Aboat travels 30 miles north, 20 miles east and 40 miles northeast. what is the angle of rotation of the boats direction from start to finish

The angle of rotation of the boats direction from start to finish = 50.36⁰ to east towards north.

Step-by-step explanation:

Let x axis be east direction and x axis be north direction.

The boat first travels 30 miles north

⇒ Displacement = 30 j

Then boat travels 20 miles east

⇒ Displacement = 20 i

And at last the boat travels 40 miles north east

⇒ Displacement = 40·cos 45 i + 40·sin 45 j

                            = 28.28 i + 28.28 j

Total displacement = 48.28 i + 58.28 j

⇒ θ = 50.36⁰

Hence, The angle of rotation of the boats direction from start to finish = 50.36⁰ to east towards north.

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