Calcolatore di variazioni dirette, inverse e congiunte

La calcolatrice troverà la costante di variazione e altri valori per i problemi di variazione diretta, inversa (indiretta), congiunta e combinata, con i passaggi indicati.

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

Calcolatore di variazioni dirette, inverse e congiunte

Calcolo delle variazioni dirette, inverse e congiunte passo per passo

Solution