Suppose there is a desert with two people, Anya and Bryce, and two goods, rocks and sand piles. Let Anya's allocation of rocks and sand piles be denoted by (rA, SA) and Bryce's by (rb, sb). Their respective utility functions are
1/2 uA(TA, SA) and ub(TB, 8B) = 1/2 =rA SA =TB + SB
In total, there are 10 rocks and 10 sand piles in the market. Anya's endowment is ea, a pair denoting her initial allocation of rocks and sand piles. Bryce's endowment es is the remaining rocks and sand piles. For Questions (3)-(5), the prices of rocks and sand piles are pr and Ps respectively. You can ignore any corner solutions in this problem. (1) Suppose Anya's endowment is ea = (6,6).
a. Find MRSA and MRSB. Suppose Anya's endowment is ea = (6,3).
b. Find MRSA and MRSB.
Answers
A. In the case where Anya's endowment is ea = (6,6), the marginal rate of substitution (MRS) of rocks for sand piles for Anya (MRSA) is 1/2. The marginal rate of substitution (MRS) of rocks for sand piles for Bryce (MRSB) is 1.
B. In the case where Anya's endowment is ea = (6,3), the marginal rate of substitution (MRS) of rocks for sand piles for Anya (MRSA) is 1/2. The marginal rate of substitution (MRS) of rocks for sand piles for Bryce (MRSB) is 2/3.
A. The marginal rate of substitution (MRS) represents the rate at which a person is willing to exchange one good for another while keeping their utility constant. It is the slope of the indifference curve.
For Anya, her utility function is given as 1/2 uA(TA, SA). Since the utility function is homogeneous of degree 1/2, the MRS of rocks for sand piles (MRSA) for Anya is equal to the ratio of the marginal utility of rocks (MUₐ) to the marginal utility of sand piles (MUₛ):
MRSA = MUₐ / MUₛ
Given that the utility function is 1/2 uA(TA, SA), the marginal utility of rocks (MUₐ) is 1/2 and the marginal utility of sand piles (MUₛ) is 1.
Therefore, MRSA = (1/2) / 1 = 1/2.
For Bryce, his utility function is ub(TB, SB) = 1/2 (TB + SB). Since the utility function is linear, the MRS of rocks for sand piles (MRSB) for Bryce is constant and equal to the ratio of the coefficients of the goods in the utility function:
MRSB = coefficient of rocks (TB) / coefficient of sand piles (SB)
Given that the utility function is 1/2 (TB + SB), the coefficient of rocks (TB) is 1 and the coefficient of sand piles (SB) is 1.
Therefore, MRSB = 1 / 1 = 1.
B. Following the same reasoning as in part A, the MRS of rocks for sand piles (MRSA) for Anya remains 1/2, as it depends on the utility function and not the endowment.
For Bryce, with Anya's endowment of ea = (6,3), Bryce's endowment is es = (4,7) (remaining rocks and sand piles in the market). The utility function for Bryce remains ub(TB, SB) = 1/2 (TB + SB).
The coefficient of rocks (TB) in the utility function is 1 and the coefficient of sand piles (SB) is 2.
Therefore, MRSB = 1 / 2 = 2/3.
By calculating the MRS for each individual, we can understand their preferences and willingness to trade one good for another while maintaining their utility level.
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Related Questions
Anyone knows how to do this? I think it’s 0 because it’s not moving————
Answers
Answer:
1 m/s
Explanation:
2 to 3 second interval would be zero.
3 to 4 is 2 m/s
so average is 1 m/s
ind the position of the center of mass of the earth-moon system. Use the data in AppendixF.
__________ m from the center of the earth
a.Appendix F Earth Moon
b.Mass 5.97e24 7.35e22
c.Orbital Radius 1.50e11 3.84e8
d.Radius 6.38e6 1.74e6
Answers
The position of the center of mass of the Earth-Moon system is located 4,676 kilometers from the center of the Earth.
First, let us recall the formula for the center of mass, which is:
center of mass = (m1r1 + m2r2)/(m1 + m2)
where,
m1 and m2 are the masses of the two objects
r1 and r2 are their distances from the reference point
Earth: m1 = 5.97 x 10^24 kg,
r1 = 0 km
Moon: m2 = 7.35 x 10^22 kg,
r2 = 384,400 km (3.84 x 10^8 m)
We can ignore the radii of the two objects because they are negligible compared to their orbital radii. So the center of mass of the Earth-Moon system can be calculated as follows:
center of mass = (m1r1 + m2r2)/(m1 + m2)
= [(5.97 x 10^24 kg)(0 km) + (7.35 x 10^22 kg)(3.84 x 10^8 m)]/(5.97 x 10^24 kg + 7.35 x 10^22 kg)
= 4.67 x 10^6 m or 4,676 km from the center of the Earth
Therefore, the position of the center of mass of the Earth-Moon system is located 4,676 kilometers from the center of the Earth.
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2
Select the correct answer.
Which statement is true about acceleration?
OA.
It is the rate of change of speed per unit time.
OB.
It is the rate of change of displacement per unit time.
Ос.
It is the rate of change of velocity per unit time.
OD.
It is the rate of change of position per unit time.
Reset
Next
Answers
Answer:
the answer is C ----- it is the rate of change of velocity per unit time
Explanation:
acceleration
\( = \frac{velocity(v)}{time(t)} \)
20 POINTS! I NEED IT ASP!
1 .
Ohm's Law
electroscope leaves repel
2 .
ion
charged atom
3 .
electromagnet
alignment of atoms
4 .
conductor
invented the lightning rod
5 .
magnetism
carries current
6 .
power
developed the light bulb
7 .
Thomas A. Edison
wire-wrapped core
8 .
Benjamin Franklin
V = I × R
9 .
like charges
I × V
Answers
Like Charges are the electroscope leaves repel, Ion is the charged atom. Magnetism is the alignment of atoms, Benjamin Franklin invented the lightning rod, Conductor carries a current.
What are Like charge?Like charges refer to the positive-positive or negative-negative charges whereas the unlike charges refers to set of positive-negative or negative-positive charges. Repulsion occurs in the like charges which refers to the force which makes the two charges move away from each other.
Like Charges are the Electroscope leaves repel. Ions are the charged atoms. Magnetism is the alignment of atoms. Benjamin Franklin invented the lightning rod. Conductor carries a current. Thomas Edison developed the light bulb. Electromagnet is a wire-wrapped core. Ohm's Law expression: V= I × R. And, Power is equal to I × V.
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Which of the following objects is NOT accelerating?
Group of answer choices
a bicyclist moving at a constant speed in a straight line
a space shuttle as it is orbiting the Earth
a truck turning a sharp corner
a car going from 5 mph to 10 mph
Answers
Answer:
A Bicycle
Explanation:
A Space shuttle accelerating because the Earth pulls on it through the gravitational force.
A Truck is accelerating because acceleration is necessary for an object to change direction.
A car is accelerating because it is speeding up unexpectedly?????
A hammer drives a nail into a piece of wood. Identify an action-reaction pair.Group of answer choicesThe hammer exerts a force on the nail; the wood exerts a force on the nail.The hammer exerts a force on the nail; the hammer exerts a force on the wood.The nail exerts a force on the hammer; the hammer exerts a force on the wood.The hammer exerts a force on the nail; the nail exerts a force on the hammer.
Answers
Newton's third law states that if an object A exerts a force on object B, then object B must exert a force of equal magnitude and opposite direction back on object A.
Let:
A = Hammer
B = Nail
so:
\(F_{AB}=-F_{BA}\)Therefore:
The hammer exerts a force on the nail; the nail exerts a force on the hammer.
The spark plug of a motor bike does NOT work because the user did not use a torque wrench to tighten spark plug, instead he/she used a regular wrench. This is an example of? *
A. What is the RPN Number?
B. What are the potential Failure Modes?
C. What are the Potential Causes?
D. What are the Potential Effects?
Answers
This is an example of potential cause and effect. The potential cause is the improper use of tools, specifically using a regular wrench instead of a torque wrench to tighten the spark plug. The potential effect is the malfunctioning of the spark plug, leading to its failure to work properly.
Using the wrong tool, in this case, a regular wrench instead of a torque wrench, can lead to overtightening or undertightening of the spark plug. A torque wrench is specifically designed to apply a specific amount of torque or rotational force to tighten the spark plug to the manufacturer's specifications. Without using a torque wrench, it becomes challenging to achieve the correct tightness, which can result in a range of issues.
In the given scenario, the potential failure mode is the spark plug not functioning correctly, leading to the bike's engine not igniting properly. This can result in poor engine performance, misfires, or complete engine failure. Using the appropriate tools and following proper procedures is crucial to ensure the reliable and safe operation of mechanical components.
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Provide an example of a product you believe is elastic and
explain your answer. Provide an example of a product you believe is
inelastic and explain your answer.
Answers
Example of an elastic product: Smartphone
Explanation: A smartphone is an example of an elastic product. When the price of smartphones decreases, consumers tend to buy more of them, and when the price increases, consumers tend to buy fewer.
Example of an inelastic product: Prescription medication
Explanation: Prescription medication is an example of an inelastic product. Inelastic goods are those for which changes in price have little impact on the quantity demanded.
Example of an elastic product: SmartphoneExplanation: A smartphone is an example of an elastic product. When the price of smartphones decreases, consumers tend to buy more of them, and when the price increases, consumers tend to buy fewer. This is because smartphones are considered non-essential goods with substitutes available in the market. If the price of a particular smartphone model increases, consumers have the option to choose a different brand or model that offers similar features at a lower price. Similarly, if the price of smartphones decreases, consumers may be more willing to upgrade their existing devices or purchase additional smartphones as they become more affordable. The demand for smartphones is responsive to changes in price, making it an elastic product.Example of an inelastic product: Prescription medicationExplanation: Prescription medication is an example of an inelastic product. Inelastic goods are those for which changes in price have little impact on the quantity demanded. Prescription medication is often essential for maintaining health and treating medical conditions, and there may be limited substitutes available. When the price of prescription medication increases, consumers may still continue to purchase it regardless of the price change, as their health and well-being depend on it. The demand for prescription medication is relatively unresponsive to changes in price because it is a necessity and does not have easily accessible alternatives. People are generally willing to pay higher prices for medications they need, even if it means reducing spending on other goods and services. Thus, prescription medication is considered an inelastic product.For more such questions on elastic and inelastic product, click on:
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Consider the polynomial
() = −0. 14 − 0. 153 − 0. 52 − 0. 25 + 1. 2
The true value of its derivative at x=0. 5 is ′
(0. 5) = −0. 9125. Use backward, forward, and centered
first finite differences to estimate the derivative numerically if the step size ∆ = 0. 25, and determine
the percent error between the true value and each of the estimated values (percent error is given by
= −
converted to a percentage. ) What value of ∆ would you have to use for the backward and forward
finite differences to get the same percent error as the centered finite difference (hint: it should be less
than 0. 25. )
Answers
The backward finite difference method for estimating the derivative at x=0.5 is:
(f(0.5) - f(0.25)) / (0.5 - 0.25) = (-0.14 - (-0.4025)) / (0.5 - 0.25) = 0.2625 / 0.25 = 10.5
The percent error between this estimate and the true value is:
|(10.5 - (-0.9125)) / (-0.9125)| * 100% = |11.4125 / (-0.9125)| * 100% = 12.48%
The forward finite difference method for estimating the derivative at x=0.5 is:
(f(0.75) - f(0.5)) / (0.75 - 0.5) = (-0.6275 - (-0.14)) / (0.75 - 0.5) = -0.4875 / 0.25 = -1.95
The percent error between this estimate and the true value is:
|(-1.95 - (-0.9125)) / (-0.9125)| * 100% = |-1.0375 / (-0.9125)| * 100% = 1.14%
The centred finite difference method for estimating the derivative at x=0.5 is:
(f(0.75) - f(0.25)) / (0.75 - 0.25) = (-0.6275 - (-0.4025)) / (0.75 - 0.25) = -0.225 / 0.5 = -0.45
The percent error between this estimate and the true value is:
|(-0.45 - (-0.9125)) / (-0.9125)| * 100% = |0.4625 / (-0.9125)| * 100% = 0.51%
To get the same percent error as the centred finite difference, we would have to use a step size of ∆ = 0.125.
This is because a smaller step size means a smaller difference between the estimates and the true value, and therefore a smaller percent error.
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What acceleration occurs if the friction force in #4 is now 4N?
Answers
The acceleration of the 20 N force is 6.67 m/s^2. The acceleration of the 4N force is 1.33 m/s^2.
What is force?We define the force that acts on a body as that which is able to cause an acceleration or that which is able to change the direction of an object. Recall that from the Newton first law, an object would continue in its state of rest or uniform motion unless the object is acted upon by an external force.
Now the frictional force is the force that tends to resist the motion of two surfaces that are in contact. Owing to the fact that it is a resistive force its direction is always opposite the force that seeks to move the object forward.
Now;
F = ma
a = F/m
a = 20 N/3Kg
a = 6.67 m/s^2
If the force is 4N;
a = F/m
a = 4N/3Kg
a = 1.33 m/s^2
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Missing parts;
How would you calculate the acceleration if you push with a 20 N horizontal force on a 3 kg block on a horizontal friction-free air table? What is the acceleration if the friction force is 4 N?
at what angle do you observe the 3rd order minimum? set-up is the same as above and with a slit separation of 0.045 mm.
Answers
The third-order minimum can be observed at an angle determined by the slit separation of 0.045 mm in the given setup.
When light passes through a double-slit setup, it diffracts and forms a pattern of bright and dark fringes. The angle at which these fringes occur depends on the wavelength of light and the slit separation.
The condition for the occurrence of a minimum is given by the equation d * sin(θ) = m * λ, where d is the slit separation, θ is the angle of observation, m is the order of the minimum, and λ is the wavelength of light.
In this case, we are interested in the third-order minimum, which corresponds to m = 3.
The given slit separation is 0.045 mm.
To find the angle of observation, we need to know the wavelength of light used in the experiment. Once we have that information, we can rearrange the equation and solve for θ. The result will give us the angle at which the third-order minimum occurs. It is important to note that without knowing the specific wavelength of light, we cannot provide a numerical value for the angle in this response.
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Freida wants to model the way atoms move when a substance changes its state. To do this, Freida makes a pyramid of marshmallows. Then, she knocked down the pyramid causing the marshmallows to fall. If the marshmallows represent the atoms in the substance, which change of state is Freida modeling? melting freezing condensation deposition
Answers
Answer:
Melting
Explanation:
I took the quiz and got it right so I am 100 percent sure the answer is, A.melting :)
Answer:
melting
Explanation:
its right lol :)
How do electromagnetic waves affect you?
Answers
Answer:
At low frequencies, external electric and magnetic fields induce small circulating currents within the body. ... The main effect of radiofrequency electromagnetic fields is heating of body tissues. There is no doubt that short-term exposure to very high levels of electromagnetic fields can be harmful to health.
Hai điện tích hút nhau bằng một lực 2,7N. Khi chúng dời xa nhau thêm 12cm thì lực hút là 0,3N. Khoảng cách ban đầu giữa chúng
Answers
Answer:
6 cm hoặc 0,06m
Explanation:
\(F=k\frac{q_{1} q_{2} }{r^{2} }\)
nên \(q_{1} q_{2} =\frac{F.r^{2} }{k}\)
Ban đầu:
\(F_{1} =k\frac{q_{1} q_{2} }{r^{2} }=2,7\)
---> \(q_{1} q_{2} =\frac{2,7.r^{2} }{k}\)
Lúc sau:
\(F_{2} =k\frac{q_{1} q_{2} }{(r+0,12)^{2} }=0,3\)
---->\(q_{1} q_{2} =\frac{0,3.(r+0,12)^{2} }{k}\)
Suy ra:
\(2,7.r^{2} = 0,3.(r+0,12)^{2}\)
Giải pt đc 2 nghiệm là 0,06 và -0,03
loại nghiệm âm được 0,06m
What is the difference between a psychologist and a psychiatrist?
Answers
Answer:
Psychiatrists are medical doctors, psychologists are not. Psychiatrists prescribe medication, psychologists can't. Psychiatrists diagnose illness, manage treatment and provide a range of therapies for complex and serious mental illness. Psychologists focus on providing psychotherapy (talk therapy) to help patients.
Explanation:
Answer:
Psychiatrists are medical doctors, psychologists are not. Psychiatrists prescribe medication, psychologists can't. Psychiatrists diagnose illness, manage treatment and provide a range of therapies for complex and serious mental illness. Psychologists focus on providing psychotherapy (talk therapy) to help patients.
Explanation:
wave motion that is parallel to wave direction describes a_ wave
Answers
A longitudinal wave is a wave in which the motion of the medium's particles is parallel to the wave's direction of propagation.
What is the name of a parallel wave?Longitudinal waves are waves in which the displacement of the medium is in the same (or the opposite) direction as the wave propagation and the medium vibration is parallel ("along") to the direction the wave travels.
What wave moves parallel to another?Two categories of mechanical waves exist: In longitudinal waves, the movement of the particles is parallel to the motion of the energy, meaning that the medium is displaced in the same direction as the wave.
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Janaki Temple and Pashupatinath Temple are increasing our pride how
Answers
Answer:
Janaki temple and Pashupatinath Temple are found in Nepal. These structures are religious and they increase the pride of the country through tourism. These temples are important in the country and are mostly visited by tourists.
This also helps to bring in income for the country and also helps by attracting many visitors and a corresponding development of its tourism industry.
can both liquid water and steam exist at 100°C
Answers
Explanation:
Yes , Both liquid water and steam exist at 100°C
Hope it will help you
Which of the following best explains work?
a. Work occurs when a force acts on an object
b. Work occurs when a force acts to hold an object in place
c. Work occurs when a force acts on an object and causes a displacement of that object
d. Work occurs when energy is exerted
Answers
Answer:
c. Work occurs when a force acts on an object and causes a displacement of that object
Explanation:
because W=Fd
work= force * displacement
The activation energy of a certain reaction is 47.1kJ/mol . At 20C , the rate constant is 0.0170s^{-1} . At what temperature in degrees Celsius would this reaction go twice as fast? Given that the initial rate constant is 0.0170s^-1> at an initial temperature of 20C , what would the rate constant be at a temperature of 140 C for the same reaction described in Part A?
Answers
The activation energy of a certain reaction is used to find the temperature at which the reaction would go twice as fast. while the Arrhenius equation can be used to find the rate constant at a different temperature for the same reaction.
We can use the Arrhenius equation, which relates the rate constant of a reaction to the activation energy and temperature. We know the rate constant at 20C and the activation energy, so we can set up the equation as follows:
k2 = 2k1
ln(k2/k1) = Ea/R * (1/T1 - 1/T2)
T2 = Ea/R * (1/T1 - ln(k2/k1)/Ea)
Plugging in the given values, we get:
T2 = 47.1 kJ/mol / (8.314 J/mol*K) * (1/293 K - ln(2)/(47.1 kJ/mol))
T2 ≈ 358 K or 85 C
For the second part of your question, we can use the same equation to find the rate constant at 140 C:
ln(k2/k1) = Ea/R * (1/T1 - 1/T2)
k2 = k1 * e^(Ea/R * (1/T1 - 1/T2))
Plugging in the given values, we get:
k2 = 0.0170 s^-1 * e^(47.1 kJ/mol / (8.314 J/mol*K) * (1/293 K - 1/413 K))
k2 ≈ 1.81 s^-1.
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How do media literacy , information literacy and technology literacy and media and information literacy differ in terms of use?
Answers
Answer:
Media literacy creates a conscious awareness, the ability to understand, analyze, the messages various media like the newspapers, the radio, that is for the consumer, and it also promotes how best media create information for production.
While information literacy and technology literacy differs from other literacy asked in the question above, as information literacy and technology could be used when describing getting information through adequate research and further dishing out this available information so as to effectively use the information with the aim to solve problems, create awareness, or educate, through technologies such as for example, email.
Lastly, media and information literacy differ in terms of use from the other two explained above, as media and information literacy describes discerning information credibility, accuracy, and objectivity of sources they come from, and it shows people how important it is to have credible information to make informed judgments and the ethical use of the information they consume.
Wil-E-Coyote drops a bowling ball off a cliff to try to catch the Roadrunner. The cliff is 132m high. how far does it fall in the first 3.0 seconds
Answers
Тесты имеют различные нормы-шкалы значений: социальные, возрастные и т.П. Индивидуальный показатель теста соотносится с его нормой. Норма теста обычно определяется в результате тестирования большой выборки испытуемых определенного возраста и пола и усреднения полученных оценок с их последующей дифференциацией по возрасту, полу и ряду других показателей. Норма теста - это средний уровень развития большой совокупности людей, похожих на данного испытуемого по ряду социально-демографических характеристик. То есть, это средний диапазон значений на шкале измеряемого свойства.
Answers
Briefly describe how polygraph tests work. According to the American Psychological Association, these tests are not accurate at all, and they compare them to the flip of a coin. After describing how polygraph test works (in two to three sentences), discuss your thoughts on the accuracy of polygraph tests. Do you agree with the American Psychological Association? Do you think the tests have any benefit, or do you think they should be completely discontinued?
Answers
Answer:
no such thing i dont think
Explanation:
Answer:
Polygraph tests are used to determine whether someone is lying or not, and display the physical signs someone is showing when they speak to be interpreted. Polygraphs measure things like heartbeat, breathing rate, and electrical conductivity of the skin, which are signs that get more and more severe when someone tells major lies or lies a lot. Polygraph tests are pretty unreliable because everyone shows different reactions to speaking depending on how anxious they are or any other medical condition, which could falsely incriminate them, but I think it is still important to determine the signs someone displays to use as a datapoint later on in the trial. For those reasons, they should still be used but shouldn't be relied on as heavily.
Explanation:
When an ambulance drives towards you, the pitch of the siren is higher. After itdrives past, the pitch of the siren is lower.The reason it is lower is that the frequency of the wavelengthA. increasesB. decreasesC. Stays the same
Answers
Doppler's effect:
The Doppler effect states that the frequency of sound increases as it source approaches you and it decreases as the source turns away from you.
When the ambulance drives past you, the pitch of the siren is lower. This is due to the fact that the frequency of the wavelength decreases.
A higher pitch means frequency increases and a lower pitch means frequency decreases.
Therefore, the correct answer is option B. decreases
Based on the equation given in the lab manual, what is the equation to find the equivalent resistance of two resistors in parallel? Note: I do not want inverse resistance, I'm asking for R = ..) R1 + R2 Req + R2 Req R2 R1 Rea R1 R2 R1+R2
Answers
This equation can be used to determine the equivalent resistance of two parallel resistors: 1/Req = 1/R1 + 1/R2 Upon solving for Req, we obtain: Requirement = (R1-R2) / (R1+R2)
What is the parallel pairing of two resistors' equivalent resistance?The equivalent resistance of two identical resistors connected in parallel is equal to one-half the value of each resistor. Both share an equal amount of the current.
How are resistance and resistance calculated?Resistors are connected in series when they are connected one after the other. This is seen below. You add up the individual resistances to determine the total overall resistance of several resistors connected in this manner. The following equation is used to accomplish this: Rtotal = R1 + R2 + R3 and so forth.
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what is the mass of a sample of lead (d = 11.35 g/ml) which has a volume of 85.0 ml?
Answers
The given density of lead is 11.35 g/ml and its volume is 85.0 ml. We can use the formula of density to determine the mass of a sample of lead.
The formula for density is
`Density = Mass/Volume`.
Solving for the mass, we have `Mass = Density × Volume`
Given the density of lead as 11.35 g/ml and the volume of the lead as 85.0 mlMass = 11.35 g/ml × 85.0 mlMass = 964.75 g
Therefore, the mass of a sample of lead (d = 11.35 g/ml) which has a volume of 85.0 ml is 964.75 g.
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What is the maximum speed at which a car can safely travel around a circular track of radius 142 meters if the coefficient of friction between the tires and the road is 1.07? Include units in your answer. Answer must be in 3 significant digits.
Answers
Given that the radius of the circular path is r = 142 m and the coefficient of the friction is
\(\mu=1.07\)The condition for the car to travel safely is
Frictional force = centrifugal force
\(\mu mg=\frac{mv^2}{r}\)Here, m is the mass of the car and the acceleration due to gravity is g = 9.8 m/s^2.
v is the maximum speed of the car.
\(\begin{gathered} v=\sqrt[]{ugr} \\ =\sqrt[]{1.07\times9.8\times142} \\ =38.58\text{ m/s} \end{gathered}\)Determine the distance a for which the maximum absolute value of the bending moment in the beam is as small as possible. (Round the final answer to two decimal places. You must provide an answer before moving to the next part.)
Answers
Sorry, I cannot answer this question without additional information such as beam dimensions and material, loads applied to the beam, and support conditions.
The position of a particle moving in the xy-plane is given by the parametric equations r = ( 3t and V = 2t 3t 2 12t _ For what values of t is the particle at rest?
Answers
All components of the velocity vector are zero for t = 0, the particle is at rest for t = 0.
For what values of t is the particle at rest?
The position of a particle moving in the xy-plane is given by the parametric equations r = (3t) and v = (2t, 3t², 12t). To find for what values of t the particle is at rest, we need to find when the velocity vector (v) is equal to zero.
The velocity vector v is given by (2t, 3t², 12t). For the particle to be at rest, all components of the velocity vector must be equal to zero.
1. For the x-component (2t) to be zero: 2t = 0. Solving for t, we get t = 0.
2. For the y-component (3t²) to be zero: 3t² = 0. Solving for t, we get t = 0.
3. For the z-component (12t) to be zero: 12t = 0. Solving for t, we get t = 0.
Since all components of the velocity vector are zero for t = 0, the particle is at rest for t = 0.
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