A ship is stationary at sea.
A tugboat is 36 km away at a bearing of 130°, and a yacht is 27 km from the tugboat at a bearing of 260°.
Draw a scale diagram showing the positions of the three vessels.
Use a scale of 1 : 450,000.
Measure the distance from the ship to the yacht to the nearest km.

Answers

Answer 1

Bearing is a topic that deals with the distance and location of a given object with respect to a reference point. Thus in the given question, the ship is 57.23 km to the yacht.

Bearing is a topic that considers the distance and position of a given object with respect to a reference point. Thus the angles are usually measured with reference to the north pole.

Thus to solve the given question, let the required distance be represented by x.

Applying the cosine rule, we have;

[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2ab Cos C

The angle C between the line from ship to tugboat and from tugboat to yacht can be determined as;

C = [tex]10^{o}[/tex] + [tex]40^{o}[/tex]

C = [tex]50^{o}[/tex]

Thus,

[tex]c^{2}[/tex] = [tex]36^{2}[/tex] + [tex]27^{2}[/tex] + 2(36 x 27) Cos [tex]50^{o}[/tex]

  = 1296 + 729 + 1944(0.6429)

  = 2025 + 1249.8

[tex]c^{2}[/tex] = 3274.8

c = [tex]\sqrt{3274.8}[/tex]

  = 57.2259

c = 57.23

Therefore, the distance from the ship to the yacht is 57.23 km.

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A Ship Is Stationary At Sea.A Tugboat Is 36 Km Away At A Bearing Of 130, And A Yacht Is 27 Km From The

Related Questions

Absolute value of (0, -4/5)

Answers

To answer this question, we need to know what absolute value is in the first place. ANSWERS ARE AT THE BOTTOM.

Absolute value represents how far something is from 0 in a number line.

For example, lets take 4.

4 is 4 units away from 0 on the number line, so the absolute value of 4 is 4.

Now lets look at another example, -4. -4 is also 4 units away from 0, just in the other direction. However, when calculating absolute value, we do not care about the direction. Therfore, the absolute value of -4 is also 4.

Now let's look at your problem.

You want the absolute value of 0 and -4/5

Following the same principle above about the distance from 0, here are your answers:

Absolute value of 0: 0

Absolute value of -4/5: 4/5

Find the y-intercept of the rational function.

A (0, -10)
B (-10, 0)
C (0 , -2)
D (-2, 0)

Answers

Answer:

C

Step-by-step explanation:

The y intercept is when the graph passes the y axis. This occurs at (0,-2)


PLEASE HELP
1-Spin the spinner 20 times, create a table to display the results. What is the experimental probability of spinning yellow?
2-Perform another 20 spins, and record them. What is the new experimental probability of spinning yellow?
3-What is the experimental probability of spinning red or yellow?

Answers

Answer:

24

Step-by-step explanation:

A с Which diagram shows all the lines of symmetry of the regular hexagon? B D A с Which diagram shows all the lines of symmetry of the regular hexagon ? B D please help​

Answers

The diagram that shows all the lines of symmetry is diagram B.

Which diagram shows all the lines of symmetry of the regular hexagon?

We define a line of symmetry as a line such that if we perform a reflection over that line, the image coincides with the preimage (so the reflection does not change the figure).

With that in mind, any line that cuts the hexagon in exactly two halves is a line of symmetry.

So the image that shows all the lines of symmetry of the regular is B, where it shows all the lines that cut the hexagon in two equal halves.

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∠C, ∠F are rt. ∠'s; AB = DE; BC = EF

Answers

abt=de yeah hope it helps

Proving Triangle Similarity


helpppppppppppppppp edge 2022


30 reward thing

edit: nvm i got it

Answers

The Triangle PQR is similar to Triangle TSR by angle-angle prostate or AA .

What is the similarity law for triangles?

It is defined as the law to prove that the two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

We have a given two triangles as shown in the picture.

As we have given QR ⊥ PT

And

Angle QPR ≅ Angle STR  (given)

From the definition of the perpendicular line, the angle at the intersection will be a right angle or 90 degrees.

Angle QRP ≅ Angle SRT

By angle-angle or AA

Triangle PQR is similar to Triangle TSR

Thus, the Triangle PQR is similar to Triangle TSR by angle-angle prostate or AA .

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which relation represents a fuction

Answers

Answer:

It should pass the horizontal and vertical line test.

hope it helps!

Write a product that converts 492 seconds into an equivalent time in minutes. Use division to find the answer.
(It will be a
decimal answer.)

Answers

Answer:

8.2 minutes

Step-by-step explanation:

[tex] \ \frac{492}{60} = 8.2[/tex]

492 seconds = 8.2 minutes

If the side length of a square is 4 inches, it’s area is how many square inches and it’s perimeter is how many inches

Answers

Answer:

The area is 16 inches squared and the perimeter is also 16 inches

Step-by-step explanation:

To find the area, you must multiply the length by the width. Since this is a square, you have to multiply one adjacent side by the other. For perimeter, you can either multiply one side by 4 or add all 4 sides.

Plsssssss answerrrrr

Answers

the answer I knew but I forgot at ate

Jessica Kim Val and twice

are any of these answers correct?

Of all video game players, 1/8 are men over age 50 and 2/5 are women. what fraction represents men younger than 50 years old?

13/40 are men under 50

21/40 are men under 50

17/40 are men under 50

23/40 are men under 50

please helm me out!​

Answers

Answer:

19/40

Step-by-step explanation:

⅛ over 50

⅖ women

5 x 8 = 40

8 x 2 = 16

1 x 5 = 5

16 + 5 = 21

40 - 21 = 19

19/40

Answer:

19/40 are men under 50

Step-by-step explanation:

Given:

2/5 of all video game players are women1/8 of all video game players are men

[tex]\begin{aligned}\textsf{Men under 50 yrs old} & = \textsf{total proportion of men} - \textsf{proportion of men over 50}\\\\& = \left(1-\dfrac{2}{5}\right)-\dfrac{1}{8}\\\\& = \dfrac{3}{5}-\dfrac{1}{8}\\\\& = \dfrac{3 \cdot 8}{5 \cdot 8}-\dfrac{1 \cdot 5}{8 \cdot 5}\\\\& = \dfrac{24}{40}-\dfrac{5}{40}\\\\& = \dfrac{19}{40}\end{aligned}[/tex]

To check this, let's assign a number to the total number of players and use this to help us calculate the proportion of players who are men under 50 years old.

Let the total number of video game players be 400.

If 2/5 of all video game players are women, then the proportion of all video game players that are men is:  1 - 2/5 = 3/5

⇒ total number of men = 3/5 of 400 = 3/5 × 400 = 240

If 1/8 of all video game players are men over 50 years old then:

⇒ number of men over 50 yrs old = 1/8 × 400 = 50

Therefore:

⇒ number of men under 50 yrs old = 240 - 50 = 190

Finally, the fraction of men under 50 years old from all video game players is the number of men under 50 divided by the total number of men.

⇒ men under 50 years old = 190/400 = 19/40

Hey guys. Need help here

Answers

answer is probably D
Here is how i did,
i can be wrong but thats how i figure it out

3. Jeff Ruiz wants to purchase chocolates. The price of a 2-ounce box is $1.10, a 16-ounce box is $8.98, and a
32-ounce box is $17.98.

Answers

Jeff should purchase 25 , 2 ounce box and it will cost him $27.5 .

What is an ounce ?

Ounce is defined as 1/16 part of a pound.

It is given that

price of a 2-ounce box is $1.10,

a 16-ounce box is $8.98

a 32-ounce box is $17.98.

As Jeff wants to purchase total 48 ounce chocolates , the box which is more cheaper has to be determined  

The price of 1 ounce in a 2 ounce box is $1.1 /2 = $ 0.55

The price of 1 ounce in a 16 ounce box is $8.98 /16 = $ 0.56

The price of 1 ounce in a 32 ounce box is $17.98 /32 = $ 0.56

Therefore Jeff should purchase 25 , 2 ounce box and it will cost him $27.5 .

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Which formulas could you use to find the volume of a right circular
cone?
OA) V = B-h where B = I-w
OB) V=B-h where B=1r'
OC) V=B-h where B = Tr
OD) V=B-h where B=1-w

Answers

Answer:

The formula for the volume of a cone is V=1/3hπr².

A bacteria culture starts with 160 bacteria and grows at a rate proportional to its size. After 5 hours
there will be 800 bacteria.

Answers

The population after t hours is 160 x (1.3797)^t.

What is the population after t hours?

The first step is to determine the growth rate of the bacteria:

growth rate = (future population / initial population) ^(1/number of years) - 1

(800 / 160)^(1/5) - 1= 37.97

The exponential function : 160 x (1.3797)^t

Here is the complete question:

A bacteria culture starts with 160 bacteria and grows at a rate proportional to its size. After 5 hours

there will be 800 bacteria. Express the population after t hours as a function of t. population:

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John is 1/8 meter shorter than Paul, and Paul is 0.25 meter taller than Andrew. John's height is 13/4 meters, what is Andrews height?

Answers

Answer:

About 2.13

Step-by-step explanation:

13/4 multiply by 7/8 to get 91/32, then multiply by 0.75(3/4), which is 273/128

what is the system of equations shown in the graph?

Answers

A

The red line goes through the y axes at -2 and goes right 2 and up 1 (1/2)

Same for the blue like it goes through -1/2 and it goes right 1/2 and up 1/2 since it is Sean as X

show that the radius of B is 2.5cm

Answers

Answer:

how?

Please Attach Figure so someone can Solve...

Step-by-step explanation:

Please help with this question thanks!!

Answers

Answer:

(-1,4)

Step-by-step explanation:

Step 1) Change both equations to slope intercept form

3x+y=1 ---> y=-3x+1

5x+y=-1 ---> y=-5x-1

Step 2) Plot lines accordingly on graph

Lines intersect at (-1,4)


Can someone help me please

Answers

Answer:  Choice A)   -3/2

===========================================================

Explanation:

Focus on the endpoints (0,15) and (10,0). They are the y and x intercepts in that order. This is the starting point and ending point of the ball.

The average rate of change is the slope of the line connecting these endpoints. This is when we consider the entire time the ball is in the air.

Let's use the slope formula to get the following:

[tex](x_1,y_1) = (0,15) \text{ and } (x_2,y_2) = (10,0)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{0 - 15}{10 - 0}\\\\m = \frac{-15}{10}\\\\m = -\frac{3}{2}\\\\[/tex]

The slope is -3/2, which is the average rate of change.

It tells us that the height is decreasing by 3/2 = 1.5 meters per second, which is an average speed.

In other words, the ball is going downward at an average speed of 1.5 meters per second.

Keep in mind the instantaneous speed of the ball is changing all the time. The result of -3/2 = -1.5 only applies to the average speed.

------------

Note how the slope formula involves computing the change in y (which was us computing [tex]y_{2} - y_{1} = 0 - 15 = -15[/tex]. It indicates the ball had gone down 15 meters when going from the start point to the ending point. This is the change in distance. The change in time is the [tex]x_{2} - x_{1} = 10-0 = 10[/tex] portion, meaning the duration is 10 seconds.

In short,

slope = rise/run

slope = (change in distance)/(change in time)

slope = (-15)/(10)

slope = -3/2

So this may be a better way to see what's going on rather than rely on a formula in the previous section.

what are the x-intercept(s) of the function

Answers

Zeros of Rational Functions

To find the zeros of a rational function, we must identify values of x that make the numerator equal to 0. We can do this by factoring and by keeping in mind the zero-product property.

The zero-product property states that if the product of two terms is 0, then one of the terms must be equal to 0.

Solving the Question

We're given:

[tex]f(x)=\dfrac{4x^2-36x}{x-9}[/tex]

First, factor 4x out of the numerator:

[tex]f(x)=\dfrac{4x(x-9)}{x-9}[/tex]

Let f(x) = 0:

[tex]0=\dfrac{4x(x-9)}{x-9}[/tex]

In this case, either x or (x-9) is equal to zero, as they are the two terms being multiplied in the numerator to get 0 as a product.

This makes the x-intercepts of this function 0 and 9.

However, the denominator in this function is x - 9. If x = 9, then it would make the denominator 0, which is not allowed. Therefore, x cannot equal 9, and the only x-intercept is 0.

Answer

x = 0

what is the area of stuvwx in the parallelogram below?

Answers

Answer:

fuz what hhde you ha thewebsite and it

John is 36 years old now. 1/4 of his age is equal to 1/3 of sam's age. find their total age in 5 years time

Answers

Answer:

John = 41 years

Sam = 32 years

Step-by-step explanation:

Triangle AA'B'C' is the image of AABC under a dilation.

Answers

The scale factor is 3

Jamaal knows that it is certain that he will win the election because he is the only person who is running for class treasurer. Which value represents the probability that he will win the election?

Answers

Answer:

1

Step-by-step explanation:

since there is no other opponent he is sure to get the position hence the probability is maximum

What is the distance between the tick marks on the number line?

A number line going from 0 to 2 in increments of 1. There are 5 equals spaces between each number.
One-fifth
One-fourth
4
5
Mark this and return

Answers

Answer:

1/5

Step-by-step explanation:

2 units divided into 5 marks each = 10 marks

2/10 = 1/5 unit each mark

1/5
2 units of divided into 5 marks each =10 marks
2/10=1/5 marks

Consider an investment of $6000 that earns 4.5% interest


What is the value of the investment after
15 years if the interest is compounded
annually?

Answers

Answer:

$11,611.69

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsed

Given:

P = $6,000r = 4.5% = 0.045n = 1 (annually)t = 15 years

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=6000\left(1+\frac{0.045}{1}\right)^{(1 \times 15)}[/tex]

[tex]\implies \sf A=6000(1.045)^{15}[/tex]

[tex]\implies \sf A=11611.69466...[/tex]

Therefore, the value of the investment after 15 years will be $11,611.69 to the nearest cent.

Given: l || m; ∠1 ∠3

Prove: p || q

Horizontal and parallel lines l and m are intersected by parallel lines p and q. At the intersection of lines l and p, the uppercase left angle is angle 1. At the intersection of lines q and l, the bottom right angle is angle 2. At the intersection of lines q and m, the uppercase left angle is angle 3.

Complete the missing parts of the paragraph proof.



We know that angle 1 is congruent to angle 3 and that line l is parallel to line m because
. We see that is congruent to by the alternate interior angles theorem. Therefore, angle 1 is congruent to angle 2 by the transitive property. So, we can conclude that lines p and q are parallel by the

.

Answers

The parts that are missing in the proof are:

It is given

∠2 ≅ ∠3

converse alternate exterior angles theorem

What is the Converse of Alternate Exterior Angles Theorem?

The theorem states that, if two exterior alternate angles are congruent, then the lines cut by the transversal are parallel.

∠1 ≅ ∠3 and l║m because we are: given

By the transitive property,

∠2 and ∠3 are alternate interior angles, therefore, they are congruent to each other by the alternate interior angles theorem.

Based on the converse alternate exterior angles theorem, lines p and q are proven to be parallel.

Therefore, the missing parts pf the paragraph proof are:

It is given∠2 ≅ ∠3converse alternate exterior angles theorem

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Answer:

it is given

angle 2

angle 3

converse alternate exterior angles theorem

Step-by-step explanation:

Analyze the graph of the given polar curve. If possible, describe the shape of the graph (circle, rose curve, limacon, etc), and state the domain, range, and maximum r-value of the graph. State whether the graph is continuous and whether it is bounded. Describe any symmetry the graph has. Give the equations of any asymptotes or state that the graph has no asymptotes. theta = pi / 5

Answers

The shape of the graph = rose

The domain = all real numbers

Range = [-2,2]

Maximum r-value = Symmetric about the x-axis

The graph is continuous = Yes

Is it bounded = Yes

Any asymptotes = No

This is further explained below.

What is a graph?

Generally, the graph is simply defined as a graph is a graphical representation of a relationship, usually between two variables, where each variable is shown along with one of two orthogonal axes.

In conclusion, there is no break in the graph, and it has finite limits.

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What number is the arrow pointing at?

Answers

Answer:

170

Step-by-step explanation:

each little mark is adding 20 to the 100 you see there and because the arrow is pointing somewhere in between two of the marks, it means it's just adding 10. Now you have to add 100 + the marks + 10

* remember you have three marks and each one of them is equal to 20 so when you add them, you get 60.

100 + 60 + 10 = 170

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