ElectricPavlov

None.    Zero.    Nada.    Nix.  

3 batches    *     7/12   cup/batch   = 21/12 =   1  3/4 cups              ( note that the number of pancakes per batch is irrelevant)

5 min = 1/12 hr      in five minutes your friend will have a  3 m/hr * 1/12 hr = 1/4 mile head start

    You are walking two miles per hour faster and will take    1/4 m / 2 m/hr = 1/8 hr to catch her = 7.5 mins

         7.5 + 5 = 12.5 mins

Find slope , m, between the points    (y1-y2) / (x1-x2) =  -1

y = -x + b    sub in one point to find b = 10

y = -x + 10       when the line crosses the x axis    y = 0

0 = - x + 10       shows   x = 10

For clarity, I re-labelled the points   alpha and beta in the diagram below

   Now if you look at point R    you can see that it is just point  b   minus the amount of point  a    ......   right?

      similarly    point   b    PLUS the maount of point  a     would land you at  S

        b   is approximately 145 degrees      2 * 145 = 290 degrees ....which would be point  U

              look at point  a     go the same amount in the clockwise direction from the x-axis to get to   -a  ...... this would be point  T

The shaded sector is  60 degrees out of the ENTIRE circle's 360 degrees

Find the area of the ENTIRE circle by using   Area = pi r²

     then multiply by   60 / 360   to get the answer in ft²

It has been a while since I did these kind of calculations, but here is my stab at it :

140 MPa  = 140 x 106  N/m²

15 m - 1.6 m free board  = 13.4 m high

Volume of the cylinder of molasses = pi r² h  = pi (12)²  * 13.4  = 1929.6 pi  m³

    mass of this volume        1929.6 pi m³  ( 1.5)(1000 kg/m³)   = 2 894 400 pi kg

Find stress using    F_s = ma     using mass above   =  28 394 064 pi  N

Now find the thickness ( if 100% weld efficiency)

   F = stress * area             where stress is  28 394 064 pi N     area = pi d t = pi 24 t  =  75.39822 t

   140 x 10^6 N/m²  =  28 394 064 pi  N  * 75.398223 t  m²

       solve for t = .0208155 m       

Now factor in the 80% efficiency of the welds     .0208155 m / .8 = .02601 m   =   ~~ 3 cm     ( I think !    ~ EP  )

2/3  of  3/4   =  2/3 * 3/4 =   6/12  = 1/2 of a large pizza

Guess I should have noted that the equation is 'balanced' ..... for the solution posted above to be true.

r = b - a

s = a + b

u = 2 b

t = - a