ElectricPavlov

Seven integers    n  + n+1   n+2 ....... n+6    =   7n + 21

    equals   6 * (n+6) = 6n+36

7n+21  = 6n+36

n = 15    the smallest

Multiply it out....

sqrt3 * 2 sqrt3           - sqrt3 sqrt5            + sqrt5 * 2 sqrt3             - sqrt5 sqrt 5

       6                         - sqr 15                   + 2 sqrt15                      -  5

        1                                   + sqrt15

from 23% to 89%  is 66%  in 30 mins (which is 1/2 hr)

66% /30min =   2.2% per minute

from 23 to 100  %   is  77%

77%  /  (2.2% /min) = 35 mins

The bar's volume = 5 x 6 x 20 cm³ = 600 cm³

Weight of bar is

600 cm³   x   20 gm/cm³  = .........   gm    (see how the cm³ cancels and you are left with gm ?)

sqrt ( 7 x 6 x 5 x 4 x 3 x 2)

2 sqrt ( 7 x   3x2   x  5   x 3   x 2)

4 sqrt (7   x  3      x 5     x 3)

12 sqrt (7 x 5)

12 sqrt 35

x=0ther dog weight

.7x = 12     solve for 'x'

or     12 = x - .3x  

sum of infinite geo series      r = 1/3 for this series

s = a1 (1/(1-r))

  =  90(1/(1-1/3))= 90 * 3/2 =.....

sqrt [2^2 +(-3)^2] =sqrt13

2(2-3i)= 4 -6i       sqrt[ 4^2 +6^2] = sqrt 52 = 2 sqrt13

scalar

Graph #3

Here is a desmos graph     area = 1/2 b h    b = 4   h = 6

https://www.desmos.com/calculator/lrdhcikak0