diff --git a/notes/.obsidian/plugins/obsidian-activity-history/data.json b/notes/.obsidian/plugins/obsidian-activity-history/data.json index 8f801d6..98e581e 100644 --- a/notes/.obsidian/plugins/obsidian-activity-history/data.json +++ b/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 } ] } diff --git a/notes/data/Absolutní hodnota_2022-02-23 09.05.43.excalidraw.md b/notes/data/Absolutní hodnota_2022-02-23 09.05.43.excalidraw.md index e85956e..0bea2a8 100644 --- a/notes/data/Absolutní hodnota_2022-02-23 09.05.43.excalidraw.md +++ b/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, - "versionNonce": 2066341623, + "version": 29, + "versionNonce": 1067443767, "isDeleted": false, "boundElements": null, - "updated": 1645603689210 + "updated": 1645603717145 }, { "type": "ellipse", - "version": 30, - "versionNonce": 371610137, + "version": 33, + "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, diff --git a/notes/mat/Absolutní hodnota.md b/notes/mat/Absolutní hodnota.md index 9528149..5158b91 100644 --- a/notes/mat/Absolutní hodnota.md +++ b/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]] \ No newline at end of file +![[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$ | $3(x-5)+2(x+1)=2$ | + +$k_1: -3(x-5)-2(x+1)=2$ +$-3x+15-2x-2=2$ +$-5x+13=2$ +$-5x=-11$ +$5x=11$ +$x=\frac{11}5$; $\frac{11}5 \not\in (-\infty; -1)$ +$k_1=\emptyset$ +$k_2: \emptyset$ +$k_3: -3(x-5)+2(x+1)=2$ +$-3x+15+2x+2=2$ +$-x+17=2$ +$-x=-15$ +$x=15$; $15\not\in <-1; 5)$ +$k_3 = \emptyset$ +$k_4: 3(x-5)+2(x+1)=2$ +$3x-15+2x+2=2$ +$5x-13=2$ +$5x=15$ +$x=3$; $3\not\in <5; \infty)$ +$k_4=\emptyset$