{"id":1205,"date":"2015-07-29T23:07:53","date_gmt":"2015-07-29T14:07:53","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1205"},"modified":"2021-10-30T20:13:13","modified_gmt":"2021-10-30T11:13:13","slug":"tkb201403","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkb201403\/","title":{"rendered":"\u6771\u5927\u6587\u7cfb2014\uff1a\u7b2c3\u554f"},"content":{"rendered":"
\n

\u5ea7\u6a19\u5e73\u9762\u306e\u539f\u70b9\u3092 O \u3067\u8868\u3059.
\r\n\u7dda\u5206 \\(y = \\sqrt{3} x \\quad ( 0 \\leqq x \\leqq 2 )\\) \u4e0a\u306e\u70b9 P \u3068, \u7dda\u5206 \\(y = -\\sqrt{3} x \\quad ( -3 \\leqq x \\leqq 0 )\\) \u4e0a\u306e\u70b9 Q \u304c, \u7dda\u5206 OP \u3068\u7dda\u5206 OQ \u306e\u9577\u3055\u306e\u548c\u304c \\(6\\) \u3068\u306a\u308b\u3088\u3046\u306b\u52d5\u304f. \u3053\u306e\u3068\u304d, \u7dda\u5206 PQ \u306e\u901a\u904e\u3059\u308b\u9818\u57df\u3092 \\(D\\) \u3068\u3059\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(s\\) \u3092 \\(-3 \\leqq s \\leqq 2\\) \u3092\u307f\u305f\u3059\u5b9f\u6570\u3068\u3059\u308b\u3068\u304d, \u70b9 \\((s,t)\\) \u304c \\(D\\) \u306b\u5165\u308b\u3088\u3046\u306a \\(t\\) \u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(D\\) \u3092\u56f3\u793a\u305b\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

    (1)<\/strong><\/p>\r\n

    \u70b9 P , Q \u306e \\(x\\) \u5ea7\u6a19\u3092\u305d\u308c\u305e\u308c \\(p , q \\ ( 0 \\leqq p \\leqq 2 , \\ -3 \\leqq q \\leqq 0 \\quad ... [1] )\\) \u3068\u304a\u304f.
    \r\n\\(\\text{OP} = 2p\\) , \\(\\text{OQ} = -2q\\) \u306a\u306e\u3067 \\(p , q\\) \u304c\u307f\u305f\u3059\u6761\u4ef6\u306f\r\n\\[\\begin{align}\r\n2p -2q & = 6 \\\\\r\n\\text{\u2234} \\quad q & = p-3\r\n\\end{align}\\]\r\n[1] \u3088\u308a\r\n\\[\\begin{align}\r\n0 \\leqq p \\leqq 2 & , \\ -3 \\leqq p-3 \\leqq 0 \\\\\r\n\\text{\u2234} \\quad 0 & \\leqq p \\leqq 2 \\quad ... [2]\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u7dda\u5206 PQ \u306e\u5f0f\u306f\r\n\\[\\begin{align}\r\ny & = \\dfrac{\\sqrt{3} p +\\sqrt{3} (p-3)}{3} ( x-p ) +\\sqrt{3} p \\\\\r\n& = \\dfrac{2p-3}{\\sqrt{3}} (x-p) +\\sqrt{3} p \\quad \\left( p-3 \\leqq x \\leqq p \\right)\r\n\\end{align}\\]\r\n\u3053\u308c\u304c, \u70b9 \\(( s , t )\\) \u3092\u901a\u308b\u3068\u3059\u308c\u3070\r\n\\[\\begin{align}\r\nt & = -\\dfrac{2}{\\sqrt{3}} p^2 +\\dfrac{2 (s+3)}{\\sqrt{3}} p -\\sqrt{3} s \\\\\r\n& = -\\dfrac{2}{\\sqrt{3}} \\left( p -\\dfrac{s+3}{2} \\right)^2 +\\dfrac{\\sqrt{3}}{6} s^2 +\\dfrac{3 \\sqrt{3}}{2} \\quad ( s \\leqq p \\leqq s+3 \\ ... [3] )\r\n\\end{align}\\]\r\n\\(f(p) = t\\) \u3068\u304a\u3044\u3066 \\(p\\) \u306e\u95a2\u6570\u3068\u307f\u306a\u3057\u305f\u3068\u304d, \u76f4\u7dda \\(x = s\\) \u4e0a\u306e\u70b9\u306e\u3046\u3061, \u9818\u57df \\(D\\) \u306b\u542b\u307e\u308c\u308b\u90e8\u5206\u306f\r\n\\[\r\n( \\ f(p) \\text{\u306e\u6700\u5c0f\u5024} ) \\leqq t \\leqq ( \\ f(p) \\text{\u306e\u6700\u5927\u5024} )\r\n\\]\r\n\u3068\u306a\u308b.
    \r\n[2] [3] \u306b\u6ce8\u610f\u3059\u308b\u3068, \\(f(p)\\) \u306e\u6700\u5927\u5024, \u6700\u5c0f\u5024\u306e\u5019\u88dc\u306f\r\n\\[\\begin{align}\r\nf(0) & = -\\sqrt{3} s \\\\\r\n& \\left( \\ s \\leqq 0 \\leqq s+3 \\ \\text{\u3059\u306a\u308f\u3061} \\ -3 \\leqq s \\leqq 0 \\ \\text{\u306e\u3068\u304d\u306e\u307f} \\right) , \\\\\r\nf(2) & = \\dfrac{s}{\\sqrt{3}} +\\dfrac{4}{\\sqrt{3}} \\\\\r\n& \\left( \\ s \\leqq 2 \\leqq s+3 \\ \\text{\u3059\u306a\u308f\u3061} \\ -1 \\leqq s \\leqq 2 \\ \\text{\u306e\u3068\u304d\u306e\u307f} \\right) , \\\\\r\nf \\left( \\dfrac{s+3}{2} \\right) & = \\dfrac{\\sqrt{3}}{6} s^2 +\\dfrac{3 \\sqrt{3}}{2} \\ ( \\text{\u6700\u5927\u5024\u306e\u307f} ) \\\\\r\n& \\left( \\ 0 \\leqq \\dfrac{s+3}{2} \\leqq 2 \\ \\text{\u3059\u306a\u308f\u3061} \\ -3 \\leqq s \\leqq 1 \\ \\text{\u306e\u3068\u304d\u306e\u307f} \\right) , \\\\\r\nf(s) & = f(s+3) = \\sqrt{3} s \\ ( \\text{\u6700\u5c0f\u5024\u306e\u307f} )\\\\\r\n& \\left( \\ 0 \\leqq s \\leqq 2 \\ \\text{\u306e\u3068\u304d\u306e\u307f} \\right)\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u305d\u308c\u305e\u308c\u306e\u5927\u5c0f\u3092\u6bd4\u8f03\u3059\u308b\u3068, \u6c42\u3081\u308b \\(t\\) \u306e\u7bc4\u56f2\u306f\r\n\\[\\begin{align}\r\n\\underline{\\left\\{ \\begin{array}{ll} -\\sqrt{3} s \\leqq t \\leqq \\dfrac{\\sqrt{3}}{6} s^2 +\\dfrac{3 \\sqrt{3}}{2} & ( \\ -3 \\leqq s \\lt 0 \\text{\u306e\u3068\u304d} \\ ) \\\\ \\sqrt{3} s \\leqq t \\leqq \\dfrac{\\sqrt{3}}{6} s^2 +\\dfrac{3 \\sqrt{3}}{2} & ( \\ 0 \\leqq s \\lt 1 \\text{\u306e\u3068\u304d} \\ ) \\\\ \\sqrt{3} s \\leqq t \\leqq \\dfrac{s}{\\sqrt{3}} +\\dfrac{4}{\\sqrt{3}} & ( \\ 1 \\leqq s \\leqq 2 \\text{\u306e\u3068\u304d} \\ ) \\end{array} \\right.}\r\n\\end{align}\\]\r\n

    (2)<\/strong><\/p>\r\n

    \u9818\u57df \\(D\\) \u306f\u4e0b\u56f3\u659c\u7dda\u90e8\uff08\u5883\u754c\u542b\u3080\uff09.<\/p>\r\n\"tkb20140301\"\r\n","protected":false},"excerpt":{"rendered":"\u5ea7\u6a19\u5e73\u9762\u306e\u539f\u70b9\u3092 O \u3067\u8868\u3059. \u7dda\u5206 \\(y = \\sqrt{3} x \\quad ( 0 \\leqq x \\leqq 2 )\\) \u4e0a\u306e\u70b9 P \u3068, \u7dda\u5206 \\(y = -\\sqrt{3} x \\quad ( -3 \\le … \u7d9a\u304d\u3092\u8aad\u3080 →<\/span><\/a>","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":[123],"tags":[149,112],"class_list":["post-1205","post","type-post","status-publish","format-standard","hentry","category-tokyo_b_2014","tag-tokyo_b","tag-112"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1205","targetHints":{"allow":["GET"]}}],"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=1205"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1205\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1205"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1205"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1205"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}