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30 9999999999999999 20 V$=" wwedite otwet" 20 V$=" wwedite nomer otweta": 20 P;" ": 20 ;"znakomitxsq!"; 20 ;"wa%e imq"; 20 ;"u@itelq!": 20 ;"temy zada@ werno" 20 ;"tema ";W 20 ;"priglasi"; 20 ;"o@enx priqtno,"; 20 ;"napi%ite"; 20 ;"i navmite"; 20 ;"dlq wyhoda w men# wwedite"; 20 ;"dawajte"; 20 ;"a menq zowut"; 20 ;" prawilxno ! ": 20 ;" newerno ! ": 20 ;" ENTER ": 20 ;" ENTER " 20 ;" N wsego"; 20 ;" i navmite "; 20 ;" ": 20 ;" " 20 ;" ": 20 ;" ": 20 ;" ": 20 "normalxno!tak","dervatx!!!" 20 "4";"DISK VERSION BY NRS SOFT"; 20 "10";"MOSCOW 1991": 20 ", zatem"; 20 " Otli@no!! ty","prosto molodec!!" 20 " ploho!!"," ty ne gotow!" 19 V$=" otwe@ajte D(d) ili N(net)": 19 ;" m e n # "; 19 ;" "; 18 S2=S2+o(J,2 18 S1=S1+o(J,1 18 ;"ENTER.": 16 ;"impulxs!": 16 "","","","","","","" 14 ;"potehe @as!": 13 ;"zdrawstwujte!" 12 ))))))))))) 11 ;"delu wremq-"; 7 "","","","","" 6 k(I),l(I): 6 ;"zdrawstwujte!!" 6 ;"tema 2:"; 6 ;"tema 1:"; 6 ;"tema 1:" 6 ;"delu wremq -"; 6 :::::::::::: 6 99999999999999 6 9999999999 6 )))))))))))) 6 )!!!!!!!!!))) 5 999999999999 5 ,","razdelqq ih zapqtymi.","","","" 5 "","","","","","","","","","","","" 4 ;"tema 2:" 4 ;"parno perpendikulqrny."; 4 ;"najdite dlinu otrezka"; 4 ;"impulxs": 4 ;"TEMA 2:" 4 ;"CD, esli:"; 4 ;" lelepipeda po trem ego"; 4 ;" otwet wwesti w wide:"; 4 ;" ( 4 889999889999 4 .","","","" 4 ","","","" 4 .","","","","" 4 wwedite otwetN 3 yrlf`[VQLHD@=9630-+(&$" 3 aws.","ploskostx,parallelxnaq","prqmoj aw,peresekaet","storonu as _togo","treugolxnika w to@ke a 3 =20,",""," 3 ;"w granqh dwugrannogo"; 3 ;"ugla,opu&eny perpendi-"; 3 ;"ty,prowedena ploskostx"; 3 ;"storona osnowaniq 3 ;"rebro ugla."; 3 ;"prawilxnyj mnogougolx-"; 3 ;"potehe @as": 3 ;"postroennogo se@eniq." 3 ;"osnowaniq." 3 ;"osnowaniq i protiwoleva-"; 3 ;"kulqry aa1 i ww1 na"; 3 ;"golxnoj prizme,u kotoroj"; 3 ;"bokowye storony kwadra-"; 3 ;"@erez storonu nivnego"; 3 ;"2. najdite diagonali"; 3 ;"1.iz to@ek a i w,leva&ih"; 3 ;"1. w prawilxnoj %estiu-"; 3 ;"&u# ej storonu werhnego"; 3 ;" izmereniqm: 3 ;" najdite plo&adx"; 3 ;" ": 3 999:::9999 3 999999:::999 3 88888888888888888888888888888888889)))))))))))))9))))))))))8888888(((((9)))))))))))))((((((88888 3 .","najdite dlinu otrezka","ww 3 ."," nadite dlinu","otrezka mm 3 ,esli aw","ne peresekaet ploskostx","i esli aa 3 ,","a storonu ws w to@ke"," w 3 ,"," 3 )))))))))))))@ 3 )))))))))))))))))))) 3 )))))))))) 3 "@erez konec a otrezka aw","prowedena ploskostx.","@erez konec w i to@ku s","_togo otrezka prowedeny","parallelxnye prqmye,","pereseka#&ie ploskostx","w to@kah w 3 "@erez koncy otrezka aw","i ego seredinu m prowe-","deny parallelxnye prq-","mye,pereseka#&ie nekoto-","ru# ploskostx w to@kah","a 3 "","dany storona i dwa","","ugla treugolxnika: 3 "","","","","","","","","","","","","","","","","" 3 "",""," dany storona i dwa","ugla treugolxnika:"," 3 " dan treugolxnik 3 HELLO ! WELCOME TO GEOMETRY. PRESS ANY KEY TO CONTINUE (C) 1991 RT - SOFT LAB. 3 .","najdite dlinu otrezka","a 3 ,","esli 2 x(I),y(I): 2 prosto molodec!! 2 aws,","<a=40 2 B$="6,28": 2 B$="4,25": 2 B$="2,1,-2": 2 B$="14sm": 2 A$="62.8": 2 A$="6.28": 2 A$="4.25": 2 A$="2,1,-2": 2 A$="0,0,1": 2 ;"use@ennogo konusa"; 2 ;"u@enxe - swet,"; 2 ;"tema 3:"; 2 ;"tema 3:" 2 ;"rasstoqniq ot to@ek A i"; 2 ;"prqmougolxnika, esli"; 2 ;"osewogo se@eniq." 2 ;"nik, esli kavdyi iz"; 2 ;"najdite dlinu otrezka"; 2 ;"lomanoj;"; 2 ;"golxnika,esli ego"; 2 ;"dwugrannyj ugol rawen"; 2 ;"a neu@enxe -"; 2 ;"TEMA 2:"; 2 ;"TEMA 1:"; 2 ;"TEMA 1:" 2 ;"B do ploskosti rawny"; 2 ;"3. skolxko storon imeet"; 2 ;"2. radiusy osnowanij"; 2 ;"2. prqmye AB,AC,AD po-"; 2 ;"1. prqmye AB,AC,AD po-"; 2 ;"1. osnowanie piramidy -"; 2 ;"1. @emu rawny storony"; 2 ;" prqmougolxnogo paral-"; 2 ;" prqmougolxnogo paral-"; 2 ;" 3.2sm i 5.3sm." 2 ;" otwet wwedite @erez"; 2 ;" najdite rasstoqnie"; 2 ;" najdite koordinaty"; 2 ;" zapqtu#." 2 ;" "; 2 ...","...a 2 .","","najdite storonu 2 .","","","","" 2 ,to prqmaq 2 ,","razdelqq ih zapqtymi.","","" 2 )-x(I),y(I+1 2 )-k(I),y(I-1 2 )-k(I),l(I+2 2 "PLANIM_30" 2 "PLANIM_22" 2 ","","","","","","","","","","","","","","","" 2 ","","","","","","" 2 ",""," V:V 2 "," ADD 2 "," ABB 2 "," 2 "","najdite to@ku pere-","se@eniq treh ploskostej,","zadannyh urawneniqmi:"," 1) 2 "","dany tri to@ki a(1,0,1),","w(-1,1,2),s(0,2,-1) .","najdite to@ku D( 2 "","","w treugolxnike 2 "","","","","","","","","","","","","","","","","","","","","","" 2 "","","","","","","","","","","","","","","","","","","" 2 "","","","","","","","","","","","","","","" 2 "","","","","","","","","","","","","","" 2 "","","","","","","","","","","" 2 "","","","","","" 2 "",""," u treugolxnika 2 "",""," dany storona i dwa ","ugla treugolxnika.","najdite storonu 2 ""," najdite postoqnnye"," 2 " 360 2 .","najdite storonu 2 wwedite otweth 2 wwedite otwetT 2 otwe@ajte D(d) ili N(net)T 1 x(I)-k(I),y(I)-l(I): 1 wpisannyj w ok-","ruvnostx osnowaniq konu-" 1 snum=snum+1 1 s=5:3 .","","" 1 s=10 sm ,","aw:ws=4:5 .","","" 1 parallelxnostx prqmyh i ploskostej . ( @astx 1 ) 1 9 9 1 g o d . 1 mnogougolxniki (@astx 1) obu@a#&ij kurs 1 graf24 CX 1 graf23 CX 1 graf22 CX 1 graf21 CX 1 dekartowy koordinaty i wektory w prostranstwe ( @astx 2 ) 1991 god. 1 aws' qwlqetsq orto-" 1 aws","storony aw=5.1 sm ,","ws=6.2 sm , as=7.3 sm .","kakoj iz uglow"," naimenx%ij?",""," 1) a 2) w 3) s","" 1 aws","storony aw=5.1 sm ,","ws=6.2 sm , as=7.3 sm .","kakoj iz uglow"," naibolx%ij?",""," 1) a 2) w 3) s","" 1 aws na ploskostx 1 aplanim40B 1 agraf40 CX 1 aboot B 1 a$="36',72',108',144'": 1 a$="12,5": 1 [planim39B-SaQT 1 [graf39 CX 1 [PLANIM40BU 1 YD=(YK-YN): 1 XD=(XK-XN): 1 XD*XD<YD*YD 1 X', togda","to@ki X i X' nazywa#tsq","simmetri@nymi otnosi-","telxno ploskosti 1 Wplanim38B 1 Wgraf38 CX 1 WPLANIM39BU 1 V$=" otwe@ajde D(d) ili N(net)": 1 SPLANIM38BU 1 S .","","","" 1 Rplanim37B 1 Rgraf37 CX 1 RH","",""," R - radius sfery,"," H - wysota segmenta.","","","","","","" 1 RH","",""," R - radius cilindra,",""," H - wysota.","" 1 R/180,A uglu w 1 R.uglu w 1 1 R","","","","","","","","","","","","" 1 PLANIM25BU 1 PLANIM24BT 1 PLANIM23BT 1 PLANIM22BT 1 PLANIM21BT 1 Mplanim36B 1 Mgraf36 CX 1 MPLANIM37BU 1 H ,"," 3","H-wysota sootwetstwu#&e-","go %arowogo segmenta,","R-radius %ara","","" 1 H ,gde","","", " R-radius osnowaniq," 1 H ,gde"," 3" 1 Gplanim35B 1 Ggraf35 CX 1 GPLANIM36BU 1 Cplanim34BHE 1 Cgraf34 CX 1 CPLANIM35BU 1 B$="94,2": 1 B$="88,62": 1 B$="75sm": 1 B$="65,78": 1 B$="6366,2": 1 B$="62.8": 1 B$="62,8": 1 B$="60,300": 1 B$="6.5CM": 1 B$="6,75": 1 B$="480sm": 1 B$="4800": 1 B$="4.5,1.33": 1 B$="39sm": 1 B$="37,5": 1 B$="36,72,108,144": 1 B$="35200m 1 B$="3,66": 1 B$="3,-1,-1,6": 1 B$="251,2": 1 B$="25,12": 1 B$="22sm.": 1 B$="2,59": 1 B$="18,8": 1 B$="170,190": 1 B$="17,93": 1 B$="15sm": 1 B$="15CM": 1 B$="15,6": 1 B$="14,64": 1 B$="130,230": 1 B$="13/20": 1 B$="12sm.": 1 B$="12.5": 1 B$="105.": 1 B$="0.3M": 1 B$="0.13": 1 B$="0,028": 1 B$="-2,3,0": 1 B$="-2,-7,-28": 1 B$="-2,-2,1,9": 1 B$="-0.5,-0.5,-0.5,0.75": 1 B$="(6,2,-2)": 1 B$="(0,1,-2)": 1 B$="(0,-1,3)": 1 B$="(-1,0,3)": 1 B$="(-1,-2,1)": 1 B$="(-1,-2,-3)": 1 B$=" 188": 1 B$=" 1464": 1 B"," parallelogramm." 1 ABC wosstanowlen per-"; 1 A$="94.2": 1 A$="9/2,4/3": 1 A$="88.62": 1 A$="8,18": 1 A$="65.78": 1 A$="6366.2": 1 A$="6.75": 1 A$="6,15": 1 A$="4800": 1 A$="37.5": 1 A$="360'": 1 A$="35200": 1 A$="300,60": 1 A$="3.66": 1 A$="3,-1,-1,6": 1 A$="251.2": 1 A$="230,130": 1 A$="2.59": 1 A$="190,170": 1 A$="17.93": 1 A$="1464": 1 A$="14.64": 1 A$="12,25": 1 A$="0.65": 1 A$="0.13M": 1 A$="0.028": 1 A$="-2,3,0": 1 A$="-2,-7,-28": 1 A$="-2,-2,-1,9": 1 A$="-1/2,-1/2,-1/2,3/4": 1 A$="(6,2,-2)": 1 A$="(0,1,-2)": 1 A$="(0,-1,3)": 1 A$="(-1,0,3)": 1 A$="(-1,-2,1)": 1 A$="(-1,-2,-3)": 1 ?planim33B 1 ?graf33 CX 1 ?PLANIM34BU 1 >0, esli t. 1 =8.3 sm, ","ww 1 =8.1 sm ,"," aw:ws=11:9 .","","" 1 =8","","wwedite zna@eniq 1 =7 m.","","" 1 =6 (prawilxnyj"," %estiugolxnik)","" 1 =4.8 dm.","","" 1 =4.1 sm.","","" 1 =3.6 dm, ","ww 1 =3"," 3)3 1 =3 (rawnostoronnij"," treugolxnik).",""," 1 =2:5 .","","" 1 =15 sm ,"," as:ws=2:3 .","","" 1 =1"," 2) 1 =0, esli t. 1 =0"," 3)2 1 =",""," =CC 1 ="," 2 2","=180 1 ="," = 1 <0, esli T. 1 ;"zwenxew dlinoj 1m, 2m,"; 1 ;"zemli,k domu,gde ee pri-"; 1 ;"zapqtu#, na@inaq s"; 1 ;"wysoty?" 1 ;"wysotu,@toby obxem uwe-"; 1 ;"wysota 3 m."; 1 ;"wse bokowye rebra"; 1 ;"wpisan cilindr." 1 ;"wnutrennih uglow rawen"; 1 ;"wne%nij"; 1 ;"wne%nih uglow wypuklo-"; 1 ;"wne%nih uglow rawen"; 1 ;"welikij cilindr,"; 1 ;"waniq cilindra,ne menqq"; 1 ;"wanii bytx kwadratom?" 1 ;"waniem 14 m. werhnee"; 1 ;"w odin %ar dwa %ara s"; 1 ;"w 16 raz ?" 1 ;"w D a"; 1 ;"vatx na odnoj prqmoj?" 1 ;"vat w odnoj ploskosti."; 1 ;"uweli@itx wysotu cilin-"; 1 ;"uweli@itx radius osno-"; 1 ;"uweli@itsq plo&adx"; 1 ;"use@en-"; 1 ;"ugolxnoj prizme plo-"; 1 ;"uglow."; 1 ;"u kotorogo wysota rawna"; 1 ;"trom okruvnosti,opisan-"; 1 ;"tri iz nih levatx na"; 1 ;"tretx# prqmu#,ne leva-"; 1 ;"trapecii, u kotoroj"; 1 ;"trapecii s nivnim osno-"; 1 ;"tralx-"; 1 ;"to@ki,esli oni levat"; 1 ;"tetra_dr"; 1 ;"takoj ve wysoty."; 1 ;"storonami 9 m i 12 m."; 1 ;"stoqnie ot to@ek A i B"; 1 ;"stoqnie ot nego do osi." 1 ;"stoqnie mevdu koncami"; 1 ;"stolba,gde ona prikrep-"; 1 ;"sq po prqmoj 1 ;"sq li @etyrehugolxnik"; 1 ;"sostoqtx iz @etyreh"; 1 ;"sootwetstwenno rawny"; 1 ;"sm.,a wysota 14 sm."; 1 ;"skolxko kubi@eskih"; 1 ;"skolxko %arikow diamet-"; 1 ;"serediny otrezka AB do"; 1 ;"seka#&aq odnu iz _tih"; 1 ;"sD peresekatxsq?" 1 ;"rom 1 sm movno otlitx"; 1 ;"rehugolxnika proporci-"; 1 ;"rebrom." 1 ;"rebra rawny 9 sm." 1 ;"raznostx proekcij _tih"; 1 ;"rawnye 10sm i 17sm."; 1 ;"rawny."; 1 ;"rawny 37sm,13sm i"; 1 ;"rawny 1sm i 7sm." 1 ;"rawny 12.5 m."; 1 ;"rawnobedrennyj treu-"; 1 ;"rawnobedrennogo treu-"; 1 ;"rawno 1.5m, mevdu 1 ;"rawno 0.8m." 1 ;"rawna 12 kw.m."; 1 ;"rawen 150 1 ;"rasstoqnie mevdu 1 ;"ramidy sowpadaet s cen-"; 1 ;"ralxnaq"; 1 ;"rallelxnom proektiro-"; 1 ;"rallelogramma pri pa-"; 1 ;"radiusami: 4 i 6 sm." 1 ;"radius osnowaniq 5 sm."; 1 ;"radius osnowaniq 5 dm."; 1 ;"prqmougolxnik so"; 1 ;"prowesti @erez nih dwe"; 1 ;"prowedeny dwe naklonnye."; 1 ;"prowedeny dwe naklonnye,"; 1 ;"prowedennogo parallelxno"; 1 ;"protiwoleva&im bokowym"; 1 ;"prizme wse rebra"; 1 ;"prewratitx w rawno-"; 1 ;"prawilxnyj mnOgougolx-"; 1 ;"prawilxnaq treugolx-"; 1 ;"pqti zwenxew, dlinoj"; 1 ;"powerhnostx _togo paral-"; 1 ;"potehe @as"; 1 ;"polu@itxsq trapeciq?" 1 ;"pod uglom 30'."; 1 ;"ploskostx w to@kah a 1 ;"ploskostx @erez tri"; 1 ;"ploskosti?" 1 ;"ploskosti.@erez to@ki"; 1 ;"ploskosti, ne pereseka#-"; 1 ;"ploskosti osnowaniq"; 1 ;"ploskostej prowedeny"; 1 ;"ploskostej ne perese-"; 1 ;"ploskij"; 1 ;"plo&adi kruga,wpisan-"; 1 ;"plo&adi kruga,opisan-"; 1 ;"piramidy.)" 1 ;"piramida" 1 ;"pereseka#&ie wtoru#"; 1 ;"perese@eniq dwuh dan-"; 1 ;"pede storony osnowaniq"; 1 ;"parallelxnye storony"; 1 ;"parallelxnye prqmye,"; 1 ;"parallelxnye plos-"; 1 ;"otwet wwedite @erez"; 1 ;"otwet okruglitx do"; 1 ;"otwe@ajte w wide 5:3"; 1 ;"ot stolba do doma?" 1 ;"ot serediny otrezka AB"; 1 ;"osnowaniq _togo"; 1 ;"osnowanij." 1 ;"osnowanij naklonnyh dan-"; 1 ;"osnowanie i wysota"; 1 ;"osnowanie 120 m, a bo-"; 1 ;"osnowanie 120 m, a bo-" 1 ;"osnowa-"; 1 ;"osi cilindra na rasstoq-"; 1 ;"oni otnosqtsq kak 4:9,"; 1 ;"onalxny @islam 1,2,3,"; 1 ;"okta_dr" 1 ;"okruvnostqmi s odnim"; 1 ;"okruvnostqh oboih "; 1 ;"okruv-"; 1 ;"odnoj prqmoj?" 1 ;"odnoj desqtoj diametra"; 1 ;"odinakowye perimetry."; 1 ;"obxemow cilindrow."; 1 ;"obrazu#-"; 1 ;"obrazu#&aq - 5 dm." 1 ;"nyj ugol"; 1 ;"nyh prqmyh prowesti"; 1 ;"nyh ploskostqh.qwlqet-"; 1 ;"nyh ploskostej."; 1 ;"ny perpendikulqry AC i"; 1 ;"nowogo %ara ?" 1 ;"noj prizme rasstoqnie"; 1 ;"noj okolo osnowaniq"; 1 ;"noj nasypi imeet wid"; 1 ;"noj dliny, prowedennyh"; 1 ;"nogo w nego." 1 ;"nogo okolo kwadrata, k"; 1 ;"nik, u kotorogo kavdyj"; 1 ;"nik, esl 1 ;"nii parallelogramma" ; 1 ;"nii 4 sm ot nee." 1 ;"neparallelxnye 13 i"; 1 ;"naq prizma ,a w prizmu"; 1 ;"naklonnyh rawna 9sm."; 1 ;"najdite wysotu." 1 ;"najdite rasstoqnie"; 1 ;"najdite plo&adx"; 1 ;"najdite plo&adx se@eniq,"; 1 ;"najdite otno%enie"; 1 ;"najdite obxem piramidy."; 1 ;"najdite obxem piramidy." 1 ;"najdite obrazu#&u#." 1 ;"najdite krat@aj%ee ras-"; 1 ;"najdite dwugrannyj ug-"; 1 ;"najdite dliny naklonnyh,"; 1 ;"najdite dlinu"; 1 ;"najdite diagonalx"; 1 ;"naidite zna@eniq _tih"; 1 ;"na odnoj prqmoj?" 1 ;"na 1 km nasypi ?" 1 ;"movet li prqmaq,pere-"; 1 ;"movet li _ta lomanaq"; 1 ;"mogut li prqmye aw i"; 1 ;"mogut li ploskosti 1 ;"mogut li kakie-nibudx"; 1 ;"mogut li _ti to@ki le-"; 1 ;"mevdu prqmymi,soderva-"; 1 ;"mevdu prqmymi 1 ;"mevdu ploskostx# bolx-"; 1 ;"metrow zemli prihoditsq"; 1 ;"menx%ego zna@eniq." 1 ;"massoj 1 kg."; 1 ;"m e n #": 1 ;"lqrnyh ploskostqh opu&e-"; 1 ;"lomanoj." 1 ;"lomanoj rawnqtxsq 27m?" 1 ;"lomanaq sostoqtx iz"; 1 ;"llelxny ploskosti 1 ;"li@ilsq w 16 raz ?" 1 ;"levat w odnoj ploskos-"; 1 ;"lena na wysote 8m ot"; 1 ;"lelxnom proektirowa-"; 1 ;"lelepipeda." 1 ;"kwadrata, esli ego"; 1 ;"kruga, esli ego"; 1 ;"krepili na wysote 20m." 1 ;"kowaq storona 100 m." 1 ;"koncy dannogo otrezka" 1 ;"kavdoj iz dwuh razli@-"; 1 ;"katx drugu#?" 1 ;"kakaq iz figur imeet"; 1 ;"ka#&ej _tot otrezok,esli"; 1 ;"iz kuska ?"; 1 ;"iz dannoj to@ki estx:"; 1 ;"iz wnutrennih uglow"; 1 ;"ikosa_dr" 1 ;"i tem ve centrom i"; 1 ;"i 22 sm) trebuetsq"; 1 ;"grammom?" 1 ;"gowogo kolxca,zakl#-"; 1 ;"golxnik so storonami 6,"; 1 ;"go 9-ugolxnika?" 1 ;"esq prqmye.movno li"; 1 ;"esli oni otnosqtsq, kak"; 1 ;"ego perimetr = 74 dm"; 1 ;"edinq#&ego koncy"; 1 ;"dra,ne menqq osnowanie,"; 1 ;"do ploskosti, ne perese-"; 1 ;"do ploskosti rawno 7.4sm"; 1 ;"dlinoj 15m protqnuta ot"; 1 ;"dlinoj 10 dm levat na"; 1 ;"diametrami 25 i 35 sm."; 1 ;"diametr"; 1 ;"diametr uweli@itx:" 1 ;"diamet-"; 1 ;"diagonalx rawna 12 m." 1 ;"diagonali prizmy." 1 ;"delu wremq - "; 1 ;"cilindra ?" 1 ;"cilindra 2 m,"; 1 ;"celogo." 1 ;"cami lomanoj rawno 11m"; 1 ;"bolx%u# plo&adx ?"; 1 ;"bolx%oj"; 1 ;"bolx%aq"; 1 ;"bokowaq powerhnostx"; 1 ;"aw,esli:"; 1 ;"apofema" 1 ;"aa1=3,ww1=4,aw=7 i"; 1 ;"aa1=3,ww1=4,a1w1=6 i"; 1 ;"a1w1=6 i aw=7 ?" 1 ;"a1w1,esli:"; 1 ;"a i w odnoj iz _tih"; 1 ;"a ego plo&adx = 3 m 1 ;"a ego plo&adx = 144 m 1 ;"TEma 3:"; 1 ;"TEma 2:"; 1 ;"TEma 1:"; 1 ;"TEMA 4:"; 1 ;"TEMA 3:"; 1 ;"NUMBER TOO BIG": 1 ;"NUMBER TO START (0-RESTART):";an 1 ;"FILE ";r$;" NOT FOUND !" 1 ;"F D C" 1 ;"D E C F" 1 ;"D A B" 1 ;"D C" 1 ;"C 6.2 B" 1 ;"BD=9CM,BC=16CM,AD=5CM" 1 ;"B C"; 1 ;"AB=3CM,BC=7CM,AD=1.5CM" 1 ;"A D B"; 1 ;"A E B" 1 ;"A E B" 1 ;"A D"; 1 ;"A D"; 1 ;"A C"; 1 ;"A B"; 1 ;"@toby obxem uweli@ilsq"; 1 ;"@etyreh zwenxew 3m,5m,"; 1 ;"@ennogo mevdu dwumq"; 1 ;"@emu rawna dlina"; 1 ;"@emu rawen radius"; 1 ;"@emu rawen diametr"; 1 ;"8 i 3.2 m." 1 ;"7m, 11m. movet li ras-"; 1 ;"7.3 5.1"; 1 ;"6m i 8m obrazu#t ugol"; 1 ;"60 i 20 sm, a"; 1 ;"6 i 8 sm. wse bokowye"; 1 ;"4. kaku# @astx obxema"; 1 ;"3m, 4m?" 1 ;"3.w prqmoj treugolxnoj"; 1 ;"3.w prawilxnoj @etyreh-"; 1 ;"3.w naklonnoj treugolx-"; 1 ;"3. wo skolxko raz"; 1 ;"3. wo skolxko raz nado"; 1 ;"3. w prqmougolxnom pa-"; 1 ;"3. w prqmom parallelepi-"; 1 ;"3. trebuetsq pereplawitx"; 1 ;"3. summa dlin zwenxew"; 1 ;"3. najdite plo&adx kru-"; 1 ;"3. najdite otno%enie"; 1 ;"3. najdite powerhnostx"; 1 ;"3. imeetsq kusok swinca"; 1 ;"3. skolxko storon imeet"; 1 ;"3 m, 6 m, wysota 4 m."; 1 ;"3 dm, 7 dm,"; 1 ;"25 sm naklonena k"; 1 ;"2.skolxko wer%in imeet"; 1 ;"2.skolxko reber imeet"; 1 ;"2.skolxko granej imeet"; 1 ;"2. wo skolxko raz nado"; 1 ;"2. w cilindr wpisana"; 1 ;"2. use@enyj konus"; 1 ;"2. obrazu#&aq konusa"; 1 ;"2. najdite plo&adx"; 1 ;"2. movno li prowesti"; 1 ;"2. movet li proekciq pa-"; 1 ;"2. movet li pri paral-"; 1 ;"2. kwadrat i romb ime#t"; 1 ;"2. dlina otrezka, so-"; 1 ;"2. dany dwe parallelxnye"; 1 ;"2. dany dwe ne pereseka-"; 1 ;"2. AC=4M, BD=7M, CD=1M" 1 ;"2. @etyre to@ki ne le-"; 1 ;"2. @emu rawna summa wseh"; 1 ;"2. @emu rawna plo&adx"; 1 ;"2. ugly wypuklogo @ety-"; 1 ;"2. movet li zamknutaq"; 1 ;"2) romb" 1 ;"1m,2m,3m,4m,11m?" 1 ;"1:2,i proekcii naklonnyh"; 1 ;"13 20"; 1 ;"11.4 g/sm 1 ;"10sm,16sm i 22sm." 1 ;"1. wysota cilindra 6 sm,"; 1 ;"1. wysota cilindra 6 dm,"; 1 ;"1. to@ki a,w,s levat w"; 1 ;"1. to@ki a,w,s i D ne"; 1 ;"1. se@enie veleznodorov-"; 1 ;"1. rasstoqnie mevdu kon-"; 1 ;"1. radius osnowaniq"; 1 ;"1. ploskosti 1 ;"1. parallelogrammy awsD"; 1 ;"1. najdite plo&adx"; 1 ;"1. movno li @erez to@ku"; 1 ;"1. koli@estwo zwenxew"; 1 ;"1. iz to@ek A i B, leva-"; 1 ;"1. dlina lomanoj _to:"; 1 ;"1. dany dwe skre&iwa#&i-"; 1 ;"1. AC=6M, BD=7M, CD=6M" 1 ;"1. lomanaq sostoit iz"; 1 ;"1)S3-S2;2)S2-S3;3)S2+S3." 1 ;"1) w 5 raz " 1 ;"1) w 2 raza" 1 ;"1) kwadrat"; 1 ;"-wysota"; 1 ;"," 2*SIN30 1 ;"(ukazanie.osnowanie pi-"; 1 ;"(radiusy osnowanij 4"; 1 ;"( plotnostx swinca"; 1 ;"&u# s nimi w odnoj"; 1 ;"&imi bokowye rebra,"; 1 ;"&ih w dwuh perpendiku-"; 1 ;"&ej otrezok, esli ras-"; 1 ;"&adx osnowaniq 144 kw."; 1 ;"%ej bokowoj grani i"; 1 ;"%arowogo segmenta,"; 1 ;"%ara sostawlqet obxem"; 1 ;"#&iesq ploskosti."; 1 ;" zdrastwujte!!" 1 ;" wyrazite S1 @erez S2"; 1 ;" wwedite @erez zapqtu#)" 1 ;" wtorogo konca otrezka -"; 1 ;" wer%iny D parallelo-"; 1 ;" wenno rawny S1, S2, S3."; 1 ;" weder koni@eskoj formy,"; 1 ;" utwervdenie:@erez l#bu#"; 1 ;" udalennoj ot centra"; 1 ;" treh drugih ego wer%in:"; 1 ;" torogo 12sm."; 1 ;" to@nostx# do 2 znakow)" 1 ;" to@ku prqmoj w prost-"; 1 ;" to@ki, simmetri@noj ej"; 1 ;" to@ki B."; 1 ;" to@ka C - w to@ku D,"; 1 ;" te diametr lista." 1 ;" talla wy%tampowan ci-"; 1 ;" sm i,esli na 1m 1 ;" skolxko olify potrebu-"; 1 ;" serediny _togo otrezka."; 1 ;" sektor kruga imeet ra-"; 1 ;" ronnego treugolxnika"; 1 ;" renose to@ka A(2,1,-1)"; 1 ;" ranstwe movno prowesti"; 1 ;" rallelepipede storony"; 1 ;" radiusa R,ugla 1 ;" radius %ara rawen 15sm."; 1 ;" prqmu#?" 1 ;" pri kotorom to@ka A"; 1 ;" perpendikulqrnu# ej"; 1 ;" perehodit w to@ku"; 1 ;" perehodit w to@ku B,"; 1 ;" pendikulqr AD k plos-"; 1 ;" parallelxnyj perenos,"; 1 ;" parallelepipeda." 1 ;" otwet wwedite @erez"; 1 ;" otwerstie, diametr ko-"; 1 ;" otrezka AB, esli:" 1 ;" otnositelxno na@ala"; 1 ;" ot to@ki D do storony"; 1 ;" osnowaniq rawny 0.7m"; 1 ;" nostej %arow sootwetst-"; 1 ;" noj powerhnosti tela?" 1 ;" niq konusa."; 1 ;" nej powerhnosti 100"; 1 ;" najdite radius osnowa-"; 1 ;" najdite polnu#"; 1 ;" na 0.8m." 1 ;" lq#tsq diametrami treh"; 1 ;" lindri@eskij stakan di-"; 1 ;" levat:"; 1 ;" kotoraq widna iz to@ki,"; 1 ;" kosti treugolxnika."; 1 ;" koordinat."; 1 ;" koni@esku# powerhnostx." 1 ;" ke ne izmenilasx,najdi-"; 1 ;" kaku# plo&adx imeet"; 1 ;" izwestny koordinaty "; 1 ;" izmereniqm:"; 1 ;" i S3."; 1 ;" i 6.1sm." 1 ;" i 30sm,obrazu#&aq 27.5"; 1 ;" i 2.4m, a wysota raw-"; 1 ;" gramma ABCD, esli"; 1 ;" gipotenuza i katety qw-"; 1 ;" etsq dlq pokraski wne%-"; 1 ;" etsq 150 grammow olify?"; 1 ;" esli izwestno:" 1 ;" esli diametry weder 25"; 1 ;" dusow.sektor swernut w"; 1 ;" dius 3m i ugol 120 gra-"; 1 ;" dit na@alo koordinat?"; 1 ;" diagonalxnogo se@eniq"; 1 ;" cilindri@eskoe osewoe"; 1 ;" ametrom 25sm i wysotoj "; 1 ;" D(1,2,0)."; 1 ;" BC,esli AD=15sm,BC=6sm." 1 ;" B(0,1,2), C(0,0,3),"; 1 ;" AB i to@ki C(1,1,1) -"; 1 ;" A(2,3,-1)-konca otrezka"; 1 ;" A'(1,-1,0)."; 1 ;" @emu rawna plo&adx pol-"; 1 ;" @astx ego powerhnosti,"; 1 ;" 50sm."; 1 ;" 3. w ploskosti YZ ? " 1 ;" 3. kwadrat" 1 ;" 2. okruvnostx"; 1 ;" 2. na osi Z ? " 1 ;" 2. A(0,1,2),B(-1,0,1),"; 1 ;" 2 4"; 1 ;" 1. w ploskosti XY ?" 1 ;" 1. krug"; 1 ;" 1. A(-2,3,5),B(1,2,4),"; 1 ;" (plo&adx sektora kruga"; 1 ;" (otwet wwesti w kg s"; 1 ;" (gde neobhodimo,otwet"; 1 ;" &adx lista pri %tampow-"; 1 ;" %arow. plo&adi powerh-"; 1 ;" %ara na 25sm?" 1 ;" %ar radiusa 10sm imeet"; 1 ;" perpendikulqrnye plos-"; 1 ;" najdite rasstoqnie"; 1 ;" VR/& BOOTER B " 1 ;" BD=0.36M, BC=0.64M,"; 1 ;" AB=0.12M, BC=0.28M,"; 1 ;" A(2,3,2), B(0,2,4),"; 1 ;" w kaku# to@ku pereho-"; 1 ;" telefonnaq prowoloka"; 1 ;" pri parallelxnom pe-"; 1 ;" predpolagaq, @to plo-"; 1 ;" najdite rasstoqnie ot"; 1 ;" najdite dlinu"; 1 ;" najdite koordinaty "; 1 ;" kakie iz _tih to@ek"; 1 ;" iz wer%iny rawnosto-"; 1 ;" iz to@ki ploskosti"; 1 ;" iz to@ki k ploskosti"; 1 ;" iz kruglogo lista me-"; 1 ;" geometri@eskoe mesto"; 1 ;" dany to@ki A(1,2,3),"; 1 ;" dany koordinaty to@ki"; 1 ;" dana to@ka C(1,0,-3)." 1 ;" dana to@ka B(0,-1,2)." 1 ;" dana to@ka A(1,2,3)." 1 ;" @emu rawno rasstoqnie"; 1 ;" otwet wwesti w dm"; 1 ;" najdite proekcii"; 1 ;" najdite plo&adx"; 1 ;" C(4,-3,6),D(7,-2,5)." 1 ;" C(3,-2,2),D(2,-3,1)" 1 ;" su&estwuet li"; 1 ;" sprawedliwo li"; 1 ;" A"; 1 ;" @erez zapqtu#" 1 ;" 3)240/ 1 ;" naklonnyh."; 1 ;" 3)60 1 ;" zapqtu#" 1 ;" C(4,1,0)."; 1 ;" AD=0.2M " 1 ;" AD=0.06M" 1 ;" ili 5/3" 1 :planim32BAL 1 :graf32 CX 1 :as=2:3 .","","" 1 :PLANIM33BU 1 8$$8 K|AB< 1 6planim31BF;B:< 1 6graf31 CX 1 6PLANIM32BU 1 3PLANIM31BU 1 3;"," 2*SIN60 1 3/2."," 2*TG30 1 3,228,36,40,40,48,48,32,0,0,0,0,255,0,0,0 1 3)."," 2*TG60 1 2planim30B,3 1 2graf30 CX 1 2 sm i 5 sm obrazu#t","ugol 45 1 1991 god " 1 1991 god 1 /planim29B 1 /graf29 CX 1 /PLANIM30BU 1 /2. zna@it","wos-rawnobedrennyj treu-","golxnik.","","" 1 /2",""," V=( 1 /180 .","","" 1 .per-","waq iz _tih ploskostej","prohodit @erez prqmye as","aa 1 .najti tretij"," ugol i dwe storony.",""," re%enie.",""," tak kak summa uglow"," treugolxnika rawna 180 1 .menx%aq diago-","nalx parallelepipeda","rawna 7 sm.","najdite ego ob'em.","otwet wwedite w kubi-","@eskih santimetrah.","","" 1 .@emu rawen otrezok"; 1 .","wo skolxko raz uweli-","@itsq ego ob'em?","","","" 1 .","plo&adi diagonalxnyh se-","@enij 3m 1 .","najdite rebro rawno-","welikogo kuba.","otwet wwedite w","santimetrah.","" 1 .","najdite plo&adx se@eniq,","prohodq&ego @erez boko-","woe rebro i osx piramidy","(sowpadaet s osx# soot-","wetstwu#&ej polnoj ","piramidy)." 1 .","na kakom rasstoqnii ot","osnowaniq nahoditsq","se@enie,parallelxnoe ","emu,esli plo&adx","se@eniq rawna 50 m 1 .","@emu rawno rebro kuba?","","","","","","" 1 .","","otwet wwedite w kwadrat-","nyh metrah.","" 1 .","","najdite ugol 1 .","","","otwet wwedite w gradu-","sah,razdelqq zna@eniq","zapqtoj.","","","","","" 1 .","","","","otwet wwedite w gradu-","sah,razdelqq zna@eniq","zapqtoj.","","","","","","","" 1 .","","","","","","","","","","","","","","","","","","","" 1 .","","","","","","","","" 1 .","","","","","","","" 1 .","","","","","","" 1 .",""," uglom mevdu prqmoj i","ploskostx# nazywaetsq","ugol mevdu prqmoj i ee" 1 .",""," takim obrazom,@etyreh-"," ugolxnik levit w "," ploskosti parallelxnyh"," prqmyh AA 1 .",""," koordinatoj 1 .",""," re&enie.","ploskostx se@eniq razbi-","waet prizmu na dwe @asti","parallelxnym perenosom","odnoj iz nih sowme&aem" 1 ."," zatem nahodim storonu 1 ."," summa uglow 1 ."," sledowatelxno, 1 ."," (ss' perpendikulqrna 1 ."," esli XX 1 ."," 2","" 1 ."," 1 . w itoge","summa 1 . sledo-","watelxno prqmaq 1 . po nerawenstwu","treugolxnika lomanaq" 1 . koordinaty"," 1 . bokowaq po-"," werhnostx rawna S." 1 . w plos-"; 1 . _to"," ozna@aet, @to AA 1 -ugolxnoj,esli ee osno-","waniem qwlqetsq 1 -ugolxniki podobny." 1 -ugolxnika" 1 -ugolxnika s","dostato@no malymi storo-","nami.","","" 1 -ugolxnika rawna",""," 180 1 -ugolxnika r raw-","na 180 1 -ugolxnik","so storonoj 1 -ugolxnik" 1 -ugolx-","nikow otno%eniq perimet-","row,radiusow wpisannyh","i radiusow opisannyh","okruvnostej rawny.",""," r 1 -ugolx-","nikow ko_fficient podo-","biq rawen otno%eni#","storon,radiusow wpisan-","nyh i radiusow opisannyh","okruvnostej.","" 1 -ugolx-"," nik.",""," treugolxnaq piramida","nazywaetsq takve tetra-" 1 -seku&aq ploskostx" 1 -se@enie mnogo-"," grannika ABCDA 1 -prqmu# BB 1 -podobny.","","" 1 -perimetr, 1 -linejnye razmery"," prqmougolxnogo paralle-"," lepipeda." 1 -apofema.","" 1 -2AB*AD"," (ris.1)",""," BC 1 -2,-2,1,9V 1 -2,-2,-1,9B 1 -2).",""," teorema dokazana.","","","","" 1 -","ugolxnika r rawna summe","uglow mnogougolxnika r2","pl#s 180 1 -"," -ugolxniki"," A 1 - wysota, S=(2 1 - paral-"," lelogrammy, t.k. u nih"," protiwoleva&ie storony"," rawny.","","","","","","","" 1 ,w ploskosti 1 ,ploskostx"," 1 ,planim28B 1 ,graf28 CX 1 ,esli:aa1=3,ww1=4,"; 1 ,esli ugol mevdu"," 1 ,esli aw=7.5sm?" 1 ,esli aw=6 sm ,"," as:ss 1 ,bokowoe rebro rawno"; 1 ,a wtoraq-@erez prq-","mye wD i ww 1 ,PLANIM29BU 1 ,... -","zwenxqmi lomanoj.",""," lomanaq nazywaetsq pro-","stoj, esli ona ne imeet","samoperese@enij. (to@ka","B na wtorom risunke)" 1 ,","razdelqq zapqtymi.","","" 1 ,","esli ugol mevdu 1 ,","a rasstoqnie mevdu dwumq","bokowymi granqmi 2 m .","najdite ob'em prizmy.","","otwet wwedite w m 1 ,"," to ego ob'em wy@islqet-"," sq po formule","",""," V= 1 ,"," perpendikulqrnaq 1 ,"," perpendikulqrna i 1 ,"," budu@i perpendikulqrna"," 1 ,"," a w ploskosti prqmyh"," 1 ,"," to 1 ,"," 2 2",""," 1 , sledowatelxno prqmaq"," 1 , perpendikulqrna 1 , dlina kotorogo","ne bolx%e dliny a 1 , sledowa-"," telxno i ploskostej 1 +2AB*AD"," (ris.2)","","","","","" 1 +2=0"," 2)2 1 +1=0","","wwedite zna@eniq 1 *R"," S= 1 *2."," takim obrazom na ( 1 )nazywa-","#tsq perpendikulqrnymi,","esli kakaq-libo plos-","kostx ( 1 ).","","","","","","","","","","","","","","","","","" 1 ).","",""," esli storona kwadra-" 1 )-trehgrannyj "," ugol,( 1 )-k(I),y(I-2 1 ),@toby"," 1 ),","peresekaet ih po perpen-","dikulqrnym prqmym( 1 ),","esli izwestno,@to","wektory aw i sD rawny.","","wwedite zna@eniq 1 ),","esli izwestno,@to","summa wektorow aw i sD","rawna nul#.","","wwedite zna@eniq 1 ),"," gde 1 ), perpendiku-" 1 ))","","","","" 1 )","ili iz %arowogo segmenta","konus udalqetsq ( 1 )","","","","" 1 )","","","" 1 )"," sledu#&im obrazom:" 1 )"," nazywaetsq @islo:",""," 1 )"," imeet koordinaty :"," 1 )"," budut kollinearny.","","wwedite zna@eniq 1 )"," 3","","","" 1 )"," 2","","","" 1 )"," 3"," obxem %arowogo sekto-"," ra:" 1 ) w ","dekartowyh koordinatah","imeet wid:","" 1 ) perehodit"," w to@ku ( 1 ) na @islo 1 ) i wy-","sotoj 1 ) i kon-"," com w t. a 1 ) ego"," grani.","" 1 ) rawno:","",""," 1 (planim27B47 1 (graf27 CX 1 (YD)*XD)/YD,YN+K* 1 (XD),YN+(K* 1 (XD)*YD)/XD: 1 (PLANIM28BU 1 '.","","","","","","","","","","","","" 1 '-ortogonalxnaq pro-","ekciq 1 %planim26B 1 %graf26 CX 1 %PLANIM27BU 1 "wypuklye mnogougolxniki.",""," lomanaq nazywaetsq zam-","knutoj, esli ee koncy","sowpada#t."," prostaq zamknutaq loma-" 1 "wwedenie dekartowyh","koordinat w prostranstwe.","preobrazowanie figur","w prostranstwe.","prakti@eskoe zadanie.","wyhod." 1 "waetsq bolx%im krugom,a","se@enie sfery - bolx%oj","okruvnostx#.",""," teorema",""," l#baq diametralxnaq" 1 "ugolxnika.",""," osx piramidy-prqmaq,","soderva&aq ee wysotu.",""," apofema-wysota boko-","woj grani prawilxnoj pi-" 1 "ugly mevdu prqmymi i","ploskostqmi.","plo&adx ortogonalxnoj pro-","ekcii mnogougolxnika.","wektory w prostranstwe.","urawnenie ploskosti.","prakti@eskoe zadanie.","wyhod." 1 "torema kosinusow.","teorema sinusow.","re%enie treugolxnikow.","prakti@eskoe zadanie.","wyhod." 1 "teorema:dlina lomanoj ne","menx%e dliny otrezka,so-","edinq#&ego ee koncy.","","dokazatelxstwo:","w dannoj lomanoj a 1 "ta 100 m,to plo&adx bu-","det w gektaraX.","",""," esli storona kwadra-","ta 1 km,to plo&adx budet","w kwadratnyX kilometraX","i t.p." 1 "stej s ploskostx# 1 "sa,a wer%inoj qwlqetsq","wer%ina konusa.",""," bokowye rebra takoj","piramidy qwlq#tsq obra-","zu#&imi konusa.","" 1 "sa,a wer%inoj qwlqetsq","w 1 "rawny:aw=ws, wo-ob&aq.","storona, ugly pri wer%i-","ne w rawny 1 "ramidy,prowedennaq iz ee","wer%iny.",""," SO - osx piramidy"," SP - apofema piramidy","","" 1 "radius wpisannoj okruv-","nosti:"," CB 1 "radius opisannoj okruv-","nosti:"," sw 1 "r","e","%","e","n","i","e"," "," ","t","r","e","u","g","o","l","x","n","i","k","o","w"," "," "," "," "," "," "," "," ","1","9","9","1"," ","g","o","d"," "," "," "," "," "," "," "," "," "," "," "," "," "," "," "," "," "," "," "," "," "," "," "," "," "," "," "," "," "," "," "," "," " 1 "r rawna summe uglow mno-","gougolxnika r1:","a 1 "proekciej na ploskostx.","","","","","","" 1 "prawilxnye mnogogran-"," niki.",""," wypuklyj mnogogrannik","nazywaetsq prawilxnym,","esli ego grani qwlq#tsq","prawilxnymi mnogougolx-","nikami s odnim i tem ve" 1 "postroenie ploskih se@enij.","parallelepiped.","prakti@eskoe zadanie.","wyhod." 1 "ponqtie plo&adi, plo&adx"," prqmougolxnika.","plo&adx prostyh figur.","plo&adx kruga.","prakti@eskoe zadanie.","wyhod." 1 "ponqtie ob'ema.","ob'em parallelepipeda.","ob'em naklonnogo ","parallelepipeda.","ob'em prizmy.","prakti@eskoe zadanie.","wyhod." 1 "polu@ennyX @astej otno-","sqtsq kak"," (1/8):(1-1/8)=1:7","","","","" 1 "podobnu# piramidu.",""," awsS - piramida",""," aws - osnowanie ee","","a 1 "podobie prawilxnyh wypuklyh","mnogougolxnikow.","dlina okruvnosti.","centralxnyj ugol i duga","okruvnosti.","prakti@eskoe zadanie.","wyhod." 1 "ploskostx %ara qwlqetsq","ego ploskostx# simmetrii","centr %ara qwlqetsq ego","centrom simmetrii.","","" 1 "ploskosti.","","","","","","" 1 "planim40" 1 "planim39" 1 "planim38" 1 "planim37" 1 "planim36" 1 "planim35" 1 "planim34" 1 "planim33" 1 "planim32" 1 "planim31" 1 "planim30" 1 "planim29" 1 "planim28" 1 "planim27" 1 "planim26" 1 "planim25" 1 "planim24" 1 "planim23" 1 "planim22" 1 "planim21" 1 "piramidy rawna:"," 1 "piramidy estx podobnye","mnogougolxniki,bokowye","grani-trapecii.","","","","" 1 "piramida.","prawilxnye mnogogranniki.","prakti@eskoe zadanie.","wyhod." 1 "perpendikulqrnostx","ploskostej.","rasstoqnie mevdu","skre&iwa#&imisq prqmymi.","prakti@eskoe zadanie.","wyhod." 1 "perpendikulqrnostx prqmyh.","prakti@eskoe zadanie.","wyhod." 1 "parallelxnye prqmye ","w prostranstwe .","parallelxnostx prqmoj i ","ploskosti .","prakti@eskoe zadanie.","wyhod." 1 "parallelxnostx prqmyh i ploskostej . ( @astx 1 ) 1 9 9 1 g o d . " 1 "parallelxnostx ploskostej.","izobravenie prostranstwen-","nyh figur na ploskosti.","prakti@eskoe zadanie.","wyhod." 1 "osnowaniq prizmy.polu@im","prqmu# prizmu,u kotoroj","osnowanie-se@enie ishod-","noj.ob'em _toj prizmy","rawen Q* 1 "osnowaniq na wysotu:","",""," V= SH = 1 "osnowanie prqmogo pa-","rallelepipeda - romb,","plo&adx kotorogo 1 m 1 "osnowanie prizmy - tre-","ugolxnik,u kotorogo odna","storona rawna 2 sm,a dwe","drugie po 3 sm.bokowoe","rebro rawno 4 sm i","sostawlqet s ploskostx#","osnowaniq ugol 45 1 "obxem piramidy,"," obxemy podobnyh tel.","obxemy cilindra i konusa.","obxem %ara i ego @astej.","prakti@eskoe zadanie.","wyhod." 1 "nazywa#tsq wer%inami, a","otrezki a 1 "naq nazywaetsq mnogougo-","lxnikom, esli ee sosed-","nie zwenxq ne levat na","odnoj prqmoj."," mnogougolxnik s 1 "na@alom nazywa#tsq do-","polnitelxnymi.",""," centralxnyj ugol w","okruvnosti -_to ploskij","ugol s wer%inoj w ee","centre." 1 "moj w _toj ploskosti.","","","","" 1 "mnogougolxniki (@astx 1) obu@a#&ij kurs 1 "mnogogrannye ugly.","mnogogrannik.","prizma.","prakti@eskoe zadanie.","wyhod." 1 "midy,leva&ie w paral-","lelxnyh ploskostqh,nazy-","wa#tsq osnowaniqmi,os-","talxnye-bokowymi gra-","nqmi.",""," osnowaniq use@ennoj" 1 "menx%ej 180 gradusow, i","tolxko odin.","",""," kakow by ni byl treu-" 1 "lqrnaq prqmoj perese@e-","niq _tih ploskostej ( 1 "lomanaq.","wypuklye mnogougolxniki.","prawilxnye mnogougolxniki.","prakti@eskoe zadanie.","wyhod." 1 "levat w kasatelxnoj","ploskosti %ara.","","","" 1 "kowu# powerXnostx po ok-","ruvnosti s centrom na","osi konusa.","","" 1 "kosinus ugla mevdu plos-","kostx# mnogougolxnika i","ploskostx# proekcii.","",""," S( 1 "izmereniq prqmougolx-","nogo parallelepipeda","3 sm,4 sm,5 sm.","esli uweli@itx kavdoe","rebro na 1 "izmereniq prqmougolx-","nogo parallelepipeda","15 m,50 m,36 m.","najdite rebro rawnowe-","likogo emu kuba.","","","","","","","" 1 "grani-prawilxnye treu-","golxniki;w kavdoj wer%i-","ne shoditsq po @etyre","rebra.","","","" 1 "golxnik, su&estwuet raw-","nyj emu treugolxnik w","dannoj ploskosti w zada-","nnom raspolovenii otno-","sitelxno dannoj poluprq-" 1 "gogrannikow:prawilxnyj","tetra_dr,kub,okta_dr,","dodeka_dr,ikosa_dr.","","","","" 1 "dlina ne bolx%e dliny","ishodnoj i tak dalee."," w itoge pridem k otrez-","ku a 1 "dikulqr,opu&ennyj iz","wer%iny k ploskosti","osnowaniq.",""," osx konusa-prqmaq,so-","derva&aq wysotu konusa.","" 1 "dekartowy koordinaty i wektory w prostranstwe ( @astx 2 ) 1991 god. " 1 "dannoj.","","","","" 1 "cilindr","konus","prakti@eskoe zadanie.","wyhod." 1 "bokowaq powerhnostx","prawilxnoj piramidy raw-","na proizwedeni# polu-","perimetra osnowaniq na","apofemu.","","bokowaq powerhnostx" 1 "aksiomy stereometrii.","nekotorye sledstwiq","aksiom stereometrii.","prakti@eskoe zadanie.","wyhod." 1 "a otrezki,soedinq#&ie","sootwetstwu#&ie wer%iny-","bokowymi rebrami prizmy.","","","","" 1 "a bokowye rebra 1 "_drom.",""," awsS - tetra_dr.","","","","" 1 "PLANIM_24" 1 "@islom storon i w kavdoj","wer%ine mnogogrannika","shoditsq odno i to ve","@islo reber.",""," su&estwuet pqtx tipow","prawilxnyh wypuklyh mno-" 1 "@aetsq ot perimetra","wpisannogo w nee pra-","wilxnogo 1 "2. prawilxnyj mnogogran-","nik,u kotorogo grani -","- prawilxnye @etyreh-","ugolxniki i w kavdoj","wer%ine shoditsq tri","rebra - _to ....","","1)dodeka_dr.2)ikosa_dr","3)tetra_dr. 4)kub.","5)okta_dr.","","" 1 "1.2 u prawilxnoj use@en-","noj treugolxnoj piramidy","storona bolx%ego osno-","waniq 8 sm,a 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storon","treugolxnika naibolx%aq?","",""," 1) aw 2) ws 3) as","" 1 ","bokowaq storona odnogo 1 ","(@itaetsq 'pi'):"," 1 ","","awsS podobna a 1 ","","","","","","","","","","","","","","","","","","","","","","","","","","","","" 1 ","","","","","","","","","","","","","" 1 ","","","","","","","","","","","","" 1 ","","","","","","","","" 1 ","","","","","" 1 ","","",""," 1 ","",""," esli centrom sfery","qwlqetsq na@alo koordi-","nat,to urawneniem sfery","qwlqetsq:" 1 ","",""," R - radius osnowaniq,",""," 1 ","",""," storony treugolxnika"," proporcionalxny sinusam"," protiwoleva&ih uglow.","",""," 1 ",""," ots#da 1 ",""," nazywaetsq wektor",""," 1 ",""," ""-"" esli 1 ",""," krugowoj segment-ob&aq"," @astx kruga i poluplos-"," kosti.","","","","","","","","","","" 1 ",""," kwadrat l#boj storony"," treugolxnika rawen sum-"," me kwadratow dwuh dru-"," gih storon bez udwoen-"," nogo proizwedeniq _tih"," storon na kosinus ugla"," mevdu nimi." 1 "," to tretij ugol wyrava-"," etsq @erez zadannye." 1 "," t.e. prqmye 1 "," seku&ej ploskostx# 1 "," po teoreme sinusow.","","","","","" 1 "," perpendikulqrny.",""," teorema dokazana" 1 "," perpendikulqrny." 1 "," kak protiwoleva&ie sto-"," rony parallelogrammow.","" 1 "," estx ugol mevdu 1 "," ""+"" esli 1 "," wektor 1 "," DO=OB 1 "," CO=OA 1 "," AO=OC 1 "," 2 2 2",""," 1 "," TG 1 "," SIN 1 "," 2R" 1 "," +( 1 "," 3"," obxem %arowogo seg-","menta wysotoj H:" 1 "," P 1 "," 2","","","" 1 "%arowogo segmenta i ko-","nusa. %arowoj segment","dopolnqetsq konusom ( 1 "%ar.","urawnenie sfery.","prakti@eskoe zadanie.","wyhod." 1 "%age my pridem k treugo-","lxniku a 1 "","prawilxnyj mnogogrannik,","u kotorogo grani - pra-","wilxnye treugolxniki i w","kavdoj wer%ine shoditsq","pqtx reber _to ....","","1)dodeka_dr.2)ikosa_dr.","3)okta_dr. 4)kub."," 5)tetra_dr.","","" 1 "","najdite radius okruv-","nosti,esli ee dlina ","rawna 94.2 .","","otwet wwedite s","to@nostx# 2 znaka.","","","","","","","","" 1 "","najdite radius okruv-","nosti,esli 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ki figury izobrava#tsq"," na ploskosti @erteva"," parallelxnymi otrezkami"," ili otrezkami,leva&imi"," na odnoj prqmoj." 1 "","","",""," teorema.", ""," dwe prqmye,parallelx-"," nye tretxej prqmoj,"," parallelxny.","","" 1 "","","",""," summoj wektorow"," 1 "","","",""," plo&adx prqmougolxni-"," ka rawna proizwedeni#"," dlin ego storon.","" 1 "","","",""," osnowanie naklonnoj -","_to konec otrezka, leva-","&ij w ploskosti.","" 1 "","","",""," teorema.","",""," esli prqmaq,pereseka-"," #&aq ploskostx,perpen-"," dikulqrna dwum prqmym w"," _toj ploskosti, proho-"," dq&im @erez to@ku pere-"," se@eniq,to ona perpen-"," dikulqrna ploskosti.","","","","","","","","","","","","","","","","","","","","","","" 1 "","","",""," teorema.","",""," esli ploskostx per-"," pendikulqrna odnoj iz"," dwuh parallelxnyh prq-"," myh, to ona perpendiku-"," lqrna i drugoj prqmoj.","","","","","","","","","","","","","","","","","","","","","","" 1 "","","",""," teorema.","",""," dwe prqmye, perpendi-"," kulqrnye odnoj i toj ve"," ploskosti, parallelxny.",""," ","","","","","","","","","","","","","","","","","","","","","","","" 1 "","",""," u treugolxnika storony","rawny 20,21,13 m .","najdite kosinus ugla 1 "","",""," storony treugolxnika","rawny 2 , 5 i 4 sm .","najdite kosinus ugla 1 "","",""," C2: esli dwe razli@nye","ploskosti ime#t ob&u#","to@ku,to oni pereseka#t-","sq po prqmoj." 1 "","",""," plo&adx powerhnosti"," sferi@eskogo segmenta"," rawna:","",""," S=2 1 "","",""," ugol mevdu skre&iwa#-"," &imisq prqmymi-_to ugol" 1 "","",""," skalqrnym proizwede-"," niem wektorow:"," 1 "","",""," rasstoqnie ot to@ki","do ploskosti -_to dlina","perpendikulqra,opu&enno-","go iz dannoj to@ki." 1 "","",""," proizwedeniem wektora"," 1 "","",""," prizma nazywaetsq"," prqmoj,esli ee bokowye"," rebra perpendikulqrny"," osnowaniqm.","" 1 "","",""," plo&adx treugolxnika"," rawna polowine proizwe-"," deniq ego storony na"," wysotu, prowedennu# k"," _toj storone.","","" 1 "","",""," plo&adx bokowoj"," powerhnosti konusa"," rawna:","",""," S= 1 "","",""," otrezok, soedinq#&ij","osnowaniq perpendikulqra","i naklonnoj iz odnoj i","toj ve to@ki, estx pro-","ekciq naklonnoj.","" 1 "","",""," na ploskosti @erez","to@ku, ne leva&u# na","dannoj prqmoj,movno pro-","westi ne bolee odnoj","prqmoj , parallelxnoj" 1 "","",""," teorema.",""," esli prqmaq, ne pri-"," nadleva&aq ploskosti,"," parallelxna kakoj-"," -nibudx prqmoj w _toj"," ploskosti,to ona paral-"," lelxna i samoj plos-"," kosti." 1 "","",""," teorema.",""," @erez to@ku wne dan-"," noj prqmoj movno pro-"," westi prqmu#,parallelx-"," nu# _toj prqmoj,i pri-"," tom tolxko odnu.","" 1 "","",""," teorema.",""," otrezki na paral-"," lelxnyh prqmyh,zakl#-"," @ennye mevdu dwumq pa-"," rallelxnymi ploskostq-"," mi,rawny.","" 1 "","",""," teorema.",""," esli dwe to@ki prqmoj"," prinadlevat ploskosti,"," to wsq prqmaq prinad-"," levit _toj ploskosti.","" 1 "","",""," teorema.",""," esli dwe parallelxnye"," ploskosti pereseka#tsq"," tretxej,to prqmye pere-"," se@eniq parallelxny." 1 "","",""," teorema.",""," @erez tri to@ki,ne"," leva&ie na odnoj"," prqmoj,movno prowesti"," ploskostx,i pritom"," tolxko odnu.","","" 1 "","",""," teorema.",""," @erez to@ku wne"," dannoj ploskosti movno"," prowesti ploskostx,"," parallelxnu# dannoj,"," i pritom tolxko odnu.","" 1 "","",""," sledstwie.",""," ploskostx i ne leva-"," &aq na nej prqmaq libo"," ne pereseka#tsq,libo"," pereseka#tsq w odnoj"," to@ke." 1 "","",""," teorema",""," ploskostx,perpendi-"," kulqrnaq osi cilindra," 1 "",""," u treugolxnika dwe","storony rawny 5 sm i ","6 sm .","movet li ugol,protiwo-","leva&ij storone 5 sm","bytx tupym?","","" 1 "",""," u treugolxnika dwe","storony rawny 20 m i","21 m,a 1 "",""," prqmaq 1 "",""," pri kakih zna@eniqh "," 1 "",""," plo&adx-_to polovitelx-"," naq weli@ina,kotoraq"," obladaet sledu#&imi"," swojstwami:","","","","","","","","","","","","","" 1 "",""," obxem use@ennogo konusa","s radiusami osnowanij","R 1 "",""," dany storona i dwa ","ugla treugolxnika.","najdite ugol 1 "",""," plo&adx segmenta",""," 1 "",""," otno%enie dliny okruv-","nosti k diametru obozna-","@a#t gre@eskoj bukwoj 1 "",""," krugowoj sektor-@astx"," kruga ,leva&aq wnutri"," sootwetstwu#&ego cent-"," ralxnogo ugla.",""," plo&adx krugowogo sek-"," tora",""," 1 "",""," 1.rawnye figury ime#t"," rawnye plo&adi.","",""," 2.esli figura razbiwa-" 1 "",""," use@ennaq piramida,","kotoraq polu@aetsq iz","prawilxnoj piramidy,","takve nazywaetsq pra-","wilxnoj." 1 "",""," ugol mevdu parallelx-"," nymi ploskostqmi rawen"," nul#.","","","","" 1 "",""," u parallelepipeda wse"," grani-parallelogrammy.","","" 1 "",""," to@ka C- seredina ot-"," rezka A 1 "",""," prqmaq prizma nazywa-"," etsq prawilxnoj,esli ee"," osnowaniq qwlq#tsq pra-"," wilxnymi mnogougolxni-"," kami.","","","" 1 "",""," plo&adx kruga rawna"," polowine proizwedeniq"," dliny , ograni@iwa#&ej"," ego okruvnosti , na"," radius.","","" 1 "",""," plo&adx ABCD rawna:","" 1 "",""," obxemy podobnyh tel"," otnosqtsq kak kuby ih"," sootwetstwu#&ih"," linejnyh razmerow","" 1 "",""," naklonnaq iz dannoj","to@ki k dannoj ploskosti","estx l#boj otrezok, soe-","dinq#&ij dannu# to@ku s","l#boj to@koj ploskosti i","ne qwlq#&ijsq perpendi-","kulqrom." 1 "",""," konec otrezka (to@ka"," B),leva&ij w ploskosti,"," nazywaetsq osnowaniem"," perpendikulqra AB." 1 "",""," ko_fficienty 1 "",""," esli 1 "",""," diagonalx prizmy -"," otrezok,soedinq#&ij dwe"," wer%iny,ne prinadleva-"," &ie odnoj grani.","" 1 "",""," bokowye grani pra-","wilxnoj use@ennoj pira-","midy-rawnye rawnobokie","trapecii,ih wysoty","nazywa#tsq apofmami." 1 "",""," bokowoj powerhnostx#"," prizmy nazywaetsq summa"," plo&adej bokowyh granej","",""," teorema.",""," bokowaq powerhnostx"," prqmoj prizmy rawna"," proizwedeni# perimetra" 1 "",""," teorema","","ploskostx,perpendikulqr-","naq osi konusa,pereseka-","et konus po krugu,a bo-" 1 "",""," po tretxemu priznaku"," rawenstwa treugolxnikow"," treugolxniki ABC i"," A 1 "",""," parallelxnyj perenos"," w prostranstwe-_to pre-"," obrazowanie,pri kotorom"," to@ka ( 1 "",""," parallelxnyj perenos"," w prostranstwe zadaetsq"," formulami:","",""," 1 "",""," ikosa_dr:","","grani-prawilxnye tre-","ugolxniki;w kavdoj wer-","%ine shoditsq po pqtx","reber." 1 "",""," dodeka_dr:","","grani-prawilxnye pqti-","ugolxniki;w kavdoj wer-","%ine shoditsq po tri","rebra." 1 "",""," AC 1 "",""," ABCD 1 "",""," teorema","","@erez l#bu# to@ku %aro-","woj powerhnosti prohodit","beskone@no mnogo kasa-","telxnyh,pri@em wse oni" 1 "",""," teorema","",""," liniq perese@eniq dwuh",""," sfer estx okruvnostx." 1 "",""," teorema.",""," ploskostx,parallelx-","naq osnowani# piramidy i","pereseka#&aq ee,otsekaet" 1 "",""," teorema:",""," pereseka#&iesq prqmye,","sootwetstwenno paral-","lelxnye perpendikulqrnym","prqmym, sami perpendiku-","lqrny." 1 "",""," 1 "",""," 1 ""," tri latunnyh kuba s","rebrami 3 sm,4 sm,5 sm","pereplawleny w odin kub.","kaku# dlinu imeet rebro","_togo kuba?","","","","","","" 1 ""," skolxko gradusow soder-","vit centralxnyj ugol,","esli sootwetstwu#&aq emu","duga sostawlqet 1/5 ot","dliny okruvnosti.","","","","","","","","","" 1 ""," skolxko gradusow soder-","vit centralxnyj ugol,","esli sootwetstwu#&aq emu","duga sostawlqet 1/4 ot","dliny okruvnosti.","","","","","","","","","","","" 1 ""," skolxko gradusow soder-","vit centralxnyj ugol,","esli sootwetstwu#&aq emu","duga sostawlqet 1/3 ot","dliny okruvnosti.","","","","","","","","","","" 1 ""," otrezok dlinoj 10m","peresekaet ploskostx;","koncy ego nahodqtsq na","rasstoqniqh 2m i 3m ot","ploskosti."," najdite ugol mevdu","otrezkom i ploskostx#.","","otwet wwedite w ","gradusah.","","" 1 ""," ortogonalxnaq proekciq","prqmoj na ploskostx estx","prqmaq na kotoroj levat","osnowaniq perpedikulq-","row,opu&ennyh iz to@ek","dannoj prqmoj na plos-","kostx." 1 ""," awsD,wsFe,...-grani.",""," aw,ws,sF,eF,...-rebra.",""," a,w,s,D,e,F...-wer%iny.","","","","","" 1 ""," R-radius osnowaniq,",""," H-wysota","","","" 1 ""," @erez katet rawnobed-","rennogo prqmougolxnogo","treugolxnika prowedena","ploskostx pod uglom 45 1 ""," @emu rawna plo&adx","ortogonalxnoj proekcii","kwadrata so storonoj","6 sm na ploskostx 1 ""," w ploskosti parallelx-"," nyh prqmyh 1 ""," to@ka perese@eniq dia-"," gonalej parallelepipeda"," qwlqetsq ego centrom"," simmetrii." 1 ""," rasstoqniem mevdu"," skre&iwa#&imisq prqmy-"," mi nazywaetsq dlina ih"," ob&ego perpendikulqra.","" 1 ""," prqmoj parallelepiped,"," u kotorogo osnowaniem"," qwlqetsq prqmougolxnik,"," nazywaetsq prqmougolx-"," nym parallelepipedom.","" 1 ""," powerXnostx konusa"," sostoit iz osnowaniq"," i bokowoj powerXnosti.","","","","","","" 1 ""," podobie prawilxnyh","wypuklyh mnogougolxnikow","",""," teorema.",""," prawilxnye wypuklye"," 1 ""," ob'em prqmougolxnogo",""," parallelepipeda.","","","" 1 ""," nazywaetsq wektor"," 1 ""," dlina okruvnosti wy-","@islqetsq po formule",""," 1 ""," @etyrehugolxniki"," CAA 1 ""," 3.plo&adx kwadrata so"," storonoj,rawnoj edinice"," izmereniq,rawna edinice","" 1 ""," 2. prqmye ne levat w"," odnoj ploskosti.",""," togda 1 ""," wwedenie dekartowyh","koordinat w prostranstwe","",""," wzaimoperpendikulqrnye"," prqmye 1 ""," uglom mevdu ploskos-"," tqmi 1 ""," trehgrannyj ugol-_to"," figura,sostawlennaq iz"," treh ploskih uglow,ko-"," torye nazywa#tsq granq-"," mi trehgrannogo ugla,"," a ih storony-rebrami." 1 ""," teorema.","",""," otno%enie dliny okruv-","nosti k ee diametru ne","zawisit ot okruvnosti,","t.e. odno i to ve dlq","l#byh dwuh okruvnostej." 1 ""," teorema kosinusow."," 1 ""," storony granej nazy-"," wa#tsq rebrami mnogo-"," grannika.","" 1 ""," sledstwie.",""," kwadrat storony treu-"," golxnika rawen summe"," kwadratow dwuh drugih"," storon + ili - udwoen-"," noe proizwedenie odnoj"," iz nih na proekci# "," drugoj.","" 1 ""," prqmougolxnik so sto-"," ronami 1 ""," prqmaq,prohodq&aq","@erez to@ku a %arowoj","powerhnosti perpendiku-","lqrno k radiusu,prowe-","dennomu w _tu to@ku,","nazywaetsq kasatelxnoj." 1 ""," preobrazowanie t.X w","t.X' nazywaetsq preob-","razowaniem simmetrii.",""," figura, kotoraq pri","preobrazowanii simmet-","rii perehodit w sebq,","nazywaetsq simmetri@noj","otnositelxno ploskosti." 1 ""," ploskostx,prohodq&aq","@erez to@ku a %arowoj","powerhnosti i perpen-","dikulqrnaq radiusu,pro-","wedennomu w _tu to@ku,","nazywaetsq kasatelxnoj","ploskostx#."," a- to@ka kasaniq." 1 ""," ploskosti bokowyX","granej opisannoj pirami-","dy qwlq#tsq kasatelx-","nymi ploskostqmi konusa.","","","" 1 ""," piramida nazywaetsq","prawilxnoj,esli ee osno-","waniem qwlqetsq prawilx-","nyj mnogougolxnik,a os-","nowanie wysoty sowpadaet","s centrom _togo mnogo-" 1 ""," perpendikulqrnostx"," prqmoj i ploskosti.","","","",""," prqmaq, pereseka#&aq"," ploskostx,perpendiku-"," lqrna _toj ploskosti,"," esli ona perpendikulqr-"," na l#boj prqmoj plos-"," kosti." 1 ""," perpendikulqrnostx"," ploskostej.","",""," dwe pereseka#&iesq","ploskosti ( 1 ""," perpendikulqrnostx"," prqmyh.","",""," dwe prqmye perpendi-","kulqrny,esli oni perese-","ka#tsq pod prqmym uglom." 1 ""," parallelxnye prqmye"," w prostranstwe.","","","",""," dwe prqmye w prost-"," ranstwe nazywa#tsq"," parallelxnymi,esli oni"," levat w odnoj ploskosti" 1 ""," parallelxnostx prqmoj"," i ploskosti.","","","",""," prqmaq i ploskostx na-"," zywa#tsq parallelxnymi,"," esli oni ne pereseka#t-"," sq.","" 1 ""," osnowaniq prizmy raw-"," ny i levat w parallelx-"," nyh ploskostqh.",""," bokowye rebra prizmy"," parallelxny i rawny.","" 1 ""," obxem konusa wy@islq-","etsq po formule:",""," 1"," V=- 1 ""," ob&aq wer%ina ploskih"," uglow nazywaetsq wer%i-"," noj trehgrannogo ugla.","","","","","","","","" 1 ""," ob&aq @astx takoj"," ploskosti i powerhnosti"," wypuklogo mnogogrannika"," nazywaetsq granx#.","","" 1 ""," kasatelxnaq ploskostx","cilindra proXodit @erez","obrazu#&u# i perpendiku-","lqrna osewomu se@eni#." 1 ""," granica %ara nazywa-"," etsq sferoj ili %aro-"," woj powerhnostx#.","" 1 ""," dlq prostyh tel ob'em"," -_to polovitelxnaq we-"," li@ina,@islennoe zna@e-"," nie kotoroj obladaet"," sledu#&imi swojstwami:","" 1 ""," dlina okruvnosti s","centrom o rawna dline","otrezka Aa''",""," dlina okruvnosti","skolx ugodno malo otli-" 1 ""," diagonalxnym se@enie"," prizmy nazywaetsq se@e-"," nie ploskostx#,kotoraq"," prohodit @erez dwa bo-"," kowyh rebra,ne prinad-"," leva&ih odnoj grani.","" 1 ""," bokowaq powerhnostx"," cilindra.","","",""," plo&adx bokowoj"," powerhnosti cilindra"," opredelqetsq po"," formule:","",""," S=2 1 ""," aws 1 ""," V:V 1 ""," Ob'em prizmy.","",""," ob'em l#boj prizmy"," rawen proizwedeni#"," plo&adi osnowaniq na" 1 ""," 6.pri parallelxnom"," perenose w prostranstwe"," kavdaq ploskostx pere-"," hodit libo w sebq,libo"," w parallelxnu# ej plos-"," kostx.","" 1 ""," 5.dwa parallelxnyh"," perenosa, wypolnennyh"," posledowatelxno, estx"," parallelxnyj perenos." 1 ""," 4.kakowy by ni byli"," to@ki A i A',su&estwuet"," edinstwennyj parallelx-"," nyj perenos,pri kotorom"," t.A perehodit w t.A'." 1 ""," u @etyrehugolxnika"," ABB 1 ""," teorema:","",""," w prqmougolxnom pa-"," pallelepipede kwadrat"," l#boj diagonali rawen"," summe kwadratow treh"," ego storon (reber)." 1 ""," teorema:","",""," u parallelepipeda"," protiwoleva&ie grani"," parallelxny i rawny." 1 ""," teorema.",""," dwe ploskosti paral-"," lelxny,esli odna iz"," nih parallelxna dwum "," pereseka#&imsq prqmym,"," leva&im w drugoj plos-"," kosti." 1 ""," teorema sinusow."," 1 ""," takim obrazom,"," AB=A 1 ""," rasstoqnie mevdu"," skre&iwa#&imisq"," prqmymi.","",""," ob&im perpendikulqrom"," dwuh skre&iwa#&ihsq"," prqmyh nazywaetsq otre-"," zok s koncami na _tih"," prqmyh ,qwlq#&ijsq per-"," pendikulqrom k kavdoj"," iz nih." 1 ""," ponqtie plo&adi","",""," figura nazywaetsq"," prostoj,esli ee movno"," razbitx na kone@noe"," @islo treugolxnikow.","",""," dlq prostyX figur" 1 ""," osnowaniq cilindra"," rawny i levat w paral-"," lelxnyX ploskostqX.",""," u cilindra obrazu#-"," &ie parallelxny i rawny","" 1 ""," kub:","grani-kwadraty. w kavdoj","wer%ine shoditsq po tri","rebra.",""," okta_dr:" 1 ""," O-to@ka perese@eniq"," diagonalej."," BO=OD 1 ""," 1"," V=- 1 ""," 1 1 ""," zada@a 3",""," dany dwe storony 1 ""," zada@a 2.",""," dany dwe storony i"," ugol mevdu nimi.","" 1 ""," teorema",""," kasatelxnaq ploskostx","imeet s %arom tolxko","odnu ob&u# to@ku-to@ku","kasaniq." 1 ""," re%enie.",""," po teoreme kosinusow"," nahodim tretx# storonu."," imeq tri storony i odin"," ugol po teoreme sinusow"," nahodim dwa ostaw%ihsq"," ugla.","","","","","","","","" 1 ""," plo&adx sfery.","","",""," plo&adx sfery radiusa"," R rawna:","",""," S=4 1 ""," dokazatelxstwo:",""," pustx 1 ""," teorema",""," plo&adx ortogonalxnoj","proekcii mnogougolxnika","na ploskostx rawna pro-","izwedeni# ego plo&adi na" 1 ""," teorema:","",""," esli ploskostx prohodit","@erez prqmu#,perpendiku-","lqrnu# drugoj ploskosti,","to _ti ploskosti perpen-","dikulqrny." 1 ""," teorema:","",""," esli prqmaq, leva&aq w","odnoj iz dwuh ploskostej","perpendikulqrna ih linii","perese@eniq, to ona per-","pendikulqrna i drugoj","ploskosti." 1 ""," teorema:","",""," dwe skre&iwa#&iesq"," prqmye ime#t ob&ij"," perpendikulqr,i pritom"," tolxko odin. on qwlqet-"," sq ob&im perpendikulq-"," rom parallelxnyh plos-"," kostej,prohodq&ih @erez"," _ti prqmye." 1 ""," teorema","(o treh perpendikulqrah)",""," prqmaq,prowedennaq na","ploskosti @erez osnowa-","nie naklonnoj perpendi-","kulqrno ee proekcii,","perpendikulqrna i samoj","naklonnoj.",""," i obratno,",""," esli prqmaq na plos-","kosti perpendikulqrna","naklonnoj , to ona per-","pendikulqrnaq i proek-","cii naklonnoj." 1 ""," swojstwa"," parallelxnogo perenosa.","",""," 1.parallelxnyj pere-"," nos estx dwivenie.",""," 2. pri parallelxnom"," perenose to@ki sowme&a-"," #tsq po parallelxnym"," prqmym na odno i to ve"," rasstoqnie.",""," 3.pri parallelxnom"," perenose prqmaq pereho-"," dit w parallelxnu# ej"," prqmu#.","" 1 ""," AB * CE"," S= 1 ""," H"," V= 1 ""," 1 " zna@it summa uglow 1 " wysotu.","",""," V=S*H , gde",""," S - plo&adx ABCDE ,","" 1 " wse wer%iny mnogougolx-","nika levat na okruvnosti","s centrom o i radiusom,","rawnym bokowym storonam","treugolxnikow.","" 1 " wse storony mnogougolx-","nika kasa#tsq okruvnosti","s centrom o i radiusom,","rawnym wysotam treugolx-","nikow,prowedennym iz t.o","","" 1 " wne%nim uglom wypuklogo","mnogougolxnika nazywaet-","sq ugol,smevnyj wnutren-","nemu uglu pri dannoj","wer%ine.","","-neprawilxnyj 1 " wektory w prostranstwe","",""," wektorom w prostran-"," stwe nazywaetsq napraw-"," lennyj otrezok.","",""," 1 " w prqmom parallele-","pipede storony osnowaniq"," 1 " w prqmoj treugolxnoj","prizme storony osnowa-","nij rawny 4 sm,5 sm,","7 sm. bokowoe rebro","rawno bolx%ej wysote","osnowaniq.","najdite ob'em prizmy.","","","","","" 1 " w prawilxnoj %esti-","ugolxnoj prizme plo&adx","naibolx%ego diagonalx-","nogo se@eniq rawna 4 m 1 " uglom wypuklogo mnogou-","golxnika dannoj wer%iny","nazywaetsq ugol, obrazo-","wannyj ego storonami,is-","hodq&imi iz odnoj wer-","%iny." 1 " to@ki _tiX krugow.",""," krugi nazywa#tsq"," osnowaniqmi cilindra.",""," otrezki,soedinq#&ie"," sootwetstwu#&ie to@ki" 1 " tela wra&eniq (@astx 1) obu@a#&ij kurs 1991 god. " 1 " summa uglow mnogougolx-","nika r1 rawna summe ug-","low mnogougolxnika r2:","a 1 " storony treugolxnika","rawny:13 sm,14 sm,15 sm.","najdite rasstoqnie ot","ploskosti treugolxnika","do centra %ara ka-","sa#&egosq wseh storon","treugolxnika.radius ","%ara 5 sm.","","otwet wwedite w ","santimetrah.","" 1 " soedinqq t.o s wer%ina-","mi mnogougolxnika,polu-","@im rawnobedrennye treu-","golxniki;osnowaniem kav-","dogo qwlqetsq storona","mnogougolxnika.zna@it:","" 1 " rogo w ob&em slu@ae"," qwlq#tsq to@kami pere-"," se@eniq seku&ej plos-"," kosti s rebrami mnogo-"," grannika, a storony -"," s ego granqmi.","" 1 " rebra qwlq#tsq obrazu#-"," &imi cilindra.","","" 1 " re%enie treugolxnikow.","",""," zada@a 1.",""," dany storona 1 " radiusy %arow rawny","25 dm i 29 dm,a rasstoq-","nie mevdu ih centrami","36 dm.","najdite dlinu linii,","po kotoroj pereseka#tsq","ih powerhnosti.","otwet wwedite w wide","@isla,umnovennogo na 1 " prqmougolxnika wokrug"," ego storony kak osi.","","","" 1 " ploskosti osnowaniq-"," wer%iny piramidy i wseh"," otrezkow,soedinq#&ih "," wer%inu s to@kami osno-"," waniq-bokowyh reber.",""," awsDE - osnowanie" 1 " ploskim mnogougolxnikom","nazywaetsq figura,sosto-","q&aq iz mnogougolxnika i","ograni@ennoj im ploskos-","ti.","","" 1 " plo&adi powerhnostej tel obu@a#&ij kurs 1991 god " 1 " plo&adi figur obu@a#&ij kurs 1991 god. " 1 " perpendikulqrnostx prqmyh i ploskostej (@astx 2) 1991 god " 1 " perpendikulqrnostx prqmyh i ploskostej (@astx 1) 1991 god. " 1 " perpendikulqrnostx prqmyh obu@a#&ij kurs 1991 god " 1 " peresekaet ploskosti 1 " peresekaet ego bokowu#"," powerXnostx po ok-"," ruvnosti,rawnoj okruv-"," nosti osnowaniq.",""," R=R'" 1 " parallelxnostx prqmyh i ploskostej (@astx 2) 1991 god. " 1 " parallelxnaq proekciq w"," naprawlenii,perpendiku-"," lqrnom dannoj ploskosti","",""," 1 " osnowaniq na wysotu"," prizmy t.e. na dlinu "," bokowogo rebra.","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","" 1 " okruvnostej krugow,"," nazywa#tsq obrazu#-"," &imi cilindra.","" 1 " obxemy tel (@astx 2) obu@a#&ij kurs 1991 god. " 1 " nekotoryh aksiom plani-"," metrii:","",""," prqmaq,prinadleva&aq","ploskosti,razbiwaet _tu","ploskostx na dwe polu-" 1 " nekotorye sledstwiq"," aksiom stereometrii.","",""," teorema.",""," @erez prqmu# i ne"," leva&u# na nej to@ku"," movno prowesti plos-"," kostx i pritom tolxko"," odnu." 1 " nazywa#tsq koordinatny-"," mi osqmi .",""," t.O-na@alo koordinat.",""," ploskosti 1 " najdite radius zemnogo","%ara,ishodq iz togo,@to","1 metr sostawlqet odnu","40-millionnu# dol# ","_kwatora.","","","otwet wwedite w kilo-","metrah,s to@nostx#","5 znakow.","","","","","","","","","" 1 " na wysotu.","",""," V=S*CC 1 " na powerhnosti %ara","dany tri [email protected]","linejnye rasstoqniq ","mevdu nimi 6 sm,8 sm,","10 sm.radius %ara 13 sm.","najdite rasstoqnie ot","centra do ploskosti,","prohodq&ej @erez _ti","to@ki.","otwet wwedite w santi-","metrah." 1 " mnogougolxniki ( @ a s t x 2 ) 1 9 9 1 g o d . " 1 " mnogougolxnik nazywaet-","sq wypuklym, esli on le-","vit w odnoj poluploskos-","ti otnositelxno l#boj","prqmoj, soderva&ej ego","storonu." 1 " mnogougolxnik nazywaet-","sq wpisannym, esli ego","wer%iny levat na nekoto-","roj okruvnosti.","" 1 " mnogougolxnik nazywaet-","sq opisannym,esli wse","ego storony kasa#tsq ne-","kotoroj okruvnosti.","","" 1 " mnogogranniki (@astx 3) obu@a#&ij kurs 1991 god. " 1 " mnogogranniki (@astx 2) obu@a#&ij kurs 1991 god " 1 " mevdu pereseka#&imisq"," parallelxnymi im prqmy-"," mi.","",""," 1 " kubi@eskih metrah"," i t.d.","","","","","","" 1 " kotorogo rawno edinice"," dliny,rawen edinice.",""," esli kub imet rebro"," 1 sm,to ob'em budet w"," kubi@eskih santimetrah;"," esli rebro kuba rawno"," 1 m ,to ob'em budet w" 1 " izobravenie prostrans-"," twennyh figur na plos-"," kosti.","",""," swojstwa:",""," 1. prqmolinejnye ot-"," rezki figury izobrava-"," #tsq na ploskosti @er-"," teva otrezkami." 1 " i wseh otrezkow,soedi-"," nq#&ih sootwetstwu#&ie"," to@ki _tih mnogougolx"," nikow",""," mnogougolxniki nazywa#-","tsq osnowaniqmi prizmy," 1 " i ne pereseka#tsq.","","","","","","","","","","","","","","","","","","","" 1 " i gruppa aksiom 'C',wy-"," rava#&aq osnownye swoj-"," stwa ploskostej w"," prostranstwe.","","","","" 1 " gonalxnoj proekciej "," 1 " golxniki,opisannye oko-"," lo osnowanij cilindra."," ploskosti ee granej"," kasa#tsq bokowoj po-"," werXnosti cilindra.","" 1 " etsq na @asti,qwlq#&ie-"," sq prostymi figurami,to"," plo&adx _toj figury"," rawna summe plo&adej"," ee @astej.","" 1 " dwa rawnobedrennyh tre-","ugolxnika ime#t ob&ee","osnowanie,rawnoe 16m. ih","ploskosti obrazu#t <60 1 " dlinoj lomanoj nazywa-","etsq summa dlin ee zwe-","nxew.","","" 1 " diagonali romba rawny","15 sm,20 sm. %arowaq ","powerhnostx kasaetsq ","wseh ego storon.","radius %ara 10 sm.","najdite rasstoqnie ot","centra %ara do plos-","kosti romba."," otwet wwedite w ","santimetrah","","" 1 " dekartowy koordinaty i wektory w prostranstwe (@astx 1) 1991 god " 1 " aksiomy stereometrii obu@a#&ij kurs 1 " S(ABCD)= 1 " H-wysota.","","","","","","" 1 " C3: esli dwe razli@nye","prqmye ime#t ob&u# to@ku","to @erez nih movno pro-","westi ploskostx,i pritom","tolxko odnu.","",""," uto@nennye formulirowki" 1 " @emu rawna plo&adx","proekcii prqmougolxnogo","rawnobedrennogo treu-","golxnika s gipotenuzoj-","-osnowaniem 16m na plos-","kostx 1 " @emu rawna plo&adx ","ortogonalxnoj proekcii","kruga s radiusom 10m ","na ploskosti 1 " @astx okruvnosti,raspo-","lovennoj wnutri ploskogo","ugla estx duga,otwe@a#-","&aq _tomu centralxnomu","uglu.","","","" 1 " %kiw imeet diametr 1 m.","i delaet 80 oborotow w","minutu. najdite skorostx","to@ki na okruvnosti","%kiwa.","","otwet wwedite w m/min.","s to@nostx# 4 znaka.","","","","","","","","","" 1 " %e dannogo ( radiusa"," kruga).","","","","","","" 1 " %ara na seku&u# plos-"," kostx.",""," oo' perpendikulqr na 1 " ",""," sledstwie:",""," w treugolxnike protiw"," bolx%ego ugla levit"," bolx%aq storona,protiw"," bolx%ej storony levit"," bolx%ij ugol.","" 1 " "," "," "," "," "," "," "," "," 1 " "," sledstwie:",""," summa kwadratow dia-"," gonalej parallelogramma"," rawna summe kwadratow"," ego storon.","","","","AC 1 " "," C -prqmaq perese@eniq"," ploskostej 1 " wysotoj piramidy na-","zywaetsq perpendikulqr,","opu&ennyj iz wer%iny pi-","ramidy na ploskostx os-","nowaniq.","","" 1 " urawnenie sfery .",""," urawnenie sfery s ra-","diusom R i centrom ","w to@ke a( 1 " urawnenie ploskosti.","",""," urawnenie ploskosti"," imeet wid",""," 1 " ugol mevdu prqmymi"," i ploskostqmi.","","",""," dwe pereseka#&iesq"," prqmye obrazu#t werti-"," kalxnye i smevnye ugly.",""," 1 i 2 -wertikalxnye"," ugly;"," 3 i 4 -smevnye ugly","","" 1 " u prawilxnyh 1 " u prqmougolxnogo"," parallelepipeda wse"," grani - prqmougolxniki.",""," prqmougolxnyj paralle-"," lepiped,u kotorogo wse"," rebra rawny,nazywaetsq"," kubom." 1 " tela wra&eniq (@astx 2) obu@a#&ij kurs 1991 god . " 1 " skalqrnoe proizwedenie"," wektorow rawno proizwe-"," deni# ih absol#tnyh we-"," li@in na kosinus ugla"," mevdu wektorami.","","" 1 " preobrazowanie figur"," w prostranstwe.",""," prqmaq XX' perpendi-","kulqrna ploskosti 1 " ploskostx,prohodq&aq","@erez centr %ara nazywa-","etsq diametralxnoj plos-","kostx#.",""," se@enie %ara diamet-","ralxnoj ploskostx# nazy-" 1 " plo&adx sfery."," bokowaq powerhnostx"," cilindra."," prakti@eskoe zadanie."," wyhod." 1 " plo&adx ortogonalxnoj","proekcii mnogougolxnika.","",""," ortogonalxnoj proek-"," ciej figury na dannu#"," ploskostx nazywaetsq ee" 1 " piramidoj,wpisannoj w","konus,nazywaetsq pirami-","da,osnowanie kotoroj","estx prawilxnyj mnogou-","golxnik,wpisannyj w ok-","ruvnostx osnowaniq konu-" 1 " perpendikulqrnostx"," prqmoj i ploskosti."," perpendikulqr i"," naklonnaq."," prakti@eskoe zadanie."," wyhod." 1 " osewoe se@enie-_to se-","@enie ploskostx#,proXo-","dq&ej @erez osx konusa.","","" 1 " ob'em naklonnogo"," parallelepipeda.","",""," ob'em l#bogo paralle-"," lepipeda rawen proizwe-"," deni# plo&adi osnowaniq" 1 " mnogogranniki. @astx 1. 1 " mnogogrannik wypuklyj,"," esli on raspoloven po"," odnu storonu ploskosti"," kavdogo ploskogo mnogo"," ugolxnika na ego po-"," werhnosti." 1 " konus movno rassmatri-","watx kak telo,polu@ennoe","pri wra&enii prqmougolx-","nogo treugolxnika wokrug","ego kateta kak osi.",""," wysota konusa- perpen-" 1 " esli storony paralle-"," lepipeda,rawny 1 " H -wysota prizmy (FF')","","","","","","" 1 " %arowoj sloj-@astx","%ara,raspolovennaq mevdu","dwumq parallelxnymi","ploskostqmi.",""," %arowoj sektor - telo,","kotoroe polu@aetsq iz" 1 " ",""," kwadrat so storonoj","1m imeet plo&adx 1 kwad-","ratnyj metr (1m 1 " wer%iny granej nazy-"," wa#tsq wer%inami mnogo-"," grannika.","",""," naprimer:" 1 " uglowaq mera menx%ego"," iz smevnyh uglow nazy-"," waetsq uglom mevdu"," prqmymi.","","","","","","","","","","","","","","" 1 " u prawilxnyh 1 " sfera-wse to@ki %ara,"," udalennye ot centra na"," rasstoqnie , rawnoe"," radiusu.","","","" 1 " razwernutomu uglu so-","otwetstwuet duga dlinoj"," 1 " rasstoqnie ot to@ki","do ploskosti -_to dlina","perpendikulqra,opu&enno-","go iz dannoj to@ki.","","","","" 1 " radius cilindra-_to","radius ego osnowanij.",""," wysota cilindra-_to","rasstoqnie mevdu plos-","kostqmi ego osnowanij.","" 1 " pustx dan 1 " prizmoj,wpisannoj w"," cilindr,nazywaetsq priz"," ma,osnowaniq kotoroj -"," rawnye mnogougolxniki,"," wpisannye w osnowaniq"," cilindra.ee bokowye" 1 " prizma nazywaetsq"," opisannoj,esli ee osno-"," waniq - rawnye mnogou-" 1 " postroenie ploskih"," se@enij.","",""," se@enie wypuklogo"," mnogogrannika estx wy-"," puklyj ploskij mnogo-"," ugolxnik,wer%iny koto-" 1 " poluploskosti nazywa-"," #tsq granqmi,a ograni@i-"," wa#&aq ih prqmaq - reb-"," rom dwugrannogo ugla.","" 1 " ploskostx,parallelx-","naq osnowani#,rassekaet","piramidu na dwe figury:","podobnu# ej piramidu i","use@ennu# piramidu.",""," grani use@ennoj pira-" 1 " ploskostx 1 " piramidoj,opisannoj","okolo konusa,nazywaetsq","piramida,osnowanie koto-","roj opisano okolo okruv-","nosti osnowaniq,a wer-","%ina sowpadaet s wer%i-","noj konusa." 1 " piramida nazywaetsq"," 1 " ot poluprqmoj na so-","derva&ej ee ploskosti w","zadannu# poluploskostx","movno otlovitx ugol s","zadannoj gradusnoj meroj" 1 " osx cilindra-_to prq-","maq,proXodq&aq @erez","centry osnowanij.",""," osewoe se@enie-_to se-","@enie,proXodq&ee @erez","osx cilindra." 1 " obxem %ara radiusa R:",""," 4"," V=- 1 " ob'emy tel (@astx 1) obu@a#&ij kurs 1991 god . " 1 " najdite ob'em.",""," re%enie: "," 1 " mnogogrannye ugly.","",""," dwugrannyj ugol -_to"," figura , obrazowannaq"," dwumq poluploskostqmi s"," ob&ej ograni@iwa#&ej"," ih prqmoj.","" 1 " mera dwugrannogo ugla"," ne zawisit ot wybora"," linejnogo ugla.","","","","" 1 " imeq storonu i wse"," ugly,po teoreme sinusow"," nahodim ostalxnye sto-"," rony.",""," ","","","","","","","","","","","","","","","","","" 1 " gruppa aksiom C.",""," C1: kakowa by ni byla","ploskostx , su&estwu#t","to@ki,prinadleva&ie _toj","ploskosti,i,to@ki, ne","prinadleva&ie ej." 1 " grani parallelepipe-"," da, ne ime#&ie ob&ih"," wer%in, nazywa#tsq "," protiwoleva&imi.","","" 1 " esli u nih storony"," odinakowy,to oni rawny.","" 1 " dlina okruvnosti.","","esli nitx w forme okruv-","nosti razrezatx i rastq-","nutx za koncy,to dlina","polu@ennogo otrezka i","estx dlina okruvnosti." 1 " centralxnyj ugol i"," duga okruvnosti.","","ugol razbiwaet ploskostx","na dwe @asti , kavdaq iz","kotoryh-ploskij ugol."," ploskie ugly s ob&im" 1 " bokowaq powerhnostx","piramidy-summa plo&adej","ee bokowyh granej.",""," teorema.","" 1 " bokowaq powerhnostx"," sostoit iz parallelog-"," rammow.",""," wysotoj prizmy nazy-"," waetsq rasstoqnie mev-"," du ploskostqmi ee osno-"," wanij.","","","","","","","","","","","","","" 1 " aksiomy stereometrii.",""," stereometriq-_to raz-","del geometrii,w kotorom","izu@a#tsq figury w pros-","transtwe.",""," osnownye figury:" 1 " S - wer%ina",""," aS,BS i t.d.- "," - bokowye rebra","","","","" 1 " 2.esli telo razbito"," na @asti ,qwlq#&iesq"," prostymi telami ,to"," ob'em _togo tela rawen"," summe ob'emow ego @as-"," tej.",""," 3.ob'em kuba,rebro" 1 " 1.rawnye tela ime#t"," rawnye ob'emy.","","","","","" 1 " %ar,tak ve,kak ci-"," lindr i konus,qwlqetsq"," figuroj wra&eniq. on"," polu@aetsq wra&eniem"," polukruga wokrug ego"," diametra kak osi.","" 1 " zada@a",""," w prqmougolxnom paral-"," lelepipede storony os-"," nowaniq 1 " tetra_dr:","grani-prawilxnye treu-","golxniki,w kavdoj wer%i-","ne shoditsq po tri rebra"," tetra_dr predstawlqet","soboj prawilxnu# pirami-","du." 1 " teorema:",""," diagonali parallele-"," pipeda pereseka#tsq w"," odnoj to@ke i to@koj"," perese@eniq delqtsq"," popolam." 1 " powerXnostx cilindra"," sostoit iz osnowanij i"," bokowoj powerXnosti.",""," cilindr movno ras-"," smatriwatx kak telo,"," polu@ennoe pri wra&enii" 1 " ploskostx,proXodq&aq"," @erez obrazu#&u# konusa"," i perpendikulqrnaq"," osewomu se@eni#,pro-"," wedennomu @erez _tu"," obrazu#&u#,nazywaetsq"," kasatelxnoj ploskostx#." 1 " ploskostx,perpendi-"," kulqrnaq osi konusa,ot-"," sekaet ot nego menx%ij"," konus. ostaw%aqsq @astx"," nazywaetsq use@ennym"," konusom.","" 1 " obxem piramidy",""," obxem l#boj piramidy","rawen odnoj treti proiz-","wedeniq plo&adi ee osno-","waniq na wysotu.","" 1 " mnogogrannik.",""," mnogogrannik - telo,"," powerhnostx kotorogo"," sostoit iz kone@nogo"," @isla ploskih mnogo-"," ugolxnikow.","" 1 " k o n u s",""," konus-_to figura , so-"," stoq&aq iz:","-kruga(osnowaniq konusa)","-to@ki , ne leva&ej w"," ploskosti _togo kruga"," (wer%iny)" 1 " ili:",""," plo&adx kruga rawna"," proizwedeni# kwadrata"," radiusa na @islo pi:","","" 1 " dokazatelxstwo:","","r-wypuklyj mnogougolxnik","a 1 " V=(S*n)/3","",""," obxem use@ennoj pira-","midy s plo&adqmi osnowa-","nij Q 1 " R 180","","radiannaq mera ugla","polu@aetsq iz gradusnoj","umnoveniem na 1 " ABCD = A 1 " teorema",""," wsqkoe se@enie %ara"," ploskostx# estx krug."," centr _togo kruga estx"," osnowanie perpendikulq-"," ra,opu&ennogo iz centra" 1 " prawilxnye"," mnogougolxniki.",""," wypuklyj mnogougolxnik","nazywaetsq prawilxnym,","esli u nego wse storony","i wse ugly rawny.","" 1 " ponqtie ob'ema."," ob'em parallelepipeda.",""," telo nazywaetsq pros-"," tym,esli ego movno raz-"," bitx na kone@noe @islo"," treugolxnyh piramid." 1 " plo&adx kruga.","","","",""," krug-_to figura,so-"," stoq&aq iz wseX to@ek"," ploskosti,rasstoqnie ot"," kotoryX do dannoj to@ki"," (centra kruga),ne bolx-" 1 " perpendikulqr"," i naklonnaq.","",""," perpendikulqr,opu&en-"," nyj iz dannoj to@ki na"," ploskostx,estx otrezok,"," soedinq#&ij dannu# to@-"," ku s to@koj ploskosti i"," leva&ij na prqmoj, per-"," pendikulqrnoj ploskosti" 1 " parallelxnostx"," ploskostej.","",""," dwe ploskosti nazy-"," wa#tsq parallelxnymi,"," esli oni ne pereseka#t-"," sq.","" 1 " parallelepiped.","",""," esli osnowanie prizmy"," estx parallelogramm, to"," ona nazywaetsq paralle-"," lepipedom." 1 " obxem %ara"," i ego @astej",""," %arowoj segment-@astx","%ara,otsekaemaq ot nego","ploskostx#.","" 1 " zada@a.","w naklonnoj prizme pro-","wedeno se@enie,perpendi-","kulqrnoe bokowym rebram","i pereseka#&ee wse rebra","najdite ob'em prizmy,","esli plo&adx se@eniq Q," 1 " zada@a","@erez seredinu wysoty ","piramidy prowedena plos-","kostx,parallelxnaq osno-","wani#. w kakom otno%enii","ona delit obxem piramidy","" 1 " re%enie","prowedennaq ploskostx ot","sekaet podobnu# piramidu","ko_fficient podobiq=1/2","zna@it obxemy piramid","otnosqtsq kak (1/2) 1 " prizma.",""," prizma -mnogogrannik,"," kotoryj sostoit iz dwuh"," ploskih mnogougolxni"," kow,sowme&aemyh paral-"," lelxnym perenosom," 1 " plo&adi"," prostyX figur","","",""," plo&adx parallelogram-"," ma rawna proizwedeni#"," ego storony na wysotu,"," prowedennu# k _toj sto-"," rone." 1 " cilindr",""," cilindr-_to telo,ko-"," toroe sostoit iz dwuX"," krugow,sowme&aemyX pa-"," rallelxnym perenosom,"," i wseX otrezkow,soedi-"," nq#&iX sootwetstwu#&ie" 1 " S = aB * AE","","","","","","","" 1 " 180",""," radiannaq mera ugla -","-_to otno%enie dugi k","radiusu okruvnosti"," 1 " teorema:","","prawilxnyj mnogougolxnik","qwlqetsq wpisannym w ok-","ruvnostx i opisannym","okolo okruvnosti.","" 1 " piramida.",""," piramidA - mnogogran-"," nik,kotoryj sostoit iz"," ploskogo mnogougolxnikA"," -osnowaniq piramidy,"," to@ki , ne leva&ej w" 1 " dokazatelxstwo:","","ao,wo-bissektrissy uglow","a i w.","treugolxnik aow rawno-","bedrennyj.","treugolxniki aow i wos" 1 " %ar.",""," %ar- telo , sostoq&ee"," iz wseh to@ek prostran-"," stwa , nahodq&ihsq ot"," centra na rasstoqnii,"," ne bolx%em dannogo (ra-"," diusa %ara)." 1 " teorema:",""," summa uglow wypuklogo"," 1 " obxemy"," cilindra i konusa","","",""," obxem cilindra rawen","proizwedeni# plo&adi" 1 " lomanaq.",""," lomanoj a 1 " 2"," V=- 1 " 1"," S= 1 " 1 !planim25B 1 !graf25 CX 1 !PLANIM26BU 1 zamenim a 1 wer-","%inami nazywaetsq 1 wektory"," 1 w"," urawnenii ploskosti"," qwlq#tsq koordinatami"," wektora,perpendikulqr-"," nogo ploskosti." 1 w urawnenii ","sfery,prohodq&ej @erez","to@ki (0,0,0),(4,0,0),","(0,4,0) .radius rawen","3 sm.","","wedite zna@eniq 1 w urawnenii ","sfery,prohodq&ej @erez","to@ki (0,0,0),(0,0,1),","(0,1,0),(1,0,0) .","","","wedite zna@eniq 1 w urawnenii ","ploskosti,kotoraq ","prohodit @erez to@ku","a i perpendikulqrna","prqmoj aw , esli","a(-1,1,2) , w(2,0,1)","","","","" 1 ugla mevdu","nimi rawen 0.6 .","najdite tretx# storonu.","","","" 1 ty ne gotow! 1 to@ki C wyrava#t-"," sq @erez koordinaty"," koncow otrezka "," A 1 to@ki A","nazywaetsq @islo,rawnoe","dline otrezka o 1 tela wra&eniq (@astx 1) obu@a#&ij kurs 1991 god. 1 t.k."," aa 1 soot-","wetstwuet duga,dlinoj"," 1 sm,to powerh-","nostx uweli@itsq na ","54 sm 1 skre&iwa#&iesq"," prqmye.","","","","","","","","","","","","","","","","","","","","" 1 s na@alom w" 1 rawny.",""," <A 1 prowedena prqmaq"; 1 prohodit","@erez t.A i parallelxna","ploskosti 1 prohodit @erez prqmu#"," 1 pro-"," wedem prqmu# AA 1 podoben r 1 plo&adi powerhnostej tel obu@a#&ij kurs 1991 god 1 plo&adi figur obu@a#&ij kurs 1991 god. 1 pl#s summa","uglow treugolxnika","a 1 perpendikulqrny,","prqmaq 1 perpendikulqrnostx prqmyh i ploskostej (@astx 2) 1991 god 1 perpendikulqrnostx prqmyh i ploskostej (@astx 1) 1991 god. 1 perpendikulqrnostx prqmyh obu@a#&ij kurs 1991 god 1 perpendikulqrna 1 perpendikulqr-","na ploskosti 1 perpendi-"," kulqrnye prqmye."," 1 peresekatxsq?" 1 perese-"," ka#tsq."," dokavem, @to 1 parallelxnostx prqmyh i ploskostej (@astx 2) 1991 god. 1 parallelo-"; 1 obxemy tel (@astx 2) obu@a#&ij kurs 1991 god. 1 obrazu#t"," ugol 30 1 nazywaetsq"," ugol mevdu prqmymi 1 na-","zywaetsq figura, kotoraq","sostoit iz to@ek a 1 na ploskostx 1 mnogougolxniki ( @ a s t x 2 ) 1 9 9 1 g o d . 1 mnogogranniki (@astx 3) obu@a#&ij kurs 1991 god. 1 mnogogranniki (@astx 2) obu@a#&ij kurs 1991 god 1 levit"," na polovitelxnoj polu-"," osi 1 levit"," na otricatelxnoj polu-"," osi;" 1 levat w"," odnoj ploskosti.",""," t.k. 1 levat w raz-"; 1 imeet plo-"," &adx",""," S = 1 imeet dlinu ne","bolx%u#,@em ishodnaq."," analogi@no perehodim k","lomanoj a 1 i","ploskostx# kwadrata ","rawen 60 1 i wysotoj 1 i ploskostx# treugolx-","nika rawen 60 1 i dwa"," ugla 1 i soedinq#&ih ih","otrezkow a 1 i perpendi-","kulqrna prqmoj 1 dekartowy koordinaty i wektory w prostranstwe (@astx 1) 1991 god 1 aksiomy stereometrii obu@a#&ij kurs 1 :1","sledowatelxno obxemy" 1 3.14 - @islo 'pi',",""," R - radius sfery.","","","" 1 2*SIN(180 1 1991 kazanx " 1 1991 kazanx 1 .","otwet wwedite w kwadrat-","nyh santimetrah.","","","" 1 .","najdite ugol 1 .","najdite ob'em paralle-","lepipeda.","","","","","","" 1 .","","otwet w kwadratnyh","metrah.","","","" 1 .","",""," re%enie.",""," po teoreme sinusow"," nahodim ugol 1 ."," 2","","","","","","","","" 1 -wypuklye 1 -skre&iwa#&iesq"," prqmye,"," 1 -prqmye perese-"," @eniq 1 -ploskostx,perpen-"," dikulqrnaq s;"," 1 -parallelxnye"," prqmye,",""," ugol mevdu 1 -","ugolxnikom." 1 - postoqnnye." 1 - dlina obrazu#&ej.","","","","","" 1 - S(aow)" 1 ,to",""," 1 ,perese-"," ka#&iesq w to@ke O," 1 ,gde","",""," S - plo&adx awsD." 1 ,esli","ploskostx kruga per-","pendikulqrna 1 ,esli aw=8 sm ,","aa 1 ,esli aw=15 sm ,","aa 1 ,",""," 1 ,"," prohodq&ie @erez soot-"," wetstwu#&ie osi , nazy-"," wa#tsq koordinatnymi .","","","","","","","","","" 1 , BC > AC","","","","","","","","","","","","","","","" 1 (aw+CD)*Ce ,"," 2",""," Ce=aF-wysoty trapecii.","","","","","","","","","","","" 1 tela wra&eniq (@astx 2) obu@a#&ij kurs 1991 god . 1 sow-"," padaet s t. O.",""," analogi@no opredelq-","#tsq koordinaty 1 po parallelxnym"," prqmym AB i A 1 pereseka#t-"; 1 per-","pendikulqrna ploskosti 1 mnogogranniki. @astx 1. 1 prinadlevit","ploskosti 1 parallelxny,"," AB-ob&ij perpendikulqr"," prqmyh 1 ob'emy tel (@astx 1) obu@a#&ij kurs 1991 god . 1 1991 kazanx " 1 1991 kazanx 1 +"," S= 1 "," 2R 1 i t.d.","" 1 "; 1 1