Answer:
Step-by-step explanation:
Given
i.e. 10 people
Required
Probability of being next to each other
First, we calculate the total possible arrangements (without any restriction)
If the three are to be next to each other,
First, we arrange the three
Now, the 3 will be seen as 1; so, we have a total of 8 people i.e. (1 + 7 others)
The arrangement is:
So, the total arrangement, when they have to be next to one another is:
The probability is:
Expand
Express as percentage
Answer:
The drift angle is approximately 7.65° towards the East from the plane's heading
Step-by-step explanation:
The speed of the plane = 350 mph
The direction in which the plane flies N 40° E = 50° counterclockwise from the eastern direction
The speed of the wind = 40 mph
The direction of the wind = S 70° E = 20° clockwise from the eastern direction
The component velocities of the plane are;
= (350 × cos 50)·i + (350 × sin 50)·j
= (40 + cos 20)·i - (40 × sin 40)·j
The resultant speed of the plane = +
= 265.915·i +242.404·j
The direction the plane is heading = tan⁻¹(242.404/265.915) ≈ 42.35°
Therefore, the drift angle = Actual Angle - Direction of the plane = 50 - 42.35 ≈ 7.65° towards the East