{"id":1942,"date":"2021-10-26T23:16:14","date_gmt":"2021-10-26T14:16:14","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=1942"},"modified":"2021-10-26T23:16:14","modified_gmt":"2021-10-26T14:16:14","slug":"tkb201603","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkb201603\/","title":{"rendered":"\u6771\u5927\u6587\u7cfb2016\uff1a\u7b2c3\u554f"},"content":{"rendered":"
\n

\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e \\(2\\) \u3064\u306e\u653e\u7269\u7dda\r\n\\[\\begin{align}\r\nA : & \\ y = x^2 \\\\\r\nB : & \\ y = -x^2 +px +q\r\n\\end{align}\\]\r\n\u304c\u70b9 \\(( -1 , 1 )\\) \u3067\u63a5\u3057\u3066\u3044\u308b. \u3053\u3053\u3067, \\(p\\) \u3068 \\(q\\) \u306f\u5b9f\u6570\u3067\u3042\u308b. \u3055\u3089\u306b, \\(t\\) \u3092\u6b63\u306e\u5b9f\u6570\u3068\u3057, \u653e\u7269\u7dda \\(B\\) \u3092 \\(x\\) \u8ef8\u306e\u6b63\u306e\u65b9\u5411\u306b \\(2t\\) , \\(y\\) \u8ef8\u306e\u6b63\u306e\u65b9\u5411\u306b \\(t\\) \u3060\u3051\u5e73\u884c\u79fb\u52d5\u3057\u3066\u5f97\u3089\u308c\u308b\u653e\u7269\u7dda\u3092 \\(C\\) \u3068\u3059\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(p\\) \u3068 \\(q\\) \u306e\u5024\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u653e\u7269\u7dda \\(A\\) \u3068 \\(C\\) \u304c\u56f2\u3080\u9818\u57df\u306e\u9762\u7a4d\u3092 \\(S(t)\\) \u3068\u3059\u308b. \u305f\u3060\u3057, \\(A\\) \u3068 \\(C\\) \u304c\u9818\u57df\u3092\u56f2\u307e\u306a\u3044\u3068\u304d\u306f \\(S(t) = 0\\) \u3068\u5b9a\u3081\u308b. \\(S(t)\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(t \\gt 0\\) \u306b\u304a\u3051\u308b \\(S(t)\\) \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

    A \u306e\u5f0f\u3088\u308a\r\n\\[\r\ny' = 2x\r\n\\]\r\nB \u306e\u5f0f\u3088\u308a\r\n\\[\r\ny' = -2x +p\r\n\\]\r\nA , B \u304c \u70b9 \\(( -1 , 1 )\\) \u3067\u63a5\u3059\u308b\u306e\u3067, \u50be\u304d\u306b\u7740\u76ee\u3057\u3066\r\n\\[\\begin{align}\r\n-2 & = 2+p \\\\\r\n\\text{\u2234} \\quad p & = \\underline{-4}\r\n\\end{align}\\]\r\n\u307e\u305f\r\n\\[\\begin{align}\r\n1 & = -1 +4 +q \\\\\r\n\\text{\u2234} \\quad q & = \\underline{-2}\r\n\\end{align}\\]\r\n

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

    C \u306e\u5f0f\u306f\r\n\\[\\begin{align}\r\ny & = -( x -2t )^2 -4 ( x -2t ) -2 +t \\\\\r\n& = -x^2 +4 ( t-1 ) x -4t^2 +9t -2\r\n\\end{align}\\]\r\nA , C \u306e\u5f0f\u3088\u308a, \\(y\\) \u3092\u6d88\u53bb\u3059\u308c\u3070\r\n\\[\r\n2x^2 -4 ( t-1 ) x +4t^2 -9t +2 = 0 \\quad ... [1]\r\n\\]\r\n[1] \u306e\u5224\u5225\u5f0f\u3092 \\(D\\) \u3068\u3059\u308c\u3070\r\n\\[\\begin{align}\r\n\\dfrac{D}{4} & = 4 ( t-1 )^2 -2 ( 4t^2 -9t +2 ) \\\\\r\n& = -4 t^2 +10 t \\\\\r\n& = -4 t \\left( t -\\dfrac{5}{2} \\right)\r\n\\end{align}\\]\r\n

      \r\n

    1. 1*<\/strong>\u3000\\(D \\gt 0\\) \u3059\u306a\u308f\u3061 \\(0 \\lt t \\lt \\dfrac{5}{2}\\) \u306e\u3068\u304d
      \r\n[1] \u306e \\(2\\) \u89e3\u3092 \\(\\alpha , \\beta \\ ( \\alpha \\lt \\beta )\\) \u3068\u304a\u3051\u3070\r\n\\[\r\n\\alpha = \\dfrac{2 ( t-1 ) -\\sqrt{D}}{2} , \\ \\beta = \\dfrac{2 ( t-1 ) +\\sqrt{D}}{2}\r\n\\]\r\n\u306a\u306e\u3067\r\n\\[\r\n\\beta -\\alpha = \\dfrac{\\sqrt{D}}{2}\r\n\\]\r\nA , C \u306f\u305d\u308c\u305e\u308c\u4e0b, \u4e0a\u306b\u51f8\u306e\u653e\u7269\u7dda\u306a\u306e\u3067\r\n\\[\\begin{align}\r\nS(t) & = \\displaystyle\\int _ {\\alpha}^{\\beta} ( [1] \\text{\u306e\u5de6\u8fba} ) \\, dx \\\\\r\n& = \\dfrac{2}{6} ( \\beta -\\alpha )^3 \\\\\r\n& = \\dfrac{1}{3} \\left( \\underline{-4t^2 +10t} _ {[2]} \\right)^{\\frac{3}{2}}\r\n\\end{align}\\]<\/li>\r\n

    2. 2*<\/strong>\u3000\\(D \\leqq 0\\) \u3059\u306a\u308f\u3061 \\(t \\geqq \\dfrac{5}{2}\\) \u306e\u3068\u304d
      \r\nA \u3068 C \u306f\u9818\u57df\u3092\u56f2\u307e\u306a\u3044\u306e\u3067\r\n\\[\r\nS(t) = 0\r\n\\]<\/li>\r\n<\/ol>\r\n

      \u4ee5\u4e0a\u3088\u308a\r\n\\[\r\nS(t) = \\underline{\\left\\{ \\begin{array}{ll} \\dfrac{1}{3} \\left( -4t^2 +10t \\right)^{\\frac{3}{2}} & \\left( \\ 0 \\lt t \\lt \\dfrac{5}{2} \\ \\text{\u306e\u3068\u304d} \\right) \\\\ 0 & \\left( \\ t \\geqq \\dfrac{5}{2} \\ \\text{\u306e\u3068\u304d} \\right) \\end{array} \\right.}\r\n\\]\r\n

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

      \\(0 \\lt t \\lt \\dfrac{5}{2}\\) \u306e\u3068\u304d\u306b\u3064\u3044\u3066\u8003\u3048\u308c\u3070\u3088\u3044.
      \r\n\u4e0b\u7dda\u90e8 [2] \u3092 \\(f(t)\\) \u3068\u304a\u3051\u3070\r\n\\[\r\nf(t) = -4 \\left( t -\\dfrac{5}{4} \\right)^2 +\\dfrac{25}{4}\r\n\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u6700\u5927\u5024\u306f\r\n\\[\r\n\\dfrac{1}{3} \\{ f(4) \\}^{\\frac{3}{2}} = \\dfrac{1}{3} \\left( \\dfrac{25}{4} \\right)^{\\frac{3}{2}} = \\underline{\\dfrac{125}{24}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u5ea7\u6a19\u5e73\u9762\u4e0a\u306e \\(2\\) \u3064\u306e\u653e\u7269\u7dda \\[\\begin{align} A : & \\ y = x^2 \\\\ B : & \\ y = -x^2 +px +q \\end{align}\\] \u304c\u70b9 \\(( -1 , 1 )\\) … \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":[160],"tags":[149,162],"class_list":["post-1942","post","type-post","status-publish","format-standard","hentry","category-tokyo_b_2016","tag-tokyo_b","tag-162"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1942","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=1942"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1942\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1942"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1942"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1942"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}