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Citrus2011 [14]
3 years ago
8

If 9x + 2a =ac - bx, then x equals

Mathematics
1 answer:
suter [353]3 years ago
3 0

Answer: x=\bold{\dfrac{a(c-2)}{9+b}}

<u>Step-by-step explanation:</u>

9x + 2a = ac - bx

9x         = ac - bx - 2a    <em>subtracted 2a from both sides</em>

9x + bx = ac - 2a           <em>added bx to both sides</em>

x(9 + b) = a(c - 2)           <em>factored out x from the left and a from the right</em>

  x=\large\boxed{\dfrac{a(c-2)}{9+b}}\\          <em>divided both sides by 9+b</em>

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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.
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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)

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\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

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