ElectricPavlov

The arc is a fraction of the total circumference:  85 / 360

TOTAL circumference =  2  pi  r

arc length  =   85/360  x   2 pi (8)     cm 

W = F x d     joules

W = 4.0  x  55  = ......... j

1/8  /3 = 1/24 = 0.0416666666666667      this last digit is rounded up to 7

                            .04166      would be   .0417   rounded

                            .0416        would be   .042

                             .041         would be  .04

2 sin (4x) = 1                      Divied by 2

sin (4x) = 1/2                      arcsin

4 x =  pi/6  and   5pi/6         divide by  4    

x = pi/24    5pi/24

                       Length is   4/7     width is     3 / 7

                                        32                        24   

EACH side is                   16                        12

Diagonal (via Pythagorean theorem)     sqrt (16^2  + 12^2)   

2miles  /   f mile/m     +   8 miles  /  (f+.5) mile/min  =   2min     +   10 miles  /  (f+.5) mile /min

solve for 'f'

2/f  +  8(f + .5)  = 2 + 10/(f + .5)

2/f = 2 + 2/(f+.5)

2(f+.5)  = 2(f+.5)f + 2f

2f+1 = 2f^2 +f + 2f

2f^2 +f - 1 = 0                              f = .5          then faster speed =   1 mile /min

2miles / .5 mile/min     +     8 miles/ 1 mile/min    = 12 minutes for 10 miles   

   10 miles/12 min =   5/6 mile / min  average         (Note:  this is 50 miles per hour average....on a bike !   Was it a MOTORbike ??)

Use Heron's Fomula....Try it !

h=600-16t^2.

h-600 = -16t^2

sqrt  [(600-h)/16)  = t      Taking only the positive square root ...for a positive time value 

sqrt(600-h)/4 = t        Put in 50 for h

sqrt(550)/4 = t     = 5.86 seconds

Area of WHOLE circle =  pi r^2

this sector covers a FRACTION of the whole circle      (5pi/12 ) / 2pi  = 5/24

5/24    x   5^2   =   5.21 in²

each subsequent term is multiplied by -3 and the term before it       r = -3