From 4d7ba52b28d81df3b47cda72e676d4596d0e81f3 Mon Sep 17 00:00:00 2001 From: Daniel Bulant Date: Thu, 6 Oct 2022 11:37:38 +0200 Subject: [PATCH] vault backup: 2022-10-06 11:37:38 --- .../obsidian-activity-history/data.json | 14 +- .../plugins/various-complements/data.json | 16 ++ notes/data/Pasted image 20221004133629.png | Bin 0 -> 10308 bytes notes/data/Pasted image 20221004140412.png | Bin 0 -> 66342 bytes notes/data/Pasted image 20221004142221.png | Bin 0 -> 30362 bytes notes/data/Pasted image 20221005111551.png | Bin 0 -> 253414 bytes .../Mechanika tekutin/Atmosférický tlak.md | 3 + .../Hydrostatická tlaková síla.md | 3 + .../Hydrostatický paradox.md | 3 + .../Mechanika tekutin/Mechanika tekutin.md | 3 + notes/fyz/Mechanika tekutin/Tekutiny.md | 3 + .../Mechanika tekutin/Torricelliho pokus.md | 3 + notes/mat/Funkce/Exponenciální funkce.md | 154 ++++++++++++++++++ notes/mat/Funkce/Funkce.md | 1 + notes/mat/Funkce/Inverzní funkce.md | 21 +++ notes/mat/Příklady 2.md | 26 ++- 16 files changed, 245 insertions(+), 5 deletions(-) create mode 100644 notes/data/Pasted image 20221004133629.png create mode 100644 notes/data/Pasted image 20221004140412.png create mode 100644 notes/data/Pasted image 20221004142221.png create mode 100644 notes/data/Pasted image 20221005111551.png create mode 100644 notes/mat/Funkce/Exponenciální funkce.md diff --git a/notes/.obsidian/plugins/obsidian-activity-history/data.json b/notes/.obsidian/plugins/obsidian-activity-history/data.json index 8c7515d..b3766cf 100644 --- a/notes/.obsidian/plugins/obsidian-activity-history/data.json +++ b/notes/.obsidian/plugins/obsidian-activity-history/data.json @@ -12,8 +12,8 @@ "checkpointList": [ { "path": "/", - "date": "2022-10-04", - "size": 912075 + "date": "2022-10-06", + "size": 915382 } ], "activityHistory": [ @@ -846,7 +846,15 @@ }, { "date": "2022-10-04", - "value": 3008 + "value": 4713 + }, + { + "date": "2022-10-05", + "value": 732 + }, + { + "date": "2022-10-06", + "value": 870 } ] } diff --git a/notes/.obsidian/plugins/various-complements/data.json b/notes/.obsidian/plugins/various-complements/data.json index 3367ee9..b3340c7 100644 --- a/notes/.obsidian/plugins/various-complements/data.json +++ b/notes/.obsidian/plugins/various-complements/data.json @@ -154,6 +154,22 @@ "lastUpdated": 1664881334067 } } + }, + "zdole": { + "zdole": { + "currentFile": { + "count": 1, + "lastUpdated": 1664961362660 + } + } + }, + "x\\in\\mathbb{R}": { + "x\\in\\mathbb{R}": { + "currentFile": { + "count": 1, + "lastUpdated": 1665047506617 + } + } } } } \ No newline at end of file diff --git a/notes/data/Pasted image 20221004133629.png b/notes/data/Pasted image 20221004133629.png new file mode 100644 index 0000000000000000000000000000000000000000..ecd15bb4f7e49d2796253d0163c8b99e224e03a8 GIT binary patch literal 10308 zcmdUVXIE2Qv^7-$1w=ulqbNBz{)=rz<;4avyJwZTV? z<^uT7D_g>Q@Q2*j5c-&`qKES@_(J9UNaqn5+2^E7$F|hqJFU06nJ*dH^*iSuat*`V 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z0D6K`W7byPv8xRGlH53y47ic`jp>mdnCV*pDj0!IS{MOC71&Gi@Slu_-Zm06({dMn;!Bmg#<5IjQ%4*7EUb z;|VX{{(g3G>ud;k5RX$vOTVH4sO|U7{=#%PS?K8kEtgi_bL?tWIreCMM=-;sHSHnk zQwSp;3t`wlM4*R8BH~^n86aM(2+05n4&Z+H!#t0E*FIZuTUZ$he5D?$kjts(bq9Y6 zU7EajKAm;*>#BS{{cf_kQvovv3^^SgS|whu;hAT}StifY<_jJbOWc-tP!IpcYSp?r z>9Q}?eCX=rcRBwQw{-J3e$w%uN*=+ZSNs2E$q_07Rfny+*>Yw1P|my@lL z;(4b78QD`oaEEDm_!k=vZ}scX89s#YdklA6P!@D~teet{FQL%xue@aN4g9CS@6cZQ I?voe(2brLvGXMYp literal 0 HcmV?d00001 diff --git a/notes/fyz/Mechanika tekutin/Atmosférický tlak.md b/notes/fyz/Mechanika tekutin/Atmosférický tlak.md index 482c1bd..085121b 100644 --- a/notes/fyz/Mechanika tekutin/Atmosférický tlak.md +++ b/notes/fyz/Mechanika tekutin/Atmosférický tlak.md @@ -1,3 +1,6 @@ +--- +tags: [fyz, fyz/tekutiny] +--- # Atmosférický tlak $h=75cm$ diff --git a/notes/fyz/Mechanika tekutin/Hydrostatická tlaková síla.md b/notes/fyz/Mechanika tekutin/Hydrostatická tlaková síla.md index 4bd49f1..3eeecfc 100644 --- a/notes/fyz/Mechanika tekutin/Hydrostatická tlaková síla.md +++ b/notes/fyz/Mechanika tekutin/Hydrostatická tlaková síla.md @@ -1,3 +1,6 @@ +--- +tags: [fyz, fyz/tekutiny] +--- # Hydrostatická tlaková síla ![](Pasted%20image%2020221004125503.png) diff --git a/notes/fyz/Mechanika tekutin/Hydrostatický paradox.md b/notes/fyz/Mechanika tekutin/Hydrostatický paradox.md index e3e385d..cff1bbd 100644 --- a/notes/fyz/Mechanika tekutin/Hydrostatický paradox.md +++ b/notes/fyz/Mechanika tekutin/Hydrostatický paradox.md @@ -1,3 +1,6 @@ +--- +tags: [fyz, fyz/tekutiny] +--- # Hydrostatický paradox Velikost tlakové síly kapaliny na dno nádoby nezávisí na hmotnosti kapaliny v nádobě. diff --git a/notes/fyz/Mechanika tekutin/Mechanika tekutin.md b/notes/fyz/Mechanika tekutin/Mechanika tekutin.md index 8bca3fb..2af3bf2 100644 --- a/notes/fyz/Mechanika tekutin/Mechanika tekutin.md +++ b/notes/fyz/Mechanika tekutin/Mechanika tekutin.md @@ -1,3 +1,6 @@ +--- +tags: [fyz, fyz/tekutiny, MOC, generated] +--- # Mechanika tekutin %% Zoottelkeeper: Beginning of the autogenerated index file list %% - [[fyz/Mechanika tekutin/Atmosférický tlak|Atmosférický tlak]] diff --git a/notes/fyz/Mechanika tekutin/Tekutiny.md b/notes/fyz/Mechanika tekutin/Tekutiny.md index 498251d..4f1e05e 100644 --- a/notes/fyz/Mechanika tekutin/Tekutiny.md +++ b/notes/fyz/Mechanika tekutin/Tekutiny.md @@ -1,3 +1,6 @@ +--- +tags: [fyz, fyz/tekutiny] +--- # Tekutiny kapaliny a plyny diff --git a/notes/fyz/Mechanika tekutin/Torricelliho pokus.md b/notes/fyz/Mechanika tekutin/Torricelliho pokus.md index aefdd52..d85d2cb 100644 --- a/notes/fyz/Mechanika tekutin/Torricelliho pokus.md +++ b/notes/fyz/Mechanika tekutin/Torricelliho pokus.md @@ -1,3 +1,6 @@ +--- +tags: [fyz, fyz/tekutiny] +--- # Torricelliho pokus [Torricelliho pokus – Wikipedie](https://cs.wikipedia.org/wiki/Torricelliho_pokus) diff --git a/notes/mat/Funkce/Exponenciální funkce.md b/notes/mat/Funkce/Exponenciální funkce.md new file mode 100644 index 0000000..566d779 --- /dev/null +++ b/notes/mat/Funkce/Exponenciální funkce.md @@ -0,0 +1,154 @@ +--- +tags: [mat, mat/funkce] +--- +# Exponenciální funkce +Exponenciální funkce o základu $a$ je funkce $y=a^x$, kde $a\in\mathbb{R}^+-\{1\}$ + +## Vtip +přijde matematik a objedná si pivo. +přijde další matematik a objedná si půlku piva.. +| matematik. č. | část piva | +| ------------- | --------------------------------- | +| 0 | 1 | +| 1 | $\frac12$ | +| 2 | $\frac14$ | +| 3 | $\frac18$ | +| x | $y=\frac1{2x}=2^{-x}=(\frac12)^x$ | +| -1 | 2 | +| -3 | 8 | +| $\frac12$ | $\sqrt\frac12$ | + +## Vlastnosti +- $x\in\mathbb{R}$ +- exponenciála (typ grafu) +- $D=\mathbb{R}$ +- $H=(0;\infty)=\mathbb{R}^+$ +- je prostá (na celém $D$) +- extrémy nemá +- je omezena zdole +- není sudá ani lichá +- graf prochází (v základním tvaru) $[0;1]$ + +$f: y=a^x$ + +Rozšířený tvar: +$f: y=a^{x-n}+m$ + +$n$ udává posun doprava ($+n$ pro posun doleva o $n$). +$m$ udává posun nahoru ($-m$ pro posun dolů o $m$). + +a nesmí být $\lt0;=0;=1$ + +pro $a < 1$, graf klesá +pro $a > 1$, graf roste + +## Převody +$\frac{x^p}{x^q}=x^{p-q}$ +$x^p*x^q=x^{p+q}$ +$(x^a)^b=(x^b)^a=x^a*b$ +$x^{-p}=\frac1{x^p}$ +$(\frac{x}y)^p=(\frac{y}x)^{-p}$ +$\sqrt[a]{x^b}=x^{\frac{b}a}=\sqrt[a]x^b$ +$x^0=1;\space [x\ne0]$ +$x^py^p=(xy)^p$ + +## Příklady +![](Pasted%20image%2020221005111551.png) + +graf $\frac12^x$ +![](Pasted%20image%2020221004142221.png) + +--- + +S použitím grafů exp.fcí porovnejte (doplněny znaménka (ne)rovnosti): + +a) $1.5^p > 1.5^r$ + +$p > r$ + +b) $(\frac37)^{6.24}<1$ + +c) $(\frac85)^{2\pi} > (\frac85)^{0.5\pi}$ + +--- + +### Řešte rovnice pro $x\in\mathbb{R}$ + +$(\frac13)^{x-4}=(\frac13)^{19x+2}$ + +$x-4=19x+2$ +$-6=18x$ +$x=-\frac13$ + +$K=\{\frac13\}$ + +--- + +$15^3*15^{x2}=15^{-x}$ + +$15^{3+2x}=15^{-x}$ +$3+2x=-x$ +$x=-1$ + +$K=\{-1\}$ + +--- + +$\frac{6.8^{x^2}}{6.8^3}=6.8^{-2}$ + +$6.8^{x^2-3}=6.8^{-2}$ +$x^2-3=-2$ +$x^2-1=0$ +$(x-1)(x+1)=0$ + +$K=\{-1;1\}$ + +--- + +$13^{2+x}=(\frac1{13})^x$ + +$13^{2+x}=13^{-x}$ +$2+x=-x$ +$-2x=2$ +$x=-1$ + +$K=\{-1\}$ + +--- + +$25^x=5^2*5^3:5^5$ +$25^x=5^{2+3-5}$ + +$25^x=5^5:5^5$ +$25^x=5^0$ +$x=0$ + +$K=\{0\}$ + +--- + +$\sqrt{3}^5=3^{2x-1}$ + +$3^{\frac52}=3^{2x-1}$ +$\frac52=2x-1$ +$\frac72=2x$ +$x=\frac74$ + +--- + +$8^{x+3}=1$ + +$8^{x+3}=8^0$ +$x+3=0$ +$x=-3$ + +$K=\{-3\}$ + +--- + +$2^{x+1}3^{x+1}=6$ +$6^{x+1}=6^1$ +$x+1=1$ +$x=0$ + +$K=\{0\}$ diff --git a/notes/mat/Funkce/Funkce.md b/notes/mat/Funkce/Funkce.md index edf38e3..2098184 100644 --- a/notes/mat/Funkce/Funkce.md +++ b/notes/mat/Funkce/Funkce.md @@ -9,6 +9,7 @@ imagePrefix: 'data/' %% Zoottelkeeper: Beginning of the autogenerated index file list %% - [[mat/Funkce/Cosinus|Cosinus]] - [[mat/Funkce/Cotangens|Cotangens]] +- [[mat/Funkce/Exponenciální funkce|Exponenciální funkce]] - [[mat/Funkce/Funkce vs Rovnice|Funkce vs Rovnice]] - [[mat/Funkce/Funkční přepis|Funkční přepis]] - [[mat/Funkce/Inverzní funkce|Inverzní funkce]] diff --git a/notes/mat/Funkce/Inverzní funkce.md b/notes/mat/Funkce/Inverzní funkce.md index 255b593..93c5f9b 100644 --- a/notes/mat/Funkce/Inverzní funkce.md +++ b/notes/mat/Funkce/Inverzní funkce.md @@ -6,6 +6,8 @@ Značíme $f^{-1}$ "Prohození os" na grafu grafy jsou osově souměrné podle přímky $y=x$ (vlevo dole doprava nahoru) musí být prosté +inverzní funkce inverzní funkce je původní funkce + → $f^{-1}(f^{-1}(x))=f(x)$ $f$ → $x$ na $y$ $f^{-1}$ → $y$ na $x$ @@ -64,3 +66,22 @@ $y(x+3)=1$ $x+3=\frac1y$ $x=\frac1y-3$ + +--- + +$k: y=(x-4)^2$ +$y=x^2-16$ + +není prostá +na celém $D_f$ → +→ vybereme pouze $<4;\infty)$ kde prostá je + +$k^{-1}: x=(y-4)^2$ +$x=y^2-16$ +$\sqrt{x}=y-4$ +$-y=-\sqrt{x}-4$ +$y=\sqrt{x}+4$ + +![](Pasted%20image%2020221004140412.png) + +inverzní funkce modře diff --git a/notes/mat/Příklady 2.md b/notes/mat/Příklady 2.md index 13fa455..169679f 100644 --- a/notes/mat/Příklady 2.md +++ b/notes/mat/Příklady 2.md @@ -185,8 +185,7 @@ $\frac{x^5*(x^n*6*y^{4n})^3}{9*y^{4n}*(x^5*2*y^6)^2}$ $\frac{x^5*(x^n*6*y^{4n})(x^n*6*y^{4n})(x^n*6*y^{4n})}{9*y^{4n}*(x^5*2*y^6)(x^5*2*y^6)}$ -$x^{5+3n}*216*y^{12n}$ -$36*y^{4n+12}*x^{10}$ +$\frac{x^{5+3n}*216*y^{12n}}{36*y^{4n+12}*x^{10}}$ $\frac{x^{5+3n}*216*y^{12n}}{36*y^{4n+12}*x^{10}}$ @@ -194,6 +193,9 @@ $x^{3n-5}*6*y^{8n-12}$ $6x^{3n-5}y^{8n-12}$ +$[x\neq0]$ +$[y\neq0]$ + --- $\frac{(16b^3a^{-1})^{-3}}{(a^3b^{-2}*4)^{-2}}$ @@ -201,3 +203,23 @@ $\frac{(16b^3a^{-1})^{-3}}{(a^3b^{-2}*4)^{-2}}$ $\frac1{(16b^3a^{-1})^3}:\frac1{(a^3b^{-2}*4)^2}$ $\frac{(a^3b^{-2}*4)^2}{(16b^3a^{-1})^3}$ + +$\frac{a^6*16}{16^3b^9a^{-3}}$ + +$\frac{a^9}{16^2b^9}$ + +$\frac{a^9}{256b^{13}}$ +$[b \ne 0]$ +$[a\neq0]$ + +--- + +$\frac{(27r^3s^4)^{n-1}}{(3rs^{-2})^{3n+1}}$ + + + +$\frac{s^{10n-2}}{81r^4}$ + +$[r \ne 0]$ +$[s\neq0]$ +