# Y varies directly as the square of x

• Sep 29th 2011, 10:23 AM
FailInMaths
Y varies directly as the square of x
Question:
Given that $\displaystyle y$ varies directly as the square of $\displaystyle x$ and that $\displaystyle y=12$ when $\displaystyle x=2$, find
(a) the equation relating $\displaystyle x$ and $\displaystyle y$
(b) the values of $\displaystyle x$ when $\displaystyle y=-27$

My solution: (a)

$\displaystyle y=k(x^2)$
$\displaystyle k=y/x^2$
$\displaystyle =12/2^2$
$\displaystyle =12/4$
$\displaystyle =3$
$\displaystyle y=3x^2$

(b)

$\displaystyle -27=3x^2$
$\displaystyle x^2=-27/3$
$\displaystyle =-9$
$\displaystyle x= ?$

How do I solve for (b)?

Thanks
• Sep 29th 2011, 11:36 AM
Quacky
Re: Y varies directly as the square of x
This is annoying me because I can't see a mistake with your work. Is that *exactly* the wording of the question? I mean, I honestly doubt you're expected to put $\displaystyle x=\pm 3i$ as your answer.
• Sep 29th 2011, 11:49 AM
FailInMaths
Re: Y varies directly as the square of x
Quote:

Originally Posted by Quacky
This is annoying me because I can't see a mistake with your work. Is that *exactly* the wording of the question? I mean, I honestly doubt you're expected to put $\displaystyle x=\pm 3i$ as your answer.

Yeah, every detail of the question is stated here. Got to agree with you, but that answer you gave is about Imaginary number?
• Sep 29th 2011, 11:51 AM
Quacky
Re: Y varies directly as the square of x
Quote:

Originally Posted by FailInMaths
Yeah, every detail of the question is stated here. Got to agree with you, but that answer you gave is about Imaginary number?

Yes, and this doesn't seem to be the sort of question that would involve imaginary numbers.