Hello juliak Originally Posted by
juliak If y is directly proportional to x^2 and y=1/8 when x=1/2, what is the positive value of x when y=9/2?
a) 3/4
b) 3/2
c) 9/4
d) 3
e) 9
what i did:
y: 1/8
x^2: 1/4
1/8 * 36 = 9/2
therefore
1/4 * 36 = 9
but the answer is 3, not 9...
Translate the phrase "$\displaystyle y$ is directly proportional to $\displaystyle x^2$" in symbols as:
$\displaystyle y = kx^2$, where $\displaystyle k$ is a constant
Then plug in the two values that you've been given:
When $\displaystyle y = \tfrac18, x= \tfrac12$. So:
$\displaystyle \tfrac18=k(\tfrac12)^2$$\displaystyle =\tfrac14k$
$\displaystyle \Rightarrow k = \tfrac12$ So the equation is:
$\displaystyle y = \tfrac12x^2$
When $\displaystyle y = \tfrac92$:
$\displaystyle \tfrac92=\tfrac12x^2$
$\displaystyle \Rightarrow x^2 = 9$
$\displaystyle \Rightarrow x = 3$
Grandad