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