radix

Guten Tag  sigreid !

f(x) = $${\mathtt{\,-\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{10}}}{\mathtt{\,-\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{17}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{2}}$$

f'(x) =  $${\mathtt{\,-\,}}{\mathtt{51}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{16}}}{\mathtt{\,-\,}}{\mathtt{30}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{9}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{x}}$$

f'(2) = $${\mathtt{\,-\,}}{\mathtt{51}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{16}}}{\mathtt{\,-\,}}{\mathtt{30}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{9}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{2}} = -{\mathtt{3\,357\,684}}$$

f''(x) = $${\mathtt{\,-\,}}{\mathtt{816}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{15}}}{\mathtt{\,-\,}}{\mathtt{270}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{8}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}$$

f''(2) = $${\mathtt{\,-\,}}{\mathtt{816}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{15}}}{\mathtt{\,-\,}}{\mathtt{270}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{8}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}} = -{\mathtt{26\,807\,802}}$$

 Gruß radix !

Hallo Anonymous,

hier 3 Berechnungsmöglichkeiten:

1.)   $${\mathtt{119}}{\mathtt{\,-\,}}{\mathtt{20}}\% = {\frac{{\mathtt{476}}}{{\mathtt{5}}}} = {\mathtt{95.2}}$$           => 95,20 €

2.)  100 % -20 % = 80 % = 80/100 = 0,8

       $${\mathtt{119}}{\mathtt{\,\times\,}}{\mathtt{0.8}} = {\frac{{\mathtt{476}}}{{\mathtt{5}}}} = {\mathtt{95.2}}$$      =>    95,20 €

3)  20 % von 119 € =     $${\mathtt{119}}{\mathtt{\,\times\,}}{\mathtt{0.2}} = {\frac{{\mathtt{119}}}{{\mathtt{5}}}} = {\mathtt{23.8}}$$   [ € ]

      119 € - 23,80 € =    $${\mathtt{119}}{\mathtt{\,-\,}}{\mathtt{23.8}} = {\frac{{\mathtt{476}}}{{\mathtt{5}}}} = {\mathtt{95.2}}$$    [ € ]

Antwort:  119 € -20 % = 95,20 €

Gruß radix !

Guten Morgen Anonymous,

" man sollte meinen man glaubt es kaum ! "

Papier falten:  0.1 mm => 0,2 mm => 0,4 mm => 0,8 mm => 1,6 mm = 3.2 mm ...

Nach 5 mal falten => 3,2 mm            h =  $${\mathtt{0.1}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{5}}} = {\frac{{\mathtt{16}}}{{\mathtt{5}}}} = {\mathtt{3.2}}$$   mm

Nach 50 mal falten  =>   h = $${\mathtt{0.1}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{50}}} = {\mathtt{112\,589\,990\,684\,262.4}}$$ mm

= $${\frac{{\mathtt{0.1}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{50}}}}{{\mathtt{1\,000\,000}}}} = {\mathtt{112\,589\,990.684\: \!262\: \!4}}$$   km  !!!

Antwort:

Nach 50 mal falten hat man eine Höhe von knapp  112 589 991 km erreicht !

 $${\frac{{\mathtt{0.1}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{{\mathtt{50}}}}{\left({\mathtt{1\,000\,000}}{\mathtt{\,\times\,}}{\mathtt{40\,000}}\right)}} = {\mathtt{2\,814.749\: \!767\: \!106\: \!56}}$$    mal um die Erde !!!

Etwa 2815 mal um die Erde !

Was schätzt du?  Wie oft kann man eine Zeitungsseite maximal falten ?

Bitte ausprobieren und antworten !

Gruß radix !

Siehe ein Frage höher !

Gruß radix !

Maßstab  1 : 50 bedeutet:

    1 cm  auf der Karte     =>  50  cm Wirklichkeit

100 cm  auf der  Karte    =>   50 * 100 cm = 5000 cm = 50 m = 0,05 km Wirklichkeit  

Hallo Anonymous,

du hast wohl Schwierigkeiten mit den 10 Minuten:  

33 Std +10 min = (33+10/60) h = (33+1/6) h = 33,1666... h  =  $${\frac{{\mathtt{199}}}{{\mathtt{6}}}}$$ h

Nun machen wir die proportionale Zuordnung:

in                  1 h verdient Frau W.       9  €

in    (33+1/6) h verdient sie   (33+1/6) * 9  €  =   295,50 €

Rechnung:   $$\left({\mathtt{33}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{6}}}}\right){\mathtt{\,\times\,}}{\mathtt{9}} = {\frac{{\mathtt{597}}}{{\mathtt{2}}}} = {\mathtt{298.5}}$$

oder:                 $${\frac{{\mathtt{199}}{\mathtt{\,\times\,}}{\mathtt{9}}}{{\mathtt{6}}}} = {\frac{{\mathtt{597}}}{{\mathtt{2}}}} = {\mathtt{298.5}}$$    [ € ]

Antwort:     Frau W. verdient in  33 h und 10 min    298,50 €.

Zusatz:       In  10 min würde sie  1,50 € verdienen !    (   9 * $${\frac{{\mathtt{1}}}{{\mathtt{6}}}}$$ = 9 : 6 = 1,50 )

Gruß radix !      ( und einen Gruß auch an Frau W. !)

Gruß radix !

Hallo Anonymous , hallo gandalf ,

als kleines Feriengeschenk gibt es heute einen Zeit-Einheitenrechner !

$${\mathtt{136}}{d}{\mathtt{\,\times\,}}{\mathtt{24}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{h}}}{{\mathtt{d}}}}\right) = {\mathtt{3\,264}}{h}$$               Das  d  kürzt sich heraus :     $${\frac{{\mathtt{d}}{\mathtt{\,\times\,}}{\mathtt{h}}}{{\mathtt{d}}}} = {\mathtt{h}}$$

Gruß radix !

164 : 12,9 = 1640 : 129 =  $${\frac{{\mathtt{1\,640}}}{{\mathtt{129}}}} = {\mathtt{12.713\: \!178\: \!294\: \!573\: \!643\: \!4}}$$

$${\frac{{\mathtt{164}}}{{\mathtt{12.9}}}} = {\frac{{\mathtt{1\,640}}}{{\mathtt{129}}}} = {\mathtt{12.713\: \!178\: \!294\: \!573\: \!643\: \!4}}$$

1640 : 129 = 12 Rest 92

Gruß radix !

Eine Frage tiefer findest du die  Zinseszinsformel  und ein Rechenbeispiel !

$${\mathtt{Kn}} = {\mathtt{K0}}{\mathtt{\,\times\,}}{\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{p}}}{{\mathtt{100}}}}\right)}^{{\mathtt{n}}}$$