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20221213 evening

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WangWeiye 2022-12-13 19:47:08 +08:00
parent e637eeb514
commit 258a6678b6
2 changed files with 6 additions and 6 deletions
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8
工具/修改题目数据库.ipynb
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@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": 7,
"execution_count": 11,
"metadata": {},
"outputs": [
{
@ -11,7 +11,7 @@
"0"
]
},
"execution_count": 7,
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
@ -19,7 +19,7 @@
"source": [
"import os,re,json\n",
"\"\"\"这里编辑题号(列表)后将在vscode中打开窗口, 编辑后保存关闭, 随后运行第二个代码块\"\"\"\n",
"problems = \"12502\"\n",
"problems = \"12505\"\n",
"\n",
"def generate_number_set(string,dict):\n",
" string = re.sub(r\"[\\n\\s]\",\"\",string)\n",
@ -51,7 +51,7 @@
},
{
"cell_type": "code",
"execution_count": 6,
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [

4
题库0.3/Problems.json
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@ -308056,7 +308056,7 @@
},
"012504": {
"id": "012504",
"content": "如图所示圆锥$P-O$中,$CD$为底面的直径, $A, B$分别为母线$PD$与$PC$的中点, 点$E$是底面圆周上一点, 若$\\angle DCE=30^{\\circ}$, $|AB|=\\sqrt 2$, 圆锥的高为$\\sqrt {14}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\r{1.6}\n\\def\\h{3}\n\\draw ({-\\r},0,0) node [left] {$D$} coordinate (D) -- (0,\\h,0) node [above] {$P$} coordinate (P) -- (\\r,0,0) node [right] {$C$} coordinate (C);\n\\draw (0,0,0) node [above right] {$O$} coordinate (O);\n\\draw (D) arc (180:360:{\\r} and {\\r/4});\n\\draw [dashed] (D) arc (180:0:{\\r} and {\\r/4});\n\\draw [dashed] (D) -- (C) (O) -- (P);\n\\draw ({\\r*cos(-130)},{\\r/4*sin(-130)}) node [below] {$E$} coordinate (E);\n\\draw [dashed] (E) -- (C);\n\\draw ($(C)!0.5!(P)$) node [right] {$B$} coordinate (B);\n\\draw ($(D)!0.5!(P)$) node [left] {$A$} coordinate (A);\n\\draw [dashed] (E) -- (A) -- (B);\n\\end{tikzpicture}\n\\end{center}\n(1) 求圆锥的侧面积$S$;\\\\\n(2) 求证: $AE$与$PC$是异面直线, 并求其所成角的大小.",
"content": "如图所示圆锥$P-O$中, $CD$为底面的直径, $A, B$分别为母线$PD$与$PC$的中点, 点$E$是底面圆周上一点, 若$\\angle DCE=30^{\\circ}$, $|AB|=\\sqrt 2$, 圆锥的高为$\\sqrt {14}$.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\r{1.6}\n\\def\\h{3}\n\\draw ({-\\r},0,0) node [left] {$D$} coordinate (D) -- (0,\\h,0) node [above] {$P$} coordinate (P) -- (\\r,0,0) node [right] {$C$} coordinate (C);\n\\draw (0,0,0) node [above right] {$O$} coordinate (O);\n\\draw (D) arc (180:360:{\\r} and {\\r/4});\n\\draw [dashed] (D) arc (180:0:{\\r} and {\\r/4});\n\\draw [dashed] (D) -- (C) (O) -- (P);\n\\draw ({\\r*cos(-130)},{\\r/4*sin(-130)}) node [below] {$E$} coordinate (E);\n\\draw [dashed] (E) -- (C);\n\\draw ($(C)!0.5!(P)$) node [right] {$B$} coordinate (B);\n\\draw ($(D)!0.5!(P)$) node [left] {$A$} coordinate (A);\n\\draw [dashed] (E) -- (A) -- (B);\n\\end{tikzpicture}\n\\end{center}\n(1) 求圆锥的侧面积$S$;\\\\\n(2) 求证: $AE$与$PC$是异面直线, 并求其所成角的大小.",
"objs": [],
"tags": [
"第六单元"
@ -308077,7 +308077,7 @@
},
"012505": {
"id": "012505",
"content": "企业经营一款节能环保产品, 其成本由研发成本与生产成本两部分构成. 生产成本固定为每台$130$元. 根据市场调研, 若该产品产量为$x$万台时, 每万台产品的销售收入为$I(x)$万元, 两者满足关系:$I(x)=220-x$($0<x<220$).\\\\\n(1) 甲企业独家经营, 其研发成本为$60$万元. 求甲企业能获得利润的最大值;\\\\\n(2) 乙企业见有利可图, 也经营该产品, 其研发成本为$40$万元. 问: 乙企业产量多少万台时获得的利润最大; (假定甲企业按照原先最大利润生产, 并末因乙的加入而改变)\\\\\n(3) 由于乙企业参与, 甲企业将不能得到预期的最大收益. 因此会作相应调整, 之后乙企业也会随之作出调整, $\\cdots$, 最终双方达到动态平衡(在对方当前产量不变的情况下, 己方达到利润最大). 求动态平衡时, 两企业各自的产量和利润分别是多少.",
"content": "企业经营一款节能环保产品, 其成本由研发成本与生产成本两部分构成. 生产成本固定为每台$130$元. 根据市场调研, 若该产品产量为$x$万台时, 每万台产品的销售收入为$I(x)$万元, 两者满足关系:$I(x)=220-x$($0<x<220$).\\\\\n(1) 甲企业独家经营, 其研发成本为$60$万元. 求甲企业能获得利润的最大值;\\\\\n(2) 乙企业见有利可图, 也经营该产品, 其研发成本为$40$万元. 问: 乙企业产量多少万台时获得的利润最大; (假定甲企业按照原先最大利润生产, 并未因乙的加入而改变)\\\\\n(3) 由于乙企业参与, 甲企业将不能得到预期的最大收益. 因此会作相应调整, 之后乙企业也会随之作出调整, $\\cdots$, 最终双方达到动态平衡(在对方当前产量不变的情况下, 己方达到利润最大). 求动态平衡时, 两企业各自的产量和利润分别是多少.",
"objs": [],
"tags": [
"第二单元"