ElectricPavlov

If the tuition is raised to $ 1000  that is a raise of 200 over the current 800 and represents x = 8  (25 * 8 = 200)

  substitute x= 8 in to the equation

(12000-300(8))(800+25(8)) = revenue        I'll let you do the math from here...

B has to be 5 x 5   since it is whole number w and d

so  A = 5 *x = 40     x = 8   A = 5 x 8

Then C = 6 x 5 = 30

and D is 6 x 8 = 48

= 3^(2(x+1)) + 3^(3(x+1)) = 36

(3^2 +3^3)^(x+1) = 36                           this is incorrect!!!  See CPhil answer below!

36^(x+1) = 36

(x+1) Log 36 = log 36

x+1 = 1

x=0

Center at 7,-3  and passes thru the origin...

  Radius is distance from center to origin

     sqrt(7^2 +3^2) = SQRT 58 = r

circle with center at h,k      (x-h)^2 +(y-k)^2 = r^2

so the circle in question is given by        (x-7)^2 + (y+3)^2 = 58

The previous examples had very few choices and hence a low number of possible combinations.  THIS example has

6 x 4 x 20 x4  combinations =1920 combinations.....   THAT is a very large tree to draw!

(12000-300x)(800+25x) = $ revenue

I am just looking t it and can see x = 0....I'll let Chris work out the details.....

Look at x= 3    go straight up to intersect the graph at  5

Here is a graph of the arch:

Let's put one base leg at 0,0 and the other leg at 20,0

and write the equation of a parabola in vertex form

the vertex will be at (h,k) = 10,80 

  Vertex from = a(x-h)^2 + k  so:

      f(x) = a (x-10)^2 + k

             = a (x^2-20x +100) + 80

      We know that point 0,0 is on the graph, so let's sub that in to help find 'a'

             0 = a(0^2-20(0) +100) + 80

             0 = 100a +80

             a = -80/100 = -4/5

So the equation is     f(x) = -4/5 (x-10)^2 + 80

at f(x) = 20        20 = -4/5(x-10)^2 + 80

                          60 = 4/5 (x-10)^2

                           75 = (x-10)^2

                          +- sqrt 75 = x-10

      x = sqrt 75 +10      and - sqrt 75 + 10

      x = 18.66   and  1.34 ft       The width is the difference between these x coordinates = 17.32 ft