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修改31379题面

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wangweiye7840 2023-06-26 18:01:41 +08:00
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题库0.3/Problems.json
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@ -561189,7 +561189,7 @@
},
"031379": {
"id": "031379",
"content": "某公园为了美化环境和方便顾客, 计划建造一座圆弧形拱桥, 已知该桥的剖面如图所示, 共包括一段圆弧形桥面$ACB$和两段长度相等的直线型桥面$AD, BE$, 拱桥$ACB$所在圆的半径为$3$米, 圆心$O$在$DE$上, 且$AD$和$BE$所在直线与圆$O$分别在连结点$A$和$B$处相切. 根据空间限制及桥面坡度的限制, 桥面跨度$DE$的长要苴不大于$18$米, 不小于$12$米. 己知直线型桥面的修建费用是每米$0.6$万元, 弧形桥面的修建费用是每米$2.5$万元. 设$\\angle ADO=\\theta$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below] {$O$} coordinate (O);\n\\draw (0,1) node [above] {$C$} coordinate (C);\n\\draw (70:1) node [above right] {$B$} coordinate (B);\n\\draw (110:1) node [above left] {$A$} coordinate (A);\n\\draw ({-1/cos(70)},0) node [below] {$D$} coordinate (D);\n\\draw ({1/cos(70)},0) node [below] {$E$} coordinate (E);\n\\draw (B)--(E)(A)--(D)(B) arc (70:110:1);\n\\draw [dashed] (-4,0) -- (4,0) (B) arc (70:-250:1);\n\\filldraw (O) circle (0.03);\n\\end{tikzpicture}\n\\end{center}\n(1) 若桥面(线段$AD, BE$和弧$ACB$)的修建总费用为$W$万元, 求$W$关于\n$\\theta$的函数表达式, 并写出$\\theta$的取值范围;\\\\\n(2) 当$\\theta$为何值时, 桥面修建总费用$W$最低?(角$\\theta$的取值精确到$0.1^{\\circ}$)",
"content": "某公园为了美化环境和方便顾客, 计划建造一座圆弧形拱桥, 已知该桥的剖面如图所示, 共包括一段圆弧形桥面$ACB$和两段长度相等的直线型桥面$AD, BE$, 拱桥$ACB$所在圆的半径为$3$米, 圆心$O$在$DE$上, 且$AD$和$BE$所在直线与圆$O$分别在连结点$A$和$B$处相切. 根据空间限制及桥面坡度的限制, 桥面跨度$DE$的长要求不大于$18$米, 不小于$12$米. 己知直线型桥面的修建费用是每米$0.6$万元, 弧形桥面的修建费用是每米$2.5$万元. 设$\\angle ADO=\\theta$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below] {$O$} coordinate (O);\n\\draw (0,1) node [above] {$C$} coordinate (C);\n\\draw (70:1) node [above right] {$B$} coordinate (B);\n\\draw (110:1) node [above left] {$A$} coordinate (A);\n\\draw ({-1/cos(70)},0) node [below] {$D$} coordinate (D);\n\\draw ({1/cos(70)},0) node [below] {$E$} coordinate (E);\n\\draw (B)--(E)(A)--(D)(B) arc (70:110:1);\n\\draw [dashed] (-4,0) -- (4,0) (B) arc (70:-250:1);\n\\filldraw (O) circle (0.03);\n\\end{tikzpicture}\n\\end{center}\n(1) 若桥面(线段$AD, BE$和弧$ACB$)的修建总费用为$W$万元, 求$W$关于\n$\\theta$的函数表达式, 并写出$\\theta$的取值范围;\\\\\n(2) 当$\\theta$为何值时, 桥面修建总费用$W$最低?(角$\\theta$的取值精确到$0.1^{\\circ}$)",
"objs": [],
"tags": [],
"genre": "解答题",
@ -561199,7 +561199,8 @@
"usages": [],
"origin": "2023届四校联考(复兴奉贤松二金山)试题19",
"edit": [
"20230326\t王伟叶"
"20230326\t王伟叶",
"20230626\t王伟叶"
],
"same": [],
"related": [],