Calculadora de variación directa, inversa y conjunta

Calcule variaciones directas, inversas y conjuntas paso a paso

La calculadora encontrará la constante de variación y otros valores para los problemas de variación directa, inversa (indirecta), conjunta y combinada, con pasos mostrados.

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.

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