diff --git a/notes/.obsidian/plugins/obsidian-activity-history/data.json b/notes/.obsidian/plugins/obsidian-activity-history/data.json index b9ab8c6..b6d6e52 100644 --- a/notes/.obsidian/plugins/obsidian-activity-history/data.json +++ b/notes/.obsidian/plugins/obsidian-activity-history/data.json @@ -12,8 +12,8 @@ "checkpointList": [ { "path": "/", - "date": "2022-03-03", - "size": 800369 + "date": "2022-03-04", + "size": 801459 } ], "activityHistory": [ @@ -495,6 +495,10 @@ { "date": "2022-03-03", "value": 826 + }, + { + "date": "2022-03-04", + "value": 1264 } ] } diff --git a/notes/mat/Nerovnice.md b/notes/mat/Nerovnice.md index 2956881..027503b 100644 --- a/notes/mat/Nerovnice.md +++ b/notes/mat/Nerovnice.md @@ -29,3 +29,75 @@ $$x-2\geq1(x+3)$$ $$x-2\geq x+3 |-x+2$$ $$0\geq5$$ $$x=\emptyset$$ +--- +$[x\neq-1]$ +$$\frac{x-\sqrt7}{x+1} \geq 0$$ +$[x>-1]$ +$$x-\sqrt7\geq0(x+1)$$ +$$x\geq\sqrt7$$ + +$[x<-1]$ +$$x-\sqrt7\leq0(x+1)$$ +$$x\leq0$$ +$$k=(-\infty;-1)\wedge<\sqrt7;\infty)$$ + +--- +$$\frac{5x-3}{3x+4} \geq -1$$ +$[x\neq -\frac43]$ +$[x\lt-\frac43]$ + +$$5x-3\geq-1(3x+4)$$ +$$5x-3\geq-3x-4$$ +$$5x\geq-3x-1$$ +$$8x\geq-1$$ +$$x\geq -\frac18$$ +$$x\in\emptyset$$ +$[x\gt-\frac43]$ +$$5x-3\le-1(3x+4)$$ +$$5x-3\le-3x-4$$ +$$5x\leq-3x-1$$ +$$8x\le-1$$ +$$x\leq-\frac18$$ +$$k=(-\frac43;-\frac18>$$ +--- +$$\frac{4x-7}{3x-2}\leq4$$ +$[x\neq-\frac23]$ +$[x\gt-\frac23]$ +$$4x-7\leq4(3x-2)$$ +$$4x-7\leq12x-8$$ +$$-7\leq8x-8$$ +$$1\leq8x$$ +$$\frac18\leq x$$ +$[x\lt-\frac23]$ +$$4x-7\ge4(3x-2)$$ +$$4x-7\ge12x-8$$ +$$-7\ge8x-8$$ +$$1\ge8x$$ +$$\frac18\ge x$$ +$$x\in\emptyset$$ +$$k=(-\frac23;\frac18>$$ + +--- + +$$\frac{3x-2}{4x}\leq1$$ +$[x\ne0]$ +$[x\gt0]$ +$$3x-2\leq4x$$ +$$-2\leq x$$ +$$x\in\emptyset$$ +$[x\lt0]$ +$$3x-2\ge4x$$ +$$-2\ge x$$ +$$k=(-\infty;-2>$$ + +--- +$$\frac1{x-3}\geq\frac1{x+5}$$ +$$x+5\geq x-3$$ +$$-5\geq-3$$ +$$k=\emptyset$$ + +--- +$$\frac{x+1}{x+3}\gt\frac{x+5}{x+6}$$ + +--- +$$\frac{x+3}{x+5}\geq\frac{x+2}{x-1}$$