ElectricPavlov

 Slope = m  =  rise / run    or    (y1-y2) / (x1-x2)    =    ( -1 -  -2) / ( -3-9 ) =  1/(-12) = - 1/12      = m

a is directly proportional to m and n^2, and inversely proportional to y^3.  

  means   a = k mn^2 / y^3

     or    a y^3 / (mn^2) = k    a constant

             9 (4^3) / (2(8^2)) = k

                k = 4.5

       then    a  (3)^3 / ( 6(7^2)) = k = 4.5      solve for 'a'

(The amount of the bill)  x  .05 = amount of tax to be paid

paralellogram rule

2 (30)² + 2(20)²  = 40² + d²

d = sqrt 1000 = 10 sqrt (10)

h(t) = -16t^2 +32t +48       Max will occur at   t = - b/2a =  -  32/(2 *(-16)) = 1

   use this value of 't' in the equation to calculate the max height attained.....

Via Pythag theorem:

Distance from origin =   sqrt ( (4 + 8 cos 60 + 4)²  + (8 sin 60)² )  

From the graph  g(1) = -2

    then f(-2) = 3

     then g(3) = 2

       then f(2) = 1

Even numbers must end in 2 or 4

   first number must be 1 2 3  or  4

         ends in 4     x  y   4        x = 3 choices    y = 3      3*3 = 9 choices

         ends in 2     x y    2        x = 3 choices    y = 3      3*3 = 9 choices                    18 even numbers between 100- 500

To be odd, the number must end in 1 3 5 or 7    4 choices for the last position

   8 choices for each of the other four positions

8 x 8 x 8 x 8 x 4 = .......

Sum of interior anges =   ( n-2) * 180 

     now divide by n to find the measure of each interior angle    (n-2)* 180/n

        the exterior angles are supplementary   ( and exterior is 10 times bigger) 

                                                                            10*  ( 180 - (n-2)*180/n)   =   (n-2)*180/n

                                                                             1800 - 10(n-2)*180/n = (n-2)*180/n

                                                                             1800 = 11 (n-2)*180/n

                                                                             1800n = (11n-22) * 180 

                                                                              -180n = -3960 

                                                                                n = 22 sides