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Daniel Bulant
parent
03f3681dc0
commit
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29 changed files with 43470 additions and 48 deletions
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```
|
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%%
|
||||
17
notes/data/Priklady 2024-02-22 13.12.47.excalidraw.svg
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17
notes/data/Priklady 2024-02-22 13.12.47.excalidraw.svg
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@ -12,6 +12,7 @@ imagePrefix: 'data/'
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- [[data/2 kružnice 2024-02-16 12.14.40.excalidraw|2 kružnice 2024-02-16 12.14.40.excalidraw]]
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- [[data/2 kružnice 2024-02-16 12.15.11.excalidraw|2 kružnice 2024-02-16 12.15.11.excalidraw]]
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- [[data/2 kružnice 2024-02-16 12.15.54.excalidraw.svg|2 kružnice 2024-02-16 12.15.54.excalidraw.svg]]
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- [[data/2 kružnice 2024-02-16 12.15.54.excalidraw|2 kružnice 2024-02-16 12.15.54.excalidraw]]
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- [[data/Absolutní hodnota_2022-02-23 09.05.43.excalidraw|Absolutní hodnota_2022-02-23 09.05.43.excalidraw]]
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- [[data/akabus.png|akabus.png]]
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@ -38,6 +39,8 @@ imagePrefix: 'data/'
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- [[data/Buffer Overflow recap 2024-01-28 11.25.31.excalidraw|Buffer Overflow recap 2024-01-28 11.25.31.excalidraw]]
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- [[data/Ekvigonala 2023-09-08 12.19.22.excalidraw|Ekvigonala 2023-09-08 12.19.22.excalidraw]]
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- [[data/Ekvigonala 2023-09-08 12.31.39.excalidraw|Ekvigonala 2023-09-08 12.31.39.excalidraw]]
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- [[data/Elipsa 2024-03-01 11.39.24.excalidraw|Elipsa 2024-03-01 11.39.24.excalidraw]]
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- [[data/Gravitace.excalidraw|Gravitace.excalidraw]]
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- [[data/Kartézský součin_2022-01-19 09.25.49.excalidraw|Kartézský součin_2022-01-19 09.25.49.excalidraw]]
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- [[data/Kmitový pohyb 2023-04-25 12.31.10.excalidraw|Kmitový pohyb 2023-04-25 12.31.10.excalidraw]]
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|
|
@ -57,6 +60,13 @@ imagePrefix: 'data/'
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- [[data/Kružnice 2024-02-15 11.29.46.excalidraw|Kružnice 2024-02-15 11.29.46.excalidraw]]
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- [[data/kružnice a přímka 2024-02-22 10.35.36.excalidraw|kružnice a přímka 2024-02-22 10.35.36.excalidraw]]
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- [[data/kružnice a přímka 2024-02-23 12.14.30.excalidraw|kružnice a přímka 2024-02-23 12.14.30.excalidraw]]
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- [[data/kružnice a přímka 2024-02-23 12.19.00.excalidraw|kružnice a přímka 2024-02-23 12.19.00.excalidraw]]
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- [[data/kružnice a přímka 2024-02-29 10.17.55.excalidraw.svg|kružnice a přímka 2024-02-29 10.17.55.excalidraw.svg]]
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- [[data/kružnice a přímka 2024-02-29 10.17.55.excalidraw|kružnice a přímka 2024-02-29 10.17.55.excalidraw]]
|
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|
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- [[data/Kužolosečky 2024-02-15 10.22.05.excalidraw|Kužolosečky 2024-02-15 10.22.05.excalidraw]]
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|
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|
|
@ -423,6 +433,8 @@ imagePrefix: 'data/'
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|
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|
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|
||||
- [[data/Priklady 2024-02-22 13.12.47.excalidraw|Priklady 2024-02-22 13.12.47.excalidraw]]
|
||||
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|
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|
||||
- [[data/Rovinné zrcadlo 2023-11-09 13.03.10.excalidraw|Rovinné zrcadlo 2023-11-09 13.03.10.excalidraw]]
|
||||
|
|
|
|||
2264
notes/data/kružnice a přímka 2024-02-22 10.35.36.excalidraw.md
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notes/data/kružnice a přímka 2024-02-22 10.35.36.excalidraw.md
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notes/data/kružnice a přímka 2024-02-23 12.14.30.excalidraw.md
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notes/data/kružnice a přímka 2024-02-23 12.19.00.excalidraw.md
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notes/data/kružnice a přímka 2024-02-29 10.17.55.excalidraw.md
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|
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0
notes/eko/Podnikání fyz.md
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0
notes/eko/Podnikání fyz.md
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9
notes/eko/Podnikání fyzy.md
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9
notes/eko/Podnikání fyzy.md
Normal file
|
|
@ -0,0 +1,9 @@
|
|||
---
|
||||
date: 15.2.
|
||||
---
|
||||
|
||||
## OSVČ
|
||||
Podnikajicí fyzická osoba je osoba samostatně výdělečně činná.
|
||||
|
||||
### Živnost
|
||||
Podníkání na vlastní jméno, účet a riziko.
|
||||
|
|
@ -8,7 +8,7 @@ Před 19.st. feudalismus, nevolnictví
|
|||
|
||||
| TH | CPH |
|
||||
| -------------------------------------------------------------------- | ---------------------------------------------------------------- |
|
||||
| Soukromé vlastniství podniků | státní vlastnictví podniků |
|
||||
| je možné soukromé vlastniství podniků | státní vlastnictví podniků |
|
||||
| Právní samostnatnost - rozhoduje o oboru, partnerech a zaměstnancích | právní nesamostnatnost |
|
||||
| Ekonomická samost. - rozdělení zisku | Ekonomická nesamost. - stát centrálně určoval ceny, platy a pod. |
|
||||
| Volný zahraniční obchod | Státní monopol ZO |
|
||||
|
|
|
|||
|
|
@ -1,7 +1,7 @@
|
|||
---
|
||||
tags: [fyz, fyz/tekutiny]
|
||||
---
|
||||
# Archimédův zákon
|
||||
w# Archimédův zákon
|
||||
|
||||
|
||||
Těleso ponořené do kapaliny je nadnášeno vztlakovou silou jejíž velikost je rovna tíze kapaliny o stejném objemu jako těleso.
|
||||
|
|
|
|||
|
|
@ -64,3 +64,51 @@ $Q=800\micro F * 500V=400 000 \micro C=400 mC$
|
|||
$I=\frac{Q}t$
|
||||
$I=400mC/20s=20mA$
|
||||
|
||||
---
|
||||
|
||||
$Ue=1.5V$
|
||||
$R_i=0.8\ohm$
|
||||
$R=5.2\ohm$
|
||||
|
||||
$I=\frac{1.5}{0.8+5.2}=\frac{1.5}6=0.25A$
|
||||
|
||||
---
|
||||
|
||||
![[Priklady 2024-02-22 13.12.47.excalidraw]]
|
||||
|
||||
$U=6V$
|
||||
$U_1=U_2=3V$
|
||||
$U_3=6V$
|
||||
$R_1=4\ohm$
|
||||
$R_2=2\ohm$
|
||||
$R_3=3\ohm$
|
||||
|
||||
$R=\frac1{\frac1{R_3}+\frac1{R_1+R_2}}=2\ohm$
|
||||
|
||||
$I=U/R=3A$
|
||||
$I_1=I_2=1A$
|
||||
$I_3=2A$
|
||||
|
||||
---
|
||||
|
||||
$t_1=20\degree C$
|
||||
$R_1=20\ohm$
|
||||
$t_2=500\degree C$
|
||||
$R_2=59\ohm$
|
||||
$\alpha=?$
|
||||
|
||||
$R_2=R_1(1+\alpha\Delta t)$
|
||||
$\Delta t=t_2-t_1$
|
||||
$\alpha=\frac{\frac{R_2}{R_1}-1}{\Delta t}$
|
||||
$\Delta t=480\degree C$
|
||||
$\alpha=\frac{\frac{59}{20}-1}{480}$
|
||||
$\alpha=4*10^{-3}K^{-1}$
|
||||
|
||||
---
|
||||
|
||||
$d=1cm$
|
||||
$m=1kg$
|
||||
$\rho_{Fe}=8.7*10^{-8}\ohm m$
|
||||
$\rho=7870kgm^{-3}$
|
||||
$R=\rho_{Fe}\frac{l}S$
|
||||
$S=\pi r^2=\pi (\frac{d}2)^2$
|
||||
|
|
|
|||
|
|
@ -36,12 +36,11 @@ $R_2=[1;-1]$
|
|||
|
||||
---
|
||||
|
||||
$x^2+y^2-2y-4=0$
|
||||
$x^2+y^2-2(0)x-2(1)y-4=0$
|
||||
$S=[0;1]$
|
||||
$r=\sqrt5$
|
||||
$(x-0)^2+(y-1)^2=5$
|
||||
|
||||
---
|
||||
|
||||
$x^2+y^2+4x-6=0$
|
||||
$S=[-2;0]$
|
||||
|
|
|
|||
|
|
@ -1,7 +1,9 @@
|
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# Analytická
|
||||
%% Zoottelkeeper: Beginning of the autogenerated index file list %%
|
||||
- [[mat/Geometrie/Analytická/2 kružnice|2 kružnice]]
|
||||
- [[mat/Geometrie/Analytická/Elipsa|Elipsa]]
|
||||
- [[mat/Geometrie/Analytická/Jednotkový vektor|Jednotkový vektor]]
|
||||
- [[mat/Geometrie/Analytická/kružnice a přímka|kružnice a přímka]]
|
||||
- [[mat/Geometrie/Analytická/Kružnice|Kružnice]]
|
||||
- [[mat/Geometrie/Analytická/Kuželosečky|Kuželosečky]]
|
||||
- [[mat/Geometrie/Analytická/Nulový vektor|Nulový vektor]]
|
||||
|
|
|
|||
28
notes/mat/Geometrie/Analytická/Elipsa.md
Normal file
28
notes/mat/Geometrie/Analytická/Elipsa.md
Normal file
|
|
@ -0,0 +1,28 @@
|
|||
# Elipsa
|
||||
|
||||
> [!SENTENCE]
|
||||
> Mějme body E, F (fixní). Množina všech bodů X, pro které platí
|
||||
> $|XE|+|XF|=d$ kde $d=const$, se nazývá elipsa.
|
||||
|
||||
![[Elipsa 2024-03-01 11.25.47.excalidraw]]
|
||||
|
||||
$o_1$ hlavni osa
|
||||
$o_2$ vedlejsi osa
|
||||
$E,F$ ohniska
|
||||
$A,B$ hlavni vrcholy
|
||||
$C,D$ vedlejsi vrcholy
|
||||
$S$ stred
|
||||
$e$ exentricita / vystrednost
|
||||
$a$ delka hl. poloosy
|
||||
$b$ delka vedl. poloosy
|
||||
|
||||
---
|
||||
|
||||
$E,F$
|
||||
$|EF|=6cm$
|
||||
$d=10cm$
|
||||
|
||||
![[Elipsa 2024-03-01 11.39.24.excalidraw]]
|
||||
![[Pasted image 20240301122558.png]]
|
||||
|
||||
osa EF je hlavni osa, osa paralelni je vedlejsi osa
|
||||
228
notes/mat/Geometrie/Analytická/kružnice a přímka.md
Normal file
228
notes/mat/Geometrie/Analytická/kružnice a přímka.md
Normal file
|
|
@ -0,0 +1,228 @@
|
|||
# kružnice a přímka
|
||||
![[kružnice a přímka 2024-02-22 10.35.36.excalidraw]]
|
||||
|
||||
|
||||
- vnější přímka
|
||||
- přímka je tečna kružnice
|
||||
- přímka je sečna kružnice
|
||||
- část přímky uvnitř kružnice je tětiva
|
||||
|
||||
|
||||
![[kružnice a přímka 2024-02-23 12.14.30.excalidraw]]
|
||||
|
||||
- P je uvnitř
|
||||
- tečna není
|
||||
- $P\in k\Rightarrow t$ tečna
|
||||
- P je vně
|
||||
- 2 tečny
|
||||
|
||||
![[kružnice a přímka 2024-02-23 12.19.00.excalidraw]]
|
||||
|
||||
rýsováním $P_T,t \perp SP$
|
||||
|
||||
rýsováním Thaletova kce $k_{sp}$ nad SP
|
||||
→ $T_1,T_2\in k \cap k_{sp}$
|
||||
→ $t_1=\overleftrightarrow{PT_1},t_2=\overleftrightarrow{PT_2}$
|
||||
|
||||
početně
|
||||
→ najdeme poláru $p$
|
||||
|
||||
---
|
||||
|
||||
Najděte spol. body (existují-li) kružnice $l: x^2+y^2-2x+4y=0$ a přímky $p: 2x-y-8=0$
|
||||
$[0;-8];[4;0]$
|
||||
|
||||
$x^2+y^2-2x+4y=0$
|
||||
$2x-y-8=0$
|
||||
|
||||
$y=2x-8$
|
||||
|
||||
$x^2+y^2+3y-8=0$
|
||||
$x^2+(2x-8)^2+3(2x-8)-8=0$
|
||||
|
||||
$x^2+4x^2-4x8+64+6x-24-8=0$
|
||||
$5x^2-26x+32=0$
|
||||
|
||||
$D=b^2-4ac$
|
||||
$x=\frac{-b\pm\sqrt{D}}{2a}$
|
||||
|
||||
$D=(-26)^2-4*5*32=36$
|
||||
$x=\frac{26\pm\sqrt{36}}{2*5}=\frac{26\pm6}{10}$
|
||||
|
||||
$x_1=2$
|
||||
$x_2=\frac65=3.2$
|
||||
|
||||
$y_1=2x-8=-4$
|
||||
$y_2=2x-8=-1.6=-\frac85$
|
||||
|
||||
$R_1=[2;-4]$
|
||||
$R_2=[3.2;-1.6]$
|
||||
|
||||
$-2x x_s=2x$
|
||||
$x_s=1$
|
||||
$4y=-2yy_s$
|
||||
$y_s=-2$
|
||||
$p=0=x_s^2+y_s^2-r^2=1+4-r^2$
|
||||
$r=\sqrt5$
|
||||
|
||||
---
|
||||
|
||||
V závislosti na parametru $m\in\mathbb{R}$ určete vzájemnou polohu přímky $q:y=x+m$ a kružnice $k:x^2-y^2-2x+6y+9=0$
|
||||
|
||||
$x^2+(x+m)^2-2x+6(x+m)+9=0$
|
||||
$x^2+x^2+2xm+m^2-2x+6x+6m+9=0$
|
||||
$2x^2+2xm+m^2+4x+6m+9=0$
|
||||
$2x^2+x(2m+4)+m^2+6m+9=0$
|
||||
|
||||
$a=2$
|
||||
$b=2m+4$
|
||||
$c=m^2+6m+9$
|
||||
|
||||
$D=(2m+4)^2-4*2*(m^2+6m+9)$
|
||||
$D=-4m^2-32m-56$
|
||||
|
||||
$m^2+8m+14=0$
|
||||
$D_m=64-4*14=8$
|
||||
$m_{1;2}=\frac{-8\pm\sqrt8}2=\frac{-8\pm2\sqrt2}2=-4\pm\sqrt2$
|
||||
|
||||
$m=-4\pm\sqrt2$ $q$ je tecna
|
||||
$m\in(-4-\sqrt2;-4+\sqrt2)$ $q$ je secna
|
||||
jinak je vnejsi primka
|
||||
|
||||
---
|
||||
|
||||
k: $x^2+y^2-2=0$
|
||||
p: $y=x+m$; $m\in\mathbb{R}$
|
||||
|
||||
$x^2+(x+m)^2-2=0$
|
||||
$x^2+x^2+2xm+m^2-2=0$
|
||||
|
||||
$2x^2+2xm+m^2-2=0$
|
||||
|
||||
$a=2$
|
||||
$b=2m$
|
||||
$c=m^2-2$
|
||||
|
||||
$D=b^2-4ac$
|
||||
$D=4m^2-4*2*(m^2-2)$
|
||||
$D=4m^2-8m^2+16$
|
||||
$D=-4m^2+16$
|
||||
|
||||
$-4m^2+16=0$
|
||||
$m^2-4=0$
|
||||
$(m+2)(m-2)=0$
|
||||
$m=2$
|
||||
$m=–2$
|
||||
|
||||
---
|
||||
|
||||
$S=[6;-2]$
|
||||
$A=[9;-3]$
|
||||
|
||||
$k(S;|SA|)$
|
||||
|
||||
tecna prochazejici bodem P
|
||||
|
||||
$P=[-2;-3]$
|
||||
|
||||
![[kružnice a přímka 2024-02-29 10.17.55.excalidraw]]
|
||||
|
||||
$k: (x-6)^2+(y+2)^2=(6-9)^2+(-2+3)^2$
|
||||
$r=(6-9)^2+(-2+3)^2=9+1=10$
|
||||
$k:x^2+y^2-2x6+2y2-p=0$
|
||||
$p=6^2+2^2-10^=36+4-10=30$
|
||||
$k:x^2+y^2-12x+4y+30=0$
|
||||
|
||||
Dosadime P za jedno z tech cisel a vznikne linearni rovnice
|
||||
|
||||
$(x-6)(x-6)+(y+2)(y+2)=10$
|
||||
$(-2-6)(x-6)+(-3+2)(y+2)=10$
|
||||
|
||||
$-8(x-6)-1(y+2)-10=0$
|
||||
$-8x-y+36=0$
|
||||
|
||||
$xx+yy-12x+4y+30=0$
|
||||
$xx+yy-6x-6x+2y+2y+30=0$
|
||||
$-2x-3y+12-6x-6+2y+30=0$
|
||||
$-8x-y+36=0$
|
||||
|
||||
$k:(x-6)^2+(y+2)^2=10$
|
||||
|
||||
$(x-6)^2+(-8x+36+2)^2=10$
|
||||
$x^2-12x+36+64x^2-608x+1444=10$
|
||||
$65x^2-620x+1470=0$
|
||||
$13x^2-124x+294=0$
|
||||
$D=88$
|
||||
$\sqrt{D}=\sqrt{88}=2\sqrt{22}$
|
||||
|
||||
$x_1=\frac{124+2\sqrt{22}}{26}=\frac{62+\sqrt22}{13}$
|
||||
$x_2=\frac{62-\sqrt{22}}{13}$
|
||||
|
||||
$y_1=-8x_1+36$
|
||||
$y_1=-8*\frac{62+\sqrt22}{13}+36$
|
||||
$y_1=\frac{-8\sqrt{22}-496}{13}+36$
|
||||
|
||||
tecna prochazejici bodem Q
|
||||
|
||||
$Q=[-4;-2]$
|
||||
|
||||
$xx+yy-6x-6x+2y+2y+30=0$
|
||||
$-4x-2y+24x-6x-4y+2y+30=0$
|
||||
$14x-4y+30=0$
|
||||
|
||||
$(x-6)(x-6)+(y+2)(y+2)=10$
|
||||
$(-4-6)(x-6)+(-2+2)(y+2)=10$
|
||||
$-10(x-6)=10$
|
||||
$-10x+60=10$
|
||||
$-10x+50=0$
|
||||
$-10x=-50$
|
||||
$x=5$
|
||||
|
||||
$xx+yy-12x+4y+30=0$
|
||||
|
||||
$5^2+y^2-12*5+4y+30=0$
|
||||
$y^2+4y-5=0$
|
||||
|
||||
$D=2b-ac=8+5=13$
|
||||
|
||||
$T_1=[5;1]$
|
||||
$T_2=[5;-5]$
|
||||
|
||||
$t_1=T_1Q$
|
||||
$t_2=T_2Q$
|
||||
|
||||
$x=Q+u\vec{s_1}$
|
||||
|
||||
$\vec{s_1}=T_1-Q=(9;3)$
|
||||
$\vec{s_2}=T_2-Q=(9;-3)$
|
||||
|
||||
$t_1:$
|
||||
$x=-4+9u$
|
||||
$y=-2+3u$
|
||||
$u\in\mathbb{R}$
|
||||
|
||||
$t_2:$
|
||||
$x=-4+9v$
|
||||
$y=-2-3v$
|
||||
$v\in\mathbb{R}$
|
||||
|
||||
tecna prochazejici bodem A
|
||||
tecna = polara v tomto pripade
|
||||
$A=[9;-3]$
|
||||
|
||||
$xx+yy-6x-6x+2y+2y+30=0$
|
||||
$9x-3y-6*9-6x-3*2+2y+30=0$
|
||||
$3x-y-30=0$
|
||||
$-y-30=-3x$
|
||||
$y=3x-30$
|
||||
^ polara
|
||||
|
||||
zbytecnost tady :) :
|
||||
$x^2+y^2-12x+4y+30=0$
|
||||
$x^2+(3x-30)(3x-30)-12x+4*(3x-30)+30=0$
|
||||
$x^2+9x^2-2*30*3x+30^2-12x+12x-120+30=0$
|
||||
$10x^2-180x+900-90=0$
|
||||
$10x^2-180x+810=0$
|
||||
|
||||
---
|
||||
|
||||
Loading…
Reference in a new issue