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Kalkulator wariancji bezpośredniej, odwrotnej i wspólnej

Obliczanie wariacji bezpośrednich, odwrotnych i łączonych krok po kroku

Kalkulator znajdzie stałą zmienności i inne wartości dla bezpośredniego, odwrotnego (pośredniego), wspólnego i połączonego problemu zmienności, z pokazanymi krokami.

varies
as the power of of `
as the power of of `
as the power of of
Write here the 'find `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.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

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 $$$k=\frac{21}{25}$$$, $$$y=\frac{7}{100}$$$.