ElectricPavlov

z = - 2.1 means 2.1 standard deviations below the mean

    2.1   x   8.2 = 17.77 years below the mean

35 - 17.22 = 17.78 =  ~~ 17.8 y/o

Rf is the mass?       Fulcrum at the far end    mass  2.5 ft from moving end ?

^

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|_________7.5ft __________________|-m-|____2.5 ft______

                                                                                                 ^_f

Calculate the entire area of the circle  pi r^2 =   64 pi

the upper R quadrant is  1/4 of this   =  16 pi

now subtract the area of the triangle   1/2 b h = 1/2 8*8 = 32

chord area =  16 pi - 32 = ......... cm^2

in 2 1/2 hours the ship travels    2.5  x 15 = 37.5 miles

the x component is   37.5 cos 214^o = -31 miles

the y component is   37.5 sin 214  =   ~ - 21 miles

if 0^o  is north :

31 miles south    and 21 miles west        ( 214 degrees would be southwest )

From 7/8 to 4/3 is     32/24 -21/24 = 11/24

     from 1 to 4/3 is    1/3   

1/3   out of   11/24     =   1/3 /  11/24 = 24/33 chance=    8/11

x component of trajectory =   73 cos 34   f/s   

    Now how long will it take to travel 49 yards (= 147 feet) ?

          147 / (73 cos 34) = 2.43 seconds

INITIAL y component of trajectory = 73 sin 34 f/s = 40.82 f/s  

     but THIS velocity is acted upon by gravity

        y = y0 + v_ot - 1/2 a t^2       

                          y0 = 0        Now we need to know the y value at 2.43 seconds to see if it will clear the uprights

        y = 40.82 (2.43)  - 1/2 (32.174)(2.43)²  = 4.2 Feet      Tooo low !   Missed it by  5.8 feet

First    sec = 1/ cos      to have a negative sec   cos must be negative (Q II and III)

- 2 sqrt 3/3  is the same as  -2/sqrt 3    and this is   1/ cos

     so cos (3x) = -sqrt 3/2

               3x = 5pi/6     and    7pi/6     

                  x = 5 pi/18            7 pi/18

q iii

t  i u

q iv

You can draw a venn diagram to help....

Assume there is 100 kids   (100%)

75 + 30 + 15 = 120     there is 20 too many      20 % must ride both

https://web2.0calc.com/questions/helpsssss