A student is bouncing on a trampoline. At her highest point, her feet are 95 cm above the trampoline. When she lands, the trampoline sags 25 cm before propelling her back up.
The time she spent in contact with the trampoline is 0.1619 seconds.
The objective of this question is to determine for how long she is in contact with the trampoline?
The conservational force is exerted on the trampoline is equivalent to the sum of the potential energy at the highest point and the elastic energy at the lowest point.
∴
From the given information;
[tex]\mathbf{mg \dfrac{(95 +25)}{100} = \dfrac{1}{2}k ( \dfrac{25}{100})^2}[/tex]
[tex]\mathbf{m\times g\times 1.2 = k(0.03125)}[/tex]
[tex]\mathbf{m\times 9.8 \times 1.2 = k(0.03125)}[/tex]
[tex]\mathbf{\dfrac{m}{k} = \dfrac{(0.03125)}{9.8 \times 1.2}}[/tex]
[tex]\mathbf{\dfrac{m}{k} = 0.002657}[/tex]
Using the Simple Harmonic Motion to determine the time at which she is in contact with the trampoline, we have;
[tex]\mathbf{t= \dfrac{T}{2}}[/tex]
[tex]\mathbf{t= \dfrac{2 \pi}{2} \sqrt{\dfrac{m}{k}}}[/tex]
where;
[tex]\mathbf{\dfrac{m}{k} = 0.002657}[/tex][tex]\mathbf{t= \dfrac{2 \pi}{2} \times \sqrt{0.002657}}}[/tex]
[tex]\mathbf{t=0.1619\ sec}}[/tex]
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F(x, y) = e−x + y2, e−y + x2 , c consists of the arc of the curve y = cos(x) from − ???? 2 , 0 to ???? 2 , 0 and the line segment from ???? 2 , 0 to − ???? 2 , 0.
Given that y = cos(x) makes up part of the boundary of C, I suspect you mean the given points to be (-π/2, 0) and (π/2, 0).
I also assume the given vector field is
[tex]\vec F(x,y) = \left\langle e^{-x} + y^2, e^{-y} + x^2 \right\rangle[/tex]
Since [tex]\vec F[/tex] has no singularities on C or in its interior, Green's theorem applies:
[tex]\displaystyle \int_C \vec F(x,y) \cdot d\vec r = \iiint_D \frac{\partial(e^{-y}+x^2)}{\partial x} - \frac{\partial(e^{-x}+y^2)}{\partial y} \, dA = 2 \iiint_D (x + y) \, dA[/tex]
where D is the interior of C, the region
[tex]D = \left\{ (x, y) : -\dfrac\pi2 \le x \le \dfrac\pi2 \text{ and } 0 \le y \le \cos(x) \right\}[/tex]
The integral then reduces to
[tex]\displaystyle 2 \iint_D (x + y) \, dA = 2 \int_{-\frac\pi2}^{\frac\pi2} \int_0^{\cos(x)} (x + y) \, dy \, dx[/tex]
[tex]\displaystyle 2 \iint_D (x + y) \, dA = 2 \int_{-\frac\pi2}^{\frac\pi2} \left( x\cos(x) + \frac12 \cos^2(x) \right) \, dx[/tex]
[tex]\displaystyle 2 \iint_D (x + y) \, dA = 2 \int_{-\frac\pi2}^{\frac\pi2} \left( x\cos(x) + \frac{1 + \cos(2x)}4 \right) \, dx[/tex]
[tex]\displaystyle 2 \iint_D (x + y) \, dA = \frac12 \int_{-\frac\pi2}^{\frac\pi2} \left( 4x\cos(x) + 1 + \cos(2x) \right) \, dx[/tex]
Since 4x cos(x) is an odd function over the symmetric interval [-π/2, π/2], its contribution to the integral is 0, and the remaining integral is trivial.
[tex]\displaystyle 2 \iint_D (x + y) \, dA = \frac12 \int_{-\frac\pi2}^{\frac\pi2} \left( 1 + \cos(2x) \right) \, dx = \boxed{\frac\pi2} [/tex]
Which specific process in the light-dependent reactions produces oxygen and hydrogen ions?.
Answer: Oxygen and hydrogen ions are also formed from the splitting of water. Keep in mind that the purpose of the light-dependent reactions is to convert solar energy into chemical carriers (NADPH and ATP) that will be used in the Calvin cycle. In eukaryotes and some prokaryotes, two photosystems exist.
Which of these best describes the point of washington in this excerpt.
Answer:
awnser choice B
Explanation:
B
The distance between two cities on a map is 3. 5 centimeters. The map uses a scale in which 1 centimeter represents 20 kilometers. What is the actual distance between these two cities in kilometers?.
Answer:
70km
Explanation:
[tex] \frac{20}{1} \times 3.5[/tex]
= 70
a mid-ocean ridge is located at the boundary of two tectonic plates which diagram correctly models the relative plate motion on each side of a mid-ocean ridge
Thank you for sharing this question, if you could please add a file or pictures of the answers I'll be happy to help.
Would sound waves travel slower through air at the north pole or at the equator?.
yes they would travel slower at the north pole than the equator because the air is more dense and is harder to pass through
Yes, sound waves would travel slower at the North Pole than at the equator because the air is denser and is harder to pass through.
What are equators?The Equator is the midline of the earth. A vibration results in a sound. We refer to these motions as "sound waves." Sound waves require a specific medium to travel through. The three different types of media are solid, liquid, and gas.
Keep in mind that since a "solid medium" is denser than the other two, sound waves move through it more quickly. Because water is more densely packed with particles than gas is, sound waves travel faster in liquid than in gas (such as air).
Therefore, yes, because the air is heavier and more difficult to get through at the North Pole than it is at the Equator, sound waves would move more slowly there.
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What is one drawback shared by both monopolies and oligopolies.
Answer:
They can harm consumers by fixing price
English nobles resisted peasant demands such as those described in the passage because agricultural labor in many parts of fourteenth-century afro-eurasia had become scarce as a result of which of the following developments?.
Answer: Significant increase in mortality due to the spread of epidemic diseases.
Explanation:
During the 14th century, many parts of Europe and Asia were completely ravaged by an epidemic plague called The Black Death. It was a form of bubonic plague caused by rats infected by bacteria.
More than half of the population of Europe was killed due to his plague, which immediately creates a shortage of labor. Shortage of labor, including agricultural ones, immediately meant that the living ones would receive a higher wage, to the consternation of the landowners who pushes for legislation that would return the status quo to how it was prior to the Black Death. This enrages the peasants who worked for them; manifesting in several revolts from May to November 1380.
Can sunlight change the distribution of traits in a population?.
Aditi ❤
Sunlight changes the distribution of traits in a population because the environment can factor into the distribution of traits.
What is the significance of Sunlight?Sunlight emits light and heat, or solar energy, which allows life to exist on Earth. Sunlight is required for plant growth. Plants are required by animals, including humans, for food and the oxygen they produce.
Earth would freeze if the sun did not provide heat. The sun is necessary for human health and well-being. The health benefits of sunlight include vitamin D production, bone health support, blood pressure reduction, disease prevention, and mental health promotion.
Therefore, because the environment influences the distribution of traits, sunlight alters the distribution of traits in a population.
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Which disease is caused by a buildup of plaque in blood vessels brainly.
Which is the percent composition of bromine in the compound nabr?.
Answer:
72%
Explanation:
Ml data can be represented in '_____________' form(s).
Machine learning (ML) data can be represented in the following forms:
1. Matrix and Spatial.
2. Scalar and Vector.
Machine learning (ML) is also referred to as Artificial intelligence (AI) and it can be defined as a subfield in computer science which is focused on the use of computer algorithms to build a smart computer-controlled robot that has the ability (capacity) to automatically perform and handle tasks that are exclusively designed to be performed by humans or by using human intelligence.
Generally, the data that are generated and used in machine learning (ML) can be represented in the following forms:
MatrixSpatialScalarVectorRead more on machine learning (ML) here: https://brainly.com/question/25523571
Promotion of learning and respect for teachers are among the traditional values of the vietnamese.
The Vietnamese believe that One of the traditional values of the Vietnamese people is the promotion of learning and the respect for teachers.
As Vietnam’s educational culture was sparked by Chinese influence, the roots of education come from the country’s belief in Confucianism.
The Vietnamese believe that One of the traditional values of the Vietnamese people is the promotion of learning and the respect for teachers. In the Feudal and Colonial periods, teacher’s were seen to have more importance than parents; their position was “only lower than the king”.
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Managers at eller manufacturing are considering purchasing a new refrigerated delivery truck that will produce equal annual cash flows of $36,000 for 6 years. The truck’s net present value is $12,780, its cost is $144,000, its useful life is 6 years, and its annual depreciation expense (no salvage value) is $24,000. What is the discount rate used by eller to evaluate this project?.
It should be noted that the discount rate that was used by Eller to evaluate this project is 10%.
From the information given, the following can be depicted:
Annual cash inflows = $36,000 Period of cash inflows = 6 years Cash outlay (initial investment) = $144,000 Depreciation expense = $24,000 Estimated useful of trucks = 6 years Net present value = $12,780It should be noted that the Present Value Annuity Factor at 10% for 6 years is given as 4.355
Therefore, the Present Value of Annuity cash inflows will be
= ($36,000 x 4.355) = $156,780
Less initial investment cash outlay = $144,000
Net present value = $12,780
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I am thinking of two positive numbers in the ratio $5:3$. The difference between the two numbers is $90$. What is the sum of the two numbers?.
The sum of the two numbers is $ 360
Let the bigger number be x
Let the smaller number be y
From the question given above, we were told that two numbers exist in ratio $ 5 : $ 3
Thus,
x : y = 5 : 3
x/y = 5/3
Cross multiply
x = 5y/3 ............ (1)
Also, we were told from the question that difference between the two numbers is $ 90 i.e
x – y = 90 ........... (2)
Substitute the value of x in equation (1) into equation (2). We have:
x = 5y/3 ............ (1)
x – y = 90 ........... (2)
5y/3 – y = 90
Multiply through by 3
5y – 3y = 270
2y = 270
Divide both side by 2
y = 270 / 2
y = $ 135
Substitute the value of y into equation 1 to obtain the value of x.
x = 5y/3 ............ (1)
y = $ 135
x = (5 × 135)/3
x = 675 / 3
x = $ 225
Finally, we shall determine the sum of the two numbers.
x = $ 225y = $ 135Sum =?Sum = x + y
Sum = 225 + 135
Sum = $ 360
Thus, the sum of the two numbers is $ 360
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Iconic memory is used when a loud thunderclap occurs during a storm.
Answer:
Memories of specific personal events are examples of semantic long-term memories. The process of storing, encoding, and retrieving information is known as memory.
Explanation:
[tex]\huge{\mathfrak{꧁HeavenMistress꧂}}[/tex]
Answer:
F
Explanation:
guys does 9+10= 21
explain please
Answer:
Yes.
Explanation:
Its 21 because a genius said it was.
Why are rules significant in writing molecular structures.
Answer:
Chemical structure determines the molecular geometry of a compound by portraying the spatial arrangement of atoms and chemical bonds in the molecule. This provides chemists with an important visual representation of a chemical formula.
Masco is a consumer discretionary company that focuses on home improvement products.
It should be noted that Masco is a consumer discretionary company that focuses on home improvement products.
Companies that can be associated to the consumer discretionary sector are those companies that deals with nonessential goods and services.
Theses nonessential goods and services could be;
appliances cars entertainmentTherefore, is a consumer discretionary company that focuses on home improvement products.
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How many atoms would be contained in 454 grams of iron (fe).
Answer:
4.90 x 10^24 atoms
Explanation:
Answer:
4.89 x 10^24 atoms
Explanation:
you can say 4.9 x 10^24 atoms too
the 24 is the exponent for the 10
Which of the following is most clearly an example of a theme.
Which of these individual actions would have the greatest impact on public policy?.
It should be noted that political parties and interest groups have a great influence on public policy.
A political party is composed of people who have similar political beliefs and aims. The candidates from this organized group aspire to be elected and thereby influence public policy.
An interest group has no intention of getting its members to hold government positions. It simply influences public policy by mainly lobbying.
Interest groups have a greater impact on determining and shaping public policy as they represent businesses and corporations. They also influence people through media campaigns.
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Where can you find your state specific lottery information.
Answer:
lottery district offices
Explanation:
Lottery district offices can be found your state specific lottery information.
What is a definition of lottery?A lottery is a low-odds process or game of chance in which winners are chosen at random. Lotteries can be utilized in decision-making circumstances, such as the distribution of scarce medical care and the selection of sports teams.
With a set of numbers, the lottery game is played in finance. Either manually or automatically, the numbers are selected at random. The picked numbers are intended to win prizes. The prize money may be awarded to the winner as a flat sum or in installments. In general, prize winners prefer receiving a lump sum of money.
The Dutch noun "lot," which means "fate," is where the English word "lottery" originates. The Golden Ambrosian Republic launched the first known Italian lottery on January 9, 1449, in Milan to raise money.
Thus, Lottery district offices.
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The image shows what happens when an antacid tablet is placed in water. A glass of water is shown with a tablet beside it. An arrow points to a second glass, where the tablet can be seen at the bottom of the glass with bubbles rising from the tablet. The process shown in the image can best be described as a rapid chemical reaction where gas is released. Slow chemical reaction where light is being given off. Slow chemical reaction where the liquid changes color. Rapid chemical reaction where heat is suddenly released.
There are different kinds of reaction. The process shown in the image can best be described Rapid chemical reaction where gas is released.
When an antacid tablets is placed in water, There is a chemical reaction. The water is known to reacts with the tablet and forms a bubbles full of carbon dioxide gas.When the water touches the tablet, suddenly, the reaction or fizzing, happens quickly.
Conclusively, when an antacid tablet is placed into a glass of water, it will produce a chemical change.
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Answer:
a
Explanation:
Sea level is currently rising at 5 mm/yr, and scientists predict that global warming could cause a rise in sea level of 7 m if left unabated. How long will it take the sea to rise 7 m at the current rate?.
Answer:
1400 years
Explanation:
Let us convert everything to the same units first. For simplicity, I will convert everything to millimeters.
7 m = 7 m x (1000 mm / 1 m) = 7000 mm
Since the rate is 5, we can use this equation:
rate*time=length
5*years=7000
solve
years=1400
Fill in the blank with the spanish word that best completes the following sentence. La ____________ es la mayor riqueza. Salud palabra mejor cara.
La Salud es la mayor riqueza. Salud palabra mejor cara.
Who is Salud Palabra?The term "health" contrasts with "illness," and it is the focus of particular attention from the fields of medicine and health sciences.
The idea that health is a resource for daily life rather than the goal of life is a positive one that places emphasis on one's social and personal resources as well as physical abilities.
As a result, the ability to maintain homeostasis and recover from insults is referred to as health. The ability of a person to manage stress, acquire skills, and maintain relationships is referred to as their mental, intellectual, emotional, and social health.
Therefore, La Salud es la mayor riqueza. Salud palabra mejor cara.
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Answer:salad
Explanation:
What factors would have the least effect on a region’s climate?.
Answer:
Longitude and Population Density
Explanation:
Longitude
Longitude won't have much effect because it is just across the earth in E to W. (east to west). While, Latitude will affect the Earth because there is something called a Equator, which is USUALLY hot, and the Polar zones, which are mostly Cold.
Population Density
Population Density won't affect much because the amount of carbon dioxide a person produces is pretty less. But yeah, the factories make a lot of more Carbon Dioxide so that is why they will be producing more than the people. But people can't produce so much to warm up their environment.
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Mrs.Hendrics said "where are the books"? Correct me please if it is incorrect.
Please
OR
Mrs.Hendrics said, "Where are the books?"Hope you could get an idea from here.
Doubt clarification - use comment section.
A 1. 5-kilogram lab cart is accelerated uniformly from rest to a speed of 2. 0 meters per second in 0. 50 second. What is the magnitude of the force producing this acceleration?.
The magnitude of the force producing this acceleration is found to be 3.0 N.
What is Force?Force may be defined as the process of pushing and pulling an object with an appropriate mass in order to cause it to change its velocity with respect to time.
Force is a vector quantity as it has both magnitude and direction. Force is an external agent which is generally capable of changing a body's state of rest or motion with respect to time.
According to the question,
The total mass of an object = 1.5 kg.
The speed of an object = 2.0 m/sec.
So, the formula for calculating the magnitude of the force is as follows:
Force = Mass × Acceleration.= 1.5 kg × 2.0 m/sec = 3.0 N.
Therefore, the magnitude of the force producing this acceleration is found to be 3.0 N.
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