A plane that travels a distance $r$ , in kilometers, with a bearing of $\theta$ sexagesimal degrees can be represented in standard position by means of the following expression:

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

We can obtain the resulting vector ( $\vec R$ ) by the principle of superposition:

$\vec R = \Sigma_{i=1}^{n} [r_{i}\cdot (\sin \theta_{i}, \cos \theta_{i})]$ (2)

If we know that $r_{1} = 5\,km$ , $\theta_{1} = 0^{\circ}$ , $r_{2} = 6\,km$ , $\theta_{2} = 60^{\circ}$ , $r_{3} = 4\,km$ and $\theta_{3} = 120^{\circ}$ , then the resulting vector is:

$\vec R = 5\cdot (\sin 0^{\circ}, \cos 0^{\circ}) + 6\cdot (\sin 60^{\circ}, \cos 60^{\circ}) + 4\cdot (\sin 120^{\circ}, \cos 120^{\circ})$

$\vec R = (5\sqrt{3}, 6) \,[km]$

The magnitude of the resultant is found by Pythagorean theorem:

$\|\vec R\| = \sqrt{R_{x}^{2}+R_{y}^{2}}$

And the bearing is determined by the following <em>inverse</em> trigonometric relationship:

$\theta_{R} = \tan^{-1} \left(\frac{R_{y}}{R_{x}}\right)$ (3)

If we know that $R_{x} = 5\sqrt{3}\,km$ and $R_{y} = 6\,km$ , then the magnitude and the bearing of the resultant is:

$\|\vec R\| = \sqrt{(5\sqrt{3})^{2}+6^{2}}$

$\|\vec R\| \approx 10.536\,km$

$\theta_{R} = \tan^{-1} \left(\frac{6}{5\sqrt{3}} \right)$

$\theta_{R} \approx 34.715^{\circ}$

The plane flies a distance of approximately 10.536 kilometers in <em>straight</em> line and with a bearing of approximately 035°.

To learn more on vectors, we kindly invite to check this verified question: brainly.com/question/21925479

6 0

2 years ago

Brandon rolls a six sided die twenty times, and records the result in the table below. how many times did brandon roll above the

Radda [10]

The average is the arithmetic mean of all the observations of a set of numbers. The number of times Brandon rolls above the average is 7.

<h3>What is average?</h3>

The average is the arithmetic mean of all the observations of a set of numbers. it is found by dividing the sum of all the observations of the set by the number of observations in the set.

$\rm{Average=\dfrac{Sum\ of\ observations}{Number\ of\ observations}$

In order to know the number of times Brandon rolls the dice above the average, we first need to calculate the average of the twenty rolls.

The average of the 20 times dice rolls,

$\rm Average = \dfrac{6+1+3+4+4+4+6+5+5+3+6+4+4+5+2+3+5+4+4+2}{20}$

$\rm Average = \dfrac{80}{20} = 4$

Thus, the average of the 20 rolls of the dice is 4.

Now, the number of times the result of the dice roll is above 4(x>4) is 7.

Hence, the number of times Brandon rolls above the average is 7.

Learn more about Average:

brainly.com/question/2426692

8 0

2 years ago

What does the equation √3/8

GalinKa [24]

Step-by-step explanation:

The square root of 3 is the positive real number that, when multiplied by itself, gives the number 3. It is denoted mathematically as √3. It is more precisely called the principal square root of 3, to distinguish it from the negative number with the same property. The square root of 3 is an irrational number.

8 0

3 years ago

What is the distance between (22,-3) and (1, -3)?

Bingel [31]

Answer:

Option D

Step-by-step explanation:

<h2>Distance between two points</h2>

The y-value of the two points is unchanged. So, the line is parralel to x-axis.

The distance will be the diffrence between the x-co ordinates.

$\sf Distance = 1 - (-2\dfrac{1}{2})$

$\sf =1+\dfrac{5}{2}\\\\= \dfrac{2}{2}+\dfrac{5}{2}\\\\=\dfrac{7}{2}\\\\=3\dfrac{1}{2}$

6 0

2 years ago