<p>So, I just did a practice test, one particular problem that I had trouble with was:</p>
<li>If x does not equal 0, and x is inversely proportional to y, which of the following is directly proportional to 1/(x^2)?</li>
</ol>
<p>A. -1/(y^2)
B. 1/(y^2)
C 1/y
D y
E y^2</p>
<p>Any help would be much appreciated :)</p>
<p>E?! if its e ill tell you want i did</p>
<p>yeah that's the answer</p>
<p>hmm, for some reason this one was weird for me.
what I tried to do was. x = k/y, then substitute (k/y) into 1/x^2
making it 1/(k/y)^2, solving for that yields Y^2/K^2</p>
<p>Is that how you solve it? I guess I was confused by the K...</p>
<p>ugh can someone do it? i know the formula is y=k/x but i don't know why. what do you do to get the answer from that?</p>
<p>none of the answers matched mine, why's this =S? even substitution doesnt work, now im doubting the question itself lol..</p>
<p>lol, it's a legitimate question, I assure you hahahaha.</p>
<p>But substitution gives me y^2/K^2 = 1/x^2</p>
<p>^I guess that seems right seeing as I got y^2 (the answer), but the k^2 is throwing me off.</p>
<p>One way to approach this is to know that if X increases, y decreases. x^2/1 will increase as x increases, but 1/y^2 wuld increase as well since y is decreasing. But thats inverse and we want direct poroportions. So 1/y^2 must somehow decrease. Only y^2 achieves that.</p>
<p>or</p>
<p>x=y^-1 or x/1=1/y
x^2= 1/y^2 = iversely poroportional. <- notice how this is in the form x= k/y </p>
<p>We want direct poroportions, thus we can just reverse the 1/y^2 to y^2/1 .
since (X^2)^-1 = 1/x^2 so -1x1/y^2 = -1/y^2 = y^2 .</p>
<p>Edit: K is the constant, in this case, 1.</p>
<p>^what happened to the K?</p>
<p>Just wondering, but from what book is this problem?</p>
<p>?/? i dont understand, i got something like shiomi's y^2/K^2 = 1/x^2, then im stucked.
i understand quix's way,but what makes u so sure that K=1? this is unsafe lol i dont like substitution.. how about we try plugging in some numbers:
Let x=2, y=3, so K=6
1/(4) would be .25
so y would be 24.</p>
<p>pluggin into E,Y^2 = 3^2= 9??
somethings wrong lol..</p>
<p>K is the CONSTANT . K is 1...</p>
<p>Besides, you don't even have to use the equation. Read the beginning of my post.</p>
<p>simple. They are inversely proportionate. </p>
<p>so 1/X = Y/1
Imagine this, 1/2 = .5/1
so as X increases, y decreases.
Legitimate?
so try x^2 as the question demands
1/4 = .25/1</p>
<p>so what happened? As you squared x, you also squared y. .5^2 = .25</p>
<p>therefore, 1/x^2 = y^2/1 (bingo, answer choice E)</p>
<p>get it?</p>
<p>Compare with <a href="http://talk.collegeconfidential.com/sat-preparation/459596-quick-math-question.html%5B/url%5D">http://talk.collegeconfidential.com/sat-preparation/459596-quick-math-question.html</a>.</p>
<p>If x does not equal 0, and x is inversely proportional to y, which of the following is directly proportional to 1/(x^2)?</p>
<p>kx = 1/y
k^2.y^2 = 1/x^2</p>
<p>So y^2 is directly proportional to (1/x^2)</p>
<p>a constant is a constant, no matter raised to what constant power.</p>