Bearings Problem Solving Question:
From a lighthouse two boats can be sighted. Boat 1 on a bearing of 60° at a distance of 2km and Boat 2 on a bearing of 340° at a distance of 3km.
a) If Boat 1 is in need of assistance, what bearing would Boat 2 need to travel on to reach it?
b) Assuming Boat 1 does not move, how far would Boat 2 have to travel?

Answers

Answer 1

9514 1404 393

Answer:

  a) 123.4°

  b) 3.3 km

Step-by-step explanation:

In (N, E) coordinates, Boat 1 is located relative to the lighthouse at ...

  2(cos(60°), sin(60°)) = (1.0, 1.732) . . . . . km

Boat 2 is located at ...

  3(cost(340°), sin(340°)) = (2.819, -1.026) . . . . . km

So, relative to Boat 2, Boat 1 is located at ...

  (1, 1.732) -(2.819, -1.026) = (-1.819, 2.758) . . . . . km

This is at a bearing of ...

  arctan(2.758/-1.819) = 123.4°

and a distance of ...

  √(1.819² +2.758²) ≈ 3.304 . . . . . km

a) Boat 2 would need to travel on a bearing of 123.4°.

b) Boat 2 would need to travel 3.3 km.

_____

Additional comment

We use (North, East) coordinates so we don't have to do the mental gyrations necessary to translate to and from (E, N) coordinates. The latter would correctly orient a map relative to the X-Y Cartesian plane. The former are equivalent to flipping the map over and looking at it from the back side. This is a "rigid transformation", so angles and distances remain unchanged.

Bearings Problem Solving Question:From A Lighthouse Two Boats Can Be Sighted. Boat 1 On A Bearing Of

Related Questions

(50 points really need help on this it's the last question)

Answers

Answer:

Pretty sure it's C

Step-by-step explanation:

trUst mE

A,C,E

Step-by-step explanation:

I got it right on my test

What is the range of the graph?​

Answers

Answer:

D

Step-by-step explanation:

the graph is forever extending to infinity, so there's no definite range

Please help me pls plsss

Answers

Answer:

c is correct

Step-by-step explanation:

If you look at it, 2x is the slope. Always remember the formula y = mx + b

The mx is your slope. And the whole number is your b or y - intercept

Hope this Helps!! :)

Pierce removes the plug from a trough to drain the water. The volume, in gallons, in the trough after it has been unplugged can be modeled by the expression 10x2 −17x + 3, where x is the time in minutes. Choose the appropriate form of the expression that would reveal the time in minutes when the trough is empty.

10(x − 3)2 − 1
10(x − 1)2 − 3
(5x − 1)(2x − 3)
10(0)2 − 17(0) + 3

Answers

Answer:

(5x - 1)(2x - 3)

10x^2 - 17 + 3 = (5x - 1)(2x - 3)

Answer:

C.(5x − 1)(2x − 3)

The price of a book, which regularly sells for $24, was marked down by 25%. A coupon reduced the price by another 10%. What was the final selling price?

Answers

Answer:

$16.20

Step-by-step explanation:

24.00 × 25%= 6.00

24.00 - 6.00 = 18.00

18.00 × 10%=1.80

18.00 - 1.80 = 16.20

A percentage is a way to describe a part of a whole. The final cost of the book will be $16.2.

What are Percentages?

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given the cost of the book is $24. Therefore, the cost of the book after a 25% discount is,

Cost of book after discount = $24×(100%-25%) = $18

Now, the cost after the 10% counpon will be,

Cost after the 10% counpon = $18×(100%-10%) = $16.2

Hence, the final cost of the book will be $16.2.

Learn more about Percentages:

https://brainly.com/question/6972121

#SPJ2

Select the correct answer.
What is the value of y?
A.3
B.8
C.4
D.16

Answers

A. It’s 3..............

Steven warms a cup of a coffee to a temperature of 195°F and then leaves it to cool in a room that is 75°F. This equation represents the
temperature, T, of the coffee in the cup after x minutes.
T = 75 + 120e-0.051
After how many minutes will the temperature of the coffee be approximately 141°F?

Answers

Answer:

12 minutes

Step-by-step explanation:

First substitute 141°F for T in the given equation.

Then isolate the exponential term.

Now rewrite the equation as a natural log, and solve for x.

After 12 minutes will the temperature of the coffee be approximately 141°F.

What is temperature?

Temperature is the degree of hotness or coldness expressed in terms of any of numerous scales, such as Fahrenheit and Celsius. Temperature suggests the route wherein heat strength will spontaneously flow—i.e., from a warmer body (one at a better temperature) to a less warm frame (one at a lower temperature).

diploma measures of temperature are typically expressed with the ° temperature scale: The sample became heated to 80 °C.

Substitute the 141°F in the equation

     ⇒T = 75 + 120e-0.051

     ⇒ 141 = 75 + 120x - 0.051

     ⇒ 120x = 141 -75 + 0.051

     ⇒120x = 66.051

   

Learn more about temperature here:-https://brainly.com/question/24746268

#SPJ2

6. Mr. Walthour is building a storage shed in a conical shape. The base of the shed is 4 meters in diameter and the height of the shed is 3.8 meters. What is the volume of the shed? Round to the nearest tenth. (Example 2)​

Answers

I think it helps you..............

What does x equal in this problem

Answers

X is equal to 277........
277
good luck!!!!!!!

find the area of the composite figure ​

Answers

Answer:

12 x 13 = 156

17 - 12 = 5 x 12 = 60

156 + 48 = 216

And angle measures 54° more than the measure of its complementary angle what is the measure of each angle

Answers

Answer:
The measure of the angles are 72 degrees and 18 degrees
Step-by-step explanation:
we know that
If two angles are complementary, then their sum is equal to 90 degrees
Let
x -----> the measure of an angle
y-----> the measure of he other angle
we know that
x+y=90 -----> y=90-x -----> equation A
x=y+54 ----> equation B
substitute equation B in equation A and solve for y
y=90-(y+54)
y=90-y-54
2y=36
y=18°
Find the value of x
x=y+54 -----> x=18+54=72°
therefore
The measure of the angles are 72 degrees and 18 degrees

aaaa helppp :((((!!!!!!!!!!

Answers

Answer:

I am pretty sure it is the third one

Step-by-step explanation:

Answer:

yea for sure the third one

Step-by-step explanation:

What is the degree measure of
A
310
34
58
D

Answers

Answer:

34

Step-by-step explanation:

A triangle always has a sum of 180 degrees

First, let us find the right angle

180-149=31

Now find v

180=31+115+x

180-146=x

x=34

Name the interval on which the function graphed below is
increasing.

1. X>1.5
2. X<1.5
3. X>0
4. -1

Answers

Answer:

Step-by-step explanation:

x > 1.5

Whats the answer to x^2=9

Answers

Answer:

x=3

Step-by-step explanation:

3 times 3 is 9

Answer:

X=3

Step-by-step explanation:


O 91.7 miles
O 55.5 miles
O 41.7 miles
O 63.8 miles

Answers

Answer:

* 55.5 miles

Step-by-step explanation:

17² + b² = 23²

289 + b² = 529

b² = 240

b = 15.491 ≈ 15.5

17 + 23 + 15.5 = 55.5

You can also simply notice B is the only answer with a .5 decimal and thus don't have to add.

Find the equation of the line between the points (10, – 5) and ( - 2,0).

Answers

Answer (assuming it can be in slope-intercept form):

[tex]y = -\frac{5}{12} x-\frac{5}{6}[/tex]  

Step-by-step explanation:

1) First, find the slope of the line between the two points by using the slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. Substitute the x and y values of the given points into the formula and solve:

[tex]m = \frac{(0)-(-5)}{(-2)-(10)} \\m = \frac{0+5}{-2-10} \\m=\frac{5}{-12}[/tex]

Thus, the slope of the line is [tex]-\frac{5}{12}[/tex].

2) Next, use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] to write the equation of the line in point-slope form. Substitute values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] in the formula.

Since [tex]m[/tex] represents the slope, substitute [tex]-\frac{5}{12}[/tex] in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point the line intersects, choose any of the given points (it doesn't matter which one, it will equal the same thing) and substitute its x and y values into the formula as well. (I chose (-2,0), as seen below.) Then, isolate y and expand the right side in the resulting equation to find the equation of the line in slope-intercept form:

[tex]y-(0)=-\frac{5}{12} (x-(-2))\\y-0 = -\frac{5}{12} (x+2)\\y = -\frac{5}{12} x-\frac{5}{6}[/tex]

1/8 to decimal number​

Answers

Answer: 0.125

Step-by-step explanation:


Brookwood High School is considering adding co-ed soccer to the sports program for the fall
season. In order to get an unbiased sample of interest in soccer, who should the school survey?
A. girls in PE class

B. members of the soccer team

C. every fifth student entering the cafeteria

D. students in freshman homerooms

Answers

Answer:

B

Step-by-step explanation:

HELP DUE IN 10 MINS! Determine whether the triangle described is right, obtuse, or acute. Show work to justify your answer.

7, 10, 13

This triangle is a obtuse, acute, right triangle?? because blank number is equal to, greater than, or less than another number??

Answers

Obtuse scalene triangle

Find the value of x.

Answers

Answer:

66

Step-by-step explanation:

subtract each external angle by 180 to find the interior angle.

Since you know that all of the interior angles add up to 540 because 180(n-2)

with n is how many sides in the polygon

so 180(5-2)=540

now take each value and subtract it by 180

180-(45)=135

180-(40)=140

180-(x)=180-x

180-(77)=103

180-(2x)=180-2x

135+140+180-x+103+180-2x=540

738-3x=540

x=66

hope that helps :)

Please give brainliest

I have to fill out the missing years can someone help me quickly

Answers

The 2 one is 200 and 4 one is 300

Find the rate of change given the following solutions: (6, 2) and (1, 12).

Answers

Answer:

The rate of change is -2

Step-by-step explanation:

f(b)-f(a)     12-2              10

---------- = ------------  = -------- = -2

 b-a         1-6               -5

A pet home owner wants to keep the ratio of cats to dogs at 3:5. She has 21 cats, how many dogs are there in the pet home?

Answers

35 dogs

Step-by-step explanation:

The ratio of cats to dogs can also be written as

3/5 = 21/x

x = 35

-6(-2x -y + 4)

It also says to use the distributive property

Answers

Answer:

The answer is 12x+6y-24

Step-by-step explanation:

Answer:

12x + 6y -24

Step-by-step explanation:

X(-9x^2-5x+9)
..................

Answers

(-9x^3-5x^2+9x)
hope it helps

Which expression is equivalent to (18x + 9k) + (2x + 6k)?
16 x + 3 k
20 x + 15 k
20 x + 16 k
36 x + 54 k

Answers

20x + 15k is the answer we just have to remove the bracket and add the terms

hope it helps

Answer:

20x + 15K

Step-by-step explanation:

just add like variables (x and Y)

Simplify the Expression

Answers

11a^3-4a^2-14a-7 is the correct answer :)

What is the value of the expression below when x=10x=10 and y=4y=4?
8x-7y
8x−7y

Answers

Answer:

Step-by-step explanation:

8(10) - 7(4)

8X10 - 7X4

80 - 28

52

Simplify

12d divided by 2

Answers

Answer:

6d

Step-by-step explanation:

6d . You divide 12 and 2 which is 6 then add the d on your answer.
Other Questions
write two (2) if the dance step is for 2/4 music and write three (3) if the dance step is for music 3/4.1.sway balance with point2.hop polka3.sway balance with a raise 4.change step5.mazurka6.slide step7.native waltz8.close step9.cross change step10.bleking step Please Help!I MET a traveller from an antique landWho said: Two vast and trunkless legs of stoneStand in the desert ... Near them, on the sand,Half sunk, a shattered visage [face] lies, whose frown,And wrinkled lip, and sneer of cold command,Tell that its sculptor well those passions readWhich still survive, stamped on these lifeless things,The hand that mocked them, and the heart that fed;And on the pedestal these words appear:"My name is Ozymandias, king of kings:Look on my works, ye Mighty, and despair!"Nothing beside remains. Round the decayOf that colossal wreck, boundless and bareThe lone and level sands stretch far away.Select one piece of evidence that supports the situational irony of the poem.A Nothing beside remainsB I met a travelerC Its sculptor well those passions read what's the function of PCT and DCT of nephron ? Identify and analyze the way fossil fuel combustion has changed the composition of Earth's atmosphere, and the way this change has affected climate. What is the equation of the line that passes through the point (-5,5) and has aslope of -1? help its ratios please ty no guessing 5 music in binary and tennary 2. Evalute (3a +6b) Which of the following helps to summarize the Eleventh Amendment?The power of the courts is limited within each state.The federal government can sue anyone it wants to sue.Other countries are not allowed to take Americans to court. States are protected from being sued by the federal government. Estimate the perimeter of the figure to the nearest whole number.perimeter: about ___ units Which of these forces does not act over a distance?A. Friction B. Electric C. Magnetic D. Gravitational Simplify (2ab)(-3ab-)A. -6abB. 6abC. 6a - bD. 6a bhelp. as a ratio in simplest form, 33.5% is express as what is an evidence log !!!!!!Help Me Plz!!!!!! In his first inaugural address, president Ronald Reagan argues that the American people are strong enough to prevail over any obstacle. Which statement is irrelevant to that claim? 1. The price for this freedom at times has been high, but we have never been unwilling to pay that price. 2. These United States are confronted with an economic problem of great proportions... it threatens to shatter the lives of millions of our people. 3. I do not believe in a fate that will fall on us no matter what we do. I do believe in a fate that will fall on us if we do nothing. 4. Here, in this land, we unleashed the energy and individual genius of a man to a greater extent than has ever been done before Which statement about the reflection below is true? HELP ME PLASE IM BEGGING YOU the one who works very Hard Please help.Name the segments parallel to the given segment :/