ElectricPavlov

web2.0calc.com/questions/help-i-need-help-again

There is   4 P 4 ways to arange the block of 4 math books ....and 4 ways to place this block int groupof 7 

     4 P4   * 4 = 24 * 4   = 96 ways to arrange and place the math books 

then there are   4 P 3 ways to arrange the remaining  Psych books = 24 ways 

24 x 96 = 2304   ways to arrange the books . 

First compute the denom  ....I will ASSUME both of the right terms are in the denominator thusly: 

(1+i) / ( (2-i)(3+i) ) 

(2-i)(3+i) = 

6 + 2i -3i - i^2 

6 - i +1

7 - i 

now you have 

(1+i) / (7-i)             multiply by   ( 7+i)  / (7+i)  to get 

(6+8i)/ 50     which reduces to    (3+4i)/25

Thanx, Chris !    

~EP

.....as an edit...the question asked for radicals in the answer 

                 x = 2 + 2 sqrt(5)     y = 6 + 2 sqrt(5) 

First,  simplify/reduce it to :

2x ^2 -12x + 18 =0      factor out '2'

2 ( x^2 -6x + 9) = 0       now it ieasier to factor 

2 ( x -3)(x-3)  = 0             shows x = 3 

Let's assume there are 100 games :

.75 * 100 * .35  = games won so far 

.25 (100) x       games remaining  times the percentage needed to get to .5(100)  <==== wins = losses

.75 (100) .35   +   .25 (100) (x)  = .5 (100)

     26.25         +  25 x = 50 

          25 x = 23.75

             x = .95                     You need to win 95% of the remaining games                

Find max of   x+y    start with standard circle form 

x^2 -4x    + y^2 - 12y   = 0 

(x-2)^2    + (y-6)^2   =  4 + 36 

(x-2)^2   + (y-6)^2 =  40

Now find the 45 degree line that goes through the center   (2,6) 

             slope    = 1          y = x + b    shows b = 4 

                   so the line is y = x + 4 

                     where the circle and the line intersect will be the max   x+y 

x+4 = y 

sub into the circle equation and solve for x = 6.47124      then y = 10.47124

Mx value of  (x+y)   is 16.94428

Here is a graph: