MAT 125 HOMEWORK PROBLEMS
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- Richard Carter
- 5 years ago
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1 MAT HOMEWORK PROBLEMS Lur # mwrk rss Ers : Cm up w w nn-smrp mpls rl-l prsss r unns n ll n sm n lnks w prnn mlmn unn n Lur # N: nn-smrp mns u n us ns lk Frl Eprss lvrmn r UPS lvrmn s mpls Pls rv; nlun purs wul plus Ers : Cm up w w nn-smrp mpls rl-l prsss r n unns n rul pln w prsss r n unns Hr nn-smrp mns u n us ns lk r lr pzz nn-unn r r-pun -n sk nn-unn s mpls Lur # mwrk rss Ers : Slv llwn lr nquls usn spl pn r m n mr mpl prlms rm Lur # Pls ls ur nswrs n ll r slun rms: numr ln nn nrvl nn n s ulr nn p n m l k j > > > > Lur # mwrk rss Ers : Evlu llwn unns n mn vlus D NOT smpl ur nswrs Ers : Fr llwn unns mpu rn qun smpln s r
2 Ers : Usn GOOD pn/bad pn ppr rm lss n mns llwn unns An p ls nn s u knw wn u n us spl pn r n wn u n n us spl pn r p n m l k j Lur # mwrk rss Ers : Gv n mpl s v nnl rmul n sk rp n mpl llwn r rul pln w n su mpl ss A unn s lws nrsn A unn s lws rsn A unn ws mn s [ n s lws rsn A unn ws mn s n s lws nrsn A unn ws mn s n ws rn s jus numr A unn ws mn s ] [ n ws rn s ] [ A unn ws mn s n ws rn s s } { Ers : Usn rpn lulr r sk m wu lulr k ur pk! mk sks rps llwn unns n n: r mns r rns nrvls wr unns r nrsn v nrvls wr unns r rsn Ers : Rp ls rs u ns n llwn ns-lkn pws-n unns: > > >
3 Lur # mwrk rss Ers : WITHOUT USING A GRAPHING CALCULATOR mk sks llwn unns Pls n unns r sussv lrns n nr s u suln rp unl u v rp n n rp llws rl rm rp E Ers : Rp ls rs w llwn unns Ers : Rp ls rs w llwn unns Ers : Rp ls rs w llwn unns Ers : Rp ls rs w llwn unns Ers : Rp ls rs w llwn unns Lur # mwrk rss Ers : T llwn r supps rps vn unns Fll n w s mssn mk m vn
4 Ers : T llwn r supps rps unns Fll n w s mssn mk m Ers : T llwn r supps rps prs unns r nvrss Fll n w s mssn s w s unns Ers : Gvn unn sk s unn r w n n sm pur Yu m us rpn lulr k ur nswrs Ers : Gvn unn sk s unn r w n n sm pur Yu m us rpn lulr k ur nswrs Ers : Gvn unn sk s unn r w n n sm pur Yu m us rpn lulr k ur nswrs Ers : Gvn unn sk s unn r w n n sm pur Yu m us rpn lulr k ur nswrs Tn ls ur pur Ers : Wr wn ls rn mpls unns nlun sks n nnl unn nns Tn rp qusn w rn mpls vn unns Tn rp qusn w rn mpls prs unns r nvrss r An s u r llw us mpls rm lss! Lur # mwrk rss Ers : Gvn unns n n SIMPLIFY llwn:
5 Ers : Rp ls rs usn unns Ers : Gvn unns n n SIMPLIFY llwn: Ers : Rp ls rs usn unns Ers : Smpl rn qun s r s pssl r llwn unns FTR u ll sn s ns-lkn rn quns l n lulus s vr n rum nu n u ASAP Ers : Rp ls rs u ns smpl lrnv rn qun Lur # mwrk rss Ers : Sk rps llwn unns vr r n--n n rr v nvrss Yu m us rpn lulrs lp w skn s rps l k j > Ers : Fn nvrss unns rm ls rs B sur k ur nswrs! Ers : Vr unn s s wn nvrs Ers : T llwn unns r n n--n n n n v nvrss Fr unn s mn upn w unn s n--n T us rpn lulr m m n n n s prlm Lur # mwrk rss Ers : Fr llwn -vrl -qun ssms rp ssm n pln rmn numr sluns Tn slv ssm usn m susun
6 Ers : Slv llwn -vrl -qun ssms usn m lmnn S w mn sluns ssm s s s u v v u Ers : On Frmr s Mrk Frmr J slls zn s $ pr zn n puns ms $ pr pun r l rvnu $ T n wk Frmr J slls zn s $ pr zn n puns ms $ pr pun r l rvnu $ W ws slln pr n zn s? W ws slln pr n pun ms? Lur # mwrk rss Ers : Wu rpn lulr sk llwn qur quns Pls ll vr n ll nrps Ers : Rp ls rs u usn llwn qur quns Ers : Fn mmum vlu n llwn qur quns Ers : Fn mnmum vlu n llwn qur quns Ers : Usn smmr nrn n rps qur quns n w rn prls n pnn up r pnn wn v llwn nrps Ers : A m s rwn upwr s uln s T nl vrl vl m s pr sn w mns m v run n lw uln s vn unn rus m! wr s m n sns r m ws rwn A w m s ll r s mmum? An w s? Ers : Cmpl squr n n n n s rmn rmul r ln vr n prl
7 Lur # mwrk rss FOR EACH OF THESE PROBLEMS YOU MUST FOLLOW THE -STEP OUTLINE FROM CLASS Ers : Fn squr mnml sn rm pn n pn n rp Ers : Fn mml r r rnl n w sum w srr ss s ns Ers : Fn mml r rnl ws prmr s ns Ers : Fn squr mml ln nl rnl ws prmr s ns Ers : Fn squr mnml sn rm pn n pn n ln Ers : Fn squr mnml sn rm pn n pn n rp Ers : Fn mml r rnulr rrl m w n rm r ss rrl ur s n rmn sr rvrnk Ers : Fn mml pru n w numrs ws sum s Ers : Fn squr mnml sn rm rn ln m Lur # mwrk rss Ers : Fn rl n mnr prs llwn mpl numrs Ers : Pl mpl numrs rm prvus rs n mpl pln Ers : Cmpu mulus mpl numr rm ls rs Ers : Gvn llwn mpl numrs prrm n rm n m Pls smpl s r r n mnr rms n nmnrs jus s w n lss F E D C B A r mpl numrs us lw B A D F C B A C F A D E B E D A C D B Ers : Drmn llwn rpls pns rm r rnls n mpl pln N: u nn smpl rw pur rmn s! Ers : Fn ll rs rl n mpl llwn quns z
8 Lur # mwrk rss Ers : Fn ll nrps llwn plnmls Ers : Fn n qun plnml s llwn nrps N: nswrs m vr ± ± ± Ers : B mkn spl-pn r n nn nrps n WITHOUT USING A CALCULATOR sk rps llwn plnmls Ers : B mkn spl pn r n nn ll nrps n WITHOUT USING A CALCULATOR sk rps llwn plnmls Ers : Fr llwn v n mpl plnml w vn prprs r pln rul w n su mpl ss s r n s rn [ s vn r n s rn s s pks n vlls n s r s r n n nrp s n nrp s v nrps n s r Lur # mwrk rss Ers : Fr llwn plnmls mk ru sk rp lln nrps n mkn lr s rpl vr wu usn rpn lulr Pls mk lr w u us L Cn Ts s u rssn vs un rpl vr nr -nrps n s u n vr sk ur umm sks l k j
9 Lur # mwrk rss Ers : Eu llwn plnml ln vsns Ers : Fn ll pssl rnl rs llwn plnmls usn Rnl R Trm p Ers : Usn plnml ln vsn Rnl R Trm n rn n ll rl rs llwn plnmls s s s s s k Lur # mwrk rss Ers : Fllwn -sp uln rm Lur # sk rps llwn rnl unns An pls kp n mn ll ur nswrs/rps m k w rpn lulr r r rpn swr k j Lur # mwrk rss Ers : Ar kn llwn r ull r prpr n ru w m rqur ll wrk mps s rnl unns n smllr rns usn C B A ; u n slv r C B A Ers : Dmps smpl rnl unns rm Ers T s k ur wrk rm ls rs n ull slv r unknwn nsns C B A
10 Lur # mwrk rss Ers : Gvn unn sk llwn rps wu usn lulr n sr r mns rns n nrps wn pssl Yu m wn k lur n rp lrns r lp! Ers : Rp ls rs u ns w unn Ers : Slv llwn quns Lur # mwrk rss Ers : Gvn unn l sk llwn unns n nlu srpn r mns n rns Pls n us rpn lulr u u m rnl k ur nswrs w rpn lulr! j Ers : Evlu llwn lrm prssns l l l l l Ers : Slv llwn quns Hn: rwr qun n pnnl rm l l l l l Ers : Usn GOOD pn/bad pn ppr n mns llwn unns l l l l Ers : T mnu R n Rr sl n rquk nns I s vn l I I R wr I s nsn rprsns nns vr smll zr lvl rquk mnn n rl l A rn rquk n Onrrn n pln Xl ws msur s n ms s nns s zr lvl rquk W ws s rquk s mnu n Rr sl?
11 Lur # mwrk rss Ers : Gvn unn sk llwn rps n sr r mns n rns j Ers : Rp ls rs r unn ln j Ers : Slv llwn quns ln ln ln ln ln ln ln Ers : Slv llwn quns Ers : Slv llwn quns Ers : Usn GOOD pn/bad pn ppr n mns llwn unns ln ln ln ln Lur # mwrk rss Ers : Us prprs lrms rwr llwn prssns s sums n/r rns n/r mulpls smpls ps snl lrms As s n lss u mus nlu sp l rul numr n rn wnvr u us l rul k j ln ln ln ln ln ln ln ln ln ln ln
12 Ers : Us prprs lrms rwr llwn prssns s snl lrms An u mus nlu sp l rul numr n rn wnvr u us l rul ln A ln B ln C l l ln ln ln ln ln [ln ln ] ln ln [ln ln ] ln [ln ln ln ] ln ln j ln ln k [ln ln ln ] Ers : Tru r ls! ln ln ln ln ln ln ln ln ln ln ln ln ln ln ln Ers : Cn u lu n rns rs r lrm ruls rm lur ns An s n ms Lur # mwrk rss Ers : Slv llwn quns n k ur nswrs I nss u jus ll ppll sps w numr l rul u us n rn l rul ln ln ln ln ln ln ln ln ln ln ln ln ln ln ln ln ln Ers : Slv llwn quns n n jus ll ppll sps Ts m I n nss u k ur nswrs u I sll rmmn s n knw u r r? ln ln ln ln ln ln ln ln ln ln ln ln ln lnlnln Ers : Fn nvrss llwn unns Pls jus ll ppll sps n pls k ur nswrs ln ln
13 Lur # mwrk rss Ers : Slv llwn quns smpln ur nswrs s r s pssl An n r ls m s s n lss u MUST jus ll sps! l l l l l l l l l ln ln j ln ln ln k l l l l Lur # mwrk rss Ers : Fr llwn snrs mpu w mu mn wll n un r rs $ nvs n n un rnn % rl nrs mpun mnl $ nvs n n un rnn % rl nrs mpun wkl $ nvs n n un rnn % rl nrs mpun qurrl $ nvs n n un rnn % rl nrs mpun l $ nvs n n un rnn % rl nrs mpun rl Ers : Rp Ers u ns mpu w mu $$$ wll n un r rs Ers : Rp Ers u ns mpu w ln wll k nl ps ul Ers : Rp Ers u ns mpu w ln wll k r nl ps rpl Ers : Rp Ers Ers n Ers u unr ssumpn un rns nrs mpun nnuusl Lur # mwrk rss Ers : In r ppulns As n Lkj ws mlln Bu rw r As ws % wrs rw r Lkj ws jus % Assumn ppulns rw pnnll sm r ppulns n r n r Ers : In r ppuln Pu ws mlln n ppuln Mnv ws mlln Bu rw r Pu ws % wrs rw r Mnv ws jus % Assumn ppulns rw pnnll sm r ppulns n r n r Hw ln wll k r r ppulns sm? Ers : In r ppuln Qzws ws mlln n ppuln Erv ws mlln T rw r Qzws ws % wrs rw r Erv ws % Assumn ppulns rw pnnll sm r ppulns n r n r Hw ln wll k r r ppulns sm? Hw ln r rs mlln n ppuln? Ers : T l-l n- s s Hw mu -rm smpl wll rmn r s? Ar s? Ar wks? Ers : T l-l rum- s rs Hw mu -rm smpl wll rmn r rs? Ar rs? Ar nurs? Ers : T l-l plunum- s rs Hw mu -rm smpl wll rmn r rs? Ar rs? Ar rs? Hw ln wll k r r jus rms l? Ers : T l-l rum- s rs Hw mu -rm smpl wll rmn r rs? Ar rs? Hw ln wll k r r jus rms l?
14 Lur # mwrk rss Ers : Cnvr llwn nls rm rs n rns w r r n rs! l k j Ers : Cnvr llwn nls rm rns n rs vn u rn r Ers : Fn rn rmnl nls r nl n Ers Pls v r msurmns n rs n rns w r r n rs! Inlu psv n nv nls n ur nswrs Ers : Cnvr llwn nls rm rs n rns w r r n rs! u us ur lulr Run ur nswrs w ml pls Ers : Sk llwn nls n n s w qurn nns rmnl s s nls r s n w s rmnl s ls l k j Lur # mwrk rss Ers : Gv rrn nl n rns r llwn nls Inlu sk jus ur nswrs Ers : Evlu s n lss usn rrn nls n lulrs! Inlu sks n ll rrn nls s sn s sn sn s sn s Ers : Evlu s n lss usn rrn nls n lulrs! Inlu sks n ll rrn nls s sn s sn sn s sn s Lur # mwrk rss Ers : Mmrz un rl T s mmrz vlus sn n sn unns ll n nls msur n rs n rns ll w run un rl Fr rr m r wll m quz n lss n m m quz nvlvn lln m s n sn n sn vlus An u ll nl v mnus M
15 Lur # mwrk rss Ers : In pr n mplu n llwn sn urvs Ers : Blw r rps sn n s rspvl Fn rns ll pns N ll ll rns r r - - ½ ½ r Lur # mwrk rss Ers : B mnn mplu n rznl s llwn rps rmn n qun r n E nswr wll rm Asn C r As C
16 Ers : Fr llwn sn urvs rmn mplu n rznl s sn s s sn s z sn z Ers : Sk n pr rps unns n Ers usn skn n ss nqu uln n ns Ll ll pks vlls n nrps Lur # mwrk rss Ers : E llwn rps rprsns unn rm Asn B r As B Ar nn pr n mplu rmn n pprpr qun r rp r r mn pssl nswrs!
17 Ers : Fr llwn sn urvs rmn mplu pr n rznl s sn s s sn s z sn z Ers : Sk n pr rps unns n Ers usn skn n ss nqu ulns n ns Ll ll pks vlls n nrps Lur # mwrk rss Ers : Gv quns llwn rps All r rm n B C r B C N: r s mr n n slun pssl r rp! Ers : Fn quns llwn rps All r rm As C r As C N: r s mr n n slun pssl r rp!
18 Ers : Blw s rp s Fn rns ll pns - - Ers : Blw s rp Fn rns ll pns N ll ll rns r r - - r Ers : Blw s rp s Fn rns ll pns N ll ll rns r r - r Ers : Blw s rp n Fn rns ll pns N ll ll rns r r - - r
19 Ers : Sk n pr llwn r unns B sur n ll ll nrps smps ll m s n ll mn s n pur Pls sk s lr rps n ss s n n lss n s k s Lur # mwrk rss Ers : Tru r ls! I ls pln w s ls n w u ul n smn mk ru Slv n wr s sm s sn n rn Slv sn wr s sm s sn n sn Slv s wr s sm s sn n rs rss n n Ers : Evlu llwn n lulrs! rn s n j rsn s n rsn rn sn rs n sn rsn n s n rs s s rn s k s n l rnsns Lur # mwrk rss Ers : Usn ssls r TRIANGLES n -- TRIANGLES n llwn r unn vlus: sn s s sn n n s j s k s l s Ers : Gvn llwn nrmn u lns ss r rnls sk rnls n n n vlus s rnmr unns smlls nl T ss r n T ss r n T ls r n Ers : Gvn llwn prs ls r rnl sk rnls n n n vlus s rnmr unns smllr nl T ls v lns n T ls v lns n T ls v lns n
20 Ers : Gvn llwn prs pnus n r rnl sk rnls n n n vlus s rnmr unns lrr nl pnus pnus pnus Ers : Gvn sn n vlus r v rnmr unns vlu Gvn n n vlus r v rnmr unns vlu Gvn s n vlus r v rnmr unns vlu Gvn s n vlus r v rnmr unns vlu Lur # mwrk rss Ers : Gvn s n s n qurn n vlus r v rnmr unns Rp w n n s n r qurn Rp w s n s n n qurn Rp w n s n qurn Rp w sn n s n r qurn Ers : Smpl llwn prssns s r s pssl n sw ll ur sps! sn n s s s s n n Ers : Drmn lrll llwn unns r vn r nr sn s sn n sn s n sn sn Lur # mwrk rss Ers : Vr llwn rnmr ns n sw ll ur sps! sn n sn s s sn s sn sn s s n s sn n s s s s sn s s sn s sn s n sn n s Ers : Prv n n A n B n A n B n l w rn nls ssu u u! A B Ers : Fr prssn s sn rll ll rn w rlr n smsr! s sn n Prv n sn s N: pr wll lp! s s
21 Lur # mwrk rss Ers : Us sum n rn rmuls r sn s n n smpl llwn prssns sn s s sn sn s s sn ss sn sn n n n n n n Ers : Us sum n rn rmuls r sn s n n vlu llwn prssns sn s n s n sn Ers : Vr llwn ns As lws pls ll n rnmr ns u us w r rrspnn numr n rn sn α β n α n β s α s β sn A Bsn A B sn A sn B sn s sn Lur # mwrk rss Ers : Evlu llwn prssns vn s n s n s qurn sn s n sn s n Ers : Rp Ers w n wr s n r qurn Ers : Us l-nl rmuls vlu llwn prssns sn s n s s n: us ur nswr rm pr sn n: s n rm pr Ers : Vr llwn ns As lws pls ll n rnmr ns u us w r rrspnn numr n rn sψ n ψ n ψ sn sn s s s s sn n n n
22 Lur # mwrk rss Ers : Us pru--sum n sum--pru rmuls nssr! smpl llwn prssns s r s pssl An n lulrs r llw! s sn sn sn sn s ] s [s s sn s s s s sn sn s s sn sn j Ers : Vr llwn ns As lws pls ll n rnmr ns u us w r rrspnn numr n rn n n n n sn sn sn sn n s s sn sn τ σ τ σ τ σ β α β α β α Lur # mwrk rss Ers : Fn ll sluns llwn r quns n sn s s s sn s sn s Ers : Fn ll sluns llwn r quns n sp nrvl r s s sn s s n sn Ers : Fn ll sluns llwn qur r quns wr rmmr ur rn ruls! s n s s sn sn s s s s sn
23 Lur # mwrk rss Ers : Us Lw Sns slv llwn rnls S nrmn rsuls n rnl rnls r n rnls Us ur lulr nl wn w nls r n n α α β α β β γ β α γ β β j α k α Ers : A lpl s nll s n run s s n sr up n wn Ar wlkn rm s lpl n sm rn pl s lnn nl lvn p pl s Hw mn rs s lpl rm n prpnulr run? Hn: rw pur! Ers : Rr sn Alp s l mls u su rr sn B B sns mk rr n w UFO Sn Alp ns n nr u s n sn B ns n su u s Hw r s sn rm UFO? An rw pur! Lur # mwrk rss Ers : Us Lw Csns slv llwn rnls Onl us ur lulr nl wn w nls r n n γ α α α β α α j k Ers : A lpl s nll s n run s s n sr up n wn In s n prpnulr run I J wlks rm s lpl n rn pl s lnn n lks p pl w s nl lvn n w sul lk? Hn: rw pur! Ers : Rr sn Alp s l mls u su rr sn B B sns mk rr n w UFO Sn Alp ns UFO s mls w n s ln Sn B ns UFO s mls w n sr ln Hw mn rs nr u s s UFO l rm sn Alp? Lur # mwrk rss Ers : Gvn llwn prs pns A n B l v r vr w nl pn A n rmnl pn B r mpu v r n rp rsuln vr v r n pln A B A B A B A B A B A B
24 Ers : F: w vrs r nsr nl v sm rn n sm ln Drmn w nn--s vrs n Ers r nl vrs Ers : Tk vr mnn w nn-- vrs rm prs n n Ers n sk r sum n pln Ers : Sk llwn vrs n pln w vn nl pns r v > ; r z > ; r w > ; r > ; r u > ; r > ; r r r r r r Ers : L rr s vrs n prs n Ers rspvl n n mpu llwn sums rn n slr mulpls r r r r r r r r r r r r r r r r r r r Ers : Fr llwn vrs mpu v r n un vr n sm rn s v r r r r r v > v > v > v > Lur # mwrk rss Ers : Gvn llwn nrmn wr wn qun prl n snr rm T vr s n us s T rr s n us s T rr s s smmr s T us s n rr s T vr s n rr s p n us s p n prl pns wn Hn: r r w pssl prls; n m! Ers : Sk prls rm ls rs; sur n rrl ll us vr rr n ll nrps prl Ers : Pu llwn quns prls n snr rm n n n s v vlu p s wll s rns us n vr n v qun rr p z z z s Lur # mwrk rss Ers : Gvn llwn ps nrmn wr wn qun llps n snr rm T npns n mjr n mnr s r n T nr s n pns n mnr s r n n T r n n T nr s r s us n Tr s vr s nrs us s vr s n nr s Tr s us n Hn: r r ur pssl llpss; n m ll!
25 Ers : Sk llpss rm ls rs Ers : Pu llwn quns llpss n snr rm n n n s v rns nr vrs n lns mjr n mnr s Lur # mwrk rss Ers : Gvn llwn nrmn wr wn qun prl n snr rm T rnrs r ± ± n r s vr T rnrs r ± ± Hn: r r w pssl quns Fn m! T prl pns l n r n sln smps r vn ± T ln rnsvrs n nju s r n prl pns up n wn n nr s T ln rnsvrs n nju s r n prl pns l n r n nr s n nr s Hn: r r w pssl prls; n m! Ers : Sk prls rm ls rs Ers : Pu llwn quns prls n snr rm n n n s v rns nr vrs quns rnsvrs n nju s n quns sln smps Lur # mwrk rss Ers : Us Lw Sns slv llwn rnls S nrmn rsuls n rnl rnls r n rnls Us ur lulr nl wn w nls r n n α α β β γ α β γ β β α β α α k j Ers : Rr sn Alp s l mls u su rr sn B B sns mk rr n w UFO Sn Alp ns n nr u s n sn B ns n su u s Hw r s sn rm UFO? Hn: rw pur!
26 Lur # mwrk rss Ers : Us Lw Csns slv llwn rnls Onl us ur lulr nl wn w nls r n n γ α α α β α α j k Ers : Rr sn Alp s l mls u su rr sn B B sns mk rr n w UFO Sn Alp ns UFO s mls w n sr ln Sn B ns UFO s mls w n sr ln Hw mn rs nr u s s UFO l rm sn Alp? Lur # mwrk rss Ers : Gvn llwn ps nrmn wr wn qun prl n snr rm T vr s n us s T rr s n us s T rr s s smmr s T us s n rr s T vr s n rr s p n us s p n prl pns wn Hn: r r w pssl prls; n m! Ers : Sk prls rm ls rs; sur n rrl ll us vr rr n ll nrps prl Ers : Pu llwn quns prls n snr rm n n n s v vlu p s wll s rns us n vr n v qun rr p z z z s Lur # mwrk rss Ers : Gvn llwn ps nrmn wr wn qun llps n snr rm T npns n mjr n mnr s r n T nr s n pns n mnr s r n n T r n n T nr s r s us n Tr s vr s nrs us s vr s n nr s Tr s us n Hn: r r ur pssl llpss; n m ll! Ers : Sk llpss rm ls rs Ll ll vrs n nrps Ers : Pu llwn quns llpss n snr rm n n n s v rns nr vrs n lns mjr n mnr s
27 Lur # mwrk rss Ers : Gvn llwn ps nrmn wr wn qun prl n snr rm T rnrs r ± ± n r s vr T rnrs r ± ± Hn: r r w pssl quns Fn m! T prl pns l n r n sln smps r vn ± j T ln rnsvrs n nju s r n prl pns up n wn n nr s k T ln rnsvrs n nju s r n prl pns l n r n nr s l n nr s Hn: r r w pssl prls; n m! Ers : Sk prls rm ls rs Ll ll vrs n nrps Ers : Pu llwn quns prls n snr rm n n n s v rns nr vrs quns rnsvrs n nju s n quns sln smps
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