A particle travels along the x-axis with velocity v ( t ) = 2 t 1 + t 2 m/s for 0 ≤ t ≤ 3 seconds. If the particle’s position at t = 0 is x ( 0 ) = 5 , what is its position at t = 3? Show all of your work.
Answers
Its position at t = 3 is 7.3025850929
How to solvev(t)=(2t)/(1+t^2)
To find the position we need to integrate the function
p(t) = ∫ v(t)
p(t) =∫(2t)/(1+t^2) dt
Using u substitution
u = 1+t^2
du =2t dt
p(t) =∫(du)/(u)
We know that the integral of 1/u du is ln |u|
p(t) = ln|u| +C
Substituting back for u
p(t) = ln|1 +t^2| +C
To find the value of C, we let t=0
p(0) = ln|1 +0| +C = 5
= ln(1) +C =5
0 +C =5 Therefore C=5
p(t) = ln|1 +t^2| +5
We want to find the position at t=3
p(3) = ln|1 +3^2| +5
= ln(10) +5
=7.3025850929
Read more about integrals here:
https://brainly.com/question/22008756
#SPJ1
Related Questions
Read the following scenario and share your opinion on which areas of EI that Samantha may need to work on.
Samantha is an employee who has been with the company for a year. She's great at her job, but she has a hard time getting along with her coworkers. She often comes off as dismissive, and she doesn't seem to understand other people's perspectives. When someone tries to give her feedback, she gets defensive and can become angry or upset. Samantha's manager has noticed that her lack of emotional intelligence is causing tension in the office.
Answers
Firstly, it seems that Samantha may need to work on her self-awareness, which is the ability to recognize and understand her own emotions. Samantha's defensive reaction to feedback suggests that she may not be aware of her own emotional triggers or how to manage them effectively. By improving her self-awareness, Samantha may be able to better regulate her emotional responses in the workplace.
Secondly, Samantha may need to work on her empathy, which is the ability to understand and connect with other people's emotions. Her dismissive attitude and lack of understanding of others' perspectives indicate a lack of empathy. By practicing empathy, Samantha may be able to build better relationships with her coworkers and work more effectively as part of a team.
Lastly, Samantha may need to work on her social skills, which involve the ability to communicate effectively, build relationships, and work collaboratively with others. Her inability to get along with coworkers and the tension she is causing in the office suggest a need for improved social skills. By developing stronger social skills, Samantha may be able to improve her relationships with coworkers, reduce tension, and work more effectively in a team environment.
In conclusion, based on the scenario, it appears that Samantha may need to work on several areas of EI, including self-awareness, empathy, and social skills. By improving these skills, Samantha may be able to build better relationships with coworkers, work more effectively as part of a team, and reduce tension in the office
Butch often steps from a situation and asks himself how he contributed to it and what he may change in the way he responds should it happen again. He likes to meditate and get in touch with what he’s feeling. What type of intelligence does Butch have?
Answers
Butch often steps from a situation and asks himself how he contributed to it and what he may change in the way he responds should it happen again. He likes to meditate and get in touch with what he’s feeling. Thus, the kind of intelligence he has is Emotional Intelligence.
What is Emotional intelligence?Emotional intelligence (EQ) is the capacity to comprehend, use, and control one's own emotions in constructive ways in order to reduce stress, communicate effectively, empathize with others, overcome problems, and diffuse conflict.
Emotional intelligence is the capacity to recognize and manage one's own emotions as well as understand the emotions of others. A high EQ assists you in developing connections, reducing team tension, defusing conflict, and increasing job satisfaction.
Learn more about Emotional Intelligence;
https://brainly.com/question/30004291
#SPJ1
the normal curve shown represents the sampling
Answers
Note that he best estimate of the standard deviation of the population is 75.
Why is this so?The area under the curve in a probability density function indicates likelihood. Because the normal distribution is a probability distribution, the total area under the curve is always one, or one hundred percent. Thus, 25 + 75 = 100.
A normal distribution, often known as a Gaussian distribution, is a form of continuous probability distribution for a real-valued random variable in statistics.
A bell curve is a form of graph used to depict the distribution of a set of chosen values within a specified group that tends to have a middle, normal value as a peak with low and high extremes tapering out pretty symmetrically on each side.
Learn more about normal curve at:
https://brainly.com/question/31391220
#SPJ1
Full Question:
Although part of your question is missing, you might be referring to this full question:
The normal curve shown represents the sampling distribution of a sample mean for sample size n = 25, selected at random from a population with standard deviation sd. Which of the following is the best estimate of the standard deviation of the population?
3
6
15
30
75
Which of the following is NOT a characteristic of scholarly sources?
Select one:
a. Using specialized vocabulary or jargon
b. Being refereed or peer-reviewed
c. Offering broad overviews of a topic
d. Having an expert author
Answers
Answer:
c. Offering broad overviews of a topic
Explanation:
Offering broad overviews of a topic. Scholarly sources typically provide in-depth analysis of specific aspects of a topic, rather than broad overviews. The other characteristics listed - using specialized vocabulary or jargon, being refereed or peer-reviewed, and having an expert author - are all typical of scholarly sources.
I need help with an AP Calc AB topic. Max/Min, Increasing/Decreasing, Concavity.
I know how to do all of it but when I try this, I am not able to figure it out. Especially when it involves e. Could all work be shown with explanations. Thanks
Answers
It should be noted that f(x) is increasing on the interval (-∞, 1).
How to explain the function2e^-x - 2xe^-x > 0
2e^-x > 2xe^-x
Dividing both sides by 2e^-x (which is always positive), we get:
1 > x
Therefore, f(x) is increasing on the interval (-∞, 1).
Also f'(x) = 2e^-x - 2xe^-x
At x = 1, we have:
f'(1) = 2e^-1 - 2e^-1 = 0
Since f'(x) changes sign from negative to positive as we move from x = 1 to x < 1, we conclude that f(x) has a relative minimum at x = 1.
Learn more about functions on
https://brainly.com/question/11624077
#SPJ1
Briefly discuss the differences between Liszt and Chopin, including their major contributions. Illustrate your discussion with musical examples.
Answers
AnswerAnswer:
while both Liszt and Chopin were virtuosic piano composers of the Romantic era, they had distinct differences in their style, compositional forms, and harmonic language. Liszt was known for his virtuosic and flamboyant piano style, innovative forms,
Explanation:
Franz Liszt and Frédéric Chopin were both renowned composers of the Romantic era, known for their virtuosic piano compositions. However, while they both contributed significantly to the piano repertoire, they had distinct differences in their compositional style, influences, and contributions to the music world.
Style and Technique:
Liszt was known for his flamboyant and virtuosic piano style, characterized by dazzling displays of technical prowess, intricate fingerings, and use of innovative piano techniques such as sweeping arpeggios, octaves, and fast scale passages. He often incorporated elements of showmanship in his performances, earning him the reputation of being one of the greatest piano virtuosos of his time. One of his most famous compositions, "La Campanella," showcases his virtuosity with its rapid-fire arpeggios and intricate fingerings.
On the other hand, Chopin's style was more delicate, poetic, and expressive. His compositions were known for their nuanced phrasing, rich harmonic language, and deep emotional expressiveness. Chopin's music often reflects his Polish heritage, with influences from Polish folk music, dance forms, and lyrical melodies. For example, his Nocturne in C-sharp minor, Op. 27, No. 1, is a beautiful example of his expressive and lyrical style, with its flowing melodies and rich harmonies.
Compositional Forms:
Liszt and Chopin also differed in their choice of compositional forms. Liszt's music spans a wide range of forms, from symphonic poems, piano concertos, and solo piano works, to choral and chamber music. He was known for his innovative approach to form, often blurring the lines between different musical genres and pushing the boundaries of traditional forms. For example, his symphonic poem "Les Préludes" is a groundbreaking work that combines elements of symphony and programmatic music, with its lush orchestrations and evocative storytelling.
In contrast, Chopin's compositions were primarily for solo piano and revolved around forms such as nocturnes, etudes, ballades, and polonaises. He is considered a master of these forms, elevating them to new heights of expressiveness and technical complexity. For instance, his Ballade No. 1 in G minor, Op. 23, is a prime example of his ability to create a narrative and emotional arc within a single piano work, with its dramatic shifts in mood, virtuosic passages, and lyrical melodies.
Harmonic Language and Influence:
While both Liszt and Chopin were known for their harmonic innovations, they had different approaches to harmony. Liszt's music often featured bold and daring harmonic progressions, pushing the boundaries of tonality and experimenting with chromaticism. He also explored unconventional tonal relationships and tonal ambiguity in his compositions, which was a departure from the traditional tonal language of his time. For example, his piano work "Un Sospiro" showcases his use of colorful harmonies and innovative tonal relationships.
Chopin, on the other hand, retained a more traditional tonal language but infused it with his own unique sense of chromaticism and harmonic sophistication. His harmonies were often characterized by rich chromatic chords, lush modulations, and colorful tonal progressions. His music had a profound influence on later composers, including Debussy and Ravel, who adopted his harmonic language in their own works.
chatgpt
1. 2x+8+9x^2+89/232
2. Cos(234)
3. integral of x^2
4. antiderivative of 5x^3+8x^2
Answers
Answer:
Below...
Explanation:
(9x^2 + 2x + 97) / 232
-0.766044443118978
(x^3) / 3 + C, where C is the constant of integration
(5/4)x^4 + (8/3)x^3 + C, where C is the constant of integration
what is anecdotal in teacher education
Answers
Answer:
Notes that teachers take observing the child
Explanation:
PLEASE HELP ASAP WILL GIVE 100 POINTS!!!!
Suppose a packet that is transmitted across the internet contains the following information (from left to right):
Bits 1-4: Packet sequence number within the message.
Bits 5-8: Total number of packets in the message.
Bits 9-16: Number identifying the sender.
Bits 17-24: Number identifying the receiver.
Bits 25-64: Part of the actual message being sent.
Here is one of the packets being sent over the internet:
01111011 10000001 11001110 01010110 00111100 10011100 11100010 10001111
Which of the following statements about this packet is true? Select one answer
A)This is packet 1 out of 8 total packets in the message.
B)This is packet 7 out of 11 total packets in the message.
C)This is packet 14 out of 22 total packets in the message.
D)This is packet 123 out of 129 total packets in the message.
Answers
Answer:Therefore, the correct answer is B) This is packet 7 out of 11 total packets in the message.
Explanation:Using the given information, we can decode the packet as follows:
Bits 1-4: 0111 -> Packet sequence number within the message is 7.
Bits 5-8: 1011 -> Total number of packets in the message is 11.
Bits 9-16: 00000001 -> Number identifying the sender is 1.
Bits 17-24: 11001110 -> Number identifying the receiver is 206.
Bits 25-64: 01010110 00111100 10011100 11100010 10001111 -> Part of the actual message being sent.
In the given packet, bits 1-4 are 0111, which represents the packet sequence number within the message. Bits 5-8 are 1011, which represents the total number of packets in the message.
Therefore, this packet is packet 7 out of 11 total packets in the message.
So, the correct answer is B) This is packet 7 out of 11 total packets in the message.
Scientists theorize that all stars started out as a nebula that
eventually condensed into a protostar, or young star. In three to five sentences, please explain the events that take place for a
protostar to move to the next stage of its life as a glowing star.
Answers
The star, at some point, enters the main sequence phase of its life, where it will remain stable for millions to billions of years, depending on its mass.
What is the next stage?The pressure and temperature at the center of a protostar rise as it disintegrates due to its own gravity, which causes hydrogen atoms to undergo nuclear fusion and produce helium atoms. The protostar glows as a result of the massive amount of energy released during this process, which also produces heat and radiation.
The star achieves equilibrium while the fusion reaction continues, with the outward pressure from the reaction counteracting the inward force of gravity.
Learn more about nebula:https://brainly.com/question/9497068
#SPJ1
What led to the idea that the Universe started out in a big bang?
1.
The observation of the cosmic microwave background
2.
The earliest galaxies observed by the Hubble Space Telescope
3.
Using the Type 1A supernovae in the measurements of the expansion of the universe
4.
The observed expansion of the universe
Answers
Answer:
A. The observation of the cosmic microwave background led to the idea that the Universe started out in a big bang.
Explanation:
The cosmic microwave background (CMB) is radiation left over from the Big Bang. It is the oldest light in the Universe and provides a snapshot of the Universe at a very early time. The CMB was discovered in 1964 by Arno Penzias and Robert Wilson, and its existence supports the Big Bang theory. The CMB is nearly uniform in all directions, with small variations that correspond to the density fluctuations in the early Universe that gave rise to the formation of galaxies and other structures. The CMB is one of the strongest pieces of evidence for the Big Bang theory and led to its widespread acceptance among scientists.
Briefly discuss the term symphonic poem. Explain the difference between symphony and symphonic poem, illustrating your discussion with musical examples and relevant composers.
Answers
A symphonic poem, also known as a tone poem, is a type of orchestral music that tells a story or evokes a particular mood or image without relying on text or lyrics. The main difference between a symphony and a symphonic poem is that a symphony is a multi-movement work for orchestra that follows a specific structure and is typically abstract example is Franz Liszt.
What is symphonic poem?A symphonic poem, often referred to as a tone poem, is a style of orchestral music that conveys meaning without the use of words or lyrics. Programmatic music, which has a narrative or descriptive nature, is a type of music that normally consists of a single movement, frequently with contrasting passages.
Franz Liszt, a Hungarian composer who produced a number of symphonic poems in the middle of the 19th century, including "Les Préludes," "Mazeppa," and "Tasso, lamento e trionfo," is credited with coining the phrase. Liszt aimed to improve programmatic music, which had been denigrated as merely entertainment, in these compositions.
Learn more about poem at:
https://brainly.com/question/9861
#SPJ1
The status of Macau and Hong Kong as shown on Map 2 would become a source of renewed international tension in the last decades of the twentieth century primarily because of
Answers
Map 2 may likely symbolize a map illustrating Macau and Hong Kong as distinctive administrative regions of China, which came into being during the later years of the 1990s.
What led to these tensions?The renewed international tension rising over the recent decades regarding the standing of Macau and Hong Kong as Chinese SARs stemmed from worries of preserving their distinct economic and political structures, diametrically antithetical to mainland China's.
At the same time, proclamations were generated from some Western countries and human rights associations alluding to insufficient protective regulations for human rights and liberties within these domains under Chinese direction.
Read more about Macau and Hong Kong here:
https://brainly.com/question/1470687
#SPJ1
Answer:
B
Explanation:
China’s growing economic power following the implementation of liberalization policies
4. Many people start smoking and/or drinking alcohol as teenagers. Choose either drinking or smoking as an example and explain why this age is a particularly vulnerable time to initiate these behaviors. Develop a behavioral intervention for a teenager who has a problem with excessive smoking or drinking.
Answers
With regards to the behavioral intervention prompt, I will choose smoking as an example. The teenage years are a particularly vulnerable time to initiate smoking because the adolescent brain is still developing, and nicotine can cause permanent changes to the brain that increase the risk of addiction.
What is the explanation for the above response?Note that social and environmental factors, such as peer pressure, stress, and exposure to tobacco advertising, can also influence a teenager's decision to start smoking.
To develop a behavioral intervention for a teenager who has a problem with excessive smoking, a comprehensive approach is needed. This may involve counseling, social support, and nicotine replacement therapy. Counseling can help the teenager to identify triggers for smoking, develop coping strategies, and set goals for quitting. Social support from family, friends, or a support group can provide encouragement and accountability.
Nicotine replacement therapy, such as nicotine gum or patches, can help to manage withdrawal symptoms and reduce cravings. Additionally, education on the health consequences of smoking and strategies to avoid triggers can be helpful in preventing relapse.
Learn more about behavioral intervention at:
https://brainly.com/question/30159682
#SPJ1
