asinus

0.4 is mulitipled by something to make 4.  What is the something?

Hello Guest!

0.4 is mulitipled by 10 to make 4.
The something is 10.

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I made an embarrassing mistake and I apologize.

Here is my correct solution:

\(y = \frac{1}{\sqrt{2}} (x^2 - 13)\\ r^2=x^2+y^2\\ r^2=x^2+\frac{1}{2}(x^2-13)^2\\ \frac{d(r^2)}{dx}=2x+\frac{1}{2}\cdot 2(x^2-13)\cdot 2x=0\\ 2x+2x^3-26x=0\\ 2x^3-24x=0\\ x(x^2-12)=0\)

\(x\in \{0,-\sqrt{12},{\color{blue}\sqrt{12}}\}\\ r^2=x^2+\frac{1}{2}(x^2-13)^2\\ r^2=12+\frac{1}{2}(12-13)^2\\ r^2=12.5\\ \color{blue}r=\sqrt{12.5}=3.5355 \)

This is Guest 2#'s solution.

Sorry again!

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Melody, I think my answer is correct.

The second line in your post proves that.

\(x^2+y^2=3.14^2\)

The exact value is: \(3.14005494464\)

You switched colors. Not correct! See answer 7#.

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Hallo Guest!

Die Folie ist für mich unlesbar, zu klein. Kannst du da etwas verbessern?

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What is the domain of the function \(j(x)= 1/(x + 8) + 1/(x^2 - 8) + 1/(x^3 - 8) \) ?

Hello Guest!

\(x\in \mathbb R\ |\ x\notin \{-8,-2\sqrt{2},2,2\sqrt{2}\}\)

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a fully simplified fraction

Hello Guest!

\(0.\overline{42}\cdot 100=42.\overline{42}\)

    \(\underline{0.\overline{42}\cdot 1=\ 0.\overline{42}}\)

  \(0.\overline{42}\cdot 99=42\\ 0.\overline{42}=\dfrac{42}{99}\\ \color{blue}\dfrac{99}{100}\cdot 0.\overline{42}=\dfrac{99\cdot 42}{100\cdot 99}=\dfrac{21}{50}\)

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Berechnung der 10. Wurzel aus 1,7727272 hoch 3

Hallo Gast!

\(\sqrt[10]{ 1,7727272^3}= 1,7727272^{\frac{3}{10}}= 1,7727272^{0.3}\)

Gib ein in den Rechner:

\( 1,7727272\ x^y\ 0,3\ =\\ Ergebnis:\ 1.1873877730124423\)

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What is the smallest distance between the origin and a point on the graph?

Hello Guest!

\(y = \frac{1}{\sqrt{2}} (x^2 - 13)\\ y=\frac{x^2}{\sqrt{2}}-\frac{13}{\sqrt{2}}\\ y'=x\cdot\sqrt{2}\ |\ the\ perpendicular\ through\ the\ origin\ is:\\ y=-\frac{1}{\sqrt{2}}x\\ \frac{x^2}{\sqrt{2}}-\frac{13}{\sqrt{2}}=-\frac{1}{\sqrt{2}}x\ |\ \cdot \sqrt{2}\\ x^2+x-13=0\)

\(x\in \{-\frac{1}{2}-\frac{\sqrt{53}}{2},\color{blue}\frac{\sqrt{53}}{2}-\frac{1}{2}\}\)

The smallest distance between the origin and a point on the graph

\(y = \frac{1}{\sqrt{2}} (x^2 - 13)\) is 3.14005. Not correct! See answer 7#.

Find all real numbers a that satisfy.

Hello Guest!

\(1/(a^3 + 7) - 7 = -a^3/(a^3 + 7) + 5\\ \dfrac{1}{a^3+7}-7=-\dfrac{a^3}{a^3+7}+5\\ \dfrac{1+a^3}{a^3+7}=12\\ 1+a^3=12a^3+84\\ 11a^3=-83\\ \color{blue}a=\sqrt[3]{-\frac{83}{11}}=-1.961\)

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the sum of all possible values of x

Hello Guest!

\(2x(x-10)=-50+x^2-30x\\ 2x^2-20x+50-x^2+30x=0\\ x^2+10x+50=0\\ \color{blue}x\in \{-5-5i,-5+5i\}\)

The sum of all possible values of x is  -10 .

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