Respuesta :

coolstick
If y varies directly as the square of x, that means that y=k*x^2. Plugging y=100 and x=5 into it, we get 100=k*5^2=k*25. Dividing by both sides, we get k=100/25=4. Going back to the original equation, we now know that y=4*x^2. Plugging 9=x in, we get 4*9^2=4*81=324=y

Answer:

324

Step-by-step explanation:

Given : y varies directly as the square of x

To Find : Find y when x=9

Solution :

We are given that y varies directly as the square of x

[tex]\Rightarrow y \propto x^2[/tex]

So, [tex]\Rightarrow y= kx^2[/tex] ---1

where k is the constant of proportionality

Now we are also given that y=100 when x=5.

Substitute the values in 1

[tex]100= k(5)^2[/tex]

[tex]100= 25k[/tex]

[tex]\frac{100}{25}=k[/tex]

[tex]4=k[/tex]

So, equation becomes  [tex]y= 4x^2[/tex]

Now substitute  x= 9

[tex]y= 4(9)^2[/tex]

[tex]y=324[/tex]

Hence The value of y when x is 9 is 324

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