Find the volume of a solid whose base is bounded by the circle x2 + y2 = 4, the cross sections perpendicular to the x-axis.

Answers

Answer 1

The given circle is x² + y² = 4. The volume of the solid is 42.6 cubic units.

We can rewrite it as y² = 4 - x². Then, we can take the square root of both sides to get:

y = ± √(4 - x²)

To find the volume of the solid with cross-sections perpendicular to the x-axis, we need to integrate the area of each cross-section from x = -2 to x = 2.

The area of each cross-section is given by:

A(x) = ∫[a,b] f(x) dx

where f(x) = 2√(4 - x²) is the height of the cross-section at x.

Thus, the volume of the solid is given by:

V = ∫[-2,2] A(x) dx

V = ∫[-2,2] 2√(4 - x²) dx

This integral can be evaluated using the substitution u = 4 - x²:

\(\frac{du}{dx} = -2x\)

dx = -du/(2x)

When x = -2, u = 0

When x = 2, u = 0

Substituting into the integral, we get:

V = ∫[-2, 2] πr²dx

 = ∫[-2, 2] π(4 - x²) dx

 = π[4x - (x³)/3]_[-2, 2]

 = π[(32 - (-32/3)]

 = 32+\(\frac{32}{3}\)

 = (128/3)

Therefore, the volume of the solid is 42. 6 cubic units.

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Related Questions

A piano has a mass of 99 kg. What is the weight of the piano?

Answers

Explanation:

weight of the piano = mg

w = 99 x 10 =990 N

In your own words define the following term and state its
importance for hypothesis testing (2 points correct definition, 3
points correct importance for hypothesis testing).
Null Hypothesis
Sampling

Answers

Sampling is the process of selecting a subset of individuals or items from a larger population in order to gather information or make inferences about the whole population. This method allows researchers to collect data from a smaller group, which is more efficient and cost-effective than collecting data from the entire population.

Sampling is a crucial process in research because it helps ensure that the data collected is representative of the population and reduces the potential for bias. There are several types of sampling methods, including random sampling, stratified sampling, and convenience sampling. The choice of sampling method depends on the research question, the population being studied, and the resources available to the researcher. The accuracy of the data obtained from a sample depends on the sample size and the sampling method used. A larger sample size is generally more representative of the population and reduces the margin of error, while a smaller sample size may be more susceptible to sampling bias.

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pls,help ASAP .the question is in attachment​

pls,help ASAP .the question is in attachment

Answers

Answer:c

Explanation:

Which of the following is a good radiator of heat option is (a) a shiny silvered surface option (b) a dull black surface option (c) a white surface option (d) a green coloured surface

Answers

Answer:

option b

Step by step explanation:

a dull black surface is a good radiator of heat

Answer:

option b is the answer

A free-body diagram represents forces acting on a system.
Question 20 options:
True
False

Answers

Answer:

False because free-body diagram is a sketch of only the object in question and the forces acting upon it, to scale.

It would be false !!!!!!!!!!

how to find the elctric field strength inside the wire using drift speed of the electrons in the wire

Answers

To find the electric field strength inside the wire, we need to know the current density, the conductivity of the wire, the number density of electrons in the wire, and the drift velocity of the electrons.

To find the electric field strength inside a wire using the drift speed of the electrons in the wire, we need to use Ohm's law:

E = J/σ

where E is the electric field strength, J is the current density, and σ is the conductivity of the wire. The current density can be expressed as:

J = nev

where n is the number density of electrons in the wire, e is the charge of an electron, and v is the drift velocity of the electrons. We can rewrite this equation as:

v = J/ne

Substituting this equation into Ohm's law, we get:

E = (J/ne) / σ

Rearranging this equation, we get:

E = Jσ / ne

So, to find the electric field strength inside the wire, we need to know the current density, the conductivity of the wire, the number density of electrons in the wire, and the drift velocity of the electrons.

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Wings of a bird what kind of motion is it

Answers

Answer:

linear motion

Explanation:

the birds in the sky show oscillatory motion when they flap their wings

there are two principal scales we use. one is the major scale; the other is:

Answers

Answer:

The other principal scale is the minor scale.

Answer: Minor

Explanation:

a dog with mass of 14kg has a kinetic energy of 135.5j. what is the speed of the dog

Answers

Answer:

v = 4.39968 m/s

v = 9.8418038654259 mi/h

v = 14.434645669291 ft/s

v = 15.838846732892 km/h

Explanation:

v=KE/1/2m

A logical and probable explanation for the movement of the Earth’s tectonic plates is:
Group of answer choices
a. the breakup of the plates by volcanic eruptions and earthquakes
b. the rapid shrinking of Earth's crust as it slowly cools
c. the result of heat convection in the plastic mantle rock which moves the cold brittle crust on top
d. the rotation of the Earth causes the plates to drag across the top of the mantle

Answers

The logical and probable explanation for the movement of the Earth's tectonic plates is the convection currents within the mantle. The Earth's mantle is made up of hot, molten rock that constantly moves due to the heat generated by the radioactive decay of elements within the Earth's core.

This movement of the mantle creates convection currents that carry the tectonic plates along with them.
As the hot, less dense rock rises within the mantle, it pushes against the bottom of the tectonic plates, causing them to move away from each other. At the same time, cooler, denser rock sinks back down into the mantle, causing the tectonic plates to move towards each other.
This movement of the tectonic plates can cause a variety of geological phenomena such as earthquakes, volcanic eruptions, and the formation of mountains and ocean trenches. It is a slow but continuous process that has been ongoing for millions of years and will continue to shape the Earth's surface in the future.
In summary, the convection currents within the Earth's mantle are the most likely explanation for the movement of the tectonic plates. While other factors such as the rotation of the Earth may play a minor role, the convection currents are the driving force behind the movement of the tectonic plates.

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The most accepted and widely supported explanation for the movement of the Earth's tectonic plates is option c: the result of heat convection in the plastic mantle rock which moves the cold brittle crust on top.

The Earth's mantle is composed of solid rock that can flow over long periods of time, and it is heated from below by the Earth's core. As the mantle heats up, it becomes less dense and rises towards the surface. This creates convection currents that move the molten rock in a circular motion, carrying the tectonic plates with them.

The movement of the tectonic plates is also influenced by the forces of gravity, as denser rock sinks and lighter rock rises. This process is known as "ridge push" and "slab pull," respectively. Ridge push occurs at mid-ocean ridges, where new crust is formed as magma rises to the surface, pushing the plates apart. Slab pull occurs at subduction zones, where old oceanic crust is pushed back into the mantle, dragging the rest of the plate along with it.

Option A (the breakup of the plates by volcanic eruptions and earthquakes) and option d (the rotation of the Earth causes the plates to drag across the top of the mantle) are not considered to be the primary drivers of plate tectonics, although they can contribute to it in certain circumstances. Option b (the rapid shrinking of Earth's crust as it slowly cools) is not a valid explanation for plate tectonics, as the Earth's crust is not shrinking rapidly enough to cause the observed movements of the plates.

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The hanging mass is referred to as M and it sets the centripetal force.
True
False

Answers

Answer:

False

Explanation:

The centripetal force is the force that points towards the center and is responsible for keeping an object in a curved path. This force is provided by the tension in the string, not the mass of the object.

Using atomic weight crystal structure and atomic radius data tabulated inside the front cover compute the theoritical densities of alminuim ,nikel......

Answers

Question

Using atomic weight, crystal structure, and atomic radius data tabulated inside the front cover of thebook, compute the theoretical densities of aluminum (Al), nickel (Ni), magnesium (Mg), and tungsten (W), and thencompare these values with the measured densities listed in this same table. The c/a ratio for magnesium is 1.624.

Explanation:

Using atomic weight crystal structure and atomic radius data tabulated inside the front cover compute
Using atomic weight crystal structure and atomic radius data tabulated inside the front cover compute

a gust of wind creates ripples on the ocean that have a wavelength of 4.7\;\mathrm{cm}4.7cm and propagate at a speed of 6.5\;\mathrm{cm/s}6.5cm/s. what is the frequency of these ocean waves?

Answers

A gust of wind creates ripples in the ocean, then the frequency of these ocean waves will be 1.4 Hz.

What is Frequency?

The percentage of waves that transfer a fixed point in a unit of time is known as the frequency in physics. It is the frequency or vibrations that a body in periodic motion perceptions in a unit of time. When a body in periodic motion moves through a sequence of incidents or positions before returning to its initial state, it is believed to have experienced one cycle or one vibration.

As per the given data mentioned in the question,

Frequency = speed/wavelength

Speed = 6.65 cm/s

Wavelength = 4.7 cm

F = (6.5 × 10⁻²)/(4.7 × 10⁻²)

F = 1.4 Hz

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Which color will absorb the most heat, and why is that so?

Answers

Answer:

Dark colors absorb more radiated heat from the sunlight while lighter colors reflect it. That's why wearing a black shirt on a sunny day makes you feel so much hotter than when you're wearing a white shirt!

Answer:

black

Explanation:

Light energy can be converted into heat energy. A black object absorbs all wavelengths of light and converts them into heat, so the object gets warm

maize is called monocot why?​

Answers

Answer:

Rice, wheat, maize all have one cotyledon in their seed, so they are monocots. Explanation: The monocot plants have a single cotyledon. They have a fibrous root system, leaves in monocots have parallel venation.

Explanation:

If two opposing forces are equal, then the net force is 0 N.

true or false?

Answers

Answer:

false

Explanation:

plz answer it..pzzzz​

plz answer it..pzzzz

Answers

Answer:

I think the answer is tempurature

Explanation:

Answer:

I think it's current.

It cannot be Temperament because temp's S.I unit is Kelvins

That all the energy of the universe remains constant, is conserved, neither created nor destroyed, but may change form is a statement of the ________.

Answers

The statement of that all the energy of the universe remains constant, is conserved, neither created nor destroyed, but may change form is called the law of conservation of energy.

The law of conservation of energy states that energy can neither be created nor destroyed. Rather, energy can be transformed from one form to another. It is stated in a simple sentence that all the energy of the universe remains constant, is conserved, neither created nor destroyed, but may change form.

This statement means that energy can be transformed from one form to another, for example, chemical energy can be converted into electrical energy. It is conserved in the universe, meaning that it cannot be created or destroyed, it only changes from one form to another. Therefore, this statement is called the law of conservation of energy.

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based on what you know about energy, what types of energy does the water balloon have? how would energy explain the water balloon’s behavior?

Answers

Energy is an important concept that affects us in many ways. It is the ability to do work, and it can come in many forms. When it comes to a water balloon, it has several types of energy that explain its behaviour.

Types of Energy: The water balloon has potential energy, which is stored energy due to its position or shape. This potential energy is converted to kinetic energy when the balloon is thrown. Kinetic energy is the energy of motion, so as the balloon moves, it has kinetic energy.

The balloon also has thermal energy, which is energy that comes from the temperature of the water in the balloon. As the water inside the balloon heats up, the thermal energy increases and the balloon becomes more elastic.

Behaviour: The water balloon's behaviour can be explained by the energy it contains. The potential energy it has will cause it to move when it is released, resulting in its kinetic energy. The thermal energy can cause the balloon to expand and become more elastic, making it more likely to burst when hit by an object. The combination of these energies explains why the balloon behaves the way it does.

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The table below provides data obtained at different geographical locations on Earth.
In which city would Earth’s gravitational field strength be the largest?

The table below provides data obtained at different geographical locations on Earth.In which city would

Answers

The city of Charleston, WV will have the largest gravitational field strength.

What is gravitational field strength?

The space around a material object in which its gravitational force can be experienced is known as gravitational field.

The gravitational field strength at a point in this field is the force experienced on unit mass placed at that point.

Here,

The data obtained at different geographical locations of earth are given in the table. The latitude of the geographical areas are provided.

Gravitational field strength,  I = -GM/r²

i.e, it follows the inverse square law.

The variation of gravitational field strength with change in latitude has been studied and the studies proved that:

As an  object moves away from the surface of earth, the gravitational force  between the object and earth decreases and therefore the gravitational field strength also decreases.

Therefore considering the latitudes of the geographical places mentioned, the place at the lowest latitude will have the strongest gravitational field strength. Charleston, WV will have largest gravitational field strength.

Hence, Charleston, WV which is at the lowest latitude will have the strongest gravitational field strength.

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a ball is thrown upward from the top of a 50 meter high building with an initial speed of 25 m/s. a. how much time does it take to reach the ground?

Answers

The time taken by the ball to fall on the ground is 2.55 seconds

The height of the building = 50 m

The initial speed = 25 m/s

The time taken to reach the ground can be found using the formula

                 v = u + at

where u is the initial speed

           a is the acceleration

           t  is the time taken

At the highest point, the speed is zero which is v = 0 and the acceleration is due to gravity which is in the opposite direction of the movement of the ball. Thus,

             0 = u - gt

Let us rearrange it,

             t = u/g

Let us substitute the known values in the above equation, we get

            t = 25 / 9.8

              = 2.55 seconds

Therefore, the time taken is 2.55 seconds.

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When electrons are lost, a ( )
ion is formed.
When electrons are
gained, a ( )
ion is formed.

Answers

When electrons are lost a positive ion is formed. When electrons are gained, a negative ion is formed. I hope this helps

A block of mass 1kg is placed on an inclined plane at an angle of 30° to the horizontal. Calculate the frictional force, normal reaction, the coefficient of the static friction​

Answers

Question:

A block of mass 1kg is placed on an inclined plane at an angle of 30° to the horizontal. Calculate the frictional force, normal reaction, the coefficient of the static friction​

Answer:

Break the mg force into components in the plane of the inclined plank. Now force acting parallel is mgsin37°. Perpendicular force is mgcos37° which is equal to normal force.  

Now calculate max value of friction force which is 0.8*mg cos37°. Since its greater than pulling force mgsin37°, the body will be at rest and acceleration is zero.  

Force applied by surface is vector sum of normal force and friction force acting.

The magnitude of the magnetic force that acts on a charged particle in a magnetic field is independent of

Answers

The magnitude of the magnetic force that acts on a charged particle in a magnetic field is independent of the sign of the charge.

What is magnetic field?

Magnetic field is the region of space where an object experiences the magnetic force.

Magnetic force is proportional to the charge's magnitude, velocity, and magnetic field. The magnitude of charge doesn't include its sign.

Therefore, the magnitude of the magnetic force is independent of the sign of the charge.

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the astronomer giovanni cassini (1625-1712) studied the family of curves with polar equations where a and c are positive real numbers. these curves are called the ovals of cassini even though they are oval shaped only for certain values of a and c. (cassini thought that these curves might represent planetary orbits better than kepler's ellipses.) investigate the variety of shapes that these curves may have. in particular, how are a and c related to each other when the curve splits into two parts?

Answers

When the oval of Cassini splits into two parts, the values of a and c are related by a² < c.

The polar equation for the ovals of Cassini is given by:

r² = (x² + y²) = (a² - c²) ± 2acosθ

where r is the distance from the origin to a point on the curve, and θ is the angle that the line connecting the origin to that point makes with the positive x-axis.

To investigate the shapes of these curves, we can consider different values of a and c. When a = c, the curve simplifies to a circle centered at the origin with radius a. When a > c, the curve is a single, closed oval shape, as shown below:

As a decreases relative to c, the oval shape becomes more elongated, as shown below:

When a = c√2, the curve splits into two separate ovals, as shown below:

As a continues to decrease, the separation between the two ovals increases, as shown below:

When a = c, the two ovals merge back into a single oval shape, but with the orientation reversed from the original shape, as shown below:

From this analysis, we can see that the relationship between a and c determines the shape of the oval of Cassini. When a = c√2, the curve splits into two separate ovals. As a decreases below this value, the separation between the ovals increases, and when a = c, the two ovals merge back into a single shape, but with the orientation reversed.

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Comment on the speed changes as it follows its parabolic arc. do they make sense physically?

Answers

(a) Duration of the ball's flight is 2.5S

(b) Angle of its velocity is 16.1

(c) Speed of the ball is 22.53 m/s

(a). To determine the duration of the ball's flight in

We calculate the whole time when the ball touches the ground, thus we enter y=0 and all other specified values in the equation.

\(25sin30t-1/210t^{2} = 0\)

\(t = 2.5 s\)

(b) After it has been in the air for one-fourth of this period, determine the angle of its velocity with respect to the ground.

t1=1/4 t = 2.5/4 = 0.625 s

\(v_{x} = 25\sqrt{3} /2 m/s\)

\(v_{y} = 25/2 - 2.5/2 = 12.5/2 m/s\)

∅= 16.1

(c) To determine speed of the ball for time \(t_{1} ,t_{2} , t_{3}\)

\(v=\sqrt{v} ^{2}{x} + \sqrt{v} ^{2} y_{}\)

vt1 = 22.53 m/s

vt2 = 21.65 m/s

vt3 = 22.53 m/s

What is the speed change on its parabolic arc?  

The turning point on the corresponding parabolic curve is where the speed is at its lowest in the xx direction. Physically speaking, the shift in speed does make sense. The ball's initial motion against gravity causes its speed to decrease, but after it reaches the turning point, its speed begins to increase as it descends.

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The electric potential at a point in space is 235V. If a 0.0 485C charge is placed there what will its potential energy u be

Answers

Answer:

PE (Energy) = V / Q * Q     where V is the electric potential at that point ( the energy required to bring a charge of 1 C to that point)

PE = 235 J/C * .0485 C = 11.4 J

What planet rotates once a day?

Answers

Earth is the only planet with a daily rotation. The only planet in our solar system known to offer the ideal circumstances for supporting life is Earth, which is located third from the Sun.

The only planet in our solar system known to offer the ideal circumstances for supporting life is Earth, which is located third from the Sun. The rotation of our planet, which creates day and night, is one of its most striking characteristics. Every 24 hours, the Earth spins on its axis, giving rise to the cycle of day and night. The Coriolis effect, which affects the direction of winds, ocean currents, and other significant motions in the atmosphere and seas, is also a result of this rotation. The molten core of the globe spins as Earth rotates, creating a magnetic field that shields humans from dangerous solar radiation.

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After an athlete has completed a 100 meter sprint, his or her breathing rate will be greatly increased, and they need time to "catch their breath. " Can you identify the process that leads to a person needing to catch their breath?

Answers

Process that leads to a person needing to catch their breath is because of a physiological process called oxygen debt or excess post-exercise oxygen consumption (EPOC).

During intense exercise, the body requires more oxygen to produce energy. However, due to the high demand for energy, the body's oxygen supply falls short. As a result, the body relies on anaerobic respiration, which produces lactic acid as a byproduct.

To restore oxygen levels and remove lactic acid, the body requires a period of recovery. The increased breathing rate post-sprint helps to take in more oxygen, which is transported to the muscles to restore energy supplies and break down lactic acid.

This process allows the body to return to its normal state, enabling the athlete to "catch their breath" and recover.

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does this man look okay? hes all pink and stuff O_O hes teaching me frickin science

does this man look okay? hes all pink and stuff O_O hes teaching me frickin science

Answers

Answer:

He is pink panther. How nerdy does he sound?

Explanation:

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