<p>xr=6r+18
x=6r/r +18/r
x=6+18/r...not an answer choice</p>
<p>Is that question from a SAT?</p>
<p>Well that's a simplified version.. 6+(18/r) = (6r+18)/r</p>
<p>I got E also.</p>
<p>The length of arc is s = (theta)(r)</p>
<p>length of smaller arc:
6 = (thata)(r)
therefore r = 6/theta</p>
<p>length of bigger arc:
x = (theta)(r+3)
x = theta[(6/theta)+3] substitute 6/theta for r
x = 3(theta+2)</p>
<p>Substitute 6/theta for r in (6r+18)/r (choice E)
Which gives the expression: (6*(6/theta)+18)/(6/theta) = 3(theta+2) = x
Therefore the answer is E.</p>
<p>I don't know the answer lol
It was like #20 on an old PSAT so i figured it was a question of hard difficulty. But since i got an answer so quickly i was doubful. So i decided to ask you guys.</p>
<p>For those who are getting 6+18/r, that IS an answer choice; it's equal to (6r+18)/r, which is E.</p>
<p>Here's another way to think about the problem. This is how I would check my answer if I were doing this on a test:
When r is very large, the sector that cuts off an arc length of 6 becomes very small. A arc of a circle subtending a very small angle is <em>almost</em> a straight line. So that region outside the circle (bounded by segments of length 3 and arcs of length 6 and x) is almost rectangular. Thus x must be very close to 6 as r becomes very large. The only answer choice that behaves like that is E.</p>
<p>^ interesting method. I would've never have thought of looking at it like that. :)</p>
<p>It's often a convenient way of doing multiple choice math tests. You can usually eliminate some of the answers on the grounds that they just can't be the answer. In this case, you can eliminate all but one of them. It's still a good idea to run the numbers and make sure the remaining one is actually right (instead of just checking that the others are all wrong), but if you're short on time or want to confirm your answer, that method works well.</p>
<p>newsflash "SAT Questions" - 6r+18/r is choice E.
no need to simplify any further as you did.</p>