Respuesta :
Since y varies directly with square root x, so
[tex]y=k\sqrt{x}[/tex]k is the constant of variation
We will find it using the initial values of x and y
Since the initial values are:
y = 49
x = 49
Substitute them in the rule to find k
[tex]\begin{gathered} 49=k\sqrt{49} \\ 49=k(7) \\ 49=7k \\ \frac{49}{7}=\frac{7k}{7} \\ 7=k \end{gathered}[/tex]The value of k is 7, so the equation will be
[tex]y=7\sqrt{x}[/tex]We need to find the value of y at x = 128, so
Substitute x in the rule by 128
[tex]\begin{gathered} y=7\sqrt{128} \\ y=56\sqrt{2}=79.1959595 \end{gathered}[/tex]Round it to two decimal places, so
y = 79.20
