Question

Y is inversely proportional to the square root of x. True or False: If Y = 7 when x = 49, thenthe constant of variation is 343.O TrueO False

Answer 1

Recall the inverse proportionality relationship: If m is inversely proportional to n, then the relationship is:

`m\propto(1)/(n)`

Substitute y and √x for m and n respectively in the relationship:

`y\propto(1)/(√(x))`

Applying a constant of proportionality, k, the relationship becomes:

`\begin{gathered} y=(k)/(√(x)) \\ \therefore \\ k=y√(x) \end{gathered}`

The question gives the following values for x and y:

`y=7,x=49`

Substituting these into the equation for k, the value of k can be gotten to be:

`\begin{gathered} k=7*√(49)=7*7 \\ k=49 \end{gathered}`

The constant of proportionality is 49.

The correct answer is FALSE.