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3 years ago

15

Find the equation of the line.

1 answer:

ExtremeBDS [4]3 years ago

7 0

Answer:

It is n 1 -9

Step-by-step explanation:

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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 the slope of the line y=5?

IceJOKER [234]

Answer:

0

Step-by-step explanation:

if you slightly change the equation to better fit standard form (without actually changing its meaning) you get

y = 0x + 5

which means the slope is 0

Also, a shortcut:

<h2><u>Horizontal lines always have a 0 slope while vertical lines have an undefined slope</u></h2>

7 0

3 years ago

In college football, the Associated Press ranked teams from 1 to 25. A first place vote gets 25 points, a second place vote gets

Stella [2.4K]

It all depends on how many wins and losse you have all together in the conference

8 0

3 years ago

Read 2 more answers

F(x)=x^3 <br><br> If g(x) is the graph of f(x) shifted up 4 units write a formula for g(x)

N76 [4]

Answer:

g(x) = x^3 + 4

Step-by-step explanation:

Not much to explain -- g(x) is larger than f(x) by four units for every x.

Of course, to shift the graph down, subtract 4 units.

To get an even deeper understanding, think of how you'd do a left or a right shift of the graph.

Here are the answers, but I'm not going to tell you which is a left shift, and which is a right shift:

g(x) = (x - 4)^3

g(x) = (x + 4)^3

If you can't do it in your head, try plotting a couple of points - don't guess.

5 0

3 years ago

Hi, can you please help?

AnnyKZ [126]

Answer:

A

Step-by-step explanation:

your photo is blurry but I made most of it out and believe that the answer is A. 16

4 0

4 years ago