directly proportional variation question, ...suppose "y" is directly proportional to the second power of "x".

Question

suppose "y" is directly proportional to the second power of "x". if "x" is halved, what happens to "y"? considering that the constant proportionality is positive. thanks for the help.

Answer 1

Hi,

So if y is proportional to x^2

y= ax^2 where a is some constant of proportionality

so if we change x to x/2, the new relationship (y') is

y'= a(x/2)^2 = (ax^2)/4

so y' is 1/4 as large as y.

Hope that helps,
Matt

Answer 2

Your verbal statement turns into the following:

y = kx^2

If you replace x with (1/2x) you get

y' = k * 1/4 x^2

So, the new y' is 1/4 of the old y. Thus, halving x multiplies y by 1/4.

Answer 3

If y prop to x^2, then apply the 1/2 to x --> (x/2)^2 = (1/4)x^2.

To preserve the proportionality:

Apply the 1/4 to both sides, meaning you apply as follows:
y --> (1/4)y, so y/4 is prop to (x/2)^2.

Answer 4

I answered one of your questions tonight. I've noticed that you are having trouble understanding Direct Variation.

I found a site that will help to clear things up for you.

Go to:

http://regentsprep.org/Regents/Math/math-topic.cfm?TopicCode=variation

Guido

Answer 5

well, y= x^2

so y will be made less by 1/4