F(x)=0.5x^2-2 and g(x)=8x^3+2

(f*g)(x) = 4x⁵ - 16x³ + x² - 4

Step-by-step explanation:

To find (f*g)(x), you need to multiply f(x) with g(x).  Use FOIL to multiply.

f(x) = 0.5x² - 2

g(x) = 8x³ + 2

(f*g)(x) = (0.5x² - 2)(8x³ + 2)

(f*g)(x) = 4x⁵ + x² - 16x³ - 4

(f*g)(x) = 4x⁵ - 16x³ + x² - 4

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