<p>Hi im new to CC and i joined purposely to end my struggle with these types of questions. Any help will be greatly appreciated. thanks!</p>
<ul>
<li>If x is directly proportional to radical y, the y is inversely proportional to:
a) x^2
b) radical x
c) 1 over radical x
d) 1/x
e) 1/x^2</li>
</ul>
<p>The other problem i could use some help on is: x is inversely proportional to y such that when x is 2, y is 1/9. What is the value of y when x is 1/3</p>
<ol>
<li><p>If y is directly proportional to x, then y is directly proportional to x^2. Therefore, y is inversely proportional to 1/x^2</p></li>
<li><p>y=k/x
(1/9)=k/2
k=2/9
y=2/9x
y=2/9(1/3)
y=2/3</p></li>
</ol>
<p>What cortana said is right, though it should’ve been typed y = (2/9)/x. In which case you would divide two ninths by one third and get two thirds. </p>
<p>Inversely proportional means in the relationship of x and y, as x (or y) gets larger y (or x) gets smaller. One goes up, the other goes down. The equation used for this is y =k/x ; k is just the product of y and x in this case and I AM NOT SURE ABOUT THIS PART, but you can think of k kind of like a rate</p>
<p>Directly proportional. You have a relationship between x and y, except as one goes up so does the other, and as one goes down so does the other. The equation would be y= kx.</p>
<p>For the first problem, shouldn’t be C because we don’t know what the radical is, so we can’t just assume it’s square root.</p>
<p>Thanks everyone! With the second problem i eventually came to see that 2 divided by a number gives me 1/3. The number i found to be six. Since i divided there the next step to find y would be 1/9 multiplied by 6 giving me 6/9 or 2/3. Any comments on this method?</p>
<p>Actual work for the first problem</p>
<p>y= k^2 x^2 ( i squared both sides). </p>
<p>y=kx is the form of direct proportionality. The form of INdirect proprotionality is y=k/x.</p>
<p>So we want y=k^2 x^2 in the form of y=k/m, with m in terms of x. Remember that in a fraction, if there is a (1/ something) term in the denominator, the (something) is really in the numerator (simplifying a complex fraction). </p>
<p>So we can rewrite y=k^2 x^2 as </p>
<p>y=k^2/(1/x^2), which is of the form y=k/m with m= 1/x^2. Therefore, y is inversely proportional to 1/x^2.</p>
<p>Hope this helps!</p>