Wow Alan. Thats .... Interesting? But it is really smart! Thanks!!!

Thanks amill Hectictar, but I’m too fucking busy pointing up my question posts and thank you posts to give you a point for answering the question.  This makes me a rude, indifferent assshole. Maybe I’ll out grow it someday, but in the mean time, everyone will just have to eatshit!

Wow! Thanks for the great solution Melody!!!

umm what are you the same guest or what

😫

this is confusing

😵

\(\text{textbook partial fractions problem}\\ x+7 = A(x+1) + B(x-2)\\ x+7 = (A+B)x + (A-2B)\\ A+B=1\\ B=1-A\\~\\ A-2B=7\\ A - 2(1-A) = 7\\ 3A - 2 = 7\\ A=3\\ B=-2\\~\\ \dfrac{x+7}{x^2-x-2}= \dfrac{3}{x-2}- \dfrac{2}{x+1}\)

Nice!

Nice!

Thanks!

Since 2,162 is the average of the 3 terms, therefore we have: 3 x 2,162 =6,486
6,486 - (5000 - 1) - (999 - 1) =489 - this is 3 times the first term.
489 / 3 = 163 - this is the first term.
N/2 * [2 * 163 + (N - 1)] =325^3, solve for N 
N =8,125 - this is the number of terms.
Last term =8,125 + 163 - 1 = 8,287 - this is the last term.
Sum=[163 + 8,287] / 2 * 8,125 = 325^3

Thank you! Glad it was helpful

Thank you! There are many different ways to explain the problem with dividing by zero, but I like that way. Maybe someone else will provide another explanation.

wow i didn't know that myself thanks hectictar

thanks amill Hectictar

edit

Here's one way to figure out, for example, what is  10 ÷ 2

We had to subtract  2  a total of  5  times before we couldn't subtract it any more (without getting a number < 0)

Or we can say that  2  "fits into"  10  a total of  5 times.

So  10 ÷ 2  =  5

Now let's try to use the same method to figure out what is  10 ÷ 0  

We keep subtracting  0  over and over again, but we aren't getting anywhere!  This is an endless loop.

There is not a number of times that we can subtract  0  from  10  to reach a number < 0.

In other words, there is not a number that is equal to  10 ÷ 0

nevermind, i got the solution

Total score for 30 students = 30 x 73 =2,190

Total score for 28 students = 28 x 72 = 2,016

Difference =2,190 - 2,016 = 174 - total marks for 2 students.

174 / 2 = 87 - Average mark  for the 2 students.

87 + (22/2) = 98 - the higher score of the 2 students.

87 - (22/2) = 76 - the lower score of the 2 students.

\(f(5) = 3f(3)-2f(4)\\ f(3) = 3f(1)-2f(2) = -3 - 2(3) = -9\\~\\ f(4) = 3f(2)-2f(3) = 3(3) - 2(-9) = 27\\~\\ f(5) = 3(-9) - 2(27) = -81\)

3Ax - 24 = 5x - 9 + x        simplify the right side

3Ax - 24  =  6x - 9

This will have no solution when    3A  = 6  ⇒   A   = 2

To see why this is so....

3(2)x   - 24   =   6x - 24    and this can never equal  6x - 9

y = 2x^2 - 6x + 3

y = x - 2     

Set the y's equal  and solve for  x

2x^2 - 6x + 3  =  x - 2         subtract x , add 2    from/to each side

2x^2 - 7x + 5  = 0          factor, if possible

(2x -5) ( x - 1)  = 0

Set each factor  to 0   and solve  for  x

2x  - 5  = 0                   x  - 1  =0

2x  = 5                         x = 1

x = 5/2 = 2.5                x  = 1

So    y  = x - 2 = 2.5 - 2  = 0.5        or   y = x - 2 =   1 - 2  = -1

So  {x,y}   =  { 2.5, 0.5}     or  { 1, -1 }         

( ( 5p+1)-2p*4) ( 3 ) + ( 4-1/3) ( 6p-9) 

[ (5p + 1) - 8p ] (3) +  ( 12/3 - 1/3) (6p-9)  =

[ -3p + 1 ] (3)  +   (11/3) [ 6p - 9)  =

[-9p + 3 ]  +  (66/3)p - 99/3  =

-9p + 3  +  22p   - 33  =

13p -  30

This was in the news yesterday-ish

(you have a typo in your question)

8/2(2+2) = ?      (edited...I had a typo in MY answer too!   I had posted :  8*2(2+2) = ? )

PEDMAS   says it's 1

BODMAS  says it's 16

See:

https://www.foxnews.com/tech/viral-math-problem-baffles-many-internet