asinus

Gleichung schnell lösbar.

Ist 2 mal x hoch 1/2 gleich x?

\(2x^{(\frac{1}{2})}=x\)

\(2\times\sqrt{x}=x\)

\(4x=x^2\)

\(x^2-4x=0\)

\(x_1=0\)

\(x_2=4\)

Ist 2 mal x hoch 1/2 gleich x?

\(Ja, \ wenn\ x \in \left\{ 0;4\right\} \ ist.\)

  !

Find a+b+c if the graph of the equation is a parabola with vertex (5,3) , vertical axis of symmetry, and contains the point (2,0).

\(f(x)=y=ax^2+bx+c\)

\(c=3\)

\(x_1=2\)

\(x_2=8\)

\(a \ is \ negative\)

\(2 = {-b + \sqrt{b^2-12a} \over 2a}\)                \(8 = {-b- \sqrt{b^2-12a} \over 2a}\)

\(16a = {-b - \sqrt{b^2-12a} }\)

.         plus

  \(4a = {-b + \sqrt{b^2-12a} }\)

\(20a=-2b\)

b=-10a

\(4a = {10a - \sqrt{100a^2-12a} }\)

\(-6a= - \sqrt{100a^2-12a}\)

\(36a^2=100a^2-12a\)

\(64a^2=12a\)

\(a=\frac{3}{16}\)  Error. CPhill was too fast.

\(\sin\beta -\cos^2 \beta=0\)

\(\sqrt{1-cos^2\beta}=cos^2\beta\)

\(cos^2\beta=z\)

\(\sqrt{1-z}=z\)

\(z^2+z-1=0\)

\(z=cos^2\beta=-\frac{1}{2}+\sqrt{(\frac{1}{2})^2+1}=\frac{-1+\sqrt{1+4}}{2}\)

\(cos^2\beta=\frac{\sqrt{5}-1}{2}\)   (equal with hectictar)

MaxWong, please tell us how to continue.

  ?

I've used cos β = x = 1, but I'm not progressing. Please give a tip.

Wie viel Volumen hat das Beet mit 20cm *108cm**108cm?

\(V=l^2\times h=108^2cm^2\times 20cm\)

\(V=233280cm^3\)\(\times\frac{dm^3}{10^3cm^3}\)\(=233,28dm^3\)

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Given that

\(\sin\beta -\cos^2 \beta\\=a\cos^8\beta +b\cos^6\beta+c\cos^4\beta-1\\=d\cos^{12}\beta + e\cos^{10}\beta + f\cos^8\beta + g\cos^6\beta\\ = 0\)

Find

\(\dfrac{ad+be+cf+g}{ag+bf+ce+d}\)

\(cos\ \beta=x\)

\(ax^8+bx^6+cx^4-1=0\)

\(dx^{12}+ex^{10}+fx^8+gx^6=0\)

If x = 1 then

\(a+b+c-1=0\) 

\(d+e+f+g=0\)

Please tell me how it goes, dear smarter biscuit.

asinus :- )

c=-b+d/a

fraction form please

\(\Large c=-b+d/a=-b+ \frac{d}{a}=\frac{-ab+d}{a}\)

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When a 15 newton force is applied to on end of a lever 100 cm long, a 60 newton weight is attached to the opposit end is lifted. What is the length of the input arm? {nl} Please show all the steps.

\(15N\times x=60N\times(100cm-x)\)

\(15N\times x = 6000Ncm - 60N\times x\)

\(x=\frac{6000Ncm}{75N}\)

\(x=80cm\)

\( The\ length \ of \ the\ input\ arm \ is \ 80cm.\)

  !

Wie viel ist 18 % von 52386,34 € ?

\( 52386,34 € \times18\%= 52386,34 € \times\frac{18}{100}=9429,54 € \)

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What is the ratio of the least common multiple of 180 and 594 to the greatest common factor of 180 and 594

\(\frac{180}{594}=\frac{2^2\cdot3^2\cdot5}{2\cdot3^3\cdot11}\ \ lcm=2^2\cdot3^3\cdot5\cdot11\ \ gcf=2\cdot3^2\)

\(\frac{lcm}{gcf}=\frac{2^2\cdot3^3\cdot5\cdot11}{2\cdot3^2}=\frac{2\cdot3\cdot5\cdot11}{1}\color{blue}=330:1\)

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