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修改4308,24742题面

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wangweiye7840 2024-03-19 15:46:43 +08:00
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题库0.3/Problems.json
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@ -133888,7 +133888,7 @@
},
"004308": {
"id": "004308",
"content": "如图, 经过村庄$A$有两条夹角为$60^\\circ$的公路$AB$、$AC$, 根据规划拟在两条公路之间的区域内建一工厂$P$, 分别在两条公路边上建两个仓库$M$、$N$(异于村庄$A$), 要求$PM=PN=MN=2$(单位: 千米). 记$\\angle MN=\\theta$.\n\\begin{center}\n \\begin{tikzpicture}\n \\draw (0,0) node [below left] {$A$} coordinate (A) -- (3,0) node [below] {$M$} coordinate (M) -- (5,0) node [below] {$B$};\n \\path [name path = lineMN] (M) --++ (135:3);\n \\path [name path = lineAN] (0,0) --++ (60:3);\n \\path [name intersections = {of = lineMN and lineAN, by= N}];\n \\draw (A) -- (N) node [above left] {$N$} --++ (60:2) node [above] {$C$};\n \\draw [dashed] (M) --++ (75:{3/sin(75)*sin(60)}) node [right] {$P$} coordinate (P) -- (N) -- (M) (P) -- (0,0);\n \\draw (2.6,0) arc (180:135:0.4);\n \\path (2.6,0) arc (180:150:0.4) node [left] {$\\theta$};\n \\end{tikzpicture}\n\\end{center}\n(1) 将$AN$、$AM$用含$\\theta$的关系式表示出来;\\\\\n(2) 如何设计(即$AN$、$AM$为多长时), 使得工厂产生的噪声对居民的影响最小(即工厂与村庄的距离$AP$最大)?",
"content": "如图, 经过村庄$A$有两条夹角为$60^\\circ$的公路$AB$、$AC$, 根据规划拟在两条公路之间的区域内建一工厂$P$, 分别在两条公路边上建两个仓库$M$、$N$(异于村庄$A$), 要求$PM=PN=MN=2$(单位: 千米). 记$\\angle AMN=\\theta$.\n\\begin{center}\n \\begin{tikzpicture}\n \\draw (0,0) node [below left] {$A$} coordinate (A) -- (3,0) node [below] {$M$} coordinate (M) -- (5,0) node [below] {$B$};\n \\path [name path = lineMN] (M) --++ (135:3);\n \\path [name path = lineAN] (0,0) --++ (60:3);\n \\path [name intersections = {of = lineMN and lineAN, by= N}];\n \\draw (A) -- (N) node [above left] {$N$} --++ (60:2) node [above] {$C$};\n \\draw [dashed] (M) --++ (75:{3/sin(75)*sin(60)}) node [right] {$P$} coordinate (P) -- (N) -- (M) (P) -- (0,0);\n \\draw (2.6,0) arc (180:135:0.4);\n \\path (2.6,0) arc (180:150:0.4) node [left] {$\\theta$};\n \\end{tikzpicture}\n\\end{center}\n(1) 将$AN$、$AM$用含$\\theta$的关系式表示出来;\\\\\n(2) 如何设计(即$AN$、$AM$为多长时), 使得工厂产生的噪声对居民的影响最小(即工厂与村庄的距离$AP$最大)?",
"objs": [],
"tags": [
"第三单元"
@ -133900,7 +133900,8 @@
"usages": [],
"origin": "2022届高三下学期测验卷12第19题",
"edit": [
"20220705\t王伟叶"
"20220705\t王伟叶",
"20240319\t徐慧"
],
"same": [],
"related": [],
@ -687173,7 +687174,7 @@
},
"024742": {
"id": "024742",
"content": "已知 $\\omega \\in \\mathbf{R}, $``$\\omega=\\pi$''是``函数 $f(x)=\\sin \\omega x \\cdot \\cos \\omega x$ 的最小正周期是 1''的\\blank{50}\n条件;",
"content": "已知 $\\omega \\in \\mathbf{R}, $``$\\omega=\\pi$''是``函数 $f(x)=\\sin \\omega x \\cdot \\cos \\omega x$ 的最小正周期是 1''的\\blank{50}\n条件.",
"objs": [],
"tags": [],
"genre": "填空题",
@ -687183,7 +687184,8 @@
"usages": [],
"origin": "自拟题目",
"edit": [
"20240319\t朱敏慧"
"20240319\t朱敏慧",
"20240319\t徐慧"
],
"same": [],
"related": [