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.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204