<p>If x doesn't equal zero and x is inversely proportional to y, which of the following is directly proportional to (1/x^2)</p>
<p>(a) -(1/y^2)
(b) (1/y^2)
(c) (1/y)
(d) y
(e) y^2</p>
<p>please explain!</p>
<p>Alright, I got E.</p>
<p>x = 1/y since it’s inversely proportional.
xy = 1, multiply by y
y = 1/x, divide by x
y^2 = 1/x^2, square both sides</p>
<p>Someone please correct me if I made a mistake here.</p>
<p>P.S. I know it should be x = k/y, but the constant can be ignored in this problem.</p>
<p>I got E as well. But just substituted ‘1/y’ for x.</p>
<p>why did you think to do that?^^</p>
<p>also, new account, how does doing that make it directly proportional to (1/x^2)? im pretty confused right now…</p>
<p>Directly proportional means a=kb, where k is a constant.</p>
<p>Since inversely proportional means a = k/b, where k is a constant, I just took k out of the equation completely. This left me with a = 1/b, or x = 1/y. I went on to manipulate the equation to get 1/x^2 on one side, as the problem was looking for. This was equal to y^2. </p>
<p>Again, the problem was looking for a direct proportionality, so we want a = kb, but recall that I got rid of k completely, so we want a = b. Our a is y^2 and our b is 1/x^2. We proved that these are equal. So E is the answer.</p>
<p>thanks, that makes sense now. Could you still do it without getting rid of k? because i dont think i would’ve thought to do that</p>
<p>Sure. Follow me here. I’m using the same steps as I did earlier.</p>
<p>x = k/y
xy = k
y = k/x
y^2 = k^2/x^2</p>
<p>Direct proportionality: a = kb, where a = y^2 and b = 1/x^2. To make it easier to see:
y^2 = (k^2)(1/x^2)</p>
<p>Should make sense…</p>
<p>
</p>
<p>Some of the answer choices had ‘1/something’ so I just assumed that k was nonexistent in the answer. Saw “directly proportional” and knew that they wanted “1/x^2” in terms of y.</p>
<p>that makes sense, thanks for the help guys</p>
<p>Was this a CB problem?</p>
<p>e
x=k*(1/y) k is a constant</p>
<p>x^2=k*[(1/y)^2]</p>
<p>the Q is asking for k(1/x^2) in terms of y</p>
<p>so k(y^2),eliminate k,answer is y^2</p>