PLSS HELP: Find the value of w

a plane flies 5.0km due north from a point O and then 6.0km on a bearing of 060° the pilot then changes course on a bearing of 1

Virty [35]

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

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

3 years ago

What is greater .06 or 60%

alexandr402 [8]

60% because you move the decimal over to the left two times for 60% you will get .6
.6 is bigger than .06

5 0

3 years ago

Read 2 more answers

Use the given area of the base and the height to find the volume of the right rectangular prism, in cubic units. Use this formul

Gelneren [198K]

Answer:

Volume = 48.75 cubic units

Step-by-step explanation:

Given the following data;

Base area = 9.75 units

Height = 5 units

To find the volume of the right rectangular prism;

Mathematically, the volume of a right rectangular prism is given by the formula;

Volume = base area * height

Substituting into the formula, we have;

Volume = 9.75 * 5

Volume = 48.75 cubic units

5 0

3 years ago

PLEASE I NEED HELP QUICKLY!!! Find the solution for the given system of equations in the form (x,y). -x+y=8 7x+3y=-6

natka813 [3]

<u>Answer:</u>

The answer D is correct.

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

-x + y = 8 ⇒ ( 1 )

7x + 3y = - 16 ⇒ ( 2 )

y = 8 + x ⇒ ( 3 )

Let us take equation 2 and let us replace y with (8+x).

Let us solve and find the value of x.

7x + 3y = -16

7x + 3 ( 8 + x ) = - 16

7x + 24 + 3x = -16

10x + 24 = -16

10x = -16 - 24

10x = -40

And now let us find the value of y.

For that, let us use equation (3)

Here, we have to replace x with -4 to find the value of y.

y = 8 + x

y = 8 - 4

Now we have to the answers in the form ( x , y )

Let us write.

( x , y ) ⇒ ( -4 , 4 )

Let me know if you have any other questions. :-)

7 0

3 years ago

DOES ANYBODY UNDERSTAND???????????????

Nady [450]

Answer: it would be the first option

Step-by-step explanation:

4 0

3 years ago