Calculadora de Variação Direta, Inversa e Conjunta

Calcule variações diretas, inversas e conjuntas passo a passo

A calculadora encontrará a constante de variação e outros valores para problemas de variação direta, inversa (indireta), conjunta e combinada, com etapas mostradas.

varies

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 $$$y=k x$$$, $$$y=5$$$ when $$$x=2$$$ and find $$$x$$$ when $$$y=3$$$.

We have that $$$y=k x$$$.

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

Solving this equation, we obtain that $$$k=\frac{5}{2}$$$.

Now find $$$x$$$.

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

From this equation, we have that $$$x=\frac{6}{5}$$$.

Answer: the constant of variation is $$$k=\frac{5}{2}$$$, $$$x=\frac{6}{5}$$$.