An airplane is flying in a direction of 75° north of east at a constant flight speed of 300 miles per hour.
The wind is blowing due west at a speed of 25 miles per hour. What is the actual direction of the
airplane? Round your answer to the nearest tenth. Show your work.

The actual direction of the plane is 75° North of west with a speed of 275 mph

Explanation:

Speed of airplane = 300mph

Direction of airplane = (300 cos 75° , 300 sin 75°)

Speed of wind = 25 mph

If the wind is blowing due east then the angle is = 90° + (90 - 75)

                                                                                 = 105°

Direction of wind = (25 cos 105° , 25 sin 105°)

So,

Direction of plane + Direction of wind = Actual Direction of airplane

(300 cos 75° , 300 sin 75°) +  (25 cos 105° , 25 sin 105°) = (x, y)

( 77.65 , 289.78 ) + ( -6.47 , 24.15 ) = (x, y)

(71.18, 265.63 ) = (x, y)

Speed =

Direction:

Therefore, the actual direction of the plane is 75° North of west with a speed of 275 mph

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: