asinus

Express k as a common fraction.

Hello Guest!

\(2x^2- 5x + k = x^2 - 4x\ |\ -(x^2-4x) \\ x^2-x+k=0\\ p-q\ formula\\ x=0.5\pm \sqrt{0.25-k}\\ 0.25-k=0\\ \color{blue}k=0.25=\frac{1}{4}\\ \color{blue}x=0.5\)

  !

Expand (2x - 1)^5*(2x + 1)^5.

Hello Guest!

\((2x - 1)^5\cdot (2x + 1)^5\\ =((2x - 1)(2x + 1))^5\\ =(4x^2-1)^5\\ =\color{blue}1024x^{10}-1280x^8+640x^6-160x^4+20x^2-1\)

  !

If it is 2:42 what time will it be in seven hours 35 minutes

Hello Guest!

\(2\frac{42}{60}+7\frac{35}{60}=\frac{2\cdot 60+42+7\cdot 60+35}{60}=\frac{617}{60}=\color{blue}10\frac{17}{60}\)

or

\(2\frac{42}{60}+7\frac{35}{60}=2+7+\frac{42+35}{60}=9+\frac{77}{60}=\color{blue}10\frac{17}{60}\)

10:17 time will it be in seven hours 35 minutes.

  !

What is the length of a side of the square?

Hello Guest!

\(a^2=4\cdot 4a\\ a^2-16a=0\\ a(a-16)\\ \color{blue}a\in \{0,16\}\)

16 is the length of a side of the square.

  !

Danke Probolobo!

Hallo Rechenbaer!

Ich freue mich sehr darüber! Ein Danke kommt hier leider selten vor.

Viel Erfolg und Spaß beim künftigen Arbeiten im Forum 

wünscht dir

Interessant wäre auch die Frage:

\(Sind\ 0,999\overline9\ dasselbe\ wie\ 1?\)

Antwort:

\(0,999\overline 9\ ist\ nicht\ dasselbe\ wie\ 1,\\ aber\\ 0,999\overline 9\ ist \ gleich\ 1,\\ denn\ zwischen\ beiden\ beiden\ Termen\ ist\ keine\ Differenz\ benennbar.\)

Ich bitte um Widerspruch.

  !

Where are points D and E?

Find the equation of the line that is tangent to both of the parabolas y^2 = 4x and x^2 = -20y.

Hello Guest!

\(f(x)=y=\pm2\sqrt{x}\\ f'(x)=\pm\ x^{-\frac{1}{2}}\\ g(x)=y=-\frac{x^2}{20}\\ g'(x)=-\frac{x}{10}\\ f'(x)=g'(x)\\ -\frac{2x}{10}=\pm \ x^{-\frac{1}{2}}\\ \color{blue}x = \pm 4,641588833408518\\ © Arndt\ Br\ddot unner\)

\(y_f=2\cdot \sqrt{4,641588833408518}=4.30886937996\\ P_f(4,641588833408518,4.30886937996)\\ y_g=-\frac{x^2}{20}=-1.07721734492\\ P_g(-4,641588833408518,-1.07721734492)\)

\(m=\dfrac{y_f-y_g}{x_f-x_g}=\dfrac{4.30886937996-(-1.07721734492)}{4,641588833408518-(-4,641588833408518)}\\ \color{blue}m=0.580198604205\)

Point-direction equation of the straight line.

\(y=m(x-x_1)+y_1\\ y=0.580198604205(x-4,641588833408518)+4.30886937996\\ The\ equation\ of\ the\ line\ that\ is\ tangent\ to\ both\ of\ the\ parabolas\\ y^2 = 4x\\ and\\ x^2 = -20y\\ is\\\color{blue}y=0.5802x+1.692\)

  !