Invitational B 2010

[adub427]

I have 3 questions on Mathematics Invitational B 2010

8. The point (6,-6) is rotated 60 degrees clockwise about the origin. The coordinates of the point after the rotation is
A) (-6.7,-2.2) B) (-8.2,-2.2) C) (5.1,-8.2) D) (-8.2,-1.1) E) (8.2,2.2)
It says the correct answer is B, but I came up with (-2.2,-8.2)... I've worked it over and over and either I'm doing something wrong or the answer key is wrong.

24. A recent visit to the planet Strangebase discovered that the equation, 3S^2 - 25S + 66 = 0, has two solutions, 4 and 9. What base was being used for the number system on planet Strangebase?
A) base 5 B) base 11 C) base 13 D) base 17 E) base 36

52. Let x= 1/(2+ 1/(3+ 1/(2+1/(3+ …)))) be the continued fraction. Find x.

A) (√15 +1)/2 B) (√2 + 1)/3 C) ( √15 - 3)/2 D) (-√15 - 3)/2 E) (√2 -1)/3

[hansond10]

[iamhe]

hey could you explain how you got the first line of the base problem?
thanks!

[hansond10]

[stupidityismygam]

[AuSmith]

[stupidityismygam]

[makjesusfreak]

well, i just have no idea how to do these problems, so i will be grateful for you help...thanks in advance

6. If y=1-x and y=2/x then (x+y)(x^2-xy+y^2)=?

42. (√x 3√x 4√x) = n√k, where k and n are relatively prime, then k = ?

56. the cowboys and the texans will play twice this season. the cowboys are twice as likely to win any game as the texans. what is the probability that they will each win one of the two games?

[Kenon]