asinus

A scientist records the motion of a particle.  A graph of that motion is shown below.

Hello DumpDude!

a) What is the period of one complete cycle?                    

           \(\color{blue}4\ units_t\)

b) What is the range of this function?                              

        \(\color{blue}\{range-f(t)\}=\{\mathbb d\ |\ -1\leq d\leq 3\}\ [units_d]\)
c) If the particle can survive for twenty complete cycles  before deteriorating,

determine the domain of the function.                                 

         \(\color{blue}\mathbb D=\{t\ |\ 0\leq t\leq 80\}\ [units_t]\)
d) Determine the equation of the axis.                             

         \(\color{blue}d=f(t)=2\ cos\ (\frac{\pi}{2} t)+1\ [units_d]\)
e) Determine the amplitude.                                               

        \(\color{blue}2\ units_d\)

  !

\(5x^2=20^3\\x^2=1600\\ x=\pm \sqrt{1600}\\ \color{blue}x\in\{-40;40\}\)

25 - (____- 20) = - 12 + (5 + (25 - 8))

Hallo Gast!

25 - (x - 20) = - 12 + (5 + (25 - 8)) | Klammern auflösen

25 - x + 20 = - 12 + 5 + 25 - 8 | addieren und subtrahieren

- x + 45 = 10 | - 45

- x = 10 - 45 | sbtrahieren

- x = - 35 | * ( - 1)

x = 35

25 - (35 - 20) = - 12 + (5 + (25 - 8))

  !

... aber was ist interessant?

Wähle das für dich interessanteste Fach.

\(\operatorname{Domain}(f) = \{x \in \mathbb R:-2 < x < 2\}\\ correctly\\ Domain\ f(x) = \mathbb R\ |\ -2 \leq x \leq 2\)

  !

m and n are integers

Hello Guest!

\(m^3 + 24m^2 - 2022 = 3^n\\ .\\ \color{blue}(m,n)\in\{(-17,0),(-15,1),(8,1)\}\\ .\\ ({\color{blue}-17})^3 + 24\cdot ({\color{blue}-17})^2 - 2022 = 3^{\color{blue}0}\\ ({\color{blue}-15})^3 + 24\cdot ({\color{blue}-15})^2 - 2022 = 3^{\color{blue}1}\\ {\color{blue}8}^3 + 24\cdot {\color{blue}8}^2 - 2022 = 3^{\color{blue}1}\\\)

  !

\(\) What is the value of x + y?

Hello Guest!

\(\frac{1}{x}=a;\ \frac{1}{y}=b\\ a+b=\frac{1}{3}\\ \underline{a-b=\frac{1}{7}}\\ 2a=\frac{1}{3}+\frac{1}{7}\\ 42a=10\\ a=\frac{5}{21}\\ \color{blue}x=\frac{21}{5}\)

\(b=\frac{1}{3}-\frac{5}{21}\\ 21b=2\\ b=\frac{2}{21}\\ \color{blue}y=\frac{21}{2}\\ x+y=\frac{21}{5}+\frac{21}{2}=\frac{42+105}{10}\\ \color{blue}x+y=\frac{147}{10}\)

What is the domain?

Hello Guest!

\( f(x) = \frac{x + 6}{\sqrt{x^2 - 4}}\)

\(\color{blue}\mathbb D=\mathbb R\ |\ x\in \{-2\leq x\leq 2\}\)

  !

What is angle Y in degrees?

Hello Guest!

law of sine

\(sin\ 60°:4\sqrt{3}=sin\ y:4\sqrt{2}\\ sin\ y=\frac{4\sqrt{2}\cdot sin\ 60°}{4\sqrt{3}}\\ y=arcsin\ \frac{4\sqrt{2}\cdot sin\ 60°}{4\sqrt{3}}\)

\(\color{blue}y=45°\)

  !