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

$y=k\sqrt{x}$

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

$\begin{gathered} 45=k\sqrt{196} \\ 45=k(14) \\ k=\frac{45}{14} \end{gathered}$

step 2

we have the expression

$y=\frac{45}{14}\sqrt{x}$

step 3

For x=83

substitute

$\begin{gathered} y=\frac{45}{14}\sqrt{83} \\ y=29.28 \end{gathered}$