<p>If x is directly proportional to (radical y), then y is INVERSELY proportional to</p>
<p>a) x squared
b) radical x
c) 1 divided by (radical x)
d) 1 divided by x
e) 1 divided by (x squared)</p>
<p>I tried looking at the answer explanation, and the correct answer was e, but it wasn't too great. Help?</p>
<p>x = root y (k)</p>
<p>That means root y = x (k)</p>
<p>That means y = x^2 (k)</p>
<p>But we want inverse proportion.</p>
<p>So y = 1/x^2 (k)</p>
<p>Therefore, y is inversely proportional to 1/x^2. E. Make any sense, or shall I elaborate further?</p>
<p>x is directly proportional to radical Y
so therefore radical Y must equal X squared .
1/x is ALWAYS inversley proportional to any number that doesn’t have anything done to it (like squared, square rooted, etc)
so 1/xsquared is inversley relayed to radical Y</p>
<p>Its kind of give and take, not much more explanation to be done. Just remember the 3rd step, and a lot of the Algebraic concepts.</p>
<p>SirWanks and Jokers - you both have some algebraic errors (although your answers are correct). Here is a correct solution:</p>
<p>x=ksqrt(y) </p>
<p>x^2=k^2 * y</p>
<p>1/k^2=1/x^2 * y</p>
<p>So (E) is the answer</p>
<p>Quicker alternate solution: </p>
<p>sqrt(y)/x = k</p>
<p>y*1/x^2 = k^2</p>
<p>Remarks:</p>
<p>(1) y directly proportional to y means y=kx for some constant x, or equivalently y/x=k for some constant x. In words, the quotients y/x always give the same number. Graphically you get a line through the origin.</p>
<p>(2) y inversely proportional to x means y=k/x, or equivalently xy=k. In words, the products xy always give the same number. Graohically you get a hyperbola.</p>