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)
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 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.
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
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.
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).
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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(NEED ASAP)
Type the correct answer in each box.
In the figure, lines m and n are parallel to each other. Lines pand are also parallel to each other. 68°.
The value of x is[-------] degrees, and the value of y is [-------] degrees.
[tex]\Large \boxed{\sf y=68, x=112}[/tex]
A transversal line cuts two parallel lines, producing pairs of angles with unique features.
y. Corresponding angles are equal (68=68)
x. Angles on a straight line add up to 180 degrees (180-68=112)
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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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!
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?
an action verb that is followed by a direct object
2. Thomas wants to add a watermark to his spreadsheet and chooses a giant black plus sign.
Assuming his spreadsheet is full of enough data to cover several pages and uses plain
styling with no filling, what issue will Thomas run into? What could Thomas possibly
do to use something similar as a watermark?
Answer:
An issue Thomas might run into is..
Explanation:
Thomas might run into the issue that people will not be able to see the data.
Thomas could make the watermark a lighter color such as a light gray or even a light blue instead of black and Thomas could add filling to his styling to make it easier to see and read.
❤❤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:
từ vẻ đẹp của Vũ Nương trong đoạn trích ở phần đọc - hiểu, viết đoạn văn ( khoảng 20 câu ) về những việc làm thể hiện lòng hiếu thảo của em với cha mẹ.
what is that mean about that
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.
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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:
