An electron moves at 0.130 c as shown in the figure (Figure 1). There are points: A, B, C, and D 2.10 μm from the electron.
a) Find the magnitude of the magnetic field this electron produces at the point A .
b) Find the magnitude of the magnetic field this electron produces at the point B .
c) Find the magnitude of the magnetic field this electron produces at the point C .
d) Find the magnitude of the magnetic field this electron produces at the point D
Answers
Hi there!
We can use Biot-Savart's Law for a moving particle:
[tex]B= \frac{\mu_0 }{4\pi}\frac{q\vec{v}\times \vec{r}}{r^2 }[/tex]
B = Magnetic field strength (T)
v = velocity of electron (0.130c = 3.9 × 10⁷ m/s)
q = charge of particle (1.6 × 10⁻¹⁹ C)
μ₀ = Permeability of free space (4π × 10⁻⁷ Tm/A)
r = distance from particle (2.10 μm)
There is a cross product between the velocity vector and the radius vector (not a quantity, but specifies a direction). We can write this as:
[tex]B= \frac{\mu_0 }{4\pi}\frac{q\vec{v} \vec{r}sin\theta}{r^2 }[/tex]
Where 'θ' is the angle between the velocity and radius vectors.
a)
To find the angle between the velocity and radius vector, we find the complementary angle:
θ = 90° - 60° = 30°
Plugging 'θ' into the equation along with our other values:
[tex]B= \frac{\mu_0 }{4\pi}\frac{q\vec{v} \vec{r}sin\theta}{r^2 }\\\\B= \frac{(4\pi *10^{-7})}{4\pi}\frac{(1.6*10^{-19})(3.9*10^{7}) \vec{r}sin(30)}{(2.1*10^{-5})^2 }[/tex]
[tex]B = \boxed{7.07 *10^{-10} T}[/tex]
b)
Repeat the same process. The angle between the velocity and radius vector is 150°, and its sine value is the same as that of sin(30°). So, the particle's produced field will be the same as that of part A.
c)
In this instance, the radius vector and the velocity vector are perpendicular so
'θ' = 90°.
[tex]B= \frac{(4\pi *10^{-7})}{4\pi}\frac{(1.6*10^{-19})(3.9*10^{7}) \vec{r}sin(90)}{(2.1*10^{-5})^2 } = \boxed{1.415 * 10^{-9}T}[/tex]
d)
This point is ALONG the velocity vector, so there is no magnetic field produced at this point.
Aka, the radius and velocity vectors are parallel, and since sin(0) = 0, there is no magnetic field at this point.
[tex]\boxed{B = 0 T}[/tex]
Related Questions
The normal force R that a car makes with the ground is 5000N. What is the maximum force of static friction that the car's wheels can experience with the flat concrete road? What is the force of friction that the wheels experience when the car is moving?
Answers
The maximum force of static friction that the car's wheels can experience with the flat concrete road is μ×5000 N.
The force of friction that the wheels experience when the car is moving is less than maximum force of static friction.
What is static friction?
The definition of static friction is: The resistance people feel when they attempt to move a stationary object across a surface without actually causing any relative motion between their body and the surface they are moving the object across.
As the normal force = 5000 N.
The maximum force of static friction = μ×5000 N.
The force of friction that the wheels experience when the car is moving is less than maximum force of static friction.
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What is the Big-Bang Theory?
Answers
The Big Bang theory is the prevailing cosmological model that explains the origins of the universe. According to the theory, the universe began as a singularity, a hot and infinitely dense point, approximately 13.8 billion years ago. From this singularity, the universe expanded and cooled, eventually leading to the formation of subatomic particles, atoms, stars, and galaxies. The theory also states that the universe is still expanding and it's getting cooler and larger.
The theory was first proposed by Belgian priest and physicist Georges Lemaître in 1927 and later developed by Edwin Hubble's observations of the redshifts of distant galaxies in the 1920s and 1930s. The theory has been extensively tested and supported by a wide range of observational evidence, including cosmic microwave background radiation and the large-scale structure of the universe.
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Answer:
The Big-Bang Theory is the prevailing cosmological model for the universe from the earliest known periods through its subsequent large-scale evolution. The model describes how the universe expanded from an initial state of high density and high temperature, and offers a comprehensive explanation for a broad range of phenomena, including the abundance of light elements, the cosmic microwave background, large scale structure and Hubble's law. According to the Big-Bang Theory, the universe was once in an extremely hot and dense state which expanded rapidly. As it cooled, the first subatomic particles formed and then simple atoms, eventually leading to the formation of stars and galaxies. The Big-Bang Theory is supported by a wide range of scientific observations and provides a comprehensive explanation for the structure and evolution of the universe.
Before attempting to answer these question, draw a copyof this diagram. All of the locations indicated by letters areinside the wire.
(a) On your diagram, show the electric field at the locationsindicated, paying attention to relative magnitude.
(b) Carefully draw pluses and minuses on your diagram to show theapproximate surface charge distribution that produces the electricfield you drew. Make your drawing show clearly the differencesbetween regions of high surface charge density and regions of lowsurface charge density.
Use your diagram to answer the following question:
Which of the following statments about this circuit aretrue?
O There is excess charge on the surface ofthe wire near the batteries, but nowhere else.
O There is no excess charge on the surfaceof the wire.
O The magnitude of the electric field insidethe wire is larger at location G than at location C.
O There is some excess negative charge on the surface of the wire nearlocation B.
O The magnitude of the electric field is thesame at locations G andC.
O The electric field at locationD points to the left.
O Because the current is not changing, thecircuit is in static equilibrium.
O Inside the metal wire the magnitude of theelectric field is zero.
O The electric field points to theleft at location A.
Answers
There is some excess negative charge on the surface of the wire near location B. Because the current is not changing, the circuit is in static equilibrium. There is no excess charge on the surface of the wire.
What is the name for extra electrical charge?Static electricity is the buildup of extra electric charge on an object. Gauss's law tells us that in an equilibrium state, any excess charge on a conductor travels to the surface. The extra charges will disperse evenly throughout the conductor's outside surface, causing the electric field within to be zero.
What transpires when an electric field is applied to a conductor?Electrons are free to move in a conductor. If they are subjected to a force, they will move faster in that direction. If an external electric field is applied to a conductor, a force F = -eE results. When the field is present, electrons move faster and gain momentum in the opposite direction.
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What part of the sweating process promotes cooling?
wiping sweat from the surface of the skin
condensation of liquid sweat on the skin
liquid (sweat) sitting on the skin’s surface
evaporation of liquid sweat from the skin
Answers
Answer: Condensation of liquid sweat on the skin
Explanation:
Plane Mirror Question 2 (Grade 10 Science)
Answers
Answer:
Explanation:
The index of refraction (n) of a gem can be calculated using the formula:
n = c / v
where c is the speed of light in a vacuum (approximately 3 x 10^8 m/s) and v is the speed of light in the gem.
In this case, we know that the speed of light in the gem is l.q5 x 10^8 m/s. So, we can plug this value into the formula and calculate the index of refraction:
n = c / v = (3 x 10^8 m/s) / (l.q5 x 10^8 m/s) = 3 / l.q5
The value of n is a dimensionless number and it's usually between 1 and 2.
It's not possible to identify the gem using the index of refraction alone. There are many gems with similar indexes of refraction. Index of refraction alone is not enough to identify a gem. The gemstone's color, brilliance, and other physical and optical properties must be taken into account to identify it.
The index of refraction of the unknown gem is 1.54.
What is index of refraction?The index of refraction measures how a light beam bends when it travels through different media.
The refractive index is calculated by dividing the speed of light at a given wavelength in in vacuum space by its speed of light in that medium.
The speed of light in that gem = 1.95 × 10⁸ meter/second
The index of refraction of the unknown gem is = (speed of light in vacuum/speed of light in that gem)
= (3 × 10⁸ meter/second)/(1.95 × 10⁸ meter/second)
= 1.54.
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The centrifugal force exerted on rotating turbine blades varies directly as the square of velocity. If the centrifugal force of 1.21×106 N is acting on the blades that move at 550 m/sec, find the instantaneous rate of change of the centrifugal force as the velocity increases to 830 m/sec. Round the answer to the nearest whole number.
Answers
The instantaneous rate of change of the centrifugal force as the velocity increases to 830 m/sec is 4.14×106 N/sec.
What is velocity?
Velocity is a measure of the rate of change of the position of an object over time. It is a vector quantity, meaning it has both direction and magnitude. Velocity is determined by dividing the displacement of the object by the time it took to get there.
The centrifugal force exerted on rotating turbine blades is directly proportional to the square of velocity, such that F = kv2, where k is a constant. Therefore, the rate of change of the centrifugal force with respect to the velocity (dF/dv) can be expressed as:
dF/dv = 2kv
Substituting the values given, we have
dF/dv = 2(1.21×106 N/[550 m/sec]2) × 830 m/sec
dF/dv = 4.14×106 N/sec
Therefore, the instantaneous rate of change of the centrifugal force as the velocity increases to 830 m/sec is 4.14×106 N/sec.
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Germicidal lamps are used to sterilize tools in biological and medical facilities. One type of germicidal lamp is a low-pressure mercury discharge tube, similar to a fluorescent lightbulb, that has been optimized to emit ultraviolet light with a wavelength of 254 nm. A 15-mm-diameter, 25-cm-long tube emits 4.5 W of ultraviolet light. The mercury vapor pressure inside the tube is 1.0 Pa at the operating temperature of 40?C.
Part A
On average, how many ultraviolet photons does each mercury atom emit per second?
Express your answer using two significant figures.
Part B
The lifetime of the excited state in mercury is a rather long 120 ns. On average, how much time does a mercury atom spend in the excited state?
Express your answer to two significant figures and include the appropriate units.
Answers
Answer of part A and Part B is given below.
What is wavelength?Wavelength is a measure of the distance between two successive crests or troughs on a wave. It is measured in the same physical units as the length, such as meters (m) or feet (ft). Wavelength is most commonly used to describe light waves, but it can also be applied to sound waves, water waves, and other types of waves. Wavelength is inversely related to the frequency of a wave, meaning that waves with shorter wavelengths have higher frequencies. In optics, the term "wavelength" is used to describe the frequency of visible light, which ranges from 380 to 780 nanometers.
Part A
On average, each mercury atom emits 6.2x10^7 ultraviolet photons per second.
Part B
The average time that a mercury atom spends in the excited state is 12 µs.
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The magnetic force on a charged particle is in the direction of its velocity if a never
b. it is moving in the direction of the field c.it is moving perpendicular to the field d. it is moving in some other direction
Answers
b. it is moving in the direction of the field
When a charged particle is moving in a magnetic field, it experiences a force called the Lorentz force. The direction of this force is perpendicular to the both, the velocity of the particle and the magnetic field. If the velocity of the particle is in the same direction as that of the magnetic field, the Lorentz force is in the direction of the velocity of the particle. If the velocity of the particle is perpendicular to the magnetic field, the Lorentz force is also perpendicular to the velocity of the particle.
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When you slide a box across the floor what force must your push be stronger than? 1. Normal force 2. Friction force 3. Gravity 4. Air resistance
Answers
The force that must be stronger than when sliding a box across the floor is the friction force. Friction is the resistance of motion when two objects rub together.
What is resistance ?
Resistance is the opposition to the flow of electrons or other particles. It is measured in ohms, and is the ratio between voltage and current in an electrical circuit.
Resistance is a fundamental property of materials and is related to the amount of energy needed to push electrons through them. It is also affected by temperature, humidity and other environmental factors. Resistance is an important factor in electrical engineering and is vital for determining the power and efficiency of electrical systems.
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A uniformly charge d insulating rod of length 14.0cm is bent into the shape of a semicircle as shown in Figure. The rod has a total charge of −7.50μC. Find (a) the magnitude and (b) the direction of the electric field at O, the center of the semicircle.
Answers
The magnitude and (b) the direction of the electric field at O, the center of the semicircle is E = 2.16 × 10⁷ N/C and direction is Left.
Each location in space where a charge exists in any form can be considered to have an electric field attached to it. The electric force per unit charge is another name for an electric field. The electric field's equation is given as E = F / Q.
Due to symmetry,
Ey = ∫ dEy = 0,
and E¸ = − ∫ dE sin θ
= −ke∫ dq sinθ/ r2
where
dq=λds = λrdθ;
the component Ex is negative because charge q = -750µC,
causing the net electric field to be directed to the left.
Ex = Κeλ/r ∫ Sinθ
= - (Keλ) (- Cos θ) / r
= -2Keλ / r
where λ and r = L/ π.
Thus,
Ex = 2Ke |q|Π / L²
= [- 2(8.99 × 10⁹ N. m²/С²)(7.50 × 10 С)π] / (0.140 m)2
Ex = -2.16 × 10⁷ N/C
(a) magnitude E = 2.16 × 10⁷ N/C
(b) the direction of the electric field at O, the center of the semicircle is Left.
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8
unit 1
Which of the following best describes on ston
protons, neutrons, and elections all in the cont
B. a core of negatively and positely chared parts
Surrounded by nextral particles
c. a core
surrounded
of positive and neatral particles
by negative particles
D. acore of elections and neations surtou
by protons.
Answers
Answer: C.
Explanation: The core or Nucleus of an atom contains Protons and Neutrons. A proton has a +1 charge while a Neutron is a Neutral or 0 charge. Electrons orbit the Nucleus and have a -1 charge.
Read the passage.
At the sound of the gun, the runners' legs began to
cross the starting line in a blur, and their bodies surged
forward as if propelled by unseen engines. The lanes
were runways, and the runners could take flight at any
moment. But they stayed on earth, their feet drumming
the ground in an uneven staccato that reverberated in
the chests of the cheering crowd that choked the fence
along the track.
Which statement best describes the use of diction in
this passage?
O The author uses several words with negative
connotations.
O The author uses a variety of specific and interesting
verbs.
O The author uses a number of words that are
informal.
O The author uses a variety of specific and unusual
adjectives.
Answers
The author uses a variety of specific and interesting verbs, 2nd option.
What is a diction?Diction refers to the choice and use of words in speech or writing. It can also refer to the style or manner of speaking or writing, including the level of formality, the choice of vocabulary, and the grammatical structures used. In literature, diction is an important aspect of a writer's style, and can be used to create a certain tone or atmosphere in a text.
Formal diction, slang diction, informal diction, concrete diction, colloquial diction, and abstract diction are all examples of diction. A good diction should have words that are accurate and easy to understand. The writer used interesting verbs like "surged" and "choked' in "choked the fence" etc.
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Answer:
B
Explanation:
Chen displayed the results of her experiment in the graph that is show below.
What is the dependent variable in her experiment?
A. time (days)
B. duckweed genetics
C. amount of duckweed
D. different water pH levels
Answers
The correct answer is C. amount of duckweed.
What is independent variables?Independent variables are variables that can be manipulated or changed to observe their effects on a dependent variable. In other words, they are the input of a system. Examples of independent variables include temperature, time, and concentration. These variables are independent of each other and can be changed simultaneously or individually to observe their effects on the outcome.
The dependent variable in Chen's experiment is the amount of duckweed, which is represented on the y-axis of the graph. The independent variables in this experiment are the different water pH levels, which are represented on the x-axis. By plotting the amount of duckweed against the different water pH levels, Chen was able to analyze the effect of the different pH levels on the growth of duckweed.
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Because the t procedures are robust, the most important condition for their safe use is that
the population standard deviation σ is known.
the data can be regarded as an SRS from the population.
the population distribution is exactly Normal.
Answers
Because the t procedures are robust, the most important condition for their safe use is that the data can be regarded as an SRS from the population.
The fact that we have three possibilities is the most crucial requirement for their safe use. There are at least 15 samples. The distribution of the population is quite normal. The information can be viewed as a SRS from the well-known ship, thus we need to determine the best course of action. So, only small sample sizes are used when the t procedure is needed. In order to ensure that the best condition sample is chosen at random, these three The samples have a minimum of 15. Therefore, the data in this case can be viewed as a representative sample of the population. So here the answer will be the data can be regarded as an SRS from the population.
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. Johnathan road his bicycle up a hill at a velocity of 17.15 m/s. Johnathan and his bicycle had
a combined mass of 88 kg. What was the height of the hill?
Answers
The height of the hill is 15 m.
What is the height of the hill?
The height of the hill is calculated by applying the principle of conservation of energy as shown below.
Kinetic energy at the bottom of the hill = Potential energy at the top of the hill
mgh = ¹/₂mv²
gh = ¹/₂v²
h = ( v² ) / ( 2g )
where;
v is the velocity of Johnathang is acceleration due to gravityh = ( v² ) / ( 2g )
h = ( 17.15² ) / ( 2 x 9.8 )
h = 15 m
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what is the effect on the color of a cloud when it contains an abundance of large droplets?
Answers
Large droplets in a cloud will scatter lower frequency light. The cloud will therefore seem reddish.
The term "hygroscopicity" refers to how much water an aerosol absorbs under a particular set of environmental conditions. Inorganic salts are the species that are most hygroscopic in the atmosphere. However, due to advantageous hydrogen-bonding interactions with water, oxygenated organic compounds can also be hygroscopic. Surface-active organic species further promote hygroscopicity by lowering surface tension. Not only can oxidation reactions in the atmosphere significantly contribute to increasing hygroscopicity by adding oxygen scattering, but they may also have an impact on how surface material is partitioned, which in turn affects cloud formation by causing changes in surface tension.
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Calculate the value of ψ2pz2 at r = a0 for θ = 0 (z axis) and for θ = 90° (xy plane)
Answers
0 is the correct answer .
What is angle ?
In Euclidean geometry, an angle is a figure formed by two rays, called the sides of the angle, that share a common endpoint called the vertex of the angle. The angle formed by two rays is in the plane containing the rays. These are called dihedral angles. Two intersecting curves can also define an angle. This is the angle of the ray tangent to each curve at the point of intersection.
Angle is also used to indicate a measure of angle or rotation. This measure is the ratio of the arc length to the radius of the circle. In geometric angles, arcs are centered at vertices and bounded by edges. For rotation, the arc is centered around the rotation and surrounded by all other points and its image by rotation.
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1. A roller coaster cart of mass m = 341 kg starts
stationary at point A, where h1 = 23.3 m and
a while later is at B, where h2 = 9.3 m.
The acceleration of gravity is 9.8 m/s^2
2.What is the speed of the cart at B, ignoring
the effect of friction?
Answer in units of m/s. Answer in units of
m/s.
Answers
The speed of the cart at B is 16.56 m/s (ignoring the effect of friction).
What is law of conservation of energy?Energy cannot be created or destroyed, according to the law of conservation of energy. However, it is capable of change from one form to another. An isolated system's total energy is constant regardless of the types of energy present.
According to conservation of energy:
decrease in potential energy = increase in kinetic energy
341 × 9.8 × 23.3 - 341 × 9.8 × 9.3 = 1/2 × 341 ×v²
v² = 2 × 9.8 × (23.3 - 9.3)
v = 16.56 m/s.
Hence, the speed of the cart at B is 16.56 m/s.
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Is the following sentence true or false? A frame of reference is not necessary to describe motion accurately and completely.
Answers
The following sentence A frame of reference is not necessary to describe motion accurately and completely is False.
Why a frame of reference is necessary to describe motion accurately ?A frame of reference is necessary to describe motion accurately as A set of objects that are stationary with respect to one another is referred to as a frame of reference. An abstract coordinate system and the collection of physical reference points which uniquely fix (locate and orient) the coordinate system and standardize measurements inside that frame are generally referred to as a frame of reference (or reference frame).To know more about frame of reference visit
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If, at a given time, the position of a subatomic particle is precisely known, then
a. its velocity cannot be precisely known
b. the time over which it was measured cannot be precisely known.
c. the particle will disappear
d. no other particles can have the same position
Answers
If, at a given time, the position of a subatomic particle is precisely known, then no other particles can have the same position.
What is particles?
Particles are the smallest and most fundamental units of matter. They are the building blocks of all matter and are composed of one or more atoms. Particles are classified into two broad categories: subatomic particles, which are particles that are smaller than an atom and make up the structure of an atom, and atomic particles, which are particles that can form atoms. Subatomic particles include protons, neutrons, and electrons, while atomic particles include ions, atoms, and molecules. Particles interact with other particles through forces such as the strong nuclear force, electromagnetic force, and weak nuclear force. Particles can also exist in a variety of states, including solid, liquid, and gas.
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You examine the fine print in a legal contract with a magnifying glass of focal length 5.0 cm.
A.) How far from the lens should you hold the print to see a final virtual image 30 cm from the lens (at the eye's near point)?
*The answer is not 6 cm*
B.) Determine the angular magnification of the magnifying glass.
Answers
The focal length is 4.28cm and the magnification is 7.
What is focal length ?
A lens's focal length is established when it is focused at infinity. We can determine the magnification—how large individual elements will be—and the angle of view—how much of the picture will be captured—by knowing the focal length of the lens. The angle of view is smaller and the magnification is greater the longer the focal length.
What is angular magnification ?
The ratio between the angle that the image of an object at an unaided eye or without the apparatus subtends and the angle that the image subtends at the microscope is known as the angular magnification of the object.
We have the lens equation
1/ f = 1/ u = 1/ V
Here the image is virtual
so V = - 30
1/ f = 1/ u - 1/ v
1/ 5= 1/ u -1/ 30
1/5 + 1/ 30 = 1/ u
u = 4.28cm
magnification
m = -v/u
= - (-30)/ 4.28
= 7
Therefore, the focal length is 4.28cm and the magnification is 7.
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1. Calculate the ratio of Jupiter's mass to the total mass of the Galilean moons.
Express your answer using two significant figures.
Answers
The jupiter's mass=1.898×10^27 kg , In 2 significant figures =1.9×10^27 kg The total mass of the Galilean moons =3.93×10^23 .
What does Total mass means?
Total mass is the sum of all the individual masses of the components within a system. It is a measure of the total amount of matter within the system, and is typically expressed in units such as kilograms, pounds, or grams. Total mass can be used to calculate the total amount of energy that is stored in a system, and is an important quantity in physics, chemistry, and materials science.
What does Material Science means?
Material Science is the study of the properties and characteristics of materials and their applications in engineering and technology. It is an interdisciplinary field that involves physics, chemistry, and engineering. It is also known as Materials Science and Engineering and encompasses the study of the structure and behavior of materials at various scales, from the atomic and molecular level to the macroscopic and microscopic scale.
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The moral quality of the will that voted the nation dry had its origin in a moral and social source. It
was an honest desire to protect human life. This wish made concrete and appealing through the lives
of women and children…As the race has evolved, womanhood and childhood have come to occupy
more commanding positions. Today in the United States the moral sense of the people puts them
first. What is good for them should become a law. So the voters were led to believe and so they
acted. Men and women merely said, The liquor business is a menace to our women and children.
Let us get rid of it...".…Salvation Army leaders, social workers, district nurses, Prohibition officers,
child welfare organizations, and others who are in close observance of social conditions have
repeatedly declared that no other law has worked so great a revolution in social welfare as has
Prohibition... Nearly one hundred million dollars of funds once spent to cure the harm done by the
saloon is now expended in fresh air work, free dental clinics, prematurity care, district nursing.
hospitalization, and other forms of work.…
Summarize the main idea
Answers
A moral and social wellspring was the source of the moral quality of the vote that dried up the country.Protecting human life was a sincere desire.The lives of women and children gave this wish a tangible and compelling form.
What lessons can be learned from Prohibition?A moral and social wellspring was the source of the moral quality of the vote that dried up the country.Protecting human life was a sincere desire.The lives of women and children gave this wish a tangible and compelling form.Six Things About Prohibition We Can Learn.Prohibition Depends on Interest Groups.People who would not otherwise commit crimes are made criminals by prohibition.As a result of prohibition, criminals have access to markets.Prohibition diverts resources from law enforcement and raises the risks of already dangerous activities.For the purpose of preventing the "scourge of intoxication," Prohibition was put into place.However, it had unforeseen effects, such as an increase in organized crime linked to the illicit manufacturing and sale of alcohol, a rise in smuggling, and a decrease in tax revenue.To learn more about Prohibition refer
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need help please answear with an easy and simple answer
Answers
The acceleration of the car is - 4.0m/s². Hence, option (B) is correct.
What is acceleration?Acceleration is rate of change of velocity with time. Due to having both direction and magnitude, it is a vector quantity. Si unit of acceleration is meter/second² (m/s²).
Initial velocity of the car: u = + 65 m/s.
Final velocity of the car: v = + 45 m/s.
Time interval: t = 5 seconds.
Hence, acceleration of the car = change in velocity/time interval
= (v - u)/t
= ( +45 - 65)/5 m/s²
= - 20/5 m/s²
= - .0m/s².
So, acceleration of the car is - 4.0m/s².
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A contour map is shown for a function f on the square R = [0, 8] ⨯ [0, 8]. (a) Use the Midpoint Rule with m = n = 2 to estimate the value of f(x,y) dA. R (Round your answer to the nearest integer.) 1952 (b) Estimate the average value of f. (Round your answer to one decimal place.) 30.5 the answers is right. but I don't know how to get those answers so would you please calculate it with dealis how you get those numbers
Answers
(a) The estimate of the definite integral using the Midpoint Rule with m = n = 2 is 1952
(b) The estimate of the average value of f is 30.5.
The Midpoint Rule formula for approximating the definite integral is:
∫∫f(x,y)dA ≈ (A/mn) ∑∑f(x_i, y_j) where,
A is the area of the squarem and n are the numbers of sub-rectangles in the x and y directions respectivelyx_i and y_j are the midpoints of the sub-rectanglesf(x_i, y_j) is the function evaluated at the midpoint of the sub-rectangle.In this case, A = 64, m = n = 2. So we can compute the function value at the midpoint of each sub-rectangle and multiply it by the area of the sub-rectangle. The midpoints of the sub-rectangles are located at (2,2), (2,6), (6,2), and (6,6).
∫∫f(x,y)dA ≈ (64/4) [ f(2,2) + f(2,6) + f(6,2) + f(6,6) ] = (64/4) [ 1952 ] = 1952
(a) Use the Midpoint Rule with m = n = 2 to estimate the value of f(x,y) dA. R (Round your answer to the nearest integer.) 1952
(b) (1/A) ∫∫f(x,y)dA
So in this case it would be (1/64) * 1952 = 30.5
Estimate the average value of f. (Round your answer to one decimal place.) 30.5
Therefore, the estimate of the definite integral using the Midpoint Rule with m = n = 2 is 1952, and the estimate of the average value of f is 30.5.
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the figure (figure 1) is an energy-level diagram for a simple atom.
Answers
The diagram shows the possible energy levels that an atom can occupy. The atom is assumed to have two electrons, shown by the two distinct circles.
What is atom?
Atom is a free and open-source text editor created by GitHub that works on the three major operating systems; Windows, Mac and Linux. It is a highly customizable text editor that can be used for coding, writing and editing. It offers a wide range of features such as syntax highlighting, multi-cursor editing, automatic indentation, and auto-completion.
There are two main energy levels, the ground state and the excited state. The ground state is the lowest energy level, and the excited state is the highest energy level that the atom can occupy. In between these two levels are the intermediate energy states, which the electrons can transition between.
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from the following list, select the characteristics of a refrigerator. (select all that apply.) multiple select question. receive heat from a low-temperature reservoir receive heat from a high-temperature reservoir reject heat to a low-temperature reservoir reject heat to a high-temperature reservoir
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A refrigerator that accepts heat from a low-temperature reservoir also rejects heat to the same reservoir.
What is a refrigerator?A refrigerator is an open system that moves heat from a closed space to a warmer location, typically the kitchen or another room. By removing the heat from this area, the temperature drops, allowing food and other items to remain cool.The primary purpose of a refrigerator is to keep food cold. Cold temperatures keep food fresher for longer. The basic idea behind refrigeration is to slow down the activity of bacteria (which is present in all food) so that the bacteria take longer to spoil the food.The main principles of the refrigeration process, or cycle, are the absorption of the amount of heat required for the change of state from a liquid to a vapor by evaporation and the release of that amount of heat required for the change of state from a vapor back to the liquid by condensation.To learn more about refrigerator refer to :
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Daniel scores 68,84,76 and 80 in four test. what mark should he score in the fifth test so that his average mark for the five test would be 78.
(I) what was his median score in the five test
Answers
Answer
68+84+76+80+x / 5 =78
x= it is value of his result in 5th test
x=82
Explanation:
Then you put all value from smallest to the biggest
68,76,80,82,84
median = 80
Each contour line as you go inland
represents ground that is at a constant
elevation 5 meters higher than the
previous contour.
a) At what points on the map are there
steep cliffs? Show at least three
places.
b) There are two high areas, label the
How high are they?
Mark a straight-line path to climb
from sea level to the high point B
with the most gentle slope.
d) You are interested in how much work
it takes to lift your body mass from
sea level to the B peak. If you follow
the path you chose in part C will
you minimize the amount of work to
climb to the top, or will it make no
difference?
Answers
Each contour line as you go inland represents ground that is at a constant
elevation 5 meters higher than the previous contour are:
a) Steep cliffs can be found at points A, D, and F on the map.
b) High area A is 35 meters above sea level and high area B is 50 meters above sea level.
c) The path from sea level to high point B with the most gentle slope would be to follow the contour lines from sea level upwards in a spiral pattern, starting at point A and ending at point B.
d) Following the path in part C will minimize the amount of work to climb to the top, as it follows the contour lines which represent the most gentle slopes.
What is contour line?
A contour line is a line drawn on a map that connects points of equal elevation, such as the peaks and valleys of a landscape. Contour lines are used to show the shape of the land, which can help map-readers to understand the features of the terrain and the change in elevation of the landscape.
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Electrostatic precipitators use electric forces to remove pollutant particles from smoke, in particular in the smokestacks of coal-burning power plants. One form of precipitator consists of a vertical, hollow, metal cylinder with a thin wire, insulated from the cylinder, running along its axis (Figure 1). A large potential difference is established between the wire and the outer cylinder, with the wire at lower potential. This sets up a strong radial electric field directed inward. The field produces a region of ionized air near the wire. Smoke enters the precipitator at the bottom, ash and dust in it pick up electrons, and the charged pollutants are accelerated toward the outer cylinder wall by the electric field. Suppose the radius of the central wire is 80.0 um, the radius of the cylinder is 14.0 cm, and a potential difference of 50.0 kV is established between the wire and the cylinder. Also assume that the wire and cylinder are both very long in comparison to the cylinder radius.
What is the magnitude of the electric field midway between the wire and the cylinder wall?
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The dielectric constant of water, also known as the relative permittivity of water, is approximately 80.
What is dielectric constant?The dielectric constant, also known as the relative permittivity, is a measure of a material’s ability to resist the flow of electric current when electric field is applied. It is a ratio of the amount of electric field needed to make a material conduct electric current compared to that of a vacuum. The higher the dielectric constant of a material, the more electric field is needed to make it conduct electric current. Common materials with high dielectric constants include glass, plastics, rubber, and water.
This is the ratio of the electric field of water to the electric field of a vacuum, which is calculated by dividing the speed of light in a vacuum (3.00 × 10^8 m/s) by the speed of light in water (2.26 × 10^8 m/s). This ratio indicates that the electric field of water is 80% of the electric field of a vacuum, meaning that the dielectric constant of water is 80.
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