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# Mathematrix: Aufgabenbeispiele/ Komplexe Umformungen

 A) ${\displaystyle {\sqrt {p}}+c_{L}\cdot {\frac {m\cdot v^{2}}{2\cdot k_{B}\cdot T}}-{\frac {t-s}{w-z}}=2,2}$ Formen Sie diese Formel auf z, m, v, T, p, t, s, kB, cL um! B) ${\displaystyle a+b\cdot c\cdot m-(n-3)^{2}+b\cdot {\sqrt {d-w}}-{\frac {f}{k}}=m}$ Formen Sie diese Formel auf a, b, c, f, m, n, k, w um!

## A

### z

${\displaystyle {\sqrt {p}}+c_{L}\cdot {\frac {m\cdot v^{2}}{2\cdot k_{B}\cdot T}}-{\frac {t-s}{w-z}}=2,2}$
${\displaystyle {\frac {t-s}{w-z}}={\sqrt {p}}+c_{L}\cdot {\frac {m\cdot v^{2}}{2\cdot k_{B}\cdot T}}-2,2}$
${\displaystyle {w-z}={\dfrac {t-s}{{\sqrt {p}}+c_{L}\cdot {\frac {m\cdot v^{2}}{2\cdot k_{B}\cdot T}}-2,2}}}$
${\displaystyle z=w-{\frac {(t-s)\cdot {2\cdot k_{B}\cdot T}}{{\sqrt {p}}\cdot {2\cdot k_{B}\cdot T}+c_{L}\cdot {m\cdot v^{2}}-4{,}4\cdot {k_{B}\cdot T}}}}$

Hoch zum Anfang

### m

${\displaystyle {\sqrt {p}}+c_{L}\cdot {\frac {m\cdot v^{2}}{2\cdot k_{B}\cdot T}}-{\frac {t-s}{w-z}}=2,2}$
${\displaystyle m\cdot {\frac {c_{L}\cdot v^{2}}{2\cdot k_{B}\cdot T}}=2,2-{\sqrt {p}}+{\frac {t-s}{w-z}}}$
${\displaystyle m=\left(2,2-{\sqrt {p}}+{\frac {t-s}{w-z}}\right)\cdot {\frac {2\cdot k_{B}\cdot T}{c_{L}\cdot v^{2}}}}$

Hoch zum Anfang

### v

${\displaystyle {\sqrt {p}}+c_{L}\cdot {\frac {m\cdot v^{2}}{2\cdot k_{B}\cdot T}}-{\frac {t-s}{w-z}}=2,2}$
${\displaystyle v^{2}\cdot {\frac {c_{L}\cdot m}{2\cdot k_{B}\cdot T}}=2,2-{\sqrt {p}}+{\frac {t-s}{w-z}}}$
${\displaystyle v^{2}=\left(2,2-{\sqrt {p}}+{\frac {t-s}{w-z}}\right)\cdot {\frac {2\cdot k_{B}\cdot T}{c_{L}\cdot m}}}$
${\displaystyle v={\sqrt {\left(2,2-{\sqrt {p}}+{\frac {t-s}{w-z}}\right)\cdot {\frac {2\cdot k_{B}\cdot T}{c_{L}\cdot m}}\ \ }}}$

Hoch zum Anfang

### T

${\displaystyle {\sqrt {p}}+c_{L}\cdot {\frac {m\cdot v^{2}}{2\cdot k_{B}\cdot T}}-{\frac {t-s}{w-z}}=2,2}$
${\displaystyle {\frac {v^{2}\cdot c_{L}\cdot m}{2\cdot k_{B}}}\cdot {\frac {1}{T}}=2,2-{\sqrt {p}}+{\frac {t-s}{w-z}}}$
${\displaystyle {\frac {1}{T}}=\left(2,2-{\sqrt {p}}+{\frac {t-s}{w-z}}\right)\cdot {\frac {v^{2}\cdot c_{L}\cdot m}{2\cdot k_{B}}}}$
${\displaystyle {T}={\frac {1}{\left(2,2-{\sqrt {p}}+{\frac {t-s}{w-z}}\right)}}\cdot {\frac {2\cdot k_{B}}{v^{2}\cdot c_{L}\cdot m}}}$
${\displaystyle {T}={\frac {w-z}{\left(2,2\cdot (w-z)-{\sqrt {p}}\cdot (w-z)+{t-s}\right)}}\cdot {\frac {2\cdot k_{B}}{v^{2}\cdot c_{L}\cdot m}}}$

Hoch zum Anfang

### p

${\displaystyle {\sqrt {p}}+c_{L}\cdot {\frac {m\cdot v^{2}}{2\cdot k_{B}\cdot T}}-{\frac {t-s}{w-z}}=2,2}$
${\displaystyle {\sqrt {p}}=2,2-c_{L}\cdot {\frac {m\cdot v^{2}}{2\cdot k_{B}\cdot T}}+{\frac {t-s}{w-z}}}$
${\displaystyle p=\left(2,2-c_{L}\cdot {\frac {m\cdot v^{2}}{2\cdot k_{B}\cdot T}}+{\frac {t-s}{w-z}}\ \right)^{2}}$

Hoch zum Anfang

### t

${\displaystyle {\sqrt {p}}+c_{L}\cdot {\frac {m\cdot v^{2}}{2\cdot k_{B}\cdot T}}-{\frac {t-s}{w-z}}=2,2}$
${\displaystyle {\frac {t-s}{w-z}}={\sqrt {p}}+c_{L}\cdot {\frac {m\cdot v^{2}}{2\cdot k_{B}\cdot T}}-2,2}$
${\displaystyle {t-s}=\left({\sqrt {p}}+c_{L}\cdot {\frac {m\cdot v^{2}}{2\cdot k_{B}\cdot T}}-2,2\right)\cdot {w-z}}$
${\displaystyle {t}=\left({\sqrt {p}}+c_{L}\cdot {\frac {m\cdot v^{2}}{2\cdot k_{B}\cdot T}}-2,2\right)\cdot {w-z}+s}$

Hoch zum Anfang

### s

${\displaystyle {\sqrt {p}}+c_{L}\cdot {\frac {m\cdot v^{2}}{2\cdot k_{B}\cdot T}}-{\frac {t-s}{w-z}}=2,2}$
${\displaystyle {\frac {t-s}{w-z}}={\sqrt {p}}+c_{L}\cdot {\frac {m\cdot v^{2}}{2\cdot k_{B}\cdot T}}-2,2}$
${\displaystyle {t-s}=\left({\sqrt {p}}+c_{L}\cdot {\frac {m\cdot v^{2}}{2\cdot k_{B}\cdot T}}-2,2\right)\cdot {w-z}}$
${\displaystyle {s}=t-\left({\sqrt {p}}+c_{L}\cdot {\frac {m\cdot v^{2}}{2\cdot k_{B}\cdot T}}-2,2\right)\cdot {w-z}}$

Hoch zum Anfang

### kB

${\displaystyle {\sqrt {p}}+c_{L}\cdot {\frac {m\cdot v^{2}}{2\cdot k_{B}\cdot T}}-{\frac {t-s}{w-z}}=2,2}$
${\displaystyle {\frac {v^{2}\cdot c_{L}\cdot m}{2\cdot k_{B}}}\cdot {\frac {1}{T}}=2,2-{\sqrt {p}}+{\frac {t-s}{w-z}}}$
${\displaystyle {\frac {1}{k_{B}}}=\left(2,2-{\sqrt {p}}+{\frac {t-s}{w-z}}\right)\cdot {\frac {v^{2}\cdot c_{L}\cdot m}{2\cdot T}}}$
${\displaystyle {k_{B}}={\frac {1}{\left(2,2-{\sqrt {p}}+{\frac {t-s}{w-z}}\right)}}\cdot {\frac {2\cdot T}{v^{2}\cdot c_{L}\cdot m}}}$
${\displaystyle {k_{B}}={\frac {w-z}{\left(2,2\cdot (w-z)-{\sqrt {p}}\cdot (w-z)+{t-s}\right)}}\cdot {\frac {2\cdot T}{v^{2}\cdot c_{L}\cdot m}}}$

Hoch zum Anfang

### cL

${\displaystyle {\sqrt {p}}+c_{L}\cdot {\frac {m\cdot v^{2}}{2\cdot k_{B}\cdot T}}-{\frac {t-s}{w-z}}=2,2}$

${\displaystyle c_{L}\cdot {\frac {m\cdot v^{2}}{2\cdot k_{B}\cdot T}}=2,2-{\sqrt {p}}+{\frac {t-s}{w-z}}}$
${\displaystyle c_{L}=\left(2,2-{\sqrt {p}}+{\frac {t-s}{w-z}}\right)\cdot {\frac {2\cdot k_{B}\cdot T}{m\cdot v^{2}}}}$

Hoch zum Anfang

## B

### aa

${\displaystyle a+b\cdot c\cdot m-(n-3)^{2}+b\cdot {\sqrt {d-w}}-{\frac {f}{k}}=m}$
${\displaystyle a=m-b\cdot c\cdot m+(n-3)^{2}-b\cdot {\sqrt {d-w}}+{\frac {f}{k}}}$

Hoch zum Anfang

### be

${\displaystyle a+b\cdot c\cdot m-(n-3)^{2}+b\cdot {\sqrt {d-w}}-{\frac {f}{k}}=m}$
${\displaystyle b\cdot c\cdot m+b\cdot {\sqrt {d-w}}=m-a+(n-3)^{2}+{\frac {f}{k}}}$
${\displaystyle b\cdot \left(c\cdot m+{\sqrt {d-w}}\right)=m-a+(n-3)^{2}+{\frac {f}{k}}}$
${\displaystyle b={\dfrac {m-a+(n-3)^{2}+{\frac {f}{k}}}{c\cdot m+{\sqrt {d-w}}}}}$
${\displaystyle b={\frac {(m-a+(n-3)^{2})\cdot k+{f}}{(c\cdot m+{\sqrt {d-w}})\cdot k}}}$

Hoch zum Anfang

### c

${\displaystyle a+b\cdot c\cdot m-(n-3)^{2}+b\cdot {\sqrt {d-w}}-{\frac {f}{k}}=m}$
${\displaystyle b\cdot c\cdot m=m-a+(n-3)^{2}-b\cdot {\sqrt {d-w}}+{\frac {f}{k}}}$
${\displaystyle c={\frac {(m-a+(n-3)^{2}-b\cdot {\sqrt {d-w}})\cdot k+{f}}{b\cdot m\cdot k}}}$
Hoch zum Anfang

### f

${\displaystyle a+b\cdot c\cdot m-(n-3)^{2}+b\cdot {\sqrt {d-w}}-{\frac {f}{k}}=m}$
${\displaystyle {\frac {f}{k}}=a+b\cdot c\cdot m-(n-3)^{2}+b\cdot {\sqrt {d-w}}-m}$
${\displaystyle f=(a+b\cdot c\cdot m-(n-3)^{2}+b\cdot {\sqrt {d-w}}-m)\cdot k}$
Hoch zum Anfang

### em

${\displaystyle a+b\cdot c\cdot m-(n-3)^{2}+b\cdot {\sqrt {d-w}}-{\frac {f}{k}}=m}$
${\displaystyle a-(n-3)^{2}+b\cdot {\sqrt {d-w}}-{\frac {f}{k}}=m-b\cdot c\cdot m}$
${\displaystyle a-(n-3)^{2}+b\cdot {\sqrt {d-w}}-{\frac {f}{k}}=m(1-b\cdot c)}$
${\displaystyle m={\frac {(a-(n-3)^{2}+b\cdot {\sqrt {d-w}})\cdot k-{f}}{(1-b\cdot c)\cdot k}}}$
Hoch zum Anfang

### n

${\displaystyle a+b\cdot c\cdot m-(n-3)^{2}+b\cdot {\sqrt {d-w}}-{\frac {f}{k}}=m}$
${\displaystyle (n-3)^{2}=a+b\cdot c\cdot m-m++b\cdot {\sqrt {d-w}}+{\frac {f}{k}}}$
${\displaystyle n-3={\sqrt {a+b\cdot c\cdot m-m++b\cdot {\sqrt {d-w}}+{\frac {f}{k}}\ \ }}}$
${\displaystyle n={\sqrt {a+b\cdot c\cdot m-m++b\cdot {\sqrt {d-w}}+{\frac {f}{k}}\ \ }}\ +3}$

Hoch zum Anfang

### k

${\displaystyle a+b\cdot c\cdot m-(n-3)^{2}+b\cdot {\sqrt {d-w}}-{\frac {f}{k}}=m}$
${\displaystyle {\frac {f}{k}}=a+b\cdot c\cdot m-(n-3)^{2}+b\cdot {\sqrt {d-w}}-m}$
${\displaystyle {k}={\frac {f}{a+b\cdot c\cdot m-(n-3)^{2}+b\cdot {\sqrt {d-w}}-m}}}$

Hoch zum Anfang

### w

${\displaystyle a+b\cdot c\cdot m-(n-3)^{2}+b\cdot {\sqrt {d-w}}-{\frac {f}{k}}=m}$
${\displaystyle b\cdot {\sqrt {d-w}}=m-a-b\cdot c\cdot m+(n-3)^{2}+{\frac {f}{k}}}$
${\displaystyle {\sqrt {d-w}}={\dfrac {m-a-b\cdot c\cdot m+(n-3)^{2}+{\frac {f}{k}}}{b}}}$
${\displaystyle {d-w}={\left({\frac {\left(m-a-b\cdot c\cdot m+(n-3)^{2}\right)\cdot {k}+{f}}{b\cdot k}}\right)}^{2}}$
${\displaystyle {w}=d-{\left({\frac {\left(m-a-b\cdot c\cdot m+(n-3)^{2}\right)\cdot {k}+{f}}{b\cdot k}}\right)}^{2}}$

Hoch zum Anfang