Recall the angle sum identity for cosine,
cos(α + β) = cos(α) cos(β) - sin(α) sin(β)
We're given sin(α) = -1/3 and tan(β) = 7/3. Since α terminates in quadrant IV, we know that cos(α) is positive, and since β terminates in quadrant III, both sin(β) and cos(β) are negative.
Recall the Pythagorean identities,
cos²(x) + sin²(x) = 1
and
1 + tan²(x) = sec²(x)
Using the first identity, we find
cos²(α) = 1 - sin²(α)
cos(α) = + √(1 - (-1/3)²)
cos(α) = + √(8/9)
cos(α) = √8/3
Using the second identity,
sec²(β) = 1 + tan²(β)
sec(β) = - √(1 + tan²(β))
sec(β) = - √(1 + (7/3)²)
sec(β) = - √(58/9)
sec(β) = -√58/3
cos(β) = -3/√58
Then by definition of tangent,
tan(β) = sin(β) / cos(β)
sin(β) = tan(β) cos(β)
sin(β) = (7/3) (-3/√58)
sin(β) = -7/√58
Putting everything together,
cos(α + β) = cos(α) cos(β) - sin(α) sin(β)
cos(α + β) = (√8/3) (-3/√58) - (-1/3) (-7/√58)
cos(α + β) = -(7 + 3√8)/(3√58)
what technologies did this empire utilize or develop to establish and maintain their sea based empire
The type of technologies that the European empire utilized or developed to establish and maintain their sea based empire are; New ships and other maritime technology which includes lateen sails and improved charts.
The empire being referred to here is the European empire. This was a period called the Trans-Ocenanic Interactions that spanned a period from the year 1450 to the year 1750.
This was a period when the Europeans arrived in Americas, Africa's, and Asia and as a result had to create maritime empires which is also called sea based empires. For these their trans oceanic movement they had some tools and instruments that were very helpful to their foray via their empires and these include new ships and other maritime technologies like lateen sails and improved charts which were very useful in their maritime reconnaissance.
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When you use a match to light a candle, multiple _______ of energy occur
Answer:
transformations (missing word)
Explanation:
When you use a match to light a candle, multiple transformations of energy occur.
To light a match, mechanical energy must first be converted to thermal energy. The particles in the match release chemical energy that has been accumulated as a result of the thermal energy, which then transforms into further thermal energy and the electromagnetic energy that you see as light.
Multiple energy transformations involving mechanical, thermal, chemical, and light energy occur when you light a match.
Therefore, when you use a match to light a candle, multiple transformations of energy occur.
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A special promotion for its 20-ounce bottle of soda, a soft drink company printed a
message on the inside of each cap. Some of the caps said, "Please try again," while
others said, "You're a winner!" The company advertised the promotion with the
slogan "] in 6 wins a prize.
Suppose the company is telling the truth and that every 20-ounce bottle of soda it
fills has a 1-in-6 chance of being a winner. Seven friends each buy one 20-ounce
bottle of the soda at a local convenience store. Let X = the number who win a prize.
Using the principle of binomial probability, the probability that more than 3 friends win a prize is
Recall :
P(x = x) = nCx * p^x * q^(n-x)Given the Parameters :
Probability of success, p = 1/6 q = 1 - p = 5/6 Number of trials, n = 7x≥3Hence,
P(x ≥ 3) = p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6) + p(x = 7)
P(x ≥ 3) = 0.0781 + 0.0156 + 0.0019 + 0.0001 + 0.000003
P(x ≥ 3) = 0.095703
Therefore, the probability that more than 3 friends win a prize is 0.0957
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There is a 20% chance it will rain today. If it rains, there is a 10% chance that we will be allowed to go outside; otherwise, there is an 80% chance we will be able to go outside. What is the probability that we will be allowed to go outside?
Answer:
82
Explanation:
20%x10%=2
80%+2% = 82%
Mga Batayang Salik sa pagkakaroon ng pagkakaroon ng kabihasnan
1
2
3
4
5
6
pls I need your help
Explanation:
Matatag na suplay ng pagkain.
Sosyal na istraktura.
Sistema ng pamahalaan.
Sistemang panrelihiyon.
Mataas na binuo na kultura.
Mga pag-unlad sa teknolohiya.
Mataas na binuo nakasulat na wika.
Describe If each statement describes England, or Spain, France and Russia.
Parliament had important powers.
Monarchs had limits on their power
Absolutism was increasing
Monarchs grew more powerful
Answer:
Look at the screenshot below.
Have a great day
Explanation:
What is the quantity of books that this individual is carrying in the image provided.
Answer:
3
Hope it helps
Your sister is looking for a way to increase the amount of money she is earning in her savings account what should she do
Answer:
a good why to make some rly good money on the side id to either sell the items u don't need nor use and also as well u can be a photographer and sell pics online or take some creative pictures for people its super easy and simple.
magbigay ng halimbawa na nagpapakita ng pagkakaisa ng mga Pilipino at paano ito nakatulong sa bansa at sa mga mamamayang Pilipino?
Need na po..
Answer:
mag linis at tumulong sa kapwa para maging mabuti ang kapaligiran
Explanation:
sana maka tulong ang answer ko!
A prerequisite is something you need before you can continue in a training or educational program.
False
True
Answer:
The answer is True
Explanation:
It might be difficult to comprehend information if you do not have the necessary prerequisites. What is a prerequisite? It is something that is necessary to be familiar with or comprehend before learning or understanding anything new. In our example, you would need to know how to walk before you could learn to run since it is a requirement to learning how to run.
Assume that a 100 cm3 soil core weighs 78g when oven-dried and 123 g when saturated. Calculate the total pore space and total porosity. Show all of you work.
To calculate the total pore space, we will find the difference between the mass of the soil when it is oven - dried and when it is saturated. Therefore, the value of the total pore space and total porosity are 45g and 45% respectively
Given that a 100 cm3 soil core weighs 78g when oven-dried and 123 g when saturated.
The given parameters are;
Volume of soil V = 100[tex]cm^{3}[/tex]
Mass ( Oven dried) [tex]M_{1}[/tex] = 78g
Mass ( Saturated) [tex]M_{2}[/tex] = 123g
In the soil formation, pore space refers to the volume of soil. And to calculate the total pore space, we will find the difference between the mass of the soil when it is oven - dried and when it is saturated. That is,
Total pore space = [tex]M_{2}[/tex] - [tex]M_{1}[/tex]
Total pore space = 123 - 78
Total pore space = 45g
And total porosity will be the percentage of the ratio of total pore space to the given volume of the soil. That is,
Total porosity = (Total pore space / volume of the soil) x 100
Total porosity = 45/100 x 100
Total porosity = 0.45 x 100
Total porosity = 45%
Therefore, the value of the total pore space and total porosity are 45g and 45% respectively
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Which of the following sentences is punctuated correctly? A. Tory was waiting for her mom, at the mall, which was going to close soon. B. Tory was waiting (for her mom at the mall) which was going to close soon. C. Tory was waiting for her mom at the mall, which was going to close soon. D. Tory was waiting, for her mom at the mall—which was going to close soon.
Answer:
C is the correct sentence
compare relative motion and relative velocity
Psychological tools are used to understand human behavior and psychological processes
case studies ,surveys ,naturalistic observation , and laboratory observation are examples of descriptive or correlational researches methods . using these methods researchers can describe different events ,experiences,or behaviours and look for links between them
Psychologists study mental processes and human behavior by observing, interpreting, and recording how people and other animals relate to one another and the environment. ... Research methods vary with the topic which they study, but by and large, the chief techniques used are observation, assessment, and experimentation.
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Which of the following best explains why the region of Catalonia in Spain could be a viable country?
Answer: Catalonia is well developed economically compared to other regions in Spain.
Explanation:
in the second paragraph, the question with which the narrator confronts her mother (“i took....my dad”) reveals which of the following about there contrasting values?
Answer:
Matilda's anger is tempered by her mother's sense of humor. Her mother's leniency is at odds with Matilda's more objective point of view.
Explanation:
Hereditary spherocytosis (HS) is a disorder of red blood cells that causes the cells to be smaller and spherical instead of having the usual flattened, biconcave shape. The average diameter of normal red blood cells is 7.2μm, and the average diameter of red blood cells in a person with HS was found to be 6.7μm. The normal red blood cell has an average surface area of 136μm2 and an average volume of 91μm3.
Which of the following provides an accurate calculation of the surface area to volume ratio of an HS red blood cell, as well as a prediction of its effect on the efficient transferring of oxygen compared to a normal red blood cell?
The statement that provides an accurate calculation of the surface area to volume ratio of an HS red blood cell is The ratio is 0.89, and the cells are less efficient at transferring oxygen.
The ratio 0.89 is less than the ratio that is seen in a normal red blood cell, therefore, the cell would be less organized at moving oxygen.Hereditary spherocytosis (HS) is often referred to as a disease that can be inherited. It is known to affects the red blood cells.
Its symptoms includes the killing of red blood cells in the spleen and their removal from the blood stream amidst others.
See full question below
Hereditary spherocytosis (HS) is a disorder of red blood cells that causes the cells to be smaller and spherical instead of having the usual flattened, biconcave shape. The average diameter of normal red blood cells is 7.2μm, and the average diameter of red blood cells in a person with HS was found to be 6.7μm. The normal red blood cell has an average surface area of 136μm2 and an average volume of 91μm3.
Which of the following provides an accurate calculation of the surface area to volume ratio of an HS red blood cell, as well as a prediction of its effect on the efficient transferring of oxygen compared to a normal red blood cell?
A The ratio is 0.45, and the cells are more efficient at transferring oxygen.
B The ratio is 1.12, and the cells are less efficient at transferring oxygen.
C The ratio is 0.89, and the cells are less efficient at transferring oxygen.
D The ratio is 141, and the cells are more efficient at transferring oxygen.
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Is it bad to love someone even after you have broken up?
Answer:
Nope :)
Explanation:
I don't believe so. The heart wants what the heart wants. If you truly love that other person and not for body features then there is no shame. After all, you broke up with the other person for a reason and you already broke ties with. Do consider it might come off as if you move on too quickly but other than it's not really bad.
