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Don't you know the formula for Arithmetic Series?

S = N/2 [2F + (N - 1)*D], where N=Mumber of terms, F=First term, D =Common difference

S = 19/2 [2*3 + (19 - 1)*5]

S = 9.5 [6 + (18*5) ]

S = 9.5 [6 +  90 ]

S = 9.5 x 96

S = 912

Im sorry! I am curious though, what was the answer??

-Hayley

It wasn't correct, but I had already put my answer in and it was right. Thank you so much for the effort though. 

Correct me if I am wrong, lol. But is it

3,8,13,18,23,28,33,38,43,48,53,58,63?

-Hayley

Did my answer ever send?

-Hayley

To find the height, H, we can use :

sin (45°) =  H  / 80      rearrange as

H  =  80 *  sin (45°)   ≈  56.6  ft  

There isn't a 'cookbook" metrhod  for these.....your approach (as long as it's sound) is as good as any.....!!!

Very nice, X²   !!!

Hey there! So, I got the right answer, but I did the long verson I guess. LOL

-25+7-(-2-3)+(1-3)^4

-25+7-(-5)+(-3)^4

-25+12+(1-3)^4

-13+(1-3)^4

-13+(-2)^4

-13+16

=3

an  = 2(1/3)^{(n - 1)}

Hey, Hayley  !!!

-25+[7-(-2-3)]+(1-3)^4  =

-25 + [  7 - (-5) ] + (-2)^4  =

-25 +  [ 12 ] + 16  =

-25  +  28  =

3

a₁  =   3

a_n  =   a_n-1 * (1/6)

This puzzle has a very elegant solution to it!
 

Actually, I think the best way to think about this one is to think two-dimensionally first! We have 3 points that we place on a circle! 

I have picked arbitrary points for A, B, and C. I want to determine the probability when the three points form a triangle wherein the center is included. No matter what three points you pick, there are four options

Option 1: Point A, Point B and Point C are where they are in the diagram.

Option 2: Point A is moved to the other side of line, Point B stays and Point C stays

Option 3: Point A stays, Point B moves to the other side of line, and Point C stays

Option 4: Point A moves to the other side of the line, Point B moves to the other side of the line, and Point C stays

In these 4 cases, only one of the situations has a polygon that includes the center, so for a circle, the probability is \(\frac{1}{4}\).

Actually, let's go down to one dimension! Let's just worry about a segment.

There are two possibilities.

1) Point B is on the left of O

2) Point B is on the right of O

In this case, there is 1 case that results in the center being included, so the probability is \(\frac{1}{2}\).

If a one-dimensional case yielded \(\frac{1}{2^1}\) and the two-dimensional case yielded \(\frac{1}{2^2}\), then it would seem logical to me to assume that the three-dimensional case would be \(\frac{1}{2^3}=\frac{1}{8}\). In fact, if you try the cases again, you will see that this is the case.

602.88cm³ is correct!

You're learning well!

Solution:

\(\text{Period } = \dfrac{2\pi}{c} = 1, \text{so } c = 2\pi\\ \text{Then } x = 20e^{(-bt)}* cos(2\pi*t)\\ \text{When t = 3, then x = 10}\\ \Rightarrow 10 = 20e^{(-3b)}cos(6\pi)\\ 0.5 = e^{(-3b)} * 1\\ Ln(0.5) = (-3b)\\ -3b = Ln(0.5)\\ -3b = -0.69314718\\ b= 0.23104906018\\ \text { }\\ 20e^{(-0.23104906018*3)}cos(6\pi*3)= 10 \text{ (check)}\\ a=20, \; b=0.23104906018, \; c=2\pi \)

_{Edit: Cosmetic}

GA

Mount Everest?

Here is my rationale!

1) This infamous mountain is buried underneath that Earth crust!

2) The mountain towers into the sky, and reaches an incredible altitude of 29,000 feet!

3) I believe the most recent statistic states that the mountain has claimed over 200 experienced yet valiant climbers! The air at that altitude of 29000 feet is gruesomely and lethally thin--even with the aide of supplemental oxygen tanks. 

Thanks, X²

Here's another way to do this

Irma  paints   1/9  of a room in one hour

Paulo  paints  1/8  of a room in one hour

So.....Rate  * Time  =  Total Job Finished

(1/9)x + (1/8)x   =  1

(9  + 8) x

________      =  1        cross-multiply

    72

17x  =  72       divide both sides by 17

x  =  72/17  ≈  4.24  hrs

Notice something else, NSS....  if we add  1/8  and 1/9   and then take the reciprocal of that answer, we will get the total time  !!!!

I think this question is one where some people might want to pull out their hair in frustration. I suggest gathering all your information into an organized table. 

We may not be able to fill in all the information, but that is OK! Do not forget what the end goal is! The end goal is to figure out how much time it will take if Paulo and Irina work together. This is the information we know:

• Irina painted 1 room
• Irina painted that room in 9 hours
• Paulo painted the same room
• Paulo painted that room in 8 hours
• Together, Paulo and Irina will paint one room

Now that we know all this information, let's fill in the table. 

Now, what is the painting speed of Paulo? I think you would agree that Paulo can paint at 1 room per 8 hours. This is the rate for Paulo! We can use the same logic for Irina. Irina paints at a speed of 1 room per 9 hours. Let's fill that information in!

In order to fill in the rest of the table, we will have to introduce variables! I will use "x" to represent the number of hours it takes for Paulo and Irina collectively to paint this room. This means that the rate of them together is \(\frac{1\text{ room}}{x \text{ hours}}\). Let's fill that in, as well!
 

We can assume that, if Paulo and Irina work together at their individual rates, then the rate will be the sum. 

Therefore, \(\frac{1}{8}+\frac{1}{9}=\frac{1}{x}\). Let's solve this!
 

Therefore, the correct answer choice is the last one (which is really just a manipulation of the equation I created).

Thanks, Coop!!!!!....here's one more way to determine this :

If direct  we have that

y  =  ax     so

2  = a(5)

a  = 2/5

So......looking at  x  =  10

y  = (2/5)* 10   =   4

But y  should   =  1

So....not direct

If inverse, we have that

y  =  a/x

2  =  a/ 5

10  = a

So.....looking at x  = 10, we have that

y  =  10  / 10   =    1

Which is exactly what we require......so.......inverse

d^2 - 7d + 12               d^2 + 5d + 6

___________     +     ______________

d^2  - d  - 6                  d^2 - 2d  -  15

(d - 4) ( d - 3)            (d + 3) (d + 2)

___________   +     ____________

(d - 3) (d + 2)           (d - 5) (d + 3)

( d - 4)               ( d + 2)

______     +       _____

( d + 2)              (d - 5 )

(d - 4) (d - 5)  + (d + 2)(d + 2)

________________________

  (d + 2)  ( d - 5)

d^2 - 9d + 20  + d^2 + 4d + 4

_______________________

 (d + 2) (d - 5)

   2d^2  - 5d + 24

______________

   (d + 2) (d - 5)

Thank you very much!

15)

\(\frac{\frac{n-4}{n^2-2n-15}}{\frac{n+1}{n+3}}\)

Simplify the polynomial.

\(\frac{\frac{n-4}{(n-5)(n+3)}}{\frac{n+1}{n+3}}\)

Multiply the top and the bottom fraction by the common equation, which is \((n-5)(n+3)\) .

\(\frac{n-4}{(n-5)(n+1)}\)

Choice 3

-----------------

16)

Take all the bottom numbers and make them equal to 0.

\(a^2-16=0, a-4=0, a+4=0\)

\(a^2=16, a=4, a=-4\)

\(a=4, a=4, a=-4\)

So that means \(a\) can NOT be 4 or -4.

Choose the option without those 2 numbers.

Choice 4.

n^2 + 3n + 2                 2n

___________   -    __________

n^2  + 6n + 8            n  +  4

(n + 2) ( n + 1)             2n (n + 2)

____________  -      ____________

(n + 4) ( n + 2)           (n + 4) ( n + 2)

( n + 2) ( n + 1)  - 2n ( n + 2)

________________________

  (n + 4)  ( n + 2)

n^2 + 3n + 2  - 2n^2 - 4n

____________________

  (n + 4) ( n + 2)

-n^2 - n + 2

____________

(n + 4) ( n + 2)

- ( n^2 + n - 2)

____________

(n + 4) ( n + 2)

- (n + 2) (n - 1)

____________

( n + 4) ( n + 2)

- (n - 1)

____________

(n + 4) 

    (1 - n)

____________

   ( n + 4)

Thank you all for your help!!

The graph shows an inverse variation.

Inverse variations are \(z=xy\). \(z\) in this case ​is 10. If you take each column and multiply them together, you get 10. This shows that the relation is inversed.