4. The diagram shows two forces of 5 N and 8 N acting at 120° to each other. Calculate the resultant of these two forces and state its direction relative to the 5 N force. Illustrate your answer with an appropriate vector diagram.​

4. The Diagram Shows Two Forces Of 5 N And 8 N Acting At 120 To Each Other. Calculate The Resultant Of

Answers

Answer 1

The magnitude of the resultant force is 11.4 N.

What is the resultant force?

The resultant force is the force that has the same effect both in magnitude and in direction as the two or more forces acting at the same time. We know that force is a vector quantity, this implies that both the magnitude and the direction of the force are all important. This is why we have to factor in the direction of the force at all times.

Now, we can see that, it is possible to obtain the resultant force from the parallelogram law of vectors. We can see that;

R = √ P^2 + Q^2 - 2PQ Cos θ

P = 5 N

Q = 8 N

θ =  120°

R = √(5^2 + 8^2 - (2 * 5 * 8) cos 120

R = 11.4 N

The direction of the 5N force is obtained as;

Tan^-1 (8/5)

= 58 degrees

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Related Questions

what is the wavelength (in nanometers) of gamma rays of frequency 6.52×1021 hz ? express your answer in nanometers.

Answers

We can use the equation c = λf, where c is the speed of light, λ is the wavelength, and f is the frequency. Therefore, the wavelength of these gamma rays is approximately 0.459 nanometers.

We can use the equation c = λf, where c is the speed of light, λ is the wavelength, and f is the frequency.

c = 299,792,458 m/s (speed of light)

f = 6.52 × 10^21 Hz (given frequency)

Solving for λ:

λ = c / f

λ = 299,792,458 m/s / 6.52 × 10^21 Hz

λ = 4.59 × 10^-14 m

To express the wavelength in nanometers, we can multiply by 10^9:

λ = 4.59 × 10^-14 m * 10^9 nm/m

λ ≈ 0.459 nm

Therefore, the wavelength of these gamma rays is approximately 0.459 nanometers.

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During cellular respiration, light energy is converted into cellular energy.

True
False

Answers

Answer:

true

Explanation:

i think it's true I'm not exactly sure

Of the five zones to consider when discussing human fitness which do you believe is the most important and why do you believe this

Answers

I believe the most important zone is cardiovascular, as it is essential for maintaining a healthy heart and lungs.

why  human fitness important? Human fitness is important for several reasons. Firstly, it helps maintain good physical health. Regular physical activity helps to strengthen bones and muscles, reduce the risk of heart disease, maintain a healthy weight, and reduce the risk for other chronic diseases. Secondly, fitness can improve mental health. Exercise releases endorphins, which can reduce stress, improve mood, and increase self-confidence. Additionally, fitness can help improve cognitive functioning. Research has shown that physical activity can improve focus and concentration, and can lead to better academic performance. Lastly, regular physical activity can help improve sleep quality. Exercise can help people fall asleep faster and stay asleep longer, leading to increased energy and alertness during the day. In conclusion, human fitness is important for physical, mental, and cognitive health. Regular physical activity can lead to a healthier and happier lifestyle.

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A vector quantity is one that has both a magnitude and a direction. For instance, a velocity vector will have a magnitude (24 m/s) and a direction (northeast or 45 degrees). These simulations will demonstrate how vectors can be summed to produce a resulting vector, and how the acceleration vector affects the velocity vector. Part I: 2D Motion Simulation: Open the simulation Motion in 2D 1. Click Stop. Drag the object around with your mouse and notice the actions of the two vectors. Spend some time investigating the vectors. Which vector is velocity and which is acceleration (blue or green)? 2. Click on Linear Acc 1. Observe the motion. a. What orientation must the vectors be for the object to speed up? Draw and label this. b. What orientation must the vectors be for the object to slow down? Draw and label this. 3. Click Simple Harmonic (this is simple motion of a mass on a spring). Observe the motion. 4. Click Circular. Observe the motion. What orientation must the vectors (relative to each other) have to turn the object? Draw and label this. 5. Click Stop. Attempt to move the object like a planet in orbit (an ellipse, like an oval). What must the object do in order to turn?

Answers

1. The vector for velocity is represented by the blue arrow, and the vector for acceleration is represented by the green arrow in the simulation.

2. a. For the object to speed up, the orientation of the vectors should be in the same direction.

b. For the object to slow down, the orientation of the vectors should be in opposite directions.

3. In the Simple Harmonic motion, the object moves back and forth in a linear path.

4. In the Circular motion, the orientation of the vectors (relative to each other) determines the turning of the object: The blue (velocity) vector should be tangent to the circular path, indicating the direction of the object's motion.

5. When attempting to move the object like a planet in orbit (an ellipse), the object must follow an elliptical path.

1. The vector for velocity is represented by the blue arrow, and the vector for acceleration is represented by the green arrow in the simulation.

2. When observing the Linear Acc 1 motion, we can determine the orientation of the vectors for the object to speed up or slow down:

a. For the object to speed up, the orientation of the vectors should be in the same direction. This means that the blue (velocity) and green (acceleration) vectors should be pointing in the same direction.

b. For the object to slow down, the orientation of the vectors should be in opposite directions. This means that the blue (velocity) and green (acceleration) vectors should be pointing in opposite directions.

3. In the Simple Harmonic motion, the object moves back and forth in a linear path. The orientation of the vectors does not play a significant role in this motion.

4. In the Circular motion, the orientation of the vectors (relative to each other) determines the turning of the object:

The blue (velocity) vector should be tangent to the circular path, indicating the direction of the object's motion. The green (acceleration) vector should be pointing towards the center of the circle, providing the centripetal acceleration necessary to maintain circular motion.

5. When attempting to move the object like a planet in orbit (an ellipse), the object must follow an elliptical path. This requires the object to continuously change its velocity vector and direction. The object must constantly accelerate towards the center of the ellipse to maintain the curved path.

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7. What causes some metallic bonds to be stronger than others?

A.the number of donated valence electrons


B.the number of metallic bonds


C.the fineness of the metal


D.the number of metal ions

Answers

Answer:

the number of donated valence electrons

Explanation:

  A metallic bond is formed when atoms come together in a metallic crystal lattice.

The metal atoms are usually ionized such that in a metallic crystal lattice consists of metal ions and a sea of mobile electrons. Attraction between these positively charged ions and the sea of electrons constitutes the metallic bond.

Hence, the more the number of donated valence electrons, the stronger the metallic bond.

What happens to the density of an object if the mass increases, but the volume remains the same?

Answers

A measure of mass per unit of volume. It is how much material a certain volume contains. ... If the volume of the object stays the same but the mass of the object increases then its density becomes greater.

a.) What happens when a force is applied to an atom? b.) What is this called? ​

Answers

Answer:

it binds the negatively charged electrons to the positively charged atomic nucleus.

Explanation:

its called Electromagnetic Force

Electrostatic force. As the number of protons inside a nucleus increases the electrostatic repulsion between protons increase reducing the binding energy.

Those of you who have recently finished high school physics-did you struggle? If you did, where did you most struggle in? Was it the tests? Or a specific topic?
Thank you!

Answers

Answer:

I'm over halfway through it so don't have a complete answer but i think you just need to keep ontop of everything and write down all the key equations on flashcards or something and aim to learn them at the beginning of each topic. i found the longer questions hard so recommend practising those

Explanation:

A type of organism that makes its own food. __________
The highest taxonomic classification of organisms.__________
The process through which organisms make new organisms of the same kind. _______
The taxonomic classification below domains._________
A type of organism that is made of more than one cell and is more specialized and eukaryotic.__________
A characteristic passed from female and male parents to their offspring.________

FILL IN THE BLANKS PLEASEEE WILL GIVE BRAINLIEST AND 50 POINTS

Answers

Answer:

1. An autotroph

2. Domain

3. Reproduction

4. Kingdom

5. Multicellular Organism

6. Genetic trait

Explanation: Took Bio honors 1 & 2

5. In the image below, the focus lines are shown. What can be done to bring the apple into focus?
A. Make the lens rounder.
B. Make the lens flatter.
C. Move the apple farther from the eye.
D. Nothing should be done because the apple is already in focus.

Answers

In the image below, the focus lines are shown. The step can be done to bring the apple into focus is make the lens rounder. The correct option is A.

What is lens?

The lens is in spherical shape may be diverging or converging.

As light enters the eye, it is focused on the retina. Changing the pupil diameter, regulates the amount of light entering the eye. Changing lens shape will focus the light.

The changes in lens shape needed to maintain focus as the object distance changes.

Thus, the correct option is A.

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5. In the image below, the focus lines are shown. What can be done to bring the apple into focus?A. Make

an oscilloscope is set in the 0.5volt per division scale. the signal measures four whole divisions. what is the value of voltage?

Answers

The voltage measured by the oscilloscope is 2 volts.

What is an oscilloscope and how is the voltage scale calibrated on it?

An oscilloscope is a device used to display and analyze the waveform of electronic signals. The voltage scale on an oscilloscope is usually calibrated in volts per division. This means that each division on the screen represents a certain amount of voltage.

In the given scenario, the oscilloscope is set in the 0.5 volts per division scale. This means that each division on the screen represents 0.5 volts of voltage. The signal measures four whole divisions, which means the total voltage can be calculated by multiplying the number of divisions by the volts per division.

Therefore, the value of voltage can be calculated as follows:

4 divisions x 0.5 volts per division = 2 volts

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Decide whether the following statement is true (T) or false (F).

Original seat belt designs were 2-point or lap belts

1. True
or
2. False

Answers

I really hope this is true. also pay no attention to this answer I'm doing it to finish my account

Answer:

True

Explanation:

See picture.

Decide whether the following statement is true (T) or false (F).Original seat belt designs were 2-point

What happens to speed when you decrease the time needed to run the same distance?

Answers

Answer:

Faster

Explanation:

What happens when a proton is placed directly in the path of the proton cannon?

Answers

Answer:

Proton is positively charged and is thus, attracted to the negative plate. Hence, it will take the path D after leaving the region between the charged plates.

When a proton is placed directly in the path of the proton cannon, it will experience a strong electromagnetic force. The proton cannon emits a beam of protons at high energy and velocity. When the proton in the path of the cannon interacts with the beam, there will be a collision between the two protons.

During the collision, the protons may undergo a process called scattering, where they change direction and momentum. The exact outcome of the collision depends on the energy and angle of the incoming proton, as well as the properties of the target proton. It is possible that the protons may scatter off each other, transferring energy and momentum in the process.

In some cases, the collision may result in the absorption of the incoming proton by the target proton. This can lead to the formation of a more massive particle or the emission of other particles. The specifics of the interaction will depend on the energy and conditions of the proton cannon and the characteristics of the protons involved.

Overall, placing a proton directly in the path of a proton cannon will result in a collision and potential scattering or absorption of the protons, causing changes in their momentum and possibly leading to the creation of other particles.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The starting velocity was 0 m/s, and the final velocity

was -15.35 m/s. Based on this, what was the average

velocity of the rock? In general, to find the average of

any 2 things, you add them together and divide by how

many things there are.

Answers

Answer:

The average velocity is -7.675 m/s

Explanation:

Given;

initial velocity, u = 0 m/s

final velocity, v = -15.35 m/s

Based on the follow up state " In general, to find the average of any 2 things, you add them together and divide by how many things there are", the average velocity will be calculate as ;

Sum of the velocities = 0 m/s + (-15.35 m/s) = -15.35 m/s

Number of velocites = 2

AVERAGE VELOCITY = (-15.35 m/s) / (2)

AVERAGE VELOCITY = -7.675 m/s

A trip is taken that passes through the following points in order
Point A 0 m
Point B 15.0 m
Point C -30.0 m
Point D -20.0 m
Point E 10.0 m
Point F 5.0 m
What is the distance from Point B to Point E?

A) -35.0 m
B) -5.0 m
C) 85.0 m
D) 55.0 m

Answers

Answer:

B) - 5.0 m

Explanation:

B is located on a positive location, 15m from the starting point A. Hence, since E is located a positive distance 10m from A, the difference becomes 10 - 15 = - 5.0 m

A uniform rod with mass 6M and length 2L is rotating freely around an axis.
(1)
(2)
A) What is the angular velocity at position 1?
B) What is the velocity of the center of mass at position 2, given the angle theta relative to position 1?

Answers

(1) The angular velocity at position 1 of a uniform rod rotating freely around an axis can be determined.

(2) The velocity of the center of mass at position 2.

(1) To determine the angular velocity at position 1, we need to consider the conservation of angular momentum. Since the rod is rotating freely, there are no external torques acting on it.

The initial angular momentum is zero, and at position 1, the angular momentum is given by L = Iω, where I is the moment of inertia of the rod and ω is the angular velocity. By substituting the values of mass and length of the rod into the formula for moment of inertia, we can solve for ω.

(2) To calculate the velocity of the center of mass at position 2, relative to position 1 and at an angle theta, we can use the concept of angular velocity and linear velocity. The linear velocity of the center of mass is given by v = ωr, where ω is the angular velocity and r is the distance between the center of mass and the axis of rotation. By considering the given angle theta and the length of the rod, we can determine the distance r.

Substituting the value of ω calculated in part (1) into the formula, we can find the velocity of the center of mass at position 2, relative to position 1 and at angle theta.

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A racecar on a straight track, starting from rest*, steps on the
accelerates towards the finish line at 10.0 m/s^2. If the finish line is
500.0m away, how yong does it take the car to cross the finish line?"
A 5.08
B 10.05
C 20.05
D 50.0s
E 100.0

Answers

I think the answer is C

Four students travelling to a sporting event make a
mistake with their directions and end up travelling out of their way. They are able to use a map to get
themselves back on track, but their mistake caused
them to travel 15 km [N] and then 5.3 km [W].
What displacement resulted from their wrong
directions? (2.2)

Answers

The displacement for wrong directions is 6.6 km

if the jet in ngc 5128 is traveling at 5000 km/s and is 40 kpc long, how long will it take for gas to travel from the core of the galaxy to the end of the jet?

Answers

It would take approximately 2.4688 × 10^17 seconds or 7.82 million years for gas to travel from the core of the galaxy to the end of the jet, assuming a constant speed of 5000 km/s.

To calculate the time it would take for gas to travel from the core of the galaxy to the end of the jet, we need to use the formula: time = distance / speed.

Given that the jet in NGC 5128 is traveling at 5000 km/s and is 40 kpc (kiloparsecs) long, we first need to convert the distance from kpc to km. 1 kpc = 3.086 × 10^16 meters, which means 1 kpc = 3.086 × 10^19 km.

Therefore, the length of the jet in kilometers is 40 x 3.086 × 10^19 km = 1.2344 × 10^21 km.

Now we can calculate the time it would take for gas to travel from the core of the galaxy to the end of the jet as follows:

time = distance / speed
time = 1.2344 × 10^21 km / 5000 km/s
time = 2.4688 × 10^17 seconds

So, it would take approximately 2.4688 × 10^17 seconds or 7.82 million years for gas to travel from the core of the galaxy to the end of the jet, assuming a constant speed of 5000 km/s.

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A 2-kg mass weighs 20 N and is held 4 m above the ground. Its potential energy relative to the ground isa) 80 J.b) 8 J.c) 60 J.d) 20 J.e) none of the above

Answers

The potential energy of the 2-kg mass relative to the ground is approximately 80 J.

A sort of energy known as potential energy is one that an object holds as a result of its location or circumstance. It is the energy that is conserved inside a system and has the capacity to be transformed into different types of energy, such as thermal or kinetic energy. Affected by variables like height, distance, and forces operating on it, an object's potential energy relies on where it is in relation to other objects or reference points.

The correct answer is a) 80 J.

The potential energy of an object is given by the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity (9.8 \(m/s^2\)), and h is the height of the object above a reference level (in this case, the ground).

Using the given values, we have:

PE = (2 kg)(\(9.8 m/s^2\))(4 m)
PE = 78.4 J

Therefore, the potential energy of the 2-kg mass relative to the ground is approximately 80 J.


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I need severe help

a cat ran west for 30 meters and it took them 5 seconds, what was the average speed of the cat? Don’t forget units!

Answers

Distance= 30 meters
Time= 5 seconds
Average speed= distance/time
30m/5sec= 6m/s

A bungee jumper jumps off a bridge and bounces up and down several times.
She finally comes to rest 16 m below the bridge from which she just jumped.
If her mass is 50 kg and the spring constant of the bungee cord is 35 N/m,
how much energy was lost due to air resistance while she was bouncing?
(Recall that g = 9.8 m/s²)
OA. 5420 N
OB. 3360 N
OC. 4280 N
O D. 6550 N

Answers

The energy that was lost due to air resistance while she was bouncing is determined as 3,360 J.

Conservation of energy

The amount of energy lost due to  air resistance while she was bouncing is determined from the principle of conservation of energy.

ΔE = P.E - Ux

ΔE = mgh - ¹/₂kx²

ΔE = (50)(9.8)(16) - ¹/₂(35)(16)²

ΔE = 3,360 J

Thus, the energy that was lost due to air resistance while she was bouncing is determined as 3,360 J.

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Nathan applies 40 newtons of force to a shopping cart. He moves the cart a distance of 5 meters. Nathan did how many newton-meters of work on the cart.

Answers

Answer:

                   200 newton-meters

what was the rule of the sticks on each atom model​

Answers

Answer:

That they must die

Explanation:

Stick = Die

Answer: That they must die


Excellent

How do Cirrus Clouds create a positive feedback mechanism?

Answers

Cirrus clouds create a positive feedback mechanism through their impact on Earth's radiation balance, amplifying the greenhouse effect and contributing to further warming of the atmosphere.

Cirrus clouds are high-altitude clouds composed of ice crystals and typically form at altitudes above 20,000 feet (6,000 meters). They are thin and wispy in appearance and are commonly associated with fair weather conditions. However, despite their benign appearance, cirrus clouds have a significant impact on Earth's climate system.

Greenhouse Effect: The greenhouse effect is a natural process by which certain gases in the Earth's atmosphere trap heat from the sun, preventing it from escaping back into space. These gases, including carbon dioxide (CO2) and water vapor (H2O), act as a blanket, warming the Earth's surface and lower atmosphere. The greenhouse effect is essential for maintaining habitable temperatures on Earth.

Radiative Forcing: Cirrus clouds play a role in the greenhouse effect through a process called radiative forcing. When sunlight reaches the Earth's surface, it is absorbed and re-emitted as thermal radiation (infrared radiation). This thermal radiation can escape into space or be absorbed by greenhouse gases in the atmosphere, which then re-radiate it in all directions, including back toward the Earth's surface. This downward re-radiation contributes to the warming of the lower atmosphere and is an important component of the greenhouse effect.

Positive Feedback Mechanism: Cirrus clouds have a unique property known as "infrared trapping." They are effective at trapping outgoing thermal radiation emitted by the Earth's surface, preventing it from escaping into space. The ice crystals in cirrus clouds act as efficient absorbers and emitters of infrared radiation, enhancing the greenhouse effect. This leads to an additional warming of the lower atmosphere.

Amplification of Warming: As the Earth's surface temperature increases due to various factors such as greenhouse gas emissions, the presence of cirrus clouds becomes more pronounced. The warming caused by greenhouse gases leads to an increase in the amount of water vapor in the atmosphere, which can then form more cirrus clouds.

This forms a positive feedback loop, as the increased cirrus cloud cover further enhances the greenhouse effect, amplifying the initial warming. The amplified warming can have significant implications for global climate patterns and weather systems.

In summary, cirrus clouds create a positive feedback mechanism by trapping outgoing thermal radiation, amplifying the greenhouse effect, and contributing to further warming of the atmosphere. This feedback loop reinforces the initial warming caused by greenhouse gases and can have important implications for the Earth's climate system.

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Who was awarded the highest-ever rank in the u. S. Armed forces? george patton douglas macarthur george washington dwight d. Eisenhower.

Answers

He attained the rank of military officer during the combat on the Western Front in World War I and was once more nominated for a Medal.

How do you define forces?

The pushing or push on a phalanx item alters its speed. An unseen factor is an agent that possesses the power to change the resting or traveling position of a body. It has a direction as well as a quantity.

What kind of force is it?

Contact forces and non-forces are two different kinds of forces. Nuclear force, gravitational force, frictional force, magnetic force, electrostatic force, spring force, and others are a few examples of forces.

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A marble is dropped into a graduated cylinder that is filled with water. Use the words

from the word bank to describe the speed and forces. Words may be used more than

once.

Point A: Speed

force

A

Point B: Speed

force

ml

Point C: Speed

force

30

B

20

is constant

increases

decreases

balanced

unbalanced

C

Answers

Answer:

v_t = \(\frac{2 g \ ( \rho_b - \rho_l ) r^2 }{9 \ \eta }\)

Explanation:

Let's describe the motion and forces on the marble when it falls into the graduated cylinder filled with water.

Initially, the marble in the air falls under the influence of its weight (gravity force), when it enters the water, a friction force appears that INCREASES with SPEED and opposes the movement, this force is called Stokes force.

             

              Fr = 6π R η v

where η is the viscosity of water

also because of this in a liquid it has an upward thrust, given by Archimedes' law, this thrust is CONSTANT

              B = ρ_l g V_l

in that case the volume of liquid(V_l)  is equal to the volume of the marble.

Constant force of gravity

               W = mg

using the concept of density

                ρ_body = m / V

                W = ρ_body g V_body

we apply Newton's second law

                Fr + B - W = ma

the friction force increases and the other two are constant, so acceleration decreases until reaching zero, at this point the forces are in BALANCE

                Fr + B - W = 0

and the speed remains constant, being called TERMINAL SPEED

                v_t = \(\frac{2 g \ ( \rho_b - \rho_l ) r^2 }{9 \ \eta }\)

from this point on, the displacement is proportional to the time

Question 6
Marks: 1
A ______ is a dimensionless unit to express physical intensity or sound pressure levels.
Choose one answer.

a. noise level

b. decibel

c. hertz

d. sound pressure level (SPL)

Answers

A decibel is a dimensionless unit to express physical intensity or sound pressure levels.

A decibel is a dimensionless unit to express physical intensity or sound pressure levels. The decibel, in turn, measures the power of the sound, its energy, and the stronger or weaker it is emitted. Measures the volume of the sound.  It is a logarithmic scale that quantifies the relative loudness or softness of a sound compared to a reference level. The decibel scale is based on powers of 10, where an increase of 10 dB represents a tenfold increase in sound intensity. The reference level for the decibel scale varies depending on the context. In the field of acoustics, the commonly used reference level is 0 dB, which corresponds to the threshold of human hearing. Positive decibel values indicate increasing sound levels, while negative values indicate decreasing sound levels or the absence of sound.

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Compare the amplitude of these waves.

Compare the amplitude of these waves.

Answers

Answer:

Explanation:

The answer to your question would be number 2 amplitude and frequency are the same so the higher the frequency the higher the amplitude. As you can see in the picture wave E has the  highest frequency. which means since A has the lowest  frequency and E has the highest frequency answer 2 would be correct the amplitude increases from A to E.

Amplitude of a wave is the strength of the wave. It is measured from the central line of the wave to the top of the crest or bottom of the trough. Thus, higher amplitude waves will gives sharp crests and troughs. Here amplitude is increasing from A to E.

What is amplitude?

Amplitude is a parameter measuring the strength of a wave. It is the maximum displacement moved by the wave from its equilibrium position. The vibrational path will be twice that of the amplitude of the wave.

As the amplitude of the wave increases its intensity increases. Both are in direct proportion with the frequency and energy of a wave. For instance the amplification of sound waves increases the intensity of waves that we hear.

The distance between two consecutive crests or troughs is the wavelength of the wave not amplitude. Amplitude is measured from the axis line to the top of the crest thus, from exact middle of the wave crest to the top or to the bottom of trough.

Thus, higher amplitude waves will gives sharp crests and troughs. Here amplitude is increasing from A to E

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Were interested in learning about some of the ways that you explore your interests. list some resources and outlets that you enjoy, including but not limited to websites, publications, journals, podcasts, social media accounts, lectures, museums, movies, music, or other content with which you regularly engage. 4x + 6+ 3= 17Show answer Find the exact values of x and y. (x,y) 14 y 60 xthe hypotenuse is 14theta (acute angle) is 60adjacent is xopposite is yfind exact values of x & y of the right triangle -1 + (-1) can anyone help Nick is making a fruit salad. He buys apples for $1.29 per pound and oranges for $1.35 per pound. He spends no more than $12.Let x represent the number of pounds of apples that Nick buys. Let y represent the number of pounds of oranges that Nick buys.Which inequality represents this situation?1.29x+1.35y>121.29x+1.35y121.29x+1.35y121.29x+1.35y How many days after Jackson's bank veto did Senator Daniel Webster write this reply? write a equation in slope intercept form that is parallel to the line y=-5/3x-1 and passes through the coordinates (9,5) Solve the problem involving consecutive integers.If three times the smaller of two consecutive integers is added to four times the larger, the result is 109. Find the smaller integer. A. 14 B. 45 C. 15 D. 16 Find a general solution of the given ODE (a) by first converting it to a system, (b), as given. Show the details of your work. 10. y" + 3y' + 2y = 0) 11. 4y" 15y' 4y = 0 12. y'' + 2y" y' 2y = 0 Mr. Andrews is trying to lose weight. He starts the year weighing 254 pounds. If he plans to burn enough calories to lose 4 pounds per week, then how many weeks will pass before Mr. Andrews weigh 228 pounds ? 22. U-turns in business districts are: A. Always illegal because they are dangerous B. Legal whenever oncoming vehicles are not a hazard C. Legal only at intersections, unless a sign prohibits them A growing trend in food advertising is to market heavily to ___ What is the primary role of most forensic scientists?O A.to arrest criminalsOB.to train police officersOC. to testify in courtOD.to analyze evidence Using the AE-PC Model illustrate graphically the impact of each these factors in separate and neatly labeled diagrams. You need to identify the impact on a particular curve, the direction of shift and the resulting impact on the equilibrium interest rates, inflation rates and GDP. Note: Label the axis please. (b) The US government cuts taxes. (a) Adverse AS supply shock hits the economy Calculate Marginal Revenue when output rises from 310 to 370 pounds.Total Output (Q)(Pounds)(1) Price per Pound($1.50)(2) Total Revenue(3) Marginal Revenue(4)0 $1.50 $150.00 -100 $1.50 $375.00 250 $1.50 $465.00 310 $1.50 $555.00 370 $1.50 $660.00 440 $1.50 $690.00 460 $1.50 $840.00 380 $1.50 $570.00$1.00$2.50$2.00$1.50 wesson company provides health care to its retirees. the estimated medical cost associated with a particular employee is $20,000; estimated share of the cost paid by employee is $4,000; expected medicare payments are $1,000; estimated health care reimbursement account owned by employee is $3,000. the net cost of the benefit to the employer is 6. let n be a positive integer and d be a digit such that the value of the numeral 32d in base n equals 263, and the value of the numeral 324 in base n equals the value of the numeral 11d1 in base six. what is n d ? What gross and histological features do all tissues in this major tissue type exhibit? I sell shoes for $250 per pair. They cost me $25 to produce. My markup on cost is:______ A. $2 B. 9096 C. 900% D. None of the above. find the function v(t) that satisfies the following differential equation and initial condition 10^2 dv(t)/dt + v (t) =0, v(0) = 100 V