ElectricPavlov

See image below:

(15 m * 60 m       *    1 ft /.3048 m   *  1 ft / .3048 m  )  /  ( 400 ft^2 / gal ) = 24.22 gal    ~~   25 gallons required 

Distance = rate X time 

  the distance is the same for both speeds....so equate them 

    40 mi/hr * t   =   55 mi/hr * (t - .41667)                  <==== 25 minutes is .41667 hr

      -15t = -22.9167

            t =1.53 hr 

at 40 mi / hr   the distance is then    40 mi/hr * 1.53 hr = 61.11 miles 

x = ORIGINAL number of students            3/5 are juniors     2/5 are seniors

then add 12 juniors and subtract 1 senior to get : 

(3/5 x + 12 ) / (2/5 x -1)  = 2/1             cross multiply and solve for x = original # of students = 70 

after adding 11 more = 81 students 

This is the equation of a circle ....look for the right side of the circle ....

x^2 - 4x + 4      + y^2  - 5y   + 6.25 =   10.25 

(x-2)^2   + ( y- 2.5)^2   = 10.25                This is the cirlce....with center at  2,2.5    and radius sqrt (10.25) 

                                                                      the largest 'x' value will be   2 + sqrt (10.25) = 5.2015 units 

Edith runs  14 km in the time it takes Foley to run 9 km 

Edith has 10 km to go to finish 

10/14  =  x/9         shows   x = distance Foley covers while Edith finishes      6 3/7 km 

           so when Edith finishes , Folyey has covered   6 3/7  + 9 =  15 3/7 km and is thus  8 4/7  km  behind Edith 

Given 

J/5 = D     or  5D = J 

  and 

J/ (5+1) = D - 4     Sub in '5D' for 'J'

5D / 6 = D- 4 

shows D = 24  days 

   24 days x 5 workers = 120 Worker Days for the job 

    if you have 6 workers it will take   120/ 6 = 20 Days     (which is FOUR days less...Check !) 

Now ....how many workers to get the job done in  only  FOUR days  ( which is 20 days earlier) 

120 Worker Days / 4 Days =   30 workers needed         or    hire 25 ADDITIOANL workers to add to the original five 

Each of these points is the same radius distance from the center to the point.....using distance formual for the first two points 

(x-22)^2 + (y-15)^2      =   ( x+25)^2 + (y-0)^2     reduces to 

-94x - 30y + 84 = 0 

For the last two points:

(x+25)^2 + y^2 = ( x-22)^2 + ( y+29)^2   reduces to 

94x-58y-700 = 0 

Add the two reduced equations to get 

-88y = 616

y = -7 

Now put this valueof 'y' into either of the reduced equations to find   

x = 3.12765

Center = ( 3.12765, -7) 

I will assume you have this :

(1+i) / ( 2-i) (3+i) )       Multiply the bottom part (the denominator ) to get :

(1+i) / ( 7 -i)                 Now rationalize 

(1+i) (7+i)    /   (7-i)(7+i) 

(6 +8i)   / ( 50) 

1/25 ( 3 + 4i)  

Double root occurs when discrimonant  (b^2 - 4ac)   of the quadratic equation = 0 

First one:   x^2 -2x +1

                               a = 1     b = -2      c = +1   

                             ( -2) ^2 - 4 (1)(1) = 0   ?             yes  =====>    the first one has a double root