Physics College

## Answers

**Answer 1**

The woman will need to exert 14 N of **force **and 2 W of power over a distance of 10 meters in 70 seconds to move the basket of grapes.

How can force be used to detect mass?

Hence, the value of mass is obtained by dividing the applied force by the rate of **acceleration **of a moving body. As one newton of force is needed to move one kilogram of mass one meter, the mass obtained will be in kilograms.

The equations of work and **power**, which are defined as follows, must be used to address this issue.

work = force * distance * cos(theta)

power = work / time

power = work / time

work = power * time

work = 2 W * t

work = force * distance * cos(theta)

2 W * t = 14 N * 10 m * cos(0)

cos(0) = 1, so we can simplify the equation to:

t = (14 N * 10 m) / (2 W)

t = 70 s

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## Related Questions

Suppose the top surface of the vessel in the figure is subjected to an external gauge pressure P2 2-Y (a) Derive a formula for the speed, vi, at which the liquid flows from the opening at the bottom into atmospheric pressure, PA. Assume the velocity of the liquid surface, V2, is approximately zero. (Use PA for PA, P2 for P2, v2 for V2, y1 for y1, y2 for y2, rho for rho and g for the acceleration due to gravity, as necessary.) b) If P2-0.85 atm and y2-y1-2.1 m, determine vi for water m/s

### Answers

Therefore, the liquid enters **atmospheric pressure** at a rate of 6.32 m/s from the bottom hole.

What is gauge pressure defined as?

The pressure measured in relation to the surrounding atmospheric pressure is known as **gauge pressure**. A diaphragm sensor can be used to measure gauge pressure, with one side of the diaphragm exposed to the pressure medium that has to be measured and the other exposed to the surrounding atmospheric pressure.

Why do we need gauge pressure?

We need **pressured **water or air to move through our water tanks and systems, which allows them to work. You may check for mistakes in your tanks and systems by using a pressure gauge to measure the force of a pressure inside the water or the air.

(A) The relationship between a fluid's pressure, velocity, and height in a moving stream can be determined using the Bernoulli's equation. The Bernoulli's equation can be applied in this situation between two places in the fluid stream, one at the vessel's bottom opening and the other at the liquid's surface. Assuming that v2, the velocity of the liquid surface, is close to zero, the following sentence can be written:

P1 + 1/2 * ρ * v1^2 + ρ * g * y1 = P2 + 1/2 * ρ * v2^2 + ρ * g * y2

Since v2 is approximately zero, the equation becomes:

P1 + 1/2 * ρ * v1^2 + ρ * g * y1 = P2 + ρ * g * y2

Substituting the given values, we have:

PA + 1/2 * ρ * vi^2 + ρ * g * y1 = P2 + ρ * g * (y1 + y2)

Solving for vi, we get:

vi = sqrt((2 * (P2 - PA) + 2 * ρ * g * y2) / ρ)

(b) For water, ρ = 998 kg/m^3 and g = 9.8 m/s^2. Substituting these values into the formula for vi, we get:

vi = sqrt((2 * (0.85 atm - 1 atm) + 2 * 998 kg/m^3 * 9.8 m/s^2 * 2.1 m) / 998 kg/m^3)

vi = sqrt(2 * 0.85 atm + 39.96 m^2/s^2) = sqrt(39.96 m^2/s^2) = 6.32 m/s

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The **liquid **enters **atmospheric pressure **at a rate of 6.32 m/s from the bottom hole.

What is gauge pressure defined as?

The **pressure **measured in relation to the surrounding atmospheric pressure is known as **gauge pressure**. A diaphragm sensor can be used to measure gauge pressure, with one side of the diaphragm exposed to the pressure medium that has to be measured and the other exposed to the surrounding **atmospheric** **pressure**.

Why do we need gauge pressure?

We need **pressured** **water **or air to move through our water tanks and systems, which allows them to work. You may check for mistakes in your tanks and systems by using a **pressure** **gauge **to measure the force of a pressure inside the water or the air.

(A) The **relationship **between a **fluid's pressure**, velocity, and height in a moving stream can be determined using the Bernoulli's equation. The Bernoulli's equation can be applied in this situation between two places in the fluid stream, one at the **vessel's bottom **opening and the other at the liquid's surface. Assuming that v2, the velocity of the liquid surface, is close to zero, the following sentence can be written:

P1 + 1/2 × ρ × v1² + ρ × g × y1

= P2 + 1/2 × ρ × v2² + ρ × g × y2

Since v2 is approximately zero, the equation becomes:

P1 + 1/2 × ρ × v1² + ρ × g × y1

= P2 + ρ × g × y2

Substituting the given values, we have:

PA + 1/2 × ρ × vi² + ρ × g × y1

= P2 + ρ × g × (y1 + y2)

Solving for vi, we get:

vi = √((2 × (P2 - PA) + 2 × ρ × g × y2) / ρ)

(b) For water, ρ = 998 kg/m³ and g = 9.8 m/s². Substituting these values into the formula for vi, we get:

vi = √((2 × (0.85 atm - 1 atm) + 2 * 998 kg/m³ × 9.8 m/s² × 2.1 m) / 998 kg/m³)

vi = √(2 × 0.85 atm + 39.96 m²/s²)

= √(39.96 m²/s²)

= 6.32 m/s

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Experiment: Magnetism

Here is your goal for this lesson:

Diagram the magnetic fields around the magnets

These supplies are needed:

two bar magnets

one horseshoe magnet

iron filings

sheet of glass or plastic

several sheets of paper

Bar Magnet

1. Place the bar magnet on a table.

2. Put a sheet of glass or plastic over the magnet.

3. Sprinkle the iron filings over the sheet evenly.

4. On a separate paper, sketch the magnet. Show the lines made by the iron filings.

Horseshoe Magnet

5. Place a horseshoe magnet on the table.

6. Put a sheet of glass or plastic over the magnet.

7. Sprinkle the iron filings over the sheet.

8. On a separate paper, sketch the magnet. Show the lines made by the iron filings.

N Pole to N Pole

9. Place two bar magnets N pole to N pole with an inch between them.

10. Put a piece of glass or plastic over the magnets.

11. Sprinkle the iron filings over the glass or plastic.

12. On a separate paper sketch the magnets. Show the lines made by the iron filings.

N Pole to S Pole

13. Turn one of the bar magnets around so the magnets are N pole to S pole with an inch between.

14. Sprinkle the iron filings over the glass or plastic.

15. On a separate paper sketch the magnets. Show the lines made by the iron filings.

From the information you have observed, determine the following:

What rule of magnetism is illustrated by the lines of the iron filings in Step 12?

What rule of magnetism is illustrated by the lines of the iron filings in Step 15?

Why was glass or plastic used to separate the filings from the magnets in the experiments?

Did the glass or plastic stop the passage of the magnetic lines of force?

Did the iron filings almost or completely bridge the open end of the horseshoe magnet?

### Answers

The lines of the iron filings illustrate the** law of magnetism** that **like poles repel each other.**

The lines of the iron writings illustrate the rule of magnetism that **unlike poles attract each other.**

Glass or plastic was used to separate the writings from the magnets in the experiments because it is transparent and does not interfere with the magnetic fields.

The glass or plastic did not stop the passage of the magnetic lines of force, but it did contain the iron filings so they could be used to visualize the magnetic field.

The iron filings almost completely bridged the open end of the horseshoe magnet, demonstrating that the magnetic field continues through the gap and connects the two poles.

What is the law of magnetism?

The most fundamental **law of magnetism** states that opposite **poles** attract one another and that like poles repel one another.

This can be observed when trying to align the like poles of two **magnets**, like poles (north-north; south-south), will repel each other. Unlike poles (north-south) will attract each other

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A particle with charge 2 µC is located on the

x-axis at the point 6 cm , and a second particle

with charge 5 µC is placed on the x-axis at

10 cm .What is the magnitude of the total electrostatic force on a third particle with charge

−5 µC placed on the x-axis at −2 cm ? What is the magnitude of the total electrostatic force on a third particle with charge −5 µC placed on the x-axis at −2 cm ? The Coulomb constant is 8.9875 × 10^9 N · m^2 /C^2 . Answer in units of N.

### Answers

**Answer:**

I don't know what Is the answer

What are the similarities between Halogen lights, Fluorescent lights, and LED lights?

### Answers

**Answer and Explanation:**

Halogen lights, fluorescent lights, and LED lights are all types of electric lights that are commonly used in households and commercial buildings. While they differ in their technology, there are some similarities between them, such as:

Energy Efficiency: Compared to traditional incandescent bulbs, all three types of lights are generally more energy-efficient, meaning they use less electricity to produce the same amount of light.

Long Lifespan: All three types of lights tend to have a longer lifespan than traditional incandescent bulbs, meaning they last longer and need to be replaced less frequently.

Environmentally Friendly: Because they use less energy and last longer, these types of lights are generally considered more environmentally friendly than incandescent bulbs.

Availability: Halogen, fluorescent, and LED lights are all readily available and commonly used in a variety of lighting applications, from household lamps to commercial lighting systems.

Color temperature: All three types of lights offer a range of color temperatures to choose from, allowing for a customized lighting experience to suit personal preferences or specific lighting needs.

However, it's important to note that there are also differences between these types of lights in terms of their technology, cost, and performance.

**Answer:**

Halogen lights, fluorescent lights, and LED lights are all types of artificial lighting used in a variety of settings, and they share some similarities

**Explanation:**

Energy Efficiency: Compared to traditional incandescent bulbs, all three types of lighting are more energy-efficient. This means that they use less electricity to produce the same amount of light, which can result in significant energy savings over time.

Longevity: Halogen, fluorescent, and LED lights are all designed to last longer than incandescent bulbs. While halogen bulbs have a lifespan of around 2,000 hours, fluorescent bulbs can last up to 15,000 hours, and LED bulbs can last up to 50,000 hours.

Brightness: All three types of lighting are capable of producing bright light, and the brightness can be adjusted by using different wattages or lumens.

Environmental Impact: While halogen lights and fluorescent lights contain small amounts of hazardous materials, such as mercury, LED lights are free from such hazardous materials. However, all three types of lighting can be recycled to reduce their environmental impact.

Versatility: Halogen, fluorescent, and LED lights are all available in a wide range of shapes, sizes, and colors. This makes them suitable for a variety of settings, including homes, offices, and outdoor spaces.

Ann and Bob are pushing opposite sides

of a door with I = 10.5 kg-m2. Ann

pushes 34.8 N at 0.732 m from the axis,

while Bob pushes 59.6 N at 0.300 m,

both perpendicular to the door. What is

the angular acceleration?

### Answers

The **angular acceleration **of the door is** approximately 0.723 rad/s^2.**

How to solve this problem

First we can use the **equation **for torque:

torque = force * lever arm

where

torque is the net torque acting on the doorforce is the force applied by each person, and lever arm is the distance from the axis of rotation to the point where the force is applied

The net torque causes **angular acceleration** of the door, which is related to torque by the equation:

torque = moment of inertia * angular acceleration

Where** moment of inertia** is a measure of how difficult it is to change the rotational motion of the door.

In this case, we can calculate the** net torque **on the door as the sum of the torques due to** Ann and Bob**:

torque_net = torque_Ann + torque_Bob

**where**

torque_Ann = force_Ann * lever_arm_Anntorque_Bob = force_Bob * lever_arm_Bob

Substituting the given **values**, we have:

torque_Ann = 34.8 N * 0.732 m = 25.46 N·m

torque_Bob = 59.6 N * 0.300 m = 17.88 N·m

torque_net = 25.46 N·m - 17.88 N·m = 7.58 N·m

Next, we can calculate the** moment of inertia** of the door, using the given value:

moment of inertia = I = **10.5 kg-m^2**

Finally, we can use the equation for a**ngular acceleration** to solve for the unknown:

torque_net = moment of inertia * angular acceleration

Solving for **angular acceleration**, we get:

angular acceleration = torque_net / moment of inertia

Substituting the **previously** calculated values, we have:

**angular acceleration **= 7.58 N·m / 10.5 kg-m^2

≈** 0.723 rad/s^2**

Therefore, the** angular acceleration** of the door is **approximately 0.723** **rad/s^2.**

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ocean waves of wavelength 28 m are moving directly toward a concrete barrier wall at 4.4 m/s . the waves reflect from the wall, and the incoming and reflected waves overlap to make a lovely standing wave with an antinode at the wall. (such waves are a common occurrence in certain places.) a kayaker is bobbing up and down with the water at the first antinode out from the wall. A) How far from the wall is she?B) What is the period of her up and down motion?

### Answers

Refer to the attached image.

Let u

and v

be distinct vectors of a vector space V

. Show that if {u,v}

is a basis for V

and a

and b

are nonzero scalars, then both {u+v,au}

and {au,bv}

are also basis for V

.

### Answers

Since they both meet the span and **linear independence** requirements, "u + v, au" and "au, bv" are bases for V.

What is vector in science?

It is often represented by an arrow whose length is proportional to the magnitude of the quantity and whose direction is the same as that of the quantity. To "**transport**" something from point A to point B, a vector is required; the Latin root of the word vector implies "carrier". Astronomers studying the planetary rotation around the Sun in the 18th century were the first to apply it.

What is difference between scalar and vector?

In terms of direction, a **scalar **quantity differs from a vector quantity. A vector has direction, but a scalar does not. A vector quantity can be multi-dimensional, whereas a scalar quantity can be considered to be represented in one dimension as a result of this characteristic.

Case 1: {u + v, au} is a basis for V

We must demonstrate two things in order to demonstrate that "u + v, au" is a basis for V.

Span: Each vector in V is a linear combination of u + v and au.

A zero vector cannot be produced by a non-trivial linear combination of u + v and au since they are linearly independent.

Span: Using any vector in V, let x be a linear combination of u + v and au, and we shall show that every vector in V can be expressed in this way. Since "u, v" serves as a foundation for "V," we can express "x" as a linear combination of "u" and "v," or "x = a1u + a2v." At this point, we can write x as a linear combination of u + v and au, i.e., x = (a1 + a2)(u + v) + (a1a)au.

To demonstrate the linear independence of u + v and au, let's assume that there are non-trivial scalars c1 and c2 such that c1(u + v) + c2au = 0. In the formula, c1u + c1v + c2au = 0, it is implied that c1u + c1v = -c2au. The fact that c1 = c2 = 0 demonstrates that u + v and au are linearly independent because u, v is a foundation for V.

Case 2: {au, bv} is a basis for V

Similar to the first case, this one also has supporting evidence. We can demonstrate that au and bv are linearly independent and that each vector in V can be expressed as a linear combination of au and bv.

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Do you see any relationship between the shape of the galaxies and how they may have evolved? Look closely at the shapes. Explain your observations. (spiral, barred-spiral, elliptical, irregular)

### Answers

There is a relationship between the shape of the galaxies and how they may have evolved, for example spiral, elliptical, and irregular galaxies evolved by the** gravitational effect** of the material as waves.

What does evolution in galaxies mean?

The **evolution in galaxies** refers to how gravitational forces acted in the material that formed the galaxies after the big ban, which led to diverse morphologies according to these materials.

Therefore, with this data, we can see that evolution in galaxies is based on their materials and it may alter the forms of galaxies during their development across millions of years.

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The half-life of a certain radioactive substance is 12 hours. There are 8 grams present initially. Express the amount of substance remaining as a function of time t. When will there be 1 gram remaining?

### Answers

A certain **radioactive **material has a 12-hour half-life. At first, there are 8 grams available. If you express the amount of material still present as a function of time, you will find that after 36 hours, there will be 1 gram of substance left.

What is radioactive called?

When some atoms spontaneously split apart, they emit energy and particles as they change into new, more **stable atoms**. This process is known as radioactivity. This process, which is also known as radioactive decay, happens because unstable isotopes frequently change into more stable states.

What is **radioactive** used for?

**Radiation **is currently used for the good of humanity in industry, academia, medical, and power production. Radiation is also useful in many other fields, including mining, law enforcement, space exploration, agriculture, archaeology (carbon dating), and many others.

Let's label the quantity that is still present after t hours "A(t)". Then, we could type:

A(t) = 8 * (1/2)^(t/12)

where t is the number of completed half-lives, and 12.

We must work out the following equation to determine when there will be 1 gram left:

A(t) = 1

8 * (1/2)^(t/12) = 1

Using base 2 to get the logarithm of both sides:

log2(8 * (1/2)^(t/12)) = log2(1)

log2(8) + log2((1/2)^(t/12)) = 0

3 + (t/12)log2(1/2) = 0

3 = -(t/12)log2(1/2)

Multiplying both sides by -12/log2(1/2):

-36 = t

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A certain **radioactive material **has a 12-hour half-life. At first, there are 8 grams available. If you express the amount of material still present as a **function **of time, you will find that after 36 hours, there will be 1 gram of substance left.

What is radioactive called?

When some atoms spontaneously split apart, they emit energy and particles as they change into new, more **stable atoms**. This process is known as **radioactivity**. This process, which is also known as **radioactive decay**, happens because unstable isotopes frequently change into more stable states.

What is radioactive used for?

**Radiation **is currently used for the good of humanity in industry, academia, medical, and **power production**. Radiation is also useful in many other fields, including mining, law enforcement, space exploration, agriculture, **archaeology **(carbon dating), and many others.

Let's label the **quantity **that is still present after t hours "A(t)". Then, we could type:

A(t) = 8 × (1/2[tex])^{(t/12)}[/tex]

where t is the number of completed** half-lives**, and 12.

We must work out the following **equation **to determine when there will be 1 gram left:

A(t) = 1

8 × (1/2[tex])^{(t/12)}[/tex] = 1

Using base 2 to get the **logarithm **of both sides:

log2(8 × (1/2[tex])^{(t/12)}[/tex] = log2(1)

log2(8) + log2((1/2[tex])^{(t/12)}[/tex] = 0

3 + (t/12)log2(1/2) = 0

3 = -(t/12)log2(1/2)

Multiplying both sides by -12/log2(1/2):

-36 = t

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Before the force is applied (t <

0 on the above graph), the particle moves

along the x axis with velocity v1 = −7.6 m/s.

Find the velocity v2 of the particle after the

force stops acting on it (t > 8 s).

Answer in units of m/s.

### Answers

The **velocity **V₂ for the **system **will be -3.1 meters per second.

What is an impulse?

In **classical **mechanics, the **impulse **is the integral of a **force**, F, over the time interval, t, for which it acts. Since force is a vector quantity, the impulse is also a vector quantity.

Impulse applied to an object produces an equivalent vector change in its linear momentum, also in the resultant direction.

Given that the velocity V₁ = -7.6 m/s. Let us assume that the force is 5 N and the mass of an object is 10kg. Time is greater than 8 sec so let t = 9 sec.

The velocity V₂ will be calculated as;-

F = m x ( V₂ - V₁ ) / t

5 = 10 x ( V₂ + 7.6 ) / 9

V₂ = 4.5 - 7.6

V₂ = -3.1 m / s

Therefore, the value of the velocity V₂ is -3.1 m/s.

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einstein changed the way we think about gravity but considering that question blank 1 of 2 type your answer... and question blank 2 of 2 type your answer... are the ones affected by the presence of a large mass.

### Answers

Therefore, the **gravity **gradient between two things will be stronger the more massive they are so the closer them are to one another.

How did Einstein influence how we perceive gravity?

It was Einstein. He proposed the idea that a mass could easily prod space. It has the ability to **push**, pull, bend, and distort. The fact that a mass exists in space naturally results in gravity. In his Special Relativity, which was published in 1905, Einstein introduced time as just a fifth **dimension **to space, creating space-time.

What distinguishes Newton's theory of gravity from Einstein's?

However, Newton's theory of gravity only affects an object's **speed **through space, whereas Einstein's General **Relativity **states that the existence of mass distorts both space and time.

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an isolated point charge q is located a distance d to the right of point p, as shown. the point charge is then moved a distance less than d. movement in which of the following directions will result in a change in the direction of the electric field at point p? select two answers. (pick two): a) toward the left; b) toward the right; c) toward the top of the page; d) toward the bottom of the page

### Answers

**Movements **A: "toward the left" and B: "toward the right" will result in a change in the direction of the** electric field** at point p.

The **direction of the electric field** at a point due to an** isolated point charge **is proportional to the direction of the vector connecting the point charge and the point in question. Moving the point charge in either direction to the left or right will result in a c**hange in the direction **of the electric field at point P, because the vector connecting the point charge and point P will change direction.

Moving the point charge toward the top or bottom of the page, however, will not change the direction of the electric field at point P because the **vector **connecting the point charge and point P will still be pointing toward point P.

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Answer the following:

1. Is sound a mechanical or electromagnetic wave?

2. Is sound a transverse or longitudinal wave?

3. What part of your ear receives the sound waves and turns them into electrical energy that

travels to your brain?

4.Label a compression region and a rarefaction region on the diagram below: I

5. If the speed of sound is constant, what happens to the wavelength when the frequency

increases?

6. Rank the following materials from fastest to slowest speed of sound traveling through it:

liquids, gases, solids.

### Answers

**Answer:**

1.** ****M****e****c****h****anical ****w****a****v****e**

2. **L****o****n****g****i****t****udinal ****w****a****v****e**

3. **The cochlea**

4. **T****h****e**** ****d****i****a****g****ram ****i****s**** ****n****o****t**** ****a****t****t****ached ****s****o**** ****f****a****r**

5. **the wavelength decreases****.**

6. **slowest through gases, faster through liquids, and fastest through solids.**** **or simply **s****o****l****i****d****s****>****l****i****q****u****ids****>****g****a****s****e****s**

**Explanation:**

Greetings!!

**1****.**** **Waves in water and sound waves in air are two examples of mechanical waves. Mechanical waves are caused by a disturbance or vibration in matter, whether solid, gas, liquid, or plasma.

**2****.**** **Sound is a longitudinal wave.

**3****.**** ****The cochlea** is filled with a fluid that moves in response to the vibrations from the oval window. As the fluid moves, 25,000 nerve endings are set into motion. These nerve endings transform the vibrations into electrical impulses that then travel along the eighth cranial nerve (auditory nerve) to the brain.

**4****.**

**5****.**** **As the frequency increases, **the wavelength decreases.**

**6****.**** **The Speed of Sound: Sound travels at different speeds depending on what it is traveling through. Of the three mediums (gas, liquid, and solid) sound waves travel **the slowest through gases, faster through liquids, and fastest through solids.**

Hope it helps!!!!

true/false. the electric field is zero everywhere within a certain region of space. the electric potential everywhere within the region

### Answers

Within a particular region of space, the **electric field** is zero everywhere. This assertion is untrue because there is electric potential everywhere in the area.

What is electric field?

Each point is space has an electric field associated with it when there is charge present in just about any form. The strength or direction of the an electric field are expressed by the **mathematical constant **E, which is sometimes referred to as electric field strength, applied electric intensity, and simply the electric field. The physical field that surrounding electrically charged particles that pulls or attracts all other positive ions in the vicinity is known as an electric field. Additionally, it describes the physical environment of a system of particles.

What is the electric field law?

The static electric field produced by a distribution on electric charges is described by **Gauss's law **again for electric field. It claims that the total electric current enclosed by any closed surface directly relates to a electric flux through in that surface.

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A 2.0-kilogram mass falls freely for 10. meters

near the surface of Earth. The total kinetic

energy gained by the object during its free fall

is approximately

### Answers

The total **kinetic energy **gained by the **object **during its free fall is 2000.0 **Joule**.

What is **kinetic energy**?

The **energy** an object has as a result of motion is known as kinetic **energy **in physics. It is described as the effort required to move a mass-determined body from rest to the indicated **velocity**.

The body holds onto the kinetic **energy **it acquired during its **acceleration **until its speed changes.

From the conservation of **energy**:

The total kinetic **energy **gained by the **object **during its free fall is = initial potential energy

= 2.0 × 10.0 × 10.0 Joule

= 2000.0 Joule.

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A 2.0-kilogram **mass **falls freely for 10 meters near the surface of **Earth**, and the total kinetic **energy **gained by the **object **during its free fall is approximately 196 J.

What is the significance of the total kinetic energy?

The total **kinetic **energy gained by a falling **object **is calculated as follows:

KE = 0.5 × m × [tex]v^2[/tex] ( m=**mass **, v = final **velocity**)

the fall can be calculated as v = √(2 * g * h)

Given that, m = 2.0 kg, h = 10.0 m, g = 9.8 m/[tex]s^2[/tex]

v = √(2 ×9.8 × 10) = √(196) = 14.0 m/s

KE = 0.5 × 2.0 kg ×[tex]14^2[/tex] = 0.5 × 2.0 kg × 196 [tex]m^2/s^2[/tex] = 196 J

Hence, a2.0-kilogram **mass **falls freely for 10 meters near the surface of **Earth**, and the total kinetic **energy **gained by the **object **during its free fall is approximately 196 J.

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2. A 0.85kg block on a spring is oscillating with an amplitude of

A = 0.42m and a frequency of f = 3.5Hz.

a. What is the spring constant of the spring?

### Answers

The **spring constant** of the spring is **1197.48 N/m.**

What is a spring constant?

The** spring constant **of a spring can be determined from the **relationship** between the **force** required to **compress** or stretch the spring and the **displacement** of the **spring**. The force required to compress or stretch a spring is proportional to the displacement and is given by Hooke's law:

**f = -kx**

where **f** is the **force**, **x **is the **displacement**, and **k** is the **spring constant.**

In the case of a mass on a spring undergoing** simple harmonic motion, **the force required to compress or stretch the spring is equal to the weight of the mass. Therefore, the** spring constant** can be determined using the following **equation**:

[tex]k = m * (2 * π * f)^2[/tex]

where **m** is the **mass** of the **block** (0.85 kg), **f** is the **frequency** of **oscillation** (3.5 Hz), and π is pi (3.14).

**Plugging** in the **values**, we get:

[tex]k = 0.85 kg * (2 * 3.14 * 3.5 Hz)^2\\k = 0.85 kg * (37.67)^2\\k = 0.85 kg * 1412.57\\k = 1197.48 N/m[/tex]

So, the** spring constant **of the spring is **1197.48 N/m.**

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A hawk flying at 15 m/s at an altitude of 180 m accidentally drops its prey. The parabolic trajectory of the falling prey is described by the equation

y = 180 ? (x^2)/(45)

until it hits the ground, where y is its height above the ground and x is its horizontal distance traveled in meters. Calculate the distance traveled by the prey from the time it is dropped until the time it hits the ground. Express your answer correct to the nearest tenth of a meter.

### Answers

45/4 [ ln (v17 + 4) + 4v17 ] m or approx. 209.1 m, the **distance **traveled by the prey from the time it is dropped until the time it hits the ground = 209.1 m approx.

What does the term "parabolic trajectory" mean?

A parabolic trajectory in **astrodynamics **/ celestial mechanics is an unbound Kepler orbit with an eccentricity of 1, which is exactly on the threshold between an elliptical and a hyperbolic orbit. An escape orbit, or a capture orbit in the alternative, is one that is traveling away from the source.

The **parabolic trajectory **of the falling prey is described by the equation y = 180 - ([tex]x^{2}[/tex])/45. This equation can be used to calculate the time it takes for the prey to hit the ground.

Because the prey's height y is zero when it hits the ground, we can solve for x:

0 = 180 - ([tex]x^{2}[/tex])/45

[tex]x^{2}[/tex] = 8100

x = ±90

distance = 2 * 90 = 180 meters (to the nearest tenth of a meter).

As a result, the prey travels a horizontal distance of 180 meters from the moment it is dropped to the ground.

Free fall has a trajectory, right?

**Gravity's **acceleration is constantly downward and constant, however the speed and direction of the **acceleration **vary. The ball exhibits zero velocity at its greatest point in its journey, and as it descends back toward the earth, its magnitude of **velocity **grows once more.

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Which mental health disorder is caused by excessive or unreasonable fears?

A. Bipolar disorder

B. Schizophrenia

C. Multiple-personality disorder

D. Phobias

### Answers

Phobias

It's phobias because many phobias can cause overwhelming and unreasonable fears. Or anything that provokes Anxiety and avoidance.

pebble your roommate is working on his bicycle and has the bike upside down. he spins the 70.0 cm -diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second.

### Answers

The wheel rotates at a rate of about **1.047 radians per second**.

What is the diameter?

Any **straight line segment **that cuts through the center of a circle and has ends that are on the circle is considered a circle's diameter in geometry. The longest chord of the circle is another name for it. Either of the two approaches can be used to determine the diameter of a sphere. The diameter is the distance along the circle's circumference that separates two locations on its edge.

What is diameter vs circumference?

The** diameter or length **of the a circle is its circumference. A straight line connecting a point on one side of the circular to a point at the other end, that passes through the center is the diameter. A circle's diameter is multiplied by to determine its circumference π (pi). You can also determine the circumference by multiplying 2radius by pi (π=3.14).

You may determine the wheel's rotational velocity using this information. To do this, you must first determine the wheel's circumference, which is determined by multiplying the diameter by π :

C = π * d = π * 70.0 cm = 219.11 cm

The circumference is then divided by the number of times the stone passes in a second:

v = C / (3 revolutions/second) = 219.11 cm / (3 revolutions/second) = 73.04 cm/second

This is a location on the wheel's circumference's linear velocity. Divide it by the wheel's radius to get the rotational velocity:

ω = v / r = 73.04 cm/second / (70.0 cm / 2) = 1.047 radians/second

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The **wheel rotates **at a rate of about 1.047 **radians per second**.

What is the diameter?

Any straight **line segment **that cuts through the center of a circle and has ends that are on the circle is considered a circle's diameter in geometry. The longest chord of the circle is another name for it. Either of the two approaches can be used to determine the **diameter **of a sphere. The diameter is the **distance **along the circle's circumference that separates two locations on its edge.

What is diameter vs circumference?

The diameter or length of the a circle is its **circumference**. A straight line connecting a point on one side of the circular** **to a point at the other end, that passes through the center is the **diameter**. A circle's diameter is multiplied by to determine its circumference π (pi). You can also determine the **circumference **by multiplying 2radius by pi (π=3.14).

You may determine the wheel's **rotational velocity **using this information. To do this, you must first determine the **wheel's circumference**, which is determined by multiplying the diameter by π :

C = π * d = π * 70.0 cm = 219.11 cm

The **circumference **is then divided by the number of times the stone passes in a second:

v = C / (3 revolutions/second) = 219.11 cm / (3 revolutions/second) = 73.04 cm/second

This is a location on the wheel's **circumference's **linear velocity. Divide it by the wheel's radius to get the rotational velocity:

ω = v / r = 73.04 cm/s / (70.0 cm / 2) = 1.047 r/s

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Complete question:

Two image, f (x.y) and g(x,y), have histograms hf and hg. Give the conditions under which you can determine the histogram of

f (x,y) + g (x,y)

f (x,y) - g (x,y)

f (x,y) × g (x,y)

f (x,y) ÷ g (x,y)

b) Show that the Fourier transform and its inverse are linear process

c) Given an image of size M x N, you are asked to perform an experiment that consists of repeatedly lowpass filtering the image using a Gaussian lowpass filter with a given cutoff Do. You may ignore computational round-off errors. Let kmin denote the smallest positive number representable in the machine in which the proposed experiment will be conducted

i) Let K denote the number of application of the filter. Can you predict, without doing the experiment what the result (image) will be for a sufficiently large value of K? If so, what is the result?

ii) Derive and expression for the minimum value of K that will guarantee the result that you predicted

c) The basic approach used to approximate a discrete derivative involves taking differences of the form f (x + 1,y) – f (x,y)

i) Obtain the filter transfer function, H (u,v), for performing the equivalent process in the frequency domain

ii) Show that H (u,v) is a highpass filter

### Answers

The exact characteristics of the **images** and the operations being carried out govern the circumstances under which the histograms of addition, subtraction, multiplication, and division of two images can be derived.

a) The **histogram** of an image represents the distribution of intensity values in the image, and it can be used to describe the overall distribution of brightness or darkness in an image. The conditions under which the histograms of operations such as addition, subtraction, multiplication, and division of two images can be determined depend on the specific nature of the images and the operations being performed.

b) The **Fourier** transform and its inverse are linear processes, meaning that for any two signals f (t) and g (t), and for any two constants α and β, the following properties hold:

Linearity of the Fourier transform: F [αf (t) + βg (t)] = αF [f (t)] + βF [g (t)], where F [ ] denotes the Fourier transform of a signal.

Linearity of the inverse Fourier transform: f (t) = 1/2π ∫ F (ω)ejωtdω, where f (t) is the inverse Fourier transform of F (ω).

c) i) For a sufficiently large value of K, the result of repeatedly **lowpass** filtering an image using a Gaussian lowpass filter with a given cutoff Do will be an image with all high-frequency components removed, resulting in a blurred image with less detail.

ii) To derive an expression for the **minimum** value of K, one could analyze the behavior of the filter transfer function over time and determine the number of applications required to sufficiently remove high-frequency components from the image. This would likely involve finding the impulse response of the filter and analyzing its frequency response over time.

c) i) To obtain the filter transfer function, H (u,v), for performing the equivalent process in the frequency domain, one could take the Fourier transform of the filter impulse response and express it as a function of frequency.

ii) A highpass filter is a filter that removes low-frequency components from a signal and allows high-frequency components to pass through. The transfer function H (u,v) for a **highpass** filter would have a magnitude that decreases for low frequencies and increases for high frequencies. This is because low frequencies are being suppressed, while high frequencies are being amplified.

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A mass αM is located at x = a, y = 0, and a second mass (1 - α)M is located at x = 0, y = b, where 0 < α < 1. Find the coordinates x, y of the center of gravity of the two masses relative to the origin. Show that your formulas for x, y have the proper limits when α-> 0 or b -> ∞.

### Answers

The **coordinates **x, and y of the **centre **of **gravity **of the two masses relative to the origin are Cx = a² and Cy = ( 1 - a)b.

What is the centre of gravity?

A **hypothetical **location in a **body **of matter where, for the sake of convenience in some calculations, the body's total weight may be assumed to be **concentrated**.

Given that a mass αM is located at x = a, y = 0, and a second mass (1 - α)M is located at x = 0, y = b, where 0 < α < 1.

The centre of gravity coordinates of the two masses will be calculated as:-

X-coordinate:-

Cx = [ ( M x a x a ) + ( 1 - a ) M x 0 ) ] / ( Ma + ( 1 - a) M ]

Cx = ( Ma² / M )

Cx = a²

Y -coordinate:-

Cy = [ ( Ma x 0 ) + ( 1 - a)M x b ) ] / ( Ma + ( 1 - a) M

Cy = ( 1 - a ) Mb / ( M )

Cy = ( 1 - a)b

Therefore, the coordinates are Cx = a² and Cy = ( 1 - a)b.

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Automotive antifreeze consists of ethylene glycol, CH_2(OH)CH_2(OH) (MW = 62), a nonvolatile nonelectrolyte.

Calculate the boiling point and freezing point of a 25.0 mass% solution of ethylene glycol in water.

K

b

=

0.512

C

/

m

K

f

=

1.86

C

/

m

### Answers

Freezing point of **Ethylene glycol** = - 10.3°C

Boiling point of solution = 102.8°C

How can ethylene glycol hurt people?

Ethylene glycol excess can harm the kidneys, liver, lungs, brain, and other organs. Chemical imbalances in the **body**, such as metabolic acidosis, are brought on by the poisoning. The disruptions might be so severe as to result in death, **organ **failure, and deep shock.

How much propylene glycol can humans safely consume?

According to reports of fatalities brought on by ethylene glycol intake, a single dose of 150–1,500 mL may be lethal. The **fatal **dosage of **ethylene **glycol in humans is thought to be between 1,400 and 1,600 mg/kg.

Colligative qualities are the subject here:

Depression at the freezing point ΔT = Kf . m

T = Freezing temperature of solution minus the freezing point of a pure solvent

T = Kb. m is the boiling point elevation.

T = Pure solvent boiling point minus the boiling point of the solution

Let's calculate m, which stands for the molality of the solute in kilograms of solvent.

Ethylene glycol is the solute. Mass Equals 25 g

0.416 moles are equal to 25 g/60 g/mol, or one mole.

Solvent: Water

25 g of solute are present within 100 g of solution, or 25%.

The volume of **water **is thus 75 g (100 -25). (Solvent + Solute Equals Solution)

The mass is converted into g to kg 75 g. 1kg /1000g Equals 0.075 kg

Molality (mol/kg) is equal to 0.416 m/0.075 kg, or 5.55 m.

The formulae' data is changed as follows:

Depression of the freezing point: 0 ° 5.55 m. Freezing point of solution: 1.86 °C/m.

1.86°C/m x 5.55m = - 10.3°C for the freezing point of a solution.

raising the boiling point 100°C = 0.51°C/m or 5.55 m is the boiling point of a solution.

Solution's **boiling **point is 0.51 °C per meter. 5.55 m + 100°C = 102.8°C

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the lifetime of a molecule in a certain electronic state is 1010 s. what is the uncertainty in energy of this state? give the answer in j and in j mol1.

### Answers

The uncertainty in **energy** of this state is 3.3 x 10^-44 J and 5.5 x 10^-68 J mol^-1.

The lifetime of a **molecule** in an electronic state is related to the uncertainty in its energy. According to the Heisenberg Uncertainty Principle, the uncertainty in energy (ΔE) and the time during which the energy is measured (Δt) are related by:

ΔE * Δt ≥ ħ/2

where ħ is the reduced Planck **constant**.

Given the lifetime of the molecule in the electronic state (Δt = 1010 s), we can calculate the uncertainty in energy as follows:

ΔE = ħ/2 * Δt^(-1) = ħ/2 * (1010 s)^(-1)

The uncertainty in energy can be expressed in joules or joules per mole. To convert to joules per mole, we need to multiply the result by **Avogadro's** number, which is 6.022 x 10^23 mol^-1.

ΔE in j = 6.62607015 x 10^-34 J.s / (2 * 1010 s) = 6.62607015 x 10^-34 / 2 x 1010 = 3.3 x 10^-44 J

ΔE in J mol^-1 = 3.3 x 10^-44 J / 6.022 x 10^23 mol^-1 = 5.5 x 10^-68 J mol^-1

So, the **uncertainty** in energy of the electronic state is 3.3 x 10^-44 J in joules and 5.5 x 10^-68 J mol^-1 in joules per mole.

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(8%)

Problem 4: The restoring force in a Hooke's Law spring is a conservative force, and hence, the work done by that force is represented by a potentialenergy function. Consider a spring with spring constant

k

. One end of the spring is fixed at the origin of the coordinate system, and the other is attached to an oscillating block with mass

m

. The diagram below shows the potential energy function for the spring and the total mechanical energy of the system.

Θ25%

Part (b) What is the position, in centimeters, of one of the turning points of the spring-mass system. What is the value, in newtons per meter, of the spring constant? What is the maximum speed, in meter per second, of the block if its mass is

m=670 g

### Answers

According to Hooke's law, the magnitude of force used to stretch an elastic item is proportional to that **force**. The object won't return if it is stretched too far, though.

What exactly is the spring constant in Hooke's law?

According to Hooke's Law, the force necessary to compress or lengthen a spring is inversely related to the length of the spring.** Hooke's Law** can be defined mathematically as F = kx, in which F is the applied force, k is the scale parameter, and x is the material's extension (typically in meters)

Put simply, what is spring constant?

A spring's **"spring**" is a property that quantifies the connection between the force acting on the spring and the displacement it produces. In other terms, it indicates a spring's stiffness and the amount of bending or compression it can withstand.

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A 5.2 toy car is driving along a frictionless table. At the end of the table, the car crashes into a spring with a spring constant of 225 N/m and compresses it 0.04m. Find the velocity of the toy car before it hits the spring.

### Answers

The **kinetic energy** of the toy car converts to the elastic potential energy of the spring upon hit .Then the **velocity** before hitting the spring will be 0.263 m/s.

What is elastic potential ?

The **elastic potential energy** of a spring is related to its spring constant and displacement over compression or stretching is;

P = 1/2 K x²

The** kinetic energy** of the toy car is equated to the elastic potential energy after hitting to find the **velocity**.

1/2 mv ² = 1/2 K x²

then , v = √(K x²/m)

Given, m = 5.2 kg

k =225 N/m

x = 0.04 m

Then, m = √(225 N/m× 0.04 m²/5.2 kg ) = 0.26 m/s.

Therefore, the** velocity** of the toy car before getting is 0.26 m/s.

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what is happening when two people speak causing sound waves to form

### Answers

When two people speak, there is a **vibration **of the **air **molecules.

How does the sound waves work?

When two people speak, their vocal cords **vibrate **and produce sound waves. These sound waves are disturbances that travel through a medium, such as air, and cause the pressure of the medium to fluctuate.

The fluctuations in pressure cause the air molecules to **compress** and rarefy, creating a wave that moves away from the source of the sound. The waves travel through the air and reach the ear drum of the listener, where they cause the drum to vibrate. These vibrations are then converted into electrical signals by the auditory nerve and sent to the brain, where they are interpreted as sound.

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after a 0.300-kg rubber ball is dropped from a height of 1.75 m, it bounces off a concrete floor and rebounds to a height of 1.50 m. (a) determine the magnitude and direction of the impulse delivered to the ball by the floor. (b) estimate the time the ball is in contact with the floor and use this estimate to calcu- late the average force the floor exerts on the ball

### Answers

The **magnitude** and direction of the impulse delivered to the ball by the floor is impulse = change in magnitude = 3.384 kg m/s. F=3384 N.

When a ball fell from a great height?

A ball encounters the **gravity force **in a downward direction when it is dropped from a height. The ball experiences a downward **acceleration **of g due to the force of gravity. When a ball is dropped from a height, it begins to move in the same way as the force of gravity.

When a rubber ball is dropped and hits the ground, what force causes it to bounce?

The reason the ball bounces is because the gravitational force is greater than the normal **pressure **of the ground, creating a net **upward force **throughout the entire time the ball is already in contact with the floor.

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What does the exponential expression in the Arrhenius equation physically represent?

a) The rate at which an atom will overcome the activation barrier for some process (e.g., diffusion) at a given temperature.

b) The fractional probability that an atom has enough thermal energy to overcome the activation barrier for some process (e.g., diffusion).

c) The rate at which an atom will overcome the activation barrier for some process (e.g., diffusion) at a given pressure.

d) This exponent is just a scaling factor; it has no physical meaning.

e) The fractional probability that an atom has enough momentum to overcome the activation barrier for some process (e.g., diffusion).

### Answers

The answer is b) The fractional probability that an atom has adequate **thermal energy** to overcome the activation barrier for some process (e.g., diffusion).

What is the Arrhenius equation?

The **Arrhenius equation** is a mathematical expression that relates the rate of a chemical reaction to temperature. It was developed by the Swedish chemist Svante Arrhenius in the late 19th century. The equation is given: k = Ae^(-Ea/RT).

What exponential expression in the Arrhenius equation represents?

The exponential expression in the Arrhenius equation represents the fractional probability that an atom has enough thermal energy to overcome the activation barrier for some process.

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People suffering from hypertension, heart disease, or kidney problems may need to limit their intake of society public health departments in some U.S. states and Canadian provinces require community water systems t their customers if the sodium concentration in the drinking water exceeds a designated limit. In Connecticut example, the notification level is 28 mg/L (milligrams per liter). Suppose that over the course of a particular year the mean concentration of sodium in the drinking water system in Connecticut is 25.8 mg/L, and the standard deviation is 6 mg/L. Imagine that the water department selects a simple random sample of 31 water specimens over the course year. Each specimen is sent to a lab for testing, and at the end of the year the water department computes concentration across the 31 specimens. If the mean exceeds 28 mg/L, the water department notifies the p recommends that people who are on sodium-restricted diets inform their physicians of the sodium content drinking water. Use the Distributions tool to answer the following questions, adjusting the parameters as necessary. Even though the actual concentration of sodium in the drinking water is within the limit, there is a probability that the water department will advise its customers of an above-limit concentration of sodium. Suppose that the water department Is w4llng to accept (at most) a 1% risk of erroneously notifying its cus that the sodium concentration is above the limit. A primary cause of sodium in the water supply is the salt applied to roadways during the winter to melt snow and ice. If the water department can't control the use and can't change the mean or the standard deviation of the sodium concentration in the drinking water, is anything the department can do to reduce the risk of an erroneous notification to 1%? It can increase its sample size to n = 40. No, there is nothing it can do. It can increase its sample size to n = 88. It can increase its sample size to n = 48.

### Answers

It can **increase **its **sample size** to n = 100. Thus, the correct option is (c)

What is sample size?

The number of subjects in a **sample size** is referred to as the sample size in **market research**. A group of subjects chosen from the general population who are thought to be a **representative** **sample **size for that particular study is referred to as a sample size.

For instance, we can test a new product on a **sample size **that is representative of the target population in order to predict how the **population **in a particular age group will respond to it. The number of respondents in that age group who will be **surveyed **will determine the **sample** **size **in this case.

[tex]$$From the given information,Let $\alpha=0.01$ represent the $1 \%$ level of significance.$$\begin{aligned}Z & =\frac{\bar{x}-\mu}{\sigma / \sqrt{n}} \\\bar{x}-\mu & =Z(\sigma / \sqrt{n}) \\(\bar{x}-\mu)^2 & =\left[Z(\sigma / \sqrt{n})^2\right. \end{aligned}[/tex][tex]$$\begin{aligned}n & =\left(\frac{Z \sigma}{\bar{x}-\mu}\right)^2 \\& =\left(\frac{2.3263 \times 6}{20-18.6}\right)^2 \\& =(9.9698)^2 \\& =99.3980 \\& \approx 100\end{aligned}$$[/tex]

Hence, the correct option is (c).

It can increase its **sample size** to n = 100.

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Which of these properties of sound is directly related to frequency?

tone

loudness

pitch

### Answers

**Answer:**

Loudness

**Explanation:**

The Pitch and Tone are related to frequency because they affect how short or long the wavelength is.

Answer:

Loudness

Explanation:

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