20220919 evening
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 2,
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"1 填空题 1\n",
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"2 填空题 1\n",
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"3 填空题 1\n",
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"4 填空题 1\n",
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"5 填空题 1\n",
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"6 填空题 1\n",
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"1 填空题 8\n",
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"2 解答题 1\n",
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"3 解答题 2\n",
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"4 选择题 1\n",
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"5 解答题 1\n",
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"6 选择题 1\n",
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"7 填空题 1\n",
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"8 填空题 1\n",
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"9 解答题 1\n",
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"10 解答题 1\n",
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"11 解答题 2\n",
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"12 解答题 1\n",
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"13 解答题 1\n",
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"14 解答题 1\n",
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"15 填空题 1\n",
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"16 选择题 1\n",
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"1 填空题 1\n",
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"2 填空题 1\n",
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"3 填空题 1\n",
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"4 填空题 1\n",
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"5 填空题 1\n",
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"6 选择题 1\n",
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"7 选择题 1\n",
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"10 填空题 1\n",
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"1 填空题 8\n",
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"2 解答题 1\n",
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"3 解答题 3\n",
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"4 解答题 1\n",
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"5 解答题 2\n",
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"6 解答题 1\n",
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"7 填空题 1\n",
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"8 解答题 1\n",
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"9 解答题 1\n",
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"10 解答题 1\n",
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"11 解答题 1\n",
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"12 选择题 1\n"
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"9 选择题 1\n",
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"10 选择题 1\n",
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"11 解答题 4\n"
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]
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}
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],
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"source": [
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"import os,re\n",
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"#修改文件名\n",
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"filename = r\"C:\\Users\\Wang Weiye\\Documents\\wwy sync\\23届\\第一轮复习讲义\\12_和差倍角公式.tex\"\n",
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"filename = r\"C:\\Users\\Wang Weiye\\Documents\\wwy sync\\23届\\第一轮复习讲义\\15_周期性与其他三角函数.tex\"\n",
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"outputfile = \"临时文件/题目状态.txt\"\n",
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"\n",
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"outputstr = \"\"\n",
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"with open(filename,\"r\",encoding = \"utf8\") as f:\n",
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" data = f.read()\n",
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"data = re.sub(r\"\\\\begin\\{center\\}[\\s\\S]*?\\\\end\\{center\\}\",\"\",data)\n",
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"sections = re.findall(r\"\\\\begin\\{enumerate\\}([\\s\\S]*?\\\\end\\{enumerate\\})\",data)\n",
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"for sec in sections:\n",
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" sec = sec.replace(\"\\\\item\",\"\\\\enditem\\\\item\").replace(\"\\\\end{enumerate}\",\"\\\\enditem\")\n",
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@ -84,7 +78,7 @@
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3.8.8 ('base')",
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"display_name": "Python 3.9.7 ('base')",
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"language": "python",
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"name": "python3"
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},
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@ -98,12 +92,12 @@
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.8"
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"version": "3.9.7"
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},
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"orig_nbformat": 4,
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"vscode": {
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"interpreter": {
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"hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac"
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"hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba"
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}
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}
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},
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@ -9,8 +9,8 @@
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"import os,re,json,time\n",
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"\n",
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"\"\"\"---设置原题目id与新题目id---\"\"\"\n",
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"old_id = \"333\"\n",
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"new_id = \"30022\"\n",
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"old_id = \"1166\"\n",
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"new_id = \"30025\"\n",
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"\"\"\"---设置完毕---\"\"\"\n",
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"\n",
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"old_id = old_id.zfill(6)\n",
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@ -50,7 +50,7 @@
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3.8.8 ('base')",
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"display_name": "Python 3.9.7 ('base')",
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"language": "python",
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"name": "python3"
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},
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@ -64,12 +64,12 @@
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.8"
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"version": "3.9.7"
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},
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"orig_nbformat": 4,
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"vscode": {
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"interpreter": {
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"hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac"
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"hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba"
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}
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}
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},
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@ -2,7 +2,7 @@
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"execution_count": 7,
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"metadata": {},
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"outputs": [
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{
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@ -13,11 +13,9 @@
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"题块 1 处理完毕.\n",
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"正在处理题块 2 .\n",
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"题块 2 处理完毕.\n",
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"正在处理题块 3 .\n",
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"题块 3 处理完毕.\n",
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"开始编译教师版本pdf文件: 临时文件/九月月考_教师_20220918.tex\n",
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"开始编译教师版本pdf文件: 临时文件/15_周期性与其他三角函数_教师_20220919.tex\n",
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"0\n",
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"开始编译学生版本pdf文件: 临时文件/九月月考_学生_20220918.tex\n",
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"开始编译学生版本pdf文件: 临时文件/15_周期性与其他三角函数_学生_20220919.tex\n",
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"0\n"
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]
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}
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@ -30,30 +28,29 @@
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"\"\"\"---设置模式结束---\"\"\"\n",
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"\n",
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"\"\"\"---设置模板文件名---\"\"\"\n",
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"# template_file = \"模板文件/第一轮复习讲义模板.tex\"\n",
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"template_file = \"模板文件/测验周末卷模板.tex\"\n",
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"template_file = \"模板文件/第一轮复习讲义模板.tex\"\n",
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"# template_file = \"模板文件/测验周末卷模板.tex\"\n",
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"\"\"\"---设置模板文件名结束---\"\"\"\n",
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"\n",
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"\"\"\"---设置其他预处理替换命令---\"\"\"\n",
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"#2023届第一轮讲义更换标题\n",
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"# exec_list = [(\"标题数字待处理\",\"12\"),(\"标题文字待处理\",\"和差倍角公式\")] \n",
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"# enumi_mode = 0\n",
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"exec_list = [(\"标题数字待处理\",\"15\"),(\"标题文字待处理\",\"周期性与其他三角函数\")] \n",
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"enumi_mode = 0\n",
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"\n",
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"#2023届测验卷与周末卷\n",
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"exec_list = [(\"标题替换\",\"九月月考\")]\n",
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"enumi_mode = 1\n",
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"# exec_list = [(\"标题替换\",\"周末卷03\")]\n",
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"# enumi_mode = 1\n",
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"\"\"\"---其他预处理替换命令结束---\"\"\"\n",
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"\n",
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"\"\"\"---设置目标文件名---\"\"\"\n",
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"destination_file = \"临时文件/九月月考\"\n",
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"destination_file = \"临时文件/15_周期性与其他三角函数\"\n",
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"\"\"\"---设置目标文件名结束---\"\"\"\n",
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"\n",
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"\n",
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"\"\"\"---设置题号数据---\"\"\"\n",
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"problems = [\n",
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"\"4080,4122,4312,4451,4557,4276,30019,4356,4320,4359,30020,4091\",\n",
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"\"4400,8101,4157,4440\",\n",
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"\"4370,4224,4328,4444,4184\"\n",
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"\"1496,1497,136,3154,6096,3179,1535,3172,9612,3152,10109\",\n",
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"\"1492,1498,1513,9597,1495,1538,3177,1537,6225,6062,6097\"\n",
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"]\n",
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"\"\"\"---设置题号数据结束---\"\"\"\n",
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"\n",
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@ -197,7 +194,7 @@
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3.8.8 ('base')",
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"display_name": "Python 3.9.7 ('base')",
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"language": "python",
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"name": "python3"
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},
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@ -211,12 +208,12 @@
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.8"
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"version": "3.9.7"
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},
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"orig_nbformat": 4,
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"vscode": {
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"interpreter": {
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"hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac"
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"hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba"
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}
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}
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},
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@ -29290,7 +29290,9 @@
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"20220625\t王伟叶"
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],
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"same": [],
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"related": [],
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"related": [
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"030025"
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],
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"remark": "",
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"space": "12ex"
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},
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@ -34945,7 +34947,7 @@
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},
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"001378": {
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"id": "001378",
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"content": "[选做]\n在三角形$ABC$中, 已知三条边上的高$h_a,h_b,h_c$分别为$1/3,1/4,1/5$, 解这个三角形.",
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"content": "在三角形$ABC$中, 已知三条边$a,b,c$上的高$h_a,h_b,h_c$分别为$1/3,1/4,1/5$, 求$A$.",
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"objs": [
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"K0315003B"
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],
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@ -68075,7 +68077,7 @@
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},
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"002745": {
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"id": "002745",
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"content": "使不等式$2x^2-5x-3\\ge 0$成立的一个充分不必要条件是\\bracket{20}. \n\\fourch{$x<0$}{$x\\ge 0$}{$x\\in \\{-1,3,5\\}$}{$x\\le \\dfrac12$或x$\\ge 3$}",
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"content": "使不等式$2x^2-5x-3\\ge 0$成立的一个充分不必要条件是\\bracket{20}. \n\\fourch{$x<0$}{$x\\ge 0$}{$x\\in \\{-1,3,5\\}$}{$x\\le \\dfrac12$或$x\\ge 3$}",
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"objs": [
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"K0106001B"
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],
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@ -77258,7 +77260,7 @@
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},
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"003128": {
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"id": "003128",
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"content": "在三角形$ABC$中,\n(1) 用三个角$A,B,C$及外接圆半径$R$表示三角形的面积$S$, 得$S=$\\blank{50};\\\\\n(2) 用三条边$a,b,c$及外接圆半径$R$表示三角形的面积$S$, 得$S=$\\blank{50};\\\\\n(3) 用内切圆半径$r$, 周长$2p$表示三角形面积$S$, 得$S=$\\blank{50}.",
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"content": "在三角形$ABC$中,\\\\\n(1) 用三个角$A,B,C$及外接圆半径$R$表示三角形的面积$S$, 得$S=$\\blank{50};\\\\\n(2) 用三条边$a,b,c$及外接圆半径$R$表示三角形的面积$S$, 得$S=$\\blank{50};\\\\\n(3) 用内切圆半径$r$, 周长$2p$表示三角形面积$S$, 得$S=$\\blank{50}.",
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"objs": [
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"K0314004B",
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"K0314006B"
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@ -77553,7 +77555,7 @@
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},
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"003141": {
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"id": "003141",
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"content": "在三角形$ABC$中, $(a+b)^2-c^2=4$, $C=\\dfrac{\\pi}3$, 则面积$S=$\\blank{50}.",
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"content": "在三角形$ABC$中, 若$(a+b)^2-c^2=4$, $C=\\dfrac{\\pi}3$, 则面积$S=$\\blank{50}.",
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"objs": [
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"K0314001B",
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"K0315003B"
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},
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"003145": {
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"id": "003145",
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"content": "已知$D,C,B$三点在地面同一直线上, $DC=a$, 从$C,D$两点测得$A$点的仰角分别为$\\alpha,\\beta$($\\alpha>\\beta$), 则点$A$离地面的高$AB=$\\blank{50}.\n\\begin{center}\n \\begin{tikzpicture}[>=latex]\n \\draw (0,0) node [below left] {$D$} -- (4,0) node [below] {$C$} -- (7,0) node [below right] {$B$} -- (7,3) node [above right] {$A$};\n \\draw (4,0) -- (7,3);\n \\draw (0,0) -- (7,3);\n \\draw (4.5,0) arc (0:atan(1):0.5);\n \\draw (5,0) node [above] {$\\alpha$};\n \\draw (0.5,0) arc(0:atan(3/7):0.5);\n \\draw (1.5,0) node [above] {$\\beta$};\n \\end{tikzpicture}\n\\end{center}",
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"content": "已知$D,C,B$三点在地面同一直线上, $DC=a$, 从$C,D$两点测得$A$点的仰角分别为$\\alpha,\\beta$($\\alpha>\\beta$), 则点$A$离地面的高$AB=$\\blank{50}.\n\\begin{center}\n \\begin{tikzpicture}[>=latex,scale = 0.6]\n \\draw (0,0) node [below left] {$D$} -- (4,0) node [below] {$C$} -- (7,0) node [below right] {$B$} -- (7,3) node [above right] {$A$};\n \\draw (4,0) -- (7,3);\n \\draw (0,0) -- (7,3);\n \\draw (4.5,0) arc (0:atan(1):0.5);\n \\draw (5,0) node [above] {$\\alpha$};\n \\draw (0.5,0) arc(0:atan(3/7):0.5);\n \\draw (1.5,-0.2) node [above] {$\\beta$};\n \\end{tikzpicture}\n\\end{center}",
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"objs": [
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"K0317002B"
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],
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},
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"003146": {
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"id": "003146",
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"content": "在一个特定时段内, 以点$E$为中心的$7$海里以内海域被设为警戒水域. 点$E$正北$55$海里处有一个雷达观测站$A$. 某时刻测得一艘匀速直线行驶的船只位于点$A$北偏东$45^\\circ$且与点$A$相距$40\\sqrt 2$海里的位置$B$, 经过$40$分钟又测得该船已行驶到点$A$北偏东$45^\\circ+\\arcsin\\dfrac{\\sqrt{26}}{26}$且与点$A$相距$10\\sqrt{13}$海里的位置$C$.\n(1) 求该船的行驶速度(单位: 海里$/$小时);\n(2) 若该船不改变航行方向继续行驶, 判断它是否会进入警戒水域, 并说明理由.\n\\begin{center}\n \\begin{tikzpicture}[>=latex, line cap = round, scale = 0.5]\n \\draw (0,0) -- (0,5.5) node [left] {$A$} coordinate (A);\n \\draw (0,5.5) -- ++ (45:{4*sqrt(2)}) coordinate (B) node [right] {$B$};\n \\draw (A) ++ ({45-asin(1/sqrt(26))}:{sqrt(13)}) coordinate (C) node [right] {$C$} -- (B);\n \\draw (C) -- (A);\n \\end{tikzpicture}\n\\end{center}",
|
||||
"content": "在一个特定时段内, 以点$E$为中心的$7$海里以内海域被设为警戒水域. 如图, 点$E$正北$55$海里处有一个雷达观测站$A$. 某时刻测得一艘匀速直线行驶的船只位于点$A$北偏东$45^\\circ$且与点$A$相距$40\\sqrt 2$海里的位置$B$, 经过$40$分钟又测得该船已行驶到点$A$北偏东$45^\\circ+\\arcsin\\dfrac{\\sqrt{26}}{26}$且与点$A$相距$10\\sqrt{13}$海里的位置$C$.\\\\\n(1) 求该船的行驶速度(单位: 海里$/$小时);\\\\\n(2) 若该船不改变航行方向继续行驶, 判断它是否会进入警戒水域, 并说明理由.\n\\begin{center}\n \\begin{tikzpicture}[>=latex, line cap = round, scale = 0.5]\n \\draw (0,0) node [below] {$E$} -- (0,5.5) node [left] {$A$} coordinate (A);\n \\draw (0,5.5) -- ++ (45:{4*sqrt(2)}) coordinate (B) node [right] {$B$};\n \\draw (A) ++ ({45-asin(1/sqrt(26))}:{sqrt(13)}) coordinate (C) node [right] {$C$} -- (B);\n \\draw (C) -- (A);\n \\end{tikzpicture}\n\\end{center}",
|
||||
"objs": [
|
||||
"K0317002B"
|
||||
],
|
||||
|
|
@ -78090,7 +78092,7 @@
|
|||
},
|
||||
"003164": {
|
||||
"id": "003164",
|
||||
"content": "*设函数$f(x)=\\dfrac{2\\sin x\\cos x+\\dfrac 52}{\\sin x+\\cos x}, 0\\le x\\le \\dfrac{\\pi}2$, 求$f(x)$的最大值与最小值.",
|
||||
"content": "设函数$f(x)=\\dfrac{2\\sin x\\cos x+\\dfrac 52}{\\sin x+\\cos x}, 0\\le x\\le \\dfrac{\\pi}2$, 求$f(x)$的最大值与最小值.",
|
||||
"objs": [
|
||||
"K0320002B"
|
||||
],
|
||||
|
|
@ -78159,7 +78161,7 @@
|
|||
},
|
||||
"003167": {
|
||||
"id": "003167",
|
||||
"content": "设$A>0$, $\\omega>0$, $0\\le \\varphi<2\\pi$. 如图为定义在$\\mathbf{R}$上的函数$f(x)=A\\sin (\\omega x+\\varphi)$的图像的一部分, 则$f(x)$的解析式为\\blank{50}.\n\\begin{center}\n \\begin{tikzpicture}[>=latex, line cap = round, scale = 0.8]\n \\draw [->] (-1,0) -- (7,0) node [below] {$x$};\n \\draw [->] (0,-3) -- (0,3) node [left] {$y$};\n \\draw (0,0) node [below right] {$O$};\n \\draw [domain = -pi/6:25*pi/12, samples = 1000] plot (\\x, {2*sin(2*\\x/3/pi*180+20)});\n \\draw [dashed] (7*pi/12,2) -- (0,2) node [left] {$2$};\n \\draw [dashed] (25*pi/12,0) node [above] {$\\dfrac{25\\pi}{12}$} --++ (0,-2) -- (0,-2) node [left] {$-2$};\n \\draw (-pi/6,0) node [below] {$-\\dfrac{\\pi}{6}$};\n \\end{tikzpicture}\n\\end{center}",
|
||||
"content": "设$A>0$, $\\omega>0$, $0\\le \\varphi<2\\pi$. 如图为定义在$\\mathbf{R}$上的函数$f(x)=A\\sin (\\omega x+\\varphi)$的图像的一部分, 则$f(x)$的解析式为\\blank{50}.\n\\begin{center}\n \\begin{tikzpicture}[>=latex, line cap = round, scale = 0.5]\n \\draw [->] (-1,0) -- (7,0) node [below] {$x$};\n \\draw [->] (0,-3) -- (0,3) node [left] {$y$};\n \\draw (0,0) node [below right] {$O$};\n \\draw [domain = -pi/6:25*pi/12, samples = 1000] plot (\\x, {2*sin(2*\\x/3/pi*180+20)});\n \\draw [dashed] (7*pi/12,2) -- (0,2) node [left] {$2$};\n \\draw [dashed] (25*pi/12,0) node [above] {$\\dfrac{25\\pi}{12}$} --++ (0,-2) -- (0,-2) node [left] {$-2$};\n \\draw (-pi/6,0) node [below] {$-\\dfrac{\\pi}{6}$};\n \\end{tikzpicture}\n\\end{center}",
|
||||
"objs": [
|
||||
"K0323003B"
|
||||
],
|
||||
|
|
@ -78341,7 +78343,7 @@
|
|||
},
|
||||
"003175": {
|
||||
"id": "003175",
|
||||
"content": "已知函数$f(x)=(2\\sin(x+\\dfrac{\\pi}3)+\\sin x)\\cos x-\\sqrt 3\\sin^2 x$.\\\\\n(1) 求函数$f(x)$的值域与周期;\\\\\n(2) 若$x\\in [0,\\dfrac{\\pi}2]$, 求$f(x)$的单调递减区间;\\\\\n(3) *设常数$a>0$, 若函数$y=f(x)$的图像关于直线$x=a$对称, 求$a$的最小值;\\\\\n(4) 设常数$m\\in \\mathbf{R}$, 若存在$x_0\\in [0,\\dfrac{5\\pi}{12}]$, 使得$mf(x_0)-2=0$成立, 求$m$的取值范围.",
|
||||
"content": "已知函数$f(x)=(2\\sin(x+\\dfrac{\\pi}3)+\\sin x)\\cos x-\\sqrt 3\\sin^2 x$.\\\\\n(1) 求函数$f(x)$的值域与周期;\\\\\n(2) 若$x\\in [0,\\dfrac{\\pi}2]$, 求$f(x)$的单调递减区间;\\\\\n(3) 设常数$a>0$, 若函数$y=f(x)$的图像关于直线$x=a$对称, 求$a$的最小值;\\\\\n(4) 设常数$m\\in \\mathbf{R}$, 若存在$x_0\\in [0,\\dfrac{5\\pi}{12}]$, 使得$mf(x_0)-2=0$成立, 求$m$的取值范围.",
|
||||
"objs": [
|
||||
"K0319005B",
|
||||
"K0320002B",
|
||||
|
|
@ -78367,7 +78369,7 @@
|
|||
},
|
||||
"003176": {
|
||||
"id": "003176",
|
||||
"content": "设$A\\ne 0$, $\\omega>0$, $-\\dfrac{\\pi}2<\\varphi<\\dfrac{\\pi}2$, 函数$f(x)=A\\sin(\\omega x+\\varphi)$的部分图像如右图所示, 则$f(x)$的解析式为\\blank{50}.\n\\begin{center}\n \\begin{tikzpicture}[>=latex, line cap = round, scale = 0.4]\n \\draw [->] (-4,0) -- (11,0) node [below] {$x$};\n \\draw [->] (0,-5) -- (0,5) node [left] {$y$};\n \\draw (0,0) node [below right] {$O$};\n \\draw [domain = -2:11, samples = 1000] plot (\\x, {-4*sin(180*\\x/8+45)});\n \\draw [dashed] (2,-4) -- (0,-4) node [left] {$-4$} (10,4) -- (0,4) node [left] {$4$};\n \\draw (-2,0) node [above] {$-2$};\n \\draw (6,0) node [below] {$6$};\n \\end{tikzpicture}\n\\end{center}",
|
||||
"content": "设$A\\ne 0$, $\\omega>0$, $-\\dfrac{\\pi}2<\\varphi<\\dfrac{\\pi}2$, 函数$f(x)=A\\sin(\\omega x+\\varphi)$的部分图像如图所示, 则$f(x)$的解析式为\\blank{50}.\n\\begin{center}\n \\begin{tikzpicture}[>=latex, line cap = round, scale = 0.3]\n \\draw [->] (-4,0) -- (11,0) node [below] {$x$};\n \\draw [->] (0,-5) -- (0,5) node [left] {$y$};\n \\draw (0,0) node [below right] {$O$};\n \\draw [domain = -2:11, samples = 1000] plot (\\x, {-4*sin(180*\\x/8+45)});\n \\draw [dashed] (2,-4) -- (0,-4) node [left] {$-4$} (10,4) -- (0,4) node [left] {$4$};\n \\draw (-2,0) node [above] {$-2$};\n \\draw (6,0) node [below] {$6$};\n \\end{tikzpicture}\n\\end{center}",
|
||||
"objs": [
|
||||
"K0321004B"
|
||||
],
|
||||
|
|
@ -78484,7 +78486,7 @@
|
|||
},
|
||||
"003181": {
|
||||
"id": "003181",
|
||||
"content": "*设常数$a\\in \\mathbf{R}$. 若函数$y=\\sin 2x+a\\cos 2x$的图像关于直线$x=-\\dfrac{\\pi}6$对称, 则$a=$\\blank{50}.",
|
||||
"content": "设常数$a\\in \\mathbf{R}$. 若函数$y=\\sin 2x+a\\cos 2x$的图像关于直线$x=-\\dfrac{\\pi}6$对称, 则$a=$\\blank{50}.",
|
||||
"objs": [
|
||||
"K0321001B"
|
||||
],
|
||||
|
|
@ -99291,7 +99293,7 @@
|
|||
},
|
||||
"004119": {
|
||||
"id": "004119",
|
||||
"content": "如图, $A,B,C$三地在以$O$为圆心的圆形区域边界上, $AB=30$公里, $AC=10$公里, $\\angle BAC=60^\\circ$, $D$是圆形区域外一景点, $\\angle DBC=90^\\circ$, $\\angle DCB=60^\\circ$.\n\\begin{center}\n \\begin{tikzpicture}\n \\draw (0,0) node [left] {$A$} -- (3,0) node [right] {$B$} -- (60:1) node [above] {$C$} coordinate (C) -- (0,0);\n \\draw (1.5,-0.288675) node [below] {$O$} circle (1.52752523);\n \\filldraw (1.5,-0.288675) circle (0.03);\n \\draw (43.90:6.245) node [above] {$D$} coordinate (D) -- (C) (D) -- (3,0) (D) -- (0,0);\n \\end{tikzpicture}\n\\end{center}\n(1) $O$、$A$相距多少公里(精确到小数点后两位)?\n(2) 若一汽车从$A$处出发, 以每小时$50$公里的速度沿公路$AD$行驶到$D$处, 需要多少小时(精确到小数点后两位)?",
|
||||
"content": "如图, $A,B,C$三地在以$O$为圆心的圆形区域边界上, $AB=30$公里, $AC=10$公里, $\\angle BAC=60^\\circ$, $D$是圆形区域外一景点, $\\angle DBC=90^\\circ$, $\\angle DCB=60^\\circ$.\n\\begin{center}\n \\begin{tikzpicture}\n \\draw (0,0) node [left] {$A$} -- (3,0) node [right] {$B$} -- (60:1) node [above] {$C$} coordinate (C) -- (0,0);\n \\draw (1.5,-0.288675) node [below] {$O$} circle (1.52752523);\n \\filldraw (1.5,-0.288675) circle (0.03);\n \\draw (43.90:6.245) node [above] {$D$} coordinate (D) -- (C) (D) -- (3,0) (D) -- (0,0);\n \\end{tikzpicture}\n\\end{center}\n(1) $O$、$A$相距多少公里(精确到小数点后两位)?\\\\\n(2) 若一汽车从$A$处出发, 以每小时$50$公里的速度沿公路$AD$行驶到$D$处, 需要多少小时(精确到小数点后两位)?",
|
||||
"objs": [
|
||||
"K0317002B"
|
||||
],
|
||||
|
|
@ -104415,7 +104417,7 @@
|
|||
},
|
||||
"004328": {
|
||||
"id": "004328",
|
||||
"content": "经济订货批量模型, 是目前大多数工厂、企业等最常采用的订货方式, 即某种物资在单位时间的需求量为某常数, 经过某段时间后, 存储量消耗下降到零, 此时开始订货并随即到货, 然后开始下一个存储周期. 该模型适用于整批间隔进货、不允许缺货的存储问题. 具体如下:\\\\\n年存储成本费$T$(元)关于每次订货$x$(单位: 吨)的函数关系为$T(x)=\\dfrac{Bx}2+\\dfrac{AC}x$, 其中$A$为年需求量, $B$为每单位物资的年存储费, $C$为每次订货费.\\\\\n某化工厂需用甲醇作为原料, 年需求量为$6000$吨, 每吨存储费为$120$元/年, 每次订货费为$2500$元.\n(1) 若该化工厂每次订购$300$吨甲醇, 求年存储成本费;\\\\\n(2) 每次需订购多少吨甲醇, 可使该化工厂年存储成本费最少? 最少费用为多少?",
|
||||
"content": "经济订货批量模型, 是目前大多数工厂、企业等最常采用的订货方式, 即某种物资在单位时间的需求量为某常数, 经过某段时间后, 存储量消耗下降到零, 此时开始订货并随即到货, 然后开始下一个存储周期. 该模型适用于整批间隔进货、不允许缺货的存储问题. 具体如下:\\\\\n年存储成本费$T$(元)关于每次订货$x$(单位: 吨)的函数关系为$T(x)=\\dfrac{Bx}2+\\dfrac{AC}x$, 其中$A$为年需求量, $B$为每单位物资的年存储费, $C$为每次订货费.\\\\\n某化工厂需用甲醇作为原料, 年需求量为$6000$吨, 每吨存储费为$120$元/年, 每次订货费为$2500$元.\\\\\n(1) 若该化工厂每次订购$300$吨甲醇, 求年存储成本费;\\\\\n(2) 每次需订购多少吨甲醇, 可使该化工厂年存储成本费最少? 最少费用为多少?",
|
||||
"objs": [
|
||||
"K0222002B"
|
||||
],
|
||||
|
|
@ -113044,7 +113046,7 @@
|
|||
},
|
||||
"004672": {
|
||||
"id": "004672",
|
||||
"content": "在$\\triangle ABC$中, $b=2,c=1$, $\\angle B-\\angle C=\\dfrac{\\pi}2$, 则$\\triangle ABC$的周长为\\blank{50}.",
|
||||
"content": "在$\\triangle ABC$中, $b=2,c=1$, $B-C=\\dfrac{\\pi}2$, 则$\\triangle ABC$的周长为\\blank{50}.",
|
||||
"objs": [
|
||||
"K0315003B"
|
||||
],
|
||||
|
|
@ -234717,7 +234719,6 @@
|
|||
"id": "010109",
|
||||
"content": "求下列各式中$x$的值(其中$x>0$):\n(1) $x^3=27$;\\\\\n(2) $x^4=121$;\\\\\n(3) $x^\\frac 32=1000$;\\\\\n(4) $x^{-\\frac 43}=\\dfrac{16}{625}$.",
|
||||
"objs": [
|
||||
"K0324006B",
|
||||
"K0203002B",
|
||||
"K0201004B"
|
||||
],
|
||||
|
|
@ -253602,7 +253603,7 @@
|
|||
},
|
||||
"010965": {
|
||||
"id": "010965",
|
||||
"content": "已知全集$U=\\mathbf{R}$, 集合$A=\\{x||x-1|>1\\}$, $B=\\{x|\\dfrac{x-3}{x+1}<0\\}$, 则$\\complement _UA\\cap B=$\\blank{50}.",
|
||||
"content": "已知全集$U=\\mathbf{R}$, 集合$A=\\{x||x-1|>1\\}$, $B=\\{x|\\dfrac{x-3}{x+1}<0\\}$, 则$\\overline{A}\\cap B=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
""
|
||||
|
|
@ -253665,7 +253666,9 @@
|
|||
"same": [
|
||||
"000499"
|
||||
],
|
||||
"related": [],
|
||||
"related": [
|
||||
"030023"
|
||||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
|
|
@ -253801,7 +253804,9 @@
|
|||
"20220817\t王伟叶"
|
||||
],
|
||||
"same": [],
|
||||
"related": [],
|
||||
"related": [
|
||||
"030024"
|
||||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
|
|
@ -281706,5 +281711,77 @@
|
|||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"030023": {
|
||||
"id": "030023",
|
||||
"content": "若$S_n$是等差数列$\\{a_n\\}$($n\\in \\mathbf{N}$且$n\\ge 1$): $-1,2,5,8,\\cdots$的前$n$项和, 则$S_n=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第四单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2022届高三上学期周末卷3试题3-20220919修改",
|
||||
"edit": [
|
||||
"20220817\t王伟叶",
|
||||
"20220919\t徐慧"
|
||||
],
|
||||
"same": [],
|
||||
"related": [
|
||||
"010967"
|
||||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"030024": {
|
||||
"id": "030024",
|
||||
"content": "已知数列$\\{a_n\\}$($n\\in \\mathbf{N}^*$), 若$a_1=1$, $a_{n+1}+a_n=(\\dfrac 12)^n$, 则$a_{2n}=$\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第四单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2022届高三上学期周末卷3试题9-20220919修改",
|
||||
"edit": [
|
||||
"20220817\t王伟叶",
|
||||
"20220919\t徐慧"
|
||||
],
|
||||
"same": [],
|
||||
"related": [
|
||||
"010973"
|
||||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
},
|
||||
"030025": {
|
||||
"id": "030025",
|
||||
"content": "若函数$f(x)=\\sqrt{kx^2+4kx+3}$的定义域为$\\mathbf{R}$, 则实数$k$的取值范围为\\blank{50}.",
|
||||
"objs": [],
|
||||
"tags": [
|
||||
"第二单元"
|
||||
],
|
||||
"genre": "填空题",
|
||||
"ans": "",
|
||||
"solution": "",
|
||||
"duration": -1,
|
||||
"usages": [],
|
||||
"origin": "2016届创新班作业\t1131-函数与函数的三要素-20220919修改",
|
||||
"edit": [
|
||||
"20220625\t王伟叶",
|
||||
"20220919\t徐慧"
|
||||
],
|
||||
"same": [],
|
||||
"related": [
|
||||
"001166"
|
||||
],
|
||||
"remark": "",
|
||||
"space": ""
|
||||
}
|
||||
}
|
||||
Reference in New Issue