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We are not  taking  3125 * (1/5)

We  are  taking  the fifth root  of 3125 =     (3125)^(1/5)    =   5    =   r

This is because   5*5*5*5*5   =  3125

Does that  make sense   ???

I got r = 625 because I multiplied 1/5 times both sides. That was what I was taught but it didn't seem right. Shouldn't performing the square root and multiplying by 1/5 give me the same answer?

It is really good to practice these.  

I'm getting in a mess trying to explain it, maybe my method is a bit 'muffled'

I will think about the cos curve first    The parent cos curve can be presented as   

y= amplitude * cos[(2pi/wavlength)(x-phaseshift)+vertical shift  = 1cos [(2pi/2pi)(x+0)+0 = cosx

But your curve has amplitude = 3 and it is upside down so that is -3

the wavelength is pi

there is no phaseshift (not if you put the - in front of the 3)

And it has a vertical shift of -1

so

\(y=-3cos[(\frac{2\pi}{\pi})(x-0)]-1\\ y=-3cos(2x)-1\\\)

or

\(y=3cos[\frac{2\pi}{\pi}(x-\frac{\pi}{2})]-1\\ y=3cos(2x-\pi)-1\\ \)

For the sin curve the wavelength and vertical shift stays the same.  The amplitude also stays the same I will look at only the +3 version

To find the phase shift I want the middle of the wave to sit on the y axis s, at present the closest (to the y axis) middle of the graph with a positive gradient, sits at (pi/4,-1)  I need to move the graph back pi/4

The phase shift is pi/4

So

\(y=3sin[\frac{2\pi}{\pi}(x-\frac{\pi}{4})]-1\\ y=3sin(2x-\frac{\pi}{2})-1\\\)

I have an interactive graph so you can see that all 3 of these are in fact the same wave.

We  can solve this for the common ratio , r

-4 (r)^5  =   -12500      divide both sides  by   -4

r^5  =  3125   take the  5th root of both sides

r   =  5

So  the missing terms are

-20   -100     -500    -2500  

Probably  easiest  to  covert   314₅    into  base 10.....multiply this by  27  and convert this answer back to base 5

3(5)^2  +1(5)  + 4   =   84

84 * 27 =    2268 ₁₀

To  convert  back to base 5

2268 / 5   =   453 R 3

453 / 5     =    90 R  3

90 / 5      =     18 R  0

18 / 5  =          3   R 3

3/5      =          0   R 3

Read  the remainders  from  the  bottom  up to  get  the   base 5 result  of 2268₁₀   =

33033₅

Because its a square, each side must have a perimeter of 37.5 meters. 150/4 = 37.5

Now, because the 4 congruent rectangles are divided evenly, it means that one of the short sides of these rectangles are 1/4 of a side. 

In each rectangle we have 2 square like sides: 37.5 x 2 = 75, and 2 1/4 sides. 

It would be 

1/2 of 37.5 + 75

or 93.75!

The special properties a cyclic quadrilateral has is that 

1. All 4 vertices lie on the edge of some circle. 

2. Opposite angles add up to $180°$ 

Thus, applying #2 here gives us $2x-50 + 3x+20 = 180 \rightarrow \boxed{x = 42}$, which is our answer. 

I also have a method to upload a picture using imgur. Here are the steps. 

1. Go to Imgur.com

2. Click the New Post button in the upper left-hand corner. 

3. Create a new post by dropping the image in or opening it from your computer. 

4. Drag the image into a new tab (like the image below). 

5. Copy the I.Imgur link into the insert image section on web2.0calc and adjust the height accordingly. 

tysm!

Thank you so much mworkhard222!

well, it's an arithmetic sequence and it's clearly increasing, we just need to figure out how much it's increasing by each time.

22 - (-13) = 22 + 13 = 35

there are 4 slots in between but u acually divide it by 5 so, 35/5 = 7

for each term (from left to right) it's increasing by 7.

final answer: -13, -6, 1, 8, 15, 22

CPhill has continued this here:       (Thanks Chris)

yes, that makes sense, thanks!

For guests, you can just message via a post like this one.

One of us will probably see it.

Messaging privately is a nicer, more sure way of doing it though

Either way, don't forget that 'please' goes a long way though.

If are positive and one neg then you have   

1+1-1-1=0

If 2 are neg and one is pos you have

-1-1+1+1=0

There are 2 cases for this (negative, negative, positive) or (positive, positive, negative). 

For this problem, order doesn't matter. 

negative, negative, positive

a and b are negative, and c is positive. 

a/|a| would be -1 since a is negative. 

b/|b| would be -1 since b is negative. 

c/|c| would be 1 since c is positive. 

abc/|abc| would be 1, since negative * negative * positive is positive. 

-1 - 1 + 1 + 1 = 0

positive, positive, negative

a and b are positive, and c is negative. 

a/|a| would be 1 since a is positive. 

b/|b| would be 1 since b is positive. 

c/|c| would be -1 since c is negative. 

abc/|abc| would be -1, since positive * positive * negative is negative. 

1 + 1 - 1 - 1 = 0

So I think there is only one value, 0. 

=^._.^=

I expect you are over thinking it.

if a+b+c=0 and none are 0 (and all are reak)  then one must be neg, one pos and the other either one.  

So when you multiply them together the answer could be positive or negative

a/|a|= plus or minus 1    etc

so maybe you are looking for all the possible combinations of

\(\pm 1\pm1\pm1\pm1\)

Or maybe you can discount some of those answers off.    Think about it a bit.

Anyway, I know someone else is also answering this right now.

It is fixed, thanks Admin  

sqrt  [( x + h)^2  + 9 ]   -  sqrt  [ x^2  + 9]

_________________________________

                              h

sqrt  [  x^2  + 2xh  + h^2   +  9 ]  -  sqrt  [ x^2 + 9]

__________________________________________   

                                    h 

Multiply top / bottom  by    sqrt  [ x^2  + 2xh  + h^2 + 9 ]  +  sqrt [  x^2 + 9 ]

               x^2  + 2xh   + h^2  + 9   - x^2 - 9

________________________________________     =

       h   [ ( sqrt x^2 + 2xh + h^2 + 9)  +  (sqrt (x^2 + 9) ] 

          2xh  + h^2

______________________________________    =       

 h   [ ( sqrt x^2 + 2xh + h^2 + 9)  +  (sqrt (x^2 + 9)  ]

                    h (2x + h)

_______________________________________  = 

 h   [ ( sqrt x^2 + 2xh + h^2 + 9)  +  (sqrt (x^2 + 9)  ]

                      2x  +  h

______________________________________           let   h approach  0     and we have

    [ ( sqrt x^2 + 2xh + h^2  + 9)  +  (sqrt (x^2 + 9)  ]

                         2x

_______________________________________      =

     sqrt (x^2 + 9)   +  sqrt (x ^2  + 9)

                          2x

_________________________________  =

            2sqrt (x^2 + 9)

                                         x

                         ____________________

                               sqrt (x^2 + 9)

If you take Calculus.....you  will   learn  that   the  derivative of  (x^2 + 9)^(1/2)  =

(1/2)  (2x)  / ( (x^2 + 9)^(1/2)  =       x   /  sqrt ( x^2 + 9)        =   our result  !!!!

message them

There is missing information. How many stickers and how many pieces of paper?

Just a slight mistake  by xC.....

2(1/3)  + 2(3/4)  +  1(1/2)  +  1(1/4)  =

2/3   +  6/4  + 1/2  +  1/4  =

2/3   + 3/2  + 1/2  + 1/4   =

2/3 + 1/4  +  2  =

(4*2 + 1*3)  /12   +   24/12

(11/12)  + 24/12  =

35/12   gals  left over

well, y must be greater than x, so x + 2 = y.

\(y^2-x^2=384\) and \(x + 2 = y\)

so solving that system of equations... u get \(x=95, \: y=97\)

so 97 + 2 = 99

2 out of 5 students voted for John. The other students voted for Tommy. If 9 students voted for Tommy, how many students voted in all?

In every group  of 5,  2 voted for John and 3 voted for Tommy

So

2/3  of Tommy's vote  = Jonh's vote

(2/3) (9)  =   6  voted for John

9 +  6   =    15   voted

Let     y  =   n      x =  n - 2      and z = n + 2

So

n^2   -  ( n - 2)^2  =  384

n^2  - n^2  + 4n   -  4   =  384

4n  =  384 + 4

4n =  388

n  =  388/  4    =    97

So

z =  n + 2   = 99