Rechner für direkte, inverse und gemeinsame Variation

Der Rechner ermittelt die Variationskonstante und andere Werte für direkte, inverse (indirekte), gemeinsame und kombinierte Variationsprobleme, wobei die Schritte angezeigt werden.

varies

as the power of of

Write here the 'find

$\displaystyle{\large{{k}}}$ ' condition. For example, write x=3, y=5, z=15, if you are given "z=15, when x=3, y=5".

Write here the 'find variable' condition. For example, write y=2, z=10, if you are given "find x, when y=2, z=10".

If you don't need to find a variable, leave this field empty.

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Solution

Your input: find the constant of variation $k$ given $z=k \frac{x^{2}}{y}$ , $z=7$ when $x=5$ and $y=3$ and find $y$ when $z=12$ and $x=1$ .

We have that $z=k \frac{x^{2}}{y}$ .

Plug in the given values to find $k$ : $7=k \cdot \frac{5^{2}}{3^{1}}$ .

Solving this equation, we obtain that $k=\frac{21}{25}$ .

Now find $\mathtt{\text{y}}$ .

Plug in the given values and found $k$ to find $y$ : $12=\frac{21 \frac{1^{2}}{y^{1}}}{25}$ .

From this equation, we have that $y=\frac{7}{100}$ .

Answer: the constant of variation is $k=\frac{21}{25}$ , $y=\frac{7}{100}$ .

Rechner für direkte, inverse und gemeinsame Variation

Berechnung von direkten, inversen und gemeinsamen Variationen Schritt für Schritt

Solution