a pure resistance or 14.0 ohms is connected to an ac voltage source of 184 v (max) that oscillates at a linear frequency of 40.9 hz. determine the current in the circuit after 5.12 s. g

Answers

Answer 1

The current in the circuit is 9.31 A after 5.12 s.

Since the circuit contains only a pure resistance, the current in the circuit can be determined using Ohm's law, which states that the current in a circuit is equal to the voltage divided by the resistance:

I = V/R

where I is the current, V is the voltage, and R is the resistance.

In this case, the resistance is 14.0 ohms, and the voltage is given as 184 V (max).

However, we need to find the root-mean-square (rms) voltage to use in the formula, since the voltage given is the maximum voltage, not the rms voltage.

The relationship between the maximum voltage and the rms voltage is:

\(V_{rms}\) = \(V_{max}\) / √2

\(V_{rms}\) = 184 V / √2 = 130.3 V

Substituting the values into the formula, we get:

I = V/R = 130.3 V / 14.0 ohms = 9.31 A

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Related Questions

A possible answer to a scientific problem is called a

Answers

Answer:

A hypothesis is a possible explanation for a set of observations or an answer to a scientific question. A hypothesis must be testable and measurable.

Explanation:

Answer:

hypothesis is likely tobe the answer, im indian

4. If the velocity of the particles is high, they will collide with each other with less force.
a. TRUE
b. FALSE

Answers

Answer:

7657

Explanation:

b. FALSE

If the velocity of particle is high then they will collide with each other with a greater force because their momentum will be high

What is force?

force is a push or pull on a body .

What is momentum?

Momentum is the product of mass and velocity,

More the velocity, higher will be the momentum.

since force is  directly proportional to rate of change of momentum

F = Δp/Δt

so on when bodies having higher velocities collide their rate of change of momentum is higher hence more will be the force

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explain how the colors of the rainbow are formed

Answers

Explanation:

a ray of light pass through raindrops which acts like prism and split the light into its 7 constituent...which when seen by our eyes , we presume it to be a rainbow

Define Impulse And Momentum

Plsss Answer Now I Need Now​

Answers

Answer:

Impulse-The effect of force acting over time to change the momentum of an object.

momentum-The product of mass of a particle and its velocity.

Can someone buy me
it will make my day

Answers

Answer:

how much?

Explanation:

What is it that your looking to buy?

Who was the first person to study polarization of light?
-Huygens
-Newton
-Galileo
-Copernicus

Answers

Answer:

HUYGENS, CAN I S HAVE BRAINLIST?

Answer:

None

Explanation:

It is erasmus bartholinus

a space shuttle travels in orbit at 21,000 km/hr. how far will it travel in 5 hr

Answers

Answer:

Explanation:

distance = speed * time  

distance = 21000 * 5 = 105000 km

please mark me as Brainliest

"Representing data is not an important part of scientific investigations." Describe why this statement is incorrect.​

Answers

The reason why the given statement is incorrect is because representing data is an important part of scientific investigations.

A scientific investigation is a method of finding an answer to a question which  no one has ever asked before. It is done using various research methods. For this lot of observations are done and then experiments are conducted.

Since a lot of observations and experiments are done, a lot of data is created. Usually more than one experiment is done, because the first one is most likely to be unsuccessful. But that does not mean that it is a waste. Because the mistakes from the first experiment is corrected / altered in the upcoming ones. Since a lot of experiments are done, keeping data of each experiment to alter data in further experiments is an important part of a scientific investigation.

Therefore, the given statement "Representing data is not an important part of scientific investigations" is incorrect.

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A satellite is in circular orbit just above the surface of the Moon.
What is the satellite's acceleration?
The value of gravitational constant is 6.67259 X 10^-11 Ncdotm^2/kg^2 and the mass of the moon in 7.36 X 10^22 kg and its radius is 865.2km.
what is the satellite's speed
what is the period of the satellites orbit

Answers

To determine the satellite's acceleration, we can use the centripetal acceleration formula:

a = v^2 / r

where a is the acceleration, v is the satellite's speed, and r is the radius of the orbit.

Given the values:

Gravitational constant (G) = 6.67259 x 10^-11 N·m^2/kg^2

Mass of the Moon (M) = 7.36 x 10^22 kg

Radius of the Moon (r) = 865.2 km = 8.652 x 10^5 m

To find the satellite's acceleration, we need to calculate the radius of the orbit first. Since the satellite is in a circular orbit just above the surface of the Moon, the radius of the orbit is equal to the radius of the Moon:

r = 8.652 x 10^5 m

Now we can calculate the acceleration:

a = (G * M) / r^2

a = (6.67259 x 10^-11 N·m^2/kg^2 * 7.36 x 10^22 kg) / (8.652 x 10^5 m)^2

Simplifying the expression:

a ≈ 1.622 m/s^2

Therefore, the satellite's acceleration is approximately 1.622 m/s^2.

To find the satellite's speed, we can use the following formula:

v = √(G * M / r)

Substituting the values:

v = √(6.67259 x 10^-11 N·m^2/kg^2 * 7.36 x 10^22 kg / 8.652 x 10^5 m)

Simplifying the expression:

v ≈ 1,678.14 m/s

Therefore, the satellite's speed is approximately 1,678.14 m/s.

To find the period of the satellite's orbit, we can use the following formula:

T = 2πr / v

Substituting the values:

T = (2π * 8.652 x 10^5 m) / 1,678.14 m/s

Simplifying the expression:

T ≈ 3,263.81 seconds

Therefore, the period of the satellite's orbit is approximately 3,263.81 seconds.

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A light wave with an electric field amplitude of 2E0 and a phase constant of zero is to be combined with one of the following waves. Which of these combinations produces the least intensity

Answers

The combination that has the greatest intensity is C. Wave C has an amplitude of 2E0 and a phase constant of zero.

What does amplitude mean?

An amplitude is a variable that measures changes in a single variable. Such as the distance between the mean position and an extreme that a vibrat movement (such as a pendulum) travels. The largest difference between an alternating current's or wave's value and its average value.

What does electromagnetic wave mean?

Electromagnetic waves, such as radio waves, infrared, visible light, ultraviolet, X-rays, and gamma rays, that are propagated by periodic fluctuations in the strength of the electric and magnetic fields occurring simultaneously.

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Electron affinity is the energy associated with the gain of an electron by an atom in the gaseous state. Which element will release the most energy when gaining an electron?.

Answers

The element which release most energy while gaining an electron is Chlorine.

Chlorine has a higher affinity for electrons than fluorine does, despite the fact that fluorine is intended to have halogens with higher electron affinity .Therefore, chlorine has the highest electron affinity among the all elements in the group.

When an electron is added to a neutral atom to create a negatively charged ion, how much energy is released. Only a few chemical elements, primarily the halogens, have values available since it is difficult to determine the affinities of atom’s electrons.

Low melting and boiling points characterize the halogens. They all react with hydrogen to create acids. Salts are easily formed when they react with metals. Their outer shell contains seven valence electrons.

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A body at rest is given an initial uniform acceleration of 8m/s2 for 30s after which the acceleration is reduced to 5m/s2 for the next twenty seconds. The body maintains the speed attained for 60s, after which it is brought to rest in 20s.​

Answers

Explanation:

v=u+at, where v,u,a and t are the final velocity, initial velocity, acceleration and time, respectively.

For t=0 s to t=30 s , a =8 m/s 2.

For t=30 s to t=50 s , a = 5 m/s 2.

For t=50 s to t=110 s , a = 0 m/s 2.

For t=110 s to t=130 s , a is such that the body comes to rest at the end of this period.

For t=0 s to t=30 s ,v=0+8t⇒v=8t m/s.

At t=30s,v=8×30=240 m/s.

For t=30 s to t=50 s ,v=240+5(t−30)⇒v=90+5t m/s

At t=50s,v=90+5×50=340 m/s.

For t=50 s to t=110 s ,v=340 m/s.

For t=110 s to t=130 s ,v=340+a(t−110).

The body comes to a halt at t=130 s ⇒0=340+a(130−110).

0=340+20a⇒a=−34020=−17 m/s2.

For t=110 s to t=130 s ,v=340−17(t−110)=2210−17t m/s.

The acceleration due to gravity on Pluto is less than that on the Earth. The mass of a person on Pluto will be

Answers

The exact same.  gravity has no effect on mass.

Answer:

The acceleration due to gravity on Pluto is less than that on the Earth. The mass of a person on Pluto will be Less

Explanation:

Please help ASAP !!

Explain how genetic variation is an important part of natural selection.

Please help ASAP !!Explain how genetic variation is an important part of natural selection.

Answers

Genetic variation can be bad or good to an organism . If it affects positively then, the organism can have more adaptable features to survive in the environment. For those in which worse genetic variations are happens cannot survive and will given out the way to the fittest to live.

What  are genetic variations?

Genes are the basic hereditary material in living things. Genes from the parent are inherited to their offsprings. Genes undergo variations or mutations by some internal factors. These can produce both good and bad results.

The given passage can be completed as follows:

Natural selection is defined as a process in which organisms that do will in an environment pass their genes on next generation. Over time, these genes can become more common in a population.

However, natural selection doesn't work in all situations. It works only when there are variations within the population. Some individual are more suited to the environment. This means that they are  better able to survive or reproduce. There must be variations in the genes.

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explain how you could predict the amount of water displaced by a block that sinks without putting it into the water. read this to me hint: in your data table, look at the amount of water displaced by sinking blocks. what else does that amount equal?

Answers

To predict the amount of water displaced by a sinking block, you can determine its volume using its dimensions and applying the Archimedes' principle.

To predict the amount of water displaced by a block that sinks without actually placing it in water, you can use the following steps:
1. Measure the dimensions of the block (length, width, and height).
2. Calculate the volume of the block by multiplying its length, width, and height (Volume = Length × Width × Height).
3. Apply Archimedes' principle, which states that the weight of the water displaced is equal to the weight of the submerged object. In other words, the volume of the water displaced will be equal to the volume of the block.
4. Assuming the block is fully submerged, the amount of water displaced would be equal to the volume of the block, which you calculated in step 2.
By following these steps, you can estimate the amount of water displaced by a block without actually submerging it.

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Dimas reads that it takes 270 N to lift a firefighter's equipment. If a firefighter does 5400 J of work carrying the equipment up a staircase, how high does the firefighter climb? (Work: W = Fd) 20 m 200 m 5130 m 1,458,000 m

Answers

Answer:

h = 20 m

Explanation:

Given that,

Force to lift a firefighter's equipment, F = 270 N

Work done, W = 5400 J

We need to find the height climbed by the firefighter. We know that,

Work done, W = Fd

So,

\(d=\dfrac{W}{F}\\\\d=\dfrac{5400}{270}\\\\d=20\ m\)

So, the firefighter climb from a height of 20 m.

Answer:

Its A

Explanation: I got it right on Edge *lip bite*

Rock layer that must be rich in organic matter that was subjected to heat and pressure overtime during the formation of oil and natural gas

Answers

The lowest rock layer is a layer that must be rich in organic matter that was subjected to heat and pressure over time during the formation of oil and gas.

The lowest rock layer can be explained as;

The lowest rock layer refers to the lowermost part of the Earth's mantle, which is a thin rock layer (approximately 250 km).

In the Earth, the layers of rocks are progressively deposited, thereby pressing them to the bottom to generate sedimentary rocks.

The lowest rock layers on the bottom must be rich in organic matter to form fossil fuels.

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NEED HELP!!! ANSWER THESE 5 QUESTIONS FOR 25 POINTS!!!! PLEASE ANSWER!! I WILL GIVE YOU BRAINLIEST

1. Therese plays lacrosse, but she has injured her ankle and has to take a few weeks off. She is finding that she has a lot of trouble sleeping since she is no longer practicing several days a week. What BEST explains this?
A.
She needs regular exercise to move oxygen through the blood.
B.
She clearly requires more exercise than most people to relieve stress.
C.
She is not releasing the endorphins that she used to, and that impacts her sleep.
D.
She is likely not maintaining the healthy habits that she did when she was practicing.


2. Imagine that you are running and want to track your heart rate. What is the easiest way to do this?
A.
Check your pulse at the wrist or neck.
B.
It can’t be done without special equipment.
C.
Close your eyes and count to 30 very slowly.
D.
Take off your shoe and check the top of your foot.


3. Guillermo has decided that he wants to be healthier, so he starts jogging. He has been at it for a week, but he is getting frustrated because he cannot run very far without getting out of breath. He is beginning to think that this is not a good exercise for him since he is not very good at it. What BEST explains why Guillermo is struggling?
A.
He probably does not have good form when he is exercising.
B.
He likely has heart or lung problems that he was not aware of.
C.
He does not have much endurance since he is new to exercise.
D.
He is just not good at jogging and needs to try something else.

4. Li Wei loves cardio and finds it very easy to fit into his schedule. Because he knows it is important to diversify his exercise routine, sometimes he runs and other days he rides his bike. What else should Li Wei consider regarding his routine?
A.
He should add some strength training.
B.
He needs to add one more form of cardio.
C.
He has too much cardio and should cut half of it.
D.
His program works for him, so he should not change it.


5. Jamar has decided that he is going to train for a marathon. He knows that it will take a lot of training, and that he will need to build his muscles. What part of the muscle does he need to build?
A.
oxygen levels
B.
fast twitch fiber
C.
slow twitch fibers
D.
large muscle mass


PLEASE NO LINKS

Answers

Answer:

1.A

2.C

3.A

4.B

5.D

Explanation:

CORRECT ME IF IM WRONG

To determine the location of her center of mass, a physics student lies on a lightweight plank supported by two scales 2.50m apart, as indicated in the figure . If the left scale reads 290 N, and the right scale reads 112 N. What is the student's mass and find the distance from the student's head to her center of mass.

Answers

The location of her centre of mass, a physics student lies on a lightweight plank supported by two scales 2.50m apart, as indicated in the figure. If the left scale reads 290 N and the right scale reads 112 N The student's mass is approximately 41 kg, and the distance from her head to her centre of mass is approximately 0.696 m.

To determine the student's mass, we can sum up the readings from both scales, which are measures of force (Newtons) and then convert it to mass using the gravitational acceleration (g = 9.81 m/s²).
Step 1: Calculate the total force acting on the plank:
Total Force = Force_left_scale + Force_right_scale
Total Force = 290 N + 112 N
Total Force = 402 N
Step 2: Convert the total force to mass using gravitational acceleration:
Mass = Total Force / g
Mass = 402 N / 9.81 m/s²
Mass ≈ 41 kg
Now, to find the distance from the student's head to her centre of mass, we'll use the principle of torque equilibrium.
Step 3: Set up the torque equation:
Torque_left_scale = Torque_right_scale
Force_left_scale × Distance_left_scale = Force_right_scale × Distance_right_scale
Let x be the distance from the student's head to her centre of mass. Then, the distance from the left scale to the centre of mass is x, and the distance from the right scale to the centre of mass is (2.50 - x).
Step 4: Plug in the known values and solve for x:
290 N × x = 112 N × (2.50 - x)
Step 5: Simplify the equation and solve for x:
290x = 112(2.50) - 112x
290x + 112x = 112(2.50)
402x = 280
x ≈ 0.696 m
The student's mass is approximately 41 kg, and the distance from her head to her centre of mass is approximately 0.696 m.

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3. A 100 kg crate is sliding at a rate of 30.0 m/s, when a force of 250 N is applied opposite the
direction of motion, in addition to the friction, until the crate stops 5.0 s later. What is the
coefficient of kinetic friction between the crate and the floor?

Answers

Take the direction of motion to be the positive direction. The crate slows to a rest from 30.0 m/s in a matter of 5.0 s, so it has acceleration a such that

0 = 30.0 m/s + a (5.0 s)   →   a = -6.0 m/s²

At the moment its speed is 0, the crate has a net force of s + f acting in negative direction, where s and f denote the magnitudes of the stopping force (s = 250 N) and the friction force, respectively. By Newton's second law, we have

(-s) + (-f) = (100 kg) (-6.0 m/s²)

250 N + f = 600 N

f = 350 N

The friction force is proportional to the normal force by a factor of µ, the coefficient of kinetic friction. There is no movement in the up- and downward directions, so Newton's second law says

(-w) + n = 0

where w is the weight of the crate and n is the magnitude of the normal force. So

n = w = (100 kg) (9.80 m/s²) = 980 N

Then

f = µ n

350 N = µ (980 N)

µ = (350 N) / (980 N) ≈ 0.357

The steepest street in the world is Baldwin Street in Dunedin, NZ. It is inclined at an angle of 380 , with the horizontal. A child slides down the street with a constant velocity on a sled with high friction runners. What is the coefficient of friction between the sled runners and the street?

Answers

Newton's second law allows to find the result for the friction coefficient of the street is:

The friction coeficinwete is: μ = 0.78

Newton's second law establishes a relationship between the net force, the mass and the acceleration of the body.

           ∑ F = m a

Where bold indicates vectors, m is to mass and acceleration.

In the attached we see a free body diagram, it is a diagram of the forces without the details of the body, the x-axis is parallel to plane also shown with the positive in the direction of movement, going down the plane and the y-axis perpendicular to the plane.

Let's use trigonometry to break down the weight.

        Sin θ = \(\frac{W_x}{W}\)  

        cos θ = \(\frac{W_y}{W}\) / W

        Wₓ = W sin θ

         \(W_y\)  = W cos θ

We write Newton's second law for each axis.

y-axis

         N- \(W_y\)  = 0

         N = mg cos θ

x-axis

        Wₓ - fr = ma

Since they indicate that the body goes down at a constant speed, the acceleration is zero.

         W sin θ = fr

The friction force is the macroscopic representation of the interactions between the two surfaces and the formula.

         fr = μ N

we substitute.

          fr = μ mg cos θ

         mg sin θ = μ cos θ  

        μ = tan θ

Let's calculate.

         μ = tan 38.0

         μ = 0.78

In conclusion using Newton's second law we can find the results for the friction coefficient of the street is:

The frivtion coefficient is:  μ = 0.78

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The steepest street in the world is Baldwin Street in Dunedin, NZ. It is inclined at an angle of 380

Which of the following situations would violate the second law of thermodynamics?
A. Ice melting in a glass of lemonade on a hot day
B. A cup of lemonade turning to ice in freezing weather
C. A glass of lemonade starting to freeze in a warm room
D. Lemonade being frozen into ice in a freezer

Answers

Answer:

C. A glass of lemonade starting to freeze in a warm room.

Explanation:

This is because there is no source of cold to properly freeze the lemonade, freezing happens when a cold source starts to slow down the movement of atoms. So if there's nothing there to freeze it, it can't freeze.

Alternatively, there are some materials that harden when not subjected to heat, but that's not freezing. It's just cooling.

why does a thrown football have both potential and kinetic energy?what is the combined energy called?
i will give brainliest to who ever answers this question in a paraghraph

Answers

Answer:

The thrown football has Potential or stored Energy, PE, by virtue of its position in the air and the ability for it to fall by itself. The thrown football also has Kinetic Energy, KE, given that the ball is in motion and requires an equal and opposite amount of energy to stop it. Both the PE and the KE  are forms of Mechanical Energy, ME and the Mechanical Energy of the football is equal to the sum of its Potential and Kinetic Energy. That is ME = PE + KE

Explanation:

Potential energy, PE, is the energy that is the held or stored energy of a body such that the body is able to do work without the addition of energy from an external source

A thrown football that has an elevation or height above the floor level has the capacity to come back down and bounce on the floor without the presence of assistance at the topmost height of the football. Therefore, the thrown football has potential energy, given to it by the thrower

Kinetic Energy, KE, is the energy possessed by a moving that comes from the motion of the object

Given that the thrown football is in motion, it posses kinetic energy

Therefore, the thrown football possesses both potential energy and kinetic energy which are forms of mechanical energy ME

The combined energy of the football is therefore called the Mechanical Energy ME of the ball which is the sum of the potential and kinetic energies of the football, given as follows;

The Mechanical Energy of the football = The Potential Energy of the football + The Kinetic Energy of the football

∴ ME = PE + KE

a driver travels 135 km east in 1.5 h stops for 45mins for lunch and then resumes driving fir the next 2.0h through a displacment of 215 kn east. what is the drivers average velocity?

Answers

A driver travels 135 km east in 1.5 h stops for 45mins for lunch and then resumes driving fir the next 2.0h through a displacement of 215 kn east.  the drivers average velocity is 82.3 km / hr.

given that :

distance travel d1 = 135 km

time taken t1 = 1.5 h

hault time t = 45 mins = 0.75 h

distance travelled d2 = 215 km

time t2 = 2.0 h

Average velocity  =  Total time taken / time

Average velocity = ( 135 km + 215 km ) / ( 1.5 h + 0.75 h + 2.0 h)

                            = 350 km / 4.25

                            = 82.3 km / hr

Thus, A driver travels 135 km east in 1.5 h stops for 45mins for lunch and then resumes driving fir the next 2.0h through a displacement of 215 kn east.  the drivers average velocity is 82.3 km / hr.

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an astronomer wants to observe a cloud of cold neutral (not ionized) hydrogen, far away from any stars. what would be an instrument that could help in this task?

Answers


A radio telescope, tuned to a wavelength of about 21 centimeters.

Which of the following examples represent a bony joint, or synostosis?
Multiple Choice
A synostosis develops at the ends of the tibia and fibula to help hold them together.
Cranial sutures form as a synostosis when the baby's fontanels close.
A synostosis occurs in the jaw when a child's permanent teeth come in.
An infant is born with right and left mandibular bones, but they soon fuse into a single bone.
When the two maxillary bones unite to form the anterior two-thirds of the hard palate, a synostosis develops.

Answers

A synostosis develops at the ends of the tibia and fibula to help hold them together. synostosis, or the fusion of separate bones, occurs at the ends of the tibia and fibula, during the fusion of the mandibular bones, and when the two maxillary bones unite to form the hard palate.

Among the given options, the examples that represent a bony joint or synostosis are:

A synostosis develops at the ends of the tibia and fibula to help hold them together.

An infant is born with right and left mandibular bones, but they soon fuse into a single bone.

When the two maxillary bones unite to form the anterior two-thirds of the hard palate, a synostosis develops.

A synostosis at the ends of the tibia and fibula refers to the fusion or joining of these two bones, resulting in a bony joint. This fusion provides stability and strength to the leg.

In the case of an infant being born with separate right and left mandibular bones, they eventually fuse together into a single bone. This fusion of the mandible represents a synostosis, forming the lower jaw bone.

The fusion of the two maxillary bones to form the anterior two-thirds of the hard palate is another example of a synostosis. The maxillary bones fuse during development to create a single, solid structure that forms the hard palate in the roof of the mouth.

In summary, synostosis, or the fusion of separate bones, occurs at the ends of the tibia and fibula, during the fusion of the mandibular bones, and when the two maxillary bones unite to form the hard palate.

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Do you think it’s wise for scientists not to accept a theory immediately, even if the theory has a lot of evidence to support it? Explain your reasoning.

Answers

The scientific theory cannot be accepted immediately, because there is always the possibility of discovering new information or modification.

What is a scientific theory?

A scientific theory is an explanation of the natural world and universe that has been repeatedly tested in accordance with the scientific method. Theories are tested under controlled conditions in an experiment and are evaluated through principles of abductive reasoning.

A scientific theory differs from scientific law in that a theory explains how or why is a basic observation, whereas a law is a statement about a relationship between facts. Newton’s Law of Gravity is a mathematical equation that can be used to find the attraction between objects, but it is not a theory to describe how gravity works.

If experimental results contrary to predictions of the theory are observed, scientists evaluate whether the experimental design was good and confirm the results by independent replication.

Solutions may need some changes to the theory, or none at all, and after the successive modifications, theories consistently improve and greater accuracy is achieved.

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2. What is the period of 350 waves passing a point in 5 seconds?​

Answers

Answer:

IF SHE BREATHS SHES A T.H.OT

Explanation:

Pls dont hate me its meme k ,_.

There is concern that extra additives in detergents can
have negative health and environmental impacts. Is
it wise to use detergents containing these additives?

Answers

Answer:

Look below.

Explanation:

If additives are having negative effects on health and the environment, it would be wise to not use detergents containing these additives. These additives could threaten living things such as humans and animals.

There is concern that extra additives in detergents can have negative health and environmental impacts, then it would be very unwise to use detergents containing these additives

What is pollution?

It can be defined as the origination of the contaminant substance that poisonous or harmful to our natural environment.

There are several types of pollution that exist in our nature depending on the state and composition of the contaminant, for example, water pollution can exist due to the eutrophication process.

It would be quite unwise to use surfactants that include these additional ingredients since there is fear that they might have a harmful influence on your well-being and the environment.

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The position of a particle moving in the xy-plane is given by the parametric equations r = ( 3t and V = 2t 3t 2 12t _ For what values of t is the particle at rest?

Answers

All components of the velocity vector are zero for t = 0, the particle is at rest for t = 0.

For what values of t is the particle at rest?

The position of a particle moving in the xy-plane is given by the parametric equations r = (3t) and v = (2t, 3t², 12t). To find for what values of t the particle is at rest, we need to find when the velocity vector (v) is equal to zero.

The velocity vector v is given by (2t, 3t², 12t). For the particle to be at rest, all components of the velocity vector must be equal to zero.

1. For the x-component (2t) to be zero: 2t = 0. Solving for t, we get t = 0.

2. For the y-component (3t²) to be zero: 3t² = 0. Solving for t, we get t = 0.

3. For the z-component (12t) to be zero: 12t = 0. Solving for t, we get t = 0.

Since all components of the velocity vector are zero for t = 0, the particle is at rest for t = 0.

Learn more about parametric equations.

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