A ship travels due west for 83 miles . It then travels in northwest direction for 111 miles and ends up 165 miles from its original position. To the nearest tenth of a degree how many degrees north of west did it turn when it changed direction? Show your work.

Answers

Answer 1

*see attachment for the diagram of the information given

Answer:

115.8°

Step-by-step explanation:

Due west = 83 miles

Northwest = 111 miles

Distance to its original position = 165 miles

Let x represent the degree north of west that it turned when it changed direction which is the opposite angle of 165 miles.

Thus, to find x, we'd apply the Law of Cosine which is given as:

c² = a² + b² - 2ab*cos C

Where,

C = x

a = 83 miles

b = 111 miles

c = 165 miles

Plug in the values

165² = 83² + 111² - 2*83*111*Cos x

27,225 = 19,210 - 18,426*Cos x

27,225 - 19,210 = - 18,426*Cos x

8,015 = -18,426*Cos x

8,015 = -18,426*Cos x

8,015/-18,426 = Cos x

-0.434983176 = Cos Cmx

Cos x = -0.434983176

x = cos^{-1}(-0.434983176)

x = 115.784223°

x = 115.8°

A Ship Travels Due West For 83 Miles . It Then Travels In Northwest Direction For 111 Miles And Ends

Related Questions

Mrs. Williamson had 18 students in her homeroom at the beginning of the school year and 24 students at the end of the year. What was the approximate percent increase in the number of students in Mrs. Williamson’s homeroom?

25%
33%
57%
75%

Answers

Answer:

25%

Step-by-step explanation:

An easy way to figure this out is just by dividing the initial amount of students (18) by the current amount of students (24), and then subtracting 1.

So, 18/24 = 0.75 (aka 75%), and  1 - 0.75 = 0.25 (aka 25%)

15. What is the volume of a rectangular prism with a length 8 cm, width 5 cm and height 3 cm?

Answers

Answer:

120cm³

Step-by-step explanation:

V=w·h·l=5·3·8=120cm³

Answer: i hope it help u

Step-by-step explanation:

what is 5 2/3 divided by 3/2

Answers

The answer to your question is 20/9

Answer:

≈3.8

Your Welcome!

An angle measures 162º more than the measure of its supplementary angle. What is the
measure of each angle?​

Answers

Answer:

there is only one straight angle which measures 180°

Step-by-step explanation:

if an angle is 162° then its supplementary angle is 18°

Help please! I'll mark you as Brainliest!

Answers

Answer:

c

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Since we are working with tenths all we have to do is add the numerators of each fraction.

4 + 3 + 1 + 1 = 9

9/10

** 20 points ! find the surface area, in square inches :)

Answers

Answer:

 

Surface area

103.109in²

Step-by-step explanation:

Hope this helps! I would appreciate if you make me brainliest!

105.8^2 is what I got

please HELPL I WILL MARK BRAINLIST FOR FIRST AND CORRECT ANSWER

Answers

Answer:

Characteristics of Autocratic Governments

Explanation:

The definition is ‘a system of government by one person with absolute power.’

0
1
N
3 4 5 6 7
8 9 10
Number of Snacks
What is the median of the data values?

Answers

Answer: it would be 5

Step-by-step explanation:

0,1,2,3,4,5,6,7,8,9,10 the middle #is 5

Help me please I am struggling with this question

Answers

Answer:

a: 153

Step-by-step explanation:

Do cross multiplication.

find the missing measurement

Answers

9514 1404 393

Answer:

  4.2 km

Step-by-step explanation:

The altitude of the triangle can be found using the triangle area formula:

  A = 1/2bh

  22.7 km² = 1/2(10.8 km)h

  h = (22.7 km²)/(5.4 km) ≈ 4.2037... km

The missing measurement is about 4.2 km.

I need this please.Give the right answer.It’s a huge grade that I NEED!

Answers

Answer:

Line 2 will be the best fit for the data

Step-by-step explanation:

hope it helps...

have a great day!!

Line 4

People lose height because the discs between the vertebrae in the spine dehydrate and compress. The aging spine can also become more curved, and vertebrae can collapse (compression fracture) due to loss of bone density (osteoporosis). Loss of muscle in the torso can also contribute to stooped posture.

5.4.PS-12
Trains Two trains, Train A and Train B, weigh a total of 260 tons. Train A is heavier than Train B.
The difference of their weights is 212 tons. What is the weight of each train?
Train A weighs tons

Answers

The answer is c
I took the test

Answer:

the answer is c

Step-by-step explanation:


A pet store advertises
a 30% off sale or dog crates.
What is the regular price of a
large crate that costs $85.50
on sale?

Answers

Answer:

the answer is 1.99 I think im not sure I guessed

Step-by-step explanation:

To wash a window that is 12 feet off the ground, Mason leans a 20-foot ladder against the side of the building. To reach the window, how far away from the building should Mason place the base of the ladder?

Answers

Answer:

by clumbing the ladder

Step-by-step explanation:

The base of the ladder should be placed so that it is one foot away from the building for every four feet of hight to where the ladder rests against the building. This is known as the 4 to 1 rule.

Expand -2/10(1-2x + 2

Answers

Answer:

[tex]\frac{2x}{5} - \frac{3}{5}[/tex]

Math help help please

Answers

Answer is 5,004,300

Answer:

5,000,000+4,000+300=5,004,300

Step-by-step explanation:

hope this helps

Pleasee help thanks!​

Answers

Answer:

I believe your answer is A.

Step-by-step explanation:

2x2x2

2x2=4

4x2=8

Therefore, x=2.

Answer: c

Step-by-step explanation:

2(1/5m-2/5)+3/5 Combine like terms to create and equivalent expression, please help :).

Answers

Answer:

Step-by-step explanation:

First, carry out the indicated multiplication.  We get:

2m/5 - 4/5 + 3/5, which condenses to

                        2m - 1

2m/5- 1/5 or ---------------

                              5

Help me plz ………………?…;

Answers

Answer:

9.04ft

Step-by-step explanation:

This will help you

Solve: Four more than a number is more than 13
Inequality :
Solution :

Answers

Answer:

x + 4 > 13

x > 9

Step-by-step explanation:

In this equation, the value of the "number" is unknown, so I used a variable (x) to represent the unknown value.

FOUR more than x would mean addition.

x + 4.

According to this word problem, four more than x is larger than thirteen, so a greater than symbol was used.

Like this,

x + 4 > 13.

We can find the solution to 'x' by subtracting 4 from 13.

Like this,

13 - 4 = 9

Therefore, the solution is x > 9

And, the inequality is x + 4 > 13.

Without properly working spark plugs, a vehicle will not run. For a specific vehicle, the spark plugs are supposed to have a gap between 3.9mm and 4.3mm. Any spark plugs with gaps larger or smaller than this will fail inspection and be discarded. At the factory, the machine that sets the gap follows a normal distribution with a mean of 4.1mm and standard deviation of 0.075mm. What is the probability that a randomly selected spark plug passes inspection

Answers

Answer:

The probability that the spark plugs are supposed to have a gap between 3.9mm and 4.3mm.

P(3.9≤X≤4.3)  = 0.9922

Step-by-step explanation:

Step(i):-

Given that the mean of the Normal distribution = 4.1mm

Given that the standard deviation of the Normal distribution = 0.0075mm

Let 'X' be the random variable in a normal distribution

Given that X₁ = 3.9mm

[tex]Z_{1} = \frac{X_{1} -mean}{S.D}[/tex]

[tex]Z_{1} = \frac{3.9 -4.1}{0.075} = -2.666[/tex]

Given that X₂ = 4.3mm

[tex]Z_{2} = \frac{X_{2} -mean}{S.D}[/tex]

[tex]Z_{1} = \frac{4.3 -4.1}{0.075} = 2.666[/tex]

Step(ii):-

The probability that the spark plugs are supposed to have a gap between 3.9mm and 4.3mm.

P(3.9≤X≤4.3) = P(-2.666≤Z≤2.666)

                     = P(Z≤2.666)-P(Z≤-2.666)

                    = 0.5 +A(2.666) - (0.5-A(2.666)

                   = 2 × A(2.666)

                 = 2×0.4961

                 = 0.9922

Final answer:-

The probability that the spark plugs are supposed to have a gap between 3.9mm and 4.3mm.

P(3.9≤X≤4.3)  = 0.9922

help! i need an equation for this

Answers

Answer:

y = -2/3x + 8

Step-by-step explanation:

Format: y = mx + b

m = slope (rise over run) - 2/3 The graph is negative so the slope is also negative.

b = y - intercept (8)

Can we make a triangle out of one angle that measure 20 degrees and another that measures 45 degrees

Answers

Answer:

Yes. If the third angle is equal to 115 degrees.

Step-by-step explanation:

The sum of all the angles in a triangle must equal 180 degrees.

If the two angles are 20 degrees and 45 degrees the third angle must be

180-45-20= 115 degrees

A triangle having three different angles is called a scalene triangle.

A scalene triangle also has three different sides.

But if the third angle is less or greater than 115 degrees the triangle cannot be formed.

This is the called the sum property of triangle.

There is another property which must also be satisfied i.e  the sum of any 2 sides must be greater than the third side.

Joan is planning a party. She wanted to serve nachos as an appetizer dish for her guests. Joan went to Costco and found a huge can of pre-made nacho cheese. When she got home, she wondered, "how much cheese is in this giant can?" So, she grabbed a ruler, measured the can, and concluded that it is 12-inches tall with a diameter of 6-inches. Continue Joan's calculation and find the amount of space inside that nacho cheese can.

Answers

Answer:

339.29

Step-by-step explanation:

V=πr²h

1. Lilly has two cousins. One of the cousins is 7 years older than Lilly. The other cousin is 3 years younger than Lilly. The product of Lilly’s cousins' ages is 24. How old is Lilly?

2. Jackie is building a rectangular football field that has an area of 6000 square yards. The football field must be 40 yards longer than its width. Determine the width of the football field, in yards.

3. James is reading a book and noticed the page numbers are consecutive integers whose product is 1640. What is the value of the larger page number?

Answers

Answer: a. 5 years

b. 60 yards

c. 41

Step-by-step explanation:

1. Let Lily's age be x.

One of the cousins is 7 years older than Lilly. The age will be = x + 7

The other cousin is 3 years younger than Lilly. The age will be = x - 3

Therefore, (x + 7)(x - 3) = 24

x² - 3x + 7x - 21 = 24

x² + 4x - 21 - 24 = 0

x² + 4x - 45 = 0

x² + 9x - 5x - 45 = 0

(x² + 9x) - (5x - 45) = 0

x(x + 9) - 5(x + 9) = 0

(x - 5)(x + 9) = 0

(x - 5) = 0

x = 0 + 5

x = 5

Therefore, Lily is 5 years

2. Let the width be represented by x

Therefore, length will be x + 40.

Area = length × width

6000 = x(x + 40)

x² + 40x = 6000

x² + 40x - 6000 = 0

x² + 100x - 60x - 6000 = 0

x(x + 100) - 60(x + 100) = 0

(x - 60)(x + 100) = 0

x - 60 = 0

x = 0 + 60 = 60

Therefore, the width is 60 yards

3. Let the consecutive numbers be x and x+1.

Therefore, x(x + 1) = 1640

x² + x = 1640

x² + x - 1640 = 0

x² + 41x - 40x - 1640 = 0

x(x + 41) - 40(x + 41) = 0

(x - 40) = 0

x = 0 + 40

x = 40

Larger number = x + 1 = 40 + 1 = 41

In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Olivia sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below. 144 visitors purchased no costume. 182 visitors purchased exactly one costume. 9 visitors purchased more than one costume. Based on these results, express the probability that the next person will purchase no more than one costume as a decimal to the nearest hundredth.

Answers

Answer:

There is a 54.328% probability that the next person will purchase no more than one costume.

Step-by-step explanation:

Since in a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance, and Olivia sets up a website where players can buy and sell these costumes online, and information about the number of people who visited. the website and the number of costumes purchased in a single day states that 144 visitors purchased no costume, 182 visitors purchased exactly one costume, and 9 visitors purchased more than one costume, to determine, based on these results, the probability that the next person will purchase no more than one costume as a decimal to the nearest hundredth, the following calculation must be performed:

144 + 182 + 9 = 335

335 = 100

182 = X

182 x 100/335 = X

18,200 / 335 = X

54,328 = X

Therefore, there is a 54.328% probability that the next person will purchase no more than one costume.

A person is standing 215 feet above the ocean
watching a ship come in. Initially the angle of elevation
from the boat to the person is 31 degrees. After
traveling towards the person for a few minutes, then
angle is 48 degrees. How far did the boat travel
between the two points? Round to the nearest foot.

Answers

Answer:

Step-by-step explanation: I don’t know I just want my extra points

Answer: 164 ft

Step-by-step explanation:

tan 48=215/x

-> x.tan48=215

->x =215/tan 48

->x = 193.6

tan 31=215/y

-> y.tan31 = 215

-> y= 215/ tan 31

-> y= 357.82

BC= y-x

= 357.82-193.6

= 164.22 = 164 ft

Which statement BEST describes how the pipe player in Passage 1 influenced Caesar's crossing of the Rubicon?
A ) The pipe player's song distracted the opposition, which allowed Caesar to mount a suprise attack.
B ) The pipe player had a striking appearance that Caesar admired.
C ) The pipe player convinced other soldiers to join Caesar in his fight.
D ) The pipe player's song brought nearby trumpeters to the area, which inspired Caesar to sound the advance.

Answers

Answer:a or d

Step-by-step explanation:

Hi i'm in the 5th grade almost 6th I struggle a lot with math and i have a lot of anxiety so sometimes i get stressed and i just needed a little help with my exam so here is a question i need help with .
Question/ 34 Divide by 26

Answers

Answer:

1.31

Step-by-step explanation:

I used a calculator and just rounded this number 1.30769230769

if the number is five or higher then you would round the number next to the 7. So 7 rounded 0 is 1.31. Sorry i tried to explain it in the best way possible!

Can someone please help me on this homework ASAP!!

Answers

Answer:

Step-by-step explanation:

Multiply each term of (x² + 2x - 1) by x  and multiply each term of            (x² + 2x - 1) by 3

Area of parallelogram = bh

  = (x² + 2x - 1)(x + 3)

  = (x² + 2x - 1)*x + (x² + 2x - 1)*3

 =x²*x + 2x*x  - 1*x + x²*3 +2x*3 - 1*3

 = x³ + 2x² - x + 3x² + 6x - 3

 = x³ + 2x² + 3x²   -x + 6x - 3

 = x³ + 5x² + 5x - 3

Other Questions
PLS HELP MEEE I WILL GIVE BRAINLY THINGY What is the final temperature of a system if 10.0 grams of cold water, originally at 10C is mixed with 120.0 grams of hot water, originally at 77.0C?A. 83.1CB. 100.0CC. 71.8 CD. 95.1C What is meant by a carbohydrase? 30POINTS!!!Compared to traditional subjects like computer science and communications, some college majors seem unusual. Students can earn degrees in subjects such as bagpipe performance and adventure education. What do you think?When it's time to choose a major, it's best to think outside the box.1) Agreeor2) Disagree Please help me! 50 points and brainliest for best answer! check attachment how can i solve this problem if its congruent or not PLS HELP NOW In the late 1960s, the United Farm Workers used protesting tactics, such as ____, to accomplish their goals. (boycotts, riots, occupations, sit-ins)???? Help with these True or False questions pls! 201Which equation, when paired with y = 2x+5,creates an inconsistent system?O 2x + y = 5o y = 2x + 5O 2x - 4y = 10O 2y - 4x = -1010X-2020DONE-101-20 Detoxification is the process of __________.A.receiving counseling for drug addictionB.using medication to build tolerance to addictive drugsC.managing addictive and self-destructive behaviorD.weaning a body from an addictive drugAnswer: The Answer is D Explain the difference between a colony and a polis. Can someone help me please ? What is the volume of the triangular prism below? Help me find the volume Figure ABCD is a parallelogram. What is the value of x? B O 6 07 8 5x + 3 38 9 D C Please help I will mark Brainliest!! ( be honest plz The energy transformation in an electromagnetic is from chemical to electrical to electromagnetic waves.True or False?The energy transformation in an electromagnetic is mechanical energy to electrical energy chemical energy.True or False?Giving brainliest Before serving as vice president for John F. Kennedy, Lyndon B. Johnson ________________. a. served in the House of Representatives b. served as director of the Civil Rights Council c. served in the Senate d. Both a. and c. List one goal you want to achieve in the next 5 year and explain why you want to achieve it in the next 5 yearI'll give brainless if you give a suitable answer Which is the correct Lewis structure for carbon monoxide?A. AB. BC. CD. D