Math game

[Sikamies]

May I ask how you obtained that value ?

probability.jpg

A is Alfa's arrival time and B is Bravo's. The yellow area contains all the points (A,B) that lead to meeting. Thus, the probability is the yellow area / the whole area.

[bduddy]

Well, I myself did some "fuzzy math" on a sticky note, but that way works too... anyway, this one is from an exam I had a couple years ago, slightly modified to make it easier to understand...

A line runs from the point (0,0,0) to (1,9,-3). Five other lines run from the point (0,0,0) to specified points. Which one is perpendicular to the original line?

a:(-1, -9, 3)
b:(-1, 9, 3)
c:(-3, 1, 2)
d:(3, -1, 2)
e:(-3, 1/3, 1)

(if you don't have a reason, please don't guess...)

[Sikamies]

c, the scalar product of perpendicular vectors is 0.

[bduddy]

(It was originally a vector problem, I just wrote it that way so people that didn't know about vectors would have a chance...)

[Sikamies]

Next one then:

Three circles pass through each other's centres (in the picture).

area.jpg

What is the area of the orange domain if the radius of each circle is equal to 1?

[Darjo]

Is it (π-√3)/2 ?

[Sikamies]

Is it (π-√3)/2 ?

Yes, that's correct

[Darjo]

A sidamob and a very fast formula are going around an oval track which is 3km long at a constant speed.
The formula is faster and it overtakes the sidamob every 60 seconds.
If the formula goes in the opposite direction it will "meet" the sidamob every 20 seconds.

What are the values of the 2 speeds?

[AleksiNir]

Formula goes 360 km/h and Sidamob 180 km/h?

[Darjo]

The answer is correct.

[AleksiNir]

Woo!

I'll be away for the weekend, so I'll give you an easy one. I took this from my maths school book (and I've solved this myself)

How much weave is needed for this tent? (you can ignore bottom and joints)

[OlafK]

13π m² ?

15chars

[bduddy]

14.5 pi m^2?
Right?

[AleksiNir]

Olaf nailed it! Your turn.

[OlafK]

It's hard to calculate at 1 AM

Another rather easy one, because recently I like lurking better than posting How long is the perimeter of this triangle?

[Paw]

Is it 3*sqrt(13) + sqrt(26) + sqrt(39) ?

[OlafK]

Yes, It's your turn

[Paw]

Okay, so here you are.

You got following function:

mathgame.png

analyse, for which values of n this equation has only one "zero point", so in other words: for which n there's only one x which makes the value equal to 0.

hint: there are two answers of n=(?).

[XYY]

Is n represantative for a Natural number or is it just the name of one variable?

[Sikamies]

n = -1 or n = -4.

The discriminant must be 0.
(n+2)^2 - 4(-n)*(1/4) = 0

[Paw]

Well, Sikamies has this one right. "n" is just a variable, so it's value can be any real number.

[bduddy]

Well, in many problems n is intended to just represent an integer, or a "natural number" (taught to me as a "counting number")... but it wouldn't really make sense in this problem, because both solutions are negative...

[Sikamies]

Next one:

For which x the function x^x has its minimum when x > 0?

[Paw]

Well, without really any thinking, but maybe it's 1/3?

[bduddy]

Err... which "x" do you mean, exactly?