Answers
For a particle with some position function y(t), we're given its velocity function v(t) = 1 - tan⁻¹(eᵗ ) and we're told that it starts with a position of y = -1 at the start.
(a) Acceleration is the rate of change of velocity, so to get the acceleration function a(t), you have to differentiate v(t) :
a(t) = d/dt v(t)
a(t) = d/dt [1 - tan⁻¹(eᵗ )]
a(t) = - d/dt [tan⁻¹(eᵗ )]
Apply the chain rule: take f(u) = tan⁻¹(u) and u(t) = eᵗ, so that
df/dt = df/du × du/dt
→ a(t) = - 1/(1 + u ²) × eᵗ = - eᵗ / (1 + e²ᵗ )
Then when t = 2, the acceleration is
a (2) = - e² / (1 + e⁴) ≈ -0.1329
(b) The acceleration of the particle at t = 2 is negative, so the particle's speed at this moment is decreasing. (Recall the first derivative test.)
(c) Note that at t = 0, the particle's velocity is v (0) = 1 - tan⁻¹(e⁰) = 1 - π/4 ≈ 0.2416 > 0. This means that the particle is moving upward at the start.
From part (a), we see that the acceleration is always negative, so the particle would be slowing down until it reaches zero velocity, after which point its velocity will become negative (meaning its speed would increase again as it starts to accelerate in the negative direction).
This means the particle's highest position on the y-axis occurs at the same time v(t) becomes 0, so you solve:
1 - tan⁻¹(eᵗ ) = 0
1 = tan⁻¹(eᵗ )
tan(1) = tan(tan⁻¹(eᵗ ))
tan(1) = eᵗ
ln(tan(1)) = ln(eᵗ )
ln(tan(1)) = t ≈ 0.443
(d) Use the fundamental theorem of calculus to find an expression for y(t) :
y(t) = y (0) + ∫₀ᵗ v(s) ds
(where s is just a dummy variable)
Then the particle's position at t = 2 is
y (2) = y (0) + ∫₀² v(s) ds
v(t) unfortunately does not have a nice antiderivative, so you'll have to use a calculator. (I hope this question is given in the calculator portion!) You would find
∫₀² v(s) ds ≈ -0.3607
so that
y (2) ≈ -1 + (-0.3607) ≈ -1.3607
The sign of the particle's velocity at this time tells you in which way the particle is moving. We have
v (2) = 1 - tan⁻¹(e²) ≈ -0.4363
which is negative, so the particle is moving away from the origin. This is consistent with the answer found in part (c):
• before t ≈ 0.443, the particle is moving upward toward the origin;
• at t ≈ 0.443, the particle reaches its highest point at y (2) ≈ -1.3607, then turns around and accelerates back downward and away from the origin
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Which medium does Wi-Fi use to send data between networks and devices?
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I need help with this one I would really appreciate it a lot
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Answer:
Its B
Explanation:
I took the test already.
5. A room is 13 m long and 10 m broad. Find the cost of carpeting the floor at the rate of 6 per m^2
Answers
[tex]{\large{\bold{\rm{\underline{Let's \; understand \; the \; concept}}}}}[/tex]
★ This question says that a room is 13 metres as it's length and 10 metres as it's breadth. We have to find out the cost of carpeting the floor at the cost of 6 Rupees per metre²
[tex]{\large{\bold{\rm{\underline{Given \; that}}}}}[/tex]
★ Length of the room = 13 m
★ Breadth of the room = 10 m
★ Carpeting the floor at cost of 6 Rupees per metres²
[tex]{\large{\bold{\rm{\underline{To \; find}}}}}[/tex]
★ The cost of carpeting the floor at the cost of 6 Rupees per metre²
[tex]{\large{\bold{\rm{\underline{Solution}}}}}[/tex]
★ The cost of carpeting the floor at the cost of 6 Rupees per m² = Rupees 780.
[tex]{\large{\bold{\rm{\underline{Using \; concept}}}}}[/tex]
★ Area of rectangle formula.
[tex]{\large{\bold{\rm{\underline{Using \; formula}}}}}[/tex]
★ Area of rectangle = Length × Breadth
[tex]{\large{\bold{\rm{\underline{Full \; Solution}}}}}[/tex]
☆Firstly let us find the area of room..! We have to use the formula to find area of rectangle.
↝ Area of rectangle = Length × Breadth
↝ Length of floor = 13 m
↝ Breadth of floor = 10 m
↝ Area of floor = Length × Breadth
↝ Area of floor = 13 × 10
↝ Area of floor = 130 m²
☆ Now it's given that the cost of carpeting the floor at the cost of 6 Rupees per metre²
↝ Cost = 6 × 130
↝ Cost = Rupees 780
Describe one social factor leading to gender inequality in agriculture?
Answers
Students usually go to middle school for
4 points
four years
three years
two years
one year
Other:
Answers
What determines the number of representatives each U.S. State receives in the House of Representatives?
The physical size of the state
b
The percentage of Democrats
c
The latest U.S. Census population figures
d
The number of registered voters
e
The economic importance of the state
Answers
Answer:
C. The latest U.S. Census population figures
Explanation:
The Census taken in each state every ten years tells us the population of a state and the demographics about that population. The HOR has a set number of 435 members total, but the number of members from each state fluctuates depending on the # of people living in the state.
Feel free to ask questions! Live, laugh, and love!
The House of Representatives is the lower house that makes the bicameral legislature. The number of representatives is based on the census report on the population of the US. Thus, option C is correct.
What is a census report?A census report is a collection and survey report that represents the population estimation of the people that lives in a particular area and is recorded at an interval of times.
The census report tells about the demographic population once in ten years and is used to determine the number of representatives in the lower house. As the number of the population decides the number of the states that will be represented.
Therefore, option c. the US census report determines the HOR representatives.
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Two types of monocular depth cues are
A. motion parallax.. pictorial depth cues
B. convergence...retinal disparity
C. motion parallax retinal disparity
D. convergence.
pictorial depth cues
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I hope this helps.
Lava is hot liquid rock. When lava flows over solid ground, the solid ground beneath it increases in temperature. What happens to the molecules in the solid ground when the temperature is increasing?
Answers
Answer:
Energy of the molecules in the solid ground increases.
Explanation:
3
Type the correct answer in the box. Spell all words correctly.
What term refers to the gases and vapors, particulate materials, gunpowder, and metallic chips that explode from the gaps of a weapon when
fired?
Gunshot
explodes from the gaps of a weapon when it is fired.
Reset
Next
Answers
Answer: Smoke
Explanation:
Gunshot smoke or gun smoke refers to the gases and vapors that come out of a gun when it is fired. This smoke contains gunpowder, metallic chips and particulate materials but when put together simply looks like smoke.
Overexposure to these substances have been shown to be dangerous to humans as they will be deposited in the lungs where they can contribute to long-term health problems.
Answer:
Explanation:
residue
Describe one economic factor leading to gender inequality in agriculture?
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Map image of the congressional districts of Texas. District 1 is located in eastern Texas. It is a small district that is relatively uniform in size and shape. District 11 is located in central Texas. The district is fairly large and comprises several Texas counties. District 13 is a large district that takes up much of the panhandle in northern Texas. District 23 is largest district in Texas in terms of physical size. This district spans across much of its southwestern region. District 25 is located in southern Texas. It is a long, narrow district that spans from the southern border to central Texas.
© 2011 The Exploration Company
Which of the following districts could be the result of gerrymandering? (4 points)
a
District 4
b
District 10
c
District 15
d
District 2
e
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Answer:
Bbecause it is the way
Explanation:
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Answer:
Filler
Explanation:
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(in yo own wurds)
Answers
Answer:
There are many signs of having social anxiety. You might have some signs/symptoms but not the diagnosis.
Explanation:
Signs that you might have social anxiety:
Fear of situations in which you may be judged
Worrying about embarrassing or humiliating yourself
Intense fear of interacting or talking with strangers
Fear that others will notice that you look anxious
Fear of physical symptoms that may cause you embarrassment, such as blushing, sweating, trembling or having a shaky voice
Avoiding doing things or speaking to people out of fear of embarrassment
Avoiding situations where you might be the center of attention
Having anxiety in anticipation of a feared activity or event
Enduring a social situation with intense fear or anxiety
Spending time after a social situation analyzing your performance and identifying flaws in your interactions
Expecting the worst possible consequences from a negative experience during a social situation
Physical Signs:
Blushing
Fast heartbeat
Trembling
Sweating
Upset stomach or nausea
Trouble catching your breath
Dizziness or lightheadedness
Feeling that your mind has gone blank
Muscle tension
Things that could help:
Interacting with unfamiliar people or strangers
Attending parties or social gatherings
Going to work or school
Starting conversations
Making eye contact
Dating
Entering a room in which people are already seated
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“The Roman Emperor is Julius Caesar.” is ...
A. The "is" of a part-whole relationship
B. The "is" of predication
C. The "is" of identity
Answers
Answer:
B. The "is" of predicationExplanation:
Gaius Julius Caesar was a Roman general and statesman who played a critical Gaius Julius Caesar was a Roman general and statesman who played a critical role in the events that led to the demise of the Roman Republic and the rise of the Roman Empire. In 60 BC, Caesar, Crassus and Pompey formed the First Triumvirate, a political alliance that dominated Roman politics for several years.
#Carry on learning
120 men working 9 hours a day can construct a road in 40 days.how long would it take to construct the same road if 150 men work 6 hours a day on it?
Answers
This is a question from Ratio and Proportion based concept.
Given that,120 men working for 9 hours a day, construct a road in 40 days. We are required to calculate the number of days to construct the road if 150 people work for 6 hours.
Let's assume the number of days taken for constructing is 'x'.
So normally we take 2 ratios and obtain the unknown value by cross multiplication.
Applying the same approach we get:
[tex]\implies \frac{ 120\:men}{150\:men}=\frac{9\:hours}{6\:hours}=\frac{40\:days}{x\:days}[/tex]
Since the first two fractions are inversely related, we multiply the numerators and denominators respectively.
Hence we get:
[tex]\begin{gathered}\implies \dfrac{ 120\: men \times 9\: hours}{150\: men \times 6\: hours} = \dfrac{ 40\: days}{x\: days}\\\\\\\implies \dfrac{1080}{900} = \dfrac{40}{x}\\\\\\\sf{Cross~ multiplying ~these~ 2 ~fractions~ we~ get:}\\\\\\\implies 1080 \times x = 40 \times 900 \\\\\\\implies x = \dfrac{ 40 \times 900}{1080}\\\\\\\implies x = \dfrac{36000}{1080}\\\\\\\implies x = \boxed{ 33.33 \:\: days}\end{gathered}[/tex]
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According to the 2017 career builder survey 54% of employers did not hire a candidate for what reason
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Answer:
They did not hire because of their content of social media. or the candidate had poor communication skills.
Due to their social media content, they decided not to hire. Because the applicant lacked effective communication abilities.
What is content of social media?Social media content, which includes text updates, photographs, videos, links, and more, is essentially whatever you share on social media. Although practically anything might serve as content for social media, not everything necessarily needs to be. That is the point we are trying to make today.
Social content is unstructured material that has been created, evaluated, annotated, or communicated via a social process or channel and is meant for human consumption.
The content of communication media is the information included within. Internet material, live events, tangible art, live television, radio, audio CDs, books, and periodicals are all included in this. Its intended audience or end-users are those in the publishing, creative, and communication industries.
Thus, Due to their social media content, they decided not to hire.
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a description of the three topics, concepts, or theories you learned about in the module that you consider most important; choose topics, concepts or theories from at least three lessons in the module
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at least one paragraph for each topic, concept, or theory, for a total of at least three paragraphs; use this organizer to help you format your work
What type of media would be considered digital?
a
Magazine
b
Cell Phone
c
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d
TV