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)
List and explain the 4 things that contribute to one’s self-esteem
Genetics.
Personality.
Life experiences.
Age.
Insecure but I'm working with it
Many things that I could get rid of
Ain't about to give it up
I made a few mistakes, I regret it nightly
I broke a couple hearts that I wear on my sleeve
My mama always said, girl, you're trouble
And now I wonder, could you fall for a woman like me
And every time we touch, boy, you make me feel weak
I can tell you're shy and I think you're so sweet
Spending every night under covers and
Still I wonder, how could you fall for a woman like me (A woman)
Answer:
its called women like me
Explanation:
i looked it up
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:
line 14 the speaker says "a thousand virgins
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.
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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who greets the speaker and the speakers friends
Answer:
In the poem "The Blessing" By James Wright
Explanation:the internet
if you had one person to save in 5 sec who would it be.
Keanu Reeves :3
hes a national treasure
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:
What is the quantity of books that this individual is carrying in the image provided.
Answer:
3
Hope it helps
Discuss the reality of satisfying the need for self-actualization. Is this ability of being a self-actualized person realistic? Or is it an aspect of life that always has room for improvement? EXPLAIN.
Answer:
we human can not be satisfied
Explanation:
because we need every thing in the nature and many other thing so weren't never satisfied ok
❤❤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:
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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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.
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?
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:
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.
compare relative motion and relative velocity
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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what are the pros and cons of federal and unitary states
Answer:
Advantages of Unitary System
The advantages of unitary government are it is single and decisive legislative. It is also has a simple management of an economy and the government are smaller.
Disadvantages of Unitary System
The disadvantages of using this type of system are it has slow government response.
Advantages of Federalism
Provincial government representatives live in close proximity to the people and are most of the times from the same community, so that they are in a better position to understand these problems and offer unique solutions for them.
Disadvantages of Federalism
there can be overlapping of work and subsequent confusion regarding who is responsible for what.
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:
Kendle wants to play several games of laser tag. She has $35, 5 to play g games. Each game of laser tag costs $5
Answer:
35 ÷ 5 = g
Explanation:
First, you snatch her/his money to do math, then you take the $35 and look the the thing that tells you how much games cost then do 35 ÷ 5 but since you cant solve it just put 35 ÷ 5 = g , and last but not least you take Kendle's money because no lazer tag during a pandemic and run home before you get yelled at because you were at a lazer tag place and took someones money.
¿Cuál personaje desempeña el rol del "gracioso" o "donaire" en el fragmento?
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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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.
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.