11A cone-shaped mountain has its base on the ocean floor and has a height of8000 feet. The top18of the volume of the mountain is above water. What isthe depth of the ocean at the base of the mountain, in feet?
(A)4000(B)2000(4−√2)(C)6000(D)6400(E)7000
12For each positive integern, the mean of the firstnterms of a sequence isn.What is the 2008th term of the sequence?
13VertexEof equilateral△ABEis in the interior of unit squareABCD. LetRbe the region consisting of all points insideABCDand outside△ABEwhosedistance fromADis between13and23. What is the area ofR?
14A circle has a radius of log10(a2) and a circumference of log10(b4).What islogab?
2π15On each side of a unit square, an equilateral triangle of side length 1 is con-structed.On each new side of each equilateral triangle, another equilateraltriangle of side length 1 is constructed. The interiors of the square and the 12triangles have no points in common. LetRbe the region formed by the unionof the square and all the triangles, andSbe the smallest convex polygon thatcontainsR. What is the area of the region that is insideSbut outsideR?
(A)14(B)4(C)1(D)16A rectangular floor measuresabybfeet, whereaandbare positive integerswithb > a.An artist paints a rectangle on the floor with the sides of therectangle parallel to the sides of the floor.The unpainted part of the floorContributors:worthawholebean,mathgeniuseˆln(x),Altheman,infinity4ever,Eˆ(pi*i)=-1, Xantos C. Guin, azjps, MellowMelon, archimedes1, TZF, andersonw,nickster08, 123456789, randomdragoon, n0vad3m0n, krsattack, CatalystOfNostalgia,rrusczyk
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2008 AMC 12/AHSMEforms a border of width 1 foot around the painted rectangle and occupies halfof the area of the entire floor. How many possibilities are there for the orderedpair (a, b)?
17LetA,B, andCbe three distinct points on the graph ofy=x2such thatlineABis parallel to thex-axis and△ABCis a right triangle with area 2008.What is the sum of the digits of they-coordinate ofC?
18A pyramid has a square baseABCDand vertexE. The area of squareABCDis 196, and the areas of△ABEand△CDEare 105 and 91, respectively. Whatis the volume of the pyramid?
19A functionfis defined byf(z) = (4 +i)z2+αz+γfor all complex numbersz, whereαandγare complex numbers andi2=−1. Suppose thatf(1) andf(i) are both real. What is the smallest possible value of|α|+|γ|?
(A)1(B)√2(C)2(D)2√2(E)4