asinus

Complete the expression by filling in the missing operator.

Hello Guest!

\(3 * 4 [BLANK] 5 =2-->3 * 4\ \ {\color{OliveGreen}-\ 2*}\ 5\ =2\)

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Hallo Gast!

a)

Die kleinste Zahl, die ein  Quadrat ist, ist die Eins. Denn

\(1\times 1=1^2=1\\ \sqrt{1 }=1\)

b)

dito, denn

\(1\times 1\times 1=1^3=1\\ \sqrt[3]{1}=1\)

Rein matematisch wäre es die Null, aber Quadrate und Würfel mit Seiten-, bzw. Kantenlänge Null gibt es nicht.

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Danke!

\(7(x+y+z) = 150\\ x+y+z=\frac{150}{7}\\ S=(x+y+z)^2=(\frac{150}{7})^2=\color{blue}459,184\)

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What is sin GIH?  What is sin GHI?

\(sin\ GIH=sin \ arccos\ \frac{9}{10}=sin\ 25.842°=\color{blue}0.43589\\ sin\ GHI=sin\ (180-2\cdot 25.842)°=sin\ 128.316°=\color{blue}0.7846\)

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 Find u/v + v/u.

Hello Guest!

\(3x^2+5x+7=2x^2-6x+1\\ x^2+11x+6=0\\ x=-\frac{11}{2}\pm \sqrt{\frac{121}{4}-6}\\ \{u,v\}=\{ -5.5+\sqrt{\frac{97}{4}}, -5.5-\sqrt{\frac{97}{4}}\}\)

\(\dfrac{u}{v}=\frac{ -5.5+\sqrt{\frac{97}{4}} }{ -5.5-\sqrt{\frac{97}{4}}}=0.05521\)

\(\dfrac{v}{u}=18.111\)

\({\color{blue}\dfrac{u}{v}+\dfrac{v}{u}=}\frac{ -5.5+\sqrt{\frac{97}{4}} }{ -5.5-\sqrt{\frac{97}{4}}}+\frac{ -5.5-\sqrt{\frac{97}{4}} }{ -5.5+\sqrt{\frac{97}{4}}}=\color{blue}18.1\overline 6=\frac{109}{6}\)

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What is sin GIH?  What is sin GHI?

Hello Guest!

law of cosines:

\(a^2= c^2+b^2-2bc\cdot cos\ \alpha\\ \color{blue}sin\ \alpha=sin\ (arc cos\ \dfrac{c^2+b^2-a^2}{2bc})\)

You can calculate it yourself.

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Bitte teile mit, was du eingegeben hast.

What is the longest possible value of AC?

Hello Guest!

\(\sqrt{12^2-x^2}+\sqrt{13^2-x^2}=13\\ x=\dfrac{12\sqrt{133}}{13}\)

 \(The\ longest\ possible\ value\ of\ AC\ is\ {\color{blue}2x}=2\cdot \dfrac{12\sqrt{133}}{13}=\color{blue}21.291\)

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