Given 4/ (-2 - cos(theta))

what is the distance between the pole and the directrix?

  the distance from pole to directrix is 4 units

Step-by-step explanation:

Rewritten to the form ...

  r = ed/(1+e·cos(theta))

you find ..

  ed = 4/-2 = -2 . . . . . where d is the distance from the pole to the directrix

  e = -1/-2 = 1/2 . . . . . the eccentricity

so d = ed/e = -2/(1/2) = -4 and the ellipse has the equation ...

  r = (1/2)(-4)/(1 + 1/2·cos(theta))

The directrix is a vertical line 4 units from the focus in the -x direction.

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you

hello from mrbilldoesmath!

answer:

x - 3

discussion:

x^2 - 9 = (x-3) (x+3)   so

(x^2-9)/ (x + 3) = x-3

you,

mrb