ޥ
դʤȤǤޤ..ϣʤޤΡ˥Хȥ֥бɤ졢Ķû֤äƤޤäʸľۤȤɤƤʤ...ˤΤǥߥʤѿۤʤΤǤ...פǤ礦䳧
PowerBook 719ڡ 0:08:13 MAIL:masaru-y@sansu.org HomePage:30289

ľѻѷȤȤϻȤʤΤǤϡ
á͡СѤȳ٤ơΤǤϡ
719ڡ 0:09:20 30290
banyanyan
֤Ƥƽ٤ޤ
ãͣѢ梤ͣУ
ᣴУѡУѡᣱ
ãͣ͡С᣷
ãͣ͡СߣãСߣʣݣˡߣᣳ

Իԡ 719ڡ 0:10:32 MAIL:banyanyanmi@yahoo.co.jp HomePage:뤤²ײݻ30291
ʸ
ľѻѷϻȤ鷺
ǤȤޤ
719ڡ 0:12:17 MAIL:kyorofumi@msn.com HomePage:ʸ30292
banyanyan
裴Ʊ꤬ޤ
Իԡ 719ڡ 0:12:23 MAIL:banyanyanmi@yahoo.co.jp HomePage:뤤²ײݻ30293
㡼ߡ
2 Τˤޤ̾ܤޤ (2 ʬȤĤä)
𡡡 719ڡ 0:12:41 MAIL:ojamaru@amber.plala.or.jp 30294
Taro
MCQDz򤱤Ǥ͡
դĹȳѤǷޤ褦Ǥ
719ڡ 0:14:19 30295
ޥ
Ϥ꼺ԤƤޤޤ.........

̾ηϡߥǤ....orz
PowerBook 719ڡ 0:14:58 MAIL:masaru-y@sansu.org HomePage:30296

ȳѤʬʬʬ
Dz򤭤ޤ
褽140٤餤 719ڡ 0:15:19 30297
⡼ޥ
餤ƱǤ^^v
åǤ^^
719ڡ 0:18:29 30298
ޥ
ߥޥ󡢤ʾ֤˥ꥸʥǺȤΤְ㤤Ǥ.......꤬˲ƤʤäΤʤΤʤΤ...ĤޤʤˤʤäƤޤäƥߥޥ...

줫顢뤴23:50餤ޤǤδ֡Фʤ԰ʤĽŤˤˤʤäƤޤδ֤˻䰸Ƥ˥ᥤꡢβ줿ꤷϡ⤷ȥᥤ뤬Ƥ뤫Τޤפʥᥤޤ顢ƤйǤ

䡦Ԥ줿ޤǤ....
PowerBook 719ڡ 0:20:25 MAIL:masaru-y@sansu.org HomePage:30299
ߤ
(#30291)banyanyanΤƱˡǤ޷϶
Ǥ⻻ˡDz򤱤ΤǰפʤǤ礦

(#30299)ޥ뤵
ĤޤʤˤʤäƤޤäƥߥޥ...
äǺޤƤޤåγû֤
Ƥʤ褦˻פΤϵΤ
719ڡ 0:27:50 30300
tl
ϤꡢľѤϻȤʤɤäǤ͡
719ڡ 0:34:50 30301
banyanyan
ѤʬϰϤǤΤǡDz򤭤ޤ
Իԡ 719ڡ 0:54:16 MAIL:banyanyanmi@yahoo.co.jp HomePage:뤤²ײݻ30302
ǥ
ɤǣͤ¤B=90ȤΤȻפĤġդ˾ϳǤ
ʤȹꤷƤʤɢAMQPǤξMCĹ
ޤ뤳Ȥ˵ĤޤʵĤΤ٤ä夦ˡ
¿˵ĤΤϡ졼ȤƤΩäƤޤ
ޤˤϰȡ
719ڡ 0:57:11 30303
Ѥ
ãͣѤãͤ򼴤ˤޤ֤Ѥΰ֤ѡǤȤȡ
ѡǣäȣ¤ʿԤˤʤäΤǡֲ򤱤롪פȻפäΤǤ˿ʤޤ
ãͣѤǹͤѤƲ򤱤뤳Ȥ˵դ
ʺˤ٤ǿǤᵯΤȾȤꥺ졣
֡ 719ڡ 1:10:29 HomePage:ʥڡ30304
ma-mu-ta
Ĥǡ٤Ƥλá
CMQ梤MPQǡ74ȤäơMC33/48.25cm
8.25Ǥ̤ʤ
MľѻѷȤȤʤäΤǡʤˤ㤤򤷤
ȿޤ٤⸫ľȤФġ
ɤͤƤˤʤ롣
ǤäȵĤʬǤäƤߤɤ
Ϥäޤ
ɵؤǤʬ̤ΤȤǤǤϿ̤ɽΤ˲ʬꡢ
ڤϾ̤ǤʬɤǤȤΤǤġ

719ڡ 3:16:29 30305

ФͣäʿԤҤͣѤȤθҤȤ
ãͣѢ梤ͣУѡУѡᣱ/ʤΤ
ѣУҢ梤ѣãͤϣĭ
ѣҡͣҡᣱˣͣѡᣴʤΤ
ͣҡᣱ/ͣУҤϣͣҡУҤջѷʤΤ
Уҡͣҡᣱ/ͣáᣴУ/ʤΤ
ͣáᣴ/ߣ/ᣳ/
719ڡ 8:14:10 30308
uchinyan
Ϥˤϡơϡ
Ϥ䤵ȤľѤȤȤȤޤǤΤʡ
MPQ = 2 * MCP = CMQ ʤΤǡMPQ CMQ Ǥ
ǡPQMQ = MQCQPQ4 = 47PQ = 16/7 cm ǡCP = CQ - PQ = 7 - 16/7 = 33/7 cm Ǥ
ޤPCM = PMC MP = CP = 33/7 cm Ǥ
ǡ١MPQ CMQ ꡤCMMP = CQMQCM33/7 = 74CM = 33/4 cm ˤʤޤ
ͥνȡ 719ڡ 9:23:35 MAIL:uchi@sco.bekkoame.ne.jp 30309
ƿ̾
Dz򤤤Ƥޤäorz
⤽äΤۤ󤴤ƻ
719ڡ 10:47:57 30310
uchinyan
ǼĤɤߤޤ

#30289#30296#30299
Хȥ֥ʤɤѤä褦ǤϫͤǤ
ߥϤʤ褦Ǥפʾ郎褦Ǥ͡

#30290#30291#30292#30295#30297#30298#30300#30301#30303#30304#30305#30309
㴳ΥХꥨϤ褦ǤMPQ CMQ Ȥˡˤ줬¿줷ʤ褦Ǥ
ľѤξϡϤפʤ褦Ǥ͡
#30305
ǷǼĤʤä褦Ǥޤ衣

#30308
ФͣäʿԤҤͣѤȤθҤȤ
⡤MPQ CMQ ȤޤȾ㴳ŤäƤΤǡʬˤޤ

#30310
Dz򤤤Ƥޤäorz
䤷⤽äΤۤ󤴤ƻ
ͤƤߤޤۤݤȤϻפʤŻǤǤϰϡȻפޤ
ܳѤ䣳ܳѤθμꤴ꤫ʤ
ͥνȡ 719ڡ 11:18:16 MAIL:uchi@sco.bekkoame.ne.jp 30311
ޥ
ޤФŤ֤ˤʤäƤ褦Ǥ...ࡢƤΤǤޤʬޤ󡣤ʤ٤᤯бޤΤǡ򤤤йǤm(__)m
PowerBook 719ڡ 11:42:16 MAIL:masaru-y@sansu.org HomePage:30312
ޥ
кǤ...ȻפޤǤ򤪤ޤm(__)m
PowerBook 719ڡ 12:02:45 MAIL:masaru-y@sansu.org HomePage:30313
㡼ߡ
褯ͤ麣ǯƤ 1 ̤2 ̤ϲäƤΤˡ
𡡡 719ڡ 15:10:43 MAIL:ojamaru@amber.plala.or.jp 30314
ϥ饮㡼ƥ
ФϡMATHEMATICAˤ׻Ǥ
;Dz򤱤ޤ
719ڡ 17:03:36 HomePage:湩ؤ˥30315
⡼ޥ
ޤ^2 ͧ ^^v Orz


a1,a2,ġ..
an=2^n+3^n+6^n-1(n=1,2,ġ..)롣
οΤɤιȤߤǤǤ褦ʼ1ʳˤʤȤ򼨤

錄ˤ񤷤ʬޤǤ^^;
720ʶ 10:36:07 30316

äѤ껰ѷȳѤΣʬλȤޤ
ǤϤ狼ޤǤ
720ʶ 11:42:25 30317
uchinyan
#30316
ޤ餫ˡߤǤɤĴ٤뼫ǿ˸¤äOKǤ
ʤʤС̤˸ǿޤߡǿξ˵夹Τǡ
ǡǿˤĤƹͤޤ
a(n) = 2^n + 3^n + 6^n - 1(n = 1, 2, ...)
ˤơ
a(1) = 2 + 3 + 6 - 1 = 10, a(2) = 4 + 9 + 36 - 1 = 48
ʤΤǡ2, 3, 5 ȤϸߤǤǤϤʤǤǡp 7 ʾǿȤޤ
ȡ2, 3, 6 p ȸߤǤʤΤǡեޡξꡤmod p
2^(p-1) 1, 3^(p-1) 1, 6^(p-1) 1
ǡ칩פǤʤͤƤҤᤤ ^^/
6 * a(p-2) = 6 * (2^(p-2) + 3^(p-2) + 6^(p-2) - 1) = 3 * 2^(p-1) + 2 * 3^(p-1) + 6^(p-1) - 6
mod p Ȥȡ
6 * a(p-2) 3 * 1 + 2 * 1 + 1 - 6 = 6 - 6 = 0
Ĥޤꡤ6 * a(p-2) p dzڤޤp 6 ȸߤǤäΤǡa(p-2) p dzڤޤ
ʾǷɡ٤ƤǿФƸߤǤǤʤ a(n) ¸ߤ뤳ȤʬäΤǡ
ߤǤʼ 1 ˤʤޤ
ͥνȡ 720ʶ 15:57:47 MAIL:uchi@sco.bekkoame.ne.jp 30318
⡼ޥ
#30318
uchinyanء
ήСŷˤ餷^^v
ޤƱǤ Ǥ͡
錄ˤϡ#30318 褯ʬޤOrz
ʤߤ˰ʲǤ

1ʳˤʤȤ򼨤
ǤդǿpФơan0(modp)Ȥʤ뼫n¸ߤ뤳Ȥ
Ф褤a2=4823ܿʤΤǡʲp>=5Ȥ
a(p-2)0(modp)򼨤
ΤȤp2,3,6ϸߤǤʤΤǥեޡξ
2^(p-1)3^(p-1)6^(p-1)1 (mod p)
äơ6(2^(p-2)+3^(p-2)+6^(p-2)-1)=3*2^(p-1)+2*3^(p-1)+6^(p-1)-6
3+2-1-6=0 (mod p)
a(p-2)=2^(p-2)+3^(p-2)+6^(p-2)-6 (mod p)狼롣

720ʶ 18:29:13 30319
tfnt
ξ狼黻ϰϤ
ABĹޤǤϵޤߤǤ
720ʶ 20:45:07 30320
moarith55
#30305ma-mu-taΡ־ǧߤפ˰ɼǤ͡^^;
kyoto 720ʶ 22:11:15 30321
ȤޤԤ
ʬγѤǤǤޤABCľѻѷǤ뤳ȻȤޤǤ

Ȥǡ򻻿Dz򤱤ͤޤ󤫡
ͤʹǤ

ؤǤ
֣ܤߤȤȾ¤Ȥ˰Ϥޤ줿Ѥ
Ϳޡhttp://sakura.canvas.ne.jp/spr/space_yhnt/others/img.jpg
720ʶ 22:44:09 30322
tomh
ֹȽ֤轵ΤޤޤǤ͡ (^^;
ԡ 721ڡ 0:25:42 MAIL:tomh@yahoo.co.jp HomePage:H to M30323
ȤޤԤ
#30322
޷оΤμȣߤθߡߤ濴ȤʬȤΤʤѤ򤽤줾졢¡Ȥȡʥ饸ñ̡
ϡcos¡52/8cos2/4ߤԳѤǤ롣

¤Ѥ
Ѥϡʦ-+2sin¡/4
Ȥʤ褦Ǥ͡
򥨥ǿͲƤ⤭줤ˤʤ󡩡
0.146ȤǤƤޤ

721ڡ 8:52:22 30324
ǥ
ȤޤԤ󤵤#30323
ؤDz򤤤Ƥߤ顢ߤθ֤εΥȢ144Ȥʤ
򤽤Τޤ޻Ȥ碌Ƥ餦
Ѥϡ28¡ܢ7/8Ȥʤޤ
ϡʦ-+2sin¡/4 ȰפơȤޤԤ󤵤Ⱦ㤦
Υߥʡ

>Ȥǡ򻻿Dz򤱤ͤޤ󤫡
ȤȤǤ¤ͭɽˤʤ壷ͭǤ
ȤƤ⻻ϰϤǽ褽ˤޤ󤬡Τ˺ޤ򤷤ʬ
ٴȤäŬäƤ褤Τʤ̤Ǥ

⡼ޥ󤵤#30316,uchinyan#30318
ǤΤ򤤤塢񤭹⤦Ȥβˡ
ʬuchinyanβˡ񤭹ޤƤꡢäijο
ޤ
äвǤ
(1)ޤեޡξȤʤȾʤޤ
(ȤꡢȤʤΤϤ줷Τʤä
(2)ǿʣ棵ˤˤĤƣ(p-1)2(modˡ(p)10(modˤȡ
ޤʤΤǡ(p2)˾ʤꡢ6*(p2)0(modˤ˻

(3),(2)(3)(5)11(9)
ˤʤäƤ뤳Ȥdzǧơޤְ㤤Ϥʤȡ

721ڡ 11:41:20 30325
⡼ޥ
#30325
ǥ󡢤 Orz
ޤޤȤκ򴶤ФǤ^^;;

ϤǤ礦
ǿͧǤ^^v

nȤ롣a1+a2+,,,,,,,,+an=1
a1a2,,,,,,,,anФơnĤο
a1/(1+a1)a2/(1+a1+a2)ġ..an/(1+a1+a2+ġ..+an)
κǾͤAȤ
a1a2ġ..anѲȤAκͤ衣
721ڡ 11:43:53 30326
uchinyan
#30325¾
ǥء
Ѥϡ28¡ܢ7/8Ȥʤޤ
䤳ϡʦ-+2sin¡/4 ȰפơȤޤԤ󤵤Ⱦ㤦Υߥʡ
ȡȤޤԤ󤵤#30324ˤСcos = 52/8 ʤΤǡsin = (1 - 50/64) = 14/8 ǡ
ȤޤԤ󤵤 = ( - 4 + 22 * sin)/4
= ( - 4 + 22 * 14/8)/4 = ( - 4 + 7/2)/4
= (2 - 8 + 7)/8 = ǥ
ʤΤǡפƤ褦Ǥ

ʤǤäȹͤǤ񤷤Ǥ͡ɤ
ͥνȡ 721ڡ 12:28:51 MAIL:uchi@sco.bekkoame.ne.jp 30328
uchinyan
#30326
⡼ޥ󤵤ء
nȤ롣a1+a2+,,,,,,,,+an=1
a1a2,,,,,,,,anФơnĤο
졤ʤǤ
a1, a2, ..., an פä顤a1 >= 1, a2 >= 1, ..., an >= 1 ʤΤǡa1 + a2 + ... + an >= n ǡդ 1 ä顤n = 1 Ǥ
ǤˤʤʤǤ
ͥνȡ 721ڡ 12:49:34 MAIL:uchi@sco.bekkoame.ne.jp 30329
ȤޤԤ
#30328 #30325

ǥuchinyan

꤬ȤޤäѤ껻ϤӤǤ͡

http://sakura.canvas.ne.jp/spr/space_yhnt/others/ans.jpg

錄ϡʴǤ
721ڡ 13:54:39 30330
ǥ
βˡȤޤԤ󤵤#30330ȤۤȤƱǤ
S1Ȥ˦ΤۤγѤѤΤǡƤäꤳ
γѤѤȺФƦ,¤ǧ˵դˤȤäƤޤäƤ褦
ΤäߥǤ(sin2sin 礤ޤ͡

ȤޤԤ󤵤󡢼餤ޤOrz
uchinyan󡢤Ŧͭ񤦤ޤOrz
721ڡ 17:07:03 30331
⡼ޥ
#30329
uchinyanء
٤ʤޤOrz
Ǥ͡μ¿פδְ㤤ΤǤ͡^^;
722 0:51:40 30332
uchinyan
#30326#30332
Ϥꡤμ¿פʤΤǤ͡
ࡤ񤷤Ǥ
ϡտȤäʿѤȤͤȤޤǤäΤǤ郎Ωפޤ
ơīͤƤƤǤɤʤȤˡʤСΩOKΤ褦Ǥ

ޤA ϺǾͤʤΤǡʤȤ⡤
a(1)/(1 + a(1)) >= A
a(2)/(1 + a(1) + a(2)) >= A
a(3)/(1 + a(1) + a(2) + a(3)) >= A
...
a(n)/(1 + a(1) + a(2) + a(3) + ... + a(n)) >= A
ޤ줾κդϡѷȡ
1 - 1/(1 + a(1)) >= A
1 - (1 + a(1))/(1 + a(1) + a(2)) >= A
1 - (1 + a(1) + a(2))/(1 + a(1) + a(2) + a(3)) >= A
...
1 - (1 + a(1) + a(2) + ... + a(n-2))/(1 + a(1) + a(2) + a(3) + ... + a(n-1)) >= A
1 - (1 + a(1) + a(2) + ... + a(n-1))/(1 + a(1) + a(2) + a(3) + ... + a(n-1) + a(n)) >= A
Ƚ񤱤ޤǡ
1 - A >= 1/(1 + a(1))
1 - A >= (1 + a(1))/(1 + a(1) + a(2))
1 - A >= (1 + a(1) + a(2))/(1 + a(1) + a(2) + a(3))
...
1 - A >= (1 + a(1) + a(2) + ... + a(n-2))/(1 + a(1) + a(2) + a(3) + ... + a(n-1))
1 - A >= (1 + a(1) + a(2) + ... + a(n-1))/(1 + a(1) + a(2) + a(3) + ... + a(n-1) + a(n))
줫顤ξդȤʤΤξդ򤫤
(1 - A)^n >= 1/(1 + a(1)) * (1 + a(1))/(1 + a(1) + a(2)) * (1 + a(1) + a(2))/(1 + a(1) + a(2) + a(3)) * ...
* (1 + a(1) + a(2) + ... + a(n-2))/(1 + a(1) + a(2) + a(3) + ... + a(n-1))
* (1 + a(1) + a(2) + ... + a(n-1))/(1 + a(1) + a(2) + a(3) + ... + a(n-1) + a(n))
DZդʬҤʬ줬ޤ껦ơʤ褦ѷΤǤ ^^;
(1 - A)^n >= 1/(1 + a(1) + a(2) + a(3) + ... + a(n-1) + a(n)) = 1/(1 + 1) = 1/2
Ǹϡa(1) + a(2) + a(3) + ... + a(n-1) + a(n) = 1 Ȥޤǡ¿ϰϤʤΤǡ
1 - A >= (1/2)^(1/n)
A <= 1 - (1/2)^(1/n)
ǡ⤷椬ΩСA κ 1 - (1/2)^(1/n) ˤʤޤ
椬Ωʤˤϡñˡ¤ͿƤ˲᤮ޤ󡣤ǡΩĴ٤ޤ

椬Ωϡѷ򸫤ʬޤɡ٤Ƥιब A ʤΤǡ
a(1)/(1 + a(1)) = a(2)/(1 + a(1) + a(2)) = a(3)/(1 + a(1) + a(2) + a(3)) = ... = a(n)/(1 + a(1) + a(2) + a(3) + ... + a(n)) = A
ξǤΤȤ
a(1) = A/(1 - A), a(2) = A/(1 - A) * (1 + a(1)), a(3) = A/(1 - A) * (1 + a(1) + a(2)), ...,
a(n) = A/(1 - A) * (1 + a(1) + a(2) + a(3) + ... + a(n-1))
ʤΤǡa(1), a(2), ..., a(n) A ɽޤºݤ˷׻Ƥߤȡ줤ˤʤä
a(1) = A/(1 - A), a(2) = A/(1 - A)^2, a(3) = A/(1 - A)^3, ..., a(n) = A/(1 - A)^n
ȡ
a(1) + a(2) + a(3) + ... + a(n-1) + a(n) = 1
ϢΩƲ򤯤ȡ
A/(1 - A) + A/(1 - A)^2 + A/(1 - A)^3 + ... + A/(1 - A)^n = 1
A/(1 - A) * {(1 - 1/(1 - A)^n)/(1 - 1/(1 - A))} = 1
A * {(1 - 1/(1 - A)^n)/(1 - A - 1)} = 1
1/(1 - A)^n - 1 = 1
(1 - A)^n = 1/2
1 - A = (1/2)^(1/n)
A = 1 - (1/2)^(1/n)
ǡΤ A ͤƸޤ
ƤΤȤ A Ȥä a(1), a(2), a(3), ..., a(n) Τ˼¿ϰϤ¸ߤΤǡ椬Ωޤ

Ǹϥ㥴㤷ޤΩݾڤ줿ΤǡɡA κͤ 1 - (1/2)^(1/n) ˤʤޤ

ǤɤǤ礦
ͥνȡ 722 14:27:04 MAIL:uchi@sco.bekkoame.ne.jp 30333
⡼ޥ
#30333
uchinyan󡢥ѡեȡ
Ĥʤ餷 Orz

ʤߤ˰ʲΤ錄ΤϴְäƤ櫓ǤɤͤȤƤΤƲ^^; Orz

a1/(1+a1)=1/(1/a1+1)
a2/(1+a1+a2)=1/(1/a2+a1/a2+1)



an/(1+a1+a2++an)=1/(1/an+a1/an+a2/an++1)

1<1/a1+1
2<1+1/a2+a1/a2a1>a2ΤȤ



n<1/an+a1/an+a2/an++1a1>a2>>an
λʬϺ硣
a1+a2++an=1 ʤΤǡ
Ǿan κͤ Max(Min an)=1/n
ΤȤǸμǾͤκͤǡ1/(n+n-1+1)=1/2n
722 14:34:01 30334
uchinyan
#30334
äƤƤ褫ä (^^;

⡼ޥ󤵤βˡǤǤƤʤΤǤɤ⡤a1 > a2 > a3> ... > an ꤷƤ褦ʵޤ
¿ʬƳȤʤäƤ褦ʤΤǤΥåǤʤǤ

ʤߤˡn = 2 ξǶŪĴ٤Ƥߤȡ
a1/(1 + a1) - a2/(1 + a1 + a2) = (a1^2 + a1 - a2)/((1 + a1)(1 + a1 + a2))


1) a1^2 + a1 - a2 >= 0 ξ
a1/(1 + a1) >= a2/(1 + a1 + a2) ʤΤǡA = a2/(1 + a1 + a2) ȤOKǤ
ƤΤȤa1 + a2 = 1 ʤΤǡ
a1^2 + a1 - a2 >= 0
(1 - a2)^2 + (1 - a2) - a2 >= 0
a2^2 - 4 * a2 + 2 >= 0
(a2 - 2 - sqrt(2))(a2 - 2 + sqrt(2)) >= 0
餫 0 < a2 <= 1 ʤΤǡ0 < a2 <= 2 - sqrt(2) Ǥǡ
A = a2/(1 + a1 + a2) = a2/(1 + 1) = a2/2 <= (2 - sqrt(2))/2 = 1 - 1/sqrt(2)

2) a1^2 + a1 - a2 < 0 ξ
a1/(1 + a1) < a2/(1 + a1 + a2) ʤΤǡA = a1/(1 + a1) ȤOKǤ
ƤΤȤa1 + a2 = 1 ʤΤǡ
a1^2 + a1 - a2 < 0
a1^2 + a1 - (1 - a1) < 0
a1^2 + 2 * a1 - 1 < 0
(a1 + 1 - sqrt(2))(a1 + 1 + sqrt(2)) < 0
餫 0 < a1 <= 1 ʤΤǡ0 < a1 <= sqrt(2) - 1 Ǥǡ
A = a1/(1 + a1) = 1 - 1/(1 + a1) < 1 - 1/(1 + sqrt(2) - 1) = 1 - 1/sqrt(2)

ǡA κͤ 1 - 1/sqrt(2) = 1 - (1/2)^(1/2) Ȥʤꡤ̤ξ n = 2 Ǥ뤳Ȥʬޤ

碌ƶ̣ƤߤƤ

ʤߤˡϤޤäƤߤơҥȤΰĤˤʤä#30333ˤɤ夭ޤ
ͥνȡ 722 15:34:30 MAIL:uchi@sco.bekkoame.ne.jp 30335
⡼ޥ
#30335
uchinyan󡢤꤬Ȥޤ1/2n<1-(1/2)^n (3<=n ξ)Ǥ͡
ˡa1 > a2 > a3> ... > an ꡡΤ⤽⤪Ǥ͡^^; Orz
722 17:37:48 30336
ǥ
#30333
uchinyan󡢸渫

>DZդʬҤʬ줬ޤ껦ơʤ褦ѷΤ
^^;

ϡΤ褦껦AȣȤݥ
äΤǤ͡ȤƤפĤޤǤæ˹
722 18:12:54 30337
nno
ͤΤϤ򤪼ڤꤷ

x^2+(y-3)^2=4ѡxФȤ롣
ʣݣˤȤȤAP-PQ|κͤ衣

ޤ񤤤Ƥ줳äƤǤ
޷Ūʰ̣ĤʤƺäƤޤ
ꤤޤ
723ʷ 22:07:55 30338
⡼ޥ
#30338
ͤƤߤޤ
A x о A' (1,1) Ȥȡߤ濴 (0,3) A' ľx θP Ȥ
Q 餫ˤľȱߤα¦θˤʤꡢᤤ¦θQ' Ȥ
|AP-PQ|=PQ-AP=4+PQ'-PA' Ȥʤ롣
ޤ餫ˡP 礭Ƥ⾮Ƥ PQ'-PA' κϾʤΤǡ
ΤȤ硣
ʤߤˡ(0,3),(1,1) ̤ľϡy-3=(3-1)/(0-1)(x-0) 顢y=-2x+3
P ϡ(3/2,0)
PQ-PA=2+((3/2)^2+3^2)-((3/2-1)^2+1^2)=2+(45/4)-(5/4)=2+5*(3-1)/2=2+5
ʡ
724ʲС 16:04:44 30339
ǥ
#30339
⡼󡢸渫
ƱͤФƤäΤǤäȷ׻ѻʲˡǤ
ʤߤˡΤ餹񤤤Ƥߤޤ

(1) (t,0)Ȥꡢ(0,3)ȷľȱߤȤα󤤤ۤθѤȤ롣
(2) f(t)УѡݣУ f(t)(t^2+9)ݢ(t^2-2+2)2
(3) f(t)'/(t^2+9)(t-1)/(t^2-2+2)
(4) f(t)'0򤯤 2/3 ,3/4 ΤȤ
(5) f(0),f(3/4),f(2/3),f(2)׻ơӤ f(2/3)2+5
ͤǤ뤳Ȥ롣
(6)УУѤǡ(2+5)ʾξϹͤ줺̵롣

ʾǤ׻ݤǡФΤ ޤꥹޡȤǤʤˡǤ
⡼ΣоΤ'ȤäˡϤޤǤ͡
724ʲС 16:41:41 30340
doba
#30339⡼ޥ󤵤
٤äˤʤäƤޤޤ'ꤷƤޤȾƤޤޤ

ߤ濴(0,3)ȤȤ'ľ'äȱߤθ˸ꤹΤǤϤʤ
ưФФľУáʣ'äǤϤʤˤȱߤθФ˶ᤤ'''Ȥ롢
ʤ'''ϣФϢưưưȹͤơ
ФꤹȣУѡݣУˤʤΤϣѤ''ȰפȤǤ뤫顢
ΤȤУѡݣУУáݣУ'ܣ
ˣФưƤ줬ˤʤ褦ˤˤϡ
УáݣУ'ˤʤ褦ФȤФ褤ȤȤǡ
ƱǤ͡

ȡ̩˸ȡУݣУѤ2+5ĶʤȤǧɬפޤ͡
#30340Υǥ(6)ޤ

#30340ǥ
줬ޡȤǤʤȤϻפޤ衣
УáݣУ'ˤʤΤФ'þ˼äȤȤȤ
̩ΤϡϤǷ빽äȻפޤ

ȡ¤ϻƱְ㤤äƤơäŤΤǤ
(4)f'(t)=0򤯤ȡt=3/2ϽФƤޤt=3/4Ϥ褯ȲˤʤäƤޤǤ
ʺ򳰤˰ܹषξդ򣲾褷ǡɬ׽ʬǤʤʤäƤޤʴˡ
ʤߤˡ2/3ǤϤʤ3/2Ǥ͡

(6)ˤĤƤϡФꡢʤtꤷˣУݣУѤˤΤϡ
ѤФ(0,3)ľȱߤΣФ˶ᤤθΤȤʤΤǡΤȤ
УݣУѡg(t)(t^2-2+2)ݢ(t^2+9)2
lim[t+]g(t)ᣱ2+5
lim[t-]g(t)ᣳ2+5
dzǧǤޤ
724ʲС 17:38:25 30341
uchinyan
#30338¾
򸫤ơεɤȤʤΤǴ㤤Ƥ뤫Τޤ󤬡
⡼ޥ󤵤ľŪʵŪˤϡ֤ʤפȤǰϤʤǤ긷̩ˤϡ
dobaΤ褦˱ߤ濴 C(0,3) ͤơǥΤ褦ˤäȷ׻Τ̵ʴޤ
Τ˷׻ϤݤǤ
ˤ衤ʤännoϡǼǤΤʡ
ͥνȡ 724ʲС 19:04:47 MAIL:uchi@sco.bekkoame.ne.jp 30342
nno
󡢤꤬Ȥޤ

⡼ޥ󤵤
Ǹν濴äȤơѣáܣãǡᣲܢ壵ǤǤ͡
ޤ餫ˡΤȤäƽ꤬
ҤȤĥåꤷޤ夤ƿޤ񤤤ƹͤƤߤޤ

doba
ʬϤޤäƤʤΤǡ褯ʬޤ
ʤ
#30341ʬä褦ʬʤ褦ʡ
⤦äƤߤޤ

˳󤢤꤬Ȥޤ
724ʲС 19:20:28 30343
doba
#30343 nno
ۤ
գУáݣУ'ˤʤΤФ'þ˼äȤȤȤ
ո̩ΤϡϤǷ빽äȻפޤ
Ƚ񤤤Ƥޤޤ褯ͤƤߤñääߤǤ
#⡼ޥ󤵤󡢥ǥ餷ޤ

'äȣθ'ȤФΣ'ʳˤȤȡ
С'äƱľˤʤΤǡѷ
У'ܣ'áУ
äơ
УáݣУ''á'áݣ''

äơФ'ȰפȤУáݣУ'ϺȤʤ롣

ȤΤֿޤ餫פȤäΤǤ͡
ˤʤ顢ʬȤʤƤ⸷̩Ǥޤ͡

УݣУѤεϻĤޤ⹩פФʤ񤷤ϤʤǤ
724ʲС 20:04:33 30344
ǥ
#30341
⡼ޥ󤵤Σ'򸫤Ȥ󡢼ΤȤȲᤷΤǤ

,',',Ѥ򥹥⡼ޥ󤵤Τ褦˼ꡢ'¾
Фȣ(0,3)֡
'áݣ''áݣ'' ϢУ'ä¾գ'äû
äơ'ΤɤǤ⡡УáݣУ'áݣ'
󤤤ۤα߼ˤʤȣĤ羮طƱ
顢Τ褦ˣФȤäȤˡУ-Уˤʤ롣

ɤ֤ȡɽ㤦ΤdobaλŦnnoε䤬ĤäΤǤ礦
nno 󡢾ǤɤǤ礦

doba
>ʤߤˡ2/3ǤϤʤ3/2Ǥ͡
Ǥְ㤨ޤŦɤꡡ3/2 Ǥ
>t=3/4Ϥ褯ȲˤʤäƤޤǤ
ĤȤǤ͡^3 Σ0 ΤȤΤ褦ˤʤäƤΤȼ
Ƥޤ
ޤУУѤΤФγǧͭ񤦤ޤ

ǤǤ֤ˡdoba ƤꡢƤ֤äȤޤ
Τޤ޻ĤƤ餤ޤ

724ʲС 21:19:29 30345
⡼ޥ
#30343
nnoء
錄¤ϱžˡֿޤ餫פɤ꤯ΤȹͤƤޤ^^;
#30344 doba
>'äȣθ'ȤФΣ'ʳˤȤȡ
С'äƱľˤʤΤǡѷ
У'ܣ'áУ
äơ
УáݣУ''á'áݣ''
äơФ'ȰפȤУáݣУ'ϺȤʤ롣

ܤ
#30345 ǥƱȾƤޤ͢ǤȤ˥åפƤΤ˵դޤOrz
Ĥ⥢ХȤʲˡؤʤäƤȤʤOrz
ǥΤ褦ʬǤ⹶褦ȤޤǤ˻ӤĤƤƤǤʤäꡢ^^;
ޡĤΤ褦ˤɤʤͤùꤷƤ館Фʤơ
ͽ̤ꡢdobauchinyanˤ٤ΤȤʤ餷äͤùޤޤɡOrz

ʤߤˡ
>Ǹν濴äȤơѣáܣãǡᣲܢ壵ǤǤ͡

ϡPQ-PA=QC+CP-PA'=QC+CA' ϡޤ餫(^^;)Ǥ v
724ʲС 22:16:05 30346
nno
ޤƮäƤޤ
ɲ˴ǼسƤޤ
ŤͽŤ꤬ͤȤޤ
⤦äȤǥå褽Ǥ
724ʲС 21:30:18 30347
uchinyan
#30344#30345¾
ʤۤɡѷդδط򤦤ޤȤ櫓Ǥ͡ʤи̩ϰϤʤ
ͿƤϺɸǤǤޤ򤱤ƤޤǤ͡
ٶˤʤޤ
ͥνȡ 724ʲС 21:35:46 MAIL:uchi@sco.bekkoame.ne.jp 30348
nno
ΤǡۤǤˤʤäƤޤա

#30341(6)ΤȤǡݡĤޤäƤʤΤǤ
A'CαĹPˤʤʬ䤹
ʤǤ̩͡ʤƤɤǤ
٤ꤤޤ
724ʲС 21:59:59 30349
⡼ޥ
#30349
dobaˡǡ
PC > PA' ΤȤ
PA'+A'C > PC顢
PC-PA' < A'C

PC < PA' ΤȤ
PC+A'C > PA'
PA'-PC < A'C

ǤΤʡ
PC = PA' Ȥ P ޤ͡
ʤߤˡ(0,3),(3/2,0) (3/4,3/2) ʤΤǡ
y-3/2=(x-3/4)/2 y=0 顢
P ( -7/12, 0 ) ΤȤϡȾ2Ĥޤ͡(PQ-PA'=2)
Ǥ⤳ΤȤ ͤʤǤ͡^^;v
ʷ׻ʤƤ⡢PC = PA' ʤ顢PQ-PA' = 2+PC-PA' = 2 ǤǤ^^;;
졢ʤˤäƤ狼ʤʤäƤޤOrz
724ʲС 22:46:50 30350
uchinyan
#30349
t -> - ϡP xΤϤ뤫˹ԤäʤΤǡ#30341(6)Ǥϡ绨Ĥ
PA = Pxɸ + 1PQ = Pxɸ - 2
ȹͤƤǤ礦ǡPA - PQ = 3 < 2 + 5 Ȥʤޤ

ʤ⤽⡤Τ褦˹ͤƤ褵ǤA' A xоΤȤȡPQA' ǡ
|PA - PQ| = |PA' - PQ| <= QA'
ǸϡP QA' αĹˤȤǤʳ PQA' ǤȤP ϡxˤ⤢ޤ
ǡP QA' αĹˤ褦ˤơQ ư QA' κͤȡ
Q ߤ濴 C ˴ؤ A' ȿ¦ˤȤʬޤ
ǡ
|PA - PQ| = |PA' - PQ| <= QA' <= QC + CA' = 2 + 5
åꤷƤ뤫Τޤ
ͥνȡ 724ʲС 23:04:29 MAIL:uchi@sco.bekkoame.ne.jp 30351
⡼ޥ
#30351
ͤΤ֥ץޡȤǤ͢
ʬ⤤ʤ^^v Orz
724ʲС 23:21:42 30352
ǥ
#30351
ʤۤɤ͡ǤѤƱߤȤθѤ(0,3)Ф˶᤯Ƥ
Ƥ⡢ޤȤǤΤǤ͡Ǽ
Ԥ夯ȤޤǹԤ夤Ǥ͡Ǥ
725ʿ 0:24:17 30353
nno
uchinyan󡡥⡼ޥ󤵤󡡥ǥdoba
͡ˤ꤬Ȥޤ
#30351 åꤷޤʤۤɡȤǤ

725ʿ 1:05:15 30354
uchinyan
#30354
nnoǼʤä褦ʤΤǤ褫äǤ ^^/

ɤΤȤ⡼ޥ󤵤о A' ͤ륢ǥǤ͡
ͥνȡ 725ʿ 12:37:08 MAIL:uchi@sco.bekkoame.ne.jp 30355
⡼ޥ
#30355
uchinyan󡢤˫ˤꤳФ椤Ǥ^^ Orzv
Ȥǡ
λver3 ꡢäƤǤ礦顣
ˤϽ񤱤ޤ󤬼ʬʤˤ줷ʤȻפäƤΤʤ^^;
725ʿ 23:11:16 30356
ʸ
󡦡
ʤΤʡ

Ǿ夬äƤ
726ڡ 0:07:05 MAIL:kyorofumi@msn.com HomePage:ʸ30357
Ѥ
Ƥʤ褦Ǥ
̲
֡ 726ڡ 0:09:19 HomePage:ʥڡ30358
㡼ߡ
ࡣäΤ
𡡡 726ڡ 0:11:05 MAIL:ojamaru@amber.plala.or.jp 30359
Taro
դɽ⤪
Τ558
726ڡ 0:12:20 30360
ʸ
äƤ褯712 718ˤʤäƤ롣
726ڡ 0:12:42 MAIL:kyorofumi@msn.com HomePage:ʸ30361
Ѥ
ǯΣ˹ä餢̣
֡ 726ڡ 0:16:09 HomePage:ʥڡ30362

åطäꤷ
726ڡ 0:18:20 30363
UMA
мѡ
726ڡ 0:18:40 30364
ߤ
ޤǤʤˤʤäġĤȤʤǤ͡
ʤηޤ衣
726ڡ 0:21:00 30365
⡼ޥ
ޤϿ̤δطʤǤ͡
726ڡ 0:23:59 30366
doba
˻Ȥ⤢ΤǤ礦
Ŀͤ轵ꤵƤΤǤ顢Ǥ⥹ä

å餱㤤ޤ͡
726ڡ 0:25:07 30367

뻰ܤƣǤȡɴΰ̤Ȱΰ̤ο
ؤޤλʤ
ǯʾǤ
ŨʲˡƤ
726ڡ 0:29:14 30368
ޥ
ߥޥ󡢤äȻʤȤǤϤʤΤǤ...ˤäƹǤޤǤ꼫ΤѰդƤΤǡʤե뤬긵ˤʤΤǤ줫HTML񤭤ޤˡ0:50᤮˹פޤޤǤm(__)m
iMac 726ڡ 0:40:54 MAIL:masaru-y@sansu.org HomePage:30370
doba
#30368
4.5ܤƤ⣳ʤΤǡȤοɴΰ̡ʡ4.5ܤΰΰ̡ˤϣǡ
ܤΰΰ̤ϣĤޤꡢȤοΰΰ̤ϣ
4.5ܤƣˤϤʤꤨʤΤǡ
4.5᣸Ȥʤꡢ
ˤĤƲ򤯤ȡ᣹
198
ȤǤɤǤ礦
726ڡ 0:45:30 30371
Taro
#30368
ʲͤƤߤޤ

cba9ܿabc9ܿcba81ܿ
a1ʤΤcba=162,891,972ͤ졤
abcΤΤ198
726ڡ 0:47:50 30372
cocolo
#30368

9ܤ2dzȤȤϡ
ɸο4.5ܤΤƱȤʤΤǡ
夬ä3οȸοȤκϡο3.5ܤȤʤ롣
3οȡοɴΰ̤Ȱΰ̤ؤäκ99ܿˤʤΤǡ
2Ĥ3οκ3.5Ǥ99Ǥdzڤˤʤ롣
Τ褦ʺθȤƤ693ͤʤ
693ο3.5ܤΤǡ
(ο)6933.5198

ʤΤǤǤ礦
726ڡ 0:51:32 30373