Step-by-step explanation:
Since [tex]x[/tex] varies directly as [tex]\sqrt{y}[/tex] we can write the relation as
[tex]x = k\sqrt{y}[/tex]
where k is the constant of proportionality.
a) To solve for the k, we substitute the given values:
[tex]5 = k\sqrt{13} = k(13)[/tex]
[tex]\Rightarrow k = \dfrac{5}{13}[/tex]
b) The equation relation x and y can be written as
[tex]x = \dfrac{5}{13}\sqrt{y}[/tex]
c) When y = 9,
[tex]x = \dfrac{5}{13}\sqrt{9} = \dfrac{5}{13}(3) = \dfrac{15}{13}[/tex]
