<p>If x is directly proportional to (y)^.5, then y is inversely proportional to ?
a.x^2
b.X^5.5
c.1/x^.5
d.1/x
e.1/x^2</p>
<p>I am horrible with directly/inverse, whats the best way to tackle these problems?</p>
<p>“a is directly proportional to b” is equivalent to
a/b=const,
and also is equivalent to
b/a=const;
if a=0 then b=0, and vice versa; const means constant.</p>
<h1>“a is inversely proportional to b”: ab = const (a and b not=0).</h1>
<p>y^.5/x = const
square both sides
y/x^2 = const
y(1/x^2) = const
y is inversely proportional to 1/x^2.</p>
<p>Note that const may be a different constant in some equations:
y^.5/x = k
y/x^2 = k^2
y(1/x^2) = k^2</p>
<p>umm i sorta didn’t understand that… anyone else mind explaining it in a diff way?</p>
<p>[Mathwords:</a> Direct Variation](<a href=“http://www.mathwords.com/d/direct_variation.htm]Mathwords:”>Mathwords: Direct Variation)</p>
<p>[Mathwords:</a> Inverse Variation](<a href=“http://www.mathwords.com/i/inverse_variation.htm]Mathwords:”>Mathwords: Inverse Variation)</p>
<p>If thing 1 varies directly with thing 2, you can say thing 1 = constant times thing 2.</p>
<p>So in this case: x = constant times y^.5</p>
<p>If you square both sides: x^2 = constant times y [not the same constant but still a constant]</p>
<p>So y varies DIRECTLY with x^2. But they want to know what y varies INVERSELY with –</p>
<p>if y = constant times x^2 it also = constant / (1/x^2) so the answer is e.</p>
<p>i see. so after coming up with y=x^2k because it varies inversely, you just do y=k/x^2?</p>
<p>When you have y = kx^2, you know y varies DIRECTLY with x^2.</p>
<p>But the problem wants to know what y varies INVERSELY with. </p>
<p>Inverse variation is in the form y = k/something rather than y = k times something. To take y= k times x^2 and make it look like y = k/something, we can just take the reciprocal of the something…</p>
<p>y = k x^2 and y = k/(1/x^2) are equivalent. But you have to write it the second way if your goal is to come up with something that varies inversely with y.</p>
<p>I hope that makes sense. It is an annoying problem with no point at all outside of the SAT world. (I’m not saying inverse and direct proportions are not important – I teach physics! – I’m just saying that in real life, you would express the relationship as simply as possible. But this is the SAT…)</p>
<p>mmm but isn’t y=k/(1/x^2) = y=kx^2? or am i doing something wrong?</p>
<p>Yes, they are the same…so we can say one of two things that are equivalent:</p>
<p>y varies directly with x^2</p>
<p>y varies inversely with 1/x^2</p>
<p>Mathematically, those two statements are interchangeable. It just so happens that this particular question is asking about what y varies inversely with…even though that way of describing the relationship is more cumbersome, it is the one that they want.</p>
<p>I got choice (E). I did it in my head so I could be wrong.</p>
<p>ahh i think i got it. thanks for your help pckeller! and greed that’s correct. what was your method?</p>
<p>x ~ y^.5 (the “~” indicates proportionality)
y ~ x^2</p>
<p>Y is inversely proportional to 1/x^2</p>