vault backup: 2022-02-23 09:36:32

notes/.obsidian/plugins/obsidian-activity-history/data.json

@@ -13,7 +13,7 @@
     {
       "path": "/",
       "date": "2022-02-23",
-      "size": 787107
+      "size": 794915
     }
   ],
   "activityHistory": [
@@ -62,7 +62,7 @@
         },
         {
           "date": "2022-02-23",
-          "value": 6507
+          "value": 14315
         }
       ]
     }

notes/data/Absolutní hodnota_2022-02-23 09.05.43.excalidraw.md

@@ -455,7 +455,7 @@ excalidraw-plugin: parsed
 			"angle": 0,
 			"strokeColor": "#5c940d",
 			"backgroundColor": "#82c91e",
-			"fillStyle": "hachure",
+			"fillStyle": "solid",
 			"strokeWidth": 1,
 			"strokeStyle": "solid",
 			"roughness": 0,
@@ -463,19 +463,19 @@ excalidraw-plugin: parsed
 			"groupIds": [],
 			"strokeSharpness": "sharp",
 			"seed": 1428232121,
-			"version": 28,
+			"version": 29,
-			"versionNonce": 2066341623,
+			"versionNonce": 1067443767,
 			"isDeleted": false,
 			"boundElements": null,
-			"updated": 1645603689210
+			"updated": 1645603717145
 		},
 		{
 			"type": "ellipse",
-			"version": 30,
+			"version": 33,
-			"versionNonce": 371610137,
+			"versionNonce": 1588994327,
 			"isDeleted": false,
 			"id": "KZC8vwQaYU87GsgzPylAy",
-			"fillStyle": "hachure",
+			"fillStyle": "solid",
 			"strokeWidth": 1,
 			"strokeStyle": "solid",
 			"roughness": 0,
@@ -491,7 +491,7 @@ excalidraw-plugin: parsed
 			"groupIds": [],
 			"strokeSharpness": "sharp",
 			"boundElements": [],
-			"updated": 1645603711020
+			"updated": 1645603715480
 		}
 	],
 	"appState": {
@@ -499,7 +499,7 @@ excalidraw-plugin: parsed
 		"viewBackgroundColor": "#ffffff",
 		"currentItemStrokeColor": "#e67700",
 		"currentItemBackgroundColor": "#fab005",
-		"currentItemFillStyle": "hachure",
+		"currentItemFillStyle": "solid",
 		"currentItemStrokeWidth": 1,
 		"currentItemStrokeStyle": "solid",
 		"currentItemRoughness": 0,

notes/mat/Absolutní hodnota.md

@@ -43,4 +43,85 @@ $x \geq 3$
 $$\textcolor{red}{|x+1|}+\textcolor{green}{|x-1|}=4$$
 $\textcolor{red}{nulový \space bod \dots -1}$          $\textcolor{green}{nulový \space bod \dots 1}$
 
-![[data/Absolutní hodnota_2022-02-23 09.05.43.excalidraw.md]]
+![[data/Absolutní hodnota_2022-02-23 09.05.43.excalidraw.md]]
+
+| -     | $x \lt 1$           | $x\ge1$          |
+| ----- | --------------- | ------------- |
+| $x\lt-1$  | $-(x+1)+-(x-1)=4$ | $\emptyset$             |
+| $x\ge-1$ | $(x+1)+-(x-1)=4$  | $(x+1)+(x-1)=4$ |
+
+$k_1$:
+$$-(x+1)+-(x-1)=4$$
+$$-x-1-x+1=4$$
+$$-2x=4$$
+$$x=-2$$
+$$k_1=-2$$
+$k_2: \emptyset$
+$k_3$:
+$$(x+1)-(x-1)=4$$
+$$x+1-x+1=4$$
+$$0x+2=4 \space | -2$$
+$$0x=2$$
+$$k_4 = \emptyset$$
+$k_4$:
+$$(x+1)+(x-1)=4$$
+$$2x=4$$
+$$x=2$$
+$$k_4 = 2$$
+$2 \ge -1 \vee 2\ge 1$
+
+---
+$|3x-2|-|2x-3|=3$
+
+nulový bod=$\frac23$ nulový bod=$\frac32$
+
+| -               | $x\lt\frac32$               | $x\gt\frac32$          |
+| --------------- | --------------------------- | ---------------------- |
+| $x \lt \frac23$ | $k_1$: $-(3x-2)- -(2x-3)=3$ | $k_2: \emptyset$       |
+| $x\ge\frac23$    | $k_3: (3x-2)- -(2x-3)=3$    | $k_4: (3x-2)-(2x-3)=3$ |
+
+$k_1: -3x+2+2x-3=3$
+$-x-1=3$
+$-x=4$
+$x=-4$
+$k_1=\{-4\}$
+$-4 < \frac32 \vee x\lt\frac23$
+$k_2: \emptyset$
+$k_3: 3x-2+2x-3=3$
+$5x-5=3$
+$5x=8$
+$x=\frac85$
+$\frac85 \not\in <\frac23;\frac32)$
+$k_3 = \emptyset$
+
+
+---
+
+$3|x-5|+2|x+1|=2$
+nulový bod...$5$ nulový bod...$-1$
+
+| -        | $x<5$              | $x \ge 5$         |
+| -------- | ------------------ | ----------------- |
+| $x<-1$   | $-3(x-5)-2(x+1)=2$ | $\emptyset$       |
+| $x\ge-1$ | -3(x-5)+2(x+1)=2$  | $3(x-5)+2(x+1)=2$ |
+
+$k_1: -3(x-5)-2(x+1)=2$
+$-3x+15-2x-2=2$
+$-5x+13=2$
+$-5x=-11$
+$5x=11$
+$x=\frac{11}5$; $\frac{11}5 \not\in (-\infty; -1)$
+$k_1=\emptyset$
+$k_2: \emptyset$
+$k_3: -3(x-5)+2(x+1)=2$
+$-3x+15+2x+2=2$
+$-x+17=2$
+$-x=-15$
+$x=15$; $15\not\in <-1; 5)$
+$k_3 = \emptyset$
+$k_4: 3(x-5)+2(x+1)=2$
+$3x-15+2x+2=2$
+$5x-13=2$
+$5x=15$
+$x=3$; $3\not\in <5; \infty)$
+$k_4=\emptyset$