NEED HELP ASAP PLEASE!!!
An airplane is headed due south with an airspeed of 300 kph. A wind is blowing from the west at 120 kph. What is the ground speed and direction of the plane?

323 kph with a directional bearing of S 22° E
328 kph with a directional bearing of S 68° E
420 kph with a directional bearing of S 22° E
420 kph with a directional bearing of S 68° E

Answers

Answer 1

Answer:

a) 323 kph with a directional bearing of S 22° E

Step-by-step explanation:

to find the ground speed:

just do the pythagorean theorem.

c²=300²+120²

c²=104400

c=323

to find the directional bearing:

use the law of sines!

sin(90)/323 = sin(θ)/120

(*explanation: since the plane is heading due south and the wind is from due west, it makes a 90 degree angle; and the side opposite of the 90 degree angle is 323. set it equal to sin theta over 120; theta is the angle u r trying to find, and the side opposite of it is 120)

cross multiply:

120sin90=323sin(θ)

divide 323 on both sides:

sin(θ)=0.3715

use inverse sin to find out degree measure:

sin⁻¹(0.3715)=21.8

rounds up to 22.

Answer 2

The ground speed and direction of the plane is 323 kph with a directional bearing of S 22° E. Therefore, option A is the correct answer.

To find the ground speed of the plane, we need to know what a vector is

What is a vector?

A vector is a variable that has both magnitude and direction.

Since the airplane is headed due south with an airspeed of 300 kph, its vector is V = (-300 kph)j.

Also, the wind is blowing from the west at 120 kph. Its vector is v = (-120 kph)i

Now, the ground speed of the plane V' is the resultant vector of the airspeed and wind speed.

What is a resultant vector?

A resultant vector is the sum of two or more vectors.

So, V' = v + V

V' = (-120 kph)i + (-300 kph)j

So, its magnitude V' = √(x² + y²) where

x = -120 kph and

y = -300 kph.

So, V' = √[(-120 kph)² + (-300 kph)²]

= √[14400 kph² + 90000 kph²]

= √(104400 kph²)

= 323.11 kph

≅ 323 kph

The direction of the plane

Its direction, Ф = tan⁻¹(y/x)

Ф = tan⁻¹(-300 kph/-120 kph)

Ф = tan⁻¹(2.5)

Ф = 68.2°

From the South-line we have α = 90° - Ф = 90° - 68.2° = 21.8° ≅ 22°

So, the directional bearing of the plane is S22°E.

So, the ground speed and direction of the plane is 323 kph with a directional bearing of S 22° E.

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Related Questions

please tell me the answer

Answers

I think it would be; maximum 25, minimum -15

To make lemonade Jenny combines water and lemon juice in the ratio of 6:1, by volume. How many millilitres of water should she add to make 637 mL of lemonade?

Answers

Answer:

546 mL of water

Step-by-step explanation:

To make lemonade Jenny combines water and lemon juice in the ratio of 6:1, by volume.

Let the amount of water is 6x and that of lemon juice is x.

ATQ,

6x+x = 637

7x = 637

x = 91

Amount of lemon juice = 91 mL

Amount of water = 6x = 6(91) = 546 mL

So, 546 mL of water she should add to make 637 mL of lemonade.

please help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

w= -12

Step-by-step explanation:

okay I understood it now. Here you go.

You’re welcome :)

Answer:

w= -12

Step-by-step explanation:

x both sides by 24

4w + 15 + -33

move the constant to the right  and change its sign

4w= -33 -15

calculate the difference ...

4w = -48

divide both sides by 4

w= -12

Eddie found a store that sells cell phone cases for $18.50 plus $0.15 per letter engraved on the case. A second store sells cases for $18.00 plus $0.25 per letter engraved on the case. How many letters would Eddie have to engrave on his case for it to cost the same at either store?

Answers

Answer:

5 letters

Step-by-step explanation:

Let x = the number of letters engraved.

For the first store, the cost can be written as (18.50 + 0.15x).

For the second store, the cost can be written as (18 + 0.25x).

For the cost and value of x to be the same, let them equal eachother and evaluate x:

18.5 + 0.15x = 18 + 0.25

0.1x = 0.5

∴x=5

{Please Don't Troll What value of x is in the solution set of -3x+8≥14 {Answer Choices -3,-1,0,3}

Answers

Answer:

x is less than or equal to -2

This means anything equal to or less than -2 is the solution to the ORIGINAL equation. Based on the solution set the answer is -3

Step-by-step explanation:

-3x+8 is greater than or equal to 14

    -8                                               -8

-3x is greater than or equal to 6

-3x/-3                                         6/-3

*THIS WILL CAUSE US TO FLIP THE INEQUALITY SYMBOL AS WE DIVIDED BY A NEGATIVE NUMBER

x is less than or equal to -2

This means anything equal to or less than -2 is the solution to the ORIGINAL equation

Based on the solution set the answer is -3

Hope this helps!

On paper, draw and label point P. Draw and label point Q. Draw a line between the two points using a straight edge. What is the geometric term for the figure in the drawing?

Answers

Just draw what the instruction says and you will get the answer

PLS ANSWER
An employee's time at work increased from 32 hours per week to 40 hours per week. By what percentage did the
time at work per week increase?

Answers

25%
If you add 25% to 32 your answer will be 40

Answer:

You have to take the ratio so you divide the new value on the old value and compare It with 100 so you write

(40)/(32)=(x)/(100)

And this means that x = 125

So the ratio of the increase of the new time is 125%

But the real increase is 125 - 100 = 25%

Farmer collected 225 eggs from his 25 chickens. If each chicken laid the same how much would each chicken had laid

Answers

Answer:c

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

225 divided by 25 is 9.

HEEEEEEEEEEELPkjbflakbeiufakebslkja

Answers

Answer:

The answer is 20 feet..

What are the vertical asymptotes of 10/X-1​

Answers

Answer:

Enter a problem...

Algebra Examples

Popular Problems Algebra Find the Asymptotes f(x)=10/(x^2-1)

f

(

x

)

=

10

x

2

1

Find where the expression

10

x

2

1

is undefined.

x

=

1

,

x

=

1

Since

10

x

2

1

as

x

1

from the left and

10

x

2

1

as

x

1

from the right, then

x

=

1

is a vertical asymptote.

x

=

1

Since

10

x

2

1

as

x

1

from the left and

10

x

2

1

as

x

1

from the right, then

x

=

1

is a vertical asymptote.

x

=

1

List all of the vertical asymptotes:

x

=

1

,

1

Consider the rational function

R

(

x

)

=

a

x

n

b

x

m

where

n

is the degree of the numerator and

m

is the degree of the denominator.

1. If

n

<

m

, then the x-axis,

y

=

0

, is the horizontal asymptote.

2. If

n

=

m

, then the horizontal asymptote is the line

y

=

a

b

.

3. If

n

>

m

, then there is no horizontal asymptote (there is an oblique asymptote).

Find

n

and

m

.

n

=

0

m

=

2

Since

n

<

m

, the x-axis,

y

=

0

, is the horizontal asymptote.

y

=

0

There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.

No Oblique Asymptotes

This is the set of all asymptotes.

Vertical Asymptotes:

x

=

1

,

1

Horizontal Asymptotes:

y

=

0

No Oblique Asymptotes

image of graph

The vertical asymptotes of the given function are x = 1 and x = -1,

We have given the rational function is 10/(x²-1​).

We need to find the vertical asymptotes of this function.

Since Vertical asymptotes occur when the denominator of the function becomes zero and the numerator is not zero.

To determine the vertical asymptotes of the function, we need to solve the denominator for x²-1=0.

x²-1=0

x²=1

x=±√1

x=±1

Therefore, the vertical asymptotes of the given function are x = 1 and x = -1, since the denominator becomes zero at x=1 and x=-1.

To learn more about vertical asymptotes visit:

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A card is drawn from a standard deck of 52 cards. What is the probability this card will be a king or an ace?
A. about 3.9%
B. about 7.7%
C. about 15.4%
D. about 50%

Answers

Answer:

C. about 15.4%

Step-by-step explanation:

There are 52 cards in a deck

There are 4 kings and 4 aces

so, 8/52 is the chance of getting either of those two.

8/52 is about 0.1538 or 15.38%

15.38% rounded would be 15.4%

CAN SOMEONE HELP IM SO CUNFUSED

Answers

Answer:

m = 1/3

Step-by-step explanation:

Answer:

Slope can be indentified by looking t how much a point has gone up/down and to the right/left. An example can be a point at 0,0 and a point at 1,1

from 0,0 to 1,1 it goes 1 units up and 1 unit right. Therefore the slope is 1/1 or just 1.

So to find this answer we could graph the points or just find out how  many units it takes from going up/down and right/left to get from (-2, 1) to (7, 4)

From -2 to 7 is 9 units and from 1 to4 is 3 units

The slope is rise/run meaning the distance u moved in height over he distance moved right/left. Therefore the slope is 3/9 which is 1/3

Step-by-step explanation:

Six girls of differing heights are arranged in 2 rows of 3 each. Each girl is taller than the girl in front of her and also taller than the girl to her right. How many arrangements of the six girls are possible?

Answers

Answer:

5 possible ways

Step-by-step explanation:

Questions like this are a bit technical. Therefore, there are no perfect formula, all you have to do is picture the scene and count. Having said that. Let us use name the positions the girls are standing according to the question:

D E F

A B C

I have arranged this according to how the question has specified, meaning F is the tallest and A is the shortest if I take F to be at the back right and A to be at the front left.

In reality, A and F can never change their positions if we maintain the arrangement specified.

What we have left is to look for how to rearrange, D, E, B and C that will still make it fit the arrangement. Take note that E cannot be in front of B because she is taller than B.

Since positions for shortest and tallest are fixed, you are left with 4 people and you need two of them for the front position. This can be gotten using 4C2 = 6, but the two tall persons can't be in the front else it will disrupt the arrangement, so we have to eliminate that case which will occur once, therefore we have 5 possible ways we can make the arrangements as required.

Elvira used 4 cups of grape juice, 15 cups of cranberry juice, and 2 1 / 2 cup of pineapple juice to make punch. One liter is approximately equal to 4.23 cups. Which measurement is closest to the number of liters of punch Elvira made

A: 1:42 L
B: 10.23 L
C: 25.38
D: 1.77 L

Answers

Answer:

C

Step-by-step explanation:

NEED HELP ASAP!
In this geometric sequence, what is the common ratio?
104, -52, 26, -13, ...

1/2
2
-1/2
-2

Answers

Answer:

the third one: -1/2

Step-by-step explanation:

if you multiply 104 by -1/2 you get -52, and so on the pattern will continue

Answer:

C. -1/2.

Step-by-step explanation:

Common ratio = -52/104 = 28/-52 = -13/26 = -1/2.

PLS HELP ME?? The blue dot is what value on the number line?

Answers

Answer:

-3

Step-by-step explanation:

since it is a gap of 6 the first one gave ...so 3-6=-3

Consider the parent function f(x)=e^x and transformed function g(x)=-f(x)-4. Which features of function F function G are different

Y intercept
End behavior
Domain
Range
Horizontal asymptote

(More than one answer)

Answers

Answer:

y-intercept,

end behavior,

range,

and horizontal asymptote

Step-by-step explanation:

I just finished the PLATO test and these are the answers

The answers are y-intercept, end behaviour, range and horizontal asymptote.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a parent function:

f(x) = eˣ

The transformed function:

g(x) = -f(x) - 4 = -eˣ - 4

g(0) = -5

f(0) = 1

From the graph, we can say the y-intercept, end behaviour, range and horizontal asymptote are different from the parent function.

Thus, the answers are y-intercept, end behaviour, range and horizontal asymptote.

Learn more about the function here:

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Please help meh im so bad at this stuff lol

Answers

Answer:

40 Baskets

Step-by-step explanation:

4 baskets = 1/2 hour

? baskets = 5 hours

This means, 8 baskets = 1 hour

8 x 5 = 40

Therefore,

40 baskets = 5 hours

Answer:

40/1 baskets

Step-by-step explanation:

A cow is eating green grass that grows in a field.

Which type of organism is the grass in this scenario

consumer
decomposer
prey
producer

Answers

A cow is eating green grass that grows in a field. The grass in this scenario is the producer.

'This is a basic food chain. The grass is a living organism that utilizes energy from the sun to make its own food through an interaction called photosynthesis. Then, different creatures eat the grass; it is their wellspring of energy.

Every living organism (plants and creatures) should eat food for the endurance of some sort or another. Plants make their own food through an interaction called photosynthesis. Using the energy from the sun, water, and carbon dioxide from the air and nutrients, they artificially make their own food. Since they make or produce their own food they are called makers.

Organisms that don't make their own food should eat either plants or creatures. They are called buyers. A few creatures get their energy from eating plants while different creatures get energy in a roundabout way from plants by eating different creatures that previously ate the plants.

Creatures that eat just plants are called herbivores. Creatures that eat the two plants and other creatures are called omnivores. Creatures that eat just different creatures are called carnivores.

A few creatures eat just dead or decaying materials and are called decomposers.

to know more about energy click here:

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5×4^²=
(5×4)^²=
(3×4)^²​=

Answers

80x
25x^8
9x^8
THERE IN ORDER

Answer:

I think the answer would be 5.4 squared would be 80. ( 5.4) squared would be 400. And (3.4) squares would be 114. I hope that this helps.

Step-by-step explanation:

PLEASEE HELP.!! ILL GIVE BRAINLIEST.!! *EXTRA POINTS* DONT SKIP:((

Answers

9514 1404 393

Answer:

  7/3

Step-by-step explanation:

The point at the right end of segment 5 is 7 units above and 3 units to the right of the point at the left end. The slope is the "rise" divided by the "run":

  slope = m = rise/run = 7/3

The slope of segment 5 is 7/3.

need help plzz
20 points

Answers

Answer:

42 cm

Step-by-step explanation:

Area of rectangle (shaded area):

length × breadth

length: 7 cm

breadth: 7 - 2(0.5) = 6 cm

7 × 6 = 42 cm

Answer:

42 cm is the correct answer of this one

Gina is using a grid to plan where to dig her garden. She has drawn this figure.
10
9
8
7
3
2
1
0 1 2
8 9 10
Gina decides to reflect her drawing so that Point G is at (1, 1). Which of the
following points will be a corner of her garden?
r
A (6,6)
B. (5, 1)
C. (0,0)
D. (5,7)

Answers

It’s gonna be 5,7 feet

Claire is painting some doors that are all the same size. She used 2 liters of paint to cobe 1 3/5 doors. How many liters of paint are needed for 1 door.?

Answers

Answer:

[tex]1 \dfrac{1}{4} \ liters[/tex]

Step-by-step explanation:

Given that:

Claire uses 2 liters of paint to cover 1 3/5 doors

Then in order for her to paint 1 door, She will need:

2 L = 1 3/5 door

x L = 1 door

[tex]x (L) = \dfrac{2 L \times 1 door }{ 1 \dfrac{3}{5} \ door}[/tex]

[tex]x (L) = \dfrac{2 L }{ 1 \dfrac{3}{5} }[/tex]

[tex]x (L) = \dfrac{2 L }{ \dfrac{8}{5} }[/tex]

[tex]x (L) = \dfrac{2 L\times 5 }{ 8 }[/tex]

[tex]x (L) = \dfrac{10 \ L }{ 8 }[/tex]

[tex]x(L) =1 \dfrac{1}{4} \ L[/tex]

A rectangle has a length that is 12 ft longer
than its width. If its perimeter is 84 ft, what
are the dimensions of the rectangle? Write
a system of equations representing the
situation and then find the dimensions to
obtain full credit.

Answers

4x+24=84 4x=60 x=15 length =27 width = 15

Chris paid $9.18 for a necklace. This amount includes a sales tax of 8%. What was the
cost of the necklace before tax?

Answers

Answer:

8.5

Step-by-step explanation:

What is the image of (7,8) after a reflection over the line y = –x

Answers

Answer:

(-7. -8) Just flip the signs.

Answer:

[tex]\boxed {\boxed {\sf (-8,-7)}}[/tex]

Step-by-step explanation:

When a point is reflected over y=-x, the following change occurs:

[tex](x,y)[/tex]    ⇒  [tex](-y, -x)[/tex]

We are given the point (7,8).

Essentially, we change the signs for both coordinates, then flip the x-coordinate and y-coordinate.

1. Change the signs

[tex](7,8)[/tex]    ⇒    [tex](-7,-8)[/tex]

2. Flip the x and y coordinates

[tex](-7,-8)[/tex]   ⇒    [tex](-8,-7)[/tex]

So the image of (7,8) after a reflection over y=-x is (-8,-7)

While hiking, Diego drank 2¼ liters of water. Lin drank 1⅗ liters of water. How much more did Diego drink than Lin?

Answers

Answer: 13/20

Step-by-step explanation:2 1/4 - 1 3/5 = 13/20

Answer:

13/20

Step-by-step explanation:

Please answer this correctly, and you'll recieve brainliest, Answers below:


28=14=0.25

63=21=2

82=41=4

36=12=0.5

Answers

I believe the scale factor would be 4, seeing as the length of triangle a's bottom side is 2, and triangle b's bottom side is 8.

(Puzzle 2 - Scientific Notation Directions: Using the digits 1 to 9 to fill in the boxes only once, write the largest and smallest absolute value. Then find the decimal equivalent. EX|3.1 X 104- 6.5 X 102| =|31000-650|=|30, 350| is this the largest or smallest? Once you find the largest, start again with new digits and find the smallest. _x10^blank - _ x 10^_

Answers

Answer:

8x(10)^9 - 2 x (10)^1

1x(10)^3 - 9 x (10)^2

Step-by-step explanation:

3.1 X (10)^4- 6.5 X (10)^2

= 31000- 650

= 30,350

For greater number

_x10^blank - _ x 10^_

8x(10)^9 - 2 x (10)^1  ( we use 9 as the power because greater number used as power gives the bigger number and the next smaller number 8 as base. Similarly we use smaller number for power to get a smaller for the greatest difference)

= 8,000,000,000 -20

= 7,999,999,980

For smaller number

_x10^blank - _ x 10^_

1x(10)^3 - 9 x (10)^2   ( we use 3 as the power because smaller number used as power gives the smaller number and the next smallest number 1 as base. Similarly we use next smaller number for power to get the next  smaller for the smallest difference)

= 1000- 900

= 100

We fill in the blanks keeping in mind that we do not have to repeat the numbers from 1-9 and also the numbers should have such an arrangement that they show the smallest and largest possible differences.

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