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.

choice b is correct

step-by-step explanation:

we have been given the following system of inequalities;

we are required to graph the solution to the system of inequalities. using a graphing tool, the graph of the system is as shown in the attachment. the continuous line represents the graph of while the dotted line represents .

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.