newton's second law in 1 dimension: a net force of 125 n is applied to a certain object. as a result, the object accelerates with an acceleration of 24.0 m/s2. the mass of the object is

Answers

Answer 1

The mass of the object  when  a net force of 125 n is applied to a certain object is  5.2 kg

Newton's second law in one dimension states that the net force acting on an object is equal to the product of the object's mass and its acceleration. In mathematical form, the law is expressed as:

F = ma

Where F is the net force, m is the mass of the object, and a is the acceleration of the object.

In this case, we are given that a net force of 125 n is applied to an object and that the object accelerates with an acceleration of 24.0 m/s2. We are asked to find the mass of the object.

We can solve for the mass using the equation above:

m = F / a

= 125 n / 24.0 m/s2

= approximately 5.2 kg

Therefore, the mass of the object is approximately 5.2 kg.

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Related Questions

A starter pistol is fired 150m away from the spectators who hear the gun 0.5s after they see it fired. How fast does sound travel?
(Please help!)

Answers

Answer:

300m/s

Explanation:

speed = distance/time

150/0.5

Nasdaq, the American Stock Exchange, and the OTC market collectively form the (1 point)
O stockbrokers.
O money market.
O brokerage firms.
O stock market.

Answers

Nasdaq, the American Stock Exchange, and the OTC market collectively form the  stock market.

What is the American Stock Exchange?

The Nasdaq (National Affiliation of Securities Merchants Robotized Citations) and the American Stock Trade are both stock trades where stocks and other securities are exchanged.

The OTC (over-the-counter) advertise may be a decentralized advertise where securities are exchanged rightly between parties, without a centralized trade.

Together, these three markets form the stock showcase, which could be a commercial center where freely exchanged companies' offers are bought and sold.

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When we say that momentum is "conserved," we meanA. The momentum of an object is the same before and after a collision.B. The momentum of the universe increases; it never decreases.C. The momentum of an isolated system is constant.D. If there are no forces acting on an object, its momentum is zero

Answers

A. The momentum of an object is the same before and after a collision.

What is momentum?

The word Momentum is defined as the product of the mass of a object and its velocity. Momentum is a vector quantity that is it has both magnitude and direction. Newton's second law of motion says that the time rate of change of momentum is equal to the force acting on the an object.

The conservation of momentum is defined as  within some problem area , the quantity of momentum stays constant; momentum is neither created nor destroyed, but just changes through the action of forces as mentioned by Newton's laws of motion.

So we can conclude that option A is the correct answer.

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Can someone answer please

Can someone answer please

Answers

Addition work required to move spring by extra 10cm is 12J.

Define sprint constant.

A restoring force that is proportional to the spring's displacement is stored in a spring when it is compressed or relaxed. The force needed to extend or compress a spring by a unit length is specified by the spring constant. The stiffness constant is another name for it.

According to Hooke's Law, the force required to compress or lengthen a spring is inversely related to the length of the spring. By deducting the initial work from the overall job or the completed work, additional work can be computed.

Work done = 1/2 kx^2

x1 = 10cm = 0.1m

x2 = 10+10 = 20cm = 0.2m

W1 = 4J

W1 = 4 = 1/2 k *0.1*0.1

k = 4*2 /0.01 = 800N/m

W2 = 1/2 *800*0.2*'0.2

W2 = 400*0.04 = 16J

So required work is W = W2-W1

W 16-4 = 12J

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A high amplitude sound wave can best be compared to a

short hill.
tall hill.
tightly coiled spring.
stretched-out spring.

Answers

A high amplitude sound wave can best be compared to a tightly coiled spring.

What is Amplitude of wave?

The amplitude of a wave is the maximum displacement of the wave.  It is the vertical distance measured from the equilibrium position of the wave.

A tight coiled spring

A tightly coiled spring will have maximum displacement or high amplitude.

A stretched - out spring

A stretched - out spring will have low amplitude

Thus, a high amplitude sound wave can best be compared to a tightly coiled spring.

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Option C is correct. A high amplitude sound wave can best be compared to a tightly coiled spring.

What is the definition of wave amplitude?

The largest displacement of a wave is known as its amplitude. It's the vertical distance between the wave's equilibrium point and the ground.

A spring that is tightly coiled. A tightly coiled spring will have a large amplitude or maximum displacement.

A spring that has been stretched out will have a low amplitude. A tightly coiled spring is the greatest analogy for a high amplitude sound wave.

Hence high amplitude sound wave can best be compared to a tightly coiled spring.

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50 N Vertical 10 N Horizontal Force X can you find force x?

Answers

Answer:

45

Explanation:

im has had an illness and an accident during the year. His combined out-of-pocket expense for both incidents was $1,000. The insurance company will now start to pay some of his medical expenses. What does the $1,000 represent? Coordination of benefits Deductible Participation (co-insurance) Internal limits

Answers

The $1,000 represents the out-of-pocket expenses that the individual had to pay for their illness and accident. This includes any deductibles, co-insurance, or internal limits that were applicable to their insurance plan. The coordination of benefits may also come into play if the individual has multiple insurance policies.

However, since the insurance company will now start to pay some of their medical expenses, it means that they have reached their out-of-pocket maximum or the maximum amount that they are responsible for paying in a given year. The insurance company will now cover the remaining medical expenses according to the terms of the insurance plan. In summary, the $1,000 represents the individual's financial responsibility for their medical expenses before their insurance plan begins to cover the costs.

In conclusion, the $1,000 represents the out-of-pocket expenses that the individual had to pay for their medical care, and it is important to note that this amount may vary depending on the individual's insurance plan and medical needs. It is crucial to understand the terms of one's insurance plan to be able to anticipate and prepare for any out-of-pocket expenses that may arise in the future.

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. Sunita is taking a train to Madurai. Her train has stopped at Trichinapally. She is facing the direction the train will be moving in . She can see a train next to her. The train is also going to Madurai and it leaves first. As the other train leaves, it seems to Sunita as if

Answers

The relative motion of the train next to her is the motion of the other train in her rest frame.

As the other train leaves, it seems to Sunita as if her train is moving backwards

Reason:

The motion of the train Sunita is taking is given by the rate of movement of

objects outside the train from the front side of the train towards the back

side of the train, that way she can tell that the train is moving.

The motion of the other train from the rear side of the train from the rear

side of the train to the front side is a reverse motion to what Sunita

observes when the train is moving forward. Therefore, as the other train

leaves, it seems to Sunita as if her train is moving backwards.

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A box of mass m is initially at rest at the top of a ramp that is at an angle with the horizontal. The block is at a height h and length L

from the bottom of the ramp. The block is released and slides down the ramp. The coefficient of kinetic friction between the block and

the ramp is u. What is the kinetic energy of the box at the bottom of the ramp?

Answers

Hi there!

We can use the work-energy theorem to solve.

Recall that:
\(E_i = E_f\)

The initial energy equals the final energy (Conservation of Energy). However, we must take into account energy dissipated due to friction in this instance.

The energy lost due to friction is equivalent to the work done by friction. Recall the following:

Normal force on an incline: \(N = Mgcos\theta\)Force due to friction: \(F_f = \mu N = \mu mgcos\theta\)

The work due to a force is:
\(W = F \cdot d \\\)

Since the displacement is in the same direction as the force, the dot-product becomes Fd.

The work due to friction then becomes:

\(W_f = \mu mgdcos\theta\)
The work due to friction is SUBTRACTED from the initial potential energy.

Initial energy = GPE = mgh

Final energy = KE

Therefore:

\(\boxed{mgh - \mu mgdcos\theta = KE}\)


the average no-load voltage in a dc arc welding circuit is ____ volts. 10–20 15–30 60–80 15–40

Answers

The average no-load voltage in a DC arc welding circuit is typically in the range of 60-80 volts.

What is arc welding?

Arc welding is a welding technique that uses an electric arc to melt the base metal and fusing it with the filler metal to create a weld. The welding machine supplies an electric current to a consumable electrode or filler wire to melt the metals, forming a weld pool. The two metals fuse when the weld cools down. The weld is as strong as the base metal and can be used to construct everything from automobile components to skyscrapers.

What is the no-load voltage?

In a welding circuit, the no-load voltage is the voltage between the welding electrode and the workpiece before a welding arc is struck. Before the start of a welding operation, the circuit is energized and, as a result, the welding machine produces an open circuit voltage. It is also known as the no-load voltage, which is the voltage measured at the output terminals of the welding machine when the welding arc is inactive and the electrode is not in contact with the workpiece.

The average no-load voltage in a DC arc welding circuit is typically around 60-80 volts. This voltage range is necessary to establish and maintain an electric arc between the welding electrode and the workpiece, enabling the welding process to occur efficiently.

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A car speeds up from 10 m/s to 24 m/s. Change in velocity

Answers

Answer:

14m/s

Explanation:

subtract initial velocity by final velocity

Find the potential function and the gravitational field intensity function inside and outside of a thin ring with Radius R, in terms of r (the distance from the center of the ring to the field point.) Note: inside R >r, outside r>R. the function will be different.

Answers

The potential function and the gravitational field intensity function inside and outside of a thin ring with radius R, in terms of r (the distance from the center of the ring to the field point), are as follows:

Inside the ring (r < R): The potential function is given by V = -GM/r, and the gravitational field intensity function is E = GM/r², where G is the gravitational constant and M is the mass of the ring.

Outside the ring (r > R): The potential function is V = -GM/r + GM/R, and the gravitational field intensity function is E = GM/r², where G is the gravitational constant, M is the mass of the ring, and R is the radius of the ring.

Inside the ring (r < R), the potential function is given by V = -GM/r. This represents the gravitational potential due to the mass of the ring at a point inside the ring. The negative sign indicates that the potential decreases as the distance from the center of the ring decreases. The gravitational field intensity function is E = GM/r², representing the strength of the gravitational field at a point inside the ring. The field intensity decreases as the distance from the center of the ring increases, following an inverse square relationship.

Outside the ring (r > R), the potential function is V = -GM/r + GM/R. In addition to the potential due to the mass of the ring, there is an additional potential term GM/R, which arises from considering the ring as a point mass located at its center. The gravitational field intensity function remains the same as E = GM/r², indicating that outside the ring, the gravitational field follows an inverse square relationship with the distance from the center of the ring.

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on a wet road, you would need to adjust your speed to _____ slower than normal.
a. 5-10 mph
b. 20-30 mph
c. 40-50 mph

Answers

On a wet road, you would need to adjust your speed to 5-10 mph slower than normal.So option a is correct.

On a wet road, you should adjust your speed to ensure that you can drive safely. This is because water causes tyres to lose traction with the road. If you increase your speed on a wet road, you'll have less control over your vehicle. When the road is wet, your vehicle's tyres may not be able to grip the road as well as they would on a dry road.When driving on wet roads, you should maintain a safe distance between your vehicle and the car in front of you. This provides you with enough space to stop safely if the car in front of you stops suddenly.In addition, when driving on wet roads, it's best to avoid sudden steering or braking movements. This will cause your car to skid. Therefore, you should slow down and move more gently on a wet road, and always adjust your speed to 5-10 mph slower than normal.Therefore option a is correct.

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consider a tug-of-war where scales are at opposite ends of the rope. is it possible for the scales to have different readings when participants pull?

Answers

There are two forces at play in a tug of war. The force produced by stretching the rope is indeed called tension. This power drives these people forward.

Another force acting on them is the friction of the soles of the feet. In tug-of-war, if two teams exert the same force on the rope, the net force on the rope is zero, so the rope stays in the same place. A rope has zero tension when both ends of the rope are pulled by two opposing forces of 100 N each. This is because both forces have the same magnitude but act in opposite directions on the same object and cancel each other out.

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Which explains how to calculate the average acceleration of a moving object?
1.Divide the change in velocity by the change in time.
2.Multiply the change in time by the change in velocity.
3.Divide the change in time by the change in velocity.
4.Subtract the velocity from the change in time.

Answers

Answer Multiply the acceleration by time to obtain the velocity change: velocity change = 6.95 * 4 = 27.8 m/s . Since the initial velocity was zero, the final velocity is equal to the change of speed.

​  

v, start subscript, a, v, g, end subscript, equals, start fraction, delta, x, divided by, t, end fraction, equals, start fraction, minus, 4, start text, space, m, end text, divided by, 5, start text, space, s, end text, end fraction, equals, minus, 0, point, 8, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction

The minus sign indicates the average velocity is also toward the rear of the plane.

The average velocity of an object does not tell us anything about what happens to it between the starting point and ending point, however. For example, we cannot tell from average velocity whether the airplane passenger stops momentarily or backs up before he goes to the back of the plane. To get more details, we must consider smaller segments of the trip over smaller time intervals. For instance, in the figure below, we see that the total trip displacement,

 

Answer:

bdjdiosfjigjdigjtrht <3

Explanation:

30. 0 gram of Aluminum at 80. 0 °C is added to 30. 0 g of water at 10 °C. Predict the final temperature


of the water and explain your reasoning. (no math, just logic!)

Answers

When the aluminum and water are mixed together, heat transfer occurs between the two substances until thermal equilibrium is reached. The aluminum, initially at a higher temperature of 80.0 °C, will transfer heat to the water, which is initially at a lower temperature of 10.0 °C.

Since aluminum has a higher specific heat capacity than water (0.897 J/g°C for aluminum compared to 4.186 J/g°C for water), it can hold more heat energy per gram per degree Celsius. This means that the aluminum will transfer its heat energy to the water, causing its temperature to increase.

Based on the given information, we can expect that the final temperature of the water will be somewhere between 10.0 °C and 80.0 °C. However, without knowing the exact values of the specific heat capacities of aluminum and water, as well as the amount of heat transferred between them, it is not possible to predict the final temperature accurately. In real-world scenarios, the final temperature will depend on several factors, such as the exact masses of aluminum and water, their specific heat capacities, and the heat transfer mechanism (e.g., conduction). To determine the final temperature accurately, precise measurements and calculations involving heat transfer equations would be necessary.

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find the relationship between the height at which the ball is released and distance it rolls along the artificial turf it stops​

Answers

Answer:

The height at which a ball is released affects its rolling distance on artificial turf. Factors such as the angle of release, initial velocity, surface characteristics of the turf, and friction play a role. Generally, a higher release height gives the ball more potential energy, converting to kinetic energy as it moves towards the turf, resulting in a longer rolling distance. However, air resistance and turf surface characteristics can affect the rolling distance. Wind can also be a factor. Therefore, the relationship is complex and dependent on multiple factors.

On april 15, 1912, the luxury cruise liner titanic sank after running into an iceberg, what was the cruise liners speed when it collided with the iceberg if it had a mass of 4.23*10^8 kg ship and a momentum of 4.9* 10^9 kg*m/s?

REPLY FAST

Answers

On april 15, 1912, the luxury cruise liner titanic sank after running into an iceberg the Titanic's collision speed with the iceberg was 11.6 m/s.

Evaluating :

An object's momentum is calculated by multiplying its mass by its velocity. The Titanic's momentum in this instance is :

                                          4.9 x 10⁹ kg ×m/s.

The Titanic has a mass of 4.23 x 10⁸ kilograms. As a result, we can divide the momentum by the mass to determine the Titanic's velocity before it hit the iceberg  :

                                 momentum = mass x velocity

                                           4.9 x 10⁹ kg×m/s

                                = (4.23 x 10⁸ kg) x velocity

velocity = 4.9 x 10⁹ kg ×m/s / (4.23 x 10⁸ kg)

                                              = 11.6 m/s

So the speed of the Titanic when it collided with the iceberg was 11.6 m/s.

Momentum :

Momentum is the sum of a particle's velocity and mass. The quantity momentum is a vector; that is, it has magnitude as well as direction. According to Isaac Newton's second law of motion, the particle's force equals the time rate of momentum change.

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III.2. We have seen that a NOR gate can be built using AND, OR and NOT gates. But there is a surprising converse: any gate can be drawn using just the NOR gate. To see this, what is the output of the gate

Answers

The output of a gate refers to the logical result or value produced by the gate based on its inputs. In the context of the statement regarding the NOR gate, the surprising fact is that any logical gate can be constructed using just NOR gates. This means that the NOR gate is functionally complete, as it can be used to build any other gate.

What is And Gate?

AND Gate: The AND gate produces an output of 1 (or true) only when both of its inputs are 1. Using NOR gates, an AND gate can be constructed as follows:

Input A NOR Input A = NOT A

Input B NOR Input B = NOT B

(NOT A) NOR (NOT B) = (A AND B)

Therefore, by combining two NOR gates, we can create an AND gate.

OR Gate: The OR gate produces an output of 1 if at least one of its inputs is 1. Using NOR gates, an OR gate can be constructed as follows:

Input A NOR Input A = NOT A

Input B NOR Input B = NOT B

(NOT A) NOR (NOT B) = (A OR B)

By combining two NOR gates, we can create an OR gate.

NOT Gate: The NOT gate (also known as an inverter) produces the complement of its input. Using a single NOR gate, we can create a NOT gate as follows:

Input A NOR Input A = NOT A

Therefore, a single NOR gate can function as a NOT gate.

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Why do prokaryotic cells usually reproduce more quickly than eukaryotic cells?

Choose 1 answer:

(Choice A) A Eukaryotic cells are more structurally complex than prokaryotic cells.

(Choice B) B Eukaryotic cells have less DNA than prokaryotic cells.

(Choice C) C Eukaryotic cells have more cell walls than prokaryotic cells.

(Choice D) D Eukaryotic cells are smaller than prokaryotic cells.

Answers

Prokaryotic cells reproduce more quickly than eukaryotic cells because the latter are more structurally complex. The correct option is A.

Structural complexity of cells

Eukaryotic cells have nuclei and membrane-bound organelles such as mitochondrion. This is unlike prokaryotic cells whose DNA lies freely in the cytoplasm and lacks membrane-bound organelles.

In order words, eukaryotic cells are structurally more complex than prokaryotic cells. Thus, reproductive times in prokaryotes are usually quicker than in eukaryotes.

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You are searching for a connector to add between a battery and a light bulb. You should select a material that has the ability toResist electron flowAccept neutron flowResist proton flowAccept electron flow

Answers

Answer:

Accept electron flow

Explanation:

The battery gives a change in the potential and the light bulb works like a resistor, so we will need a material that allows the flow of current. Therefore, we need a material that has the ability to accept electron flow.

So, the answer is:

Accept electron flow

An apple is thrown across the cafeteria with a force of 10 N and at an acceleration of 6 m/s2. What is the mass of the apple? ... please answer asap

Answers

Answer:

Explanation:

F = m * a

The apple's acceleration is not influenced by the acceleration due to gravity for this question.  In real life it most certainly is influenced by gravity.

F = m * a

F = 10 Newtons.

a = 6 m/s^2

m = 10/6 = 1.66 kg. Mighty  large apple

does anyone know what this safety symbol means??​

does anyone know what this safety symbol means??

Answers

Safety symbols, danger symbols, or safety labels are graphical symbols that warn of or indicate hazards linked with an area or object. Images, pictograms, forms, words, phrases, sentences, or statements placed on walls, boards, buildings, doors, entrances, machinery, equipment, tools, transportation, roadways, or any other visible location are examples of safety symbols. The symbol alerts people to the presence of hazardous products or substances, as well as a hazardous environment, and warns them on how to stay safe or the potential repercussions if not avoided.

The given symbol means hammer.

A hammer is a hand tool that consists of a weighted "head" attached to a long handle and swung to produce an impact to a limited region of an item. This may be used to drive nails into wood, shape metal, or crush rock.

While all of these hammers have a round head for driving nails, the claw end may be used for prying, splitting wood, ripping drywall, and other minor demolition chores. A claw hammer's claw is curved, whereas a framing hammer's claw is straight. These hammers are ideal for the following tasks: woodworking

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1. Locate three words or phrases used by the cartoonist to identify objects or
people within the cartoon
2. Explain the message (idea) of the cartoon. What is its purpose?
3. Describe how this picture relates to America today?

Answers

The  three words or phrases used by the cartoonist to identify objects or people within the cartoon are:

Cloth workersLinen workersLumber workers

Explain the message (idea) of the cartoon. What is its purpose?

The message (idea) of the cartoon is to show how the employs are maltreating and underpaying their slaves or their employees/workers and the purpose is for them to see and change.

Describe how this picture relates to America today?

The  picture relates to America today as it talks about racism in America and its effect on African America.

Therefore, The  three words or phrases used by the cartoonist to identify objects or people within the cartoon are:

Cloth workersLinen workersLumber workers

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1. Locate three words or phrases used by the cartoonist to identify objects orpeople within the cartoon2.

women today make up ____% of the u.s. labor force.

Answers

As of September 2021, women made up approximately 47% of the U.S. labor force.

This percentage reflects the significant progress women have made in workforce participation over the years. The increased representation of women in the labor force is the result of various factors, including advancements in gender equality, improved access to education and career opportunities, and changing societal norms.

Women have made significant contributions to various industries and sectors, assuming roles across a wide range of professions. However, it's important to note that workforce demographics can change over time due to numerous factors, including economic conditions, cultural shifts, and policy changes.

Thus, it is recommended to refer to the most recent data from reliable sources, such as the U.S. Bureau of Labor Statistics, for the most accurate representation of women's participation in the U.S. labor force.

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You arrive in my class 45 seconds after leaving math which is 90 meters away. How fast did you travel?

Answers

Answer:

2m/s

Explanation:

speed = distance÷time

speed =90÷45=2m/s

If the rate at which the oceanic ridge is spreading is 5 cm/yr. How much farther (in kilometers) will continents A and B be from each other in one million years? Hint: Speed = Time Dis tan ce ​, so Distance = Speed × Time. 1 km=1000 m,1 m=100 cm. Show your work. (2)

Answers

In one million years, continents A and B will be 50 kilometers farther apart.

The rate at which the oceanic ridge is spreading is given as 5 cm/yr. To find how much farther continents A and B will be from each other in one million years, we can use the formula Distance = Speed × Time.


First, let's convert the speed from cm/yr to km/yr. Since 1 km = 1000 m and 1 m = 100 cm, we divide the speed by 100,000 to convert cm/yr to km/yr. Therefore, the speed is 5 cm/yr ÷ 100,000 = 0.00005 km/yr.
Next, we multiply the speed by the time (1 million years) to find the distance. Distance = 0.00005 km/yr × 1,000,000 years = 50 km.

Therefore, in one million years, continents A and B will be 50 kilometers farther from each other.
To summarize:
- Convert cm/yr to km/yr by dividing by 100,000.
- Multiply the speed in km/yr by the time (1 million years) to find the distance.
- The continents will be 50 kilometers farther from each other.

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A car travels 50 kilometers in 30 minutes. Which
about the motion of the car are true?

Answers

Answer:

1500

Explanation:

is that all the question?

HELP HAVING BAD DAY NEED ANSWER QUICK!!!!







Jan can run at 7.5 m/s and Mary at 8.0 m/s. On a race track Jan is given
a 25 m head start, and the race ends in a tie. How long is the track?

Answers

SOLUTION:

Let's call the length of the race track as "x".

To solve for "x", we can use the formula:

\(\implies\text{ Time} = \dfrac{\text{ Distance}}{\text{ Speed}}\)

Since the race ends in a tie, we know that Jan and Mary both took the same amount of time to run the race. Let's call this time "t".

For Jan:

\(\implies \text{ Time} = \dfrac{\text{ Distance}}{\text{ Speed}}\)

\(\implies t = \dfrac{x - 25}{7.5}\)

For Mary:

\(\implies\text{ Time} = \dfrac{\text{ Distance}}{\text{ Speed}}\)

\(\implies t = \dfrac{x}{8.0}\)

Since both expressions represent the same time, we can set them equal to each other and solve for "x":

\(\implies \dfrac{x - 25}{7.5} = \dfrac{x}{8.0}\)

Multiplying both sides by 60 (the least common multiple of 7.5 and 8.0) to get rid of the decimals:

\(\implies 8(x - 25) = 7.5x\)

\(\implies 8x - 200 = 7.5x\)

\(\implies 0.5x = 200\)

\(\implies x = 400\)

\(\therefore\) The length of the race track is 400 meters.

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The equation x"+6x'+1320 represents an undriven damped harmonic oscillator. Which of the following is true?
O The general solution is C_1et+C_2e^-5t, and the system is underdamped.
OThe general solution is C_1et+C_2e^-5t, and the system is overdamped.
O The general solution is C_1e 3t cos(2t) + C_2e^-3 sin(2t), and the system is overdamped
OThe general solution is C_1e 3 cos(2t) + C_2e^-3 sin(2t), and the system is underdamped.
ONone of the above

Answers

The equation x"+6x'+1320 represents an undriven damped harmonic oscillator. The correct option is The general solution is \(C_1E^3t cos(2t) + C_2e^-^3t sin(2t)\) , and the system is overdamped (Option C).

To determine the behavior of the system and the form of the general solution, we can analyze the characteristic equation associated with the given second-order linear differential equation:

\(r^2 + 6r + 1320 = 0\)

By solving this quadratic equation, we can find the roots (or eigenvalues) of the equation. The roots will help us determine the nature of the solutions and the behavior of the system.

The characteristic equation can be factored as:

(r + 30)(r + 44) = 0

So the roots are:

r = -30 and r = -44

Since the roots are both real and distinct (not complex conjugates), the system is overdamped. In an overdamped system, the motion gradually approaches equilibrium without oscillation.

The general solution for an overdamped system with distinct real roots is of the form:

x(t) =\(C_1e^r1t + C_2e^r2t\)

Plugging in the values for the roots (-30 and -44), the general solution becomes:

x(t) = \(C_1e^-^3^0t + C_2e^-^4^4t\)

Therefore, the correct statement is: The general solution is \(C_1E^3t cos(2t) + C_2e^-^3t sin(2t)\) and the system is overdamped.

Learn more about harmonic oscillator here:

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