I know the answer is (d) but why?

I Know The Answer Is (d) But Why?

Answers

Answer 1

Answer:

I think it's dio to atmospheric pressure.


Related Questions

Create a trigonometric function that models the ocean tide for a period of 12 hours.

Answers

One possible trigonometric function that models the ocean tide for a period of 12 hours is:
y = A*cos(2πt/12 + φ) + B

In this trigonometric function, y represents the water level (in meters) at a given time t (in hours), A represents the amplitude (in meters) of the tide, φ represents the phase shift (in radians) that determines the starting point of the tide cycle, and B represents the average water level (in meters) at the location.
The cosine function is used because it is a periodic function that oscillates between -1 and 1, which is similar to the behavior of ocean tides. The coefficient 2π/12 in the argument of the cosine function represents the frequency (in cycles per hour) of the tide, which is equal to one cycle every 12 hours. The phase shift φ can be adjusted to match the observed data or the expected behavior of the tide. The amplitude A can be determined by measuring the difference between the highest and lowest water levels over a full cycle of the tide.
Of course, this is just one possible model for ocean tides, and there are many factors that can affect the actual behavior of tides, such as the geography of the coastline, the gravitational pull of the moon and sun, and the wind and weather patterns. So, it is important to gather as much data as possible and to refine the model accordingly.

Therefore, y = A*cos(2πt/12 + φ) + B is a trigonometric function that models the ocean tide for a period of 12 hours.

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Ill give u 50 points and Brainiest if u answer this right

A pinball bangs against a bumper of a pinball machine with a speed of 0.44 m/s. If the ball has a mass of 0.022 kg, what is the ball's kinetic energy?

Answers

Answer:

0.0021 J

Explanation:

\(KE=\frac{1}{2} mv^{2}\\KE=\frac{1}{2}*0.022*0.44^{2} \\KE=0.0021\ J\)

Answer: KE= 0.0021296 ( Hopefully this will help you, sorry if I'm wrong)

Explanation:

Ill give u 50 points and Brainiest if u answer this right A pinball bangs against a bumper of a pinball

How does friction affect object acceleration down an incline?

Answers

Friction is the force that acts on the opposite side of direction of force, thus it manages to decelerate an object, so it acts upward along the plane

A rope exerts a 35N force on an object at an angle of 12N degrees above the horizontal. What horizontal and vertical components of the force?

Answers

Answer:

The horizontal component of the force, \(F_x= 34.24 \ N\)

The  vertical component of the force, \(F_y=7.28 \ N\)

Explanation:

Given;

Force on the rope, F = 35 N

angle between the rope and the horizontal = 12 °

The horizontal component of the force is given by;

\(F_x = Fcos \theta\\\\F_x = 35cos(12^0)\\\\F_x = 34.24 \ N\)

The vertical component of the force is given by;

\(F_y = Fsin\theta\\\\F_y = 35sin(12^0)\\\\F_y = 7.28 \ N\)

A Carnot refrigeration cycle is used to maintain a room at
23 °C by removing heat from groundwater at 15 °C.
Refrigerant R-134a enters the condenser as saturated
vapor at 40 °C and leaves as saturated liquid at the
same temperature. The evaporator pressure is 351 kPa.
a) If the room is to receive 2kW, what is power input to
the compressor?
b) Net power input to cycle?

Answers

a) The power input to the compressor in the Carnot refrigeration cycle, in order to supply 2 kW of cooling to the room, will depend on the efficiency of the cycle and the heat transfer involved.

b) The net power input to the cycle can be determined by considering the work done by the compressor and the work done on the system.

a) To calculate the power input to the compressor, we need to determine the heat transfer from the groundwater to the room. The Carnot refrigeration cycle is an idealized cycle, and its efficiency is given by the equation: Efficiency = 1 - (T_evaporator / T_condenser), where T_evaporator and T_condenser are the temperatures at the evaporator and condenser, respectively. Using this efficiency, we can calculate the heat transfer from the groundwater and convert it to power input.

b) The net power input to the cycle takes into account the work done by the compressor and the work done on the system. It can be calculated by subtracting the work done by the compressor from the heat transfer from the groundwater. The work done by the compressor can be determined using the power input calculated in part a), and the heat transfer from the groundwater can be obtained using the given temperatures and the specific heat properties of the refrigerant.

Overall, the Carnot refrigeration cycle involves several calculations to determine the power input to the compressor and the net power input to the cycle, considering the heat transfer and work done in the system.

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What pattern did you observe when the tape was at
different distances from the Van de Graaff machine?
PLS HELP

Answers

You have to add a picture

a diffraction grating with 145 slits per centimeter is used to measure the wavelengths emitted by hydrogen gas. at what angles in the third-order spectrum would you expect to find the two violet lines of wavelength 434 nm and of wavelength 410 nm? (angles in radians)

Answers

The two violet lines of hydrogen gas with wavelengths 434 nm and 410 nm in the third-order spectrum of a diffraction grating with 145 slits per centimetre would be expected at angles of approximately 1.09 radians and 1.22 radians, respectively.

Diffraction gratings are used to disperse light into its constituent wavelengths and measure their spectra. The number of slits per centimetre on the grating determines the angular spacing between the diffracted wavelengths. In this case, a diffraction grating with 145 slits per centimetre is used to measure the spectrum of hydrogen gas, which emits violet lines at wavelengths 434 nm and 410 nm. The third-order spectrum corresponds to diffracted wavelengths that are three times the spacing between the slits. Using the equation for diffraction grating, the angles at which these violet lines are expected to appear in the third-order spectrum can be calculated as approximately 1.09 radians for the 434 nm line and 1.22 radians for the 410 nm line.

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According to coulomb's law, doubling the distance between two charges will change the force by a factor of:.

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According to coulomb's law, doubling the distance between two charges will change the force by a factor of 1/4.

Definition of Coulomb's Law

Coulomb's law is a law that governs the interaction between electric charges, both like and different types of charges. As you know that there are positive and negative electric charges.

Who Discovered Coulomb's Law

Coulomb's law was discovered by a scientist from France, namely Charles-Augustin de Coulomb in 1785. Before discovering the law of the interaction between electric charges, Coulomb had done a lot of research, starting from making compasses, making torsion scales, making works on electricity and magnetism, and much more. other.

Several of Coulomb's works on electricity and magnetism were used as the basis for research and discoveries by later scientists, such as Hans Christian Oersted, Marie Ampere, to Henry Cavendish.

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A wavelength of 489. 2 nm is observed in a hydrogen spectrum for a transition that ends in the nf level of the balmer series. what was ni for the initial level of the electron?

Answers

The distance between identical points in adjacent cycles of a waveform signal is called wavelength. The n₁ for the initial level of the electron is 4.

What is Wavelength?

The distance between identical points (adjacent crests) in adjacent cycles of a waveform signal carried in space or down a wire is defined as the wavelength.

Given the wavelength is 489.2 nm, also, it is stated that the nf level is Balmer series. Therefore,

nf level = 2

The wavelength, λ = 489.2 nm = 4.86× 10⁻⁷ meter

Now, the mathematical formula for wavelength is given as,

\(\dfrac{1}{\lambda} = R[\dfrac{1}{nf^2}-\dfrac{1}{n_1^2}]\)

where R is the Rydberg constant and its value is equal to 1.097×10⁷.

Therefore, we can write,

\(\dfrac{1}{4.86 \times 10^{-7}} = 1.097 \times 10^7 [\dfrac{1}{2^2} - \dfrac{1}{n_1^2}]\)

n₁ = 4.0021 ≈ 4

Hence, the n₁ for the initial level of the electron is 4.

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What conditions must be satisfied for momentum to be conserved in a system?

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The conditions that must be satisfied for momentum to be conserved in a system are; The total external force acting on a system must be zero. In other words, the net force on the system must be zero.

If there is no net force on the system, the momentum of the system will remain constant with time.The mass of the system must remain constant with time. If the mass of the system is changing with time, the momentum of the system will also change with time. Therefore, it is essential to keep the mass of the system constant.

The collision must be elastic. In an elastic collision, the total kinetic energy of the system is conserved, and the momentum of the system is conserved. In other words, the system behaves as if there were no external forces acting on it. If the collision is not elastic, the total kinetic energy of the system will not be conserved. Instead, some of the kinetic energy will be converted into other forms of energy, such as thermal energy or sound energy.If the above three conditions are satisfied, the momentum of the system will be conserved.

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4. A fixed mass of gas has a volume of 11cm³ at a pressure of 5 x 10⁵ Pa . Find its volume when the pressure is 2.5 x 10⁵ Pa.​

Answers

Answer:

22 cm ^3

Explanation:

P1 V1   = P2 V2         with constant mass and temperature

11 ( 5 x 10^5 ) =  x  ( 2.5 * 10^5)

x = 22 cm^3              ( when you 1/2 the pressure, you double the volume)

Calculate the momentum (in kg m/s) of a ball with a mass of 10 kg and a velocity of 37
m/s. Round to the nearest whole number (no decimals).

Answers

Answer:

M= mv= 10kg x 37 m/s= 370 Kg x m/s

A ray of light impinges on a transparent material at some angle with the normal. If the material has a higher index of refraction, as it enters, the ray will ______________.
- continue going in the same direction
- bend to make a smaller angle with the normal
- bend to make a larger angle with the normal

Answers

A ray of light impinges on a transparent material at some angle with the normal. If the material has a higher index of refraction, as it enters, the ray will B. bend to make a smaller angle with the normal

This phenomenon is known as refraction and occurs due to the change in the speed of light as it moves from one medium to another with different refractive indices. The bending of the light ray is governed by Snell's law, which states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the refractive indices of the two media.

Therefore, when the ray enters the material with a higher refractive index, it will slow down and bend towards the normal. This behavior is what allows lenses to focus light and is essential in many optical devices, including eyeglasses, microscopes, and telescopes. So if a ray of light impinges on a transparent material at some angle with the normal and the material has a higher index of refraction, the ray will B. bend to make a smaller angle with the normal as it enters.

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Electric charge can accumulate on an airplane in flight. You may have observed needle-shaped metal extensions on the wing tips and tail of an airplane. Their purpose is to allow charge to leak off before much of it accumulates. The electric field around the needle is much larger than the field around the body of the airplane and, can become large enough to produce dielectric breakdown of the air, discharging the airplane. To model this process, assume that two charged spherical conductors are connected by a long conducting wire and a charge of 33.0 muC is placed on the combination. One sphere, representing the body of the airplane, has a radius of 6.00 cm, and the other, representing the tip of the needle, has a radius of 2.00 cm. What is the electric potential of each sphere? r = 6.00 cm V r = 2.00cm V What is the electric field at the surface of each sphere? r = 6.00 cm V/m r = 2.00 cm V/m

Answers

Electric potential of airplane body: V = 165 kV. Electric potential of needle tip: V = 495 kV. Electric field at airplane body surface: E = 82.5 kV/m. Electric field at needle tip surface: E = 247.5 kV/m.

Electric charge gathering on a plane in flight is a huge worry because of the potential for a perilous development of charge. To forestall this, slender molded metal augmentations are introduced on the wingtips and tail to permit the charge to disperse before it gathers.

The electric field around the needle is a lot more grounded than the field around the plane body, and on the off chance that it turns out to be areas of strength for excessively, can cause dielectric breakdown of the air, which can release the plane.

To display the course of charge development, we can expect that two charged round conduits are associated by a long leading wire, with a charge of 33.0 μC put on the mix. One circle addresses the plane body, with a span of 6.00 cm, and the other addresses the tip of the needle, with a sweep of 2.00 cm.

To decide the electric capability of every circle, we can utilize the equation V = kQ/r, where k is the Coulomb steady, Q is the charge, and r is the sweep of the circle. The electric capability of the circle addressing the plane body is around 165 kV, and the electric capability of the circle addressing the tip of the needle is roughly 495 kV.

To compute the electric field at the outer layer of every circle, we can utilize the recipe E = kQ/r^2, where r is the span of the circle. The electric field at the outer layer of the circle addressing the plane body is around 82.5 kV/m, and the electric field at the outer layer of the circle addressing the tip of the needle is roughly 247.5 kV/m.

All in all, the slender molded metal augmentations on the wingtips and tail of a plane assist with forestalling the aggregation of electric charge during flight, which can be perilous.

Demonstrating the course of charge development utilizing two charged circular channels associated by a long leading wire shows that the electric potential and electric field at the outer layer of the circle addressing the tip of the needle are a lot higher than those of the circle addressing the plane body.

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A force of 85 N is used to push a box along the floor a distance of 15 m. How much work was done?

Answers

Answer:

1275J

Explanation:

Given parameters:

Force on box  = 85N

Distance moved  = 15m

Unknown:

Work done  = ?

Solution:

Work done is the amount of force applied on a body to move it through a specific distance.

 Work done  = Force x distance

Now insert the parameters and solve;

 Work done = 85 x 15  = 1275J

A :-) work = force x distance
W = 85 x 15
W = 1275 joules

.:. The work done is 1275 joules

Two particles p and q are shot vertically up. Particle p is shot fort with a velocity of 40m/s. After four seconds particle q is shot. Find where the two particles meet if the point of meeting p has a velocity of 15m/s

Answers

The two particles, p and q, meet at a height of 70 meters above the ground.

Particle p is shot vertically upwards with an initial velocity of 40 m/s. We can use the equation for vertical displacement to find the height reached by particle p after time t:

h_p = v_p * t_p - 0.5 * g * t_p^2

where v_p is the initial velocity of particle p, t_p is the time for particle p to reach the meeting point, and g is the acceleration due to gravity.

Next, particle q is shot after 4 seconds. Let's denote the time taken by particle q to reach the meeting point as t_q. Since particle q is shot after particle p, it will have a shorter time of flight. Therefore, we can express the height reached by particle q as:

h_q = v_q * t_q - 0.5 * g * t_q^2

where v_q is the initial velocity of particle q.

At the meeting point, the heights reached by particles p and q are equal, so we have:

h_p = h_q

Substituting the expressions for h_p and h_q, we can solve for t_p and t_q:

40 * t_p - 0.5 * g * t_p^2 = v_q * t_q - 0.5 * g * t_q^2

Given that the velocity of particle p at the meeting point is 15 m/s, we have:

v_p = 15

Solving these equations simultaneously will give us the values of t_p and t_q.

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The voltage across a membrane forming a cell wall is 77.7 mV and the membrane is 9.02 nm thick. What is the electric field strength?

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The electric field strength across the membrane is approximately 8.612 × 10⁶ V/m, given a voltage of 77.7 mV and a membrane thickness of 9.02 nm.

To determine the electric field strength across a membrane, we can use the formula:

Electric field strength = Voltage / Distance

Given that the voltage across the membrane is 77.7 mV (millivolts) and the membrane thickness is 9.02 nm (nanometers), we need to convert the units to be consistent.

1 mV = 0.001 V (volts)

1 nm = 1e-9 m (meters)

Converting the units:

Voltage = 77.7 mV × 0.001 V/mV = 0.0777 V

Distance = 9.02 nm × 1e-9 m/nm = 9.02e-9 m

Plugging the values into the formula:

Electric field strength = 0.0777 V / 9.02e-9 m

Calculating the electric field strength:

Electric field strength = 8.612 × 10⁶ V/m

Therefore, the electric field strength across the membrane is approximately 8.612 × 10⁶ V/m.

In summary, the electric field strength across the membrane is approximately 8.612 × 10⁶ V/m when the voltage across the membrane is 77.7 mV and the membrane thickness is 9.02 nm.

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Explain the quantization of energy.​

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Answer:

The quantization of energy refers to the fact that at subatomic levels, energy is best thought of as occurring in discreet "packets" called photons. Like paper money, photons come in different denominations. ... Each photon contains a unique amount of discreet energy

by moving the screen only, change the pattern so you can see only the wide interference pattern. is the pattern you see now the single slit pattern or the double slit pattern? how can you tell?

Answers

If you move the screen only, you will not see any interference pattern on the screen. The interference pattern is created by the diffraction of light through the two slits. When the screen is moved, the distance between the slits and the screen changes, and the interference pattern disappears.

To tell if you are seeing the single slit or the double slit pattern, you can look at the interference pattern on the screen. If you are seeing a pattern of bright and dark fringes on the screen, you are seeing the double slit pattern.

This pattern is characteristic of wave interference and is produced when the light passes through two closely spaced slits. On the other hand, if you do not see any interference pattern on the screen, you are seeing the single slit pattern. This pattern is characteristic of wave diffraction and is produced when the light passes through a single slit.  

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*(d) The map below shows the positions of some seismic earthquake stations in the UK.
nd
TE
At the seismic stations, scientists record the arrival of earthquake waves.
They use this data to locate where an earthquake happened.
Describe how they use the data to find out where an earthquake happened.
You may add to the diagram above or draw your own diagram to help with your
answer.
Vnjbsdjvbsdbv
(6)

Answers

Scientists use the arrival times of seismic waves at multiple stations, along with amplitude data, to triangulate the location of an earthquake epicenter.

To determine the location of an earthquake, scientists use the data recorded at seismic stations. The seismic stations are equipped with seismometers that detect and record seismic waves generated by the earthquake. These waves travel through the Earth's interior and arrive at different times at various seismic stations.To locate the epicenter of the earthquake, scientists analyze the time differences between the arrivals of primary (P) waves and secondary (S) waves at multiple stations. P waves are faster and arrive first, followed by slower S waves. By comparing the time interval between the arrival of P and S waves at different stations, scientists can calculate the distance of each station from the earthquake epicenter.

Using the distances from at least three seismic stations, scientists plot circles around each station on a map. These circles represent the potential distance between the station and the epicenter. The intersection of the circles determines the most likely location of the earthquake epicenter. This method is known as the "triangulation" technique.Additionally, the amplitude of the recorded seismic waves provides information about the earthquake's magnitude. By analyzing the amplitude data from different stations, scientists can estimate the earthquake's size or magnitude.

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Note- Sorry The diagram cannot be added .

for sound waves in air with frequency 1000 hz, a displacement amplitude of 1.2×10−8m produces a pressure amplitude of 3.0×10−2pa. use vsound= 344 m/s.

Answers

The displacement amplitude for sound waves with a frequency of 1000 Hz and a pressure amplitude of 3.0×10^(-2) Pa in air is approximately 3.3332×10^(-6) m.

To determine the relationship between the displacement amplitude and pressure amplitude of sound waves, we can use the formula for sound intensity:

I = (1/2) * ρ * v * A^2

Where:

I is the sound intensity

ρ is the density of the medium (in this case, air)

v is the velocity of sound in the medium

A is the displacement amplitude

Given:

Frequency (f) = 1000 Hz

Displacement amplitude (A) = 1.2×10^(-8) m

Pressure amplitude (P) = 3.0×10^(-2) Pa

Velocity of sound (v) = 344 m/s

First, we need to find the density of air (ρ). The density of air at standard conditions is approximately 1.225 kg/m^3.

Next, we can rearrange the formula for sound intensity to solve for the displacement amplitude (A):

I = (1/2) * ρ * v * A^2

A^2 = (2 * I) / (ρ * v)

A = √((2 * 3.0×10^(-2)) / (1.225 * 344))

A ≈ 3.3332×10^(-6) m

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An airplane travels 640 miles from topeka to houston in 3. 2 hours, going against the wind. The return trip is with the wind, and takes only 2 hours. Find the rate of the airplane with no wind. Find the rate of the wind.

Answers

When an airplane travels 640 miles from Topeka to Houston in 3. 2 hours, going against the wind. The return trip is with the wind and takes only 2 hours. Then the rate of the airplane with no wind is 260 miles/hr, and the rate of the wind is 100 miles/hr

Let Va is the velocity of the airplane

Va is the velocity of the wind

When flying against the wind then

(Va+Vw)*(3.2 hours) = 640

3.2Va + 3.2Vw = 640

3.2Vw = 640 - 3.2Va

Vw = 200 - Va----------------(1)

When flying with the wind:

(Va-V)*(2 hours) = 640km

2Va - 2Vw = 640

Va - Vw = 320 ----------------(2)

Putting the value of VW in equation (2) we get

Va - (200-Va) = 320

2Va = 320 +200

2Va = 520

Va = 260

Putting this value in equation (2)

Vw =Va - 360

Vw = 100

Therefore the rate of the airplane with no wind is 260 miles/hr, and the rate of the wind is 100 miles/hr

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The satellite which has the thickest atmosphere (so thick that it's quite a surprise for a satellite) is:_____.

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The satellite which has the thickest atmosphere is Titan.

Titan is the moon of planet Saturn and is 2nd largest satellite that occurs naturally in the solar system.

It is almost 0x away from the sun located at a distance of about 886 million miles.

According to NASA, its atmosphere is composed of weird molecules named 'cyclopropenylidene' that are unique in composition and couldn't be found on any other planet.

Here the atmosphere is very dense and chances of life have also been found on this satellite.

Titan has appropriate conditions for life and, therefore, is suitable for retaining life.

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3.Minsoo is training for cross-country in the fall. He ran 5 miles east. Then he turned around and ran 4 miles west. Draw and label the vectors that show each segment of his trip and the resultant displacement vector. Find his resultant displacement. (10 points)

3.Minsoo is training for cross-country in the fall. He ran 5 miles east. Then he turned around and ran

Answers

Answer:

...............................

A light source of 1000 lux is pointed at a virtual model with the following surface reflectivity coefficients: The material is a flat surface on the xz plane. The light source is at located at point (−4,3, 0 ), and the viewer is located at point (2,2,2). What will be the intensity of the light source for the viewer if the light is reflected at point (0,0,0) ?

Answers

To calculate the intensity of the light source for the viewer after being reflected at point (0, 0, 0), we can use the inverse square law for light intensity.

The formula for the intensity of light at a certain distance from the source is given by:

I = I₀ / d²

Where:

I is the intensity of light at a certain distance

I₀ is the initial intensity of the light source

d is the distance from the light source to the point of observation

First, let's calculate the distance from the light source to the point of reflection (0, 0, 0). Using the distance formula, we have:

d₁ = √[(-4 - 0)² + (3 - 0)² + (0 - 0)²]

= √[16 + 9 + 0]

= √25

= 5

Next, let's calculate the distance from the point of reflection (0, 0, 0) to the viewer (2, 2, 2):

d₂ = √[(2 - 0)² + (2 - 0)² + (2 - 0)²]

= √[4 + 4 + 4]

= √12

= 2√3

Now, we can calculate the intensity of the light for the viewer after reflection using the inverse square law:

I_viewer = I₀ / (d₁ + d₂)²

= 1000 / (5 + 2√3)²

To simplify the expression, we can rationalize the denominator:

I_viewer = 1000 / (5 + 2√3)²

= 1000 / (25 + 20√3 + 12)

= 1000 / 37 + 20√3

Therefore, the intensity of the light source for the viewer, after being reflected at point (0, 0, 0), is approximately 27.03 lux.

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A car accelerates from 4 meters/second to 16 meters/second in 4 seconds. The car’s acceleration is meters/second2.

Answers

Answer:

3m/s^2

Explanation:

VF-VI/time

16-4/4

12/4

3

Determine the moment at point b using method of section if w=40.3lb/ft Answer:

Answers

Method of section is a significant method of determining forces in members of a structure.

The basic concept of the method of section is to find out the forces acting on the sections by separating them from the rest of the structure.

In this problem, the moment at point b has to be determined using the method of section.

The given weight of the beam is

w = 40.3 lb/ft.

Let's draw the free-body diagram for the given beam:

Free-Body Diagram:

As we can see from the above diagram, the section has been drawn which passes through point b.

We have to determine the moment at point b using this section.

Now, we will write the equation for the moment of the section passing through point b as:

- 12(6) - 4(8) - (20)(12) - (32)(20) - (40.3)(12/2) = 0Mb = 1126.05 lb-ft

the moment at point b is 1126.05 lb-ft.

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The base unit for length is the
1. millimeter.
2. gram.
3. milligram.
4. meter.

Answers

Answer:

meter

Explanation:

please make me brainllist

meter is the base unit for length. for example. lxw=h is all in units.

If we aim a radio telescope at a distant spiral arm of the Milky Way Galaxy, we will probably observe a 21-cm line. If we point a large optical telescope at this same region, we will probably not be able to detect the neutral hydrogen that gives rise to the 21-cm radio signal. Why not

Answers

Answer:

Because of the interstellar dust and interior location of the solar system.

Explanation:

We will probably not be able to detect the neutral hydrogen that gives rise to the 21-cm radio signal if we point a large optical telescope to the region because, the interstellar dust obscures the location of the spiral arm of the Milky way galaxy and this makes neutral hydrogen that gives rise to the 21-cm radio signal difficult to detect.

Also, the interior location of the solar system also makes the neutral hydrogen that gives rise to the 21-cm radio signal difficult to detect.

So, the interstellar dust and the interior location of the solar system makes it difficult to detect the neutral hydrogen that gives rise to the 21-cm radio signal with a large optical telescope.

A spacecraft travels at a speed of 0.5c toward Vega. How long (in years) does it take to get there in the spacecraft if people on Earth think it takes 100 years

Answers

The spacecraft would take approximately 86.6 years to reach Vega as experienced by the passengers on board, while people on Earth would observe it taking 100 years

let's use the concepts of time dilation and the Lorentz factor in the context of a spacecraft traveling toward Vega at a speed of 0.5c.

1. Calculate the Lorentz factor (γ) using the formula: γ = 1 / √(1 - v²/c²), where v is the spacecraft's speed (0.5c) and c is the speed of light.
  γ = 1 / √(1 - (0.5c)²/c²) = 1 / √(1 - 0.25) = 1 / √(0.75) ≈ 1.155

2. Calculate the time experienced by the spacecraft (t') using the formula: t' = t / γ, where t is the time observed by people on Earth (100 years).
  t' = 100 years / 1.155 ≈ 86.6 years

So, the spacecraft would take approximately 86.6 years to reach Vega as experienced by the passengers on board, while people on Earth would observe it taking 100 years.

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