ElectricPavlov

Triangle side length rule says the sum of any two sides must be greater than the remaining third side

17 +11 >  b       b<28

11+b > 17          b > 6

17 + b > 11        any 'b'         so        6 < b < 28      means the largest b would be   27    

Check it now! 

3/4 t    =    2/3 h        means    h = (3/2)(3/4)t = 9/8 t 

h+ t = 408     sub in the red value above for 'h'    and then solve for 't'

For this to occur, the discriminant of the quadratic formula,  b^2 - 4ac , must be <0

(-m)^2 - 4 (3)(21) <0

m^2 < 252

m<15.87              So the answer would be ________

Diagram?

Y= mx + b       m = slope    b = y -axis intercept

m = slope = rise / run = (y1- y2) / (x1-x2) = 6/7

y = 6/7 x + b      now sub in either of the two points given to calculate the value of 'b'

-11 = 6/7 (5) + b        b = -107/7

your line is then     y = 6/7 x   - 107/7

# of ten dollar increase in tix price = x

revenue =  (40 000 - 100x)(200 + 10x)

                   ( 8 000 000 + 400 000x - 20 000x - 10 000x^2 )    

                    (-10 000 x^2 + 380 000 x + 8 000 000)          this is a dome shaped parabola (due to the negative coefficient for x^2)

                               max will occur at x = -b/2a     =   380 000/ (10 000(2)) = 19  

19 ten dollar increases will make ticket price = 200 + 190 = 390 dollars

I THINK there are 24 possible delivery combinations

...for exactly two to be correct:

1 1 x x

x 1 1 x

x x 1 1

1 x x 1

1 x 1 x

x 1 x 1            6 ways to deliver two correctly      6 / 24 = 1/4

Formula for a  n-gon sum of interior angles   (n-2)(180)

   (n-2)(180) > 1970

n > 12.94

n =13    as a convex polygon has angles < 180 degrees      example: n= 14 would = 2160     which is 190 more than 1970 

(14x+22)/(2x+18)=3x+1       Multiply both sides of the equation by (2x+18)

14x +22 = (3x+1)(2x+18)     expand and simplify to

6x^2+42x-4 = 0     Now use Quadratic Formula       to find x values    

       a = 6    b = 42    c = -4    in the Quadratic Formula

\(x = {-42 \pm \sqrt{42^2-4(6)(-4)} \over 2(6)}\)