Solve the equation algebraically, and then use a calculator to find the values on the interval [0, 2π). (Enter your answers as a comma-separated list. Round your answers to four decimal places.)

I don't know what other radians I left out... any help is very much appreciated thank you.

pi/3, pi, 2pi/3

Step-by-step explanation:

1+tan²x = sec²x

sec²x - 1 - secx -1 = 0

sec²x- secx - 2 = 0

sec²x - 2secx + secx - 2 = 0

secx(secx - 2) + 1(secx - 2) = 0

secx = -1

cosx = -1

x = pi

secx = 2

cosx = ½

x = pi/3, 5pi/3

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