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Xelga [282]
4 years ago
5

A plane traveled 1012 miles each way to Warsaw and back. The trip there was with wind. It took 11 hours. The trip back was into

wind. The trip back took 22 hours. What is the speed of the plane in still air? What is the speed of the wind?
Mathematics
1 answer:
lesya [120]4 years ago
3 0

Answer: speed of plane is 69/miles per hour

Speed of wind is 23 miles per hour

Step-by-step explanation:

Let x represent the speed of the plane.

Let y represent the speed of the wind.

A plane traveled 1012 miles each way to Warsaw and back. The trip there was with wind. It took 11 hours.

This means that the speed is x+y miles/hour. Therefore

1012 = 11(x+y)

1012 = 11x + 11y - - - - - - - - 1

The trip back was into wind. The trip back took 22 hours.

Since it flew against the wind, the speed would be x-y km/hour

Distance = speed × time. Therefore

1012 = 22(x - y )

1012 = 22x - 22y

Dividing through by 2

506 = 11x - 11y- - - - - - - - - 2

Adding equation 1 and equation 2, it becomes

1518 = 22x

x = 1518/22 = 69

Substituting x = 69 into

1012 = 22(x - y )

x - y = 1012/622= 46

y = 69 - 46 = 23

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PLEASE HELP! 50 Points!
gulaghasi [49]

The bearing of the plane is approximately 178.037°. \blacksquare

<h3>Procedure - Determination of the bearing of the plane</h3><h3 />

Let suppose that <em>bearing</em> angles are in the following <em>standard</em> position, whose vector formula is:

\vec r = r\cdot (\sin \theta, \cos \theta) (1)

Where:

  • r - Magnitude of the vector, in miles per hour.
  • \theta - Direction of the vector, in degrees.

That is, the line of reference is the +y semiaxis.

The <em>resulting</em> vector (\vec v), in miles per hour, is the sum of airspeed of the airplane (\vec v_{A}), in miles per hour, and the speed of the wind (\vec v_{W}), in miles per hour, that is:

\vec v = \vec v_{A} + \vec v_{W} (2)

If we know that v_{A} = 239\,\frac{mi}{h}, \theta_{A} = 180^{\circ}, v_{W} = 10\,\frac{m}{s} and \theta_{W} = 53^{\circ}, then the resulting vector is:

\vec v = 239 \cdot (\sin 180^{\circ}, \cos 180^{\circ}) + 10\cdot (\sin 53^{\circ}, \cos 53^{\circ})

\vec v = (7.986, -232.981) \,\left[\frac{mi}{h} \right]

Now we determine the bearing of the plane (\theta), in degrees, by the following <em>trigonometric</em> expression:

\theta = \tan^{-1}\left(\frac{v_{x}}{v_{y}} \right) (3)

\theta = \tan^{-1}\left(-\frac{7.986}{232.981} \right)

\theta \approx 178.037^{\circ}

The bearing of the plane is approximately 178.037°. \blacksquare

To learn more on bearing, we kindly invite to check this verified question: brainly.com/question/10649078

5 0
3 years ago
Kai lives 3 kilometers from school, Brea lives 30,000 meters from school, and Cal lives 30,000 centimeters from school. Which st
Sedbober [7]

Answer:

D. Brea lives the farthest from school

Step-by-step explanation:

The easiest way to go about this is to get them all to the same unit. Let's do meters :)

3 kilometers = 3,000 meters (Kai)

30,000 centimeters = 300 meters (Cal)

and then of course 30,000 meters is already in the correct unit (Brea)

Given all of this, you can easily tell that the answer is D

6 0
3 years ago
!!!! PLEASE HELP !!!!!!
Keith_Richards [23]

Answer:

i got -8 but the closest is -7 so u can tried that

Step-by-step explanation:

5 0
3 years ago
A number cubed is subtracted from a different number.
Aleksandr [31]
What do you mean ?!???
8 0
3 years ago
3 A class has 6 boys and 15 girls. What is the ratio of boys to girls?​
Lubov Fominskaja [6]

Answer:

6:15

Step-by-step explanation:

Hope this helps, lemme know if you need any further help (:

7 0
3 years ago
Read 2 more answers
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