MathDB

19

Part of 2002 AMC 10

Problems(3)

Spot rebelling against his leash

Source: AMC 2002 10A Problem 19

2/11/2008
Spot's doghouse has a regular hexagonal base that measures one yard on each side. He is tethered to a vertex with a two-yard rope. What is the area, in square yards, of the region outside of the doghouse that Spot can reach? (A) 2π/3(B) 2π(C) 5π/2(D) 8π/3(E) 3π \text{(A)}\ 2\pi/3 \qquad \text{(B)}\ 2\pi \qquad \text{(C)}\ 5\pi/2 \qquad \text{(D)}\ 8\pi/3 \qquad \text{(E)}\ 3\pi
geometryAMC
Arithmetic Sequence

Source:

2/27/2008
Suppose that {an} \{a_n\} is an arithmetic sequence with a_1 \plus{} a_2 \plus{} \cdots \plus{} a_{100} \equal{} 100 \text{and}  a_{101} \plus{} a_{102} \plus{} \cdots \plus{} a_{200} \equal{} 200. What is the value of a_2 \minus{} a_1?
<spanclass=′latex−bold′>(A)</span> 0.0001<spanclass=′latex−bold′>(B)</span> 0.001<spanclass=′latex−bold′>(C)</span> 0.01<spanclass=′latex−bold′>(D)</span> 0.1<spanclass=′latex−bold′>(E)</span> 1 <span class='latex-bold'>(A)</span>\ 0.0001 \qquad <span class='latex-bold'>(B)</span>\ 0.001 \qquad <span class='latex-bold'>(C)</span>\ 0.01 \qquad <span class='latex-bold'>(D)</span>\ 0.1 \qquad <span class='latex-bold'>(E)</span>\ 1
arithmetic sequence
System of Equations

Source:

4/2/2013
If a,b,ca,b,c are real numbers such that a2+2b=7a^2+2b=7, b2+4c=−7b^2+4c=-7, and c2+6a=−14c^2+6a=-14, find a2+b2+c2a^2+b^2+c^2.
<spanclass=′latex−bold′>(A)</span>14<spanclass=′latex−bold′>(B)</span>21<spanclass=′latex−bold′>(C)</span>28<spanclass=′latex−bold′>(D)</span>35<spanclass=′latex−bold′>(E)</span>49<span class='latex-bold'>(A) </span>14\qquad<span class='latex-bold'>(B) </span>21\qquad<span class='latex-bold'>(C) </span>28\qquad<span class='latex-bold'>(D) </span>35\qquad<span class='latex-bold'>(E) </span>49
inequalitiesalgebra