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å ¥åã8/(1-1/5)=
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1 - 1/5 = 4/5
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8 ÷ 4/5 = 8 * (5/4) = 10
ãããã£ãŠã8/(1-1/5) = 10 ãšãªããŸãã
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åºåããã®åé¡ã¯ãé¶Žãšäºã®æ°ã衚ãäºã€ã®æ¹çšåŒãè§£ãããšã§çããèŠã€ããããšãã§ããŸãã以äžã«ãããè¡ããŸãïŒé¶Žãšäºã®åèšã5å¹ã§ããããšãããé¶Žã®æ°ãTãäºã®æ°ãKãšãããšãæåã®æ¹çšåŒã¯ T + K = 5 ãšè¡šããŸãã
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ãããŠãæåã®æ¹çšåŒ T + K = 5 ãäºã€ç®ã®æ¹çšåŒ T + 2K = 7 ããåŒããŸãããã®çµæãK = 2 ãšãªããŸããã€ãŸããäºã®æ°ã¯2å¹ã§ãã
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å ¥åããšã¬ããŒã¿ãŒã§1éãã5éãŸã§äžããã®ã«50ç§ããããŸããããã®ãšã¬ããŒã¿ãŒã§1éãã25éãŸã§äžããã®ã«äœç§ãããã§ããããïŒ ãªãããšã¬ããŒã¿ãŒã¯ãã€ãåãã¹ããŒãã§åããã®ãšããŸãã
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1éãã5éãŸã§äžããã®ã«50ç§ããã£ãã®ã§ã1éåäžããã®ã«ãããæé㯠50ç§ Ã· (5é - 1é) = 50ç§ Ã· 4 = 12.5ç§/é ã§ãã
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6x^2 + 9x - 8x - 12
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3x(2x + 3) - 4(2x + 3)
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(3x - 4)(2x + 3)
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â»æ£è§£ã§ãã
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6 * -12 = -72
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ãããã®æ°ãçšããŠãå ã®2次åŒã次ã®ããã«æžãæããŸãïŒ
6x^2+x-12 = 6x^2 + 8x - 9x - 12
ãããæŽã«ã°ã«ãŒãã³ã°ããŠå æ°ãåãåºããšïŒ
= 2x(3x + 4) - 3(3x + 4)
æåŸã«ãå ±éã®é (3x+4)ãåãåºããšæçµçãªå æ°åè§£ã®åœ¢ã«ãªããŸãïŒ
= (3x + 4)(2x - 3)
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â»äžæ£è§£ã§ããåã1ã«ãªããããªïŒã€ã®æ°ãèŠã€ãããšããã§ééã£ãŠããŸãã
å ¥åãæ¬¡ã®åãã«ã段éçã«æšè«ããŠçããªããã倪éã¯åå8æã«ãæ¯å60mã§æ©ããŠå®¶ããåŠæ ¡ãžåãããŸãããå¯åããæ¬¡éã¯15ååŸã®åå8æ15åã«ãæ¯å150mã®èªè»¢è»ã§å®¶ãåºçºããŸãããæ¬¡éã¯ã倪éãéäžã§è¿œãè¶ãã倪éããã9åæ©ãåŠæ ¡ãžçããŸãããå®¶ããåŠæ ¡ãŸã§ã®è·é¢ã¯äœmã§ãã?
æ§ããŒãžã§ã³ããŸãã倪éãšæ¬¡éãåŠæ ¡ã«å°çããã®ã«ããã£ãæéãèŠã€ããŸãããã
倪éãæ©ããŠããéåºŠã¯æ¯å60mã§ããæ¬¡éãèªè»¢è»ã§èµ°ã£ãŠããéåºŠã¯æ¯å150mã§ãã
次éã¯ã倪éããã15åé ããŠå®¶ãåºçºãã9åæ©ãåŠæ ¡ã«å°çããã®ã§ã倪éããã24åïŒ15å + 9åïŒéãåŠæ ¡ã«çããŸããã
次ã«ã倪éãåŠæ ¡ã«çããŸã§ã«ããã£ãæéãTãšããæ¬¡éãåŠæ ¡ã«çããŸã§ã«ããã£ãæéã¯T-24åãšããŸãã
å®¶ããåŠæ ¡ãŸã§ã®è·é¢ã¯ã倪éãšæ¬¡éãåãè·é¢ãç§»åããããšããã倪éã®é床Ã倪éã®æèŠæé = 次éã®éåºŠÃæ¬¡éã®æèŠæéãšãªããŸãã
60m à T = 150m à (T - 24)
åŒãè§£ãããã«ãäž¡èŸºãæŽçããŸãã
60T = 150T - 3600
90T = 3600
T = 40
倪éãåŠæ ¡ã«çããŸã§ã«ããã£ãæéã¯40åã§ãã
æåŸã«ãå®¶ããåŠæ ¡ãŸã§ã®è·é¢ãèšç®ããŸãã
è·é¢ = é床 à æé
è·é¢ = 60m à 40å = 2400m
å®¶ããåŠæ ¡ãŸã§ã®è·é¢ã¯2400mã§ãã
â»æ£è§£ã§ãã
æ°ããŒãžã§ã³ã倪éãšæ¬¡éãå®¶ããåŠæ ¡ãŸã§ã®è·é¢ãåãã ãšãããšãåé¡ã以äžã®ããã«è§£ãããšãã§ããŸãã
ïŒïŒæ¬¡éã倪éãã9åæ©ãåŠæ ¡ã«çããã®ã§ã倪éãåŠæ ¡ã«çããŸã§ã«èŠããæéã¯æ¬¡éãåºçºããŠããã®æé(15å)ãšæ¬¡éãæ©ãçããæé(9å)ãåããããã®ãã€ãŸã24åã«ãªããŸãã
ïŒïŒãããã£ãŠã倪éãåŠæ ¡ã«çããŸã§ã«èŠããæéã¯ã倪éãåºçºããŠããã®æé(8æãã)ãšå€ªéãåŠæ ¡ã«çããŸã§ã®æé(24å)ãåããããã®ãã€ãŸã32åã§ãã
ïŒïŒå€ªéã®éåºŠã¯æ¯å60mãªã®ã§ãå®¶ããåŠæ ¡ãŸã§ã®è·é¢ã¯å€ªéã®é床(60m/å)ãšå€ªéãåŠæ ¡ã«çããŸã§ã®æé(32å)ãæãããã®ã«ãªããŸãã
ïŒïŒãããã£ãŠãå®¶ããåŠæ ¡ãŸã§ã®è·é¢ã¯ 60m/å * 32å = 1920m ã«ãªããŸãã
以äžã®æšè«ã«ãããå®¶ããåŠæ ¡ãŸã§ã®è·é¢ã¯1920mã§ãããšçµè«ä»ããããšãã§ããŸãã
â»äžæ£è§£ã§ããïŒãšïŒã®èãæ¹ãééã£ãŠããŸãã
å ¥åãäžè§åœ¢ã®3蟺ã®é·ããa=â13ãb=3ãc=4ã®ãšãããã®äžè§åœ¢ã®å€æ¥åã®ååŸãæ±ããŠãã ããããã ããããã³ã®å ¬åŒã¯äœ¿ããªãã§ãã ããã
æ§ããŒãžã§ã³ãäžè§åœ¢ã®å€æ¥åã®ååŸãæ±ããããã«ãäœåŒŠå®çãšæ£åŒŠå®çãå©çšããŸããäžè§åœ¢ã®3蟺ã®é·ããa = â13ãb = 3ãc = 4ãšäžããããŠããŸãã
ãŸããäœåŒŠå®çã䜿ã£ãŠè§AïŒå¯ŸèŸºãaã®è§ïŒã®å€§ãããæ±ããŸããäœåŒŠå®çã¯æ¬¡ã®ããã«è¡šãããŸãã
cosA = (b^2 + c^2 - a^2) / (2 * b * c)
ãã®åé¡ã®å ŽåãcosAã¯æ¬¡ã®ããã«èšç®ã§ããŸãã
cosA = (3^2 + 4^2 - (â13)^2) / (2 * 3 * 4) = (9 + 16 - 13) / 24 = 12 / 24 = 1 / 2
cosA = 1/2ãããè§A = 60°ïŒãŸãã¯Ï/3ã©ãžã¢ã³ïŒã§ãã
次ã«ãæ£åŒŠå®çã䜿ã£ãŠå€æ¥åã®ååŸRãæ±ããŸããæ£åŒŠå®çã¯æ¬¡ã®ããã«è¡šãããŸãã
a / sinA = b / sinB = c / sinC = 2R
ãã®åé¡ã§ã¯ã蟺aãšè§Aã®å€§ãããåãã£ãŠããã®ã§ã2Rãæ±ããŸãã
a / sinA = 2R (â13) / sin(60°) = 2R
sin(60°)ã¯â3/2ãªã®ã§ã次ã®ããã«ãªããŸãã
(â13) / (â3/2) = 2R
ãããè§£ããšãRã¯æ¬¡ã®ããã«æ±ãŸããŸãã
R = (â13 * 2) / (2 * â3) = (â13) / â3
ãããã£ãŠããã®äžè§åœ¢ã®å€æ¥åã®ååŸã¯R = (â13) / â3ã§ãã
â»æ£è§£ã§ãã解説ãçè·¯æŽç¶ãšããŠããŠæå¥ã®ã€ãããããããŸããã
æ°ããŒãžã§ã³ãäžè§åœ¢ã®å€æ¥åã®ååŸ R ã¯æ¬¡ã®å ¬åŒã§æ±ããããšãã§ããŸãïŒR = (abc) / (4K)
ããã§ a, b, c ã¯äžè§åœ¢ã®å蟺ã®é·ãã§ãããK ã¯äžè§åœ¢ã®é¢ç©ã§ãããã®åé¡ã§ã¯ãa = â13ãb = 3ãc = 4 ãšäžããããŠããŸãã
ãŸãããã®äžè§åœ¢ãçŽè§äžè§åœ¢ã§ããããšã確èªããŸãããã¿ãŽã©ã¹ã®å®çã䜿çšãããšã次ã®ããã«ãªããŸãïŒ
a^2 = b^2 + c^2
â13^2 = 3^2 + 4^2
13 = 9 + 16
13 = 25
ããã«ãããäžããããäžè§åœ¢ã¯çŽè§äžè§åœ¢ã§ããããšãåãããŸãã
次ã«ãçŽè§äžè§åœ¢ã®é¢ç© K ãæ±ããŸããããã¯æ¬¡ã®å ¬åŒã䜿çšããŠèšç®ã§ããŸãïŒ
K = 1/2 * b * c
K = 1/2 * 3 * 4 = 6
æåŸã«ãäžè§åœ¢ã®å€æ¥åã®ååŸ R ãæ±ããŸããäžèšã®å ¬åŒã䜿çšãããšïŒ
R = (abc) / (4K)
R = (â13 * 3 * 4) / (4 * 6)
R = â13
ãããã£ãŠãäžè§åœ¢ã®å€æ¥åã®ååŸã¯ â13 ã§ãã
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