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...

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- Jan 1st 2010, 11:55 PMjuliakRegarding 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 AMGrandad
Hello juliakTranslate the phrase "$\displaystyle y$ is directly proportional to $\displaystyle x^2$" in symbols as:

$\displaystyle y = kx^2$, where $\displaystyle k$ is a constantThen plug in the two values that you've been given:

When $\displaystyle y = \tfrac18, x= \tfrac12$. So:

$\displaystyle \tfrac18=k(\tfrac12)^2$So the equation is:$\displaystyle =\tfrac14k$$\displaystyle \Rightarrow k = \tfrac12$

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

$\displaystyle \tfrac92=\tfrac12x^2$Grandad

$\displaystyle \Rightarrow x^2 = 9$

$\displaystyle \Rightarrow x = 3$

- Jan 2nd 2010, 12:25 AMearboth
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 AMHallsofIvy