<p>The circle above has center O and diameter AB. The two semicircles have diameters OA and OB. If the circumference of the circle is 36pi, what is the length of the curved path from A to B through O? </p>
<p>A) 6pi
B) 9pi
C) 18pi
D) 24pi
E) 36pi </p>
<p>3,5,-5,... </p>
<p>The first term in the sequence of numbers shown above is 3. Each even-numbered term is 2 more than the previous term and each odd-numbered term, after the first, is -1 times the previous term. For example, the second term is 3+2, and the third term is (-1)*5. What is the 55th term of the sequence? </p>
<p>A) -5
B) -3
C) -1
D) 3
E) 5 </p>
<p>Which of the following has the same volume as the cylinder shown above with radius x and height 2x? </p>
<p>A) A cylinder with radius 2x and height x
B) A cylinder with radius 2pix and height x
C) A cube with edge 2x
D) A cube with edge 2pix
E) A rectangular solid with dimensions x, 2x, and pix </p>
<p>In the figure above, the circle is tangent to sides BC and AD of the 8 by 12 rectangle, ABCD. What is the area of the circle? </p>
<p>Need to see the diagram in order to answer the question I believe.</p>
<p>
</p>
<p>Continue spelling out the sequence to see if there are any patterns:</p>
<p>3, 5, -5, -3, 3, 5, -5, -3, 3, 5, -5, -3</p>
<p>As you can see, the sequence repeats every interval of 4. This means that it ends on the 4th, 8th, 12th, 16th, 20th, 24th, 28th, 32nd, 36th, 40th, 44th 48th, 52nd terms. After the 52nd, it repeats again: </p>
<p>53rd: 3
54th: 5
55th: -5</p>
<p>This long process above can be done by simply dividing 55 by 4. You will get a remainder of 3, so you know the 3rd term in the 4-term repetition is the answer.</p>
<p>Answer is therefore <a href=“A”>b</a> -5**.</p>
<p>
</p>
<p>The area of a cylinder h<em>pi</em>r^2. Since r = x and h = 2x, the area is (2x)<em>pi</em>(x)^2 or:</p>
<p>(2x^3)*pi</p>
<p>Now figure out the areas of the cylinders given in the answer choices:</p>
<p>The formula for finding the circumference of a circle is pi*diameter. So from the fact that circumference of the circle is 36pi, you can tell that its diameter is 36 and as such its radius will be 18.
Also, you can tell from the question that the diameter of each semi-circle will simply be the radius of the circle.
Since there are two semi-circles each having the same diameter, you can join them to form one circle with a diameter of 18.
Hence the length of the curved path from A to B through C will simply be the circumference of the circle formed by joining the two semi-circles to form one circle.
Thus the answer is 18pi</p>