Question

Suppose that y varies directly as the square root of x, and that y = 45 when x = 196. What is y when x = 83? Round your answer to two decimal places if necessary

Answer 1

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form

y=kx

In this problem we have

`y=k√(x)`

we have that

For y=45 x=196

step 1

calculate the constant of proportionality k

substitute the value of y and the value of x in the expression above

`\begin{gathered} 45=k√(196) \\ 45=k(14) \\ k=(45)/(14) \end{gathered}`

step 2

we have the expression

`y=(45)/(14)√(x)`

step 3

For x=83

substitute

`\begin{gathered} y=(45)/(14)√(83) \\ y=29.28 \end{gathered}`