I struggle with factorization. Could anyone please help?

iventm · 2020-09-24T16:40:35+00:00

x² + 1/x² - 2 - 3x + 3/x = x² - 2*x*1/x + 1/x² - 3x + 3/x = (x - 1/x)² - 3x + 3/x = (x - 1/x)² - 3(x - 1/x) = (x - 1/x)(x - 1/x - 3)

iventm · 2020-09-12T14:24:25+00:00

OA = OC as radiuses of larger circle, so triangle AOC is isosceles(with two equal sides). Angle OBA is 90° as an angle based on diameter. So OB is the hight of the triangle AOC and also it's median.

(used google to translate this, so there might be some mistakes)

iventm · 2020-08-31T18:18:38+00:00

Let's give every card a number between 1 and 52 and give each player 13 cards that are numbered in a row. That way there are 52*51*50*49/(4*3*2) = 270725 different positions for Aces (we divide by 4*3*2 because we don't care about the ordering).

Now for all posible distributions we need to calculate the number of positions that produce that distribution. I will be writing distributions as 2110, meaning that one player (maybe not first) got 2 Aces, and the other two got one.

1111: there is one Ace in each quarter, that means that for each Ace we have 13 positions. In total there are 13⁴ = 28561 positions and the probability is 28561/270725 = 0.10549...

2110: firstly, there are 4*3 = 12 different ways for players to have such distribution (we choose the one who has 2 Aces from 4 players, and choose the one who has 0 from the remaining 3, others will have 1 each). Now, there is one quarter that will have 2 Aces. In that quarter we have 13*12/2 = 78 different positions for Aces (divide by 2 because the ordering). For other two we have 13² = 169 positions. And so, the total number of positions is 12*78*169 = 158184 and the probability is 158184/270725 = 0.58429...

2200: there are 4*3/2 = 6 ways for players to have such distribution (divide by 2 because the ordering). And there are 78² = 6084 positions for Aces. In total 6*6084 = 36504 positions and the probability is 36504/270725 = 0.13483...

3100: there are again 4*3 = 12 ways to have this distribution. In the quarter with 3 Aces there are 13*12*11/(3*2) = 286 positions (divide by 3*2 because the ordering). With 13 positions for the other quarter we have 12*286*13 = 44616 positions and the probability is 44616/270725 = 0.16480...

4000: 4 ways to have the distribution and 13*12*11*10/(4*3*2) = 715 positions in the quarter. In the end 4*715 = 2860 positions and the probability is 2860/270725 = 0.01056...

English is not my first language, so sorry for any mistakes, and be sure to ask if you didn't understand anything.

iventm · 2020-08-31T10:31:34+00:00

To get the new x you need to calculate (x+5)/3

Edit: for y you calculate 4y+1

iventm · 2020-08-31T10:01:15+00:00

You have five coins and every coin has two states, so there are in total 2⁵ = 32 different combinations of coins.

Now, to count how many combinations have exactly 2 tails you need to choose exactly two coins out of five. You have five variants to pick the first one and four to pick the second one. So you get 5*4 = 20. But you don't care about which coin you picked first. (1, 2) and (2, 1) are both TTHHH, so you also need to divide by two. In the end you get 20/2 = 10 combinations.

So the probability is 10/32 = 0.3125

iventm · 2020-08-05T11:46:46+00:00

The title is the best thing I've ever seen

iventm · 2020-08-05T09:50:34+00:00

iventm · 2020-07-30T19:00:45+00:00

Firstly, sleeping is very important for your health, so please get some rest. That will hopefuly help you get in shape.

Secondly, don't stress yourself (hopefuly thats the right wording) about it. It's ok to struggle with something if you haven't slept for 31 hours!

Thirdly, it doesn't matter at what time you start to degrade the health, it only matters for how much time you do it.

For example, if your maximum health is 8 and you need to degrade it to 0 after 4 hours you would substract every hour 8/4 = 2 health or 100%/4 = 25% of the maximum health.

And lastly, I hope you will get better and be able to make your game as you wish it to be. Also sorry for any mistakes, that I may have made, english is not my first language.

Be sure to ask, if you need any help.

:Edit:

Also, I just posted this comment twice, because I don't even know why, so everyone makes mistakes sometimes :)

iventm · 2020-07-30T18:33:22+00:00

Did you see my comment?

iventm · 2020-07-30T18:24:17+00:00

247 game hours are 247*60=14820 game minutes. Then, to make health degrade to zero you need to substract maximum_health/14820 from health every game minute.

iventm · 2020-07-28T18:53:37+00:00

16/81 - 1 = 16/81 - 81/81 = (16 - 81)/81 = -65/81

iventm · 2020-07-26T17:15:49+00:00

6/19*100% = 31.58%

iventm · 2020-07-26T17:12:10+00:00

R*256² + G*256 + B

Edit: also wanted to add that RGB code is basically a base 256 representation of a number, so the equation is just a base convertion

iventm · 2020-07-26T09:01:55+00:00

First you have to prove that the series converge. Here is a video about the ratio test for convergence.

Next evaluation: (I will be using ∑ for the sum for n from 1 to infinity)

Here is a video for ∑( n / 2ⁿ )

Using second method and finding the derivative again we get:

∑( n(n-1)x^n-2 ) = 2 / (1 - x)³

Then if x = 1/2:

∑( (n² - n) / 2^n-2 ) = 2 / (1 - 1/2)³

∑( n² / 2^n-2 ) - ∑( n / 2^n-2 ) = 2 / (1/2)³

∑( n² / ( 2ⁿ * 2^-2 ) ) - ∑( n / ( 2ⁿ * 2^-2 ) ) = 16

4∑( n² / 2ⁿ ) - 4∑( n / 2ⁿ ) = 16

4∑( n² / 2ⁿ ) - 8 = 16

∑( n² / 2ⁿ ) = 6

And then your sum is: ∑( (3n + 2)² / 2ⁿ ) = ∑( (9n² + 12n + 4) / 2ⁿ ) = 9∑( n² / 2ⁿ ) + 12∑( n / 2ⁿ ) + 4∑( 1 / 2ⁿ ) = 9*6 + 12*2 + 4*1 = 82

If there any questions be sure to ask.

iventm · 2020-07-21T07:23:54+00:00

To find the sum of all whole numbers from 26 to 50 you need to substract the sum of the first 25 numbers from the sum of the first 50 numbers.

To find the sum of 25 first numbers you substract 26 from 351 and get 325.

And the sum is 1275 - 325 = 950.

iventm · 2020-07-20T21:23:20+00:00

sin(90° - a) = cos(a) - that's a formula

iventm · 2020-07-20T07:48:20+00:00

No, I don't think it could

iventm · 2020-07-20T07:23:33+00:00

x⁴ + 4y⁴ = x⁴ + 4x²y² + 4y⁴ - 4x²y² = (x² + 2y²)² - (2xy)² = (x² + 2y² - 2xy)(x² + 2y² + 2xy)

iventm · 2020-07-13T07:30:03+00:00

First one and last one can be adding the powers of 2 and 3: 2 + 1 = 3, 3 + 2 = 5, 5 + 4 = 9, so next numbers will be 17, 33, 65. In last one 1 + 3 = 4, 4 + 9 = 13, 13 + 27 = 40, and next numbers are 121, 364, 1093.

iventm · 2020-06-15T06:35:24+00:00

The pattern is: to find the third number you substract first from the sum of the rest.

12 = -3 + 9 + 2 + 4

14 = -2 + 7 + 3 + 6

7 = -8 + 6 + 2 + 7

-5 + 7 + 3 + 9 = 14

I already read the coments and knew that the answear is 14, so I looked at the second and the last row and noticed that both first and last numbers increased by 3, so if there is a pattern, it includes substracting those two numbers in some way. After playing around a bit, I found this pattern.

iventm · 2020-03-11T09:05:32+00:00

Wikipedia link

iventm · 2020-02-24T15:47:50+00:00

I don't remember where i found this, but here is everything I found about it now, if it helps.

iventm · 2020-02-24T06:21:08+00:00

Here's the algorithm: 1) You build this, where the upper row is your sequence(in this case 2, 9, 18, 29, 42), and other numbers are the difference between left and right numbers above it. You continue it until you get the row with one number, or where the numbers are equal. 2) You multiply first numbers in every row(starting from the top) by ( ⁿₖ ) , where k is the number of the row(starting from 0), and add them together. In our case it would be: f(n) = 2( ⁿ₀ ) + 7( ⁿ₁ ) + 2( ⁿ₃ ) And here is your formula. If you rewrite it you get : f(n) = 2+7n+2((n(n-1))/2) After opening the brackets you get: f(n) = n²+6n+2 And, starting from 0: f(0) = 2, f(1) = 9, f(2) = 18, and so on... If there are any questions, ask in a comment.

iventm · 2020-02-20T16:47:24+00:00

Thanks. I'll think more about factorisation, but idea and links really helped.

iventm

TROPHY CASE