Use trigonometric identities to verify each expression is equal. csc2(x) - 2csc(x)cot(x) + cot2(x) = tan2(x/2)
By definition of csc and cot,
csc²(x) - 2 csc(x) cot(x) + cot²(x) = …
… = 1/sin²(x) - 2 cos(x) / sin²(x) + cos²(x) / sin²(x)
Combining fractions,
… = (1 - 2 cos(x) + cos²(x)) / sin²(x)
Factorize the numerator and use the Pythagorean identity,
cos²(x) + sin²(x) = 1,
to rewrite the denominator.
… = (1 - cos(x))² / (1 - cos²(x))
Cancel a factor of 1 - cos(x).
… = (1 - cos(x)) / (1 + cos(x))
Using the half-angle identities,
sin²(x) = (1 - cos(2x))/2
cos²(x) = (1 + cos(2x))/2
it follows that
1 - cos(x) = 2 sin²(x/2)
1 + cos(x) = 2 cos²(x/2)
and so
… = (2 sin²(x/2)) / (2 cos²(x/2))
… = sin²(x/2) / cos²(x/2)
Finally, by definition of tangent,
… = tan²(x/2)
Which two properties of equality could zoe use to finish solving for x? either the addition or subtraction property of equality either the multiplication or division property of equality either the addition or multiplication property of equality either the subtraction or division property of equality.
Zoe can solve the equation using (b) either the multiplication or division property of equality
The equation is given as:
[tex]3x = -6[/tex]
Zoe can solve the equation as follows.
First, divide both sides of the equation by 3
This gives
[tex]\frac{3x}{3} = -\frac 63[/tex]
[tex]x = -2[/tex]
Also, the equation can be solved by multiplying both sides by 1/3.
This gives
[tex]3x \times \frac{1}{3} = -6 \times \frac{1}{3}[/tex]
[tex]x = -2[/tex]
Hence, Zoe can solve the equation using (b) either the multiplication or division property of equality
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booker t. washington is noted for which of the following?
Answer: C. Establishing the Tuskegee Institute
Explanation:
On fridays, he prepares the weekly financial summaries for his supervisor and followed up on any outstanding invoices.
With regards to whether there is a grammatical error in the above sentence, the answer is Yes, there is.
In the above sentence:
The adjective, "prepares" is used for present tense clauses. The adjective, "followed" is used for past tense clauses.There are therefore two different clauses being used in this one sentence which would mean there is a grammatical error as only one clause should be used.
In conclusion, there is a grammatical error.
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Which of the following is true about the formation of faults.
Answer:
A fault is formed in the Earth's crust as a brittle response to stress. Generally, the movement of the tectonic plates provides the stress, and rocks at the surface break in response to this. If you whack a hand-sample-sized piece of rock with a hammer, the cracks and breakages you make are faults.
Explanation:
Which of the following details from the passage best helps the reader picture the setting.
Answer:
Can u please out a pic of the Passage so I can solve ur question?
Pauline chasse has just signed a lease agreement with landlord, wayne godbrey to rent a house he owns in delano. The lease states definite beginning (january 1, 2016) and ending (october 30, 2016) dates, and sets forth the rent amount and due dates and all additional property and personal information required in such a lease. Wayne hands a copy to pauline, but she notices that he has not signed it. When she comments about this to him, he tells her that signatures are not necessary since the lease is for less than a year. Which of the following is true of this situation?.
The correct option that is true as regards Wayne's situation about the lease is;
B; Leases of less than one year are not required to be in writing. However, if a lease IS in writing, then it must be signed by the lessor (in this case, Wayne).
The missing options are;
Under the Statute of Frauds in California,
A) leases of less than one year are not even required to be in writing, and therefore, signatures are not required.
B) Leases of less than one year are not required to be in writing. However, if a lease IS in writing, then it must be signed by the lessor (in this case, Wayne).
C) Leases of less than one year are not required to be in writing; but if there is a written lease, then it must be signed by both the lessee and lessor.
D) Because the property being leased is located in Northern California, a lease agreement is required to be both written and signed by the lessor if the lease period is for 6 months or more
Now, California has some principles that guide the regulation of the real estate industry and according to the California Principles of Real State, it has to be said that leases of less than one year are not required to be in writing. Now, even though the law stated that the consent of both parties are not enough to bind themselves in the lease agreement, it is recommended that just for the sake of keeping things legally binding as regards the agreement between both parties, then both parties may state it in written and the lessor must sign it.Read more about real estate statutes at; https://brainly.com/question/19655487
Why did the prisoner choose the bread and not the key brainly.
The Prisoner choose the bread and not the key because he prioritized the
Cat for escaping.
This was contained in Act 5 of Hamlet which was written by William
Shakespeare. Hamlet saw himself as a righteous hero and didn't want to
do the wrong thing.
He picked the bread to fill his stomach and left the key so the cat because
it needed it more in order to escape and avenge his father's death.
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A software developer wants to add a new feature to an existing application operating in the cloud, but only wants to pay for the computing time the code actually uses when it is called.
Answer:aye bro answer my question
Explanation:
Properties of protein is least likely to be affected by change in ph.
Answer:
Given
Rate of interest = 10% per annum
Principal for the first year = Rs 6000
Interest for the first year = Rs (6000 × 10 × 1) / 100
= Rs 600
Amount at the end of first year = Rs 6000 + Rs 600
= Rs 6600
Principal for the second year = Rs 6600
Interest for the second year = Rs (6600 × 10 × 1) / 100
= Rs 660
Amount for the second year = Rs 6600 + Rs 660
= Rs 7260
Therefore, compound interest for 2 years = final amount – (original) Principal
= Rs 7260 – Rs 6000
We get,
= Rs 1260
What is the trend in the morbidity rate of the cases explain brainly.
There are different reasons for changes in morbidity rate. The trend in the morbidity rate of the cases is that it fluctuated in the last ten years with an obvious increase in 2010 and a quick increasing trend from 2014-2016 until a sharp reduction in 2017.
Morbidity rateThe morbidity rate is known to be number of outcomes or proportion of which a disease is present in a population.A morbidity rate is also known as the rate at which acute and chronic diseases takes place in a population.
This rates is often used to known the general health of a population and to know health care needs of the people. These rates are often used in some industries, such as the insurance sector.
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Since customers who go to retail stores often know what they want or have a purpose to being at the store in the first place, sellers do not have to do much in the b2c selling environment.
Answer:
Explanation:Prospecting or qualifying
Select the correct answer. Consider these functions. F(x) = -2x − 5 g(x) = x − 2 which graph shows the composite function (f ◦ g)(x)? a. B. C. D.
Composite functions are functions formed by combining multiple functions that may or may not be the same.
The composite function (f o g)(x) is -2x - 1
The functions are given as:
[tex]f(x) =-2x - 5[/tex]
[tex]g(x) = x - 2[/tex]
The composite function (f o g)(x) is calculated using:
[tex](f\ o\ g)(x) = f(g(x))[/tex]
Given that:
[tex]f(x) =-2x - 5[/tex]
Substitute g(x) for x in the above equation
[tex]f(g(x)) =-2g(x) - 5[/tex]
Substitute [tex]g(x) = x - 2[/tex]
[tex]f(g(x)) =-2(x - 2) - 5[/tex]
Expand
[tex]f(g(x)) =-2x + 4 - 5[/tex]
So, we have:
[tex]f(g(x)) =-2x -1[/tex]
Hence, the composite function (f o g)(x) is -2x - 1
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if tu = 6 units, what must be true? su + ut = rt rt + tu = rs rs + su = ru tu + us = rs
Answer:
Explanation:
If TU=6 then SU+UT= RT
Highlight text that shows helen keller’s strength. Based on this passage, what full viewpoint could a prepared speaker share in a discussion? i really like helen keller’s strong writing. I think helen keller’s early outbursts were signals that she was a strong individual. I think it would be difficult to be unable to talk as a child. Helen keller failed to express herself, so she had outbursts as a child.
Answer:
B. I think Helen Keller's early outbursts were signals that she was a strong individual.
Explanation:
Answer: B is you answer
Explanation:
hope this helps
A victim of sexual abuse may be seductive toward others.
Answer:
currect
Explanation:
because excperencing that they become used to it and though they know it is bad, they are still very much used to it.
Madeline was out at a restaurant for dinner when the bill came. Her dinner came to $13. After adding in a tip, before tax, she paid $15. 34. Find the percent tip.
15.34 - 13
=2.34
2.34 ÷ 15.34 × 100
=15.25%
What is the primary purpose of these stage directions? to show interactions between characters to direct actions that take place onstage to describe a character’s appearance to indicate a character’s tone of voice.
Answer:
B) to direct actions that take place onstage
EDGE2022
Answer:
B. to direct actions that take place onstage
Explanation:
What is the primary purpose of these stage directions?
To direct actions that take place onstage
a fire destroys all trees and plants in the forest. how might this affect the birds in the area?
Answer:
They could die or have to relocate to a place with trees.
Explanation:
When a fire destroys all trees and plants in the forest, the birds in this area would be forced to migrate to another location.
What is a habitat?A habitat can be defined as a combination of resources and geographical area that defines where the particular species of a living organism generally lives, reproduces and thrives.
In this scenario, the birds living in this area (forest) would be forced to migrate to another location due to the burning of all trees and plants in this forest.
In Biology, this situation is referred to as a catastrophic disturbance.
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#SPJ2
Before writing a composition it is best to.
Answer: Before you start writing, remind yourself of the basic composition composition. Almost all articles have three parts: introduction, body of information and conclusion. The five-paragraph text is a common repetition of this and includes an introductory paragraph, three body paragraphs, and a conclusion paragraph.
Explanation:
Which statements justify that the dilation of triangle stu is an enlargement increasing its size by the magnitude of the scale factor? select two options. The triangle pre-image is closer to the point of dilation than the image. The triangle image is closer to the point of dilation than the pre-image. The value of the scale factor, , is between 0 and 1. The value of the scale factor, 6, is greater than 1. The vertices of the pre-image are collinear with the vertices of the image.
There are different ways to justify a statement. The statements that justify that the dilation of triangle STU are:
The triangle pre-image is closer to the point of dilation than the image.The value of the scale factor, 6, is greater than 1.DilationDilation is simply known as a process that is often employed for producing similar figures. All the point is said to be stretched outwards from the center point and it is then multiplied by the distances by the scale factor.
A dilation is also known to be a type of transformation that makes bigger or reduces a figure. (This is called the preimage). With this process, a new figure or image is created or produced.
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Answer:
The triangle pre-image is closer to the point of dilation than the image.
The value of the scale factor, 6, is greater than 1.
Explanation:
just did it
Select the correct answer. Which is a feature of a roth ira? a. You must pay tax if you withdraw your earnings once you're 59. 5 years old. B. You can withdraw your earnings once you're 59. 5 years old but must pay a penalty. C. You can withdraw your earnings once you're 59. 5 years old without paying a penalty.
I think the answer is C
you can withdraw your earnings once you're 59. 5 years old without paying a penalty
Which of the following sentences contains the correct usage for virtuosity?.
Answer:
a. The virtuosity of the animals was expressed in their gait
Explanation:
very far from earth (at r=[infinity]), a spacecraft has run out of fuel and its kinetic energy is zero. if only the gravitational force of the earth were to act on it (i.e., neglect the forces from the sun and other solar system objects), the spacecraft would eventually crash into the earth. the mass of the earth is me and its radius is re. neglect air resistance throughout this problem, since the spacecraft is primarily moving through the near vacuum of space.
By considering the conservation of energy, the speed V of the spacecraft when it eventually crash into the earth and its distance from the center of the earth is r are 11172.6 m/s and 3294.6 m/s respectively.
Given that, r is at infinity when a spacecraft has run out of fuel and its kinetic energy is zero. if only the gravitational force of the earth were to act on the spacecraft would eventually crash into the earth.
Where
Mass of the earth [tex]m_{e}[/tex] = 5.97 × [tex]10^{24}[/tex] kg
Radius of the earth [tex]R_{e}[/tex] = 6.38 × [tex]10^{6}[/tex] m
G = 6.67 x [tex]10^{-11}[/tex]N[tex]m^{2}kg^{-2}[/tex]
a.) Since the spacecraft is primarily moving through the near vacuum of space, the speed V of the spacecraft when it eventually crash into the earth can be calculated by considering the conservation of energy.
The total initial energy = total final energy.
[tex]E_{i} = E_{f}[/tex]
[tex]K.E_{i}[/tex] + [tex]U_{i}[/tex] = [tex]K.E_{f}[/tex] + [tex]U_{f}[/tex]
where [tex]K.E_{i}[/tex] = 0
-G[tex]m_{e}[/tex]m/(r + [tex]R_{e}[/tex]) = 1/2m[tex]V^{2}[/tex] + ( -G[tex]m_{e}[/tex]m)/[tex]R_{e}[/tex]
mass of the spacecraft will cancel out
G[tex]m_{e}[/tex]/(r + [tex]R_{e}[/tex]) = 1/2[tex]V^{2}[/tex] + ( -G[tex]m_{e}[/tex])/[tex]R_{e}[/tex]
G[tex]m_{e}[/tex]/(r + [tex]R_{e}[/tex]) = 0 since r is at infinity.
0 = 1/2[tex]V^{2}[/tex] + ( -G[tex]m_{e}[/tex])/[tex]R_{e}[/tex]
Substitute all the parameters into the equation above.
0 = 0.5[tex]V^{2}[/tex] + ( -6.67 x [tex]10^{-11}[/tex] x 5.97 x [tex]10^{24}[/tex] )/6.38 x [tex]10^{6}[/tex]
0.5[tex]V^{2}[/tex] = 62,413,636.36
[tex]V^{2}[/tex] = 62,413,636.36 / 0.5
[tex]V^{2}[/tex] = 124,827,272.7
V = [tex]\sqrt{124,827,272.7}[/tex]
V = 11172.6 m/s
b.) Given that the distance from the earth r = x([tex]R_{e}[/tex])
That is,
r = 11.5 x 6.38 x [tex]10^{6}[/tex]
r = 73,370,000 m
To find the spacecraft's speed when its distance from the center of the earth is r, we will use the same formula. That is,
[tex]K.E_{i}[/tex] + [tex]U_{i}[/tex] = [tex]K.E_{f}[/tex] + [tex]U_{f}[/tex]
0 = 1/2[tex]V^{2}[/tex] + ( -G[tex]m_{e}[/tex])/r
Substitute all the parameters into the formula
0 = 0.5[tex]V^{2}[/tex] + ( -6.67 x [tex]10^{-11}[/tex] x 5.97 x [tex]10^{24}[/tex] )/ 73,370,000
0.5[tex]V^{2}[/tex] = 5427272.727
[tex]V^{2}[/tex] = 10854545.45
V = [tex]\sqrt{10854545.45}[/tex]
V = 3294.6 m/s
Therefore, the speed V of the spacecraft when it eventually crash into the earth and its distance from the center of the earth is r are 11172.6 m/s and
3294.6 m/s respectively.
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Fill in the blank: an important part of dashboard design is ensuring that charts, graphs, and other visual elements are cohesive. This means that they are _____ and make good use of available space.
This means that data are BALANCED and make good use of available space. A dashboard can be defined as a visual display of data.
A dashboard refers to a visual display of data, which is used to track and analyze indicators, metrics, and data points.
A dashboard presents a line of work, thereby cohesion and balance should ideally be interrelated.
A dashboard is configurable and therefore it is possible to select data to show and include charts/graphs for their visualization.
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How should the following sentence end? she was smart, responsible, and learning french. Friendly to others. Studying math. Hosting the party.
Answer:
friendly to others.
Explanation:
I took the test and got it correct.
Answer: a
Explanation:
A 17 year old basketball player has collapsed on the court.
There are different reasons why players collapse in the court. It is therefore good that one knowns the right step to take. The scene is safe and the correct order of skills for lay rescuer adult CPR is Call 911, check for a pulse, start CPR.
Note that in the court, a player may collapse and it is very important to do the right thing. You can only perform the CPR , when you known how to do it. If you don't have the basic training on how to do it, do not attempt to do it. watching of videos on how to do it may help.
When doing CPR, always make sure you have to keep your elbows locked, and make sure to know who needs to do that role in this process. Be quick with it and do not be afraid of breaking bones.
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A 17-year-old basketball player has collapsed on the court. The scene is safe. What is the correct order of skills for lay rescuer adult CPR?
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Argon has a higher boiling point than neon because argon has.
Answer:
stronger intermolecular forces of attraction
Explanation:
Byron earns $11. 00 per hour. How many hours will byron have to work to earn $143. 00? 7. 7 hours 13. 0 hours 14. 3 hours 15. 7 hours.
Answer:
10 pages
Explanation:
All of the following are functions of the nervous system except.
Answer:
brain is NOT a part of the peripheral nervous system. The brain, brain stem and spinal cord are all components of the central nervous system.