From e1ec3a28b39d8aafe751c86907f949904e44b59e Mon Sep 17 00:00:00 2001
From: "weiye.wang" <kj_wangweiye@126.com>
Date: Fri, 22 Dec 2023 22:07:28 +0800
Subject: [PATCH] =?UTF-8?q?=E5=AF=BC=E5=85=A5=E9=83=A8=E5=88=862025?=
 =?UTF-8?q?=E5=B1=8A=E9=AB=98=E4=BA=8C=E4=B8=8A=E6=A0=A1=E6=9C=AC=E4=BD=9C?=
 =?UTF-8?q?=E4=B8=9A=E7=AD=94=E6=A1=88?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 题库0.3/Problems.json | 522 +++++++++++++++++++++---------------------
 1 file changed, 261 insertions(+), 261 deletions(-)

diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index 83b6a761..740af990 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -7220,7 +7220,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\sqrt{h^{2}+{\\frac{a}{4}}^{2}}$; (2) $h=1$时, $V=\\frac{1}{6}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -255579,7 +255579,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "是.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -255611,7 +255611,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\arccos\\frac{2}{5}$; (2) $\\arccos\\frac{\\sqrt{10}}{10}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -255643,7 +255643,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$8$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -255719,7 +255719,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -255993,7 +255993,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\arctan{\\dfrac{\\sqrt{5}}{2}}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -256140,7 +256140,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $\\dfrac{\\sqrt{6}}2$; (2) $\\dfrac{\\sqrt{6}}3$; (3) $\\dfrac{\\sqrt{2}}2$; (4) $\\dfrac{\\sqrt{2}}2$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -256194,7 +256194,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\arcsin{\\dfrac{3}{8}}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -256248,7 +256248,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) 错误; (2) 错误; (3) 错误; (4) 正确",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -256494,7 +256494,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -257403,7 +257403,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -290040,7 +290040,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -290094,7 +290094,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -290534,7 +290534,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$AB$和平面$\\alpha$所成角的大小为$\\arccos{\\dfrac18}$, $AC$和平面$\\alpha$所成角的大小为$\\arccos{\\dfrac34}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -290612,7 +290612,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -291596,7 +291596,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$9$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525097,7 +525097,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $A\\in l$, $B\\not\\in l$; (2) $A\\in \\beta$, $B\\not\\in \\beta$; (3) $l\\cap \\alpha=\\varnothing$; (4) $l\\subset \\alpha$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525127,7 +525127,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "错, 错, 错, 对.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525157,7 +525157,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525185,7 +525185,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{\\pi}{4}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525215,7 +525215,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$5$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525245,7 +525245,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\frac{\\pi}{4}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525275,7 +525275,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525491,7 +525491,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(0,\\sqrt{3})$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525521,7 +525521,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 略; (2) 略; (3) $\\frac{\\pi}{4}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525551,7 +525551,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{\\pi}4$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525579,7 +525579,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\dfrac{\\sqrt{6}}3$; (2) $\\dfrac{\\sqrt{3}}3$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -525609,7 +525609,7 @@
             "第六单元"
         ],
         "genre": "4em",
-        "ans": "",
+        "ans": "(1) $\\sqrt{7}$; (2) 略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -553583,7 +553583,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$P\\in l\\subset\\alpha$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -553622,7 +553622,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $M\\in\\alpha\\cap\\beta $; (2) $\\alpha\\cap\\beta=\\phi,l\\cap \\alpha=A,l\\cap\\beta=B$; (3) $\\alpha\\cap\\beta=l$, $l\\cap\\gamma=\\phi$; (4) $l\\subset\\alpha$,$M\\in\\alpha$, $M\\notin l$; (5) $\\alpha\\cap\\beta=l$, $a\\cap\\alpha=\\phi$, $a\\cap\\beta=\\phi$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -553661,7 +553661,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "错, 错, 错, 对.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -553700,7 +553700,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "若$\\alpha\\cap\\beta=l$, $\\alpha\\cap\\gamma=m$, $\\beta\\cap\\gamma=n$, $l\\parallel m$, 则$l\\parallel m\\parallel n$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -553739,7 +553739,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\textcircled{1}\\textcircled{4}.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -553778,7 +553778,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -553817,7 +553817,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$4$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -553886,7 +553886,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "三点不共线, 相交或平行.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -553929,7 +553929,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "过这一点.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -553972,7 +553972,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554004,7 +554004,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554038,7 +554038,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554104,7 +554104,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\textcircled{2}.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554147,7 +554147,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554224,7 +554224,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554267,7 +554267,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554297,7 +554297,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554327,7 +554327,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554357,7 +554357,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554387,7 +554387,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554417,7 +554417,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554456,7 +554456,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$6\\sqrt{5}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554495,7 +554495,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$16$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554578,7 +554578,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\frac{3\\sqrt{2}}{8}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554617,7 +554617,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$30^{\\circ}$或$150^{\\circ}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554656,7 +554656,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "平行.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554695,7 +554695,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$c\\parallel d$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554734,7 +554734,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554773,7 +554773,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "证明略, $EFGH$为菱形.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554812,7 +554812,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554851,7 +554851,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554890,7 +554890,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -554929,7 +554929,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -555000,7 +555000,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "平行或异面.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -555041,7 +555041,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -555073,7 +555073,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -555105,7 +555105,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -555137,7 +555137,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -555169,7 +555169,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -555242,7 +555242,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$24$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -555411,7 +555411,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\arctan\\frac{2\\sqrt{5}}{5}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -555452,7 +555452,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\frac{\\pi}{2}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -555525,7 +555525,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -555566,7 +555566,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\textcircled{3}\\textcircled{4}.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -555607,7 +555607,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\arctan\\frac{1}{2}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -555648,7 +555648,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "对, 错, 错, 对, 错, 错.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -555689,7 +555689,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$MN\\parallel $平面$ABCD$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -555730,7 +555730,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "平行.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -555771,7 +555771,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\textcircled{1}\\textcircled{2}\\textcircled{3}\\textcircled{4}.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -555812,7 +555812,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -555853,7 +555853,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -555958,7 +555958,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -555999,7 +555999,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -556031,7 +556031,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $A_1B$; (2) $AB$; (3) $B_1B$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -556106,7 +556106,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -556148,7 +556148,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$5\\sqrt{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -556190,7 +556190,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -556277,7 +556277,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -556319,7 +556319,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 错误; (2) 错误; (3) 错误; (4) 错误",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -556360,7 +556360,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$[0,\\dfrac{\\pi}2]$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -556401,7 +556401,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$30^\\circ$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -556442,7 +556442,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$45^\\circ$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -556483,7 +556483,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{\\pi}3$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -556588,7 +556588,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -556620,7 +556620,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "C",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -556652,7 +556652,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -556684,7 +556684,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -556716,7 +556716,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\dfrac{\\pi}{6}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -556757,7 +556757,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{2\\sqrt{30}}{5}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -556798,7 +556798,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) 外心; (2) 中心; (3) 垂心; (4) 内心",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -556839,7 +556839,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -556871,7 +556871,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\textcircled{1}\\textcircled{2}\\textcircled{3}\\textcircled{4}",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -556912,7 +556912,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -556985,7 +556985,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $\\theta_1>\\theta_2$; (2) $4$或$6$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -557026,7 +557026,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\textcircled{3}",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -557067,7 +557067,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 错误; (2) 错误; (3) 错误",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -557140,7 +557140,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -557181,7 +557181,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\textcircled{4}",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -557222,7 +557222,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -557263,7 +557263,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -557345,7 +557345,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{\\pi}{4}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -557386,7 +557386,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "内心.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -557427,7 +557427,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{\\sqrt{5}}3$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -557464,7 +557464,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\sqrt{3}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -557582,7 +557582,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 略; (2) $\\sqrt{13}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -557623,7 +557623,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 略; (2) $arccos\\frac{\\sqrt{7}}{7}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -557661,7 +557661,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -557699,7 +557699,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 略; (2) $\\frac{\\sqrt{6}}{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -557766,7 +557766,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$250\\sqrt{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -557837,7 +557837,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "内心",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -557876,7 +557876,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $120^\\circ$; (2) $\\sqrt{13}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -557915,7 +557915,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(0,\\sqrt{3})$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -557988,7 +557988,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $b$, $c$, $\\dfrac{bc}{\\sqrt{b^2+c^2}}$; (2) $\\dfrac{a^2-b^2}{\\sqrt{a^2+b^2+c^2}\\sqrt{a^2+b^2}}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558027,7 +558027,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 正确; (2) 错误; (3) 错误",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558066,7 +558066,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{a^2+b^2+c^2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558105,7 +558105,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$P \\supset N \\supset M \\supset Q$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558144,7 +558144,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\textcircled{1}",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558183,7 +558183,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558222,7 +558222,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558261,7 +558261,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558300,7 +558300,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\cos ^2 \\alpha+\\cos ^2 \\beta + \\cos^2 \\gamma=1$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558339,7 +558339,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$Sh$, 相等",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558376,7 +558376,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$4$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558413,7 +558413,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$48$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558450,7 +558450,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$300\\sqrt{3}\\text{cm}^3$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558487,7 +558487,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$375\\text{t}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558524,7 +558524,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$252$个",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558561,7 +558561,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$270\\sqrt{3}\\text{cm}^3$, $\\dfrac{225}{2}\\sqrt{3}\\text{cm}^3$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558598,7 +558598,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$1.1\\times 10^{-4}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558633,7 +558633,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$132$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558670,7 +558670,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{CS}{4\\pi}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558707,7 +558707,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\sqrt{3}h^2$, $\\dfrac{3h^2}{2\\pi}+\\sqrt{3}h^2$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558744,7 +558744,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$132$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558781,7 +558781,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$(6\\sqrt{3}+8)\\pi$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558850,7 +558850,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$2\\sqrt{2Ph^2+Q^2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558887,7 +558887,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 略; (2) $\\dfrac98a^2$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558924,7 +558924,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$V_1:V_2=\\pi:4$, 正方体体积小",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -558961,7 +558961,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "错, 对, 错, 错.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559001,7 +559001,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559032,7 +559032,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "\\textcircled{5}.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559072,7 +559072,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "外心.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559112,7 +559112,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "内心.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559152,7 +559152,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 两个直三棱柱; (2) 三棱锥, 四棱锥.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559192,7 +559192,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{1}{6}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559222,7 +559222,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{\\sqrt{Q^{2}P-P^{3}}}{6}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559252,7 +559252,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{\\pi}{4}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559282,7 +559282,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559312,7 +559312,7 @@
             "第六单元"
         ],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559342,7 +559342,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$96\\sqrt{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559372,7 +559372,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$0.5\\text{kg}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559402,7 +559402,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$1200\\pi \\text{cm}^{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559432,7 +559432,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{2\\pi h^{2}}{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559461,7 +559461,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$4\\pi$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559490,7 +559490,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$1$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559519,7 +559519,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$8\\sqrt{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559548,7 +559548,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{200\\pi}{3}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559577,7 +559577,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$48cm^{2}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559606,7 +559606,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\frac{\\sqrt{3}a^{2}}{4}+\\frac{\\sqrt{6}a^{2}}{4}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559635,7 +559635,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$ab+2ab\\sin\\theta$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559664,7 +559664,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$100\\pi \\text{cm}^{2}$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559693,7 +559693,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$4:6$.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559722,7 +559722,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$1$个或无穷多个",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559753,7 +559753,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$4\\text{cm}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559784,7 +559784,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$8\\sqrt{2}\\text{cm}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559815,7 +559815,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$10$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559846,7 +559846,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$4$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559877,7 +559877,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$1:2\\sqrt{2}:3\\sqrt{3}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559908,7 +559908,7 @@
             "第六单元"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\frac{\\sqrt{3}}{2}\\pi V$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559939,7 +559939,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$3\\sqrt{259}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -559970,7 +559970,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$\\pi(R^2-d^2)$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560001,7 +560001,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$2$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560033,7 +560033,7 @@
             "第六单元"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$4.5$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560065,7 +560065,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$1000$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560096,7 +560096,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$72$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560150,7 +560150,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$40$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560205,7 +560205,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$36$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560236,7 +560236,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$81$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560267,7 +560267,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $180$; (2) $100$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560298,7 +560298,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $48$; (2) $16$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560329,7 +560329,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $36$; (2) $6$; (3) $30$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560360,7 +560360,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $38$; (2) $357$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560391,7 +560391,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$11$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560422,7 +560422,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$17$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560453,7 +560453,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$42$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560484,7 +560484,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$2296$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560515,7 +560515,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$78$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560546,7 +560546,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$504$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560577,7 +560577,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$42$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560608,7 +560608,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$113$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560639,7 +560639,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$12$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560670,7 +560670,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$32760$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560701,7 +560701,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$60$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560732,7 +560732,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$6$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560763,7 +560763,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$30$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560794,7 +560794,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$240$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560825,7 +560825,7 @@
             "排列组合"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $6$; (2) $5$; (3) $4$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560856,7 +560856,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$40$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560887,7 +560887,7 @@
             "排列组合"
         ],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$6$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560918,7 +560918,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$100$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560949,7 +560949,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$1-\\dfrac{1}{n!}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -560980,7 +560980,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561011,7 +561011,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$96$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561044,7 +561044,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$8640$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561077,7 +561077,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$144$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561110,7 +561110,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$4536$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561143,7 +561143,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $240$; (2) $1200$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561176,7 +561176,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$252$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561209,7 +561209,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $240$; (2) $1440$; (3) $2520$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561242,7 +561242,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $384$; (2) $48$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561275,7 +561275,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$60480$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561308,7 +561308,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$30$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561341,7 +561341,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 排列; (2) 组合; (3) 组合; (4)排列",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561377,7 +561377,7 @@
             "排列组合"
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         "genre": "解答题",
-        "ans": "",
+        "ans": "$225$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561413,7 +561413,7 @@
             "排列组合"
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         "genre": "解答题",
-        "ans": "",
+        "ans": "$152096$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561449,7 +561449,7 @@
             "排列组合"
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         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $20475$; (2) $2457000$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561485,7 +561485,7 @@
             "排列组合"
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         "genre": "解答题",
-        "ans": "",
+        "ans": "$120$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561521,7 +561521,7 @@
             "排列组合"
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         "genre": "填空题",
-        "ans": "",
+        "ans": "(1) $8$; (2) $9$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561557,7 +561557,7 @@
             "排列组合"
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         "genre": "解答题",
-        "ans": "",
+        "ans": "略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561593,7 +561593,7 @@
             "排列组合"
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         "genre": "解答题",
-        "ans": "",
+        "ans": "$330$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561629,7 +561629,7 @@
             "排列组合"
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         "genre": "解答题",
-        "ans": "",
+        "ans": "$1176$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561665,7 +561665,7 @@
             "排列组合"
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         "genre": "解答题",
-        "ans": "",
+        "ans": "$225$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561701,7 +561701,7 @@
             "排列组合"
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         "genre": "解答题",
-        "ans": "",
+        "ans": "$116$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561737,7 +561737,7 @@
             "排列组合"
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         "genre": "解答题",
-        "ans": "",
+        "ans": "$60$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561771,7 +561771,7 @@
             "排列组合"
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         "genre": "解答题",
-        "ans": "",
+        "ans": "$4$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561805,7 +561805,7 @@
             "排列组合"
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         "genre": "解答题",
-        "ans": "",
+        "ans": "$126$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561839,7 +561839,7 @@
             "排列组合"
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         "genre": "解答题",
-        "ans": "",
+        "ans": "$2880$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561873,7 +561873,7 @@
             "排列组合"
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         "genre": "解答题",
-        "ans": "",
+        "ans": "$1084$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561907,7 +561907,7 @@
             "排列组合"
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         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $13$; (2) $27$; (3) $12$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561941,7 +561941,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $18$; (2) $27$; (3) $21$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -561975,7 +561975,7 @@
             "排列组合"
         ],
         "genre": "解答题",
-        "ans": "",
+        "ans": "$126$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -562009,7 +562009,7 @@
             "排列组合"
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         "genre": "解答题",
-        "ans": "",
+        "ans": "$44424$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -562043,7 +562043,7 @@
             "排列组合"
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         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $2$,$4$; (2) 略",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -607930,7 +607930,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$16\\pi$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -607963,7 +607963,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$(0,\\dfrac{\\pi}{2}]$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -607996,7 +607996,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{27}{4\\pi}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -608029,7 +608029,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{\\sqrt{6}}{4}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -608062,7 +608062,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\arccos{\\dfrac{\\sqrt{3}}{3}}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -608095,7 +608095,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$5\\times 2^{n-1}-3$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -608128,7 +608128,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$3\\sqrt{2}$",
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         "duration": -1,
         "usages": [
@@ -608161,7 +608161,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\arccos{\\dfrac19}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -608194,7 +608194,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$3+2\\sqrt{2}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -608227,7 +608227,7 @@
         "objs": [],
         "tags": [],
         "genre": "填空题",
-        "ans": "",
+        "ans": "$\\dfrac{4\\sqrt{6}}{3}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -608260,7 +608260,7 @@
         "objs": [],
         "tags": [],
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-        "ans": "",
+        "ans": "$[1,3]$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -608293,7 +608293,7 @@
         "objs": [],
         "tags": [],
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-        "ans": "",
+        "ans": "$3$",
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         "duration": -1,
         "usages": [
@@ -608326,7 +608326,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "D",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -608359,7 +608359,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "A",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -608392,7 +608392,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -608425,7 +608425,7 @@
         "objs": [],
         "tags": [],
         "genre": "选择题",
-        "ans": "",
+        "ans": "B",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -608458,7 +608458,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 略; (2) $\\arctan{2\\sqrt{2}}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -608491,7 +608491,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 略; (2) $\\arctan{\\dfrac{\\sqrt{5}}{5}}$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -608524,7 +608524,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $a_n=a_0(2-\\dfrac{1}{2^n})$; (2) $5000$元广告费时, 获利最大, 此时销售量为$7875$千克.",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -608557,7 +608557,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) $90^\\circ$; (2) $\\dfrac{2\\sqrt{3}}{3}$; (3) $\\dfrac{2\\sqrt{6}}{3}\\pi$",
         "solution": "",
         "duration": -1,
         "usages": [
@@ -608590,7 +608590,7 @@
         "objs": [],
         "tags": [],
         "genre": "解答题",
-        "ans": "",
+        "ans": "(1) 略; (2) $\\arcsin{\\frac{\\sqrt{5}}{5}}$; (3) 存在, $E$在$C_{1}D$上, $C_{1}E=\\frac{4\\sqrt{5}}{5}$.",
         "solution": "",
         "duration": -1,
         "usages": [