CPhill

arctan (15.4 / 11.8) = about  52.54°

50%  = .5   ...so....

.5 *  225  =

112.5

 0.00000000000000000000000001169  = 

1.169 x 10^-26  

The first part concerning the auto dealer is irrelevant since he receives the same deal no matter which of his employer's plans he opts for.

a) At 18000 km per year, he receives    18000(.223) + 2000 = 6014   under the first option

Under the second option, he receives   18000(.32)  = 5760  ......so the first option is better

b) Let x be the distance at which the reimbursements are the same....and we have....

.223(x) + 2000   =  (.32)x    rearrange as

2000   =  0.097x      divide both sides by 0.097

x = about 20619 km

(x + 4) (x - 1)  =

x^2 + 4x -1x - 4  =

x^2 + 3x  - 4

 x^2 + y^2 + 6y = 7      complete the square on y

x^2  + y^2 + 6y + 9   = 7 + 9        simplify

x^2 + ( y + 3)^2  = 16       which we can write as

(x - 0)^2 + (y + 3)^2   = 16

So.......the center is   (0, -3)    and the radius  is 4

[2/3-1/6]/[2/5-1/3]    =      get  a common denominator of 6 on top and 15 on bottom

[ 4/6 - 1/6]  /   [ 6/15 - 5/15]  =     simpiify

[3/6] / [ 1/15]    =    

[1/2] /  [1/15]   =      invert tthe denominator and multiply

1/2 *  15/1   =

15/2   =

7 + 1/2

3/15  = 1/5  = 20%

81/49 =10/ x      cross-multiply

81x = 49 *10

81x = 490       divide both sides by 81

x = 490/81

Split this up as two separate series

1 + 4 + 7 + 10 +....+ 301      and

-3  - 6  - 9  - 12 -.....- 300

The number of terms in the first series can be found as follows :

301 = 1 + (n - 1)3

300 = (n - 1)3

100 = n - 1

n = 101

So.....the sum of the first series = 

(101)(1 + 301)/2  =  15251

The number of terms in the second series can be found as follows:

-300 =  -3 - 3(n - 1)

-297  = -3(n - 1)

99  = n - 1

n = 100

So.......the sum of this series  =

(100)(-3 + -300)/2  =  - 15150

So......the sum of the two series =  15251  - 15150   =  101