A ΔV = 2.7 V battery loses E = 6 J of energy each day (t = 24 hrs) powering a cell phone.
Part (a) Input an expression for the average current, I, supplied to the phone. Expression :
I = __________________________________________
Select from the variables below to write your expression. Note that all variables may not be required. α, β, ΔV, θ, a, d, E, g, h, j, k, m, P, S, t
Part (b) What is the current in Amperes?
Numeric : A numeric value is expected and not an expression. I =

Answers

Answer 1

The current supplied to the phone is 93.75 milliamperes (mA) or 0.09375 Amperes (A).

Part (a) Expression for the average current, I, supplied to the phone:

We can use the formula for electrical power:

Power = current x voltage

The energy lost by the battery each day is given by:

Energy = Power x time

E = P x t

Substituting Power = I x ΔV and time t = 24 hrs, we get:

E = I x ΔV x t

I = E / (ΔV x t)

Therefore, the expression for the average current supplied to the phone is:

I = E / (ΔV x t)

Part (b) Numeric value for the current in Amperes:

Substituting the given values, we get:

I = 6 J / (2.7 V x 24 hrs)

I = 0.09375 A or 93.75 mA

Therefore, the current supplied to the phone is 93.75 milliamperes (mA) or 0.09375 Amperes (A).

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Related Questions

The half-life of Po-214 is 0.001 seconds. How much of a 10-gram sample is left after 0.003 seconds?

Answers

You would be left with 1.25 g.

After 0.001 second, 10 grams decays to 5 grams.

After another 0.001 second, 5 g decays to 2.5 g. (Total time 0.002 s; two half-lives have passed)

After another 0.001 second, 2.5 g decays to 1.25 g. (Total time 0.003 s; 3 half-lives have passed)

A rifle bullet is going 2760 ft/s and hits a tree. It slows to 0 ft/s in 0.13sec. What was its


acceleration?

Answers

The initial velocity of the rifle bullet is 2760 ft/s. It comes to rest after hitting the tree in 0.13 seconds.

We are supposed to find the acceleration of the rifle bullet given the initial velocity and time taken to come to rest.

Therefore, we can use the formula to calculate acceleration (a) from the given values of velocity (v) and time taken (t) which is given as follows:

a = (v - u) / t

Where,u = Initial Velocity

v = Final Velocity

a = acceleration

t = time taken

Now, substituting the given values of u, v, and t in the above formula, we get:

a = (v - u) / ta

= (0 - 2760) / 0.13

We get the acceleration of the rifle bullet as - 21230.76923076923 ft/s² (Rounding to 2 decimal places, it is -21230.77 ft/s²).

The acceleration of the rifle bullet is negative because it's coming to rest, indicating a deceleration.

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how does an objects size affect the gravity exerted by that object​

Answers

Answer:

The size of an object is directly proportional to the gravity

Explanation:

The size of an object has significant impact on the gravity exerted by such a body.

The more massive a body is, the larger the gravity it exerts.

The reason for this is because of the newton's law of universal gravitation.

It states that "the gravitational force between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distances between them". As such, gravity is directly proportional to mass

Please help!!! Which is a heterogeneous mixture?

Please help!!! Which is a heterogeneous mixture?

Answers

Answer:

pizza is a heterogeneous mixture.

Explanation:

A heterogeneous mixture is a mixture in which the composition is not uniform throughout the mixture. Vegetable soup is a heterogeneous mixture. Any given spoonful of soup will contain varying amounts of the different vegetables and other components of the soup

A box has a mass 45kg is pushed to the right with a force of 270 newtons. What will the acceleration be? ( Please help)

Answers

Answer:

6m.s‐²

Explanation:

IF there is no friction or any other force acting on the objects then use the equation Fnet=m.a

Fnet=m.a

270=45(a)

a=6

results will change if there is another force acting on the box besides the pushing force

please give brainliest

1. A 1400 kg car is moving at 15 m/s when it hits a tree and comes to rest 0.30 seconds later. How
much force does the car experience?

Answers

Answer:

F = 70000  N

Explanation:

Given that,

Mass of a car, m = 1400 kg

Initial speed of the car, u = 15 m/s

Finally, it hits the ground, v = 0

Time, t= 0.3 s

We need to find the force experienced by the car. Using Newton's second law of motion to find it.

F = ma

a is acceleration of the car.

\(F=\dfrac{m(v-u)}{t}\\\\F=\dfrac{1400\times (0-15)}{0.3}\\\\=-70000\ N\)

So, the force experienced by the car has a magnitude of 70000  N.

Which of the following is not a property of light?
a. light is a form of matter less dense than air
b. light travels in straight lines
c. light has different colors
d. light has different intensities, and cam be bright or dim​

Answers

Answer: Light is not a form of matter, so a is not a property of light.

Explanation:

What are three tips to start a healthy dating relationship mentioned in the article? (Site 1)

Answers

Faith, respect, and effective communication are the three tips to start a healthy dating relationship mentioned in the article.

What are three recommendations for beginning a happy relationship?

Trust, respect, effective communication, adaptability, a common interest, time apart, different connections (with family and friends), and appreciation. Each partner needs to have confidence in the other. Never should your partner belittle you, test you, or say anything disparaging about you.

What are good relationships?

Healthy relationships involve open communication, honesty, trust, and respect between partners as well as work and compromise from both parties. There is no imbalance of power. Partners are free to make decisions together, respect each other's independence, and take individual actions without worrying about the consequences.

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What’s the missing word??


The bond between the atoms in graphite's are ...

Answers

Answer:

a giant covalent structure

Two sumo wrestlers are in a match. At the start of the match, they both lunge at each other. They hit and miraculously come to a standstill. One wrestler was 200kg and traveling at a velocity of 2.3m/s at the instance of collision. If the other wrestler was traveling at 2.9m/s, what is his mass?

Answers

This issue can be resolved by applying the momentum conservation principle. The total amount of momentum prior to and following the impact are equal. This can be expressed as:

(M1 + M2)vf = m1v1 + m2v2

m1 equals 200 kilograms (mass of wrestler 1)

v1 = 2.3 m/s (velocity of wrestler 1) (velocity of wrestler 1)

v2 = 2.9 m/s (velocity of wrestler 2) (velocity of wrestler 2)

m2 = the wrestler's mass two (unknown)

vf is the wrestlers' combined final speed before the collision (which we know is zero)

It's the same response we previously received. The problem is that the negative sign shows that Wrestler 2's velocity is moving in the opposite direction from Wrestler 1's velocity. Wrestler 2 is therefore traveling against the current. To gather the wrestlers in bulk

If r 2 is 2, we can omit the minus sign and use the absolute value instead:

As a result, wrestler 2 weighs roughly 158.62 kg.

What's a good illustration of momentum and impulse?

In order to change the momentum of an object, you must exert a certain amount of force over a specific period of time. It is  because of this. For instance, when you strike a ball with a cricket bat, you exert power temporarily (in this case, very briefly) in order to change (or transfer) the momentum of the ball. |m2| = 158.62 kg

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What is the effect of sun heat and light to the environment?

Answers

In addition to heating the Earth's oceans and atmosphere and causing weather patterns, the Sun also gives energy to the planet's green, expanding vegetation, which provides food and oxygen for life.

Despite the fact that its heat and light are what make the Sun so well-known to us, it also has other, less obvious effects on the planet and human culture. The emission or transmission of energy as waves or particles through space or through a material medium is referred to as radiation in physics. The electromagnetic spectrum, which encompasses radio waves, microwaves, infrared, visible light, ultraviolet, x-rays, and gamma radiation, is included in this. One of a body's fundamental characteristics is mass. Before the discovery of the atom and particle, it was widely believed that it was tied to the amount of matter in a physical body.

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It emits solar energy, which enables life to exist on Earth, in the form of light and heat. To flourish, plants require sunshine. Humans and other animals alike depend on plants for food and the oxygen they create.

Why is solar energy environmentally friendly?

Solar energy is a renewable resource that plays a significant part in lowering greenhouse gas emissions and preventing climate change, which is essential for safeguarding people, animals, and ecosystems. Additionally, the usage of solar energy can minimize water consumption and enhance air quality.

What exactly is a renewable energy source?

When natural resources are restored more quickly than they are used up, it is said to be using renewable energy. Such sources that are constantly replenished include the sun and the wind, for instance.

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what is the frequency of a photon that has the same momentum as a neutron moving with a speed 1.40

Answers

The frequency of the photon is 1.06 × 10^15 Hz.

When a neutron is moving with a speed of 1.40 m/s, it has momentum p = mv, where m is its mass and v is its velocity. The momentum of the neutron is equal to that of a photon that has the same momentum. This means that the photon and the neutron have the same momentum, i.e. p_photon = p_neutron. The momentum of the neutron is given by: p_neutron = mv, where m is the mass of the neutron and v is its speed.

The mass of the neutron is approximately 1.67493 × 10^−27 kg. Therefore,

p_neutron = (1.67493 × 10^−27 kg)(1.40 m/s) = 2.34491 × 10^−27 kg m/s

Since the photon has the same momentum as the neutron, its momentum is also 2.34491 × 10^−27 kg m/s. The momentum of a photon is given by:

p_photon = h/λ, where h is Planck's constant and λ is the wavelength of the photon. Therefore,

λ = h/p_photon, where h is approximately 6.626 × 10^−34 J s.

Therefore, λ = (6.626 × 10^−34 J s)/(2.34491 × 10^−27 kg m/s) = 2.824 × 10^−7 m

The frequency of the photon is given by:f = c/λ, where c is the speed of light.

Therefore, f = (3.00 × 10^8 m/s)/(2.824 × 10^−7 m) = 1.06 × 10^15 Hz.

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A truck heading east has an initial velocity of 6 m/s. It accelerates at 2 m/s2 for 12 seconds. What distance does the truck travel in the given time?Paco was driving his scooter west with an initial velocity of 4 m/s. He accelerates at 0. 5 m/s2 for 30 seconds. What is his final velocity?

Answers

The distance the truck travel in given time is 216 m and the final velocity of acceleration at 0.5m/\(s^{2}\) for 30 seconds is 19 m /s

The following question has two parts

For part 1 we need to calculate the distance covered by the truck in 12 seconds

We know that

 s = ut + \(\frac{1}{2}a .t^{2}\) . . . . . . .  . . . . .(1)

where s = distance travelled

           u = initial velocity

           a = acceleration

           t  =  time in seconds

Now , As per the question

u = 6 m/s

a = 2 m/\(s^{2}\)

t  = 12 seconds

Putting the values in the equation (1)

                          s = 6 X 12 + \(\frac{1}{2}\) X 2 X 144

                          s = 72 + 144

                          s = 216 m

Therefore the distance travelled is 216 m

For part 2 we need to calculate the final velocity that Paco was driving

We know that

v = u + at . . . . . . . . . . .  .(2)

where v = final velocity

          u = initial velocity

          a = acceleration

           t = time in seconds

As per the question,

u = 4m/s

a = 0.5 m/\(s^{2}\)

t = 30 seconds

Putting in equation (2)

                                      v = 4 + 0.5 X 30

                                      v  =  4 + 15

                                      v = 19 m/s

Therefore the final velocity is 19 m/s

Therefore , the distance the truck travel in given time is 216 m and the final velocity of acceleration at 0.5m/\(s^{2}\) for 30 seconds is 19 m /s

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The final velocity of the scooter is 19 m/s.

Given:

Initial velocity of truck, u = 6 m/s

Acceleration of truck, a = 2 m/s²

Time taken by the truck, t = 12 s

Formula used:

s = ut + 1/2 at²

Where,

s = Distance travelled

u = Initial velocity

a = Acceleration

t = Time taken

Substituting the given values in the above formula, we get:

s = ut + 1/2 at²

 = 6(12) + 1/2 × 2 × (12)²

 = 72 + 1/2 × 2 × 144

 = 72 + 144

 = 216 m

Therefore, the truck travels 216 m in the given time.

Given:

Initial velocity of scooter, u = 4 m/s

Acceleration of scooter, a = 0.5 m/s²

Time taken by the scooter, t = 30 s

Formula used:

v = u + at

Where,

v = Final velocity

u = Initial velocity

a = Acceleration

t = Time taken

Substituting the given values in the above formula, we get:

v = u + at

 = 4 + 0.5 × 30

 = 4 + 15

 = 19 m/s

Therefore, the final velocity of the scooter is 19 m/s.

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In what kind of pot will a given volume of water boilat a higher temperature: a tall and narrow one or a short andwide one? explain.

Answers

The water in both pots will boil at the same temperature as long as the pressure is consistent. Both pots' water will reach boiling point at the same temperature.

what is boiling point?

The point at which the pressure that a liquid is subjected to from its environment equals the pressure that the liquid's vapor is subjected to; in this situation, the addition of heat causes the liquid to turn into its vapor without rising the temperature.

A liquid partially vaporizes through into space above it with any temperature up until the vapor pressure of the fluid at that temperature, which is a characteristic value. The vapor pressure rises as the temperature rises, and when the liquid reaches the boiling point, vapor bubbles develop inside the liquid and rise to the surface. A liquid's boiling point changes depending on the pressure being applied; the constant boiling refers to the temperature where the vapor pressure of the liquid is equal to the average atmospheric pressure at sea level (760 mm [29.92 inches] of mercury). Water boils at sea level at 100° C (212° F). Lower boiling point temperatures are seen at greater elevations.

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(b) In a constant head permeameter test the following results were obtained: Duration of test =300 seconds Quantity of water collected =500ml Head difference in manometer =45 mm Distance between manometer tappings =100 mm Diameter of test sample =100 mm From the data above, calculate the; (i) Hydraulic gradient. (ii) Flow rate. (iii) Hydraulic conductivity.

Answers

(i) The hydraulic gradient is 0.45.

(ii) The flow rate is approximately 0.00000167 cubic meters per second.

(iii) The hydraulic conductivity is approximately 0.000037 meters per second.

(i) Hydraulic gradient:

The hydraulic gradient (i) can be calculated by dividing the head difference (h) by the distance (L) between the manometer tappings:

i = h / L

Given:

Head difference (h) = 45 mm

Distance between manometer tappings (L) = 100 mm

Converting the units to meters:

h = 45 mm / 1000 = 0.045 m

L = 100 mm / 1000 = 0.1 m

Substituting the values into the formula:

i = 0.045 m / 0.1 m = 0.45

(ii) Flow rate:

The flow rate (Q) can be calculated using the equation:

Q = (V / t) / A

Where V is the quantity of water collected, t is the duration of the test, and A is the cross-sectional area of the test sample.

Given:

Quantity of water collected (V) = 500 ml = 0.5 L

Duration of test (t) = 300 seconds

Diameter of test sample (d) = 100 mm

Converting the units to meters:

V = 0.5 L = 0.5 / 1000 = 0.0005 m³

t = 300 seconds

d = 100 mm / 1000 = 0.1 m

Calculating the cross-sectional area (A) using the formula for the area of a circle:

A = π * (d/2)^2

Substituting the values:

A = π * (0.1/2)^2 = π * 0.005^2 = 0.00007854 m²

Substituting the values into the formula for flow rate:

Q = (0.0005 m³ / 300 s) / 0.00007854 m²

Calculating the flow rate:

Q = 0.00000167 m³/s

(iii) Hydraulic conductivity:

The hydraulic conductivity (K) can be calculated using Darcy's Law:

K = Q / (A * i)

Given the values we calculated:

Q = 0.00000167 m³/s

A = 0.00007854 m²

i = 0.45

Substituting the values into the formula:

K = 0.00000167 m³/s / (0.00007854 m² * 0.45)

Calculating the hydraulic conductivity:

K ≈ 0.000037 m/s

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Please help me!!!!!!!!

Please help me!!!!!!!!

Answers

Answer:

it’s the 2nd one

Explanation:

Answer:

second one

Explanation:

A light bulb has a resistance of 360 . What is the current in the bulb when it has a potential difference of 120 V across it?

0.33 A
3 A
480 A
43,200 A

Answers

Answer:

333 mAmps      .33 A

Explanation:

v = ir

v/r = i

120 v / 360 ohm = .3333 A

Answer:

A). 0.33A

Explanation:

You are playing tennis and return a volley. Identify a force pair.

Answers

During a tennis volley, the force pair involved is the action-reaction forces.

When playing tennis and returning a volley, the force pair involved is the action and reaction forces. In the process of hitting the ball, the tennis racket exerts a force on the ball, which is the action force.

The ball, in turn, exerts an equal and opposite force on the racket, which is the reaction force.Both the racket and the ball experience the force of impact during the volley.

The force applied by the racket causes the ball to move forward, while the equal and opposite force applied by the ball pushes the racket back.

These two forces are referred to as action-reaction forces or force pairs. A force pair refers to a pair of forces that are equal in magnitude but opposite in direction.

These forces always act on different objects and occur simultaneously. In this scenario, the action force was exerted by the tennis racket while the reaction force was exerted by the ball.

Therefore, during a tennis volley, the force pair involved is the action-reaction forces.

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When is the world going to end? Give me your opinions and the reasons why you think that.

Answers

Answer:

probably when the next pandemic happens

Which of the following happens to an object in uniform circular motion?

A. it’s velocity changes
b. it’s speed changes
c. it’s centripetal acceleration changes
d. the direction of its velocity stays the same

Answers

Answer:its velocity changes

Explanation:

Compare your everyday experiences to the simulation. Design a few tests like rolling things off a table or tossing some things into a basket or bowl to determine how well the simulation represents projectile motion. Some good objects are tightly rolled socks or paper crumpled into a ball. Write about your experiments and compare them to the simulation

Answers

If we throw a socks in to the bowl then it is going with a few unfold situation by means of the projectile and follows the trajectory. Crumpled paper use for the projectile additionally works gud for the simulation.

Crumpled paper has irregular form and mild in weight and it is able to divert in a way by air force or by means of any other motive mild weight. hence simulation and projectile interest are interlinked to every different.

Projectile motion is used in many real-life applications such as designing rockets, ballistic missiles, and artillery, as well as in sports such as baseball, golf, and archery. The concept of projectiles is also relevant in fields such as engineering, military science, and sports. For example, the design of a projectile such as a bullet or missile can affect its accuracy and effectiveness, while knowledge of projectile motion can aid in the design of sports equipment such as golf clubs or javelins.

When a projectile is launched, it follows a curved path known as a trajectory, which is determined by the initial velocity, angle of launch, and the gravitational and atmospheric forces acting on it. The motion of projectiles is studied in physics, where concepts such as projectile motion, trajectory, range, and maximum height are analyzed.

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a mass of 5 kg initially hangs from a pulley by a rope. the pulley itself has a mass of 20 kg and a radius of 0.5 m. if this system is released from rest, you observe the mass falls downward and the pulley rotates clockwise. what will be the angular acceleration of the pulley in rad/s2?

Answers

The angular acceleration of the pulley can be determined by considering the forces acting on the system and the moment of inertia of the pulley. Based on the task, the angular acceleration of the pulley is 2.45 rad/\(s^{2}\).

The angular acceleration of the pulley can be determined by considering the forces acting on the system and the moment of inertia of the pulley. The net force acting on the system is given by the weight of the hanging mass, which creates a tension in the rope that is transferred to the pulley. The tension in the rope produces a torque on the pulley, given by:

The tension in the rope produces a torque on the pulley, given by:

τ = T * r

where,

T = the tension in the rope

r = the radius of the pulley.

The net torque on the pulley can be used to determine its angular acceleration, given by:

α = τ / I

where,

I is the moment of inertia of the pulley, given by:

I = (1/2) * m * \(r^{2}\) + m * \(r^{2}\)

where m is the mass of the pulley.

Substituting the values, we get:

α = (T * r) / ((1/2) * m *  \(r^{2}\) + m *  \(r^{2}\))

= (5 * 9.8 * 0.5) / ((1/2) * 20 * \(0.5^{2}\) + 20 * \(0.5^{2}\))

= 49 / 20

= 2.45 rad/\(s^{2}\)

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Assume you have a person with a mass of 65 kg riding a skateboard down a ramp. While they are
still 4.8 m high, they are traveling at a speed of 8.0 m/s.
a) Calculate the Eg. [write here]
b) Calculate theEk [write here]
c) Calculate the Etotal. [write here)

Assume you have a person with a mass of 65 kg riding a skateboard down a ramp. While they arestill 4.8

Answers

Answer:

a) Eg = 3,060.72 j

b) Ek = 2,080 j

c) Etotal = 5,140.72 j

Explanation:

The given parameters are;

The mass of the person, m = 65 kg

The height of the person, h = 4.8 m

The speed of the person, v = 8.0 m/s

a) The gravitational potential energy, \(E_g\) = m·g·h

Where;

g = The acceleration due to gravity ≈ 9.81 m/s²

∴ Eg = 65 kg × 9.81 m/s² × 4.8 m = 3,060.72 j

Eg = 3,060.72 j

b) The kinetic energy, Ek = 1/2·m·v²

∴ Ek = 1/2 × 65 kg × (8.0 m/s)² = 2,080 j

Ek = 2,080 j

c) The constant total Mechanical Energy, Etotal = Eg + Ek

∴ Etotal = 3,060.72 j + 2,080 j = 5,140.72 j

Etotal = 5,140.72 j.

Engineers often build a prototype perfectly. It is rare that they have to improve their product.


True or false

Answers

Answer:

false

Explanation:

most prototypes are and perfect and they are build to find our mistakes

false because they might fail in the first try but they have to keep trying till it’s nearly perfect

Science project!!! For this assignment, you will ask questions about the factors that have caused a rise in global
temperatures over the past century. Then, you will conduct research to answer your questions. You will
also graph provided information, analyze the graphs, and make conclusions based on the graphs. Finally,
you will write a paper describing the conclusions of your research and graphs

Answers

My project is in the file attached, lots of thanks to Maxineishere for helping me with the essay. You may need adobe reader for this as the files are PDF files, I hope you are satisfied! :)

DATE ANSWERED: 5/8/2021

⦁ A body has weight 10 N. How much force is required to move it vertically upward with an acceleration of 3 ms-2?

Answers

Answer:

Force = 3.06 Newton.

Explanation:

Given the following data;

Weight = 10N

Acceleration = 3m/s²

To find the force required;

First of all, we would determine the mass of the body.

Weight = mass * acceleration due to gravity

We know that acceleration due to gravity is equal to 9.8m/s².

10 = mass * 9.8

Mass = 10/9.8

Mass = 1.02 kg

Now, we can find the force required by using the formula below;

Force = mass * acceleration

Force = 1.02 * 3

Force = 3.06 Newton.

a car goes a distance of 40 m in 5.25 seconds. What is it’s average velocity?

Answers

Answer:

I believe it is about 7.6 spm

Explanation:

40÷ 5.26 = 7.61904761904

The car's average speed is 7.62 m/s.

It's velocity can't be determined without knowing anything about it's position or direction.

TRUE / FALSE. a joint is a wave-like undulation of rock layers in response to stress.

Answers

A joint is not a wave-like undulation of rock layers in response to stress. False statement.

Instead, a joint is a type of fracture in rocks where there has been no significant displacement. The wave-like undulation you are referring to is called a fold, which occurs when rock layers are compressed and deformed under stress

A joint is a type of fracture or break in rock that occurs when there is no movement between the two sides of the fracture. Joints are formed in response to stresses such as tectonic activity or changes in temperature and pressure and are a common feature in many types of rocks.

While joints can sometimes give the appearance of a wave-like undulation in rock layers, this is not the same as a true wave-like undulation such as a fold or a fault. Folds are undulations in rock layers that result from compressive stresses that cause the layers to bend and deform, while faults are fractures in the rock where the movement has occurred along one side of the fracture relative to the other.

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Suppose that, while in a squatting position, you stand on your hands, and then you pull up on your feet with a great deal of force. You are applying a large force to the bottoms of your feet, but no matter how strong you are, you will never be able to lift yourself off the ground. Use your understanding of force and motion to explain why this is not possible.

A. You can't lift yourself off the floor because the net external and internal forces on you are still zero.

B. You can't lift yourself off the floor because the net external force on you is still zero.

C. You can't lift yourself off the floor because the net internal force on you is still zero.

D. None of the above.

Answers

From the given choices for force and motion, the best choice is B.

There is no external force acting on you at all. The external force is necessary in order for the body to lift.

The three forces acting on a body:

First: The normal force acting between the ground and feet.

Second: the muscle force hand between the hands and feet.

Third: weigh at the center of mass.

Your hands are pushing up against your feet, but your feet are pushing down against your hands.

Therefore, both forces cancel out, resulting in zero net external force on you.

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How to integrate 1/ 1 + x2

Answers

The integral of 1/(1 + x²) is (1/2)ln|1 + x²| + C where C is the constant of integration.

Integration is a mathematical process of finding the antiderivative of a function. To integrate the given expression 1/(1 + x²), we will use the substitution method.

Let u = 1 + x², du/dx = 2x dx, then dx = du/2x and the integral becomes:

∫1/(1 + x²) dx = ∫1/u * (1/2x) du= (1/2)∫1/u du

The antiderivative of 1/u is ln|u| + C, where C is the constant of integration.

Therefore, the final solution of the integral is (1/2)ln|1 + x²| + C.

Let us work through the steps:

Step 1:Let u = 1 + x² and then differentiate both sides with respect to x to obtain du/dx. du/dx = 2x

Substitute 2x dx = du into the integral ∫1/(1 + x²) dx to get the integral in terms of u:∫1/u * (1/2x) du = (1/2) ∫1/u du

Step 2:Calculate the antiderivative of 1/u, which is ln|u|. Thus, the final solution is (1/2)ln|1 + x²| + C, where C is the constant of integration. The constant C will vary depending on the initial conditions of the problem.

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