{"id":226,"date":"2011-12-03T00:21:48","date_gmt":"2011-12-02T15:21:48","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=226"},"modified":"2021-10-30T10:01:51","modified_gmt":"2021-10-30T01:01:51","slug":"wsr200904","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/wsr200904\/","title":{"rendered":"\u65e9\u7a32\u7530\u7406\u5de52009\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

\u4ee5\u4e0b\u306e\u554f\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u534a\u5f84 \\(r\\) \u306e\u5186\u306b\u5185\u63a5\u3057, \\(1\\) \u3064\u306e\u5bfe\u89d2\u7dda\u306e\u9577\u3055\u304c \\(l\\) \u3067\u3042\u308b\u3088\u3046\u306a\u56db\u89d2\u5f62\u306e\u9762\u7a4d\u306e\u6700\u5927\u5024\u3092 \\(r\\) \u3068 \\(l\\) \u3067\u8868\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u534a\u5f84 \\(r\\) \u306e\u5186\u306b\u5185\u63a5\u3059\u308b\u56db\u89d2\u5f62\u306e\u9762\u7a4d\u306e\u6700\u5927\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\u7a7a\u9593\u5185\u306e\u70b9 O \u3092\u9802\u70b9\u3068\u3057, \u56db\u89d2\u5f62 ABCD \u3092\u5e95\u9762\u3068\u3059\u308b\u56db\u89d2\u9310\uff08\u3059\u3044\uff09\u304c \\(\\text{OA} =\\text{OB} =\\text{OC} =\\text{OD} =1\\) \u3092\u6e80\u305f\u3057\u3066\u3044\u308b\u3068\u3059\u308b. \u305d\u306e\u3088\u3046\u306a\u56db\u89d2\u9318\u306e\u4f53\u7a4d\u306e\u6700\u5927\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \u9577\u3055 \\(l\\) \u306e\u5bfe\u89d2\u7dda\u306e\u4e21\u7aef\u3067\u306a\u3044 \\(2\\) \u70b9\u304b\u3089, \u5bfe\u89d2\u7dda\u306b\u4e0b\u3057\u305f\u9ad8\u3055\u3092 \\(a _ 1 , a _ 2\\) \u3068\u304a\u3051\u3070, \u56db\u89d2\u5f62\u306e\u9762\u7a4d \\(S\\) \u306f\r\n\\[\r\nS =\\dfrac{1}{2} a _ 1 l +\\dfrac{1}{2} a _ 2 l =\\dfrac{( a _ 1 +a _ 2 ) l}{2}\r\n\\]\r\n\\(a _ 1 +a _ 2\\) \u304c\u6700\u5927\u3068\u306a\u308b\u3068\u304d, \\(S\\) \u3082\u6700\u5927\u3068\u306a\u308a, \u3053\u308c\u306f \\(2\\) \u70b9\u3092\u7d50\u3076\u7dda\u5206\u304c\u76f4\u5f84 \\(2r\\) \u3068\u306a\u308b\u3068\u304d\u3067\u3042\u308b.
    \r\n\u3088\u3063\u3066, \\(S\\) \u306e\u6700\u5927\u5024\u306f\r\n\\[\r\n\\dfrac{2r \\cdot l}{2} = \\underline{rl}\r\n\\]\r\n

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

    (1)<\/strong> \u306e\u7d50\u679c\u3092\u7528\u3044\u308c\u3070, \u5bfe\u89d2\u7dda \\(l\\) \u304c\u6700\u5927\u3068\u306a\u308b\u3068\u304d, \u3059\u306a\u308f\u3061\u76f4\u5f84 \\(2r\\) \u3068\u306a\u308b\u3068\u304d\u306b, \u9762\u7a4d\u306f\u6700\u5927\u3068\u306a\u308b.
    \r\n\u3088\u3063\u3066, \u9762\u7a4d\u306e\u6700\u5927\u5024\u306f\r\n\\[\r\nr \\cdot 2r = \\underline{2r^2}\r\n\\]\r\n

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

    \\(4\\) \u70b9 A , B , C , D \u304c, \u534a\u5f84 \\(r \\ ( 0 \\lt r \\lt 1 )\\) \u306e\u5186\u5468\u4e0a\u306b\u3042\u308b\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b.
    \r\n\u3053\u306e\u3068\u304d, \u56db\u89d2\u9310\u306e\u9ad8\u3055\u306f \\(\\sqrt{1 -r^2}\\) .
    \r\n(2)<\/strong> \u306e\u7d50\u679c\u3088\u308a, \u56db\u89d2\u5f62ABCD\u306e\u9762\u7a4d\u306e\u6700\u5927\u5024\u306f \\(2r^2\\) \u306a\u306e\u3067, \u56db\u89d2\u9310\u306e\u4f53\u7a4d \\(V\\) \u306f\r\n\\[\r\nV = \\dfrac{1}{3} \\cdot 2r^2 \\sqrt{1-r^2} = \\dfrac{2}{3} \\underline{r^2 \\sqrt{1-r^2}} _ {\\text[A]}\r\n\\]\r\n[A] \u306e \\(2\\) \u4e57\u304c\u6700\u5927\u306e\u3068\u304d, \u4f53\u7a4d\u306f\u6700\u5927\u3068\u306a\u308b.\r\n\\[\r\n\\left( r^2 \\sqrt{1-r^2} \\right)^2 = r^4 (1-r^2)\r\n\\]\r\n\\(t = r^2\\) \u3068\u3059\u308c\u3070, \\(f(t) = t^2 (1-t)\\) \u3068\u304a\u3051\u308b.\r\n\\[\r\nf'(t) = 2t -3t^2 = -t (3t-2)\r\n\\]\r\n\\(f'(t) =0\\) \u3092\u89e3\u3051\u3070, \\(t = \\dfrac{2}{3}\\) .
    \r\n\\(f(t)\\) \u306e\u5897\u6e1b\u306f\u4e0b\u8868\u306e\u3088\u3046\u306b\u306a\u308b.\r\n\\[\r\n\\begin{array}{c|ccccc} t & (0) & \\cdots & \\dfrac{2}{3} & \\cdots & (1) \\\\ \\hline f'(t) & & + & 0 & - & \\\\ \\hline f(t) & &\\nearrow & \\text{\u6700\u5927} & \\searrow & \\end{array}\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(f(t)\\) \u306e\u6700\u5927\u5024\u306f\r\n\\[\r\nf \\left( \\dfrac{2}{3} \\right) = \\dfrac{4}{9} \\cdot \\dfrac{1}{3} = \\dfrac{4}{27}\r\n\\]\r\n\u3088\u3063\u3066, \\(V\\) \u306e\u6700\u5927\u5024\u306f\r\n\\[\r\n\\dfrac{2}{3} \\sqrt{\\dfrac{4}{27}} = \\underline{\\dfrac{4 \\sqrt{3}}{27}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u4ee5\u4e0b\u306e\u554f\u306b\u7b54\u3048\u3088. (1)\u3000\u534a\u5f84 \\(r\\) \u306e\u5186\u306b\u5185\u63a5\u3057, \\(1\\) \u3064\u306e\u5bfe\u89d2\u7dda\u306e\u9577\u3055\u304c \\(l\\) \u3067\u3042\u308b\u3088\u3046\u306a\u56db\u89d2\u5f62\u306e\u9762\u7a4d\u306e\u6700\u5927\u5024\u3092 \\(r\\) \u3068 \\(l\\) \u3067\u8868\u305b. (2)\u3000\u534a\u5f84 \\(r\\) \u306e\u5186\u306b\u5185\u63a5\u3059\u308b … \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":[36],"tags":[147,15],"class_list":["post-226","post","type-post","status-publish","format-standard","hentry","category-waseda_r_2009","tag-waseda_r","tag-15"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/226","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=226"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/226\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=226"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=226"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=226"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}