Topic, Math Whiz Quiz Game V2

  Finally, a new question :)

  Correct, but unfortunately I don't have time to add a new question now.

  x^2-4x+3=(x-1)(x-3)
R(x) can be shortened if x=1 or x=3 is a zero of x^3-4x^2+6x+a
x=1: 1-4+6+a=0 ==> a=-3
x=3: 27-4*9+6*3+a=0 ==> a=-9

  Correct, new question up!

  line through A and B y = -2x + 1
Then the line that is perpendicular to y = -2+1 is y =1/2x -3/2
Then the intersection between y=1/2x-3/2 and y=-x+4 is C.
x=11/3 and y = 1/3 thus C=(11/3, 1/3).

  Thanks F12 :)

I have solved the problem, but I won't give the answer now, because I don't want to be the only one to play your game (and btw to kill its great interest). I feel I'm a bit advantaged because I am living in the same time zone than you, challengers may be sleeping, at school or working at the moment. Let's give them a chance to participate!

  From what I can understand, your explanation looks quite right to me, so I'll award you the four points unless anybody puts in a protest. The 2nd answer is spot on :)

  1.) I hope my demonstration will be understandable, my skills in English are much lower than in Mathematics :)

A rational number can always be expressed as the ratio of 2 integers p/q, p and q having no common divider. Let's assume that sqrt(2) is a rational number. Then, it should be possible to find two integers p and q such that sqrt(2)=p/q ==> 2q^2=p^2.
This equation means that p^2 is a multiple of 2. If 2 is a divider of p^2, it must be a divider of p. Then, we can write p=2r ==> p^2=4r^2.
2q^2=p^2 ==> 2q^2=4r^2 ==> q^2=2r^2.
Consequently, q^2 is also a multiple of 2 ==> q is a multiple of 2. Since p and q must have no common divider, sqrt(2) is irrational.

2.)
x=t^2+2t = t(t+2)
y=t^2-1 = (t+1)(t-1)
x is zero for t=0 and t=-2
y is zero for t=-1 and t=1
There are 4 intersections: (0;-1) (0;3) (3;0) and (-1;0)

  Simon, how do you suggest I write the integral sign? (It may have a name, but I know nothing about integrals at all) If you can give me an explanation on that, then I think I could give you one or two questions about integrals. :)

  Correct, new questions tomorrow :)

  Which also kan be said as a googol zeroes as a googol=10^100

  10^100 zeroes as googolplex = 10^10^100

  Then I'll have to come up with one, and integrals and prime numbers aren't my strongest side (I haven't learnt too much about them yet). I could always come up with a question, but I'd have limited knowledge of wether it would be solvable or if my own calculations would be correct. If I have some spare time I could try, but right now I'm a bit busy (Trying to find out how solar panels work). :)

  Could you you maybe ask some questions about integrals or something like that. :)
Or prime number related.

  A stupid ratio, it might be, but that's how the task is written. Now that I look at it again, it would make more sense like you interpreted it, Simon, but I didn't think the stupid ratio would present a problem. I didn't have any problem with it myself when solving the task, so I just assumed everybody would think the same way as I did. (No, I didn't write task myself, it's copied from the internet). With that said, Nelson did post the correct answer first, so I can't do anything but award him with his two points.

[edit] 1jase: :P

  This topic makes me realize how terrible I am with math XD

  That's a rather stupid ratio. :) We'll see what Ferrari says. :p
Edit: damn English...

  Simon, 2/5 is the ratio of boys to girls, not the ratio of boys to the total of children.

The current total of boys is 108, you don't have to add 12 (they are not really added, it's only a supposition) :)

  Did I misinterpreted the question? 2/5 is boys, am I right?
(2/5)*150=60
(4/9)*(150+12)=72
Edit: Nelson, don't forget to add the 12 boys. :)

  if b is the number of boys, g the number of girls:
b/g=2/5
(b+12)/g=4/9 ==> b/g+12/g=4/9
2/5+12/g=4/9
12/g=4/9-2/5=(20-18)/45=2/45
g=12*45/2=270
Then, the number of boys is 2*270/5=108

  Ok solve the equation
(2/5)t=(4/9)*(t+12)-12
where t = the total amount of children at the beginning.
After solving you get t=150
The amount of boys currently is (4/9)*(150+12) = 72

  New question up!

  Angles be 30,60 and 90 degrees respectively.
With use of trigonometry you can calculate one of the other sides. Since the triangle has a straight angle, you can use the simplest form of it. The two other sides are 2 cm and 2sqrt(3) cm. With the formula of the area of a triangle I find 2sqrt(3) as answer.

*edit* wait, that's the one nelson solved... damn...

  Nelson got it right again. I always see the questions when Nelson already answered them. :p

  The third angle is (180-30-60)=90 degrees, the triangle is rectangle. Then, since the longest side is 4 cm, the others are
4*sin(30)=4*sqrt(3)/2=2*sqrt(3) and 4*cos(30)=4*1/2=2
The area is 1/2*2*sqrt(3)*2 = 2*sqrt(3)

@ Simon: to solve the equation of degree 4, you need to find a product of 2 polynomals of degree 2. To calculate the coefficients, you'll need to solve an equation of degree 3. There is a standard way to solve it, without knowing one zero point. But you are right, it's very difficult :)

  Jim got the right answer (I'm trusting that Norsk Tipping, which are in charge of the Norwegain lottery, have got the stats on their website correct), so that gives him seven points. I'll also give Simon his one point for the fruit basket. Sorry about the mistake there! :)

  I'm doing a wild guess: (34!)/(27!)*4 NOK = 34*33*32*31*30*29*28*4 NOK
Edit: Actually it's not a wild guess.

  7^34 NOK I would say.

  @Nelson about the polynomal of degree 4. That way with the solving of a polynomal of degree 3, you'll need atleast 1 zero point. And the standard way for a polynomal of degree 3 is pretty difficult. :)
Btw ferrari, you didn't read my message well either:
"13 fruits left and you have 5 fruits."

  Could the answer, by any chance, be 21518464 NOK?