Pangolin14

It should just use substitution to get x=9

4,2

4^2 = 16

2^4 = 16

please read the question. It says less than 15

6 choose 3 * 6 + 6 choose 4 * 6 etc / 6^6 which is 4897/7776 i think

Sorry about that, I just noticed that I am wrong, as x-5 must be negative.

It's 4x+5

Oops... sorry, I meant to say that the minor arc must have 360-340 =20 degrees of measure, so it is 1/18 * 2 * 18 * pi = 2pi

Somehow I found the wrong area using the diameter ^^

Maybe you can see here: https://web2.0calc.com/questions/i-got-8-possibilities-it-is-incorrect and derive the answer from that...

If we reflect the 30 60 90 triangle over the y axis, we get an equilateral triangle, congruent to the original one because they share a side. The side length is 12, as 6*2=12.

Now we have to find a formula for the area of an equilateral triangle.

If we draw an median to any side, we will have two congruent triangles, by SSS. Therefore the angles are the same and have to sum to 180, so the angles are 90. Therefore, a median is an altitude and vice versa with altitudes by AAS in an equilateral triangle. 

Let the side be x. Then, base is x/2 and height is sqrt (x^2 - x^2/4) = x sqrt 3 / 2. So, area of equilateral triangle = x^2 sqrt 3 /  4.

So, 144/4 = 36 so 36 sqrt 3.

This problem sounds interesting:

If we draw PA and PB to make ∆PDA and ∆PCB, we have that the altitudes must be equal, so the areas of PAD and PBC are in the ratio 5:7.

If PX is the altitude to AD, we can treat AD as the base instead of PD, thus PX is the altitude and same for BC and PC. Thus, we have that PX*5/2 : PY*7/2 = 5:7, so 5PX : 7PY = 5:7. Therefore, dividing both sides by 5 and then multiplying by 5/7, we get PX : PY = 1:1, so PX = PY.

This is a permutation, as order matters.

Keep in mind that that permutation will only give you the possible, but you can do combinations when there is only one possible arrangement as it returns only one arrangment: 3 choose 3 = 1, whereas 3 pick 3 = 6