CPhill

Just a slight correction.....I believe that EP  meant

200  [  tan (36° )  +  tan (22° )  ]  =    total height of  building

AB  =  √ [4^2  + 8^2 ] = √ 80  =  4√5

COT B   =   BC / AC  =  4 / 8    =   1 / 2

COS A  =   AC  / AB  =  8 / [ 4√5 ] =   2 / √5  =   2√5 / 5

CSC B  =   AB  / AC  =  4√5 / 8  =    √5 / 2

x = 10

y  = -4

r  =  sqrt  (x^2 + y^2)  = √   [  (10)^2  + (-4)^2) ]  = √ [ 100 +16 ]   = √[ 116 ]  = √ [ 4 * 29]  = 2 √29

sec A  =  r  / x    =    2 √ (29)  /  10   =     √29 / 5 

If cos  D  =  5/7

Then   sin C  =  5/7

To calculate  the number of trailing zeroes  we have

integer (380 / 5^1)  + integer (380 / 5^2 ) + integer (380 / 5^3)  =

integer  (380  / 5)   + integer (380 / 25)  + integer (380 / 125)  =

76    +    15   +     3   =

94  trailing zeroes

That seems correct, AnimalMaster......I'm giving it a "thumbs-up"

Thanks, AnimalMaster.....!!!!

We have 4 ways to choose the geography book to occupy the middle position

And  we have  C(5,2)  =  10  ways to choose the  latin textbooks.....and each of these can be arranged in 2 ways

And the other textbooks can be arranged in 6!  = 720 ways

So....the total arrangements  =

4 * C(5,2) * 2 * 720  =

4 * 10 * 2 * 720  =

57,600 possible arrangements

6 minutes 40 sec  =  400 sec

So.....each second the  cold  water fills 1/400 of the tub

8 minutes  =  480 sec

So....each second the  hot water fills  1/480  of the  tub

And  13 min 20 sec  =  800 sec

So....each second, 1/800  of the  tub  is drained

So....we  need to  solve this.....where x is the  number of seconds it takes to  fill the tub

(1/400)x + ( 1/480)x  - (1/800)x   =  1

(2/800)x  + (1/480)x - (1/800)x   = 1

(1/800)x  + (1/480) x  = 1

[ 480 + 800] x / { 800 * 480)   = 1

x  =  (800 * 480)  / { 480 + 800)    =  300 sec  to  fill the  tub =  5 minutes

Call the number of additional weeks  after the  first  five   =  W

And 15 total games have been played during the first  five weeks  = 13 + 2  =15 

The number of total  games  past week 5  =  3W

And the number of total wins past week 5  = 2W

So.....we want to solve this

2  +  2W

________   =   .60              multiply both sides by   13 + 3W

15  + 3W

2 + 2W  =  .60 ( 15 + 3W)      simplify

2 + 2W  =  9  + 1.8W       subtract 1.8W, 2  from both sides

.2W  = 7      divide both sides by .2

W  = 35

So.... 60%  of the games will  be won after week  (5 + 35)   = 40

Check.....after 40 weeks     2 + 2(35)  =  72 games will have been won

And   15 + 3(35)  =  120  games would have been played

So   72 /120    =   .60    = 60%