i need help with this problem ;-;

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

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

[tex]\vec r = r\cdot (\sin\theta, \cos \theta)[/tex] (1)

We can obtain the resulting vector ([tex]\vec R[/tex]) by the principle of superposition:

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

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

[tex]\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})[/tex]

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

The magnitude of the resultant is found by Pythagorean theorem:

[tex]\|\vec R\| = \sqrt{R_{x}^{2}+R_{y}^{2}}[/tex]

And the bearing is determined by the following inverse trigonometric relationship:

[tex]\theta_{R} = \tan^{-1} \left(\frac{R_{y}}{R_{x}}\right)[/tex] (3)

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

[tex]\|\vec R\| = \sqrt{(5\sqrt{3})^{2}+6^{2}}[/tex]

[tex]\|\vec R\| \approx 10.536\,km[/tex]

[tex]\theta_{R} = \tan^{-1} \left(\frac{6}{5\sqrt{3}} \right)[/tex]

[tex]\theta_{R} \approx 34.715^{\circ}[/tex]

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

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

Step-by-step explanation:

Answer:

5 miles

Step-by-step explanation:

add the points together.

it seems like each point is how many miles they ran each day.

1/4 + 2(1/2) + 3/4 + 3(1) = 5

Answer:

5.3333

or 5 and 1/3

Step-by-step explanation:

10 = 3x - 6

add six

16 = 3x

divide by 3

5.3333 = x

I hope this helps!!

Answer:

give heaven some hell by Hardy

Step-by-step explanation:

Answer:

hola saludos desde kansas city

Remainder=0

Quotient=7

Thanks!!

Answer:

C.

Step-by-step explanation:

You're trying to figure out how many more hours he needs to work in order to have worked for 240 hours.

Answer:

the answer should be 2.5

Step-by-step explanation:

when divided 5/8 u get 0.625 and when u divided 1/4 u get 0.25 and u divided both answer u get 2.5

708 ml

When each box contains 236 ml of juice and she pours three boxes into the bowl, you need to multiply 236 by 3. After completing the calculation, you would get 708.

Answer:

5.2%

Step-by-step explanation:

Volume of cylinder= πr²h

In Container A,

D= 18ft, r=18/2=9ft, h=15ft

volume= 22/7 × 9² × 15

= 26730/7 cubic ft.

In Container B,

D=16ft, r= 16/2=8ft, h=18ft

volume= 22/7 × 8² × 18

= 25344/7 cubic ft.

percent of amount of water left in Container A= percent of container A that is full after pumping

Amount of water left in Container A,

26730/7 - 25344/7 = 1386/7

Therefore, % of container A that is full= 1386/7 ÷ 26730/7 × 100

(1386×7×100)/(7×26730)= 5.185

To the nearest tenth= 5.2%

Answer:

  y = 1/2x +7/2

Step-by-step explanation:

The two marked points are 2 units apart vertically, and 4 units apart horizontally. The slope of it is ...

  m = rise/run = 2/4 = 1/2

The value of the y-intercept can be found from

  b = y -mx . . . . . . where (x, y) is a point on the line

Using the point (-1, 3), we find the y-intercept to be ...

  b = 3 -(1/2)(-1) = 3 1/2 = 7/2

Then the slope-intercept equation is ...

  y = mx +b

  y = 1/2x +7/2

Answer:

y=−38x−14y is equal to negative 3 eighths x minus 1 fourth is the answer.

Answer:

12

Step-by-step explanation:

You do 6+6, or 2+2+2+2+2+2=12

Answer:

D

Step-by-step explanation:

n = 5

an = 176

an = a1*x^(n -1)

a5 = a1 * x^4 = 176

a7 = a1 * x^6 = 704

a7/a6 = a1 * x^6 / a1*x^4 = 704 / 176

Cancel out a1

x^6/x^4 = 704/176      Divide numerator and denominator by 176

x^2 = 4                        Take the square root of both sides

x = 2 or - 2

176 = a1 * x^4

176 = a1 * 16

a1 = 11

a1 is going to be 11 whether x is 2 or minus 2.

hi mallllll. hehehe

once again its [tex]a_{1} = -11[/tex]

Answer:

7 inches

Step-by-step explanation:

756÷108=7

that's about it, but I just divided the area and length.

Answer:

12/q  acorns/squirrel

[tex]3 \div 4 \frac{1}{2} \\ = 3 \div \frac{9}{2} \\ = 3 \times \frac{2}{9} \\ = \frac{2}{3} [/tex]

Answer:

[tex] \frac{2}{3} [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

correct answer is explained in the picture attached

Answer:

Keegan is 16 and Jamie is 13.

Step by Step Explanation:

So if we were to take the number 39 and divide it by 2, we would get 19.5. Since Jaime is 3 years younger, we would subtract 3 from one of the 19's. Then we would add 1.5 to both of the numbers since that 3 we subtracted has to go somewhere in that 39, and we come up with the numbers 21 and 18. Since it is asking how old they are NOW and not in the future, we subtract 5 from both numbers to account for the 5 years, and we end up with the years 16 and 13.

Math:

39÷2 = 19.5

19.5 19.5

-3

___________

16.5 19.5

+1.5 +1.5

___________

18 21

-5 -5

13 16

Answer:

rubbing it against your hair it causes friction and with friction comes energy

Answer:

See below for answers

Step-by-step explanation:

1) The Fundamental Theorem of Algebra states that in an nth-degree polynomial, there are n zeroes at most, including those that are complex. Therefore, there are 6 zeroes in the function since it's a 6th-degree polynomial.

2) Reduce the polynomial and use the Zero Product Property:

[tex]0=6x^3+25x^2-24x+5[/tex]

[tex]0=(6x^2-5x+1)(x+5)[/tex]

[tex]0=(3x-1)(2x-1)(x+5)[/tex]

[tex]x_1=\frac{1}{3},x_2=\frac{1}{2},x_3=-5[/tex]

Answer:

11 mm, 21 mm, and 16 mm.

Step-by-step explanation:

since 11+21>16, 11+ 16>21>11, You can form a triangle with 11,21,16

Answer:

yeah that makes sense to me

Answer:

5: 4

6: 20

7: $3.20

8: 92

9: 22

10: $11.60

Step-by-step explanation:

6. remove 3 from 83, you will have 80 and then divide by 4 = 20 students in a class.

7. Subtract 8.80 from 24.80, you will get 16 dollars. Do 16 ÷ 5 = 3.2 as the cost of each pencil.

9. 94- 6 = 88 so, 88 ÷ 4 = 22.

10. 13.40 -7.60 = 5.8 as his weekly allowance.

I hope it helps.

Answer:

Step-by-step explanation:

P = (-4, 3)

Reflecting across the y axis negates the x value

P₁ = (4, 3)

Reflecting across the x axis negates the y value

P' = (4, -3)

option D

Answer: for 3) 427 hikers

Step-by-step explanation: b + 178 + b = 676

2b + 178 = 676

2b = 498

b = 249 bikers

h = 249 + 178 = 427 hikers