Question

Find y when x=9 if y varies directly as the square of x, and y=100 when x=5.

Answer 1

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 2

324

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

`\Rightarrow y \propto x^2`

So,
`\Rightarrow y= kx^2` ---1

where k is the constant of proportionality

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

Substitute the values in 1

`100= k(5)^2`

`100= 25k`

`(100)/(25)=k`

`4=k`

So, equation becomes
`y= 4x^2`

Now substitute x= 9

`y= 4(9)^2`

`y=324`

Hence The value of y when x is 9 is 324