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10.17.55.excalidraw|kružnice a přímka 2024-02-29 10.17.55.excalidraw]] - [[data/Kužolosečky 2024-02-15 10.22.05.excalidraw.svg|Kužolosečky 2024-02-15 10.22.05.excalidraw.svg]] - [[data/Kužolosečky 2024-02-15 10.22.05.excalidraw|Kužolosečky 2024-02-15 10.22.05.excalidraw]] - [[data/Kužolosečky 2024-02-15 10.22.28.excalidraw.svg|Kužolosečky 2024-02-15 10.22.28.excalidraw.svg]] @@ -423,6 +433,8 @@ imagePrefix: 'data/' - [[data/Posunutí o vektor 2023-12-15 11.33.14.excalidraw|Posunutí o vektor 2023-12-15 11.33.14.excalidraw]] - [[data/Pravidelný n-úhelník 2023-10-13 12.07.37.excalidraw|Pravidelný n-úhelník 2023-10-13 12.07.37.excalidraw]] - [[data/Priklady 2023-12-14 13.52.36.excalidraw|Priklady 2023-12-14 13.52.36.excalidraw]] +- [[data/Priklady 2024-02-22 13.12.47.excalidraw.svg|Priklady 2024-02-22 13.12.47.excalidraw.svg]] +- [[data/Priklady 2024-02-22 13.12.47.excalidraw|Priklady 2024-02-22 13.12.47.excalidraw]] - [[data/Rezistory 2022-06-09 11.29.33.excalidraw|Rezistory 2022-06-09 11.29.33.excalidraw]] - [[data/Rovinné zrcadlo 2023-11-02 13.00.20.excalidraw|Rovinné zrcadlo 2023-11-02 13.00.20.excalidraw]] - [[data/Rovinné zrcadlo 2023-11-09 13.03.10.excalidraw|Rovinné zrcadlo 2023-11-09 13.03.10.excalidraw]] diff --git a/notes/data/kružnice a přímka 2024-02-22 10.35.36.excalidraw.md b/notes/data/kružnice a přímka 2024-02-22 10.35.36.excalidraw.md new file mode 100644 index 0000000..ff840ae --- /dev/null +++ b/notes/data/kružnice a přímka 2024-02-22 10.35.36.excalidraw.md @@ -0,0 +1,2264 @@ +--- + +excalidraw-plugin: parsed +tags: [excalidraw] + +--- +==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== + + +# Text Elements +tětiva ^JGr3Nen3 + +sečna ^qZHZbHZS + +tečna ^f51b3a66 + +vnější +přímka ^LWlhxtmb + +%% +# Drawing +```json +{ + "type": "excalidraw", + "version": 2, + "source": "https://github.com/zsviczian/obsidian-excalidraw-plugin/releases/tag/1.9.27", + "elements": [ + { + "type": "ellipse", + "version": 194, + "versionNonce": 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at end of file diff --git a/notes/data/kružnice a přímka 2024-02-29 10.17.55.excalidraw.svg b/notes/data/kružnice a přímka 2024-02-29 10.17.55.excalidraw.svg new file mode 100644 index 0000000..e005cf3 --- /dev/null +++ b/notes/data/kružnice a přímka 2024-02-29 10.17.55.excalidraw.svg @@ -0,0 +1,17 @@ + + + + + + + + \ No newline at end of file diff --git a/notes/eko/Podnikání fyz.md b/notes/eko/Podnikání fyz.md new file mode 100644 index 0000000..e69de29 diff --git a/notes/eko/Podnikání fyzy.md b/notes/eko/Podnikání fyzy.md new file mode 100644 index 0000000..07e437d --- /dev/null +++ b/notes/eko/Podnikání fyzy.md @@ -0,0 +1,9 @@ +--- +date: 15.2. +--- + +## OSVČ +Podnikajicí fyzická osoba je osoba samostatně výdělečně činná. + +### Živnost +Podníkání na vlastní jméno, účet a riziko. diff --git a/notes/eko/Trh.md b/notes/eko/Trh.md index aba1e77..556f841 100644 --- a/notes/eko/Trh.md +++ b/notes/eko/Trh.md @@ -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 | diff --git a/notes/fyz/Molekulová fyzika/Mechanika tekutin/Archimédův zákon.md b/notes/fyz/Molekulová fyzika/Mechanika tekutin/Archimédův zákon.md index 98028b7..444829b 100644 --- a/notes/fyz/Molekulová fyzika/Mechanika tekutin/Archimédův zákon.md +++ b/notes/fyz/Molekulová fyzika/Mechanika tekutin/Archimédův zákon.md @@ -1,7 +1,7 @@ --- tags: [fyz, fyz/tekutiny] --- -# Archimédův zákon +w# Archimédův zákon ![](Pasted%20image%2020221011130332.png) Těleso ponořené do kapaliny je nadnášeno vztlakovou silou jejíž velikost je rovna tíze kapaliny o stejném objemu jako těleso. diff --git a/notes/fyz/elektrika/Priklady.md b/notes/fyz/elektrika/Priklady.md index d986563..823c6e3 100644 --- a/notes/fyz/elektrika/Priklady.md +++ b/notes/fyz/elektrika/Priklady.md @@ -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]] + +$U=6V$ +$U_1=U_2=3V$ +$U_3=6V$ +$R_1=4\ohm$ +$R_2=2\ohm$ +$R_3=3\ohm$ + +$R=\frac1{\frac1{R_3}+\frac1{R_1+R_2}}=2\ohm$ + +$I=U/R=3A$ +$I_1=I_2=1A$ +$I_3=2A$ + +--- + +$t_1=20\degree C$ +$R_1=20\ohm$ +$t_2=500\degree C$ +$R_2=59\ohm$ +$\alpha=?$ + +$R_2=R_1(1+\alpha\Delta t)$ +$\Delta t=t_2-t_1$ +$\alpha=\frac{\frac{R_2}{R_1}-1}{\Delta t}$ +$\Delta t=480\degree C$ +$\alpha=\frac{\frac{59}{20}-1}{480}$ +$\alpha=4*10^{-3}K^{-1}$ + +--- + +$d=1cm$ +$m=1kg$ +$\rho_{Fe}=8.7*10^{-8}\ohm m$ +$\rho=7870kgm^{-3}$ +$R=\rho_{Fe}\frac{l}S$ +$S=\pi r^2=\pi (\frac{d}2)^2$ diff --git a/notes/mat/Geometrie/Analytická/2 kružnice.md b/notes/mat/Geometrie/Analytická/2 kružnice.md index e5c90d5..97f601b 100644 --- a/notes/mat/Geometrie/Analytická/2 kružnice.md +++ b/notes/mat/Geometrie/Analytická/2 kružnice.md @@ -36,12 +36,11 @@ $R_2=[1;-1]$ --- -$x^2+y^2-2y-4=0$ +$x^2+y^2-2(0)x-2(1)y-4=0$ $S=[0;1]$ $r=\sqrt5$ $(x-0)^2+(y-1)^2=5$ ---- $x^2+y^2+4x-6=0$ $S=[-2;0]$ diff --git a/notes/mat/Geometrie/Analytická/Analytická.md b/notes/mat/Geometrie/Analytická/Analytická.md index dfa2e19..47fecb0 100644 --- a/notes/mat/Geometrie/Analytická/Analytická.md +++ b/notes/mat/Geometrie/Analytická/Analytická.md @@ -1,7 +1,9 @@ # 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]] diff --git a/notes/mat/Geometrie/Analytická/Elipsa.md b/notes/mat/Geometrie/Analytická/Elipsa.md new file mode 100644 index 0000000..dd5c3a1 --- /dev/null +++ b/notes/mat/Geometrie/Analytická/Elipsa.md @@ -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 diff --git a/notes/mat/Geometrie/Analytická/kružnice a přímka.md b/notes/mat/Geometrie/Analytická/kružnice a přímka.md new file mode 100644 index 0000000..87c0747 --- /dev/null +++ b/notes/mat/Geometrie/Analytická/kružnice a přímka.md @@ -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 :) : +$x^2+y^2-12x+4y+30=0$ +$x^2+(3x-30)(3x-30)-12x+4*(3x-30)+30=0$ +$x^2+9x^2-2*30*3x+30^2-12x+12x-120+30=0$ +$10x^2-180x+900-90=0$ +$10x^2-180x+810=0$ + +--- +