I NEED HELP PLEASE THANKS! An airplane is taking off headed due north with an air speed of 173 miles per hour at an angle of 18° relative to the horizontal. The wind is blowing with a velocity of 42 miles per hour at an angle of S47°E. Find a vector that represents the resultant velocity of the plane relative to the point of takeoff. Let i point east, j point north, and k point up.
(Show work)

30.7i + 135.9j + 53.4k

Step-by-step explanation:

The ' horizontal ' may act as the x - axis in this case, the airplane taking off at an angle of 173 cos 18 respective to this x - axis. Respectively it travels restricted to an angle of 173 sin 18 from the y - axis. The following shows this angle at vector( s ) j and k relative to the air -

j - ( 173 cos 18 ),

k - ( 173 sin 18 )

Thus, one can assume such -

Knowing that, this second bit here should be similar to the first bit above, given that the wind is now blowing  with a velocity of 42 miles per hour at an angle of 47 degrees. Therefore, j = 42 cos 47, i = 42 sin 47 -

Adding the two we should get the following -

  30.72i+ 135.89j +53.46k

Step-by-step explanation:

If we measure angle φ up from the horizontal and angle θ CCW from east, the direction vector of the airplane at take-off is ...

  (ρ, θ, φ) = (173 mph, 90°, 18°)

The rectangular expression of this vector will be ...

  (ρ·cos(θ)·cos(φ), ρ·sin(θ)·cos(φ), ρ·sin(φ)) = (0, 164.53, 53.46) . . . mph

__

The wind vector is ...

  (ρ, θ, φ) = (42, -43°, 0°) ⇒ (30.72, -28.64, 0) . . .  mph

And the rectangular coordinate sum of these vectors is ...

  (0, 164.53, 53.46) +(30.72, -28.64, 0) = (30.72, 135.89, 53.46)

The resultant velocity vector of the airplane is ...

  30.72i+ 135.89j +53.46k

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0