ElectricPavlov

Use Pythagorean theorem for right triangles to find the hypotenuse (distance between the towns. d)

d^2 = 5^2   + 7 ^2       solve for 'd'  miles

rate  *  time = distance

(13-c) t   = 30      13t - ct =30

(13+c) t  = 48       13t + ct = 48     add these two equations together  :   26t = 78     t = 3  

                                                                 now subtitute this value of  't'  into one of the equations to solve for 'c'

Cost will be fixed costs and costs per unit * units

c(x) == 200 000  + 300x

average will be  c(x) /x      C = ( 200 000 + 300x )/x   = 200 000/x + 300

Plug in   500   and   2000   and  4000  into C to find the average cost will go down as the number of bikes produced is increased.....

numerator =    2 ( 3 ^2/3)

denominator =  1 + 3^1/3 + 3^2/3             Multiply numerator and denominator by (1-3^1/3)

and simplify to  (after all of the steps)   to    3 - 3^2/3       or   3 - \(\sqrt[3]{9}\)

174 tix total

a = adult tix                     revenue from adult tix = $ 8a

174-a = c = children tix   revenue from child tix =  $ 6 (174-a)      the revenues summed = $ 1342

8a  + 6 (174-a) = 1342    solve for 'a' the number of adult tix .....    then 174-a = child tix

Maximum will occur at x = -b/2a =  1/ (2 ( 32/70^2)) =   4900/64 = x = 76.563 feet

Substitute this value of 'x' in to the h(x) equation to find the height at this point......

2.5 gal water  - 1/4 gal - 5/8 gal - Lettuce gal = 3/4

2.5 - 1/4 - 5/8 - L= 3/4     solve for L the amount (in gallons) used for lettuce

...or    Four point two - zero - nine.    Sometimes people will say   four point two- OH- nine

I suppose you are wondering the least number of each (buns and dogs packages) to have the same number of each :buns = dogs

LCM of 10 and 6 is 30     so Raf would buy 5 packs of hot dogs and 3 packs of buns.

Can you clear up all of that LaTex.....  I can't read it.....