Question

Write an equation describing the relationship of the given variables Y varies directly as the square root of x and when x=81, y=45

Answer 1

Step 1:

`\begin{gathered} If\text{ y varies directly as square root of x.} \\ We\text{ have,} \\ y\text{ }\propto\sqrt[]{x} \end{gathered}`

Step 2:

Plug in constant k to change the proportionality sign into an equal sign.

`\begin{gathered} y\text{ }\propto\sqrt[]{x} \\ y=k\sqrt[]{x} \end{gathered}`

Step 3:

Substitute the values of x = 81 and y = 45 to find the value of constant k.

`\begin{gathered} \text{y = k}\sqrt[]{x} \\ 45\text{ = k}\sqrt[]{81} \\ 45\text{ = 9k} \\ \text{Divide both sides by 9 to find the value of k.} \\ k\text{ = }(45)/(9) \\ k\text{ = 5} \end{gathered}`

Step 4:

Write an equation describing the relationship of the given variables.

`\begin{gathered} \text{y = k}\sqrt[]{x} \\ y\text{ = 5}\sqrt[]{x} \end{gathered}`

Final answer

`\text{y = 5}\sqrt[]{x}`