CPhill

An 8% grade means that  for every 100 horizontal feet of "run", the "rise" is 8 feet

So........using the tangent inverse, we have

tan^-1 (8 /100)  ≈ 4.57°

Profit = Revenue - Cost   ...  so...

P(x)  = R(x) - C(x)

[ 7x^2-3x+18 ] - [ 3x^2+x-89 ]  =

a.  P(x)  =  4x^2 - 4x + 107

Avg Rate of Change from Year 3 to 5   =

[ P(5)  - P(3) ]  / [ 5 - 3]

P(5)  =187

P(3)  = 131   ....so....

b.  [187 - 131] / 2    = [56/ 2} =   +$28M  per year

Assuming we're in degrees

Cos(11.3) = 65/x      rearrange as

x = 65/Cos(11.3) ≈  66.28

39-47x+18y=0     rearrange as

18y  = 47x - 39    divide through by 18

y = (47/18)x - 39/18

y = (47/18)  - 13/6

The y intercept is  at -13/6   and   the slope is 47/18

Here's the graph :

The  end point will be  ( -1/2, -√3/2 )

The line has the equation  y = -2x      (1)

The circle has the equation  x^2 + y^2  = 1     (2)

Sub (1)  into (2)

x^2 + (-2x)^2   = 1

x^2 + 4x^2  = 1

5x^2  =  1           divide both sides by 5

x^2  =   1/5           take both roots

x  = ± 1/√5

And using (1)   when   x  = 1/√5,   y  = -2/√5

And when  x = -1/√5,  y  =  -2 (-1/ √5)  =   2/√5

So.....the intersection points are   ( 1/√5, -2 /√5 )   and   ( -1/√5,  2/√5)

m/2-5m/6=7    multiply through by the common denominator of 2, 6  →  6

3m - 5m   = 42

-2m   =  42        divide both sides by -2

m = -21

We can use the tangent, here

tan (240)  = tan(60)   =  √3/1  = √3

And that will be the slope of the radius

We can use similar triangles here

30 / 52   =  H / 20        where H is the height that the shadow stries the building

Cross-multiply

20 * 30   = 52 * H

600 = 52 * H    divide both sides by 52

600 / 52  = H  ≈  11.5  ft 

Here's a pic :

ab^3  =  54         a = 2     b = 3

2 * 3^3  =

2 * 27  =

54