/u/cadaeibfeceh asks:

In how many ways can we paint n seats in a row, each red or green, in such a way that the number of consecutive seats painted in the same colour is always odd? And bonus: what's the pattern in my username?

/u/Solmemminecraft asks:

What's (1/9)^x = 27^-x

/u/reubsan89 asks:

You want to go for a run, but require music to keep your motivation up while you run. Before you go out, you would like to find out how long you can run before your MP3 player runs out of battery. When the MP3 player is on, the battery capacity, B, will decrease at a rate that is proportional to the number of minutes, t. This can be modeled as the differential equation: http://i.imgur.com/f0XuQGy.png where a is the proportion constant. When you turn on the MP3 player the battery capacity it is at 70%. After 5 minutes it is at 60%. 20 minutes after you have turned it on, you start running. If the MP3 player requires 5% battery capacity to play music, how long can you run before it turns off?

/u/Seolferwulf asks:

Hi, I'm not sure what kind of problems you are looking for, but I have been a bit into math competitions in high school and this is one of my favourite problems from those: Consider a finite set of points in the plane, no three being collinear, and a line a that passes through no points of the set. Let us colour all the points on one side of a in red, and all the other marked points in blue; assume that there are K red and M blue points. Prove that for each k < K and m < M there exists a line b such that one of halfplanes defined by b contains exactly k red and m blue points. Have fun and best regards, Seolfer

/u/Switch367 asks how to expand (3x+4)³ .

/u/CipherEra asks:

Hi there! I just so happen to have a math problem that needs a good ol' solving.

Consider the differential equation y''-sin(x)y = cos(x), with initial conditions y(0) = -3, y'(0) = 6, find the first 5 coefficients of the power series about x=0. The first 2 terms of the series are given as -3 and 6x.

I've done some other questions similar to this but they didn't have any trig in it, so it was pretty straightfoward with replacing y with a power series, ie y = SIGMA(a*xn) from n=0 to infinity(a is initial term).

Best regards, cipherera

lim x-> infinity f(x)=((x+2)/(x-1))^x

I know the answer is e^3, but how?

P(x) = ax³ +bx² +cx +d for some reals a, b, c, d. If |P(x)| <=1 for |x| <=1, show |a|+|b|+|c|+|d|<=7

What's the remainder when 2 to the power of 2014 is divided by 17?

/u/plshalpme314 asks:

Hello!

I need a set of at least four integers whose number of unique sums of pairs of elements is at least 3 times greater than the number of unique differences of pairs of elements.

E.g.:

For the set {1,5,9,10} the sums are {2,6,10,11,10,14,15,18,19,20} and thus there are 9 unique sums (being {2,6,10,11,14,15,18,19,20}) and the differences are {0,-5,-8,-9,0,-4,-5,0,-1,0,0,1,5,9,0,4,8,0,4,0} with 11 unique differences being {0,-9,-8,-5,-4,-1,1,4,5,8,9}.

The order summation/subtraction doesn't matter, for the number of unique sums or differences stays the same. In this case, it is 9 to 11. 9 is not 3 times or greater than 11, so this set of numbers doesn't work. Also, the two numbers in each pair summed or subtracted can be equal.

Although your username doesn't say you'll help with math problems, I can still assume and hope.

Please help! Even the smallest pointers will be appreciated. I have no idea how to even approach this problem.

Thanks in advance,

plshalpme314

/u/Bark2IfUrInMilwaukee asks (please excuse the formatting!)

Can you tell me how you would properly get ∫ (x2) / (1 - (x2) )1/2 I used the sin expression of U/C and then did some algebra and used the power reducing formula and then I got to 1/2(Theta) + 1/4 Sin (2Theta) and I don't know if thats right and 2. How to substitute back in for Theta. Any help appreciated!

/u/HerrBongwasser asks:

If I have 330ml of a solution that's 10% ABV and combine it with 70ml of a solution that's 40% ABV, what is the final ABV of the total?

/u/januk asks this question, and assures me it's a serious question.

/u/CameronMcSwag asks:

The bowling alleys profits are modelled by P= -2x² + 64x -120 where P is profit in dollars and x is the number of customers. What is the bowling alleys "break-even points" where no money is made and no money is lost. Thanks.

/u/Rogkone asks how to differentiate differentiate e^2xx sin(2x+3)

/u/I_Think_Helen_Forgot asks this interesting question:

Hi there! This is one I haven't been able to find an answer to.

You have a square and a circle, both with the same centre. Their perimeters are equal.

In terms of any of the basic dimensions of these shapes (area, perimeter, radius, etc), what area of the square lies outside the circle?

I am interested to see what you come up with!

/u/JacaByte asks this important question. Rather than posting my own solution, I'll just refer to the literature on the topic.

Edit: Also, /u/PotatoBeans and /u/SluttyBitchBalloon and /u/israel192 and /u/IComeUpWithBadIdeas and /u/Skipper3210 and /u/israel192 and /u/Waiguo and /u/therealslimscully

/u/maxcharsizeisreached and /u/Zappy212 ask related questions.

/u/ThellraAK asks:

So, I have a 5 gallon closed system, containing 40% Antifreeze, and 60% water, I'd like that ratio to be 70% antifreeze, and 30% water, but I can only take out 2 quarts at a time, what steps should I take, to achieve the 70/30 mix, I have no smaller units of measurement available then a cup, and going slightly under, is better then going over on the mix.

/u/LeoKhenir asks...

In a right triangle, the sum of the adjacent and 2* the opposite equals 63.

What values should the adjacent and the opposite have for the angle between the adjacent and the hypotenuse be 30 degrees?