From 7b4c8ed2bf47dd246a938eff963bd3a85efbc0be Mon Sep 17 00:00:00 2001 From: WangWeiye Date: Fri, 19 May 2023 17:27:25 +0800 Subject: [PATCH] =?UTF-8?q?=E4=BF=AE=E6=94=B913492=EF=BC=8C13493=E9=A2=98?= =?UTF-8?q?=E7=9B=AE?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具/latex界面修改题目内容.py | 2 +- 题库0.3/Problems.json | 10 ++++++---- 2 files changed, 7 insertions(+), 5 deletions(-) diff --git a/工具/latex界面修改题目内容.py b/工具/latex界面修改题目内容.py index 02fe5d83..ae9d9d30 100644 --- a/工具/latex界面修改题目内容.py +++ b/工具/latex界面修改题目内容.py @@ -1,6 +1,6 @@ import os,re,json """这里编辑题号(列表)后将在vscode中打开窗口, 编辑后保存关闭""" -problems = "15073" +problems = "13492,13493" editor = "王伟叶" def generate_number_set(string,dict): diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index a51fdff1..7cb6570e 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -355516,7 +355516,7 @@ }, "013492": { "id": "013492", - "content": "已知集合$A=\\{x | x^2-3 x+2 \\leq 0\\}$, $B=\\{x | \\dfrac{x-a}{x+2}>0, a>0\\}$, 若``$x \\in A$''是``$x \\in$$B$''的充分非必要条件, 则$a$的取值范围是\\bracket{20}.\n\\fourch{$00\\}$, 其中常数$a>0$. 若``$x \\in A$''是``$x \\in$$B$''的充分非必要条件, 则$a$的取值范围是\\bracket{20}.\n\\fourch{$0=latex]\n\\def\\l{2}\n\\draw (0,0,0) coordinate (A);\n\\draw (A) ++ (\\l,0,0) coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l) coordinate (C);\n\\draw (A) ++ (0,0,-\\l) coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0) coordinate (A1);\n\\draw (B) ++ (0,\\l,0) coordinate (B1);\n\\draw (C) ++ (0,\\l,0) coordinate (C1);\n\\draw (D) ++ (0,\\l,0) coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1);\n\\draw ($(A1)!0.5!(B1)$) -- ($(C1)!0.5!(D1)$) ($(A1)!0.5!(D1)$) -- ($(B1)!0.5!(C1)$);\n\\draw [dashed] ($(A)!0.5!(D)$) -- ($(B)!0.5!(C)$);\n\\draw [domain = 0:360] plot ({1+cos(\\x)},{1+sin(\\x)},0);\n\\draw [domain = 0:360] plot (2,{1+cos(\\x)},{-1+sin(\\x)});\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$\\dfrac{1}{2}$}{$\\dfrac{\\sqrt{2}}{2}$}{$\\sqrt{2}$}{$\\sqrt{3}$}", + "content": "刘徽在他的《九章算术注》中提出一个独特的方法来计算球体的体积: 他不直接给出球体的体积, 而是先计算另一个叫``牟合方盖''的立体的体积. 刘徽通过计算, ``牟合方盖''的体积与球的体积之比应为$\\dfrac{4}{\\pi}$. 后人导出了``牟\n合方盖''的$\\dfrac{1}{8}$体积计算公式, 即$\\dfrac{1}{8} V_{\\text {牟 }}=r^3-V_{\\text{方盖差}}$, $r$为球的半径, 也即正方体的棱长均为$2 r$, 从而计算出$V_{\\text {球}}=\\dfrac{4}{3} \\pi r^3$. 记所有棱长都为$r$的正四棱锥的体积为$V_{\\text{正}}$, 棱长为$2r$的正方体的方盖差的体积为$V_{\\text{方盖差}}$, 则$\\dfrac{V_{\\text{方盖差}}}{V_{\\text{正}}}=$\\bracket{20}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\def\\l{2}\n\\draw (0,0,0) coordinate (A);\n\\draw (A) ++ (\\l,0,0) coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l) coordinate (C);\n\\draw (A) ++ (0,0,-\\l) coordinate (D);\n\\draw (A) -- (B) -- (C);\n\\draw [dashed] (A) -- (D) -- (C);\n\\draw (A) ++ (0,\\l,0) coordinate (A1);\n\\draw (B) ++ (0,\\l,0) coordinate (B1);\n\\draw (C) ++ (0,\\l,0) coordinate (C1);\n\\draw (D) ++ (0,\\l,0) coordinate (D1);\n\\draw (A1) -- (B1) -- (C1) -- (D1) -- cycle;\n\\draw (A) -- (A1) (B) -- (B1) (C) -- (C1);\n\\draw [dashed] (D) -- (D1);\n\\draw ($(A1)!0.5!(B1)$) -- ($(C1)!0.5!(D1)$) ($(A1)!0.5!(D1)$) -- ($(B1)!0.5!(C1)$);\n\\draw [dashed] ($(A)!0.5!(D)$) -- ($(B)!0.5!(C)$);\n\\draw [domain = 0:360] plot ({1+cos(\\x)},{1+sin(\\x)},0);\n\\draw [domain = 0:360] plot (2,{1+cos(\\x)},{-1+sin(\\x)});\n\\end{tikzpicture}\n\\end{center}\n\\fourch{$\\dfrac{1}{2}$}{$\\dfrac{\\sqrt{2}}{2}$}{$\\sqrt{2}$}{$\\sqrt{3}$}", "objs": [], "tags": [ "第六单元" @@ -355550,7 +355551,8 @@ "usages": [], "origin": "2022版双基百分百", "edit": [ - "20230123\t王伟叶" + "20230123\t王伟叶", + "20230519\t王伟叶" ], "same": [], "related": [],