收录高三寒假作业28新题

工具v2/文本文件/新题收录列表.txt

@@ -82,3 +82,6 @@
 20240125-112043
 023835:023841,013014,023842:023843
 
+20240125-112538
+023844:023847
+

题库0.3/Problems.json

@@ -131433,7 +131433,9 @@
             "20220705\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "023847"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -643392,6 +643394,88 @@
         "space": "4em",
         "unrelated": []
     },
+    "023844": {
+        "id": "023844",
+        "content": "选择正确的序号填空: (\\textcircled{1} 充要; \\textcircled{2} 充分非必要; \\textcircled{3} 必要非充分; \\textcircled{4} 既非充分又非必要)\\\\\n(1) 在 $\\triangle ABC$ 中, ``$A>B$''是``$\\sin A>\\sin B$''的\\blank{50}条件;\\\\\n(2) 在 $\\triangle ABC$ 中, ``$A>B$''是``$\\tan A>\\tan B$''的\\blank{50}条件;\\\\\n(3) 在 $\\triangle ABC$ 中, ``$A>B$''是``$\\cos A<\\cos B$''的\\blank{50}条件.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023845": {
+        "id": "023845",
+        "content": "甲船在 $A$ 处测得乙船在北偏东 $70^{\\circ}$ 方向, 两船相距 $10$ 海里, 且乙船正沿着南偏东 $40^{\\circ}$ 方向以每小时 $12$ 海里的速度航行, 经过半小时, 甲船追上乙船, 则甲船的航行速度是每小时\\blank{50}海里(精确到 $0.1$).",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023846": {
+        "id": "023846",
+        "content": "$\\triangle ABC$ 的内角 $A$、$B$、$C$ 所对边的长分别为 $a$、$b$、$c$. 已知 $2 \\cos C(a \\cos B+b \\cos A)=c$.\\\\\n(1) 求 $C$;\\\\\n(2) 若 $c=\\sqrt{7}, \\triangle ABC$ 的面积为 $\\dfrac{3 \\sqrt{3}}{2}$, 求 $\\triangle ABC$ 的周长.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "023847": {
+        "id": "023847",
+        "content": "某动物园喜迎虎年的到来, 拟用一块形如直角三角形 $ABC$ 的地块建造小老虎的休息区和活动区. 如图, $\\angle BAC=90^{\\circ}$, $AB=AC=20$ (单位: 米), $E$、$F$ 为 $BC$ 上的两点, 且 $\\angle EAF=45^{\\circ}, \\triangle AEF$ 区域为休息区, $\\triangle ABE$ 和 $\\triangle ACF$ 区域均为活动区. 设 $\\angle EAB=\\alpha$($0<\\alpha<\\dfrac{\\pi}{4}$).\\\\\n\\begin{center}\n\\begin{tikzpicture}\n\\path (0,0) node [below left] {$A$} coordinate (A)-- (3,0) node [below right] {$B$} coordinate (B)-- (0,3) node [above left] {$C$} coordinate (C)-- cycle;\n\\path [name path = lineBC] (3,0) -- (0,3);\n\\path [name path = lineAE] (0,0) -- (15:3);\n\\path [name path = lineAF] (0,0) -- (60:3);\n\\path [name intersections = {of = lineBC and lineAE, by = E}];\n\\path [name intersections = {of = lineBC and lineAF, by = F}];\n\\filldraw [gray!30] (A) -- (B) -- (E) -- cycle;\n\\filldraw [gray!30] (A) -- (F) -- (C) -- cycle;\n\\draw (0,0) -- (E) node [above right] {$E$};\n\\draw (0,0) -- (F) node [above right] {$F$};\n\\draw (A) -- (B) -- (C) -- cycle;\n\\draw (2,0) node [above] {\\tiny{活动区}};\n\\draw (0,2) node [right] {\\tiny{活动区}};\n\\draw (1.2,1) node {\\small{休息区}};\n\\end{tikzpicture}\n\\end{center}\n(1) 求 $AE$ 的长 (用 $\\alpha$ 的代数式表示);\\\\\n(2) 为了使小老虎能健康成长, 要求所建造的活动区面积尽可能大 (即休息区尽可能小), 当 $\\alpha$ 为多少时, 活动区的面积最大? 最大面积为多少?",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240125\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "004266"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
     "030001": {
         "id": "030001",
         "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",