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录入高二寒假作业10

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wangweiye7840 2024-02-04 14:41:40 +08:00
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3
工具v2/文本文件/新题收录列表.txt
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@ -346,3 +346,6 @@
20240204-143106 高二寒假作业9
024527:024536,002183,024537
20240204-144112 高二寒假作业10
024538:024541,019480,024542:024543,040820,024544:024546,016469

285
题库0.3/Problems.json
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@ -8387,7 +8387,9 @@
"20220624\t王伟叶, 余利成"
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"20220701\t王伟叶"
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"20230730\t王伟叶"
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"20230209\t王伟叶"
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"content": "若直线 $l_1: a x+3 y+1=0$ 与 $l_2: 2 x+(a+1) y+1=0$ 互相平行, 则实数 $a=$\\blank{50}.",
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"024539": {
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"content": "若直线 $(a+2) x+(1-a) y-3=0$ 与 $(a-1) x+(2 a+3) y+2=0$ 互相垂直, 则实数 $a =$\\blank{50}.",
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"024540": {
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"content": "已知直线 $l$ 的方程为 $3 x+4 y-12=0$, 直线 $l$ 与 $l$ 垂直且 $l$ 与坐标轴围成的三角形面积为 6 , 则直线 $l'$ 的方程为\\blank{50}.",
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"024541": {
"id": "024541",
"content": "已知直线 $x-\\sqrt{3}y+1=0$ 与直线 $x+k y+3=0$ 的夹角为 $60^{\\circ}$, 则实数 $k=$\\blank{50}.",
"objs": [],
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"genre": "填空题",
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"duration": -1,
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"edit": [
"20240204\t杨懿荔"
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"same": [],
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"024542": {
"id": "024542",
"content": "已知动点 $M(a, b)$ 在直线 $3 x+4 y-15=0$ 上, 则 $\\sqrt{a^2+b^2}$ 的最小值是\\blank{50}.",
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"024543": {
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"content": "直线 $l_1: 3 x-2 y-6=0$ 关于直线 $l_2: 2 x-3 y+1=0$ 对称的直线 $l_3$ 的方程为\\blank{50}.",
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"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
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"024544": {
"id": "024544",
"content": "一直线过点 $P(1,2)$, 且被两条平行直线 $4 x+3 y+1=0$ 和 $4 x+3 y+6=0$ 截得线段长为 $\\sqrt{2}$, 则直线方程为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
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"024545": {
"id": "024545",
"content": "平面中两条直线 $l_1$ 和 $l_2$ 相交于点 $O$, 对于平面上任意一点 $M$, 若 $p$、$q$ 分别为 $M$ 到直线 $l_1$和 $l_2$ 的距离, 则称有序非负实数对 $(p, q)$ 是点 $M$ 的``距离坐标''. 根据上述定义,``距离坐标''是$(1,2)$的点的个数是\\blank{50}.",
"objs": [],
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"024546": {
"id": "024546",
"content": "过点 $M(-2,-1)$ 作直线 $l$, 使它与两点 $A(-3,-2)$、$B(5,-4)$ 的距离相等, 求直线 $l$ 的方程.",
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"genre": "解答题",
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"space": "4em",
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"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.",