(fd*!#:7$$!0zm7\0.#**!#:$"0CD[XGfP*!#:7$$!0a?L!zoo**!#:$"0(o@kPzQ"*!#:7$$!0UG%3(z))***!#:$"0A`tVW(e&)!#:7$$!0R/=+/f$**!#:$"0yuXt0$4y!#:7$$!0T,bwyHz*!#:$"0"GIn?;+q!#:7$$!0Y'[NuWj&*!#:$"0#f]c5'f1'!#:7$$!0MO#)R^Y@*!#:$"0/e&z7_F\!#:7$$!0P+C>la"))!#:$"0"f0En/<Q!#:7$$!0ZfuiX*G$)!#:$"03I^^r7i#!#:7$$!0Dm]Anuv(!#:$"0vTq73CO"!#:7$$!0rr*p]Yor!#:$"0)fG"R?$\=!#;7$$!0B,Evl(yk!#:$!0wY)[0ms5!#:7$$!/@@#Qurt&!#9$!0')z(*GDRI#!#:7$$!0rCFD%H))[!#:$!0)HB'**32e$!#:7$$!0euNA,")4%!#:$!03<W]J]l%!#:7$$!/Jp=F$p9$!#9$!0z/hRBK"e!#:7$$!0kv-Z],E#!#:$!.*Habgmn!#87$$!0(R\-O#QO"!#:$!0W^'=Qc4w!#:7$$!/'*4y?`vQ!#:$!0pO"Q,P!R)!#:7$$"0<\YT')R'f!#;$!/)3DPq-.*!#97$$"0iUp')zo["!#:$!0XBU)4vx%*!#:7$$"0V)y))3K>C!#:$!/:$H[K]!)*!#97$$"0Px1wp#3L!#:$!08RKW8E(**!#:7$$"0^e"*H*[RU!#:$!/dI%yB>)**!#97$$"/J)=Au4,&!#9$!0JMRWG^%)*!#:7$$"0K%))f8()\e!#:$!0C'QxopC&*!#:7$$"0'yBprK&e'!#:$!/.***ff"p!*!#97$$"0zzqW*Qcs!#:$!0[*R!fjxZ)!#:7$$"/n8sa1ly!#9$!0%**\'z!Hbx!#:7$$"0oPr=mbT)!#:$!0k">1hP&*o!#:7$$"0$eN#f&3;*)!#:$!0NnP>?N'e!#:7$$"0W%4'R*o&H*!#:$!0t?I6=T#[!#:7$$"0JSNT3Ff*!#:$!0%=$=2pjs$!#:7$$"/G#*px0A)*!#9$!0*pg#H2D\#!#:7$$"0*38"f)*z&**!#:$!.h`EE%>7!#87$$"#5!""$"/`Cc[l"G$!#A-%&COLORG6'%$RGBG$"#5!""$""!!""$""!!""-%+_ATTRIBUTEG6#/%'sourceG%,mathdefaultG-%+AXESLABELSG6$Q!6"Q!6"-%%ROOTG6'-%)BOUNDS_XG6#$"$S"!""-%)BOUNDS_YG6#$"$?"!""-%-BOUNDS_WIDTHG6#$"%I9!""-%.BOUNDS_HEIGHTG6#$"%g8!""-%)CHILDRENG6"