ޤ롩
813ڡ 0:03:22 34905
Taro
#34905
ޤʤ⡣Ҥȣ¤פȤͤ餽פޤ
ʤƲäƤꤷޤ^^;
ˤPC 813ڡ 0:08:41 34906
㡼ߡ
RQB = 45ΤȤDz򤭤ޤѤϰդˤޤޤ
Ȥ礦Ȥ䤯 813ڡ 0:07:56 MAIL:kakuromaster@star.cims.jp 34907
ߡ
ͤƤޤ

Ȥޤ褦ʤ
813ڡ 0:08:14 MAIL:amimorisama@hotmail.com 34908
mhayashi
Ƥ˺פ˻äƤߤޤ
KANSAI 813ڡ 0:11:06 HomePage:M.Hayashi's Web Site34909
tfnt
郎­ʤ褦Ǥ͡
PRABȾʬȤƲ򤭤ޤ
㡼ߡƱˤʤޤ
813ڡ 0:11:20 34910
ߥ饯
ޤʤǤ͡󡢾Ǥ͡
813ڡ 0:12:10 34911
ڤפ@ɡ
ϤQȤäȤľPQRQꤹ郎­ޤ͡
RQB=45ꤷޤ
813ڡ 0:17:06 34912
3浡Х
⤦ޤʤ
ѤSȤ
1/815S13/815
ǽФޤ
813ڡ 0:26:30 34913
kasama
դޤʤΤǤϡȤꤢܣңѣ¡ᣴȤƲ򤭤ޤ(;^_^A
²λ 813ڡ 0:36:17 34914
ޥ
𤷤ޤ

PR=AB2Ȥ郎ľޤǤäΤˡȴƤޤ...ߥޥ󡢽ˤʤ뤫Τޤm(__)m
813ڡ 1:02:57 34915

ơդޤʤȴޤϤꡣ
狼䤹45٤ǵ᤿ޤ
˺줿Τʡ
ŷϿ͡ 813ڡ 1:04:29 34916

PRABȾʬޤ¬ǤΤ˻ǰOTL
ŪˤϡRQB=45٤Ǥɡ
ŷϿ͡ 813ڡ 1:17:04 34917
ma-mu-ta
­ǰդޤʤΤԤФΤϡ
ȴΤʬ䤹ǤϤʤȡ
줿Τǰޤ
813ڡ 1:32:03 34918
Mr.ǥ
򸫤üĤλθȤȲ٤ɤľޤ
ǤʤǾϳȳοɤʾ郎ȴƤΤͽۤ뤳ȤƬڤ
ޤ

ޤδ顡RQBRQA ǤʤʤΤ RQB60,RQA30ǤϤȹͤΤǤ
ͭǤʤʤΤǥ
345λѷɤ˱ƤΤȹͤᡡ

ΤʸФơ塪
(ͽۤΩŤäࡦ

813ڡ 7:16:40 34919
doba
ФƤ鸫ΤǤǽޤǥ뤷Ƥ餺ʾС
ǧƤ⡢PQA=45Ϥ狼äΤηɤ겡Ǥ򤱤ޡ
夤ƹͤ顢Τ褦ˡĤޤ

ߤ濴OȤơ
PQRO濴ȿײ
90žΤP'Q'P
180žΤP''Q''P'
270žΤRQ'''P''
ȤȡPQRѤϡPP'P''RQQ'Q''Q'''
dzäΤǤꡢ
PP''=7QQ''=6ꡢ(49/2 - 36/2)/4 = 13/8

ʤߤˡ겡Ǥ
PQ=(31+32)/2QR=(31-32)/2Ȥʤޤ
813ڡ 8:33:31 34920
CRYING DOLPHIN
ߤ濴OȤOABM˸PQȤθSȤ롣
̤ξ狼顢PORϡOPOR3.5cmľջѷġ

ޤSOQϡOSOQ3cmľդǤ롣
ΤˡޤROQȢPOSƱǤ뤳Ȥ򼨤
(ǽñ90ٲžȻפäƤɡϤʤ褦)Orz

ꡢOROPޤ٤ξROQPOSưפȽ
dzOPQQPRᢤȤȡ(Ȣ)45١Ģ
PROޤPQRˤĤƳPRQ90ݢݢ
Ȥʤ롣ORQOPS
ʾꡢ2դȤδ֤γѤROQȢPOSιƱĢ
ǤäOSOQ3cm狼ä

ʲ( )Ͽ޷Ѥɽ
(PQR)(ͳѷPOQR)(POQ)
{(POR)(POQ)}{(SOQ)(POS))}
(POR)(SOQ)

ƤȤǡ 3.53.5233213/8 Ȥäȵޤ롪
Orzʬưפ˸ʤʤ
ï⤤ʤԳϡ 813ڡ 9:59:28 HomePage:ƻ34921
㡼ߡ @
ɤȤ PQQR ñ˵ޤ뤫ʤȹͤȤ
RQB = 45ʤ٤Ǥ˵ޤ
(AB ˴ؤ P оȤ) ΤǤΤ褦˲ᤷޤ
⺣դˤʤޤϤä񤷤äǤ
813ڡ 10:20:21 34922
uchinyan
Ϥˤϡơϡ
ȡ󤽤ʤΤǤ
ī̤򲼤ޤǥ뤻˿ޤʸ򸫤Ƭơīѻ PC ΥƬǹͤФΤǤ
ɤˤ޷ꤷʤΤǡʡȻפäƺƤ PC ʸǧǤƱ
dz򤱤ΤʤȻפäƥ뤷顤֤ͤӡפä衣𤱤ʤäǤ (^^;
ˡϡ㴳ȾФǡʴǤ

AB O ȤO ˴ؤƿ޷Τ 180žPQR ΰư P'Q'R' Ȥޤ
ȡPR = AB/2 ξꡤPRP'R' ˤʤޤ
ǡR' PQ ˡR P'Q' ˡ줾򲼤­ CC' Ȥޤ
ȡ޷оꡤQ' R'C 塤Q RC' ˤꡤPQRRC'P'P'Q'R'R'CP ϹƱCQC'Q' ˤʤޤ
ϡ̩ˤϤ⤦ڤɬפǤ礦ޤ餫äݤݤά (^^;
ơAQ'Q'QQB = 1121 ǡPP' = AB = 7 cmCC' = Q'Q = 7 * 12/(1 + 12 + 1) = 6 cm ꡤ
PQR = (PRP'R' - CQC'Q')/4 = (PP' * PP' * 1/2 - CC' * CC' * 1/2) * 1/4 = (7 * 7 - 6 * 6)/8 = 13/8 cm^2
ˤʤޤ

轵ϡ٤ߵ٤ߤǤ͡
ͥνȡ 815ڡ 14:26:55 MAIL:uchi@sco.bekkoame.ne.jp 34923
⡼ޥ
ä...^^;
Ȥ Orz
ǽȾ¤7ȻפäƤ...
(72)*6+7*x=7*y
x^2+y^2=(72)^2
7^2*(y-x)^2=42^2*2
7^2*(7^2*2-2xy)=42^2*2
ѷPQR=xy/2
=(49^2-42^2)/(2*49)
=49/2-18
=13/2
ºݤľ¤7ʤΤ...
(13/2)/2^2=13/8

...813αƧޤƤ뤳Ȥ˵դޤ
813ڡ 12:23:25 34924
uchinyan
ǼĤɤߤޤϤꡤ­ǿ޷ꤷʤȤˤꡤʬ𤬤ä褦Ǥ͡
RQB = 45ꤷˡϡPR = AB/2 -> RQB = 45ȤȤƤΡڤʬǤ

#34907#34912#34914#34916#34920#34922
RQB = 45ͳˡRQB = 45ƳΤϡ㤨С#34920ʤɤ#34921Τ褦ˤвǽǤ
θɤΤϡ󤢤ޤŪˤϽ񤭹ޤƤʤΤǤ
#34922٤#34920λʿʤɡꤽǤ
(٤⡤߼ѰʤɤȤäƾΤ̤ʤΤǡǤϤʤ⡥)

#34910
PRABȾʬȤƲ򤭤ޤ
ȡ䤷Ƥޤ
θ塤ɤ򤫤줿Τϡ񤭹ߤʤΤǤ

#34920#34923
#34920ϡPQR ߤ濴˴ؤơ90롤180롤270žĺꡤκˡ
#34923ϡ޷Τߤ濴˴ؤ 180ž롤ȡǽ꤬㴳㤤ޤ¼ƱǤ

#34921
ߤ濴 O Ȥ O AB M ˸PQ Ȥθ S ȤȤ
SOQ OS = OQ = 3 cm ľդˤʤ뤳ȤѤˡ
#34920ʤɤβˡ 1/4 ˤơܤˡͤƤ봶Ǥ

#34924
䲿Ȥ Orz
ȻʿȤäزˡ
¿ʬߤ濴 O ȤơPOR = 90ʤΤ POQR ϱߤܤ롤Ȥ顤ȥߡʡ
ɤ餽Τ褦Ǥ#34926

#34928
ѴؿܥץȤˡ

#34929
ľ PQ ȱߤȤθ S Ȥ QSR QS = QR ľջѷˤʤ뤳Ȥȡ٤Ȥˡ
ʻˡɤ̯⡣
ͥνȡ 815ڡ 14:29:29 MAIL:uchi@sco.bekkoame.ne.jp 34925
⡼ޥ
#34925
uchinyan ^^
ǤΡإȥߡ٤Ǥ
ƬޤޤΤƹԤäƤޤ...^^;;;...Orz...
813ڡ 14:04:02 34926
abcba@jugglermoka
轵꤬ñ᤮Ȥ⤢äơϼꤴޤ
ϻѷȤФ褤ȻԺΤξ꤯Ƥޤ
813ڡ 14:25:30 34927
ϥ饮㡼ƥ
Ѵؿ򶯰MATHEMATICAǽ򤷤ޤ¹äƤѤǤ¹
ʤ餤ΤǤ©ҤȲǤʤΤ;פѤǤ
813ڡ 14:51:56 HomePage:湩ؤ˥34928
abc
#34922ƱΤ褦٤Ѥޤ

ľPQȱߤȤθSȤȡQSRQS=QRľջѷǤ
衡PQ*QR=PQ*QS ٤PQ*QS=AQ*QB=(7*13/14)*(7*1/14)=13/4
äơPQRѤϡ(1/2)*PQ*QR=13/8 Ȥʤޤ
813ڡ 14:54:55 34929
⡼ޥ
#34929
ä...줬ޡȤʢ
813ڡ 15:44:43 34930

ȥԥ饹Τäˤʤޤ

ޡȤʲϻפդޤǤ
813ڡ 19:03:11 34931
doba
#34920ǡPQA=45ϼΤ褦ˤƳޤ
PRĹȾߤȾʬʤΤǡ濴POR=90ǡORP=45
POR=PQRꡢPOQRƱ߼ˤꡢ
߼ѤOQP=ORP=45
814ʶ 14:57:34 34932
doba
ɵ
󡢢PQR90뤺IJžͤǤϡ
ľѻѷγ٤δط顢PQȡRQžΤޤŤʤ뤳ȤΤǡ
¦ο޷ˤʤΤ餫ǡ
ˢPQA=45˿ɬפϤʤΤǤ
βˡפĤ˲ˡǢPQA=45ϵŤƤޤ
ΤˡդAB򼴤ޤ֤޷ȤͤƤޤ
ñʲˡ˵ŤΤ٤줿Ȥ
814ʶ 15:14:47 34933

ɤͤƤ⻻Ǥϲ򤱤ɹ⹻ؤȤäƲ򤤤Ƥޤä

ʸֻʬȴƤΤˤ⤫餺ФΤϤɤƤǤ
814ʶ 23:14:34 34934
uchinyan
#34913
ѤSȤ
1/815S13/815
֤줿ΤdzǧƤߤΤǤS = PQR Ȥ顤ϰ㤦ΤǤϤʤʤ
Ϥɤפޤ

ؤˤʤäƤޤޤηˤƤޤ礦ˤʤйͤƤߤƤ

(1)ǡPR = AB/2 ξϤʤȤʳξƱˤơ
PR Ⱦߤ AB ˤȤPQR κȺǾƤ

(2)(1)ˤơPR ȾߤǤϤʤΤα߼ˤ롤ȤѤΡPQR κȺǾƤ
ͥνȡ 815ڡ 14:51:18 MAIL:uchi@sco.bekkoame.ne.jp 34935

ʤʤ򤫤äǤ
816 17:36:40 34936
⡼ޥ
#34935
uchinyan䡦

(1)ǡPR = AB/2 ξϤʤȤʳξƱˤơ
PR Ⱦߤ AB ˤȤPQR κȺǾƤ

٤...
xy=13/4
y=13/2 ΤȤx κͤ 13/2顢Max=1313/8
y=1/2 ΤȤMin=13/8
(2)(1)ˤơPR ȾߤǤϤʤΤα߼ˤ롤ȤѤΡPQR κȺǾƤ

Ϥ狼ޤ...Ū...^^;
(7/2)^2=(13t)^2+t^2
t^2=49/4*14=7/8
Max=(13t)^2/2=169*7/16=1183/16
Min=(t)^2/2=7/16

ǤΤ...?
816 20:41:01 34937
uchinyan
#34937
⡼ޥ󤵤󡤹ͤĺƤ꤬Ȥޤ

(1)
ϹäƤ褦Ǥ褯ʬʤǤ (^^;
٤...
xy=13/4
x, y ȤϡǤ礦
ɤäơ٤ȤΤǤ礦
y=13/2 ΤȤx κͤ 13/2顢Max=1313/8
xy = 13/4 ʤСx = 1/2 Ǥϡx κ͡פȤΤϰ̣̤ޤ󡥡
xy = 13/4 ϻȤäƤʤΤǤ礦
x κ͡פϤɤäƽФΤǤ礦
y=1/2 ΤȤMin=13/8
ƱǡɤͤƤΤʬʤǤ

(2) ϡͤʬʤ㤦褦Ǥ

ҥȤˤʤ뤫ʤ

ꡤ¤ϡФʤСľʤɤ򤨤ơ޷оưפʬޤ
(1) ϤȤ⤫(2) 빽ݤʤ褦Ǥ

(1) ϡ ΤǻǤ̵ǤͤϻäݤϰϤǤǤޤ

(2) ϡʤȤϡľˡϤȤ⤫ǰʤϰϤǤϲ򤱤Ƥޤ
ּˤʬȤˡǤޤʤȡѤʤȤˤʤ褦Ǥ
ޤñ˻䤬ޤ򤱤Ƥʤ⤷ޤ󡥡
ʬȤ鷺ˡμ¿ľ˻ǡ򤯤ȤǤǤޤ
׻ϳڤʤ褦Ǥ
ͥνȡ 817ʷ 13:40:32 MAIL:uchi@sco.bekkoame.ne.jp 34938
⡼ޥ
#34938
uchinyan ^^;
øǤߤޤ...Orz...

(1)
AB 13 : 1 ʬ߼ޤǤεΥ...
BQ<RQĤޤꡢBQ û
PQ<ARĤޤꡢAR Ĺ
ʾ夫...Q οȱߤθQ' Ȥȿ¦αߤȤθ Q" Ȥ...ľѻѷPQR Q 濴˲žȤ...
MinPQR=BQ*QQ'/2=(7/14)*(13/2)*(1/2)=13/8
MaxPQR=QQ'*AR/2=(13/2)*(13/2)*(1/2)=1313/8
(٤...(13/2)*(1/2)=QQ'*QQ"QQ'=QQ" ʤΤ...)

ʤ...Ǥ礦...^^;?

(2)
ľŪ(=øǤ...^^;)...P R AB оλȹͤΤ... PQR=90٤λA ¦λǡ B ¦λǾʤʤ...
ΤȤ...ޤλѷPQ,RQ դ˻ľѻѷˤʤΤ...
PQ^2=(7/2)^2=PQ^2+RQ^2
PQ : RQ = 13 : 1 ...
(7/2)^2=(13t)^2+t^2
t^2=49/2*170=49/340
ä...
MinPQR=(49/340)/2=49/680
MaxPQR=(49/2-49/340)/2=8281/680
ʤƤȤ...
ǽΤ...ơ׻ְäƤ褦Ǥ...Orz...^^;

817ʷ 17:41:27 34939
uchinyan
#34939
(1) ϡOKǤ
äȤ뤵Ȥȡ
BQ<RQĤޤꡢBQ û
PQ<ARĤޤꡢAR Ĺ
դ餫ȤƤɤǤޤǤ礦 (^^;

(2) ϡľŪˤǤ

PQ : RQ = 13 : 1 ...
ϡǤ͡AQQB = 131 ǤPQRQ 131 ˤʤޤ
⤷ʤСPQR = 13t^2/2 = 637/680 cm^2 ˤʤäƤޤޤ
ͥνȡ 817ʷ 18:55:52 MAIL:uchi@sco.bekkoame.ne.jp 34940
⡼ޥ
#34940
uchinyan ^^
(2) ...ä......Orz...
x^2+y^2=(7/2)^2
y=x-3
x^2+(x-3)^2=2x^2-6x+9=(7/2)^2
8x^2-24x+36-49=0
x^2-3x-13=0
(x-3/2)^2=13+9/4=61/4
x=3/2ޢ61/2
y=-3/2ޢ61/2
x^2+y^2=35, 35+361
ä...
Max=(35+361)/2
Min=35/2

ˤʤޤ...׻ְ㤨Ƥʤ...^^;v
817ʷ 18:58:11 34941
uchinyan
#34941
󡤤ޤ褦ʡ
ͥνȡ 817ʷ 20:58:17 MAIL:uchi@sco.bekkoame.ne.jp 34942
̤ꤹ
#34940
Ȥá49/2-3*62Ǥ
818ʲС 12:10:33 34943
̤ꤹ
#34940
ȡMax=13/2
818ʲС 12:55:37 34944
⡼ޥ
#34941
ХʤȤˤä...ߤ濴εΥФäƻʤȤ...^^;
...49/4 ˤʤäƤʤ...׻ְäƤ뤳Ȥ...^^;

x^2+(x-3)^2=49/4
8x^2-24x=49-36=13
(x-3/2)^2=13/8+9/4=31/8
x=3/2ޢ62/4
y=-3/2ޢ62/4

2Min=((6+62)/4-3)^2+((-6+62)/4)^2
=2*((-6+62)/4)^2
=(49-662)/4

2Max=(-(6-62)/4+3)^2+(-(6+62)/4)^2
=((6+62)/4)^2+((6+62)/4)^2
=2*((6+62)/4)^2
=(36+62+1262)/8
=(98+1262)/8
=(49+662)/4

٤......^^;?...ޤ/ޤ׻ְäƤ뤫ʤ...?

818ʲС 16:45:29 34945
taku
פ֤˲򤭤ޤ⹻ؤǡ
ߤ濴ϡ¤ͤȤ
ϣͣѤ;cosܣϣͣѡ13/49ꡤ
Уѣҡᣲѣͣҡ13/8
٤Ǥʤۤɡ
818ʲС 16:29:04 MAIL:takuo@kcv.ne.jp 34946
ߤ餤
ޤꤵ󡢴ñǤ
818ʲС 18:02:20 34947
uchinyan
#34945
ǤMin, Max ϡ줾κǸͤȾʬǤ͡

Ȥ櫓ǡ̤ꤹꤵΤϡǰʤ顤㤦褦Ǥ
ͥνȡ 818ʲС 18:18:03 MAIL:uchi@sco.bekkoame.ne.jp 34948
uchinyan
#34946
ߤ濴ϡ¤ͤȤ
PR ͤȤ ʡ
ͥνȡ 818ʲС 18:57:17 MAIL:uchi@sco.bekkoame.ne.jp 34949
⡼ޥ
#34948
uchinyan ^^
Ǥ...ʲ򤪴ꤤޤ m(_ _)m...

(1)⤽Ǥ...Ȥ(2) Ϥ줬ˤȤϾǤƤʤ櫓ǤΤ...
ȤⶵƤǤ...ꤤޤOrz
819ʿ 10:53:32 34950
uchinyan
#34950
伫ȡ餫äݤˤϷ׻Ѥǡޤꤦޤ򤱤ƤʤΤǡɤʤˤޤ򤤤ߤäΤǤ
ʬޤ˻֤ʤΤǡ⤦Ф餯Ԥ
δ֤ˡɤʤޤ򤤤ƤȤ줷äꤷ (^^;
ͥνȡ 819ʿ 12:15:42 MAIL:uchi@sco.bekkoame.ne.jp 34951
⡼ޥ
#34951
uchinyan ^^
λ ̵ʤꤤʤΤˤ꤬Ȥޤ Orz
ˤʤȤ...ޤꤤޤ ^^v
819ʿ 12:26:40 34952
tutpr92
ޤơ
⹻ؤȤޥƥȤ͡Ǥ͡ġ

錄ϡˤ⤢Ȼפޤ
޷90٤IJžƽ礭
ƣdzȤ
ʤǤ򤱤ޤǤ

̲ޤʤ򤳤Ĥġ
ͤΤǺ٥󥸤Ƥߤޤ
819ʿ 14:41:47 MAIL:eb80597@gmail.com 34953
uchinyan
#34935
(1)ǡPR = AB/2 ξϤʤȤʳξƱˤơ
PR Ⱦߤ AB ˤȤPQR κȺǾƤ
(2)(1)ˤơPR ȾߤǤϤʤΤα߼ˤ롤ȤѤΡPQR κȺǾƤ
βˡǤľäơޤꤦޤ򤱤ƤʤΤǡ󡤤⤷ޤˡжƤ
ޤϡľˡ(1)(2)Ʊ˲򤱤륪ޥƥʬǤäƤߤޤ

ߤ濴 O(0,0)AB x ȤOA = OB = rOQ = c0 < c < rRQ = a > 0PQ = b > 0RQB = x0 <= x < 2СȤޤ
ȡ
R(a * cos(x) + c, a * sin(x))
P(b * cos(x + /2) + c, b * sin(x + /2)) = (- b * sin(x) + c, b * cos(x))
Ǥǡ
(a * cos(x) + c)^2 + (a * sin(x))^2 = OR^2 = r^2
(- b * sin(x) + c)^2 + (b * cos(x))^2 = OP^2 = r^2
Ĥޤꡤ
a^2 + 2c * cos(x) * a - (r^2 - c^2) = 0
b^2 - 2c * sin(x) * b - (r^2 - c^2) = 0
a > 0b > 0 ʤΤǡ
a = - c * cos(x) + sqrt(c^2 * (cos(x))^2 + (r^2 - c^2))
b = c * sin(x) + sqrt(c^2 * (sin(x))^2 + (r^2 - c^2))
ơPQR = S = S(x) Ȥȡ
S(x) = ab/2
ǤϡS(x) ʬĴ٤ФǤ
dS/dx = 1/2 * (da/dx * b + a * db/dx)
ǡ
da/dx = c * sin(x) - c^2 * cos(x) * sin(x)/sqrt(c^2 * (cos(x))^2 + (r^2 - c^2))
= c * sin(x) * (- c * cos(x) + sqrt(c^2 * (cos(x))^2 + (r^2 - c^2)))/sqrt(c^2 * (cos(x))^2 + (r^2 - c^2))
= a * c * sin(x)/sqrt(c^2 * (cos(x))^2 + (r^2 - c^2))
db/dx = c * cos(x) + c^2 * sin(x) * cos(x)/sqrt(c^2 * (sin(x))^2 + (r^2 - c^2))
= c * cos(x) * (c * sin(x) + sqrt(c^2 * (sin(x))^2 + (r^2 - c^2))/sqrt(c^2 * (sin(x))^2 + (r^2 - c^2))
= b * c * cos(x)/sqrt(c^2 * (sin(x))^2 + (r^2 - c^2))

dS/dx
= 1/2 * ab * c * (sin(x)/sqrt(c^2 * (cos(x))^2 + (r^2 - c^2)) + cos(x)/sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)))
= Sc * 1/sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)) * 1/sqrt(c^2 * (cos(x))^2 + (r^2 - c^2))
* (sin(x) * sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)) + cos(x) * sqrt(c^2 * (cos(x))^2 + (r^2 - c^2)))
= Sc * 1/sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)) * 1/sqrt(c^2 * (cos(x))^2 + (r^2 - c^2)) * f(x)
Ǹϡ
f(x) = sin(x) * sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)) + cos(x) * sqrt(c^2 * (cos(x))^2 + (r^2 - c^2))
Ȥޤ
Sc * 1/sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)) * 1/sqrt(c^2 * (cos(x))^2 + (r^2 - c^2)) > 0 ʤΤǡ
f(x) 顤0 Ĵ٤ФǤ츫ϡʤʤ񤷤Ǥ褯ȡ
0 <= x < /2 Ǥ
sin(x) >= 0cos(x) > 0f(x) > 0
/2 <= x < 3/4 Ǥϡ
sin(x) > 0cos(x) <= 0|sin(x)| > |cos(x)|
sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)) > sqrt(c^2 * (cos(x))^2 + (r^2 - c^2))
|sin(x)| * sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)) > |cos(x)| * sqrt(c^2 * (cos(x))^2 + (r^2 - c^2))
sin(x) * sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)) > - cos(x) * sqrt(c^2 * (cos(x))^2 + (r^2 - c^2))
sin(x) * sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)) + cos(x) * sqrt(c^2 * (cos(x))^2 + (r^2 - c^2)) > 0
f(x) > 0
3/4 <= x < Ǥϡ
sin(x) > 0cos(x) < 0|sin(x)| <= |cos(x)| x = 3/4
sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)) <= sqrt(c^2 * (cos(x))^2 + (r^2 - c^2))
|sin(x)| * sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)) <= |cos(x)| * sqrt(c^2 * (cos(x))^2 + (r^2 - c^2))
sin(x) * sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)) <= - cos(x) * sqrt(c^2 * (cos(x))^2 + (r^2 - c^2))
sin(x) * sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)) + cos(x) * sqrt(c^2 * (cos(x))^2 + (r^2 - c^2)) <= 0
f(x) <= 0 x = 3/4
<= x < 3/2 Ǥϡ
sin(x) <= 0cos(x) < 0f(x) < 0
3/2 <= x < 7/4 Ǥϡ
sin(x) < 0cos(x) >= 0|sin(x)| > |cos(x)|
sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)) > sqrt(c^2 * (cos(x))^2 + (r^2 - c^2))
|sin(x)| * sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)) > |cos(x)| * sqrt(c^2 * (cos(x))^2 + (r^2 - c^2))
- sin(x) * sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)) > cos(x) * sqrt(c^2 * (cos(x))^2 + (r^2 - c^2))
sin(x) * sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)) + cos(x) * sqrt(c^2 * (cos(x))^2 + (r^2 - c^2)) < 0
f(x) < 0
7/4 <= x < 2 Ǥϡ
sin(x) < 0cos(x) > 0|sin(x)| <= |cos(x)| x = 7/4
sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)) <= sqrt(c^2 * (cos(x))^2 + (r^2 - c^2))
|sin(x)| * sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)) <= |cos(x)| * sqrt(c^2 * (cos(x))^2 + (r^2 - c^2))
- sin(x) * sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)) <= cos(x) * sqrt(c^2 * (cos(x))^2 + (r^2 - c^2))
sin(x) * sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)) + cos(x) * sqrt(c^2 * (cos(x))^2 + (r^2 - c^2)) >= 0
f(x) >= 0 x = 7/4
ǡ0 <= x < 2 ǡ
0 <= x < 3/4 Ǥϡf(x) > 0dS/dx > 0S ñĴ
x = 3/4 Ǥϡf(x) = 0dS/dx = 0S ϶礫ĺ
3/4 < x < 7/4 Ǥϡf(x) < 0dS/dx < 0S ñĴ
x = 7/4 Ǥϡf(x) = 0dS/dx = 0S ϶˾ĺǾ
7/4 < x < 2 Ǥϡf(x) > 0dS/dx > 0S ñĴ
ˤʤޤʾꡤ
S(x) = ab/2
= 1/2 * (- c * cos(x) + sqrt(c^2 * (cos(x))^2 + (r^2 - c^2))) * (c * sin(x) + sqrt(c^2 * (sin(x))^2 + (r^2 - c^2)))
դơ

(1) 0 <= x <= /2 ǹͤФΤǡS(x) ñĴäǡ
S(0) <= S(x) <= S(/2)
1/2 * (r - c) * sqrt(r^2 - c^2) <= PQR <= 1/2 * (r + c) * sqrt(r^2 - c^2)
r = 7/2c = 7/2 - 7/(13 + 1) = 3 ꡤ
1/8 * sqrt(13) <= PQR <= 13/8 * sqrt(13)
ˤʤޤ

(2)
S(7/4) <= S(x) <= S(3/4)
1/2 * (r^2 - c * sqrt(2r^2 - c^2)) <= PQR <= 1/2 * (r^2 + c * sqrt(2r^2 - c^2))
r = 7/2c = 3 ꡤ
(49 - 6 * sqrt(62))/8 <= PQR <= (49 + 6 * sqrt(62))/8
ˤʤޤ

βˡΥݥȤ f(x) ɾǤľȤѤǡ줤ʷ򤷤Ƥ뤳ȤѤƲȤǤޤ
ȤǤ΢ˤϡ줤ʴطƤ櫓ǡäȴñˤǤʵ⤷ޤ
ʤŤȻפޤƱͤˤơf(x) μ
sin(x)/sqrt(c^2 * (cos(x))^2 + (r^2 - c^2)) + cos(x)/sqrt(c^2 * (sin(x))^2 + (r^2 - c^2))
ľܤɾ뤳ȤǽǤ
ͥνȡ 820ڡ 14:12:28 MAIL:uchi@sco.bekkoame.ne.jp 34954
uchinyan
#34954³

(1) ϡ⡼ޥ󤵤ȸ§ƱǤΤ褦ˤнϰϤǤǤޤ

ߤ濴 O ȤT AB T' TA T ȤϰۤʤȤޤ
ȡ
T' A ˰פT B ˰פʤϡO ϡQTT' ΰˤꡤT'Q ˴ؤ T ȿ¦ˤΤǡ
QTT' > OTT' = OT'T > QT'T ȤʤꡤT'Q > TQ ˤʤޤ
T' A ˰פT B ˰פʤϡO ϡQTT' ΰˤꡤT'Q = AQ ˤΤǡ
QTT' > OTT' = OT'T = QT'T ȤʤꡤT'Q > TQ ˤʤޤ
T' A ˰פT B ˰פϡO ϡT'Q ˴ؤ T ȿ¦ˤꡤTQ = BQ αĹˤΤǡ
QTT' = OTT' = OT'T > QT'T ȤʤꡤT'Q > TQ ˤʤޤ
T' A ˰פT B ˰פϡ餫ˡT'Q > TQ ˤʤޤ
ɡˡT'Q > TQ ʤΤǡT AB B A ˰ưȤTQ ñĴäʬޤ
ꡤPQR = PQ * RQ * 1/2 ʤΤǡPR AB ˤȤ PQRQ ˴ؤơ
Q AB ˿Ω AB Ȥθ C Ȥȡ
BQ <= RQ <= CQ <= PQ <= AQ
ޤǡ
CQ * BQ * 1/2 <= PQR = PQ * RQ * 1/2 <= AQ * CQ * 1/2
AQ = 7 * 13/(13 + 1) = 13/2BQ = 7 * 1/(13 + 1) = 1/2
OC = OA = OB = 7/2OQ = OB - BQ = 7/2 - 1/2 = 3CQ = sqrt(OC^2 - OQ^2) = sqrt((7/2)^2 - 3^2) = sqrt(13)/2
ʤΤǡ
1/8 * sqrt(13) <= PQR <= 13/8 * sqrt(13)
ˤʤޤ
ͥνȡ 820ڡ 14:02:02 MAIL:uchi@sco.bekkoame.ne.jp 34955
uchinyan
#34955³

(2) ϡΤ褦ˤСʬȤʤƤǤޤ

#34954Ʊǡ
a^2 + 2c * cos(x) * a - (r^2 - c^2) = 0
b^2 - 2c * sin(x) * b - (r^2 - c^2) = 0
a > 0b > 0 ʤΤǡ
cos(x) = - 1/2c * (a - (r^2 - c^2)/a)
sin(x) = + 1/2c * (b - (r^2 - c^2)/b)
(cos(x))^2 + (sin(x))^2 = 1 ꡤ
(1/2c * (a - (r^2 - c^2)/a))^2 + (1/2c * (b - (r^2 - c^2)/b))^2 = 1
a^2 - 2(r^2 - c^2) + (r^2 - c^2)^2/a^2 + b^2 - 2(r^2 - c^2) + (r^2 - c^2)^2/b^2 = 4c^2
a^2 + b^2 - 4(r^2 - c^2) + + (r^2 - c^2)^2 * (1/a^2 + 1/b^2) = 4c^2
(a + b)^2 - 2ab - 4(r^2 - c^2) + (r^2 - c^2)^2 * ((a + b)^2 - 2ab)/(ab)^2 = 4c^2
ǡa + b = sab = t Ȥȡab μ¿Ǥ뤳Ȥꡤ
(a - b)^2 = (a + b)^2 - 4ab = s^2 - 4t >= 0
s > 0, t > 0
Ǥդˡʤ st ¸ߤ ab ¸ߤޤޤ
PQR = ab/2 = t/2
Ǥơۤɤ ab μϡ
s^2 - 2t - 4(r^2 - c^2) + (r^2 - c^2)^2 * (s^2 - 2t)/t^2 = 4c^2
(1 + (r^2 - c^2)^2/t^2) * s^2 = 2t + 4r^2 + 2(r^2 - c^2)^2/t
ǡμꡤt > 0 ʤ s > 0 β뤳ȤǤs > 0 ޤ
ơt > 0 θǡ
s^2 - 4t >= 0
(1 + (r^2 - c^2)^2/t^2) * s^2 - (1 + (r^2 - c^2)^2/t^2) * 4t >= 0
2t + 4r^2 + 2(r^2 - c^2)^2/t - 4t - 4(r^2 - c^2)^2/t >= 0
2t - 4r^2 + 2(r^2 - c^2)^2/t <= 0
t^2 - 2r^2 * t + (r^2 - c^2)^2 <= 0
r^2 - sqrt(r^4 - (r^2 - c^2)^2) <= t <= r^2 + sqrt(r^4 - (r^2 - c^2)^2)
r^2 - c * sqrt(2r^2 - c^2) <= t <= r^2 + c * sqrt(2r^2 - c^2)
ǡr^2 + c * sqrt(2r^2 - c^2) > 0 ǡ0 < c < r ꡤ
(r^2 - c * sqrt(2r^2 - c^2)) * (r^2 + c * sqrt(2r^2 - c^2))
= r^4 - c^2 * (2r^2 - c^2)
= r^4 - 2 * c^2 * r^2 + c^4
= (r^2 - c^2)^2 > 0
ʤΤǡr^2 - c * sqrt(2r^2 - c^2) > 0 ⤤ޤǡt > 0 ΩƤޤ
ơ
(r^2 - c * sqrt(2r^2 - c^2))/2 <= PQR = t/2 <= (r^2 + c * sqrt(2r^2 - c^2))/2
ޤǡr = 7/2c = 7/2 - 7/(13 + 1) = 3 ʤΤǡ
(49 - 6 * sqrt(62))/8 <= S <= (49 + 6 * sqrt(62))/8
ˤʤޤ

ʤ硤Ǿ a = bĤޤ RQ = PQΤȤʤΤǡPQR ջѷˤʤȤǡ
RQB = 3/47/4 Ȥʤäơ#34954ȡΤ˰פƤޤ
ͥνȡ 820ڡ 14:26:58 MAIL:uchi@sco.bekkoame.ne.jp 34956
⡼ޥ
#34954,#34955,#34956
uchinyan ^^
ܺ٤ʲˡˤ꤬Ȥޤ m(_ _ )m...v
Ѥʷ׻ϤˤĤƤ뤫ɤޤ...ɴ̣Ǥ ^^;
820ڡ 22:55:55 34957

#34953tutpr92 󡣾ܺ٤򤪤ͤޤʤʤ餳ΥȤǤϻ餷ˡǤ⥨쥬ȤˡʤΤǤ顣ؤˡϤषȤΤǤꤤޤ
826ʿ 18:08:15 34958