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 Y axis be north direction.

We have first boat travels 30 miles north

  Displacement = 30 j

20 miles east

  Displacement = 20 i

40 miles northeast

  Displacement = 40 cos 45 i + 40 sin 45 j = 28.28 i + 28.28 j

Total displacement = 48.28 i + 58.28 j

Angle, tanθ = 58.28/48.28

               θ = 50.36⁰

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

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

32

step-by-step explanation: