收录24届高三寒假作业04新题

工具v2/文本文件/新题收录列表.txt

@@ -10,3 +10,6 @@
 20240124-163155
 023666:023673
 
+20240124-163621
+023674:023676
+

题库0.3/Problems.json

@@ -123286,7 +123286,8 @@
         ],
         "same": [],
         "related": [
-            "023646"
+            "023646",
+            "023675"
         ],
         "remark": "",
         "space": "4em",
@@ -525863,7 +525864,8 @@
         ],
         "same": [],
         "related": [
-            "023646"
+            "023646",
+            "023675"
         ],
         "remark": "",
         "space": "4em",
@@ -639122,7 +639124,8 @@
         "same": [],
         "related": [
             "004010",
-            "019783"
+            "019783",
+            "023675"
         ],
         "remark": "",
         "space": "",
@@ -639686,6 +639689,70 @@
         "space": "4em",
         "unrelated": []
     },
+    "023674": {
+        "id": "023674",
+        "content": "已知某生产厂家的年利润 $y$ (单位: 万元) 与年产量 $x$ (单位: 万件) 的函数关系式为 $y=-\\dfrac{1}{3}x^3+81 x-234$, 则使该生产厂家获取最大年利润的年产量为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240124\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023675": {
+        "id": "023675",
+        "content": "$, 且甲、乙两地相距 $100 \\mathrm{km}$,则当汽车以\\blank{50}$\\mathrm{km}/ \\mathrm{h}$ 的速度匀速行驶时, 从甲地到乙地的耗油量最少.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240124\t毛培菁"
+        ],
+        "same": [],
+        "related": [
+            "023646",
+            "004010",
+            "019783"
+        ],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "023676": {
+        "id": "023676",
+        "content": "某市一特色酒店由一些完全相同的帐篷构成. 每顶帐篷的体积为 $54 \\pi \\mathrm{m}^3$, 且分上、下两层,其中上层是半径为 $r(r \\geq 1) m$ 的半球体, 下层是底面半径为 $r m$, 高为 $h m$ 的圆柱体 (如图). 经测算, 上层半球体部分每平方米的建造费用为 $2$ 千元, 下层圆柱体的侧面、隔层和地面三个部分每平方米的建造费用均为 $3$ 千元, 设每顶帐篷的建造费用为 $y$ 千元.\\\\\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (-1,0) arc (180:360:1 and 0.25) --++ (0,1) arc (0:180:1) --cycle;\n\\draw (-1,1) arc (180:360:1 and 0.25);\n\\draw [dashed] (-1,1) arc (180:0:1 and 0.25) (-1,0) arc (180:0:1 and 0.25);\n\\end{tikzpicture}\n\\end{center}\n(1) 求 $y$ 关于 $r$ 的函数解析式, 并指出该函数的定义域;\\\\\n(2) 当半径 $r$ 为何值时, 每顶帐篷的建造费用最小?并求出最小值.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20240124\t毛培菁"
+        ],
+        "same": [],
+        "related": [],
+        "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.",