00020002010008main.ACT0001020012eActivity Save.EAC010000002882  ropes.EAC ACT *. $]E (',[[A Calculus Problem\" Author9gzl<fessor Wei-Chi Yang "URL: http://www.radford.edu/wy*H e-mail: @' Objective:[UWe will explore ap3 by incorporating the features of dynamic geometry UEand CAS (which are available from ClassPad); we hope to make this pro, m accessi8'oQ students. [[  A P?3 (see [1])#FPTwo vertical poles AC BDsecured by a rCED (n the Geometryrip XTbelow). Show that-shortest length of suZocls when n1=n2. (or ang CEA= DEB)\Play animationΉ(,2 C'hi `6aYYhi&V3(0  v !&r  A 'L'MC uxy qq 9  K4@6  FGs`pw LG  DEB:    ji6FdYpQb c"!Y E BRc+CHCDx @   0g8  < Ȏ8b-x@N6CO (  `^BG*:a Ĉ ވo tD93FGs0&``w x  CEA: bTv !7fCy5B1 "Q C H  C@60`  >@ '0ˈdv _xWt  `CAˆ&ˆY܈WHD92MdFGs `xE M Length ED: fv  1@6)FGs0 `E )- Length CE: $ @ v  #t h(J``"p`"p   ,tH5@.  @6*  !R@ J "0zG`eX &1WG7 #!@!R $"c͘AUWtYB`%͈a&0{W2g_+I7?';!; (ȏ8a ywR ))@  (*0(BW2g-+I7?"!:e v h$ Q[ Exploration.=1. After the anim , we collectf owing infor&:EJ*umn1= CEA,=22DEB 3=length CE4ED[90 23.49856567 5.2 10.03194896 84.68010608252150746@22495556 9.58983765Y 79.45038843k25.91666'G89408M9.151951 74.3921757Z 27.307503565#9086821 8.7190433796711654 28.84266015 9606 .291770776513 30.5432445 5.73598255Y 7.87109442B 60.807713 32.4339791 5.956d5T7.458130591 56.90281213 34.5437494$ 6.207135565 7.05423391G 3.3161269$3Y6114956 6.48424470k 6.661053962H 0.03508468 39.55966797H7846331128060 47.0411240~42802629ƈ|4892H5.915934 4424836%91047U06516Z5.56825'U41.8262 49.72311175775724295068 39.55966797 54.00850374 8.164784866$ 4.94373885 37.49111881G 8.8150253G 543660072 4.67562785Y 35.!467k 64~32457893271865 4.444249919 33.869340~ 70.041109H 9.3306868664.25583H 2.28115723H 76.390269.73225511H6 30.82107783.7788 10.1C372Y2929| 29.4758890 10.567875854[ )C2. We copy and paste the matrix above tofollowing stat editor.K43K define list58bOsum of3j!4.\ dataalysisԈ+4NDFinaForm$NGraph2D 3 LISTCAL4 SYS 4P Modify@dPSTA<Cd-xG<l\Sequence,SheetO|polveEqawr(UptupFLG1(<Lis{0DPicViewWin_osvev)#xy^hH(} 4< @,$ mLXd,ĒІ܆ ! ",!#@ $T%h  &|0'< !(H)T  *_`c+l,x-.U1234̆5؆EFHI, J KTL6M8ND O P \Æ QhdRhtST]D ^de_xj`d ab2(e x  ,Wh |̆ ؆ ͑䆹   ІfXא( ؐ< ِP ڐd, Cېx8x FinancialFormat  Eɒ  8 list3+4 system]^]=_`a b~cÎ @È@@x2<Ê= 8x;  aE seq_hb NewFoldeO` `l system]l0E]= 1<ԈRoot (c@fi-miminumuatkut x=5.2 when[La,b=9.2,cc=4. L-We obserfrom triangles CAEDBEin Geometry s-p[  a=xF= 2H=1?c|b-A4-N =1. [ ,Y4. Conclusion. This implies that tan(n1)= 2) amd since  and2 are both accute ` :angles, we chdeXT=n2W(`/4=45 degrees.[ Reference.S[1] Jam Stewart Calcu, ISBN 0-534-37718-1, 200Thompson Learning, page 315, problem 34eActfH<,a,b,c,x(a^(2)+x^(2))+((b-x)^(2)+c^(2))010009ropes.ACT0001020009ropes.EAC010000002882  ropes.EAC ACT *. $]E (',[[A Calculus Problem\" Author9gzl<fessor Wei-Chi Yang "URL: http://www.radford.edu/wy*H e-mail: @' Objective:[UWe will explore ap3 by incorporating the features of dynamic geometry UEand CAS (which are available from ClassPad); we hope to make this pro, m accessi8'oQ students. [[  A P?3 (see [1])#FPTwo vertical poles AC BDsecured by a rCED (n the Geometryrip XTbelow). Show that-shortest length of suZocls when n1=n2. (or ang CEA= DEB)\Play animationΉ(,2 C'hi `6aYYhi&V3(0  v !&r  A 'L'MC uxy qq 9  K4@6  FGs`pw LG  DEB:    ji6FdYpQb c"!Y E BRc+CHCDx @   0g8  < Ȏ8b-x@N6CO (  `^BG*:a Ĉ ވo tD93FGs0&``w x  CEA: bTv !7fCy5B1 "Q C H  C@60`  >@ '0ˈdv _xWt  `CAˆ&ˆY܈WHD92MdFGs `xE M Length ED: fv  1@6)FGs0 `E )- Length CE: $ @ v  #t h(J``"p`"p   ,tH5@.  @6*  !R@ J "0zG`eX &1WG7 #!@!R $"c͘AUWtYB`%͈a&0{W2g_+I7?';!; (ȏ8a ywR ))@  (*0(BW2g-+I7?"!:e v h$ Q[ Exploration.=1. After the anim , we collectf owing infor&:EJ*umn1= CEA,=22DEB 3=length CE4ED[90 23.49856567 5.2 10.03194896 84.68010608252150746@22495556 9.58983765Y 79.45038843k25.91666'G89408M9.151951 74.3921757Z 27.307503565#9086821 8.7190433796711654 28.84266015 9606 .291770776513 30.5432445 5.73598255Y 7.87109442B 60.807713 32.4339791 5.956d5T7.458130591 56.90281213 34.5437494$ 6.207135565 7.05423391G 3.3161269$3Y6114956 6.48424470k 6.661053962H 0.03508468 39.55966797H7846331128060 47.0411240~42802629ƈ|4892H5.915934 4424836%91047U06516Z5.56825'U41.8262 49.72311175775724295068 39.55966797 54.00850374 8.164784866$ 4.94373885 37.49111881G 8.8150253G 543660072 4.67562785Y 35.!467k 64~32457893271865 4.444249919 33.869340~ 70.041109H 9.3306868664.25583H 2.28115723H 76.390269.73225511H6 30.82107783.7788 10.1C372Y2929| 29.4758890 10.567875854[ )C2. We copy and paste the matrix above tofollowing stat editor.K43K define list58bOsum of3j!4.\ dataalysisԈ+4NDFinaForm$NGraph2D 3 LISTCAL4 SYS 4P Modify@dPSTA<Cd-xG<l\Sequence,SheetO|polveEqawr(UptupFLG1(<Lis{0DPicViewWin_osvev)#xy^hH(} 4< @,$ mLXd,ĒІ܆ ! ",!#@ $T%h  &|0'< !(H)T  *_`c+l,x-.U1234̆5؆EFHI, J KTL6M8ND O P \Æ QhdRhtST]D ^de_xj`d ab2(e x  ,Wh |̆ ؆ ͑䆹   ІfXא( ؐ< ِP ڐd, Cېx8x FinancialFormat  Eɒ  8 list3+4 system]^]=_`a b~cÎ @È@@x2<Ê= 8x;  aE seq_hb NewFoldeO` `l system]l0E]= 1<ԈRoot (c@fi-miminumuatkut x=5.2 when[La,b=9.2,cc=4. L-We obserfrom triangles CAEDBEin Geometry s-p[  a=xF= 2H=1?c|b-A4-N =1. [ ,Y4. Conclusion. This implies that tan(n1)= 2) amd since  and2 are both accute ` :angles, we chdeXT=n2W(`/4=45 degrees.[ Reference.S[1] Jam Stewart Calcu, ISBN 0-534-37718-1, 200Thompson Learning, page 315, problem 34eActfH<,a,b,c,x(a^(2)+x^(2))+((b-x)^(2)+c^(2))0301cc00200008000000001e15x}lR+{Ed*VDTZKQ)Q$"%Y_"-%Q$eQWAeԒeU 8#0DrWiNhcQ!0 ovg-׹$=g833|w7|y-d[[ /SS#G4MY퀦<%>syޞ M7WԖٶuW2|>k6g d|a>0ko_!o_!o_!k_!k_!k_ t|iO4cjyg#cG][vxdÕym;:ؤ07dqM3vLNƻe}S~k8ߌ?ߌdݤccOGZin?u@mwnrBWb#OѴ;ͼ+ێLWJt㴊UVcO7cfZlIg7!UMؾktV%bƦdnb}cCflVc#'3cOzzdkcL~{S[9@Z߮W^bT{_ZULłl*W5*֦bwXXT֪X}EzUnPu*WظWGΩXHJ*v]Q *mT%kW*vPU]{@*֡b7Ul}b_V{UlU,b!ۢbaXVŢ*֭b1S=b UMXJΪXUl]V^{Uv* =b?R]*VTl}b؇*Wqأ*P*NUCT,bOXpVOX=b*W]*6b}*vHTlQSyyAņU-Pi{[ *S[TwU쪊L^Wbob~^iώ 7]S|Jh3Y#'ԼԅyNռԃ|515ODMMAlj#[ ,[>yjl%UHףij݀.I}v{_H ɆTü,O#:~َ|>0lO5ۏ-|$T^+]ņj9Σu~$'vϸ:MsZzr))/iBYI%IW%!麤%'S3llll~rwIMm͡_oN}Zا'ק7g復oGʛqƃO˶l?Ŀu(;?u;Wx~\0prmv}LJ]PvVGԯٳg\1cGǦOMɬuΙ' NU575%lU՘N֚7Wc'&mE=ˊmߵÌj13vyk2>v$pĈCBՀ:AطWx2)\Lys cr"\N˩pؖñhtS"_&>mݲxOb[߲N928y1U/7ߤWN_9S._?vy(Δ׆?=S}+T]gI_=lípyKzQZ]ѱPq_ZEW.pyo.;ϔ w 2tts\<5rѱ)9-~797~W e6'$]3X_Z ;\&ѡ:,}Q;+,F.̸*gJF|]uz!8[t:cINWI2Qï:& A}i!B}= \vv]cSƿv7 BolȸX.od'\W(*_L%K3r`?p)U A\骣"Ғ*WJ?r _:ʫWjJs_eŻ$ݐ&]Ik%%}EMIwKH:9nW&*m=-!G^%+{KttĆMGKLlw:Z6G˨L7vL]2(󣎖2iU|Llyk g#I&gk󎤈$E%} )&CIҰ) )Ok@&Ru2J=%/r[$+j%;@7@2uBJr軥@#j]G@WeO L<*j&{@oDsFm^w-NK,~BY.'R=eUR^KJyȪRQpAޒ )[]?f#hJقu e r&~>eU.8>?tэ,xkW6_ Ϗ/Ώ^8+?/O^ޏsW_3ޏ+w\xk5,>vY4ƧE?vFznϳp͋w41_ OЋ]7VʦBם7fV20pWN 'k_w~<7oPg8uսF@>ixw%Wlc=?^:}e.6ft_c,8^ZqG${ ]ΛOy+ =w]2ی; ?k0y97*нW."7JWj'WzSiEU?l//FXX7IRiv/Wzk 5~]T|^s?lI[[Dsykߋ}vڶퟘ2/7W?Ii=jK~sCl#_,-i\%=ٶ82296uX97voS3euOf?g%o.?qVUnԉi_y(\>S>ytzc#(٩ޢ٧:YjnVlifs^ұwjY7;?/Hk%ush+ ]ηŻ[tc~VscR{?BJvO4 W}y*iaZ a(S{\.[O^W>-m^^ɮ?-Zϟf?27j|tWb\\=.4͕a^6?6ϭշfwX WZY^&j+'4}FEL&%3e+'[t:Fcda4VߙDT"Kqほ[bT:NFf6'2x&RŹ% i6w͙a5[ʂZ=Ծ0{.GrSs._~Us~)ѷ8M~h5;N*gхkoCokwқ.]fsExVVhō/kf=o,]m4; 9SSۭ+SRIyIf$TtEk$]tCһF^.|CvnJs~׶\(]}Xu¿j5x^9KĚ&2ysbkK܀RʮvPqç&%W\մ_܌);l]5mxfܒ{ԅQ' چeٜn6I풢:%J4.iF)I ^$麤ޕH^޿w;]\:9|9*vLyR9a}־}=_xzS϶E’i̽jg_Rȹq^ǡypm`b|q㪻z].o_frV;eoC.5Pg.]' sK"zznǭ?vIˮ4׆zG`ѻ!Tںr%ـKdzsF+P.O3у忮]ÁK.w[.i|;uGM}g\dͳ~7?m9׮vΗڜ׾%'kվPTcA-vzr;r56k]+64_P{[qwaXrkwέmyj*y]O>$B7񌝔T!MGjkl2F4[pFG6B \nRfk2 1LZVJڎSgpśxҷִ; RFII7ウ*\nI<#7H4U \}{X]Uo]wWary7Xr WSoa㍷s]|w]\i*jpmVy ^!>O7|1i,ZJ>V׃jzkֳIL}RHjqq뻬롤kMWkw=!ymT(ȝjz қ|ץ6o^smH՞gO׃<[l;}V=Q_6еO~W&?k6jZ>^a[>mߏ6/j rc}Q}ݹˮ 5Mtvq[;u[׹p\u7_׃C{{{}9}7 a[IM"?h~x?~~VgWd.Jҙj)[b?M%&#l4MG%RLҊx2JsT6Md)kL.LEl2QM*iYl.άH.KrQL2cTx&fdߩO"fxVH&&LΊ%X,Jd#d