What happens to the mass and to the weight of the foam rubber when it is compressed?​

Answers

Answer 1

Answer:

mass has no change; weight has no change

Explanation:

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Related Questions

The rate at which a body heats up by conduction is proportional to the difference between its temperature T and the temperature T s

of its surroundings. A fish at room temperature 20 ∘
C is cooked by putting it into boiling water at 100 ∘
C. After 5 minutes its temperature has risen to 30 ∘
C. How long will it take to be done 60 ∘
C ?

Answers

It will take 2.857 minutes (or about 2 minutes and 51 seconds) for the fish to reach a temperature of 60 °C.

To determine the time it will take for the fish to reach a temperature of 60 °C, we can use the principle of heat conduction and the concept of temperature difference.

We know that the rate of heating by conduction is proportional to the temperature difference between the body and its surroundings. Therefore, we can write the following equation:

(T - Ts) = k * t

where T is the temperature of the fish, Ts is the temperature of the surroundings (boiling water), k is the proportionality constant, and t is the time.

Given that the initial temperature of the fish is 20 °C and it takes 5 minutes to reach 30 °C, we can substitute these values into the equation:

(30 - 100) = k * 5

-70 = 5k

Solving for k, we find k = -14.

Now we can use this value of k to find the time it will take for the fish to reach 60 °C:

(60 - 100) = -14 * t

-40 = -14t

Dividing both sides by -14, we get t = 2.857 minutes.

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initially, the translational rms speed of a molecule of an ideal gas is 461 m/s. the pressure and volume of this gas are kept constant, while the number of molecules is doubled. what is the final translational rms speed of the molecules

Answers

The stated statement states that the molecules' final maximum rate of translation is 270 m/s.

What does physics define as speed?

The rate at which the position of an object shifts in any direction. Speed is described as the ratio of the area traveled to the time required to cover that distance. Time is a scalar number since it just has a heading but no magnitude.

Briefing:

temperature at the start = T

v = √(3RT/M) = 467 m/s

temperature = T' later

note PV = mRT/M = NRT/NA

so NT = constant,

now N is tripled, T reduces to T' = T/3

so v will change to v' = √(3RT'/M) = v*√(T'/T) =v*√(1/3) = 270 m/s

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Convert 400 mm to m using the method of dimensional analysis

Answers

Answer:

To convert 400 mm to m you can apply the formula [m] = [mm] / 1000; use 400 for mm. Thus, the conversion 400 mm m is the result of dividing 400 by 1000. 0.4

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ways by which static electric current can be produced

Answers

Answer:.....................

solar panels

(A) A 40-cm long massless bar with resistance 0.12 2 is pulled upward on zero-resistance rails at a constant speed of 15 cm/s, as shown below. The circuit is surrounded by a uniform magnetic field of magnitude 1.6 T directed out of the page.

(a) Using Faraday's Law, calculate the magnitude of the induced current in the circuit. (Note: You must show all your work; simply plugging numbers into a result derived in class is not enough!)
(b) Using Lenz's Law and stating your reasoning, determine the general direction of the induced current in the circuit, as well as the specific direction of the induced current in the bar.
(c) Find the magnitude of the applied force required to pull the massless bar upward at constant speed. Explain whether the magnitude of the magnetic force on the bar would increase, decrease, or remain unchanged if the bar were not massless (assuming it is still pulled upward at constant speed)

Answers

A 40-cm long massless bar with resistance 0.12 2 is pulled upward on zero resistance rails at a constant speed of 15 cm/s, as shown below. The circuit is surrounded by a uniform magnetic field of magnitude 1.6 T

(a) Calculation of magnitude of the induced current in the circuit using

Faraday's Law: When a loop of wire is exposed to a time-varying magnetic field, an electromotive force (EMF) is generated in it. This EMF is equivalent to the number of lines of magnetic flux that pass through the loop.

EMF = N(dϕ/dt),

where N is the number of loops in the circuit and dϕ/dt is the rate at which the magnetic flux through each loop varies. EMF is also equivalent to IR when the circuit has a resistance.

EMF = IR

Here, the resistance R of the circuit is 0.12Ω, the length of the massless bar is

40 cm = 0.4 m,

and the rate at which the bar moves is 15 cm/s. So, the area of the loop is

A = lb

= (0.4 m)(0.12 m) = 0.048 m².Φ

B is the magnetic flux through each loop of the circuit. In this case, a magnetic field of 1.6 T is directed out of the page, so

ΦB = BA cos θ

= (1.6 T)(0.048 m²)(cos 90°) = 0.V

= - dΦB/dt = - (d/dt)[BA cos θ]

= - [A(cos θ)] (dB/dt)

= - [0.048(cos 90°)] (15 cm/s)(0.01 m/cm)

= - 0.072 V.EMF

= IR = - 0.072 V = I(0.12Ω),

which yields I = 0.6 A.

(b) Determination of the general direction of the induced current in the circuit and the specific direction of the induced current in the bar using

Lenz's Law:The direction of the induced current is determined by Lenz's Law. Lenz's Law states that the direction of the induced current is such that it generates a magnetic field that opposes the change in the magnetic flux that produced it. In this case, the magnetic field is directed out of the page. As the bar is moved upward, the magnetic flux through each loop of the circuit increases. Therefore, the induced current must produce a magnetic field directed into the page to oppose this increase.The specific direction of the induced current in the bar is determined by the right-hand rule. The direction of the induced current is such that it produces a magnetic field that opposes the change in the magnetic flux that produced it. In this case, the magnetic flux is increasing as the bar moves upward. Therefore, the induced current must produce a magnetic field directed into the page. Using the right-hand rule, it can be seen that the direction of the induced current in the bar is from right to left.

(c) Calculation of the magnitude of the applied force required to pull the massless bar upward at constant speed:

From the free-body diagram, we can see that the force F pulling the massless bar upward at constant speed must be equal to the magnetic force FB that is exerted on the bar.

F = FB.

Therefore, F = BIL

= (1.6 T)(0.6 A)(0.4 m) = 0.384 N.

If the bar were not massless, the magnitude of the magnetic force on it would remain unchanged as long as it is still being pulled upward at constant speed. This is because the magnetic force FB is independent of the mass of the bar.

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A tudent i pulling a 25kg box acro the floor by applying a 230N tenion. The coefficient of kinetic friction between the box and the floor i 0. 4. Neglect drag

Answers

According to the above information, the box's acceleration is 6.6 m/s² and the frictional force exerted on it by the floor is 392.84 N.

In physics, what does tension mean?

Torsion is a force that runs the entire length of a substance, particularly one that is flexible like a rope or rope. An response pair of forces that act at each end of aforementioned components is tension.

Briefing:

We choose +x horizontally rightward and +y upward and observe that the 230N force has component Fx = F cos∅ and Fy = -sin∅.

(a). On the y-axis, we use Newton's second law;

\(F_{N}\) - F sin∅ - mg = 0

\(F_{N}\) = 230N sin 40° + (25kg)(9.8) = 392.84N

With \(\mu_{\mathrm{k}}\) = 0.4, Eq. leads to \(f_{k}\) = 11N

(b). To the x axis, we use Newton's second law:

F cos∅-\(f_{k}\) = ma

a = 230 cos 40° - 11/25 = 6.6 m/s²

The box is speeding there in +x (rightward) direction as the result has a positive value.

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The complete question is-

A student is pulling a 25 kg box is pushed along a horizontal floor by a force of magnitude 230 N at an angle 40 degree with the horizontal. The coefficient of kinetic friction between the box and the floor is 0.4. Calculate the magnitudes of (a) the frictional force on the box from the floor and (b) the box acceleration.

a discrete unit of energy required for an electron to jump to a different energy level is called.

Answers

A discrete unit of energy required for an electron to jump to a different energy level is called a quantum or a photon.

In atomic and molecular systems, electrons exist in specific energy levels. When an electron absorbs or emits energy in the form of a photon, it transitions between these levels.

This energy exchange occurs in quantized amounts, meaning that electrons can only occupy distinct, fixed energy levels rather than a continuous range.

The energy difference between levels is often denoted by the Planck's constant (h) multiplied by the frequency (ν) of the emitted or absorbed photon (E = hν). This quantization is a fundamental concept in quantum mechanics, and it helps explain various atomic and molecular phenomena.

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Mike swings from a vine. At the bottom of the swing, what is the direction of the net force on mike?.

Answers

Mike is swinging from a vine. The net force on Mike will be vertical upward at the bottom of the swing.

What is meant by centripetal force?

A centripetal force is a force that causes a body to move in a curved path. Its direction is always orthogonal to the motion of the body and towards the fixed point of the path's instantaneous center of curvature.

Mike is on a swing, which means he must take a circle course. In a circular motion, centripetal force acts towards the motion's center, allowing it to travel in that direction.

As a result, the net force at each point on the circular part will be towards the center. The direction of net force will be vertical upward at the bottom position.

Therefore, the net force on Mike will be vertical upward at the bottom of the swing

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A 100-kg object and a 400-kg object are separated by 4.40 m. (a) Find the magnitude of the net gravitational force exerted by these objects on a 49.0-kg object placed midway between them. ___________
Draw a picture of the three objects, including the forces exerted on the third. N
(b) At what position (other than an infinitely remote one) can the 49.0-kg object be placed so as to experience a net force of zero from the other two objects? ___________m from the 400 kg mass toward the 100 kg mass

Answers

The position where the 49.0-kg object can be placed so as to experience a net force of zero from the other two objects is 1.32 m from the 400 kg mass toward the 100 kg mass.

(a) The formula for the gravitational force between two objects is given by:

F = Gm₁m₂ / r²where G is the gravitational constant, m₁ and m₂ are the masses of the objects, and r is the distance between them.

Using this formula, the magnitude of the gravitational force between the 100 kg and 49 kg object is:

F₁ = G(100 kg)(49 kg) / (2.20 m)²

   = (6.67 × 10⁻¹¹ N m²/kg²)(4900 kg²) / (4.84 m²)

   = 6.77 × 10⁻⁹ N

The magnitude of the gravitational force between the 400 kg and 49 kg object is:

F₂ = G(400 kg)(49 kg) / (2.20 m)²

   = (6.67 × 10⁻¹¹ N m²/kg²)(19600 kg²) / (4.84 m²)

   = 2.71 × 10⁻⁸ N

The net gravitational force exerted by these objects on the 49.0-kg object placed midway between them is the sum of these two forces:

Fnet = F₁ + F₂= (6.77 × 10⁻⁹ N) + (2.71 × 10⁻⁸ N)= 3.39 × 10⁻⁸ N

(b) To experience a net force of zero from the other two objects, the gravitational force exerted on the 49.0-kg object by the 100-kg object must be equal in magnitude and opposite in direction to the gravitational force exerted on the 49.0-kg object by the 400-kg object.

Using the formula for gravitational force, we can set up the following equation:

(6.67 × 10⁻¹¹ N m²/kg²)(100 kg)(49 kg) / (x + 4.4 m)² = (6.67 × 10⁻¹¹ N m²/kg²)(400 kg)(49 kg) / (x)²

Simplifying and solving for x gives: x = 1.32 m from the 400 kg mass toward the 100 kg mass

Thus, the position where the 49.0-kg object can be placed so as to experience a net force of zero from the other two objects is 1.32 m from the 400 kg mass toward the 100 kg mass.

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A car traveling at 65 mph is an example of its

Answers

Answer:

Speed

Explanation:

The distance traveled by an object in a unit of time is speed


What is equilibrium?

Answers

Answer: Equilibrium is the state in which market supply and demand balance each other, and as a result prices become stable. The balancing effect of supply and demand results in a state of equilibrium.

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What is equilibrium?

9-8 skills practice analyzing functions with successive differences

Answers

Analyzing functions with successive differences is an important skill in mathematics. It involves identifying patterns in the differences between consecutive terms of a sequence, and using these patterns to predict future terms.

The process can be applied to a wide range of functions, including linear, quadratic, and exponential functions. To analyze a function with successive differences, you first need to identify the sequence of terms that defines the function. Then, you calculate the differences between consecutive terms and look for patterns in these differences. If the differences are constant, the function is linear. If the differences increase by a constant amount, the function is quadratic. And if the ratios of the differences are constant, the function is exponential. This skill is useful in a variety of contexts, from predicting future stock prices to analyzing data in scientific experiments, as it is a complex topic that requires explanation and context.

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If a 1.8 m tall man that weighs 90 kg stands next to a 10 kg box resting on the ground, the total work done if he lifts the box to the top of his head will be 2,940 J.
True or False

Answers

Answer:

false

Explanation:

calculate the height from which a body is released from rest if its velocity just before hitting the ground is 30 metre per seconds​

Answers

Answer:

height is 45 metres

Explanation:

KE=PE

¹/²mv² = mgh

¹/²v² = gh

but v =30m/s

(30)² / 2 =10h

450=10h

h = 45m

A vehicle is traveling at a speed of 12.5m/s. Express in light year per year.​

Answers

When we express the speed of 12.5 m/s in light year per year, the result obtained is 4.167×10⁻⁸ light year per year

How do I express 12.5 m/s in light year per year?

The conversion scale to convert from m/s to light year per year is given below:

3×10⁸ m/s = 1 Light year/year

With the above conversion scale, we can express 12.5 m/s in light year per year.

The following data were obtained from the question:

Speed (in m/s) = 12.5 m/s Speed (in light year per year) =?

3×10⁸ m/s = 1 Light year/year

Therefore

12.5 m/s = (12.5 m/s × 1 Light year/year) / 3×10⁸ m/s

12.5 m/s = 4.167×10⁻⁸ light year / year

Thus, from the above calculation, we can conclude that 12.5 m/s is equivalent to 4.167×10⁻⁸ light year per year

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1) Which of the following is the best definition of the scientific method?
A: A method used by scientists to try and find the answers to questions.
B: Used by scientists only throughout the world.
C: A method to prove the right answer to a question by a scientist.
D. The steps scientists use and follow when trying to solve a problem or to prove or
disprove a theory

Answers

d is the correct answer

The scientific method is defined as a method of research in which a problem is identified, relevant data is gathered and steps  use and follow when trying to solve a problem or to prove or disprove a theory.

Option D is correct.

The scientific method is a process with the help of which scientist try to investigate ,verify, or construct and accurate and reliable version of any natural phenomena.The scientific method consists of making observations, formulating a hypothesis, testing the hypothesis with new observations.

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What words from the vocabulary that is on the bottom left corner go in number 4-8?

What words from the vocabulary that is on the bottom left corner go in number 4-8?

Answers

Answer:

4) Inner Core

5) Outer Core

6)Crust

7) Convection

8)   Volcanoes    

Explanation:

How is the Doppler Effect used in astronomy and/or meteorology?

Answers

Astronomers use the doppler effect to study the motion of objects across the Universe.

Which of the following statement/s is/are true? Check all that apply. Jupiter's Great Red Spot is in the southern hemisphere of the planet The fastest wind speed recorded in our solar system is on the dwarf planet Pluto Neptune's Great dark spot is in the northern hemisphere of the planet Water geyser is located on the South Pole of Saturn's Moon Enceladus The Hexagon hurricane is on the North Pole of the planet Uranus

Answers

The true statements are:Jupiter's Great Red Spot is in the southern hemisphere.The fastest wind speed recorded in our solar system is on Neptune.

Among the given statements, only two are true. Jupiter's Great Red Spot, a massive storm, is indeed located in the southern hemisphere of the planet. The Great Red Spot is a prominent feature on Jupiter, visible as a giant swirling storm system. On the other hand, the fastest wind speed recorded in our solar system, reaching speeds of up to 2,100 kilometers per hour (1,300 miles per hour), is found on Neptune.

The strong winds on Neptune contribute to its dynamic atmosphere and the formation of features like the Great Dark Spot. The remaining statements about Pluto, Saturn's moon Enceladus, and Uranus are not true according to our current understanding.

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The speed of light in water is 230Mm/s. Suppose an electron is moving through water at 250 Mm/s . Does that violate the principle of relativity? Explain.

Answers

It does not violate the principle of  relativity because the speed of the electron in water can explained as its relative speed with water.

What is principle of  relativity?

The principle of relativity states that there is no physical way to differentiate between a body moving at a constant speed and an immobile body.

If the speed of light in water is 230Mm/s and an electron is moving through water at 250 Mm/s, it does not violate the principle of  relativity because the speed of the electron in water can explained as its relative speed with water.

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A very narrow beam of white light is incident at 41.00 degrees onto the top surface of a rectangular block of flint glass 13.5cm thick. The indices of refraction of the glass for red and violet light are 1.638 and 1.668, respectively.Calculate the dispersion angle (i.e., the difference between the directions of red and violet light within the glass block).2. How wide is the beam when it reaches the bottom of the block, as measured along the bottom surface of the block?3. When the rainbow-colored beam emerges from the bottom of the block, the exiting rays of light are once

Answers

1.  The dispersion angle can be calculated as follows:

The angle of refraction for red and violet light using Snell's Law. For red light:

sin(41.00°)/1.638 = sin(θ)/1, where θ is the angle of refraction.

Solving for θ, we get θ = 24.42°.

Similarly, for violet light:

sin(41.00°)/1.668 = sin(θ)/1,

solving for θ, we get θ = 24.07°.

The dispersion angle is then the difference between these two angles:

Δθ = θ_violet - θ_red = 24.07° - 24.42° = -0.35°.

Therefore, the dispersion angle is -0.35°.

2. Let w be the width of the beam at the bottom of the block, as measured along the bottom surface. Then, for red light:

sin(24.42°)/1 = sin(θ)/1.638,

solving for θ, we get θ = 16.68°.

Using the same approach for violet light, we get θ = 16.48°.

The width of the beam at the bottom of the block is then:

w = 13.5 cm × tan(16.68°) + 13.5 cm × tan(16.48°) = 6.69 cm.

Therefore, the width of the beam at the bottom of the block is approximately 6.69 cm.

3.  When the rainbow-colored beam emerges from the bottom of the block, the exiting rays of light are once again refracted at the air-glass interface, and they spread out further due to the dispersion of the glass.

Dispersion refers to the phenomenon of a wave or radiation being separated into its component frequencies as it passes through a medium. This occurs because different frequencies of the wave travel at different speeds through the medium, causing them to spread out and separate.

One common example of dispersion is the separation of white light into its constituent colors when it passes through a prism. The different colors of light are refracted differently, causing them to separate into a rainbow-like spectrum. Dispersion is also an important phenomenon in the study of materials, particularly in optics and acoustics. In materials, dispersion can result in the absorption or reflection of certain frequencies, affecting the overall properties of the material.

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Particles q1 = -20.5 UC, q2 = -9.30 uC, and q3 = -31.6.0 uC are in a line. Particles q, and q2 are separated by 0.980 m and particles q2 and q3 are separated by 0.750 m. What is the net force on particle q2?
Remember: Negative forces (-F) will point Left
Positive forces (+F) will point Right

Answers

The net force on particle q2 can be calculated by finding the net electric force acting on it. The net electric force acting on a particle is the vector sum of the forces exerted by all the other charges on it.

The electric force between two charges q1 and q2 is given by Coulomb's law: F = k * (q1 * q2)/r^2, where k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between them.

The force on particle q2 due to q1 will be:

F1 = k * (q1 * q2) / (0.980m)^2

The force on particle q2 due to q3 will be:

F2 = k * (q2 * q3) / (0.750m)^2

The net force acting on q2 will be the vector sum of F1 and F2.

Keep in mind, q1 and q3 have opposite charges, so they attract each other, while q2 has the same charge as q1, so they repel each other.

Note: The unit of charge is Coulomb (C), but in this problem you are given the charges in microCoulomb (uC) so you need to convert it to Coulomb.

Which part(s) of the electromagnetic spectrum are able to be seen by the human eye? question 2 options: radio waves microwaves infrared waves visible light ultraviolet rays x-rays gamma rays

Answers

Visible light is known as the fragment which is the part of electromagnetic spectrum that can be seen by humans.

The wavelength and frequency of light that is visible are 400nm to 700nm and  400THz to 800THz respectively. As we know, living beings are blind to a number of wavelengths of light, but it can be detected by specific instruments. But we can perceive easily that our world is aligned around this light.

For example, the sun is natural visible light. Everything around us that we’re able to see is a reflection of sunlight falling off the objects. Colour of any object that we’re able to see is actually just a reflection of light and other than that, all other colours get absorbed.

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What is electricity?

Answers

Answer:Electricity is the flow of electrons. All matter is made up of atoms, and an atom has a center, called a nucleus. When electrons are "lost" from an atom, the free movement of these electrons constitutes an electric current. Electricity is a basic part of nature and it is one of our most widely used forms of energy.

Explanation:

Answer:

Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Various common phenomena are related to electricity, including lightning, static electricity, electric heating, electric discharges and many others.a form of energy resulting from the existence of charged particles (such as electrons or protons), either statically as an accumulation of charge or dynamically as a current.

Explanation:

While falling towards the ground at 100 km/h a skydiver releases a bag of rocks when he is 800 m
above the ground and then opens his parachute. (a) What is the initial velocity (in m/s) of the bag at the moment it was released? (b) At what speed will the bag hit the ground? You can ignore air resistance for the rocks.

Answers

(a) The initial velocity of the bag at the moment it was released is 27.8 m/s downwards.

(b) The bag will hit the ground with a speed of 128.3 m/s downwards.

What is the initial velocity of the bag?

(a) To find the initial velocity of the bag at the moment it was released, we can use the following equation:

v_f^2 = v_i^2 + 2gh

where;

v_f is the final velocity (which is zero), v_i is the initial velocity, g is the acceleration due to gravity, and h is the height the bag falls before it is released (which is 800 m).

Plugging in the values, we get:

0 = v_i^2 + 2(9.8 m/s^2)(800 m)

v_i^2 = -2(9.8 m/s^2)(800 m)

v_i = -392 m/s

The negative sign indicates that the initial velocity of the bag is downwards.

However, we know that the velocity of the bag cannot be negative. This means that our assumption that the initial velocity is zero is incorrect. In reality, the bag is moving downwards at the same speed as the skydiver, which is 100 km/h or 27.8 m/s.

Therefore, the initial velocity of the bag at the moment it was released is 27.8 m/s downwards.

(b) To find the speed at which the bag will hit the ground, we can use the following equation:

v_f^2 = v_i^2 + 2gh

where;

v_f is the final velocity, v_i is the initial velocity (which is 27.8 m/s downwards), g is the acceleration due to gravity, and h is the height the bag falls after it is released (which is 800 m).

Plugging in the values, we get:

v_f^2 = (27.8 m/s)^2 + 2(9.8 m/s^2)(800 m)

v_f^2 = 16,452.84 m^2/s^2

v_f = 128.3 m/s

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(Physical science!!!)
Wetlands have characteristics of both dry land and of bodies of water. How have amphibians adapted to this environment?

A.
They can lay their eggs underwater or on dry land.
B.
Water can pass through their lungs; they have night vision.
C.
Water can pass through the skin; they have lungs.
D.
They retain a set of gills their whole lives.

Answers

Amphibians retain a set of gills their whole lives that help them to breathe in the water. So, the correct option is D.

What are Amphibians?

Amphibians are defined as the class of cold-blooded vertebrates which is made up of frogs, toads, salamanders, newts, and caecilians. All amphibians that spend part of their lives in water and part of their lives on land.

Amphibians are born with gills, and some outgrow them when they become adults while others retain them for their entire lives.

Thus, the correct option is D.

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Integrated Science- 8th grade science
Please Help ASAP!
Its almost the end of semester And I need to fix my grade for science so PLEASE help!
its almost report cards time!

Integrated Science- 8th grade science Please Help ASAP!Its almost the end of semester And I need to fix

Answers

Answer:

I do believe it is A.

Explanation:

I hope this helps :)

Answer:I believe it is A

Explanation: B just doesn't seem like something an 8th grader would be learning about, and I'm not sure about the other ones.

What is an ionic bond? Explain with an example?

Answers

A bond that is formed by a positively charged ion to a negatively charged ion is termed as an ionic bond. An example is sodium chloride.

When two atoms with great difference in electronegativities forms a bond, the electrons are completely transferred between the atoms and are ionized. These positive and negative charged ions forms a bond purely based on the electrostatic force of attraction. Such a compound is called an ionic compound.

Usually an electropositive metal in 1st and 2nd group of periodic table  reacts with non-metals in 16th and 17th group to form ionic compounds. Lets consider the example of sodium chloride.

The electronic configuration of sodium is 2, 11, 1

Electronic configuration of chlorine is 2, 8, 7

Sodium is an electropositive metal and it has a tendency to lose electron to complete octet electronic configuration. Chlorine on the other hand is an electronegative non- metal, tends to lose electrons. So the sodium when reacting with chlorine loses its outer electron and become Na⁺ and the chlorine gains the electron and become Cl⁻.

So an electrostatic force of attraction is formed between the ions and form the compound Na⁺Cl⁻.

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a particle of mass m is embedded at a distance r/4 from the center of a massless circular disc of radius r which can roll without slipping down a plane inclined at an angle a with the horizontal. Use the Lagrangian method to write the dif- ferential equation of motion for the system

Answers

The differential equation of motion for the system using the Lagrangian method is D²θ/Dt² + (g/[(19/8) r]sin α)θ = 0.

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The differential equation of motion for the system is given by the Lagrangian method when a particle of mass m is embedded at a distance r/4 from the center of a massless circular disc of radius r that can roll without slipping down a plane inclined at an angle a with the horizontal. Using the Lagrangian method, the differential equation of motion for

the system is given as follows:L = T - VL = [1/2 m(r² + (r/4)²)ω² + 1/2 Iω²] - mgrsin(α)r/4Here, I = [1/2 m(r/2)²] + m(r/4)²I = [1/2 m(r²/4 + r²/16)] + m(r²/16)I = m(r²/8)Therefore, I = mr²/4Then, the expression of Lagrangian can be given as:L = [1/2 m(r² + r²/16)ω² + 1/2 (mr²/4)ω²] - mgrsin(α)r/4L = [1/2 m(17r²/16)ω² + (1/8)mω²] - mgrsin(α)r/4L = [1/8 mω²(17r² + 2r²) - mgrsin(α)r/4]L = [1/8 mω²(19r²) - mgrsin(α)r/4]So, the Lagrangian equation of motion for the system is given as:D²θ/Dt² + (g/[(19/8) r]sin α)θ = 0

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A nutritionist who works for a fitness club helps members by evaluating their diets. As part of her evaluation, she asks members for the number of fat grams and carbohydrate grams that they consumed in a day. Then, she calculates the number of calories that result from the fat, using the following formula:

Calories from Fat = Fat Grams × 9

Next, she calculates the number of calories that result from the carbohydrates, using the following formula:

Calories from Carbs = Carb Grams × 4

The nutritionist asks you to design a modular program that will make these calculations.

Provide the following:

• Design (Pseudocode and Flowchart)

• Sample Output

Answers

Pseudocode: 1. Prompt the user to enter the number of fat grams consumed in a day. 2. Read and store the input as fatGrams.

and the rest is as followed:

3. Prompt the user to enter the number of carbohydrate grams consumed in a day.

4. Read and store the input as carb Grams.

5. Calculate calories FromFat as fat Grams multiplied by 9.

6. Calculate calories FromCarbs as carb Grams multiplied by 4.

7. Display the calculated values of calories From Fat and calories From Carbs.

Flowchart:

START

  Read fatGrams

  Read carbGrams

  Set caloriesFromFat = fatGrams * 9

  Set caloriesFromCarbs = carbGrams * 4

  Display caloriesFromFat

  Display caloriesFromCarbs

END

Sample Output:

Enter the number of fat grams consumed in a day: 50

Enter the number of carbohydrate grams consumed in a day: 200

Calories from Fat: 450

Calories from Carbs: 800

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