An electron moves in a circular path perpendicular to a uniform magnetic field with a magnitude of 2.00 mT (milli-Tesla). If the speed of the electron is 1.50 x 10^7 m/s, what is the radius of the circular path?

Answers

Answer 1

The electron moves in a circular path with a radius of approximately 0.450 meters under the influence of the perpendicular magnetic field.

The radius of the circular path can be determined using the formula r = mv / (qB)

where,

r is the radius

m is the mass of the electron

v is its velocity

q is the charge of the electron

B is the magnetic field strength

Given:

electron mass (m) = 9.1093837015 × 10^-31 kg

velocity of the electron(v) = 1.50 x 10^7 m/s

electron charge (q) = 1.60217663 × 10^-19

magnetic field strength(B) =2.00 x 10^-3 T

Substituting the values

r = (9.11 x 10^-31 kg) x (1.50 x 10^7 m/s) / ((-1.6 x 10^-19 C) x (2.00 x 10^-3 T))

r ≈ 0.450 meters

The electron moves in a circular path with a radius of approximately 0.450 meters under the influence of the perpendicular magnetic field.

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Related Questions

An object is thrown upward with an initial velocity of 40 m/s. The velocity of the object moving upward is
a.negative and increasing in magnitude.

b.positive and decreasing in magnitude.

c.negative and decreasing in magnitude.

d.positive and increasing in magnitude.

Answers

Answer:

b.positive and decreasing in magnitude.

Explanation:

The kinematics of a body can be calculated by means of the following expression.

\(v_{f}=v_{o}-g*t\)

where:

vf = final velocity [m/s]

vo = initial velocity = 40 [m/s]

g = gravity acceleration = 9.81 [m/s²]

t = time [s]

As we can see from the above equation, the final velocity of a body decreases its initial velocity as time increases. That is, as the body rises, the velocity decreases.

if it takes you 20 joules of work to move a couch 10 meters in 10 seconds, what is the power?

Answers

Answer:

Power = 2 j/s

Explanation:

Power = Work / Time

= 20/10

= 2 j/s

a coin lies submerged at the bottom of a pan of water. does refraction of light from the coin make it appear deeper or shallower than it really is?

Answers

When a coin lies submerged at the bottom of a pan of water, refraction of light from the coin make it appears shallower than it really is.

What is refraction?

Refraction is defined as "the change in a wave's direction as it passes through a medium."

Although light refraction is one of the most frequently seen phenomena, refraction can also occur with sound and water waves.

Due to the fact that light rays emerging from water will immediately turn towards the water's surface. They don't move straight ahead. (Glass experiences the same phenomenon; this is how lenses are produced.)

The bottom of the pan's light beams arc in the direction of the water's surface. As a result, the ray appears to have come from a higher location to you. So it appears to be shallower.

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A 10 kg object is hanging stationary on the end of a vertical spring which has a spring
constant of 250 N/m. What is the elongation of the spring?

Answers

To find the elongation of the spring, we can use Hooke's Law, which states that the force exerted by a spring is proportional to its elongation. The formula for Hooke's law is:

F = -kx

where F is the force, k is the spring constant, and x is the elongation.

In this case, the force is equal to the weight of the object (10 kg), which can be calculated as:

F = m * g

where m is the mass of the object (10 kg) and g is the acceleration due to gravity (9.8 m/s^2).

So, the force can be calculated as:

F = 10 kg * 9.8 m/s^2 = 98 N

Using Hooke's law, we can find the elongation of the spring:

F = -kx

98 N = -250 N/m * x

x = 98 N / 250 N/m = 0.392 m

So, the elongation of the spring is 0.392 m.

_________________________________________________________

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A force of 355 N is applied to an object that accelerates at a rate of 7.8 m/sec2 . What is the mass of the object ?

Answers

Answer:

A force of 355 N is applied to an object that accelerates at a rate of 7.8 m/sec2 . What is the mass of the object ?

Explanation:

How many millimeters of water can dissolve 5g of lead nitrate

Answers

The solubility of lead nitrate is 52 grams per 100 milliliters of water at 0°C. Since the question does not specify the temperature, we will assume it is 0°C.To calculate the number of millimeters of water required to dissolve 5 g of lead nitrate,

we must first calculate the number of milliliters of water required to dissolve 5 g of lead nitrate.52 grams of lead nitrate can dissolve in 100 milliliters of water. So,5 g of lead nitrate can dissolve in x milliliters of water.= (5 g / 52 g) × 100 mL= 9.6 mLTherefore, 5 g of lead nitrate can dissolve in 9.6 mL of water. However, the question is asking for the number of millimeters of water, not milliliters. Since 1 milliliter of water weighs 1 gram,9.6 milliliters of water will weigh 9.6 grams.Thus, 5 g of lead nitrate can dissolve in 9.6 millimeters of water.

main answer:5 g of lead nitrate can dissolve in 9.6 millimeters of water. :52 grams of lead nitrate can dissolve in 100 milliliters of water. So, 5 g of lead nitrate can dissolve in x milliliters of water.= (5 g / 52 g) × 100 mL= 9.6 mLTherefore, 5 g of lead nitrate can dissolve in 9.6 mL of water. However, the question is asking for the number of millimeters of water, not milliliters. Since 1 milliliter of water weighs 1 gram,9.6 milliliters of water will weigh 9.6 grams.Thus, 5 g of lead nitrate can dissolve in 9.6 millimeters of water.

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If we increase the distance traveled when doing work, and keep all other factors the same, what will happen?


The amount of force will go down.

The amount of force will increase.

The amount of work will decrease.

The amount of work will increase.
NO LINKS YOU WILL BE REPORTED,HAVE GREAT DAY

Answers

Answer:

The amount of force will increase

Explanation:

what does the law of conservation of energy state? energy is constantly being created to replace energy that has been lost. energy can be transformed, but it cannot be either created or destroyed. energy disappears each time it is transformed until it all ceases to exist. energy is stored in objects, but it is depleted when the objects are in motion.

Answers

The conservation of energy law similarly holds that energy cannot be created or destroyed.

What exactly is the law of energy conversion?

That's what the fundamental law of thermodynamics says. It is only possible to change the form of energy; it cannot be created or destroyed. This is sometimes known as the rule of energy conversion or perhaps the law of energy conservation.

The "law on energy conservation" was created by whom, and what does it entail?

The two aforementioned principles were unified into one when Albert Einstein published the formula E= mc2 at the start of the 20th century, resulting in the formation of the Conservation Law of Mass-Energy, which asserts that the total quantity of both mass and energy in the universe remains constant.

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what constant acceleration (in ft/s2) is required to increase the speed of a car from 24 mi/h to 56 mi/h in 5 seconds? (round your answer to two decimal places.)

Answers

The constant acceleration required to increase the speed of the car from 24 mi/h to 56 mi/h in 5 seconds is 9.78 ft/s^2 (rounded to two decimal places).

To convert 24 mi/h to ft/s, we multiply by 1.46667 (since 1 mile = 5280 feet and 1 hour = 3600 seconds):
24 mi/h * 1.46667 = 35.2 ft/s

To convert 56 mi/h to ft/s, we do the same:
56 mi/h * 1.46667 = 84.1 ft/s

The change in velocity is:
84.1 ft/s - 35.2 ft/s = 48.9 ft/s

The time is given as 5 seconds.

The constant acceleration required can be found using the formula:
acceleration = change in velocity / time

acceleration = 48.9 ft/s / 5 s
acceleration = 9.78 ft/s^2

Therefore, the constant acceleration required to increase the speed of the car from 24 mi/h to 56 mi/h in 5 seconds is 9.78 ft/s^2 (rounded to two decimal places).

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Are carbon compounds rigid and strong

Answers

yes, but it takes a lot of energy to break all those iconic bonds .

Which type of telescope is known to be difficult to keep aligned Compound Refracting Reflecting Radio

Answers

The refracting telescope uses large lenses. The larger lenses increase the weight of the telescope. The weight of the refracting telescopes makes it difficult for the observer to keep them aligned.

Thus the correct answer is option b, refracting telescopes.

Answer:

Is Reflecting telescope

Explanation:

I took the test

Please help me fast and i brainliest!! Two balls are released from the same height. Ball A is released on the surface of Earth, and ball B is released on the surface of the moon. The mass and net force on each ball are recorded in the table. Net Force (N) Mass (kg) Ball A 19.6 2 Ball B 9.6 6 Ball C 6.6 ? Which statement is correct about the mass of ball C, which is released on the surface of the moon from the same height? The mass of ball C is less than the masses of ball A and ball B. The mass of ball C cannot be determined from the information provided. The mass of ball C is greater than the masses of ball A and ball B. The mass of ball C is greater than the mass of ball A but less than the mass of ball B

Answers

Answer:

If they both start at the same height then most likely that means that each has an intical velocity  and a net force sooooo ball A 19.6

Explanation:

Answer: The mass of ball C is greater than the mass of ball A but less than the mass of ball B.

Describe Newton's contribution's to the Enlightenment

Answers

Answer:

Isaac Newton and John Locke were significant pieces in the enlightenment by applying scientific notions and giving individuals the courage to break away from government. Isaac Newton came up with the scientific study that the universe was subjugated by the force to gravity, distance, and mass.

Isaac Newton's revolutionary achievements in mathematics, physics, and astronomy made a vital contribution to the Enlightenment. English mathematician, physicist, astronomer, alchemist, theologian, and author Sir Isaac Newton PRS.

Our knowledge of the natural world and the operations of the cosmos has been fundamentally altered by his laws of motion and universal gravitation. Modern physics was founded on Isaac Newton's Mathematical Principles of Natural Philosophy and Optics, which also contributed to the development of the scientific method as a technique of learning new things. His work contributed to the replacement of the static, earth-centered Aristotelian view of the cosmos with a dynamic, universe-centered one that was guided by natural laws and mathematical concepts. The focus on reason, evidence, and scientific investigation during the Enlightenment helped establish the groundwork for contemporary science, and Newton's theories and findings were a vital contributor to this movement.

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Atoms can bond together in several different ways. Name three types of chemical bonding. Explain what happens to electrons in a each type of bonding.

Answers

Answer:

Covalent bond

Electrovalent bond

Explanation:

In covalent bond element share electrons

In electrovalent bond element donate electrons

1 point
If there is a surge in the demand for electricity in the UK, which of
these power stations can be used to meet this demand quickly? *
Nuclear
Gas
Wind
Solar
Submit

Answers

Answer:

Option A nuclear

Explanation:

The rate of electricity production in nuclear power plant is much higher as compared to the rate of electricity generation in gas, wind and solar power plants.

Thus, in case where large amount of electricity is to be produced in a short period then one must rely on nuclear power plants.

Therefore, option A is correct

Answer: Option A- Nuclear power station

Explanation: During a sudden increase in demand, Nuclear power stations can be used easily to supply the needed energy as they have an extremely short start up time. This means that the energy can be supplied in a short period of time.

Batteries are recharged by connecting them to a power supply (i.e., another battery) of greater emf in such a way that the current flows into the positive terminal of the battery being recharged, as was shown in Example 12. This reverse current through the battery replenishes its chemicals. The current is kept fairly low so as not to overheat the battery being recharged by dissipating energy in its internal resistance. Suppose the real battery of Figure 1 is rechargeable. What emf power supply should be used for a 0.75 A recharging current?

Answers

The emf power supply should be used for a 0.75 A recharging current is 2.25 V.

What is current?

The current is the stream of charges which flow inside the conductors when connected across the end of voltage.

Given is the battery having 1.5 V open circuit potential and internal resistance of 1 ohm.

From the Ohm's law, V =IR

R = V/I

Here, R is the proportionality constant.

To charge current I = 0.75 A

Voltage V = 0.75A x 1 ohm = 0.75 V

Total potential required is

= 1.5 +0.75

= 2.25 V

Thus, the emf power supply should be used for a 0.75 A recharging current  is 2.25V.

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Which of the following statements are true about conduction? Select all that apply. *
-In most solids, conduction takes place as particles vibrate in place.
-Matter is transferred great distances during conduction.
-Thermal energy is transferred without transfer of matter.
-Conduction can occur between materials that are not touching.

Answers

Answer:

Matter is transferred great distances during conduction. (t think i'm not truly sure)

Explanation:

The direct transfer of energy from one molecule to another is known as conduction. Conduction occurs in solids, liquids, and gases, but it is most effective in solids. Heat transfer by radiation, unlike conduction or convection, does not require any matter.

hope this helps

According to the concept of conduction,matter is transferred great distances during conduction.

What is conduction?

Conduction is defined as a process as a means of which heat is transferred from the hotter end of the body to it's cooler end.Heat flows spontaneously from a body which is hot to a body which is cold.

In the process of conduction,heat flow is within the body and through itself.In solids the conduction of heat is due to the vibrations and collisions of molecules while in liquids and gases it is due to the random motion of the molecules .

When conduction takes place, heat is usually transferred from one molecule to another as they are in direct contact with each other.There are 2 types of conduction:1) steady state conduction 2) transient conduction.According to the type of energy conduction is of three types:

1) heat conduction

2) electrical conduction

3)sound conduction

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1. Se tienen 10 moles de gas nitrógeno molecular: N2 en un recipiente a 400 K. Manteniendo la temperatura a 400 K y las 10 moles en el recipiente se disminuye la presión desde 10 atm a 1 atm para obtener un volumen final del gas de 20 litros. El volumen inicial del gas a. 0,5 litros b. 2 litros c. 100 litros d. 200 litros

Answers

Answer:

B. 2 litros.

Explanation:

De acuerdo con el enunciado, el gas experimenta un proceso isotérmico y se conserva su masa. Asumiendo que el gas se comporta idealmente, tenemos la siguiente relación entre los estados final e inicial:

\(P_{1}\cdot V_{1} = P_{2}\cdot V_{2}\) (1)

Donde:

\(P_{1}, P_{2}\) - Presiones inicial y final, medidos en atmósferas.

\(V_{1}, V_{2}\) - Volúmenes inicial y final, medidos en litros.

Si sabemos que \(P_{1} = 10\,atm\), \(P_{2} = 1\,atm\) y \(V_{2} = 20\,L\), entonces el volumen inicial del gas es:

\(V_{1} = \frac{P_{2}\cdot V_{2}}{P_{1}}\)

\(V_{1} = 2\,L\)

Por lo tanto, la respuesta correcta es B.

Which piece of evidence from the paage bet upport the idea that foret promote rainfall

Answers

"Planting more trees brings rain because plants transpire" is the piece of evidence from the page that support the idea that forest promote rainfall.

What is transpiration?

Water is moved through a plant during transpiration, and it is evaporated from aerial parts of the plant, such as leaves, stems, and flowers. Even though plants need water to survive, only a small portion of the water absorbed by their roots is actually utilised for cellular growth and metabolism.

Transpiration and guttation cause the remaining 97-99.5% to be lost. In most plants, the undersides of the foliage have more of the tiny pores known as stomata that decorate the surface of leaves.

The guard cells that surround the stomata are responsible for opening and closing the pore, as are their stomatal accessory cells. Transpiration occurs through the stomatal apertures and is regarded as a "cost" of the stomata opening, which allows the diffusion of carbon dioxide gas from the atmosphere for photosynthesis.

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Leah is making a chart to compare and contrast renewable and non-renewable resources. Which of the following would best complete the chart? (2 points)

Renewable Resources

Non-renewable Resources

__

Used faster than they can be replaced

Most sources do not emit greenhouse gases

Availability decreases over time

Includes solar power, wind power, and geothermal power

Includes fossil fuels, natural gas, and coal

a. Replaces all current forms of energy
b. New energy is created
c. Cannot be replaced
d. Can be replaced at the same rate or faster than they are used

Answers

Answer:

d. Can be replaced at the same rate or faster than they are used

Explanation:

I just took the test, and its the right answer. Your welcome ✌

Exercise 4 1. Explain what is meant by the limit of proportionality for the extension-load graph of a spring. 2. The unstretched length of a hanging spring is 100 mm. When a stretching force of I N is applied, the total length of the stretched spring is 118 mm. a) Calculate the extension. b) Calculate the total length of the spring if the stretching force is 2 N. Assume that the spring is within the limit of proportionality. 3. Two springs, A and B, are compared by stretching them within the limit of proportionality. For spring A it is found that extension 15 mm/N; force For spring B it is found that extension 20 mm/N. force State which of the two springs is stronger. Explain your answer.​

Answers

1. The limit of proportionality for the extension-load graph of a spring is the maximum point on the graph up to which Hooke's Law is obeyed.

(2a) The total length of the stretched spring when a stretching force of 2 N is applied is approximately 100.1112 mm.

(3) Spring A is stronger because it has greater spring constant.

What is the extension of the spring?

The extension of the spring can be calculated using the following formula:

Extension = Total length of the stretched spring - Unstretched length of the spring

Extension = 118 mm - 100 mm = 18 mm

To calculate the total length of the spring when a stretching force of 2 N is applied, we first need to determine the spring constant (k) using the given information.

k = (Force applied) / (Extension)

k = 1 N / 18 mm

k = 0.0556 N/mm

Now, we can use the following formula to calculate the total length of the stretched spring:

Total length of the stretched spring = Unstretched length of the spring + Extension due to the applied force

Total length of the stretched spring = 100 mm + (k x Force applied)

Total length of the stretched spring = 100 mm + (0.0556 N/mm x 2 N)

Total length of the stretched spring = 100 mm + 0.1112 mm

Total length of the stretched spring = 100.1112 mm

To determine which spring is stronger, we need to compare their spring constants. The spring constant (k) is a measure of the stiffness of a spring and is defined as the force required to produce a unit extension in the spring. It is usually measured in units of N/m or N/mm.

For spring A, the extension is 15 mm/N, which means that the spring constant is:

k(A) = 1 / 15 N/mm = 0.067 N/mm

For spring B, the extension is 20 mm/N, which means that the spring constant is:

k(B) = 1 / 20 N/mm = 0.05 N/mm

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I need the right answer ASAP NO LINKS!!!
This a Science question

I need the right answer ASAP NO LINKS!!!This a Science question

Answers

Models change to accommodate new discoveries.

which physical method of controlling microbial growth applies pressure to water to create steam?

Answers

The physical method of controlling microbial growth that applies pressure to water to create steam is called "autoclaving" or "sterilization by autoclave."

Autoclaving is a widely used method for sterilization in various industries, including healthcare, laboratories, and food processing. It involves subjecting materials or objects to high-pressure saturated steam at elevated temperatures. The combination of pressure and heat effectively kills microorganisms, including bacteria, viruses, fungi, and spores.

Autoclaves consist of a sealed chamber that can withstand high pressures, along with a source of heat and a means to generate steam. The process involves placing the items to be sterilized inside the autoclave chamber and then raising the temperature and pressure to the desired levels. The high-pressure steam penetrates the materials and destroys the microorganisms present, ensuring effective sterilization.

The typical conditions for autoclaving include temperatures ranging from 121 to 134 degrees Celsius (250 to 273 degrees Fahrenheit) and pressures between 15 and 30 pounds per square inch (psi). These conditions are maintained for a specified period, usually around 15 to 30 minutes, depending on the size and nature of the items being sterilized.

Autoclaving is advantageous because it provides a reliable and efficient method for achieving sterility. It can be used to sterilize a wide range of materials, including laboratory glassware, surgical instruments, medical equipment, media and solutions, textiles, and more. The high temperatures and pressure ensure thorough sterilization, and the process is relatively quick compared to other methods.

However, it is important to note that not all materials can be autoclaved, as some may be sensitive to heat or moisture. Additionally, certain biological substances, such as certain types of infectious waste or toxins, may require specialized treatment beyond autoclaving.

Overall, autoclaving is a highly effective method for controlling microbial growth by applying pressure to water to create steam. Its widespread use in various industries is a testament to its reliability and efficiency in achieving sterilization.

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A 20 N crate is held at rest on an incline by a rope that is parallel to the incline as shown on the figure to the right. The incline is 30° above the horizontal. The coefficient of static friction, us, between the crate and the incline is 0.35. 10 a) Draw two free body diagrams for the forces acting on the crate. In the first, indicate the forces pointing along the ramp and in the second, indicate the forces pointing perpendicular to the ramp b) Rank all forces acting on the crate from largest to smallest. c) Write down two separate equations for Newton's second law with static friction: one for forces pointing along the ramp and one for forces pointing perpendicular to the ramp. Do some forces appear in only one of the Newton's law equations? For forces that have some component in both, make sure you break down those force vectors correctly in the equation.

Answers

(a,i) Force acting in opposite direction; (a,ii) The tension force acting in the direction of rope. (b) Normal force, Tension force, Friction force, Force of gravity. (c,1) friction = us*N; (c,2) Force = 0.

(a) 1. For the force pointing along the ramp:

The force of gravity acting downwards (mg)

The normal force acting upwards (N)

The force of static friction acting in the opposite direction of the motion (friction)

(a) 2. For the forces pointing perpendicular to the ramp:

The force of gravity acting downwards (mg)

The normal force acting upwards (N)

The tension force acting in the direction of the rope (T)

b) Largest to smallest:

1. Normal force

2. Tension force

3. Friction force

4. Force of gravity

c) 1. For forces pointing along the ramp: f = friction = us * N

2. For forces pointing perpendicular to the ramp: T - mgsin(30) = ma = 0

The force of gravity appears in both equations and the tension force only appears in the equation for forces pointing perpendicular to the ramp. It is important to note that the force of friction is always pointing opposite to the direction of motion, the force of gravity is always pointing downwards and the normal force is always perpendicular to the surface.

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Question 6The Sun has a mass of about 1.99 x 10^30 kg. A relatively unknownplanet named Earth orbits the Sun with a mean orbital radius of about1.496 x 10^11 meters.Calculate the orbital speed of the Earth, in m/s, as it orbits the Sun

Answers

The formula for calculating the orbital speed of the eqrth as it orbits the sun is expressed as

\(V\text{ = }\sqrt[]{\frac{GM}{R}}\)

Where

G is the gravitational constant whose value is 6.673 x 10^- 11 Nm^2/kg^2

M is the mass of the central body about which the satelite orbits

R is the ardius of orbit of the satelite

From the information given,

M = 1.99 x 10^30 kg

R = 1.496 x 10^11

By substituting these values into the formula, we have

\(\begin{gathered} V\text{ = }\sqrt[]{\frac{6.673\text{ }\times10^{-11}\times1.99\text{ }\times10^{30}}{1.496\text{ }\times10^{11}}} \\ V\text{ = 29793.48 m/s} \end{gathered}\)

The orbital speed of the Earth, in m/s, as it orbits the Sun is 29793.48 m/s

Cobalt (Co) has an atomic mass of 59 and an atomic number of 27. Which statement correctly describes an atom of cobalt?
O A. An atom of cobalt contains more neutrons than protons.
B. An atom of cobalt contains more electrons than protons.
O C. An atom of cobalt contains the same number of neutrons and protons.
O D. An atom of cobalt contains the same number of neutrons, electrons and protons.

Cobalt (Co) has an atomic mass of 59 and an atomic number of 27. Which statement correctly describes

Answers

Answer:

Option A. An atom of cobalt contains more neutrons than protons.

Explanation:

From the question given above, the following data were obtained:

Mass number = 59

Atomic number = 27

Next, we shall determine the number of protons in the atom. This is illustrated below:

Atomic number of an element is simply defined as the number of protons in the atom of the element. Thus,

Atomic number = proton number

Atomic number = 27

Therefore,

Proton number = 27

Next, we shall determine the neutron number. This can be obtained as follow:

Mass number = 59

Proton number = 27

Neutron number =?

Mass number = Proton + Neutron

59 = 27 + Neutron

Collect like terms

Neutron = 59 – 27

Neutron number = 32

Next, we shall determine the number of electrons. This can be obtained as follow:

Since the atom is neutral i.e it has no charge, then, the number of protons and electrons are equal. Thus,

Electron number = Proton number

Proton number = 27

Therefore,

Electron number = 27

Summary:

Mass number = 59

Atomic number = 27

Proton number = 27

Neutron number = 32

Electron number = 27

From the above, we can see that the atom of cobalt contains:

1. More neutrons than protons.

2. The same number of protons and electrons.

Therefore, option A gives the correct answer to the question.

Which object has potential energy?(1 point)
Responses

unlit lightbulb
unlit lightbulb

rock on the ground
rock on the ground

stereo speaker
stereo speaker

can of gasoline

Answers

The object that has potential energy is the can of gasoline.

What is potential energy?

Potential energy is described as the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.

The forms of potential energy includes:

Elastic Potential Energy.Electrical (Electromagnetic) Potential Energy.Gravitational Potential Energy.Nuclear Potential Energy.

Potential energy is described as the energy a system has due to position, shape, or configuration.

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imagine that a continuous random variable X defined on the range [0,1] follows the probability density function p(X=x∣a)={(a+1)xa0​ for x∈[0,1] everywhere else ​. where a>0 is a parameter that controls the shape of the distribution. Answer the following questions; you must include appropriate working. 1. Plot the probability density function of X when a=1/2 and a=2 for x∈[0,1]. 2. Determine the expected value of X, i.e., E[X]. 3. Determine the expected value of 1/X, i.e., E[1/X]. 4. Determine the variance of X, i.e., V[X]. 5. Determine the median of X. (hint: the answers to Q4.2 through Q4.5 will all be functions of a).

Answers

The probability density function of X is plotted for a=1/2 and a=2.

The expected value of X (E[X]) is determined.

The expected value of 1/X (E[1/X]) is determined.

The variance of X (V[X]) is determined.

The median of X is determined.

When a=1/2, the probability density function of X is given by p(X=x∣a)=((1/2)+1)x(1/2)^0=(3/2)x for x∈[0,1]. When a=2, the probability density function becomes p(X=x∣a)=(2+1)x^2=3x^2 for x∈[0,1]. To plot the probability density function, we can assign different values of x within the range [0,1], calculate the corresponding probabilities using the given formulas, and plot the points on a graph.

The expected value of X (E[X]) is calculated by integrating the product of X and its probability density function over the range [0,1]. For a=1/2, E[X] = ∫(x * (3/2)x) dx from 0 to 1. For a=2, E[X] = ∫(x * 3x^2) dx from 0 to 1. By evaluating these integrals, we can determine the expected values.

The expected value of 1/X (E[1/X]) is calculated similarly to E[X], but instead of integrating X, we integrate 1/X using the respective probability density functions for different values of a.

The variance of X (V[X]) can be computed by taking the second moment of X (E[X^2]) minus the square of the first moment (E[X]) squared. V[X] = E[X^2] - (E[X])^2. By calculating E[X^2] using the probability density function and the expected values obtained in step 2, we can determine the variances for different values of a.

The median of X is the value of X such that the cumulative distribution function (CDF) is equal to 0.5. To find the median, we integrate the probability density function from 0 to the median value and set it equal to 0.5. Solving for the median provides its value in terms of the parameter a.

Learn more about probability density

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A circuit with 0.7 A running through the battery and two 16 Ω resistors in parallel. What is the voltage of the battery?

Answers

Answer:

Below

Explanation:

The two PARALLEL resistors equal:    1 / (1/16 + 1/16) = 8 Ω

V = IR        =    .7 (8) = 5.6 v

looking at the image above, which example is creating a sound wave with the shortest wavelength?

looking at the image above, which example is creating a sound wave with the shortest wavelength?

Answers

Examples w and y the first one
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