the price for one student (if they are four)=$18,50

one ticket cost (if they´re five)=$80/5=$16.00    since five tickets cost $80

so each student saves $2.50 if they find a fifth one.

y=43.5

y=-18(sin(pi/6))(x-1)

sin(pi/6)=0,5 -----> 43,5=-9(x-1)

                               43,5=-9x+9
                               43,5-9=-9x
                                       x=34,5/9=3.8

I´m not sure if I did the equation as you wanted it or if you ment y=-18sin((pi/6)*(x-1))

We have

(148,000 x  198 x 8500 x 1.3g) / 1000  = 323,809,200 kg

V(h 24) = 30 cm*20 cm*24 cm = 14400 cm³ =  14,4 liters

V(h 15) = 30 cm*20 cm*15 cm =    9000 cm³  =  9 liters

                         + 6,5 liters = + 6500 cm³      

9 liters +   6,5 liters = 15,5 liters         =>   15,5 liters -14,4 liters = 1,1 liters

now  15500 cm³   =>    1100 cm³ =1,1 liters  too much !!

Answer:  1,1 liters of water overflow the container.

Greetings radix !

There's no way to solve this unless we know what AC is.....

10w*(w-25) = 10w² - 250w

Thanks Badinage, that is good advice.

I tackle the problem a bit differently.

Firstly

I remember relatively few formulas.  I work most out from scratch, this is slower and it requires a different type of memorizing for if I had not semi memorized the working it would take far too long.  For me it is easier to semi memorize a logical procedure than it is to memorize the end result.

Secondly

I never wrote the formula out 100s of times BUT if I had to use a formula I never allowed myself to directly copy it.  At worst I would have it on a different page, I could look at it but then I had to reproduce it without directly copying it.  If I could not do this then I would write it on a peice of paper a few times first, until I could do it.

Third.

There are lots of tricks, poems, songs, etc to help you remember specific things.

Like SohCahToa for instance.   I have added to my collection of these since i have been on the forum.  If you have specific a problem remembering something then ask on the forum.  Someone may have a great idea of something that will work for you.

Last but not least,

The more you understand - the less you have to memorize!  

Hola. Como estas?

Thats easy

the number after the dot is 6

round it to the nearest whole number

14.6 would be rounded up to 15

No No, He said

I multiply 2011 natural Zahle and get an odd number . Now I add this number and get 343,234,185,271,298 .

70=-7(2x+6)     simplify

70  = -14x - 42      add 42 to both sides

112  = -14x       divide by -14 on both sides

-112/14   = x =   -8

Hi so this is what you do 

Thanks Chris,  that is really neat!

I think I understand what Bertie has done as well.  I must be on a roll.    

I think I should go looking for some introductory videos on modular arithemetic.

The basic stuff is not that hard but it is not cemented in my brain very well yet.  

Anyway I will store this thread in our "reference material" sticky thread.  

14x^2 + 3x  - 5     (factor)

(7x +5) (2x - 1)      thus.....2x + 5 doesn't divide this equally......so we have

                  7x     - 16

2x + 5     14x^2  + 3x -  5

               14x^2 + 35x

              ----------------------

                          -32x   - 5

                          -32x  - 80

                           -----------

                                    75

=    (7x - 16)    Remainder  (75) / (2x + 5)

The y intercept will occur at a point where x = 0   (Think about this  !!! )    ....so.....letting x = 0, we have

2(0) + 3y = 6 

0 + 3y = 6

3y = 6     divide by 3 on both sides

y = 2  ......so......the  y intercept occurs at (0, 2)

16a^2 - 4b^2        =

4 (4a^2 -  b^2) =

4 (2a + b) (2a - b)

Here's a "proof,"  Melody........consider  the number line......

..6n - 6   6n - 5    6n - 4   6n - 3    6n - 2    6n - 1    6n     6n+1    6n + 2   6n+3   6n+ 4    6n + 5    6n + 6..

Note that  the terms  6n-6, 6n + 6, 6n - 4, 6n+ 4, 6n - 3, 6n + 3, 6n - 2, 6n + 2 and 6n  cannot be primes

The only possible  primes are 6n - 5, 6n -1 , 6n + 1 , 6n + 5.......but note that, 6n - 5 is really just the same thing  as 6(n -1) + 1   and 6n + 5 is the same thing as 6(n + 1) - 1.....in other words, the only possible primes on the number line occur on either side of a integer which is divisible by 6, i.e., 6n - 1 or 6n + 1.......

And as Bertie points out, we have to make an exception for 2 and 3.....

The method I used in high school was to write the equation hundreds of times, night after night, until it eventually stuck in my brain. I think it becomes sort of a rhyme or mantra that tends to generate itself in your mind once you start to say it. All you need is a pencil and a dozen sheets of blank paper. Try it!

 Once you begin to make sense of maths, you'll find equations become easier and easier to understand and remember.

Good luck! 

WOW

There are a whole load of numbers for which 6n plus or minus 1 is not prime, but the important point is that

6n plus or minus one covers all of the primes greater than 3. 

I never knew that.  Is that one of those things that plebs like me just have to accept, or is there an understandable proof floating around out there in the ether?     

2x^2+9x-5  =   {factor}

(2x - 1) (x + 5)     so......dividing this by x + 5  just equals the first term......

16ax + 4x 2 +16a^ 2  =   {rearrange}

4x^2  + 16ax + 16a^2  =

4(x^2 + 4ax + 4a^2) =

4(x + 2a) (x +  2a)  =

4(x + 2a)^2

Hi Chris

I couldn't work out what was wanted either  

Your answer is a good one though. 

25 squared + 15.71 squared = ?

$$\small{\text{$
\mathbf{
25^2+15.71^2 = 871.8041
}
$}}$$