<p>Click the link. I drew it out and everything for better understanding.</p>
<p>The answer is E right?
I'm not so sure.</p>
<p>i dont know if i did this right, but i came up to answer choice E also.</p>
<p>lets say r=2
since all circles are in proportion.</p>
<p>2 = 6
5 = x</p>
<p>x would equal (6 x 5)/2 = 15.
plug 2 into the answer choices, only E gives you 15.
(6(2)+18)/2=15</p>
<p>someone confirm this?</p>
<p>I get e also, with proportional reasoning:</p>
<p>arc length/circumference = arc length/circumference</p>
<p>6 / 2(pi)(r) = x / 2(pi)(r+3)</p>
<p>cancel out the 2pi in both denominators;</p>
<p>6/r = x/(r+3)</p>
<p>multiply both sides by (r+3) to isolate x</p>
<p>6(r+3)/r = x</p>
<p>yay I was right.
wooot</p>
<p>I get: a) 9
n/360x2(Pi)r=6, therefore n/360x2(Pi)(r+3)=6+(3), or n/360x2(pi)(r+3)=9</p>
<p>What does "n" stand for in your equations?</p>
<p>when you isolate x, you should get 6+(18/r)=x
Starting at the step where the 2 pi is canceled out:
1.6/r = x/(r+3)
2.6(r+3)=x(r)
3.6r+18=x(r)
4.(6r/r)+(18/r)=x
5.6+(18/r)=x</p>
<p>As you can see that is not an answer choice.</p>
<p>n=central angle</p>
<p>Well, SAT Q's way is somewhat more tortuous, but still viable.</p>
<p>( n / 360 ) * ( 2 * pi * r ) = 6
( n / 360 ) * ( 2 * pi * ( r + 3 ) ) =
( n / 360 ) * ( 2 * pi * r + 6 * pi ) =
6 + ( n * pi / 60 ) </p>
<p>However, since the central angle isn't given as a variable, no answer choice corresponds to that method. The correct answer is E.</p>
<p>Its definitely E...</p>
<p>you do not need the central angle, the formula for arc length is n/360x2(Pi)r, since the problem already gives you the arc length, you know the equation is equal to 6, you do not need the measure of the central angle, now if you apply this formula along with reasoning you can find the arc length of x, since that is exactly what it asks for. So far no one has proved that it is E.</p>
<p>How is it definitely E? Where is you're definite method?</p>
<p>I got E...that proportionality thing in #3 is what I did.</p>
<p>What are you talking about? In your one equation, you have two unknowns: the central angle and the radius. You're right that you don't need the central angle, but you're using the wrong approach. As several people have stated, you must use proportions; knowing that the central angle is the same in both circles, you can deduce that the arc lengths are proportional to the radii.</p>
<p>x / 6 = ( r + 3 ) / r
x = ( 6r + 18 ) / r</p>
<p>The value of x can take on several values; if you doubt it, you can try visualizing it this way. Shrink the smaller circle to half its current size and enlarge the central angle so that the arc length is still 6. Now extend the lines that define the arc by 3 in each direction. Does the length of the second arc change when you apply this transformation? Yes. In fact, the second arc can take on any value in the interval (6, 6 + 6 * pi).</p>
<p>...Ok radius for new cirlce is r+3, You follow? Now the formula for arc length is n/360x2(pi)r, Still with me? Ok now plug in the radius to the arc length equation, now the arc length of the New circle with the radius (r+3) is equal to x, the original arc length is equal to 6, the only difference is the addition of the 3, now if you add that 3 to the 6 you get 9.</p>
<p>Just because the radius larger by 3 doesn't mean the arc is also larger by 3. That's your error.</p>
<p>hey OP, whats the answer.
lol, save us the arguments :D</p>
<p>Begoner is right, arc length = radius x angle.
so it would be impossible to +3 the radius and have the arc +3.</p>
<p>The central angle is 1080/(pi) r</p>
<p>so 1080/(pi) r /360 x 2 pi (r + 3)
3/pi r x 2pi (r + 3)
cancels the pi's you get</p>
<p>3/r x 2(r +3)
6(r + 3)/r or 6r + 18/r</p>
<p>Yes the answer is definitely E.</p>
<p>n/360<em>2(Pi) r =6
n/360</em>2(pi) (r+3)=9
s=r(theta)
6=r(theta)
6+3=(r+3)(theta)
9=(r+3) (theta)</p>
<p>overanalyzing this **** WAY too ****ing much guys..
r/6 = r+3/x
xr = 6r+18
x = 6r+18/r
therefore choice E.</p>