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!Załączniki/20230303101829 2023-03-03 10.18.36.excalidraw.md
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---
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excalidraw-plugin: parsed
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tags: [excalidraw]
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---
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==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
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# Text Elements
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%%
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# Drawing
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```compressed-json
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||||
|
||||
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|
||||
```
|
||||
%%
|
||||
1324
!Załączniki/20230303101829 2023-03-03 10.30.28.excalidraw.md
Normal file
1324
!Załączniki/20230303101829 2023-03-03 10.30.28.excalidraw.md
Normal file
File diff suppressed because it is too large
Load Diff
1548
!Załączniki/20230303101829 2023-03-03 10.33.57.excalidraw.md
Normal file
1548
!Załączniki/20230303101829 2023-03-03 10.33.57.excalidraw.md
Normal file
File diff suppressed because it is too large
Load Diff
3670
!Załączniki/20230303101829 2023-03-03 10.37.30.excalidraw.md
Normal file
3670
!Załączniki/20230303101829 2023-03-03 10.37.30.excalidraw.md
Normal file
File diff suppressed because it is too large
Load Diff
1008
!Załączniki/20230303101829 2023-03-03 10.48.45.excalidraw.md
Normal file
1008
!Załączniki/20230303101829 2023-03-03 10.48.45.excalidraw.md
Normal file
File diff suppressed because it is too large
Load Diff
1666
!Załączniki/20230303101829 2023-03-03 10.50.14.excalidraw.md
Normal file
1666
!Załączniki/20230303101829 2023-03-03 10.50.14.excalidraw.md
Normal file
File diff suppressed because it is too large
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!Załączniki/20230303101829 2023-03-03 11.22.36.excalidraw.md
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2
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okTp
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oilxk
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Luv
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LBO
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Filter
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Font
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FHB
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FOPZeXC
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Fvuflz
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stream
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sj
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sR
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JiY
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JvE
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JOf
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Jest
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JUvmNTb
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xM
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xw
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xfkW
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@@ -21114,6 +21120,7 @@ SNiF
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Sygnał
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Składnik
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Struktury
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Stany
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Rect
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Re
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Resources
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@@ -44851,6 +44858,7 @@ lts
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literałową
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literałów
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logicznych
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ldypnypc
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Kz
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KM
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Kw
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@@ -50024,6 +50032,7 @@ WQWSCF
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Występuje
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Wklejania
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Wiv
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Wbi
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rM
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ra
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rv
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@@ -53957,6 +53966,7 @@ wartości
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wszystkich
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wymiernych
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wEW
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wWGA
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pDJ
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parenleftbigg
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parenrightbigg
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@@ -55316,6 +55326,7 @@ pełny
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prosty
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przyjmuje
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przestaje
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prund
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HD
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Ho
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Hg
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@@ -60488,6 +60499,7 @@ Zakłócenia
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ZLOTXN
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ZuX
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ZXMFDH
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ZMuPdZsY
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mD
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ma
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mj
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@@ -63130,6 +63142,7 @@ niekoniecznie
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neJ
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nBS
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njWw
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nieustalone
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gNx
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gHI
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gri
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73
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73
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"type": "split",
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"children": [
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{
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"type": "tabs",
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"children": [
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{
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"id": "a1be2d379fe1a8a8",
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"id": "3356413dd71e0a1e",
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"type": "leaf",
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"state": {
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"type": "markdown",
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"state": {
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"file": "AMiAL/Wykłady/Wykłady.md",
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"file": "Elektrotechnika/Ćwiczenia/20230303101829.md",
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"mode": "source",
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"id": "5d3247ff23950d42",
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"id": "7c19413a18f8dc1e",
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"type": "leaf",
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"state": {
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"type": "markdown",
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"type": "release-notes",
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"state": {
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"file": "AMiAL/Ćwiczenia/Zadania/Całki/Zadanie 1.md",
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"mode": "source",
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"source": false
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"currentVersion": "1.1.16"
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}
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{
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"id": "4407a5afaa10cf0b",
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"type": "tabs",
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"children": [
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{
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"id": "7fc08672b85d53c5",
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"type": "leaf",
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"state": {
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"type": "pdf",
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"state": {
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"file": "AMiAL/!Materiały/calki_1.pdf"
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}
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}
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}
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]
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}
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],
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"direction": "vertical"
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@@ -114,7 +96,7 @@
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"state": {
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"type": "backlink",
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"state": {
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"file": "AMiAL/Ćwiczenia/Zadania/Całki/Zadanie 1.md",
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"file": "Elektrotechnika/Ćwiczenia/20230303101829.md",
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@@ -131,7 +113,7 @@
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"state": {
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"type": "outgoing-link",
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"state": {
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"file": "AMiAL/Ćwiczenia/Zadania/Całki/Zadanie 1.md",
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"file": "Elektrotechnika/Ćwiczenia/20230303101829.md",
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"linksCollapsed": false,
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"unlinkedCollapsed": true
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@@ -154,7 +136,7 @@
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"state": {
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"type": "outline",
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"state": {
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"file": "AMiAL/Ćwiczenia/Zadania/Całki/Zadanie 1.md"
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"file": "Elektrotechnika/Ćwiczenia/20230303101829.md"
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}
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}
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},
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@@ -209,40 +191,39 @@
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||||
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|
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"!Załączniki/1. Optymalizacja 2023-03-01 10.40.34.excalidraw.md",
|
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|
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||||
"!Załączniki/0. Wstęp 2023-03-01 09.49.34.excalidraw.md",
|
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|
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|
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|
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"TC/Untitled.canvas"
|
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]
|
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}
|
||||
@@ -1,6 +1,26 @@
|
||||
# Obliczyć całki.
|
||||
## 1
|
||||
$$\int x^{2}(1-x)dx=\int x^{2}-x^{3}dx=$$
|
||||
$$\int x^{2}(1-x)dx=\int x^{2}-x^{3}dx=\int x^{2}dx+\int-x^{3}dx=\frac{x^{3}}{3}+\frac{-x^{4}}{4}+C$$
|
||||
## 2
|
||||
$$\int x^{-2}dx=-x^{-1}+C$$
|
||||
## 3
|
||||
$$\int \frac{dx}{10x}=\ln|10x|+C$$
|
||||
## 4
|
||||
$$\int \frac{dx}{3x^{4}}=\ln|3x^{4}|+C$$
|
||||
## 5
|
||||
$$\int\left(\frac{3}{x^{2}}+\frac{4}{x^{3}}\right)dx=\int\frac{3}{x^{2}}dx+\int\frac{4}{x^{3}}dx=3\ln|x^{2}|+4\ln|x^{3}|+C$$
|
||||
## 6
|
||||
$$\begin{gathered}
|
||||
|
||||
\int\frac{(3-x)^{2}}{x^{3}}dx=\int\frac{9-6x+x^{2}}{x^{3}}dx=\int\frac{9}{x^{3}}dx+\int\frac{-6x}{x^3}dx+\int\frac{x^{2}}{x^{3}}dx=
|
||||
\newline
|
||||
\newline
|
||||
9\ln|x^{3}|-6\ln|x^2|+\ln|x|+C
|
||||
\end{gathered}
|
||||
$$
|
||||
## 7
|
||||
$$\int\frac{1-x^{2}}{x^{3}}dx=\int\frac{1}{x^{3}}dx+\int-\frac{x^{2}}{x^{3}}dx=\ln|x^{3}|-\ln|x|$$
|
||||
|
||||
## 9.
|
||||
$$\int x\sqrt{x}\ dx=
|
||||
\int x^{\frac{3}{2}}dx= \frac{x^{\frac{5}{2}}}{\frac{5}{2}}+c=\frac{2x^{\frac{5}{2}}}{5}+c$$
|
||||
|
||||
36
Elektrotechnika/Ćwiczenia/20230303101829.md
Normal file
36
Elektrotechnika/Ćwiczenia/20230303101829.md
Normal file
@@ -0,0 +1,36 @@
|
||||
![[20230303101829 2023-03-03 10.18.36.excalidraw]]
|
||||
|
||||
![[20230303101829 2023-03-03 10.22.33.excalidraw]]
|
||||
|
||||
Stany nieustalone:
|
||||
![[20230303101829 2023-03-03 10.28.21.excalidraw]]
|
||||
|
||||
![[20230303101829 2023-03-03 10.30.28.excalidraw]]
|
||||
|
||||
![[20230303101829 2023-03-03 10.33.57.excalidraw]]
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
Jest prund.
|
||||
|
||||
![[20230303101829 2023-03-03 10.37.30.excalidraw]]
|
||||
|
||||
![[20230303101829 2023-03-03 10.48.45.excalidraw]]
|
||||
|
||||
![[20230303101829 2023-03-03 10.50.14.excalidraw]]
|
||||
|
||||
![[20230303101829 2023-03-03 10.52.58.excalidraw]]
|
||||
|
||||
|
||||
![[20230303101829 2023-03-03 10.57.24.excalidraw]]
|
||||
|
||||
|
||||
|
||||
|
||||
![[20230303101829 2023-03-03 11.22.36.excalidraw]]
|
||||
|
||||
|
||||
|
||||
|
||||
Reference in New Issue
Block a user