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Find y when x=9 if y varies directly as the square of x and y=245 when x=7

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carlosego
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]
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