3. Spherical Trig - Direction and distance to world cities The Dunedin City Council wish to erect a sign post at the Esplanade (St Clair) that shows the direction and distance to a number of world cities. The direction of each sign indicates the azimuth to the city.
Compute the azimuth for the following three cities:
Assume that the radius of the earth is 6374 km.
ϕ (dec degrees) ⋋ (dec degrees)
Dunedin 45.9121 S 170.4897 E
London 51.5034 N 0.0000 E
Sydney 33.8675 S 151.2070 E
Los Angeles 34.0522 N 118.2437 W
[18 marks]
Answers
To compute the azimuth for each of the three cities, we need to use spherical trigonometry. The azimuth is the angle between the direction of the line connecting the observer and the city and the positive x-axis, measured in degrees clockwise from north.
The first step is to convert the latitude and longitude of each city to radians. The latitude of Dunedin is 45.9121 radians, the longitude is -170.4897 radians, the latitude of London is 51.5034 radians, the longitude is 0 radians, the latitude of Sydney is 33.8675 radians, and the longitude is 151.2070 radians.
Next, we need to use the sine and cosine functions to find the y-coordinate of the city on the Earth's surface. The y-coordinate is given by the sine of the latitude, while the x-coordinate is given by the cosine of the latitude. Therefore, for Dunedin, the y-coordinate is sin(45.9121) = 0.8307, and for London, the y-coordinate is sin(51.5034) = 0.9893.
We can then use the haversine formula to find the distance between the observer and each city. The haversine formula is given by:
d = 2 * arcsin(sqrt(haversin(Δlat) + cos(lat1) * cos(lat2) * haversin(Δlon)))
where d is the distance in radians, Δlat and Δlon are the differences in latitude and longitude between the observer and the city, and lat1 and lat2 are the latitudes of the observer and the city, respectively.
For Dunedin and Sydney, the distance is approximately 20,400 km, and for London and Los Angeles, the distance is approximately 10,000 km.
Finally, we can use the tangent function to find the azimuth for each city. The tangent function is given by:
tan(azimuth) = (y_city - y_observer) / (x_city - x_observer)
where y_city and x_city are the y- and x-coordinates of the city on the Earth's surface, respectively, and y_observer and x_observer are the y- and x-coordinates of the observer, respectively.
For Dunedin and Sydney, the azimuth is approximately 95.1 degrees clockwise from north, and for London and Los Angeles, the azimuth is approximately 189.9 degrees clockwise from north.
Therefore, the azimuths for the three cities are:
Dunedin: 95.1 degrees clockwise from north
London: 189.9 degrees clockwise from north
Sydney: 95.1 degrees clockwise from north
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Related Questions
What are 7 oceans of the world?
Answers
Answer:
Arctic, North Atlantic, South Atlantic, North Pacific, South Pacific, Indian, and Southern oceans.
Explanation:
The Arctic, North Atlantic, South Atlantic, North Pacific, South Pacific, Indian, and Southern Oceans are all parts of the current Seven Seas.
Who identified the seven oceans?Many people think the phrase "the seven seas" just means sailing some or all of the world's waters. Rudyard Kipling is credited with popularising the phrase when he released The Seven Seas, a collection of poetry, in 1896.
Which ocean is the largest in the world?The Pacific Ocean is the largest and deepest ocean basin on earth. The Pacific Ocean basin is the biggest ocean basin in the world, covering around 63 million square miles and holding more than half of the planet's free water.
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Based on the above population pyramid, what can you can predict about the population of Poland over the next 20 years?
A - Poland will experience a severe famine
B - Poland will experience a gradual decline in overall population
C - Poland’s military will double in size
D - Poland’s population will not change over the next 2 decades
Answers
The prediction that can be made on the population of Poland over the next 20 years is B - Poland will experience a gradual decline in overall population.
Facts about Poland's population pyramid Showed that most of the population were in their 20s and 40s.Showed that the younger population was relatively small.This means that Poland's population will reduce gradually in future owning to the fact that the children being born are not be born fast enough to replace the older generation that will die out.
In conclusion, option B is correct.
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A video game randomly chooses your
car color and type. The probability of
getting a red car is 0.20, and the probability of getting a convertible is 0.30.
Event A = You get a red car.
Event B = You get a convertible. a
A and B are independent events if
A.
The probability of getting a red car a or a convertible is 0.50.
B. The probability of getting a red convertible is 0.06.
C. The probability of getting a red car or a convertible is 0.06.
D The probability of getting a red convertible is 0
Answers
Answer:
Explanation:
Answer: Option 'D' is correct.
Step-by-step explanation:
Since we have given that
Event A: You get a red car
and
Similarly,
Event B: You get a convertible
and
So, if A and B are independent , then they must satisfy,
So,
Hence, Option 'D' is correct, which states that the probability of getting a red convertible is 0.08.
what is the solar system
Answers
Based what you have learned about these different models think about the nick-name for the city of Indianapolis, The Circle City. Which model do you think was originally used when the city was planned? Why do you believe this to be true?
Answers
The model design as made by Alexander Ralston and Elias Pym Fordham who were known to have designed the Circle City were known to have used the original pattern for the city via a grid style branching model.
I believed it is true because at the grid style or model used for the city is one that branching out that starts from Governor's Circle.
What is the circle city about?The city of Indianapolis known as the Circle City is one that is made up of circular street that are surrounds by Monument of proud Soldiers and Sailors.
Alexander Ralston and Elias Pym Fordham were famous as they were said to have designed the city in a form of grid model where there is branching out that starts from Governor's Circle which is often called Monument Circle.
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which system has complete public ownership of the means of production- free enterprise-market economies-communist economies-mixed economies
Answers
Communist economies have complete public ownership of the means of production. Communist economies refer to an economic system in which the means of production are publicly owned and each person is assigned work and paid according to their abilities and needs.
This means that all the resources and property of the economy are owned by the state, rather than individuals or private organizations. A communist economy is characterized by the following features:
There is no private ownership of property. All the resources and property of the economy are owned by the state, rather than individuals or private organizations.
Incomes are determined according to needs and abilities rather than market forces.
All decisions regarding the production and distribution of goods are made by the central government, rather than individual firms.
Communism is a political ideology and social movement advocating for a classless society in which all property and wealth are owned communally and each person works and is paid according to their abilities and needs. It is an economic system in which the means of production are publicly owned, and production and distribution are controlled by the state. To sum it up, communist economies have complete public ownership of the means of production.
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help me please sdjjeje
Answers
What are the names of the eras in the geologic time scale?.
Answers
The history of the Earth is divided into four time periods according to the geologic time scale : Precambrian Time, Paleozoic Era, Mesozoic Era and Cenozoic Era.
Give an account on Geological Time Scale.Geological Timescale : In the range of 3 and 3.5 billion years old are the oldest fossils. These bacteria date back to an earlier time when life on Earth was much simpler. About 565 million years ago, more sophisticated species began to emerge in the waters, and about 542 million years ago, they significantly increased in number. The Phanerozoic Eon, a period of geological time that begins at this epoch, is the most recent moment in history. Fossils are prevalent during the Phanerozoic period, which means "visible life".
Phanerozoic Eon : There are three eras that make up the Phanerozoic Eon: the Paleozoic, Mesozoic, and Cenozoic eras. The kind of fossils that were found inspired the names of these.
Paleozoic era : The Cambrian radiation, which saw a significant increase in the variety of marine animals, marks the start of the Paleozoic era. The greatest extinction of life on Earth marks its conclusion. At the conclusion of the Ordovician and Devonian periods, there were additional significant extinction events. The evolution of plants and animals to live on land also occurred during the Paleozoic Era.
Mesozoic and Cenozoic eras : The youngest portion of the Phanerozoic is made up of the Mesozoic and Cenozoic eras. Mammals and dinosaurs both underwent evolutionary change during the Triassic Epoch, the most recent period of the Mesozoic Era. At the conclusion of the Cretaceous Period, the Mesozoic saw a significant extinction. Except for birds, every dinosaur perished during this extinction. The Triassic Period ended with a second mass extinction. Communities began to look more contemporary during the Cenozoic Era. Homo sapiens, our species, had evolved by the Neogene Period's very end.
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Submit your project identifying potential customers. Be sure to follow these guidelines:Identify the type of products your new company sells.
Describe the target market for your products.
List at least 10 potential customers in your target market.
Explain why these customers would be interested in your company’s products.
Write your response in complete sentences and paragraphs.
Answers
Explanation:
target market, or target audience, is the pool of customers to whom you want to potentially sell your products or services. Your target market is not everyone who is located in your business’s area. It’s only made up of the people who are good fits for your products. Basically, you want to figure out which fish in the ocean you’re going to focus on catching.
For example, let’s look at one of my
Kayla has 5 rolls of green ribbon. Each roll has 4 meters of green ribbon. She has 6 rolls of blue ribbon. Each roll has 3 meters of blue ribbon
Answers
Kayla has a total of 20 meters of green ribbon and 18 meters of blue ribbon.
Kayla is a ribbon enthusiast and has a collection of different colored ribbons.Among her collection, she has 5 rolls of green ribbon.Each roll of green ribbon is 4 meters in length.The total length of green ribbon that she has is 5 rolls x 4 meters per roll = 20 meters.Kayla also has 6 rolls of blue ribbon.Each roll of blue ribbon is 3 meters in length.The total length of blue ribbon that she has is 6 rolls x 3 meters per roll = 18 meters.Kayla now has a total of 20 meters of green ribbon and 18 meters of blue ribbon.She can use the ribbons for various crafts and decoration projects.The green ribbon can be used to add a pop of color to her projects.The blue ribbon can be used to create a calm and peaceful atmosphere.With both the green and blue ribbon, Kayla can create a variety of different moods and styles.Kayla is happy with the amount of ribbon she has and is excited to use it in her future projects.She is always on the lookout for new ribbons to add to her collection.With her collection of green and blue ribbon, Kayla is ready to unleash her creativity.
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An ethnic group is made up of people who share
A) a common social class and level of education
B) a common government philosophy
C) a common language, history, or place of origin
D) a common trade or occupation
Answers
Answer:
C) a common language, history, or place of origin
Explanation:
Most often cited as the causative factor for acid deposition.
Answers
Answer: Sulfur dioxide
Which mountain range is located along the northern border of Iran?
a. Elburz
c. Hindu Kush
b. Kopet-Dag
d. Zagros
Answers
Answer:
Explanation:
Hindu Kush
Hindu kush is in Pakistan/India which are both closer to Iran then all the rest of the mountain ranges
Answer:
It is not C... I got it wrong on my quiz Its not B either so it is either
A. Or D.
Explanation:
Elburz or Zagros
This may help A little bit for your quiz on edge 2021
In Latin American history, the Pre-Columbian Era refers to the time __________. A. before the arrival of European explorers and colonists B. of increased immigration to the New World C. also known as the Era of Independence D. after the fall of the Aztec empire Please select the best answer from the choices provided.
Answers
Answer:
Option A will be the appropriate choice.
Explanation:
The pre-Colombian age encompasses all phase subdivisions throughout American history before the arrival of major European developments on either the American continent, overlapping the duration of the first establishment throughout the Upper Paleolithic era to European colonization mostly during the early medieval century.This applies to something like the opportunities ahead of European explorers including colonization arriving.The other three methods aren't relevant to the particular circumstance. Such that the aforementioned will be the right decision.
Answer:
A before the arrival of European explorers and colonists
Explanation:
where was the noon altitude of the sun highest and lowest on december 21? your answer should be either a latitude or a name for a specific latitude.
Answers
The noon altitude of the sun is measured in degrees above the horizon at solar noon. December 21 is the winter solstice. At this time, the northern hemisphere is tilted away from the sun at its maximum angle, resulting in the shortest day and longest night of the year.
The highest noon altitude of the sun occurs in the tropics, while the lowest noon altitude of the sun occurs at higher latitudes. The altitude of the sun is the angle between the horizon and the center of the sun. The noon altitude of the sun varies depending on the observer's latitude and the time of year. On December 21st, the noon altitude of the sun is at its lowest in the northern hemisphere, while it is at its highest in the southern hemisphere. The latitude where the noon altitude of the sun is highest on December 21 is the Tropic of Capricorn, which is located at 23.5 degrees south. The latitude where the noon altitude of the sun is lowest on December 21 is the Arctic Circle, which is located at 66.5 degrees north.
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in the 3-soils simulation shown in class, the loam soil provided the greatest drought avoidance because:
Answers
In the 3-soils simulation, loam soil provided the greatest drought avoidance. Soil type is a crucial factor in determining a plant's ability to resist drought stress. Loam soil has several physical and chemical characteristics that make it well-suited for drought resistance. Let's take a closer look at each of these features:
Loam soil has several physical and chemical characteristics that make it ideal for drought resistance. These features, combined with its well-balanced composition of sand, silt, and clay particles, make it the most drought-resistant soil type.In a loam soil, water penetrates rapidly into the soil because of its high infiltration rate. The high infiltration rate enables water to move through the soil and reach the plant roots, which minimizes the loss of water due to evaporation or runoff.
In addition to its high infiltration rate, loam soil also has a good water-holding capacity. As a result, even when the soil dries out, it retains enough moisture to support plant growth.The pore spaces in loam soil are well-connected, allowing water to move freely through the soil. This feature aids in the movement of water from the soil surface to the plant roots, where it is needed for growth. As a result, loam soil is well-suited for drought resistance.
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Name two surface features that Ganymede appears to have in common with the Moon.
In what ways are these features similar? In what ways must the origins of the features on Ganymede be different?
Answers
Ganymede, a moon of Jupiter, appears to have two surface features in common with the Moon. These features are impact craters and mare (or "seas"). Impact craters are circular depressions created when a meteor or other object collides with the surface of a celestial body. Mare are large, dark, smooth areas of solidified lava.
The impact craters on both the Moon and Ganymede have similar origins. Both were caused by asteroids and comets crashing into the surface of the two moons, creating the circular depressions. The impact craters on Ganymede and the Moon are also similar in size, though Ganymede has much larger craters.
The mare on the Moon and Ganymede are also similar in origin. Mare form when lava erupts from the surface of a celestial body and hardens in the shape of a large, dark, smooth area. However, the origins of the mare on Ganymede must be different than the origins of the mare on the Moon, as Ganymede does not have any active volcanoes, while the Moon does. The mare on Ganymede must have formed millions of years ago, as its lava has long since solidified.
In conclusion, Ganymede and the Moon have two surface features in common: impact craters and mare. The impact craters on both celestial bodies have similar origins, caused by asteroids and comets crashing into the surface. The mare also have similar origins, but the mare on Ganymede must have formed millions of years ago, as it has no active volcanoes.
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If a rising, unsaturated air parcel is colder and heavier than the air surrounding at all levels, the atmosphere is ____.
Answers
If a rising, unsaturated air parcel is colder and heavier than the air surrounding it at all levels, the atmosphere is considered to be stable. This is because the cold air parcel will not be able to rise any further as it is denser than the surrounding air, and thus, will remain in its position.
Stable atmospheric conditions are characterized by a lack of vertical air movement, with air parcels near the surface tending to stay in their original positions. This type of atmospheric condition is common in areas of high pressure, which are generally associated with clear skies and fair weather.
In contrast, unstable atmospheric conditions are characterized by rising and falling air parcels, which can lead to the formation of clouds and precipitation. These conditions are often associated with areas of low pressure, which are generally associated with stormy weather.
Understanding the stability of the atmosphere is essential for predicting weather patterns and forecasting severe weather events.
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Which of the following is NOT true?
alcohol is formed naturally
whisky begins as beer
darker beer is higher in alcohol
equila is, typically, no higher proof than vodka
B. Which of the following is true:
females metabolize alcohol more slowly than males
tequila contains more alcohol than vodka
dark beer contains more alcohol than an IPA
eating yeast slows down the metabolism of alcohol
Answers
Answer:
A.
1. false
2. true
3. false
4. true
B.
1. true
2. true
3. false
4. false
Explanation:
#CARRY On Learning
Which of these chemicals can you find in your own home? What products do you find them in?
Answers
Answer:
i think its VOC
Explanation:
and you can find it in paint and glues
Potentially dangerous chemicals can be found in every room in your home. If not properly stored or used, these products could cause.
What is the product?The object being sold is referred to as a product. A service or an object both qualify as products. It could take on a physical, virtual, or cyber form. Every product has a cost associated with it, and each one has a price. The market, the quality, the marketing, and the group that is being targeted all affect the price that can be charged.
You have undoubtedly been exposed to 2-butoxyethanol, a colorless liquid solvent if you have ever used a household cleaner to wipe down surfaces, clean bathrooms, or mop floors.
This substance, which is found in many all-purpose cleaning products and has been linked to nausea and vomiting after prolonged exposure, has been known to irritate the nose.
Therefore, properly stored or used, these products could cause.
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the best definition of the outer edge of the continental shelf is that point where ________.
Answers
The best definition of the continental shelf's outer edge is where gradient steepening happens quickly.
The term "continental shelf" refers to a continent's underwater limit. The seven major divisions of land on Earth are called continents.
From a continent's shoreline to a point known as the shelf break, a continental shelf runs.Geologists refer to the portion of the continental margin between the shoreline and the shelf break—or, in the absence of a discernible slope, between the shoreline and the point where the depth of the adjacent water is roughly between 100 and 200 meters—as the "continental shelf."To know more about Continental Shelf:
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Label the parts of the volcano using the terms in the word bank.
Word bank
Lava. Magma Pyrotechnics flow
Subducted plate
Answers
If a ship is trying to sail from the eastern united states to europe, what route would be the most efficient to take?
Answers
If a ship is trying to sail from the eastern united states to Europe, the Clipper route would be the most efficient to take.
What is the Clipper route?The clipper route, which was the customary route used by clipper ships to go between Europe and the Far East, Australia, and New Zealand, was developed from the Brouwer Route. To take advantage of the high westerly winds of the Roaring Forties, the route crossed the Southern Ocean from west to east.
In particular, at Cape Horn, which the clippers had to round on their way back to Europe, many ships and sailors perished due to the dangerous weather. With the advent of marine steam engines and the building of the Suez and Panama Canals, the clipper route fell out of commercial use. As the world's quickest sailing path, it has served as the course for a number of illustrious sailboat races.
Therefore, the Clipper route is the most efficient route from the eastern United States to Europe.
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Determine who has made the correct statement. Sean said only biologists use the fossil record to determine the age of the earth. Cade said only geologists use the fossil record to determine the age of the earth. Neither is correct. Both are correct. Cade is correct. Sean is correct.
Answers
Answer:
Neither is correct.
If you are using Odyssseyware Then this is 100% correct.
Solid A and Solid B are similar. The ratio of their volumes is 8:729. If the surface area of Solid A is 24 ft2 , what is the surface area of solid B?
Answers
Answer:
Solids A and B appear to be similar cubes.
The volume of cube A is 8 cubic feet, so each side of cube A has length 2 feet. It follows that cube A has surface area 24 square feet. The volume of cube B is 729 cubic feet, so each side of cube B has length 9 feet. It follows that cube B has surface area (9^2) × 6 = 81 × 6 = 486 square feet.
Carolus linnaeus developed a system to organize all life on earth called:.
a)Binomial nomenclature
b)Biological naming system
c) Standard protocol
d)None of these
Answers
a) Binomial nomenclature
Carl Linnaeus developed the system of binomial nomenclature to organize all life on Earth. This system assigns a unique two-part name to each species, consisting of the genus name and the species name. The binomial nomenclature provides a standardized and universally recognized way to identify and classify organisms, allowing for clear communication and understanding in the field of biology.
Linnaeus introduced this system in his landmark work "Systema Naturae" published in 1735. The use of binomial names helps in organizing and categorizing the vast diversity of species on Earth, providing a common language for scientists and researchers to study and discuss different organisms. It allows for precise identification and facilitates the classification and understanding of the relationships between different species. The system has since been expanded and refined by subsequent scientists, but the fundamental concept of binomial nomenclature remains a key contribution of Linnaeus to the field of taxonomy.
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After Christopher Columbus arrived in the Caribbean in 1492, Europeans established colonies in the Americas and trade routes across the Atlantic Ocean. How did European colonizers influence the history of Central America and the Caribbean islands?
Answers
Answer:
Tras la llegada de los europeos a las islas del Caribe en 1492, esta región adquirió un importante papel estratégico tanto para continuar la exploración y el descubrimiento de otros lugares como para organizar la conquista y colonización de nuevas áreas.
Explanation:
list down the three dimension that the relief features of the earth
Answers
The three dimensions that the relief features of the earth are Hills, valleys, and plateaus
What are the relief features of the earth?
Simply put, relief features are the landscape characteristics of a particular location. In the study of geography, relief features are the highest and lowest elevational points of an area.
They are made up of ridges, valleys, and hills in a specific location.
In conclusion, relief features are the characteristics of a particular area's landscape.
Relief features are the characteristics of a specific area's landscape. In the study of geography, relief features are the highest and lowest points of an area's elevation. They are made up of hills, valleys, and ridges in a specific area.
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Which of the following expressions is equal to 2x2 +8 ?
A. (2x - 41)(x-2)
B. (2x - 41)(x + 21)
C. (2x + 4)(x+21)
D. (2x-2)(x +61)
Answers
Answer:
B
Explanation:
(2x-41)(x+21)
B i think
Humans have great impact on biodiversity in 5 major ways. Match the 5 major impacts next to the appropriate example.
Clear-cutting Amazonian rain forests.
The spread of unproductive landscapes due to overgrazing by cattle
Increase in carbon dioxide in the atmosphere from the burning of fossil fuels.
Introduction of kudzu into North America or cane toads into Australia
ExtreminatiExterminationon Wolves of wolves in national parks
A. Desertification
B. Defrostestation
C. Invasion/Non-native species
D. Climate change/global warming
E. overhunting/overharvesting
Answers
The 5 major impacts of human activities on biodiversity can be matched with the appropriate examples as follows:
1. Clear-cutting Amazonian rainforests: This example corresponds to the impact of deforestation (B). Clear-cutting refers to the complete removal of trees and vegetation from an area, which has a significant impact on biodiversity by destroying habitats, disrupting ecological balance, and causing the loss of numerous plant and animal species.
2. The spread of unproductive landscapes due to overgrazing by cattle: This example is associated with desertification (A). Overgrazing by cattle can lead to the degradation of land, where the vegetation cover is diminished, and the soil becomes eroded, resulting in the conversion of productive landscapes into unproductive desert-like areas.
3. Increase in carbon dioxide in the atmosphere from the burning of fossil fuels: This example aligns with climate change/global warming (D). The burning of fossil fuels, such as coal, oil, and natural gas, releases large amounts of carbon dioxide into the atmosphere, contributing to the greenhouse effect and the warming of the Earth's climate. This has significant consequences for biodiversity, including shifts in habitats, altered ecosystems, and increased vulnerability for many species.
4. Introduction of kudzu into North America or cane toads into Australia: This example represents the impact of invasion/non-native species (C). The introduction of non-native species to ecosystems where they have no natural predators or controls can result in the displacement or extinction of native species, disruptions in ecological interactions, and the alteration of entire ecosystems.
5. Extermination of wolves in national parks: This example corresponds to overhunting/overharvesting (E). Overhunting or excessive harvesting of species, such as wolves, can lead to their decline or extinction. This can have cascading effects on the ecosystem, disrupting natural predator-prey relationships and causing imbalances in the populations of other species.
By matching these examples to the respective impacts, we can see the significant ways in which human activities can influence and impact biodiversity on a global scale.
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