CPhill

Excellent, Guest  !!!

Le the rate of the current  = R

Rate with the current  = 8 + R

Rate against the current  = 8 - R

So....Distance / Rate  = Time   and we have that

The time it takes to go downstream + 4 hours   = time to go upstream   ...and we have....

60/ [8 + R]  + 4   =   60 / [8 - R ]     

4   =  60 / [8 - R]   -  60/ [8 + R ]     simplify the right side

4  =   (60[8 + R]   - 60[8 -R] )  / [  ( 8 + R) (8 -R) ]      cross-multiply

4 [  ( 8 + R) (8 -R) ]  =  480 + 60R - 480 + 60R

4 [ 64 - R^2]   =  120R      divide through by 4

64 - R^2  = 30R        rearrange

R^2 + 30R - 64   =  0

Factor

(R - 2) (r + 32)  = 0

Setting each factor to 0   we have that R =-32 mph   [reject ] or R = 2 mph

So....the current = 2 mph

4/3  =   

1 + 1/3   ≈

1.33333......

-4/6 /  6    =

-4/6  /  [ 6 / 1]  =

[-4 / 6] *  [1 / 6]  = 

-4 / 36  =

-1 / 9

7 -  [2/3] x  <  x - 8       add 2/3x , 8 to both sides

15 <  [5/3]x      multiply both sides by 3/5

9 < x   →    x > 9

Total number  =    players per team * number of teams  = 15k

Given that sin(a)= √17/9 , cos(a)= 8/9, and tan(a)= √17/8 find csc(a), sec(a), cot(a).

csc(a)  = 1 / sin (a)  =   1 / [  √17/9 ]  =  9 /  √17   =   [ 9  √17 ]  / 17

sec(a)  = 1 / cos (a)  =  1 / [8/9]   = 9/8

cot (a)  =  1 / tan (a)   =  1 / [ √17/8]  = 8 √17 =  [ 8 √17 ] / 17

pi/ 16  + pi/2  =    [get a common denominator of 16]

(1)pi/16  +  8pi/ 16  =

9pi  / 16

Length  = √ [25^2 - 7^2 ]  = √ [625 - 49]  = √ 576   =  24

2√N  = 30    divide both sides by 2

√N  = 15      square both sides

N  = 225