sat ii math questions!! (attention math wiz)

optimizerdad
Sat, 29 Oct 2005 20:18:22 +0000

If X0= 0 and Xn+1 = square root(6+Xn), then X3=
X3 = sqrt(6+X2) = sqrt(6+sqrt(6+X1)) = sqrt(6+sqrt(6+sqrt(6+X0)))
Plug in X0=0 for the answer.
The cross-section radius decreases linearly as you go upwards from the base. Formally,
cross-section radius = baseradius * (coneheight - distanceabovebase)/ coneheight
or cross-section radius = baseradius * (1 - (distanceabovebase/ cone_height))
4 = 6 (1 - 8/h)
4/6 = 1-8/h
8/h = 1-(2/3) = 1/3
h = 24


(A quicker way is to notice that if you went up 8 units from the base, the radius dropped by 2, from 6 to 4. Go up another 8 units, and the radius will drop by another 2, to 4-2=2. Go up yet another 8 units, and the radius will be 2-2 = 0; you’re at the top of the cone. Total distance travelled from base = 8+8+8 = 24).


Do it in stages. If the graph ‘moves’ 3 units to the left, the new function (say h(x)) will be h(x) = -(x+3)^2. If it now ‘moves’ up 1 unit, the function g(x) will be 1 + h(x) = 1 - (x+3)^2.
Plug in x= -1.6, and compute g(-1.6) = 1 - (3 -1.6)^2 .
You just need to find the #different ways of getting a 3 person group, the remaining people automatically form a 7 person group. The answer is nC3 = 10! / (7! 3!) = (10)(9)(8) / ((3)(2)) = 120.
At x=0, y^2 =150/30 or y = +/- sqrt(5)
At y=0, x^2 =150/60 or x = +/- sqrt(2.5)

y is the major axis, and its length is from -sqrt(5) to +sqrt(5)
= 2 sqrt(5), which should be 4.47


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