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 were Austria’s aims and priorities at the congress
Answer: to reestablish peace and stability in Europe
Explanation: The goal of the conservatives at the Congress, led by Prince Klemens von Metternich of Austria, was to reestablish peace and stability in Europe. To accomplish this, a new balance of power had to be established.
1) Define family life education clearly and describe its benefit briefly
Answer:
practice of education which help in the overall development of family members
Explanation:
Family life education provides great help to make family happy and to promote family welfare. The family life education helps to know about the changes seen in or body from the early age in our life.
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%
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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Identical twins are ideal participants in epigenetic research because the twins are _________. a. genetically identical and may develop similar epigenetic patterns over time b. genetically identical but may develop different epigenetic patterns over time c. genetically different but may develop similar epigenetic patterns over time d. genetically different and may develop different epigenetic patterns over time
Answer:
b. Genetically identical but may develop different epigenetic patterns over time.
Explanation:
Twins are essentially clones of each other, they have identical genomes. Despite this, their epigenetics may differ due to the fact that these secondary genetic controls depend on the environment an organism exists in. For this reason, given enough time apart and sufficiently different conditions, twins will develop different epigenetic patterns.
compare relative motion and relative velocity
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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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.
WILL MARK BRAINLIEST IF WORK IS SHOWN
Mr. Jackson's dog Gromit jumped out of a second story window (through the screen) and fell to the ground below. The window is 15 feet high, the acceleration of gravity is 9.8m/s2, and there are 3.28 feet in each meter. What was the final velocity of this crazed dog?
Answer:
calculate with formula plz
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:
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.
Which of the following is an example of Balkanization? Please Help!!!
Answer:
Yugoslavia
Explanation:
The former Yugoslavia has become five independent countries and the province of Kosovo is currently fighting to break away of what is left of Yugoslavia.
Answer:
Balkanization. The term comes from the Balkan Peninsula of Europe, a region that has balkanized may time, and is still undergoing balkanization. EXAMPLES: The former Yugoslavia has become five independent countries and the province of Kosovo is currently fighting to break away of what is left of Yugoslavia.
Pls, choose me as brainliest!
line 14 the speaker says "a thousand virgins
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.
Read more about Maritime empires at; https://brainly.com/question/8193609
BRAINLIEST IF CORRECT
what type of cell signaling is clonal selection?
The clonal selection theory proposes that antigen selects lymphocytes for activation from a population of cells precommitted to produce specific antibody. Implicit in this theory is that antibody-forming cells are monospecific and express cell-surface receptors capable of binding foreign antigens.
Interaction of antigen with these side chains induced the cell to synthesize additional antibody molecules. This proposal seemed untenable once Karl Landsteiner demonstrated that the immune system could produce antibodies to a vast array of antigens; for over 50 years theories of antibody formation postulated that antigen instructed cells to synthesize antibodies complementary to the antigen. The introduction of the clonal selection theory of antibody formation by Macfarlane Burnet in the 1950s revived the idea that antibody-forming cells express cell-surface receptors by which they bind antigen. In 1961, Göran Möller provided the first evidence that antibody-forming cells had antibody (immunoglobulin) on their surface. The antigenbinding specificity of these immunoglobulin molecules was shown to be identical to the antibody that cells will produce when activated. Initially, many immunologists thought that the T lymphocyte receptor would also be an immunoglobulin molecule. However, studies by several laboratories in the early 1980s using a combination of monoclonal antibodies and molecular genetic techniques showed that the receptor consists of two polypeptide chains. The antigen-specific receptors on both T and B lymphocytes are associated with other trans-membrane molecules involved in the transduction of activation signals into the cell.
Bold text is answer.
- BRAINLIEST answerer
Answer:
the clonal selection theory proposes that antigen selects lymphocytes for activation from a population of cells precommitted to produce specific antibody. Implicit in this theory is that antibody-forming cells are monospecific and express cell-surface receptors capable of binding foreign antigens.
For example, memory B cells that differentiate after an adaptive immune response are thought to undergo clonal selection so that antibodies produced by newer memory B cells have considerably higher binding affinities to their antigens. And it is a receptor
Explanation:
What did anthropologists William and Jean O'Barr find in examining the factors that influence a
person's style of speech when testifying as a witness in court?
Answer:
Social influences somehow interfered with normal, biologically based behavior patterns to produce same-sex attraction.
Explanation:
Search What did anthropologists William and Jean O'Barr find in examining the factors that influence a
person's style of speech when testifying as a witness in court?
Thank-you letters should be sent out within
of the interview.
O A. one week
B. one day
C. one month
D. a few days
Answer:
B. one day
Explanation:
It's best to send a thank you letter while you're still fresh in the interviewer's mind. So you should send the email message within 24 hours of the interview (the same day as the interview or the next).
who greets the speaker and the speakers friends
Answer:
In the poem "The Blessing" By James Wright
Explanation:the internet
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!
Selected values of the derivative of the function g are given in the table above. It is known that g(3)=17. What is the approximation for g(3.2) found using the line tangent to the graph of g at x=3 ?
Answer: 16.76
Explanation: Since it says using the line tangent to the graph, you know to use point slope form, which is y-k=x(m-h). Since you are solving at x=3, y is 17 and the slope is -1.2. Plug this into your point slope form and you get y-17=-1.2(x-3). Then plug in 3.2 for your x and solve for y, should get 16.76.
¿Cuál personaje desempeña el rol del "gracioso" o "donaire" en el fragmento?
❤❤goodmorning everyone, today is going to be an amazing day dont let anyone bring you down today! remember to love your self!!!❤
Answer:
Ok thank u!
Explanation:
The embryo/fetus is most susceptible to damage from harmful environmental factors during __________.
A.
the first trimester
B.
premature labor
C.
toxoplasmosis
D.
preeclampsia
Please select the best answer from the choices provided
A
B
C
D
Answer:
A. the first trimester
Explanation:
