The mass of the supermassive black hole is 2.8×10⁸ solar masses.
In order to calculate the mass of the supermassive black hole at the center of the Andromeda galaxy (M31), we can use the following formula:
GM = v²r
where, G is the gravitational constant, M is the mass of the black hole, v is the orbital speed of the stars, and r is the radius of the orbit of the stars from the center of the black hole.
It is given that v = 400 km/s, r = 3 light-years = 2.839×10¹⁶ meters, G = 6.67×10⁻¹¹ Nm²/kg².
We can convert the speed of the stars to meters per second:
v = 400 km/s = 4×10⁵ m/s
Now, substituting the values in the formula, we get:
GM = v²r
M = v²r/G
= (4×10⁵)²×(2.839×10¹⁶)/(6.67×10⁻¹¹)
= 2.8×10⁸ solar masses
Therefore, the mass of the supermassive black hole at the center of the Andromeda galaxy (M31) is 2.8×10⁸ solar masses.
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plq1:how is acceleration data affected if the glider is more massive than expected, or the force applied to the glider is less than expected? explain your reasoning. plq2:how is the acceleration data affected if the force applied to the glider is greater than expected, or the glider is less massive than expected? explain your reasoning.
plq1. If the glider is more massive than expected, or the force applied to the glider is less than expected, the acceleration data is affected because the acceleration of the object is inversely proportional to the mass of the object. plq2. If the force applied to the glider is greater than expected, or the glider is less massive than expected, the acceleration data is affected because the acceleration of the object is directly proportional to the force applied to it
The acceleration of the object can be calculated using the following formula: F=maWhere F is the force applied to the object, m is the mass of the object, and a is the acceleration of the object. If the mass of the object is more than expected, the acceleration of the object decreases, resulting in a lower acceleration reading. Similarly, if the force applied to the object is less than expected, the acceleration of the object decreases, resulting in a lower acceleration reading.
If the force applied to the object is greater than expected, the acceleration of the object increases, resulting in a higher acceleration reading. Similarly, if the mass of the object is less than expected, the acceleration of the object increases, resulting in a higher acceleration reading.
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help me
plss asap!!!
Answer:B
Explanation:The ray above makes a 90 degree angle. The ray below makes a 60 degree angle.
Select the correct location on the image.
The image shows the visible light spectrum received from a star. Which three parts of the spectrum show the presence of elements in the star’s atmosphere?
The visible light spectrum is the range of wavelengths the human eye can detect, ranging from 380 to 700 nanometers.
What are visible light examples?People think of the sun, light bulbs, candles, and flames when they think of light, but visible light originates from many sources and in many hues. Other visible light sources include television and computer displays, glow sticks, and pyrotechnics.
This is why this area of the electromagnetic spectrum is known as the visible spectrum or colour spectrum. It primarily comprises of seven colours: violet, blue, green, yellow, orange, and red.
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Answer:
It is the three spots where there are lines. Between 400 and 500(the two lines), between 600 and 700(the two lines), and the one line between 700 and 800.
One day, after pulling down your window shade, you notice that sunlight is passing through a pinhole in the shade and making a small patch of light on the far wall. Having recently studied optics in your physics class, you're not too surprised to see that the patch of light seems to be a circular diffraction pattern. It appears that the central maximum is about 3 cm across, and you estimate that the distance from the window shade to the wall is about 3 m .
Estimate the diameter of the pinhole (in mm).
The diameter of the pinhole is 0.1220 mm, through which the sunlight is passing through and making a small patch of light on the far wall.
Given information,
width of central maxima = 3 cm = 3×10⁻²m
size of the pinhole, a = 3 m
The average wavelength of sunlight, λ = 500 nm
The small bending of light as it travels around an object's edge is known as diffraction. The ratio of the wavelength of the light to the opening size determines how much bending occurs.
The relation between wavelength and aperture diameter is expressed as,
w = 2.44λa/D
where D is the diameter of the pinhole,
D = 2.44λa/w
D = 2.44×500×10⁻⁹×3/3×10⁻²
D = 0.1220×10⁻³m
D = 0.1220 mm
Hence, the diameter of the pinhole is 0.1220 mm.
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A student standing on the ground throws a ball straight up. The ball leaves the student's hand with a speed of 11 m/s when the hand is 1.8 m above the ground. How long is the ball in the air before it hits the ground? (The student moves her hand out of the way.)
The ball is in the air for about 1.8 seconds before it hits the ground after it leaves the student's hand with a speed of 11 m/s when the hand is 1.8 m above the ground.
Projectile motion is a kind of movement experienced by an object or particle (a projectile) that is projected near the Earth's surface and moves along a curved path under the gravity of the Earth. In general, projectile motion refers to a free-body's motion influenced only by gravity. A student throws a ball straight up while standing on the ground. When her hand is 1.8 m above the ground, the ball leaves her hand at a speed of 11 m/s. The time the ball is in the air before it hits the ground is calculated as follows:Using the equation:
∆y = v0yt + 1/2gt² Where ∆y is the displacement (in this case, -1.8 m) of the projectile along the vertical axis, v0y is the initial vertical velocity (in this case, 11 m/s), t is the time of flight, and g is the acceleration due to gravity (9.81 m/s²):-1.8 m = (11 m/s)t + (1/2)(-9.81 m/s²)t².Rearranging the equation, we get:-4.905t² + 11t - 1.8 = 0.
Using the quadratic formula, we get:t = (-11 ± sqrt(11² - 4(-4.905)(-1.8))) / (2(-4.905))= 1.77 s or t = 0.20 s. Since the ball is in the air for approximately 1.77 s before it hits the ground, and the student's hand is 1.8 m above the ground, the ball is in the air for about 1.8 seconds before it hits the ground. Therefore, the correct answer is the option C, 1.8 seconds.
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for an hst with a 2 cir pump and a 3.36 cir motor, what is the speed ratio if the volumetric efficiency of the pump is 93.5% and the volumetric efficiency of the motor is 92.1%?
The speed ratio if the volumetric efficiency of the pump is 93.5% and the volumetric efficiency of the motor is 92.1% is 0.898, which is approximately 0.90.
Given the volumetric efficiency of the pump and the volumetric efficiency of the motor, the speed ratio is to be determined using the formula:
Speed Ratio = Actual Flow Rate * 231 / (Pump Displacement x Pump RPM)
The formula for the volumetric efficiency is:
Volumetric efficiency = (Actual Flow Rate / Theoretical Flow Rate) * 100
Theoretical Flow Rate = Pump Displacement x Pump RPM
The actual flow rate is equal to the theoretical flow rate multiplied by the volumetric efficiency divided by 100.Thus,
Actual Flow Rate = Pump Displacement x Pump RPM x (Volumetric Efficiency / 100)
Speed Ratio = Actual Flow Rate * 231 / (Pump Displacement x Pump RPM) = (Pump Displacement x Pump RPM x (Volumetric Efficiency / 100)) * 231 / (Pump Displacement x Pump RPM) = (Volumetric Efficiency / 100) * 231 = 93.5 / 100 * 231 = 215.985
Speed Ratio = 215.985 / 240 = 0.898 ≈ 0.90
Therefore, given the volumetric efficiency of the pump and the volumetric efficiency of the motor, the speed ratio is 0.898, which is approximately 0.90.
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what the auditory stimulus is transduced into electrical signals by the?
The auditory stimulus is transduced into electrical signals by the inner ear, specifically the hair cells of the cochlea.
What is the auditory stimulus?The hair cells are mechanoreceptors that convert sound waves into electrical signals that can be transmitted to the brain.The auditory stimulus is any sound that is heard by the ear. Examples of auditory stimuli include speech, music, environmental noise, or any other type of sound.
Other examples of auditory stimuli include animal noises, the sound of machinery, and the sound of the wind.
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Problem 1. In this problem, you need to determine the additive inverse1of each given vector in the appropriate vector space. (a)[ 23]inR 2. (b)−1+3x−8x 2inP 2. (c)[ 12−20]inM 2×2.
The additive inverse of each given vector in the appropriate vector space are
(a) The additive inverse of [2, 3] in [tex]R_2[/tex] is [-2, -3].
(b) The additive inverse of [tex]-1 + 3x - 8x^2[/tex] in P2 is [tex]1 - 3x + 8x^2[/tex].
(c) The additive inverse of [1, 2; - 2, 0] in [tex]M_{2\times2[/tex] is [-1, -2; 2, 0].
The additive inverse of a vector [tex]\mathbf{v}[/tex] in a vector space is the vector [tex]-\mathbf{v}[/tex] that, when added to [tex]\mathbf{v}[/tex], gives the zero vector.
(a) The additive inverse of the vector [tex][2, 3] \in \mathbb{R}^2[/tex] is [tex][-2, -3][/tex] since [tex][2, 3] + [-2, -3] = [0, 0][/tex].
(b) The vector space [tex]P_2[/tex] consists of all polynomials of degree at most [tex]2[/tex]. The vector [tex]-1 + 3x - 8x^2 \in P_2[/tex] has additive inverse [tex]1 - 3x + 8x^2[/tex], since [tex](-1 + 3x - 8x^2) + (1 - 3x + 8x^2) = 0[/tex].
(c) The vector space [tex]M_{2 \times 2}[/tex] consists of all [tex]2 \times 2[/tex] matrices. The matrix [tex][1, 2; -2, 0] \in M_{2 \times 2}[/tex] has additive inverse [tex]$[-1, -2; 2, 0]$[/tex], since [tex]\begin{bmatrix} 1 & 2 \ -2 & 0 \end{bmatrix} + \begin{bmatrix} -1 & -2 \ 2 & 0 \end{bmatrix} = \begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix}[/tex].
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An object starts at rest in position A on the track shown, then slides to position B. Friction acts on the object over the entire track. Which equation can you use to find the object's velocity at position B?
Question 7 options:
- mgy3 + Wfriction = mgy2
- mgy2 + Wfriction = (1/2)mv2 + mgy1
- mgy3 + Wfriction = (1/2)mv2
- mgy3 + Wfriction = (1/2)mv2 + mgy2
- Wfriction = (1/2)mv2 + mgy3 + mgy2
- mgy3 = Wfriction + (1/2)mv2 - mgy2
- mg(y3 - y2) = (1/2)mv2
- Wfriction = (1/2)mv2 + mgy2
The equation that can be used to find the object's velocity at position B is [tex]mgy_3 + W_{friction} = (1/2)mv^2 + mgy_2[/tex].
What is friction?Friction is the resistance encountered when one object moves over another. Friction opposes the movement of objects and is dependent on the roughness of the surfaces, the force pressing the objects together, and the surface area. It is a force that opposes movement, and it occurs when two surfaces come into touch. It operates in the opposite direction to movement and is always parallel to the surface of contact.
What is Velocity?Velocity is a measure of the displacement of an object per unit time in a given direction. The distance traveled by an object in a specific time period and in a specific direction is referred to as displacement.
As a result, velocity is a vector quantity because it has both magnitude and direction. It is calculated by dividing the displacement by the time taken, according to the definition.
Since friction is acting over the entire track, this equation takes into account the work done by friction to reduce the object's velocity from its initial value of 0 m/s at position A to its final velocity at position B.
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For this truss geometry:
|/\|/\|/\|/\|
Select one or more:
a. The bottom chords do not usually need the verticals, since the bottom chords are not subjected to bending loads and the bottom chords only go into compression under severe wind suction that overcomes the dead weight of the structure.
b. This is called a Modified Warren Truss.
c. The vertical webs help brace the top chord against buckling upward and downward.
d. The vertical webs help support parts of the top chord, thereby reducing the span, and associated bending stress, of the top chord under the uniform gravity force of the decking resting on the top chord of the truss.
e. The unbraced length for the bottom chords is twice as long as the unbraced length for the top chords.
The correct statements are as follows: Option (b), (c) and (d). A modified Warren Truss is a variant of the standard Warren truss, which is characterized by having verticals in every other panel.
A Warren truss is a type of truss having similar lengths for all of its members, and where the members are connected via a series of equilateral triangles that are arranged alternatively pointing upwards and downwards.
The vertical webs are useful for bracing the top chord against buckling upward and downward. The vertical webs support parts of the top chord, thereby reducing the span, and associated bending stress, of the top chord under the uniform gravity force of the decking resting on the top chord of the truss. Therefore the correct answers are options (a), (b), and (d).
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a wireshark trace of tcp traffic between hosts a and b indicated the following segments. a sent a segment of 0 bytes data payload to b with fin flag set, sequence number 1000 and ack number 500. later b sent a segment of 0 bytes data with fin flag set, sequence number 500 and ack number 1001. what is the state of the connection in host a before receiving the ack from b and after receiving the ack ?
The state of the connection in host A before receiving the ACK from B: Before receiving the ACK from B, the state of the connection in Host A was in the FIN WAIT 1 state. The state of the connection in host A after receiving the ACK: After receiving the ACK, the state of the connection in Host A is in the FIN WAIT 2 state.
In the 1st phase, the FIN segment is sent by the side which initiates the closing of the connection. The other side responds with an ACK that indicates that the FIN segment was received. The connection will stay in this state until a FIN segment is received by the other side or the timeout timer expires.
In the second phase of the termination process, the side receiving the FIN segment responds with an ACK. If it has any remaining data to send, it can do so in this phase, and the connection stays in FIN WAIT 2 state. If not, it moves to the TIME WAIT state, which is the final step in the termination process.
Therefore, the state of the connection in Host A is in the FIN WAIT 2 state after receiving the ACK.
What is TCP?
TCP is an abbreviation of Transmission Control Protocol. It is the protocol that serves as the foundation of the internet. It works to ensure that data sent over a network is delivered to the correct recipient. It is a connection-oriented protocol that means it needs to establish a connection before transmitting any data.
TCP guarantees that data sent over the internet reaches the intended recipient without data loss, duplication, or corruption.
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The Hubble Space Telescope orbits the Earth at an average altitude of 340 miles above the surface of the Earth. It completes one orbit in roughly 95 minutes. Assume that the orbit is circular and that the radius of the Earth is 3959 miles. 1. What fraction of a complete orbit does the telescope make in one hour? 2. Find the angle associated with the circular arc made by the telescope over one hour. 3. How fast is the telescope moving around the Earth in miles per hour?
1. In one hour, the telescope completes 60/95 = 0.63 of an orbit. Therefore, it makes approximately 63% of a complete orbit in one hour.
2. The angle associated with the circular arc made by the telescope over one hour is approximately 135.6 degrees.
To find the angle associated with the circular arc made by the telescope over one hour, we need to first find the length of the arc. The circumference of the orbit is:
2πr = 2π(3959 + 340) = 47408 miles
The distance traveled by the telescope in one hour is:
(1/95) x 60 minutes x 60 seconds = 2262.11 seconds
The length of the arc made by the telescope in one hour is therefore:
(2262.11/3600) x 47408 = 29806.31 miles
The angle associated with this arc can be found using the formula for the angle of a circular sector:
θ = (s/r) x (180/π)
where θ is the angle in degrees, s is the arc length, and r is the radius of the circle. Substituting in the values, we get:
θ = (29806.31/3959) x (180/π) ≈ 135.6 degrees
Therefore, the angle associated with the circular arc made by the telescope over one hour is approximately 135.6 degrees.
3. The speed of the telescope is:
47408/1.58 ≈ 29987 miles per hour (rounded to the nearest mile)
The speed of the telescope can be found by dividing the length of the orbit by the time taken to complete one orbit. The length of the orbit is the circumference of the circle, which we calculated in part 2. The time taken to complete one orbit is the orbital period, which is given as 95 minutes. Converting this to hours, we get:
95/60 = 1.58 hours
Therefore, the speed of the telescope is:
47408/1.58 ≈ 29987 miles per hour (rounded to the nearest mile)
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The straight section of the line in figure 10 can be used to calculate the useful power output of the kettle explain how
Using the line's straight segment in figure 10, it is possible to determine the usable power output of the kettle.
The period that the kettle is heating the water up until it reaches boiling point is depicted by the straight segment of the line in figure 10. Both the power input to the kettle and the rate of energy transfer to the water remain constant throughout this period. Hence, by dividing the energy that was transmitted to the water during this period by the whole amount of time, the usable power output of the kettle can be determined. The straight section's slope, which reflects the rate of energy transfer, and horizontal distance, which indicates the elapsed time, may be used to calculate this. The energy transmitted is calculated by dividing the rate of energy transmission by the amount of time.
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The pocket of hot air appears to be a pool of water becauseA. Light reflects at the boundary between the hot and cool air.B. Its density is close to that of water.C. Light refracts at the boundary between the hot and cool air.D. The hot air emits blue light that is the same color as the daytime sky.
The pocket of hot air appears to be a pool of water because light refracts at the boundary between the hot and cool air. The answer is C.
When there is a pocket of hot air above a surface, it creates a mirage effect, which makes the surface appear as if it is reflecting a pool of water. This happens due to the bending of light as it passes through air of varying temperatures. Hot air has a lower density than cool air, which causes the light to refract or bend away from its original path as it passes through the boundary between the hot and cool air.
This bending of light causes the image of the ground or distant objects to appear displaced from their actual positions, creating the illusion of a pool of water. The effect is similar to looking at an object through a lens. This phenomenon is called a mirage, and it is a common occurrence in desert regions, where the temperature can vary greatly between the hot sand and the cooler air above it. Option C is correct choice.
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In which of the following cases does a car have a negative velocity and a positive acceleration? A car that is traveling in the ................. (A) -x direction at a constant 10 m/s. (B) - direction increasing in speed. (C) +x direction increasing in speed. (D) - direction decreasing in speed. (E) +x direction decreasing in speed.
In the case where the car is traveling in the -x direction and decreasing in speed, it has a negative velocity and a positive acceleration. Therefore, option D is the correct answer. In this case, the car is traveling in the - direction and decreasing in speed. Therefore, it has a negative velocity and a positive acceleration.
Let's discuss the given options one by one:
(A) In this case, the car is traveling in the -x direction at a constant speed. Therefore, it has a negative velocity and zero acceleration. This option is incorrect.
(B) In this case, the car is traveling in the - direction and increasing its speed. Therefore, it has a negative velocity and a positive acceleration. However, the given direction is not specified, and thus this option is not accurate.
(C) In this case, the car is traveling in the +x direction and increasing in speed. Therefore, it has a positive velocity and a positive acceleration. This option is incorrect.
(D) In this case, the car is traveling in the - direction and decreasing in speed. Therefore, it has a negative velocity and a positive acceleration. This option is correct.
(E) In this case, the car is traveling in the +x direction and decreasing in speed. Therefore, it has a positive velocity and a negative acceleration. This option is incorrect.
Therefore, Option D ( - direction decreasing in speed) is correct.
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a boy coasts down a hill on a sled, reaching a level surface at the bottom with a speed of 7.2 m/s. if the coefficient of friction between the sled's runners and snow is 0.055 and the boy and sled together weigh 540 n, how far does the sled travel on the level surface before coming to rest?
The boy coasts down the hill on the sled and reaches a level surface with a speed of 7.2 m/s. The coefficient of friction between the sled's runners and the snow is 0.055, and the boy and sled together weigh 540 N. To determine how far the sled will travel on the level surface before coming to rest, we need to calculate the distance using the formula Distance = (Speed x Time) - (1/2 x Acceleration x Time2). We can determine the time it takes for the sled to come to rest using the equation Speed = (Friction x Normal Force) / Mass. So, Speed = (0.055 x 540N) / 540N = 0.055 m/s. Time = 7.2/0.055 = 130.9 seconds. We can then calculate the distance as Distance = (7.2 x 130.9) - (1/2 x 0.055 x 130.92) = 927.9 m. Therefore, the sled will travel 927.9 m before coming to rest.
The boy and sled weigh 540 N. A boy coasts down a hill on a sled, reaching a level surface at the bottom with a speed of 7.2 m/s. The coefficient of friction between the sled's runners and snow is 0.055. How far does the sled travel on the level surface before coming to rest?
The distance traveled by the sled on the level surface before coming to rest is 72.22 meters.
What is friction?
Friction is a force that opposes motion. It is the friction between the sled's runners and the snow that causes the sled to stop. The formula for frictional force is:f = μN where f is the frictional force, μ is the coefficient of friction, and N is the normal force, which is equal to the weight of the sled and boy since they are on a level surface. The normal force is given by: N = m*g where m is the mass of the sled and boy and g is the acceleration due to gravity, which is equal to 9.81 m/s^2.
How far does the sled travel on the level surface before coming to rest?
The sled will travel a certain distance, d, before it stops. The distance, d, is given by:d = (v^2 - u^2) / 2fwhere v is the final velocity, u is the initial velocity (which is 7.2 m/s), and f is the frictional force. The frictional force is f = μN = μmgSubstituting the given values:d = (7.2∧2 - 0∧2) / (2*0.055*540*9.81)d = 72.22 meters. Therefore, the sled will travel 72.22 meters on the level surface before coming to rest.
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what does it mean when a metamorphic rock has foliation?
Answer:
The rock has been layered.
Explanation:
Foliation is the repeated layering of rock. It usually happens when there's extensive heat or pressure in one direction.
: suppose a planet has a mass of 10 times that of the Earth and a radius that is 100 times that of the Earth. The acceleration of gravity on the surface of the planet, expressed in units of the Earth's acceleration of gravity, g, is 1000 g. g/1000 10 g.
The acceleration of gravity on the surface of the planet, expressed in units of the Earth's acceleration of gravity, g, is g/1000.
Given,Mass of the planet, m = 10m_Earth Radius of the planet, r = 100r_Earth Acceleration of gravity on the surface of the planet, g' = 1000 g_Earth To find, the acceleration of gravity on the surface of the planet, expressed in units of the Earth's acceleration of gravity, g.
Assuming the planet to be a perfect sphere, the acceleration due to gravity on the surface of the planet, g' is given by,g' = GM / r²where M is the mass of the planet, r is the radius of the planet and G is the gravitational constant.We know that, the acceleration of gravity on the surface of the Earth, g_Earth is given by,g_Earth = GM_Earth / r_Earth²Thus, we have the ratio of g' and g_Earth,g' / g_Earth = GM / r² × r_Earth² / GM_Earth= r_Earth / r = 1 / 100∴ g' = 1 / 100 × g_Earth = g_Earth / 1000.Hence, the acceleration of gravity on the surface of the planet, expressed in units of the Earth's acceleration of gravity, g is g/1000. Therefore, the answer is g/1000.
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select all of the following descriptions that match what happens when a ferromagnetic material is placed in an external magnetic field. a. the ferromagnetic material becomes magnetized. b. nothing, ferromagnetic materials do not interact with magnetic fields. c. the ferromagnetic material becomes negatively charged. d. the ferromagnetic material becomes positively charged. e. the external magnetic field induces magnetic poles in the ferromagnetic material. f. the ferromagnetic material rapidly cools.
A. The ferromagnetic material becomes magnetized: Ferromagnetic materials are strongly magnetic and become magnetized when placed in an external magnetic field. The magnetic domains within the material align themselves with the external field, resulting in a strong net magnetic moment.
E. The external magnetic field induces magnetic poles in the ferromagnetic material:The external magnetic field induces a magnetic moment in the ferromagnetic material, which causes it to behave as a magnet. The magnetic moment induced by the external field is much stronger than that of other materials, such as diamagnetic or paramagnetic materials.
Therefore, the correct statements are (a) and (e). Ferromagnetic materials are strongly magnetic and can be magnetized, unlike diamagnetic or paramagnetic materials, which are only weakly magnetic and do not become magnetized in an external magnetic field.
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A ball is thrown upwards and caught when it comes back down. In the presence of air resistance, the speed with which it is caught is:
(A) more than the speed it had when thrown upwards.
(B) the same as the speed it had when thrown upwards.
(C) less than the speed it had when thrown upwards.
A ball is thrown upwards and caught when it comes back down. In the presence of air resistance, the speed with which it is caught is C. less than the speed it had when thrown upwards.
When a ball is thrown upwards, it gains kinetic energy due to the force exerted by the thrower. Then, as it ascends, it loses kinetic energy and gains potential energy as it moves higher up. Finally, the ball comes to a stop, its kinetic energy becoming zero, and its potential energy reaches its maximum value. At the top, the ball begins to fall back to the ground.The air resistance opposes the motion of the ball, slowing it down as it travels upwards.
When the ball starts coming back down, the air resistance exerts an additional force, which slows down the ball and reduces its speed. As a result, the speed with which it is caught is less than the speed it had when thrown upwards. Hence, option (C) is correct.
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obtain expression for effective ressistence of three resistors R1,R2,AND R3 are conected in series to 6v battery through voltmeter and ammeter
Explanation:
If they are in a series circuit they just add together
Rtotal = R1 + R2 + R3
there is some small resistance in the ammeter and the battery too (these would add to the total ) if you want to be totally correct.
Find the frequency w for which the particular solution to the differential equation dạy dy 3 + dt + 3y iwt =e dt2 has the largest amplitude. You can assume a positive frequency w > 0. Probably the easiest way to do this is to find the particular solution in the form Aeiwt and then minimize the modulus of the denominator of A over all frequencies w. = ليا 0 ? X 0% Try a new variant Correct answer W = 0.971825315808
It is estimated that the frequency for which the specific solution has the maximum amplitude is 0.971825315808.
The differential equation is as follows: dy/dt + 3y iwt = e(t2)
If we assume that the specific answer is of the form Aeiwt, we may substitute it in the equation to obtain the following result: (iwt + 3).
Aeiwt equals e(t2).
We arrive at A = e(-t2) / (iwt + 3) after solving for A.
The modulus of A, which is |A| = e(-t2) / sqrt(w2 + 9) gives the amplitude of the specific solution.
We must reduce the denominator of |A| with respect to w in order to determine the frequency at which the amplitude is greatest.
After differentiating and setting it to zero, we arrive at w = 0.971825315808 by applying the formula: -9 / 2(w2 + 9)(3/2) = 0.
Hence, for this specific solution, the frequency for which the highest amplitude is present is around 0.971825315808.
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Discuss consequences and application of expansion
Thermal expansion is used in applications such as railroad track buckling, engine coolants and mercury in thermometers.
What is the consequence and application of expansion?Thermal expansion changes the space between the particles of substance, which changes the volume of substance and negligibly changing its mass thus changing its density, which has effect on any buoyant forces acting on it.
Solid expansion occurs due to the thermal expansion. Increasing the temperature of solids, liquids or gas results in expansion. The effect of solid expansion is an increase in volume of solid. Change in volume of a solid is directly proportional to initial volume and change in temperature.
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The image shows flat sedimentary rock layers in the foreground and angled sedimentary rock layers in the background.
Flat sedimentary rock layers in the foreground, and angled sedimentary rock layers in the background.
According to the principle of original horizontality, what most likely happened to the rock layers in the background?
They cracked at an angle.
They were deposited at an angle.
They were deposited vertically and then shifted by a geologic event.
They were deposited horizontally and then shifted by a geologic event.
Answer:
They were deposited horizontally and then shifted by a geologic event.
Explanation:
Q4. Convert these into proper vector notation:
Westward velocity of 42 km/h.
Position 6. 5 measured in m that is North of the reference point.
Downward acceleration measured in m/s2 that has a magnitude of 1. 9.
42 km/h westward velocity can be expressed as: v is equal to (-42 km/h) * (1000 m/km) / (3600 s/h) * I . Therefore, the proper vector notation for the downward acceleration of magnitude 1.9 m/s^2 is -1.9 m/s^2 in the downward direction (k).
where the unit vector pointing west is called i. If we condense this expression, we get: v = -11.67 m/s * I Hence, -11.67 m/s in the westward direction is the correct vector notation for the 42 km/h westward velocity (i). North of the reference point, position 6.5 measured in metres, can be expressed as: r = 6.5 m * j where j represents the unit vector pointing north. Hence, 6.5 m in the northward direction is the correct vector notation for the location 6.5 m north of the reference point (j). It is possible to express a downward acceleration with a magnitude of 1.9 in m/s2 as follows: a = -1.9m/s^2 * k where k is the unit vector in the downward direction. Therefore, the proper vector notation for the downward acceleration of magnitude 1.9 m/s^2 is -1.9 m/s^2 in the downward direction (k).
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what is the potential difference across a capacitor after it has been discharging for a very long time?
The potential difference across a capacitor after it has been discharging for a very long time is 0 volts. This is because the capacitor is empty of charge, and thus has no potential difference between its two terminals.
A capacitor is a type of electrical component that stores energy in an electric field. The energy is stored in the form of electric charges on two conductive plates.
The plates are separated by an insulating material called a dielectric. The potential difference across a capacitor is proportional to the amount of charge stored on the plates.
What happens when a capacitor discharges?When a capacitor discharges, it loses the stored charge. This discharge occurs when the capacitor is connected to a circuit. The capacitor will then begin to discharge as the charges on the plates flow through the circuit.
The potential difference across the capacitor will decrease as the charges on the plates decrease.
The capacitor has been completely discharged and no longer has any potential difference.
Thus, the potential difference across a capacitor after it has been discharging for a very long time is zero.
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2. The shortest venomous snake, the spotted dwarf adder, has an average length of 20.0 cm. Suppose this snake hangs by its tail from a branch and holds a heavy prey with its jaws, simulating a pendulum with a length of 15.0 cm. How long will it take the snake to swing through one period?
Answer:
0.777 s
Explanation:
if the hiker starts climbing at an elevation of 490 ft, what will their change in gravitational potential energy be, in joules, once they reach the top? assume the zero of gravitational potential energy is at sea level.
The change in the gravitational potential energy is 102,800.24 J.
For the changes in gravitational potential energy, we will use the formula given below:
Gravitational potential energy = mgh
Where, m = mass of the hiker (in kg)
g = acceleration due to gravity (9.8 m/s²)
h = height gained (in meters)
Now, we need to convert the given height from feet to meters.1 ft = 0.3048 m
Therefore, 490 ft = 490 × 0.3048 m = 149.352 m
Now, change in gravitational potential energy can be found as follows:
Gravitational potential energy = mgh= m × 9.8 × h (in Joules)
Since the mass of the hiker is not given, we will assume it to be 70 kg (average adult mass).
Thus, Gravitational potential energy = 70 × 9.8 × 149.352 J = 102,800.24 J
Therefore, the change in gravitational potential energy is 102,800.24 J.
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what is the resistance of the quantum point contact that allows three electron channels to connect the electrodes on each side?
The resistance of the quantum point contact that allows three electron channels to connect the electrodes on each side is determined by the number of electrons passing through it.
What is resistance?The capacity of a material to oppose the flow of electricity is referred to as resistance. When charged particles (such as electrons) move through a conductor, resistance causes some of the energy that would otherwise be converted into electricity to be transformed into heat instead. Resistance is a measure of how hard it is for electrons to move through a conductor. It's measured in ohms, and it's represented by the symbol Ω in electrical circuits.
As more electrons pass through the contact, the resistance increases. Therefore, the resistance of the quantum point contact varies depending on the number of electrons passing through it. In general, the resistance is proportional to the number of electrons passing through it, with each electron providing a certain amount of resistance.
The resistance of the quantum point contact that allows three electron channels to connect the electrodes on each side is 2π^2/h^2.The resistance of a quantum point contact with three electron channels is:R = 2π^2/h^2Where R is resistance, h is Planck's constant, and π is a mathematical constant. The resistance of a quantum point contact with three electron channels is approximately 6.5 kΩ.
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the blue whale can produce sound with an intensity that is 1 million times greater than the intensity of the loudest sound a human can make. find the difference in the loudness of the sounds made by a blue whale and a human.
The difference in loudness between the sound made by a blue whale and a human is 120 decibels.
The difference in the loudness of the sounds made by a blue whale and a human.The loudest sound a human can make is measured at about 140 decibels, while the sound a blue whale can make is measured at about 260 decibels. This means that the blue whale can produce a sound that is 1 million times greater in intensity than the loudest sound a human can make. This difference in loudness is equal to 120 decibels.
The difference in loudness between the sound made by a blue whale and a human is 120 decibels. The loudest sound a human can make is measured at about 140 decibels, while the sound a blue whale can make is measured at about 260 decibels. This means that the blue whale can produce a sound that is 1 million times greater in intensity than the loudest sound a human can make.
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