Question

Write an equation describing the relationship of the given variables. y varies directly as the square root of x. When x=16 then y=4. Find y when x=36.The value for y is:Answer

Answer 1

6

Explanation:

Given:

When x = 16, y = 4

We know that it varies directly with the square root of x, so we can state the following:

`y=k\cdot\sqrt[]{x}`

We substitute and calculate k, just like this:

`\begin{gathered} 4=k\sqrt[]{16} \\ k=\frac{4}{\sqrt[]{16}} \\ k=(4)/(4)=1 \\ \text{ Therefore, the function is} \\ y=\sqrt[]{x} \end{gathered}`

Now, we calculate the value of y when x = 16 substituting in the function obtained, just like this:

`\begin{gathered} y=\sqrt[]{36} \\ y=6 \end{gathered}`

The value of y is 6