Since the variation is direct, then we have an equation of the form:
[tex]y = kx ^ 2
[/tex]
From here, we must find the value of k.
For this, we use the following data:
y = 245 when x = 7
Substituting values we have:
[tex]245 = k7 ^ 2
[/tex]
Rewriting we have:
[tex]245 = 49k
[/tex]
Clearing k we have:
[tex]k = \frac{245}{49} [/tex]
[tex]k = 5
[/tex]
Therefore, the equation is given by:
[tex]y = 5x ^ 2
[/tex]
Evaluating the equation for x = 9 we have:
[tex]y = 5 (9) ^ 2
y = 5 (81)
y = 405[/tex]
Answer
The value of y when x = 9 is:
[tex]y = 405[/tex]
