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Daniel Bulant 2022-02-23 09:36:32 +01:00
parent d61b97c8a5
commit 9cbc853f7d
3 changed files with 93 additions and 12 deletions
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4
notes/.obsidian/plugins/obsidian-activity-history/data.json vendored
View file

@ -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
}
]
}

18
notes/data/Absolutní hodnota_2022-02-23 09.05.43.excalidraw.md
View file

@ -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,

83
notes/mat/Absolutní hodnota.md
View file

@ -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$ | $3(x-5)+2(x+1)=2$ |
$k_1: -3(x-5)-2(x+1)=2$
$-3x+15-2x-2=2$
$-5x+13=2$
$-5x=-11$
$5x=11$
$x=\frac{11}5$; $\frac{11}5 \not\in (-\infty; -1)$
$k_1=\emptyset$
$k_2: \emptyset$
$k_3: -3(x-5)+2(x+1)=2$
$-3x+15+2x+2=2$
$-x+17=2$
$-x=-15$
$x=15$; $15\not\in <-1; 5)$
$k_3 = \emptyset$
$k_4: 3(x-5)+2(x+1)=2$
$3x-15+2x+2=2$
$5x-13=2$
$5x=15$
$x=3$; $3\not\in <5; \infty)$
$k_4=\emptyset$