Question

Find the constant of variation and the variation equation.y varies directly as the square root of x; y=3.0 when x=25

Answer 1

In this case the answers is very simple . .

We must analyze the question and write the corresponding equation.

Direct variation equation is:

`\begin{gathered} y\text{ = k }\cdot\sqrt[]{x} \\ y\text{ = 3 when} \\ x\text{ = 25 } \\ y\text{ = k }\cdot\text{ }\sqrt[]{x} \\ 3\text{ = k }\sqrt[]{25} \end{gathered}`
`\begin{gathered} \frac{3}{\sqrt[]{25}}=\text{ k } \\ (3)/(5)=\text{ }k \end{gathered}`

The answer is:

The constant of variation k is 3/5 = 0.6