{"id":671,"date":"2013-03-08T23:01:42","date_gmt":"2013-03-08T14:01:42","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=671"},"modified":"2021-09-29T21:40:03","modified_gmt":"2021-09-29T12:40:03","slug":"thr200704","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr200704\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2007\uff1a\u7b2c4\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(xy\\) \u5e73\u9762\u4e0a\u306b \\(4\\) \u70b9 \\((0,0) , (4,0) , (4,4) , (0,4)\\) \u3092\u9802\u70b9\u3068\u3059\u308b\u6b63\u65b9\u5f62 \\(K\\) \u3092\u8003\u3048\u308b.\r\n\u70b9 \\((1,2)\\) \u3092\u901a\u308b\u5404\u76f4\u7dda\u306b\u5bfe\u3057\u3066, \u305d\u306e \\(K\\) \u306b\u542b\u307e\u308c\u308b\u90e8\u5206\u3092 \\(l\\) \u3068\u304a\u304f.<\/p>\r\n<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\\(l\\) \u306e\u9577\u3055\u306e\u6700\u5927\u5024\u3068, \u305d\u308c\u3092\u4e0e\u3048\u308b\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\\(l\\) \u306e\u9577\u3055\u306e\u6700\u5c0f\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/tohoku_r_2007_04_01.png\" alt=\"tohoku_r_2007_04_01\" class=\"aligncenter size-full\" \/>\r\n<hr \/>\r\n\r\n    <div id='extLink671'>\r\n        <p>\r\n            <a href='https:\/\/www.roundown.net\/nyushi\/thr200704\/' name='ext671' onclick=\"showHide(671,'https:\/\/www.roundown.net\/nyushi\/thr200704\/',this,'entry');return false;\">\u89e3\u7b54\u306f\u3053\u3061\u3089 &#187;<\/a>\r\n        <\/p>\r\n    <\/div>\r\n    <div id='extText671' style='display: none'>\r\n        \r\n<h2>\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\\(l\\) \u306e\u9577\u3055\u3092 \\(L\\) \u3068\u304a\u304f.<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(l : \\ x = 1\\) \u306e\u3068\u304d\r\n\\[\r\nL = 4\r\n\\]<\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(l : \\ y = a(x-1)+2\\) \u306e\u3068\u304d<br \/>\r\n\\(K , l\\) \u306f\u3068\u3082\u306b\u76f4\u7dda \\(y=2\\) \u306b\u3064\u3044\u3066\u5bfe\u79f0\u306a\u306e\u3067, \\(a \\geqq 0\\) \u306e\u3068\u304d\u3092\u8003\u3048\u308c\u3070\u3088\u3044.\r\n<ol>\r\n<li><p><strong>(i)<\/strong>\u3000\\(0 \\leqq a \\lt \\dfrac{2}{3}\\) \u306e\u3068\u304d, \\(l\\) \u306f\u4e0b\u56f3\u306e\u3088\u3046\u306b\u306a\u308b\u306e\u3067\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/tohoku_r_2007_04_02.png\" alt=\"tohoku_r_2007_04_02\" class=\"aligncenter size-full\" \/>\r\n\\[\r\nL = 4 \\sqrt{a^2+1}\r\n\\]\r\n\u3053\u306e\u533a\u9593\u3067\u306f \\(L\\) \u306f\u5358\u8abf\u5897\u52a0\u3067\u3042\u308b.<\/p><\/li>\r\n<li><p><strong>(ii)<\/strong>\u3000\\(\\dfrac{2}{3} \\leqq a \\lt 2\\) \u306e\u3068\u304d, \\(l\\) \u306f\u4e0b\u56f3\u306e\u3088\u3046\u306b\u306a\u308b\u306e\u3067\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/tohoku_r_2007_04_03.png\" alt=\"tohoku_r_2007_04_03\" class=\"aligncenter size-full\" \/>\r\n\\[\\begin{align}\r\nL & = \\sqrt{(a+2)^2 +\\left( \\dfrac{2}{a} +1 \\right)^2} \\\\\r\n& =(a+2) \\sqrt{1+ \\dfrac{1}{a^2}} \\\\\r\n& = \\left( 1+\\dfrac{2}{a} \\right) \\sqrt{a^2+1}\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\\begin{align}\r\n\\dfrac{dL}{da} & = -\\dfrac{2 \\sqrt{a^2+1}}{a^2} +\\dfrac{a+2}{a} \\cdot \\dfrac{a}{\\sqrt{a^2+1}} \\\\\r\n& = \\dfrac{-2 ( a^2+1 ) +a^2 (a+2)}{a^2 \\sqrt{a^2+1}} \\\\\r\n& = \\dfrac{a^3-2}{a^2 \\sqrt{a^2+1}}\r\n\\end{align}\\]\r\n\\(\\dfrac{dL}{da} = 0\\) \u3092\u3068\u304f\u3068\r\n\\[\r\na = 2^{\\frac{1}{3}}\r\n\\]<\/li>\r\n<li><p><strong>(iii)<\/strong>\u3000\\(a \\geqq 2\\) \u306e\u3068\u304d, \\(l\\) \u306f\u4e0b\u56f3\u306e\u3088\u3046\u306b\u306a\u308b\u306e\u3067\r\n<img decoding=\"async\" src=\"\/\/www.roundown.net\/nyushi\/wp-content\/uploads\/tohoku_r_2007_04_04.png\" alt=\"tohoku_r_2007_04_04\" class=\"aligncenter size-full\" \/>\r\n\\[\r\nL = 4 \\sqrt{1+\\dfrac{1}{a^2}}\r\n\\]\r\n\u3053\u306e\u533a\u9593\u3067\u306f \\(L\\) \u306f\u5358\u8abf\u6e1b\u5c11\u3067\u3042\u308b.<\/p><\/li>\r\n<\/ol>\r\n<strong>(i)<\/strong> \uff5e <strong>(iii)<\/strong> \u304b\u3089 \\(L\\) \u306e\u5897\u6e1b\u306f\u4e0b\u8868\u306e\u3088\u3046\u306b\u306a\u308b.\r\n\\[\r\n\\begin{array}{c|ccccccccc} a & 0 & \\cdots & \\dfrac{2}{3} & \\cdots & 2^{\\frac{1}{3}} & \\cdots & 2 & \\cdots & ( \\infty ) \\\\ \\hline \\dfrac{dL}{da} & & & & - & 0 & + & & & \\\\ \\hline L & 4 & \\nearrow & \\text{\u6975\u5927} & \\searrow & \\text{\u6975\u5c0f} & \\nearrow & \\text{\u6975\u5927} & \\searrow & (4) \\end{array}\r\n\\]<\/li>\r\n<\/ol>\r\n<p><strong>1*<\/strong> <strong>2*<\/strong> \u3088\u308a, \\(L\\) \u306e\u6700\u5927\u5024\u306e\u5019\u88dc\u306f<\/p>\r\n<ul>\r\n<li><p>\\(a = \\dfrac{2}{3}\\) \u306e\u3068\u304d\r\n\\[\r\nL = 4 \\sqrt{\\left( \\dfrac{2}{3} \\right)^2 +1} = \\dfrac{4 \\sqrt{13}}{3}\r\n\\]<\/li>\r\n<li><p>\\(a = 2\\) \u306e\u3068\u304d\r\n\\[\r\nL = \\dfrac{4}{2} \\sqrt{2^2+1} = 2 \\sqrt{5}\r\n\\]<\/li>\r\n<\/ul>\r\n<p>\u3053\u3053\u3067\r\n\\[\\begin{align}\r\n52 & = 2^2 \\cdot 13 \\gt 3^2 \\cdot 5 = 45 \\\\\r\n\\text{\u2234} \\quad & \\dfrac{4 \\sqrt{13}}{3} \\gt 2 \\sqrt{5}\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u6700\u5927\u5024\u306f\r\n\\[\r\n\\underline{\\dfrac{4 \\sqrt{13}}{3}}\r\n\\]\r\n\u307e\u305f, \u3053\u306e\u3068\u304d\u306e \\(l\\) \u306e\u5f0f\u306f, \u5bfe\u79f0\u6027\u3088\u308a \\(a = \\pm \\dfrac{2}{3}\\) \u306e\u3068\u304d\u306a\u306e\u3067\r\n\\[\\begin{gather}\r\ny = \\pm \\dfrac{2}{3} (x-1) +2 \\\\\r\n\\text{\u2234} \\quad \\underline{y = \\dfrac{2}{3} x -\\dfrac{4}{3} , \\ y = -\\dfrac{2}{3} x -\\dfrac{8}{3}}\r\n\\end{gather}\\]\r\n<p><strong>(2)<\/strong><\/p>\r\n<p><strong>(1)<\/strong> \u306e\u7d4c\u904e\u3088\u308a, \\(L\\) \u306e\u6700\u5c0f\u5024\u306e\u5019\u88dc\u306f<\/p>\r\n<ul>\r\n<li><p>\\(a = 0\\) \u306e\u3068\u304d\r\n\\[\r\nL = 4\r\n\\]<\/li>\r\n<li><p>\\(a = 2^{\\frac{1}{3}}\\) \u306e\u3068\u304d\r\n\\[\\begin{align}\r\nL & = \\left( 1 +\\dfrac{2}{2^{\\frac{1}{3}}} \\right) \\sqrt{2^{\\frac{2}{3}} +1} \\\\\r\n& = \\left( 1+2^{\\frac{2}{3}} \\right)^{\\frac{3}{2}}\r\n\\end{align}\\]<\/li>\r\n<\/ul>\r\n<p>\u3053\u3053\u3067\r\n\\[\\begin{align}\r\n\\left( 1 -2^{\\frac{1}{3}} \\right)^2 & \\gt 0 \\\\\r\n1 +2^{\\frac{2}{3}} & \\gt 2^{\\frac{4}{3}} \\\\\r\n\\text{\u2234} \\quad \\left( 1+2^{\\frac{2}{3}} \\right)^{\\frac{3}{2}} & \\gt 2^{\\frac{4}{3} \\cdot \\frac{3}{2}} = 4\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u6700\u5c0f\u5024\u306f\r\n\\[\r\n\\underline{4}\r\n\\]\r\n\r\n        <p>\r\n            <a href='#ext671' onclick=\"showHide(671,0,this,'entry');return true;\">&#171; \u89e3\u7b54\u3092\u96a0\u3059 <\/a>\r\n        <\/p>\r\n    <\/div>","protected":false},"excerpt":{"rendered":"\\(xy\\) \u5e73\u9762\u4e0a\u306b \\(4\\) \u70b9 \\((0,0) , (4,0) , (4,4) , (0,4)\\) \u3092\u9802\u70b9\u3068\u3059\u308b\u6b63\u65b9\u5f62 \\(K\\) \u3092\u8003\u3048\u308b. \u70b9 \\((1,2)\\) \u3092\u901a\u308b\u5404\u76f4\u7dda\u306b\u5bfe\u3057\u3066, \u305d\u306e \\(K\\) \u306b [&hellip;]","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[95],"tags":[148,109],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/671"}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=671"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/671\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=671"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=671"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=671"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}