Mathematrix: Aufgabenbeispiele/ Komplexe Umformungen

A) ${\sqrt {p}}+c_{L}\cdot {\frac {m\cdot v^{2}}{2\cdot k_{B}\cdot T}}-{\frac {t-s}{w-z}}=2,2$
Formen Sie diese Formel auf z, m, v, T, p, t, s, k_B, c_L um!

B) $a+b\cdot c\cdot m-(n-3)^{2}+b\cdot {\sqrt {d-w}}-{\frac {f}{k}}=m$
Formen Sie diese Formel auf a, b, c, f, m, n, k, w um!

A

z

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

Hoch zum Anfang

m

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

Hoch zum Anfang

v

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

Hoch zum Anfang

T

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

Hoch zum Anfang

p

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

Hoch zum Anfang

t

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

Hoch zum Anfang

s

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

Hoch zum Anfang

kB

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

Hoch zum Anfang

cL

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

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

Hoch zum Anfang

B

aa

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

Hoch zum Anfang

be

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

Hoch zum Anfang

c

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

f

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

em

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

n

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

Hoch zum Anfang

k

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

Hoch zum Anfang

w

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

Hoch zum Anfang