# Regarding direct proportions

• Jan 1st 2010, 11:55 PM
juliak
Regarding direct proportions
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...
• Jan 2nd 2010, 12:23 AM
Hello juliak
Quote:

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 $\displaystyle y = \tfrac92$:
$\displaystyle \tfrac92=\tfrac12x^2$

$\displaystyle \Rightarrow x^2 = 9$

$\displaystyle \Rightarrow x = 3$
• Jan 2nd 2010, 12:25 AM
earboth
Quote:

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...

If y is directly proportional to x² both values have to satisfy the equation:

$\displaystyle y = k \cdot x^2$

for a certain proportionality factor k.

You know

$\displaystyle \frac18 = k \cdot \left( \frac12 \right)^2$

Solve for k.

Then plug in $\displaystyle y = \frac92$ into the equation and solve for x.
• Jan 2nd 2010, 03:10 AM
HallsofIvy
Quote:

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...

Because, just as "1/4" was x^2= (1/2)^2 so is this 9= x^2. You need to take the square root to get x.