All Answers 355911 Answers

We can write -4 in exponential notation as 4e^(pi*i), so the equation is z^4 = 4e^(pi*i).

By Hamilton's Theorem, the solutions are z = 4^{1/4}*e^(pi*i/4), 4^{1/4}*e^(pi*i/4 + pi/4), 4^{1/4}*e^(pi*i/4 + 2*pi/4), and 4^{1/4}*e^(pi*i/4 + 3*pi/4).  Since 4^{1/4} = sqrt(2) and e^(pi*i/4) = (1 + i)/sqrt(2), the first solution is 1 + i.  Then the other roots work out as

4^{1/4}*e^(pi*i/4 + pi/4) = 1 - i,

4^{1/4}*e^(pi*i/4 + 2*pi/4) = -1 - i, and

4^{1/4}*e^(pi*i/4 + 3*pi/4) = -1 + i.

Volume of box = 20 x 20 x 20 = _________   cm³

    Subtract the volume of the b-ball   V = 4/3 pi r^3        r =10

ZY = √20

XZ = 1/2(ZY = √5

XY = 2(ZY) = √80

Such a triangle is NOT possible!!!

ZY + XZ MUST BE greater than XY!!!

Can you please tell me how u got that answer? I am being asked to show my working. I tried to backtrack to see how I can explain it, but I could not. 

Thank you but that is wrong, I appreciate the effort .

Step  by Step

The    horizontal  asymptote   =    -1

So     the  ratio  of coefficients on x  in the  numerator and denominator  =  1/B  = - 1

So  B  =  -1

The  vertical  asymptote    is   3

So....since this  value of  x  males the denominator =  0.....we  can solve  this

Bx +  C   =  0

-1x + C    =  0

-1 (3) + C  = 0

C   =  3

And  we  have   an  x  intercept    at  4

So

x  +  A  =  0

4  + A   =  0

A  =  -4

Here's  the  graph  :  https://www.desmos.com/calculator/zdco26ojf4

So

A  +  B   +  C    =

-4   + -1  +   3    =

-2

Could you plz tell me how you got that answer? I am not able to make out how you got it. I know that is the right answer though. 

y =  mx + b

mx =  slope

b =  y-intercept

y = 2 + -3

i'm not sure if this is right but this is what I thought of when I saw this.

????

it's not letting me show the photo, does anyone know how to?

The probability is 5/32.

The scale factor  of the  smaller prism  to   the   larger  =  6/8  =   3/4

The  volume of  the  smaller prism, B   =

(Volume of larger prism)  ( scale  factor  )^3   =

800 *   (3/4)^3   =

800 *  9    / 16     =

50  *  9   = 

450 m^3

25x^2  + 16y^2    =  400         divide through  by    400

x^2             y^2

____   +    ____   =      1

 16              25

The center  is   (0,0)........the  foci  lies on the  y  axis  .....so   let F  =  (0, sqrt (25 - 16)  = (0, sqrt (9) )  =

(0, 3 )  = F

The  center of the  second ellipse  is the  the  midpoint of  O   and F   =   (0,0)  and (0,3)  =   (0, 3/2)

y  intercept.....let  x  =  0              x intercept.......let  y  =  0

5(0)   - 12y  = 30                          5x   - 12(0)  = 30

-12y   =  30                                   5x =  30

y = -30/12   =  -5/2                        x =  30 / 5   =  6

Distance  =  sqrt  (  (-5/2)^2   +  6^2  )   =  sqrt  (  25/4  +  36)   =  sqrt ( 6.25 + 36)  =  sqrt (42.25)  =  

6.5   units

We can use  similar  triangles  here

Let A  be the  center  of the smaller circle  and B the  center of the  larger circle

Let BC  =    radius  of  the larger circle        AD  =  radius of smaller cirlce

And  triangles  BCQ   and   ADQ  are similar

Let  AB  be  the  distance  between the  circles' centers   =   12

And   let   x + 1   the  distance  betwen   A    and  Q

We  have  this

BQ / BC  =  AQ / AD

(12  + 1 + x)  /  2     =     (1 + x)    / 1     simplify

13 + x   =  2  (1 + x)

13 + x  =  2 + 2x

13 -  2   =  x

11  =  x

Q  =  (a , 0)  =   ( 5 - (1 + x) , 0)  =  ( 5 - (12)  , 0)  =    (-7, 0)

9  +  27/x   +  8  / x^2   =  0      multiply  through by   x^2

9x^2  +  27x  +  8   =   0         factor   as

(3x  + 1)  (3x + 8)   =  0

Setting  each factor  to 0 and solving for  x  we get  that

x = 1/ 3         or       x =    -8/3

Multiplying  a polynomial  by  a non-zero  constant  does  not change its degree

So

f(x)  +  a * g(x)    =     8th  degree  = greatest possible  degree

https://youtu.be/8wVAbsv-VJw

Yes. Thanks!

(1)         y =   3x  + 5      ......slope  =   3

(2)       2y = 4x + 5      .......slope  =     2

(3)       3y  = 9x - 2     .........slope  =    3

94)       2y  = x - 3       ........slope =  1/2

(5)        4y   =   x -  5    .......slope  =   1/4

Only  one pair    is  parallel    (1)  and (3)    

The  sum  =     sum of all the squares  1 through  42    minus  the  sum  of all the squares  1   through  20

So  we  have

42 (43) (85)/6    -  20 (21)(41)/6      =

22715

N^2  +  85  =  22N       reaarange  as

N^2  - 22N  +  85  =   0               factor as

(N  - 17)  (N - 5)  =   0

Set each factor to  0 and solve for N  and we  have  two possible  values  for N

N=  17     or    N   =  5

z = -1 - i or z = -1 + i 

z^4 = -4

  Solve:

z = -1 - i or z = -1 + i 

Does the answer help you?