A pulse of electromagnetic radiation is propagating in the +y direction. You have two devices that can detect electric and magnetic fields. You place detector #1 at location < 0, -3, 0> m and detector #2 at location < 0, 3, 0> m.
(a) At time t = 0, detector #1 detects an electric field in the -x direction. At that instant, what is the direction of the magnetic field at the location of detector #1?
(b) At what time will detector #2 detect electric and magnetic fields?

Answers

Answer 1

a. At the time \(\rm \(t = 0\)\), the magnetic field at the location of detector #1 is in the +z direction.

b. At \(\(t \approx 2 \times 10^{-8}\)\) seconds, detector #2 will detect the electric and magnetic fields.

(a) To determine the direction of the magnetic field at the location of detector #1, we can use the right-hand rule, which relates the direction of the magnetic field \(\rm (\(B\))\), the direction of the electric field \(\rm (\(E\))\), and the direction of propagation \(\rm (\(+y\))\).

Since the pulse of electromagnetic radiation is propagating in the +y direction and detector #1 detects an electric field in the -x direction, the magnetic field \(\rm (\(B\))\) must be in the +z direction.

This is because electromagnetic waves are transverse waves, and the electric and magnetic fields are perpendicular to each other and the direction of propagation.

So, at time \(\rm \(t = 0\)\), the magnetic field at the location of detector #1 is in the +z direction.

(b) To determine the time at which detector #2 will detect electric and magnetic fields, we need to consider the distance between the two detectors and the speed of propagation of the electromagnetic wave.

Let's assume that the speed of light \(\rm (\(c\))\) is \(\rm \(3.00 \times 10^8\)\) m/s.

The distance between the two detectors is \(\rm \(d = 6\)\) m (distance between the y-coordinates of the detectors).

The time \(\rm (\(t\))\) it takes for the electromagnetic wave to travel from detector #1 to detector #2 is given by:

\(\[ t = \frac{d}{c} \]\\\\\ t = \frac{6 \, \text{m}}{3.00 \times 10^8 \, \text{m/s}} \]\\\\\ t \approx 2 \times 10^{-8} \, \text{s} \]\)

So, in \(\rm \(t \approx 2 \times 10^{-8}\)\) seconds, detector #2 will detect the electric and magnetic fields.

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Related Questions

The speed of sound is 346 m/s. If a sound wave travels at a frequency of 55 Hz, what would its wavelength be?​

Answers

Answer:

6.29 meters.

Explanation:

, where v is the speed of wave and f is the frequency of wave.

We are given that ,

The speed of sound is 346 m/s.

i..e v=346 m/s

A sound wave travels at a frequency of 55 H.

i..e f=55

the wavelength would be 6.29 meters.

This is based on another brainly answer

Link: https://brainly.com/question/12538018

The decibel rules of thumb can be combined. (a) If a sound has intensity xdB, how many dB does a sound 100 times more intense have? (b) If another sound has intensity ydB, how many dB does a sound 4 times less intense have? (c) Combine what you know about (a) and (b): If a sound has intensity zdB, how many dB does a sound 25 times more intense have?

Answers

C i think hope this help

it is better to sell used paper then to burn them​

Answers

Answer:

Using sold paper is better than to burn it because burning paper may cause pollution.

Explanation:

Hope it will help ^_^

User paper is the correct answer

A driver of a car traveling 14.6 m/s must slam on the brakes to avoid hitting a black bear crossing the road. If it takes 3.00 seconds for the vehicle to slow down to a stop at 0.0 m/s, what is the acceleration over the three seconds?

Answers

Answer:

a = (V2 - V1) / t = (0 - 14.6) / 3 = -4.87 m/s^2

It might be useful to convert 14.6 m/s to mph

14.6 m/s * 39.37 in/m = 575 in /s

575 in/s / 12 in/ft = 47.9 ft/sec

47.9 ft/s / 88 ft/sec *  60 mph = 32.6 mph

Which is the load ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎

Which is the load

Answers

Answer:

A is the load in the diagram

Answer:

i think the answer is A

1) How far does sound travel in
a. 2 seconds?
b. 15 seconds?​

Answers

Explanation:

The sound travel in 2 seconds

the average late afternoon temperature in downtown areas is approximately ____ warmer than rural areas.

Answers

Late afternoon temperatures in metropolitan areas are typically 5°F higher than those in rural areas.

Urban areas are often flat and devoid of greenery. Most renewable energy is used to warm surfaces because there is often not much water available for evaporation.

In comparison to plants, buildings and other structures may retain more heat throughout the day. At night, they release some of this heat, which helps to increase the temperatures when it becomes dark outside. Cities could also reflect less sunlight, allowing them to receive more of the Sun's heat.

If you live there, the surface of a town or city will absorb more insulation than a forest or the damp soil surface of a hamlet.

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Please help with these questions

Please help with these questions

Answers

When do you gotta turn it in?

You are comparing a reaction that produces a chemical change and one that produces a physical change. What evidence could you use to determine which type of change is occurring?

You are comparing a reaction that produces a chemical change and one that produces a physical change.

Answers

Answer: A chemical change results from a chemical reaction, while a physical change is when matter changes forms but not chemical identity. Examples of chemical changes are burning, cooking, rusting, and rotting. Examples of physical changes are boiling, melting, freezing, and shredding. Often, physical changes can be undone, if energy is input.

Explanation: hope this helps have a good day

Answer:

If the reaction is a chemical change, new substances with different properties and identities are formed. This may be indicated by the production of an odor, a change in color or energy, or the formation of a solid.

A 2-kg block is thrown upward from a point 20 m above the Earth's surface. At what height above Earth's surface will the gravitational potential energy of the Earth-block system have increased by 500 J?

Answers

Answer:

45.5 m

Explanation:

m = 2 kg, h = 20 m, E = 500 J, radius of earth = R, mass of earth = M

find the new height H

at h, the potential energy = -GMm/(R + h)

at H, the potential energy = -GMm/(R + H)

increase of the potential energy

= [-GMm/(R + H)] - [-GMm(R + h)]

= GMm[1/(R + h) - 1/(R + H)] = E

1/(R + h) - 1/(R + H) = E/(GMm)

(H - h)/[(R + H)(R + h)] = E/(GMm)

R + h ≈ R, R + H ≈ R

so (H - h)/R² = E/(GMm)

H - h = ER²/(GMm)

note GM/R² = g = 9.81 m/s²

so H - h = E/(mg)

H = h + E/(mg) = 20 + 500/(2*9.81) = 45.5 m

Part A
How did Einstein’s and Newton’s theories differ in terms of explaining the cause of gravity?

Answers

Newton thinks that object falls due to gravity whereas Einstein thinks gravity is not the reason behind it.

How did Einstein’s and Newton’s theories differ in terms of explaining the cause of gravity?

Newton concluded that objects fall because they are pulled by Earth's gravity. Einstein's thinks that these objects do not fall due to gravity. According to Einstein, these objects and Earth just freely move in a curved spacetime

So we can conclude that Newton thinks that object falls due to gravity whereas Einstein thinks gravity is not the reason behind it.

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4. A hemispherical surface (half of a spherical surface) of radius R is located in a uniform electric field of magnitude E that is parallel to the axis of the hemisphere. What is the magnitude of the electric flux through the hemisphere surface? how to draw the question?

Answers

It is to be noted that the magnitude of the electric flux through the hemisphere surface  is πR²E. (Option D)

What is an Electric Flux?

The characteristic of an electric field known as electric flux may be thought of as the quantity of electric lines of force (or electric field lines) that cross a certain region.

According to this theory, electric field lines begin with positive electric charges and end with negative charges.

What is the calculation for the above?

Recall  that the A hemispherical surface (half of a spherical surface) of radius R.

In order to derive the Magnitude of the electric flux we use the following formula:

Ф = ∈ x Area of the Curve Surface

⇒ Ф = ∈ x πR²

⇒ Ф = πR²∈

Thus, option D is the correct answer.

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Full Question:

A hemispherical surface (half of a spherical surface) of radius R is located in a uniform electric field of magnitude E that is parallel to the axis of the hemisphere. What is the magnitude of the electric flux through the hemisphere surface?

A) 2πR²∈

B) 0

C) 4 πR²∈/3

D) πR²∈

4. A hemispherical surface (half of a spherical surface) of radius R is located in a uniform electric

You leave your house at 7:50

Answers

Answer:

LOL what?

Explanation:

Answer:

Um okay??????????????????

A water skier has a mass of 86 kg and accelerates at 2 m/s2. What is the net force acting on him?
Ο Α.
0.0233 N
2
B.
43 N
C. 84N
D.
172 N

Answers

Answer:

F = 172 N

Explanation:

Newton's second law of motion gives the amount of force acting on an object. Mathematically, it is given by :

F=ma

Put m =86 kg and a = 2 m/s²

So,

\(F=(86\times 2)\ N\\\\F=172\ N\)

Hence, the net force is 172 N.

How can graphs help demonstrate the qualitative relationship that may exist in a set of data to readers?

Answers

Graphs can help to demonstrate the qualitative relationship between a set of data by identifying patterns among these data.

What other information can the data show?Comparison between groups.Proportional relationships.Variation and dispersion.

Graphs can allow readers to identify a lot of information among a set of data. The most common information to be evaluated through the graphs is the existence of patterns between the data.

For example, a line graph can show the change in a variable over time, allowing readers to see if there is a consistent increase or decrease.

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2. For electric circuit shown in Figure find currents in each resistor.

2. For electric circuit shown in Figure find currents in each resistor.

Answers

The current flowing in the 2Ω and 1Ω is 1.14 A and the current flowing in the 3Ω and 4Ω is 0.286 A.

What is the current flowing in each resistor?

The value of the current in each resistor is calculated by applying Kirchoff voltage law as follows;

The total voltage in loop 1 is calculated as;

2 + 4 - I₁R₁ - (I₁ - I₂)R₂ - I₁R₃ = 0

6 - 2I₁ - 3(I₁ - I₂) - 1₁ = 0

The current flowing in loop 2 is calculated as;

I = V/R

I₂ = ( 6 V - 4 V ) / (3 + 4)

I₂ = 0.286 A

The value of the current flowing in loop 1 is calculated as;

6 - 2I₁ - 3(I₁ - I₂) - 1₁ = 0

6 - 2I₁ - 3(I₁ - 0.286) - 1₁ = 0

6 - 3I₁ - 3₁ + 0.858 = 0

-6I₁ = -6.858

I₁ = 6.858 / 6

I₁ = 1.14 A

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One point charge +Q is placed at the center of a square, and a second point charge -Q is placed at the upper-left corner of the square. It is observed that an electrostatic force of magnitude 2.0 N acts on the positive charge at the center. Now a third charge -Q is placed at the lower-left corner of the square, as shown in the figure. What is the magnitude of the net force that acts on the center charge now? The figure shows one positive charge labeled + Q placed at the center of a square and two negative charges labeled -Q placed at the upper left and the bottom left corners of the square.
a) 0.0 N
b) 2.8 N
c) 5.3 N
d) 4.0 N

Answers

Answer:

One should draw a diagram showing the placement of the charges.

When both charges of -Q are placed there will be no force in the vertical direction because of cancellation of forces.

A line from one corner of the square to the other makes an angle of 45 degrees,

2 cos 45 deg will be the force due to one charge.

2 * .707 = 1.41 N

So for both charges the force is (horizontal, vertical is zero)

2 * 1.41 = 2.82 N

b) is correct

The magnitude of the net force that acts on the center charge will be 2.82 N.Option B is correct.

what is the charge?

When the matter is put in an electromagnetic field, it has an electric charge, which causes it to experience a force. A positive or negative electric charge can exist.

Charges that are similar repel each other, whereas charges that are dissimilar attract each other. The term "neutral" refers to an item that has no net charge.

Case 1 ;

One point charge +Q is placed at the center of a square, and a second point charge -Q is placed at the upper-left corner of the square.

When both charges of -Q are placed there will be no force in the vertical direction because of the cancellation of forces.

A line from one corner of the square to the other makes an angle of 45 degrees,

The force due to the one charge at the angle of the 45° will be;

\(\rm F_1 = 2 \times cos 45^0 \\\\ \rm F_1 =1.41 \ N\)

For both the charge the net force is the double the force due to the one charge;

\(\rm F = 2 \times F_1 \\\\ \rm F = 2 \times 1.41 \\\\ F=2.82 \ N\)

The magnitude of the net force that acts on the center charge will be 2.82 N.

Hence option B is correct.

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The figure below shows a ball resting on a frictionless track at position A.

The ball has a mass of 20 kg and is released from position A, the acceleration due to gravity is 9.8 m/s. How much kinetic energy will the ball have at position B?

 The figure below shows a ball resting on a frictionless track at position A.The ball has a mass of 20

Answers

To find the kinetic energy at position B, we need to know the height or the velocity at position B. Without this information, we cannot calculate the exact value of the kinetic energy.

To determine the kinetic energy of the ball at position B, we need to consider the m conservation of Mechanical energy. Since the ball is released from position A, we can assume that there is no initial kinetic energy (velocity is zero), and the total mechanical energy at position A is equal to the potential energy.

The potential energy at position A can be calculated using the formula:

Potential energy at A = mass * gravitational acceleration * height

Potential energy at A = 20 kg * 9.8 m/s² * height

Now, at position B, all the potential energy is converted into kinetic energy. The kinetic energy at position B is given by the formula:

Kinetic energy at B = 1/2 * mass * velocity²

Since the ball is released from rest, the velocity at position B can be determined using the conservation of mechanical energy:

Potential energy at A = Kinetic energy at B

20 kg * 9.8 m/s² * height = 1/2 * 20 kg * velocity²

Simplifying the equation, we get:

9.8 m/s² * height = 1/2 * velocity²

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Temperature is most closely related to molecular A) Kinetic energy. B) Potential energy. c) Electrical energy. D) Chemical energy

Answers

Temperature is most closely related to molecular Kinetic energy. Hence, option (A) is correct.

What is kinetic theory of gases ?

The kinetic theory of gases is a theory that can be used to deduce many of the gas's macroscopic features from a simplified molecular or particle description of the gas.

The most basic kinetic model is predicated on the following premises:

The gas is made up of a large number of identical molecules moving in random directions, separated by distances that are large in comparison to their size. The molecules collide perfectly elastically (with no energy loss) with each other and with the container walls, but otherwise do not interact.The transfer of kinetic energy between molecules is heat. The characteristics of gases can now be mathematically treated thanks to these simplifications.

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calculate the force exerted between two charged objects seperated by a distance of 0.6 m. one object has a charge of -5 C and the other has a charge of +2.0 C

Answers

The electrostatic force of repulsion between the two charges is equal to 0.25 x 10¹¹ N.

What is the formula to calculate the force between 2 point charges?

The coulomb's law is used to find the force between two point charges. The force can be calculated using the formula -

F = 1/4πε₀ |Q₁||Q₂|/r²

Given is two charged objects separated by a distance of 0.6 m such that one object has a charge of -5 C and the other has a charge of +2C.

The electrostatic force of repulsion between the two charges is given by-

F = 1/4πε₀ |Q₁||Q₂|/r²

F = 9 x 10⁹ x (5 x 2)/(0.6)²

F = 90 x  10⁹/0.36

F = 9 x 10¹¹/36

F = 0.25 x 10¹¹ N

Therefore, the electrostatic force of repulsion between the two charges is equal to 0.25 x 10¹¹ N.

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estimate the work you do to mow a lawn 10m by 20m with a 50 cm wide mower. Assume you push with a force of about 15 N.

Answers

Answer:

W = 6000 Joule

Explanation:

Work is defined as force times distance

W = F * d

We know that F = 15N, we just need the distance (d)

Imagine you have a square lawn with length of 10 m and width of 20m. So, we want to know the the distance you have to travel to cover every square meter of the lawn.

The width of the mower is only 50 cm = 0.5 m.

This means that you have to go back and forth 40 times to cover 20m (lawn width), with a distance of 10 m (lawn length). So,

d = 10 (meter) * 40 (times) = 400 meter

Therefore:

W = (15) * (400) = 6000 J

A rocket’s mass is reduced by half, but the force pushing it through space remains the same. What will happen to the rocket’s acceleration

Answers

The acceleration of the rocket will increase by two times if the rocket's mass is reduced by half.

What is acceleration?

Acceleration is the amount by which a speed or velocity increases. The acceleration of a moving body can be calculated by using the following formula:

a = F/m

Where;

a = acceleration (m/s²)F = force (N)m = mass (kg)

This formula or expression shows the relationship between acceleration and mass as an inverse relationship i.e. as mass increases, the acceleration decreases and vice versa.

According to this question, a rocket’s mass is reduced by half, but the force pushing it through space remains the same. This means that the acceleration of the rocket will increase by two.

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*How much energy is
transferred in lifting a 5 kg
Mass 3m​

Answers

Answer:

147 J

Explanation:

The energy transferred to potential energy is :

U = m * g * h = (5 kg) * (9.8 m/s^2) * (3 m) = 147 J

If a 1.5-Kg physics book measures 0.260 m x 0.210 m x 0.040 m, calculate the pressure applied by the standing book on the table. (Round off answer to two sig figs)
*

Answer choices:
P = 1,600 N/m^2
P = 1,800 N/m^2
P = 1,500 N/m^2
P = 1,700 N/m^2

Answers

The pressure applied by the standing book on the table is 1,800 N/m².

option B is the correct answer.

What is the pressure applied by the book?

The pressure applied by the standing book on the table is determined from the ratio of weight of the book and the area of the standing book.

Mathematically, the formula for the pressure of a material is given as;

P = F / A

where;

F is the applied force or weight of the object standing on another surfaceA is the area of the object in contact with another surface

The weight of the book , F = mg

where;

m is the mass of the bookg is acceleration due to gravity

F = 1.5 kg  x  9.8 m/s²

F = 14.7 N

The dimension of the book include;

height of the book, h = 0.26 mwidth of the book, w = 0.21 mthickness of the book, b = 0.04 m

The height of the book is not in contact with the surface of the table, so the area of the book in contact with the table becomes;

A = w x b

W = 0.21 m  x  0.04 m

W = 8.4 X 10⁻³ m²

P = F / A

P = ( 14.7 N ) / ( 8.4 X 10⁻³ m² )

P = 1,750 N/m² ≈ 1,800 N/m²

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Add a suffix to each of the following words to make new words?​

Answers

Where's the following words?

In Milikan’s experiment, a drop of radius of 1.64 μm and density 0.851 g/cm3 is suspended in the lower chamber when a downward-pointing electric field of 1.92 * 105 N/C is applied.

What is the weight of the drop?

Find the charge on the drop, in terms of e.

How many excess or deficit electrons does it have?

Answers

(a) The weight of the drop is 1.54 x 10⁻²⁵ N,

(b) The the charge on the drop, in terms of e is 5 x 10⁻¹²e and

(c) The excess electrons is 5 x 10⁻¹² electron.

Weight of the drop

The weight of the drop is calculated as follows;

Volume of the drop; V = ⁴/₃πr³

V = ⁴/₃π(1.64 x 10⁻⁶)³ = 1.845 x 10⁻¹⁷ m³

mass = density x volume

mass =  0.851 g/cm³ x  1.845 x 10⁻²³ cm³ = 1.572 x 10⁻²³ g =  1.57 x 10⁻²⁶ kg.

Weight = 1.57 x 10⁻²⁶ kg x 9.8 m/s² = 1.54 x 10⁻²⁵ N.

Charge on the drop

q = F/E

q = (1.54 x 10⁻²⁵ N)/(1.92 x 10⁵)

q = 8.01 x 10⁻³¹ C

1.6 x 10⁻¹⁹ C = 1e

8.01 x 10⁻³¹ C = ?

= 5 x 10⁻¹²e

Excess electron on the drop

1.6 x 10⁻¹⁹ C ------- 1 electron

8.01 x 10⁻³¹ C ------- ?

= 5 x 10⁻¹² electron

Thus, the weight of the drop is 1.54 x 10⁻²⁵ N, the the charge on the drop, in terms of e is 5 x 10⁻¹²e and the excess electrons is 5 x 10⁻¹² electron.

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a heat engine that accepts heat from and rejects heat to the same thermal energy reservoir is an example of a device that violates which of the following? multiple choice question. first law clausius statement of the second law kelvin-planck statement of the second law

Answers

A heat engine is in violation of the second rule of thermodynamics if it claims to have a thermal efficiency higher than the Carnot efficiency.

In science, what is an energy?

Energy is characterized as having the "ability to accomplish work, which is the capacity to apply a force sufficient to move an object." Despite this unclear definition, the concept is essentially quite straightforward: electricity merely refers to the force that drives objects. Potential and kinetic energy are the two different categories.

Easy definition of energy

The ability to perform work is the most basic definition of energy. Things alter and move because of energy. It comes in many different shapes and is all around us. Cooking food requires energy.

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Honey is a technology company that provides online coupons to its subscribers. Honey's analytics staff has developed a classification method to predict whether a customer who has been sent a coupon will apply the coupon toward a purchase. For a sample of customers, the following table lists the classification model's estimated coupon usage probability for a customer. For this particular campaign, suppose that when a customer uses a coupon, Honey receives $1 in revenue from the product sponsor. To target the customer with the coupon offer, Honey incurs a cost of $0.05. Honey will offer a customer a coupon as long as the expected profit of doing so is positive. Using the equation
Expected Profit of Coupon Offer = P(coupon used) × Profit if coupon used + (1 - P(coupon used)) × Profit if coupon not used
determine which customers should be sent the coupon.

Customer Probability of Using Coupon
1 0.44
2 0.34
3 0.24
4 0.11
5 0.06

Determine the expected profit for each customer. Round your answers to the nearest cent. Enter negative value as negative number, if any.

Customer Expected Profit
1 $
2 $
3 $
4 $
5 $

The expected profit is positive for customers (Select your answer: 2 and 3, 4 and 5, 1, 2, and 33, 4, and 5, 1, 2, 3, and 4, 1, 2, 3, and 5, 2, 3, 4, and 5, 1, 2, 3, 4, and 5) so these customers (Select your answer: should be offered or should not be offered) the coupon.

Answers

The expected profit is positive for the customers 1, 2, 3, 4, 5.

What is expected profit?

This is the term that is used to refer to the gain that would be expected to be gotten based on the fact that a person has engaged in a business.

We have 1 - 0.05 = 0.95 profit if the coupon is used

-0.05 is the profit if the coupon is not used

for consumer 1

the probability = 0.44

expected profit = 0.44 x 0.95 - 0.05 x 0.56

= 0.418 - 0.028

= 0.39

for consumer 2

the probability = 0.34

expected profit = 0.34 x 0.95 - 0.05 x 0.66

= 0.323 - 0.033

= 0.29

For consumer 3

the probability = 0.24

expected profit = 0.24 x 0.95 - 0.05 x 0.76

= 0.228 - 0.038

= 0.19

For consumer 4

the probability = 0.11

expected profit = 0.11 x 0.95 - 0.05 x 0.89

= 0.1045 - 0.0445

= 0.06

For consumer 5

the probability = 0.06

expected profit = 0.06 x 0.95 - 0.05 x 0.94

= 0.057 - 0.047

= 0.01

The expected profits can be listed as:

0.390.290.190.060.01

The expected profits are positive for all of 1, 2, 3, 4, and 5, hence these customers can purchase the coupon.

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Sound moves at a speed of 343 meters per second through air, a gas. Which pairing is most accurate for how sound will travel through liquid and solid?
Responses


A Sound in solid- 600 m/s
Sound in liquid- 150 m/sSound in solid- 600 m/s Sound in liquid- 150 m/s


B Sound in solid- 1000 m/s
Sound in liquid- 100 m/sSound in solid- 1000 m/s Sound in liquid- 100 m/s


C Sound in solid- 6000 m/s
Sound in liquid- 1500 m/sSound in solid- 6000 m/s Sound in liquid- 1500 m/s


D Sound in solid- 6000 m/s
Sound in liquid- 100 m/sSound in solid- 6000 m/s Sound in liquid- 100 m/s
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Answers

With sound travelling through solids at a speed of 6000 m/s and liquids at a speed of 1500 m/s, Option C best describes how sound will move through liquid and solid media.

When moving at 343 metres per second, what is the speed of sound in air?

The speed of sound in air at 20 °C (68 °F) is approximately 343 m/s (1,125 ft/s; 1,235 km/h; 767 mph; 667 kn), or 2.91 s for a kilometre and 4.69 s for a mile.

Which is faster, 332 or 343 mph, for sound in air?

The right response is 332 mtr/sec. The distance that sound waves cover in a specific amount of time is known as the speed of sound. Given as 343 metres per second.

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State the hamilton's equation of
motion and derive each of them

Answers

Hamilton's equations of motion are a set of equations that describe the dynamics of a classical mechanical system in terms of a generalized coordinate and its conjugate momentum.

How to explain the equation

The equations are derived from the Hamiltonian formalism. Hamilton's equations can be derived from the Hamilton's principle, which is a variational principle that states that the action of a dynamical system is stationary.

To derive these equations, we start with the Hamiltonian function H(p, q) and use the principle of least action. The action S is defined as the integral of the Lagrangian L(q, q', t) over time:

S = ∫[L(q, q', t)] dt

To find dp/dt, we differentiate the Lagrangian with respect to q:

∂L/∂q = ∂(p * q' - H)/∂q

= -∂H/∂q

Using the chain rule, we find:

dL/dt = (∂L/∂q) * dq/dt + (∂L/∂q') * dq'/dt

= -∂H/∂q * dq/dt + p * d(q')/dt

= -∂H/∂q * dq/dt + p * d^2q/dt^2

= -∂H/∂q * dq/dt + dp/dt

Since the Lagrangian is equal to p * dq' - H, we can write:

dL/dt = -∂H/∂q * dq/dt + dp/dt

From the principle of least action, we know that the action S is stationary, so dL/dt = 0. Thus, we have:

-∂H/∂q * dq/dt + dp/dt = 0

Rearranging the equation, we obtain the first equation of motion:

dp/dt = -∂H/∂q

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