Given:
y is directly proportional to the square root of x.
y = 42 when x = 9
To find:
x when y = 28.
Solution:
We have,
y is directly proportional to the square root of x.
[tex]y\propto \sqrt{x}[/tex]
[tex]y=k\sqrt{x}[/tex] ...(i)
where, k is the constant of proportionality.
We have, y = 42 when x = 9.
[tex]42=k\sqrt{9}[/tex]
[tex]42=3k[/tex]
[tex]\dfrac{42}{3}=k[/tex]
[tex]14=k[/tex]
Putting k=14 in (i), we get
[tex]y=14\sqrt{x}[/tex]
Putting y=28, we get
[tex]28=14\sqrt{x}[/tex]
[tex]\dfrac{28}{14}=\sqrt{x}[/tex]
[tex]2=\sqrt{x}[/tex]
Taking square on both sides.
[tex]2^2=x[/tex]
[tex]4=x[/tex]
Therefore, the value of x is 4 when y=28.
