收录高三寒假作业69新题
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20240125-143605
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024137:024142
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20240125-143810
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024143:024149
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@ -283680,7 +283680,9 @@
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"20220806\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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"024148"
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],
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"remark": "",
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"space": "4em",
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"unrelated": []
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@ -649769,6 +649771,148 @@
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"space": "4em",
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"unrelated": []
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},
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"024143": {
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"id": "024143",
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"content": "一枚炮弹被发射后, 其升空高度 $h$ 与时间 $t$ 的函数关系为 $h=130 t-5 t^2$, 则该函数的定义域是\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"024144": {
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"id": "024144",
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"content": "某种商品进价为 $4$ 元/件, 当日均零售价为 $6$ 元/件, 日均销售 $100$ 件, 当单价每增加 $1$ 元, 日均销量减少 $10$ 件, 试计算该商品在销售过程中, 若每天固定成本为 $20$ 元, 则预计单价为\\blank{50}元/件时, 利润最大.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"024145": {
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"id": "024145",
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"content": "某市出租车收费标准如下: 起步价为 $8$ 元, 起步里程为 $3 \\mathrm{km}$ (不超过 $3 \\mathrm{km}$ 按起步价付费); 超过 $3 \\mathrm{km}$ 但不超过 $8 \\mathrm{km}$ 时, 超过部分按每千米 $2.15$ 元收费; 超过 $8 \\mathrm{km}$ 时, 超过部分按每千米 $2.85$ 元收费, 另每次乘坐需付燃油附加费 $1$ 元. 现某人乘坐一次出租车付费 $22.6$ 元, 则此次出租车行驶了\\blank{50}$\\mathrm{km}$.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"024146": {
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"id": "024146",
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"content": "拟定甲、乙两地通话 $m$ 分钟的电话费 (单位: 元) 由 $f(m)=1.06(0.5[m]+1)$ 给出, 其中 $m>0$, $[m]$ 是不超过 $m$ 的最大整数 (如 $[3]=3$, $[3.7]=3$, $[3.1]=3$ ), 则甲、乙两地通话 $6.5$ 分钟的电话费为\\blank{50}元.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"024147": {
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"id": "024147",
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"content": "已知正方形 $ABCD$ 的边长为 $4$ , 动点 $P$ 从点 $B$ 开始沿折线 $BCDA$ 向点 $A$ 运动. 若点 $P$ 运动的路程为 $x$, $\\triangle ABP$ 的面积为 $S$, 则函数 $S=f(x)$ 的图像是\\bracket{20}.\n\\fourch{\\begin{tikzpicture}[>=latex, xscale = 0.12, yscale = 0.2]\n\\draw [->] (0,0) -- (16,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,10) node [left] {$S$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i in {4,8,12}\n{\\draw (\\i,0.5) -- (\\i,0) node [below] {$\\i$};};\n\\foreach \\i in {4,8}\n{\\draw (0.5,\\i) -- (0,\\i) node [left] {$\\i$};};\n\\draw [domain = 0:12, samples = 100] plot (\\x,{8-(\\x-6)*(\\x-6)/36*8});\n\\draw [dashed] (6,0) -- (6,8);\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex, xscale = 0.12, yscale = 0.2]\n\\draw [->] (0,0) -- (16,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,10) node [left] {$S$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i in {4,8,12}\n{\\draw (\\i,0.5) -- (\\i,0) node [below] {$\\i$};};\n\\foreach \\i in {4,8}\n{\\draw (0.5,\\i) -- (0,\\i) node [left] {$\\i$};};\n\\draw (0,0) sin (4,8) -- (8,8) cos (12,0);\n\\draw [dashed] (4,0) -- (4,8) (8,0) -- (8,8);\n\\end{tikzpicture}}{\\begin{tikzpicture}[>=latex, xscale = 0.12, yscale = 0.2]\n\\draw [->] (0,0) -- (16,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,10) node [left] {$S$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i in {4,8,12}\n{\\draw (\\i,0.5) -- (\\i,0) node [below] {$\\i$};};\n\\foreach \\i in {4,8}\n{\\draw (0.5,\\i) -- (0,\\i) node [left] {$\\i$};};\n\\draw (0,0) cos (4,8) -- (8,8) sin (12,0);\n\\draw [dashed] (4,0) -- (4,8) (8,0) -- (8,8);\n\\end{tikzpicture}}{\n\\begin{tikzpicture}[>=latex, xscale = 0.12, yscale = 0.2]\n\\draw [->] (0,0) -- (16,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,10) node [left] {$S$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i in {4,8,12}\n{\\draw (\\i,0.5) -- (\\i,0) node [below] {$\\i$};};\n\\foreach \\i in {4,8}\n{\\draw (0.5,\\i) -- (0,\\i) node [left] {$\\i$};};\n\\draw (0,0) -- (4,8) -- (8,8) -- (12,0);\n\\draw [dashed] (4,0) -- (4,8) (8,0) -- (8,8);\n\\end{tikzpicture}\n}",
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"objs": [],
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"tags": [],
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"genre": "选择题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"024148": {
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"id": "024148",
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"content": "科学家以里氏震级来度量地震的强度, 若设 $I$ 为地震时所散发出来的相对能量程度, 则里氏震级度量 $r$ 可定义为 $r=\\dfrac{2}{3}\\lg I+2$, 则每增加一个震级, 相对能量程度扩大到\\bracket{20}.($\\sqrt{10}\\approx 3.16$)\n\\fourch{$31.6$ 倍}{$13.16$ 倍}{$6.32$ 倍}{$3.16$ 倍}",
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"objs": [],
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"tags": [],
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"genre": "选择题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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],
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"same": [],
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"related": [
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"010125"
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],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"024149": {
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"id": "024149",
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"content": "小王大学毕业后, 决定利用所学专业进行自主创业. 经过市场调查, 生产某小型电子产品需投入年固定成本 $3$ 万元, 每生产 $x$ 万件, 需另投入流动成本 $W(x)$ 万元, 在年产量不足 $8$ 万件时, $W(x)=\\dfrac{1}{3}x^2+x$ (万元). 在年产量不小于 $8$ 万件时, $W(x)=6 x+\\dfrac{100}{x}-38$ (万元). 每件产品售价 $5$ 元. 通过市场分析, 小王生产的商品当年能全部售完.\\\\\n(1) 写出年利润 $L(x)$ (万元) 关于年产量 $x$ (万件) 的函数解析式;(注: 年利润$=$年销售收入$-$固定成本$-$流动成本);\\\\\n(2) 年产量为多少万件时, 小王在这一商品的生产中所获利润最大? 最大利润是多少?",
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"objs": [],
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"tags": [],
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"genre": "解答题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "4em",
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"unrelated": []
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},
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"030001": {
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"id": "030001",
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"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.",
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