CPhill

The equation that sets the ratio of θ to the area of sector BAC equal to the ratio of 360 to the area of the circle shown above.

To see why this is so.....let the radius = 1

So the area of the circle = pi(1)^2 =  pi

Now....imagine that θ = 60°

So

60  / area of sector  =   360 / pi

60 /area of sector =  360 /pi       we can write

area of sector / 60 =   pi /360       multiply both sides by 60

area of sector =   (60 /360) pi   =    pi /6   

Since 60° is 1/6 of 360°.....the area should be  (1/6) pi   =  pi /6

Minor arc AB =  arc of whole circle - major arc ACB =  360 - 286  =  74°

2^2005 = 2^2004 + ____      subtract  2^2004 from both sides

2^2005 - 2^2004  =  -------      factor the left side  [ note that 2^2005 = 2*2^2004  ]

2^2004 ( 2 -  1) =  _______

2^2004 (1) =   ______

2^2004 =   _____

The area of the sector is x/360 times the area of the whole circle.

1 m = 100 cm

So ....the rocket flies 300 * 100 = 30,000 cm sec

So

30,000 / 300  =   100 times as fast

4ft x 5 ft =    48 in * 60 in =  2880 in^2

He already has enough tiles to fill  83 (2 * 5) = 83 * 10  =  830 in^2

So....the remaining area left to fill is   2880 - 830  =  2050 in^2   left to fil

Each piece of the wedge-shaped tile has an area of  3.14 (3)^2 ( 40/360) = 3.14 in^2

So....the number of pieces he needs =   ceiling  [ 2050 / 3.14 ]  = 653 pieces 

A square has 4 sides

The product is   4 * 11 =  44

Since AD = DC....then angles CAD and  ACD are equal

And angle ACD = 40 = angle CAD

So....angle  CDA =  180 - 40 - 40 =  100

So angle ADB = 180 - 100 =  80

And BD = BA.....so angles BAD and ABD are equal

So angle BAD =   [ 180 - angle ADB ] / 2 =  [ 180 - 80] / 2 = 100/ 2 = 50

So angle BAC = angle CAD + angle BAD  =  40 + 50  =  90°

Some info missing here...

The common difference is second term - first term =   - 9 - 6 =   - 15

So the third term is  -9 - 15  = -24

And the common ratio   is  third term / second term =   -24 /-9 =  8/3

So....the fourth term is   -24 (8/3) =  -64

So   x , y   =      -24, -64