ElectricPavlov

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Not sure of your syntax.... can you re-post it?

This makes a right triangle...hypotenuse = 80

          Height = opposite

sin 40 = opp/hyp = opp/80

.643 = opp/80

51.4 ft  = opp = height

1 / 8!  +  1 / 9*8! = x / (10*9* 8!)

9/(9*8!) + 1 /(9*8!)

10 / (9 *8!)  = x / (10*9*8!)

100/ (10*9*8!) = x / (10*9*8!)

x = 100

Rate x time = distance

m/s   x   s   = meters

Formula for CIRCUMFERENCE of a circle is   Pi * d      You are given both of these ....mutliply to get your answer   ....

The point divides the line into two segments in ratio of 3:1    the point is thus 3/4 from the end.     (3 +1 =4)  

    there are two points (depending on which end of the line you start at ) which will divide the line this way....

I will assume the point P is furthest away from A

the x coordinate will be    0  +   (10 - 0 ) x 3/4 = 7.5

the y coordinate will be  5 +  (13-5)   x 3/4  = 11

x+y = 18.5     Sorry....this was for INTERNAL  ratio division

For EXTERNAL  ratio of 3:1    m = 3 n = 1

Formula: Y={[(mx2-nx1)/(m-n)],[(my2-ny1)/(m-n)]}

3(10)-(1)(0)   /   ((3-1) = x_p =  15

3(13)-1(5)     / (3-1)      = y_{p = 17}                        

_{Thanx geno for spotting my error !}

1    The package will have its horizontal velocity of 500 m/hr  PLUS the VERTICAL velocity  which will be determined by the airplane's height...which is not given....   Need more info    but it will be more than 500, so I think the last choice is best....

2   The vehicles are approaching each other at 60 + 40 = 100/m/s

       to cover 800 m  will require   800 m / 100 m/s = 8 seconds  to metal-bending

          NOW, you should be able to calculate how far the fly can travel in 8 seconds....yah?

Higher airplane      tan 60 = opp/adj = 3150/adj

Lower airplane       tan 30 = (3150-d)/adj                     Solve this system of equations for d   tan 30 = .5774   tan 60 = 1.732

3150/1.732 = adj (from first eq)

sub into second equation

.5774 = (3150-d)/ (3150/1.732)

1050.12 = 3150-d

d= 2099.8 =~2100 m   

The total area of the 5 inch  square would be   5 x 5= 25 units^2

a 4 x5 rectangle would be 20

a 3x5 rectangle would be 15      total  60

1/2 of this (due to the diagonal would be  30

Subtract the white rectangular areas above the 4 and 3 inch squares

  30     - 4x1     - 3 x2  =   30 - 10 = 20 sq units