a wheel has a constant angular acceleration of 1.4 rad/s2. during a certain 9.0 s interval, it turns through an angle of 130 rad. assuming that the wheel started from rest, how long had it been in motion before the start of the 9.0 s interval?

Placing a pot of water over a fire transfers thermal energy to the water. When the fire heats the bottom of the pot, the molecules in the pot gain kinetic energy and start to move more rapidly. This kinetic energy is then transferred to the water molecules in contact with the pot.

As the water molecules gain kinetic energy, they start to move more rapidly as well, which causes the overall temperature of the water to increase. This transfer of thermal energy from the fire to the pot, and from the pot to the water, is what causes the water to eventually come to a boil.

Hi! Placing a pot of water over a fire transfers heat energy to the water. This process increases the water's temperature and can eventually cause it to boil, producing steam.

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To calculate the new volume of the balloon, we can use the formula:
V2 = V1 * (T2/T1)
where V1 is the initial volume of the balloon, T1 is the initial temperature, T2 is the final temperature, and V2 is the final volume.
Substituting the given values, we get:
V2 = 3.02 * (316.6/295.7)
V2 = 3.23 L (rounded to two decimal places)
Therefore, the new volume of the balloon is 3.23 L when it is heated to 43.6°C.

To calculate the new volume of the balloon, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature when the pressure and amount of gas are constant. The formula for Charles's Law is:
V1 / T1 = V2 / T2
Where V1 is the initial volume (3.02 L), T1 is the initial temperature (22.7°C), V2 is the final volume, and T2 is the final temperature (43.6°C). First, convert the temperatures to Kelvin by adding 273.15:
T1 = 22.7°C + 273.15 = 295.85 K
T2 = 43.6°C + 273.15 = 316.75 K

Now plug the values into the formula:
(3.02 L) / (295.85 K) = V2 / (316.75 K)
To find V2, multiply both sides by 316.75 K:
V2 = (3.02 L) * (316.75 K) / (295.85 K)
V2 ≈ 3.24 L
The new volume of the balloon when heated to 43.6°C is approximately 3.24 L.

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The method for determining the intensity of solar radiation incident on Saturn involves using instruments on spacecrafts that have been sent to Saturn.

One such spacecraft is the Cassini-Huygens mission, which has provided valuable data on the intensity of solar radiation on Saturn.

The instruments used to obtain this data include the Magnetospheric Imaging Instrument (MIMI) and the Cosmic Dust Analyzer (CDA).

The MIMI measures the energy and intensity of charged particles, while the CDA measures the mass and velocity of dust particles.

These measurements allow scientists to understand the intensity and distribution of solar radiation on Saturn's atmosphere and magnetic field.

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Quasar spectra are most useful in allowing us to learn about clouds of intergalactic gas.

So correct answer is A) Quasar spectra

Quasars are extremely bright and distant objects that emit large amounts of energy, including light. When light from a quasar passes through intergalactic gas clouds, it is absorbed by atoms in the gas. By analyzing the spectrum of light emitted by a quasar and comparing it to the spectrum of light that reaches us on Earth, scientists can identify the specific wavelengths of light that were absorbed by intergalactic gas. This allows them to determine the chemical composition, density, and temperature of the gas clouds, and to learn more about the processes that govern the behavior of matter in the universe. Quasar spectra have been used to study a variety of intergalactic gas clouds, including those associated with galaxies, clusters of galaxies, and the large-scale structure of the universe.

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Polaris has been used for centuries as a navigational aid in the northern hemisphere. It is located near the north celestial pole and can be easily identified due to its brightness and position.

For centuries, sailors and travelers in the northern hemisphere have used the stars to navigate. Polaris, also known as the North Star or Pole Star, has been one of the most important stars in this regard. Located near the north celestial pole, Polaris appears almost stationary in the night sky, making it a reliable reference point for determining direction. It is also one of the brightest stars in the constellation Ursa Minor, making it easy to identify even in low light conditions. By using the position of Polaris and other stars in relation to it, navigators can determine their latitude and track their course. Today, while modern technology has replaced traditional navigation methods, Polaris remains an important part of celestial navigation and astronomy.

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Sunspots are dark, cooler regions that appear on the surface of the Sun due to the Sun's magnetic field becoming twisted and concentrated in certain areas. The extent of the connection is still a topic of scientific debate.  

Sunspots typically occur in pairs or groups and can vary in size from a few hundred to tens of thousands of kilometers.There is evidence of a correlation between sunspot activity and climate change on Earth, although the extent of the connection is still a topic of scientific debate. During periods of high sunspot activity, the Sun emits more energy, including ultraviolet radiation, which can affect the Earth's atmosphere and climate. Some studies suggest that the increase in solar energy during high sunspot activity can lead to changes in global temperature and weather patterns, but other factors such as greenhouse gas emissions and natural climate variability also play significant roles in climate change.

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The charge stored in the capacitor is given by the formula:

Q = C * V

where Q is the charge, C is the capacitance, and V is the voltage.

Substituting the given values, we get:

Q = 20.0 μF * 7.90 kV = 158 μC

The amount of charge that passes through the body tissues is equal to the charge stored in the capacitor, which is 158 μC.

The average power delivered to the tissues can be calculated using the formula:

P = (1/2) * C * V^2 / t

where P is the power, C is the capacitance, V is the voltage, and t is the time taken to discharge the capacitor.

Substituting the given values, we get:

P = (1/2) * 20.0 μF * (7.90 kV)^2 / (2.00 ms) = 1.56 MW

Therefore, the amount of charge that passes through the body tissues is 158 μC, and the average power delivered to the tissues is 1.56 MW.

In a defibrillator, a capacitor is charged to a high voltage and then discharged through the body tissues to restore a normal heart rhythm. The amount of charge that passes through the body tissues is determined by the capacitance of the capacitor and the voltage to which it is charged. In this case, the capacitor has a capacitance of 20.0 μF and is charged to a voltage of 7.90 kV, resulting in a charge of 158 μC that passes through the body tissues.

The average power delivered to the tissues is a measure of the energy transferred to the tissues per unit time. It is calculated using the formula P = (1/2) * C * V^2 / t, where C is the capacitance, V is the voltage, t is the time taken to discharge the capacitor, and the factor of 1/2 accounts for the fact that the voltage decreases linearly as the capacitor discharges. In this case, the average power delivered to the tissues is 1.56 MW, which is a very large amount of power that can cause tissue damage if not controlled properly. Defibrillators are designed to deliver this power in short bursts to minimize tissue damage and restore normal heart function.

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Answer:

True

Explanation:

cables cannot utilize straight through cables using the same wiring scheme as LAN patch cables. A bus topology WAN is often the best option for an organization with only a few sites and the capability to use dedicated circuits.

True. T-1 cables are not designed to utilize the same wiring scheme as LAN patch cables. T-1 cables are specifically used for transmitting data at a high speed over long distances, typically between different locations. They require a special wiring scheme that is different from the standard wiring used for LAN patch cables.

Straight-through cables, on the other hand, are used for connecting devices within the same network and utilize the standard wiring scheme. Attempting to use a straight-through cable with a T-1 connection can result in poor connectivity or even damage to the equipment. Therefore, it is essential to use the appropriate cable for the specific type of connection.
True. T-1 cables cannot utilize straight-through cables using the same wiring scheme as LAN patch cables. T-1 cables require a different wiring scheme known as a T1 crossover, which ensures proper transmission of data signals. In LAN patch cables, straight-through wiring is commonly used for connecting devices with different functionalities, such as connecting a computer to a switch. However, in T-1 connections, the crossover wiring allows proper communication between devices, like routers and CSU/DSU units, which have identical pin configurations. Therefore, it is essential to use the correct wiring scheme in T-1 cables to maintain reliable and efficient data transmission.

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The voltage halfway between the 50 V positive and 0 V negative charges on a dipole is approximately 25 V. The equipotential line would be a straight line perpendicular to the dipole's axis with a voltage of 25 V.

A dipole is a system consisting of two equal and opposite charges separated by a distance, which creates an electric field. The voltage between two points in an electric field is defined as the difference in electrical potential energy per unit charge. In this scenario, there is a 50 V positive charge and a 0 V negative charge, creating a dipole. The voltage halfway between the charges can be calculated as the average of the voltage at the positive and negative charges, which is approximately 25 V. The equipotential lines are a set of points in an electric field that have the same voltage. The equipotential line halfway between the charges would be a straight line perpendicular to the axis of the dipole, connecting points with a voltage of approximately 25 V.

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The vectors. Based on the information provided, I assume you have a figure with vectors M, N, and S, and you need to determine the correct answer, compare the given figure with each of these options and identify which one accurately represents the relationship between vectors M, N, and S.

A) S = N + M In this case, vector S is the sum of vectors N and M. To check if this option is correct, observe the figure and see if S can be represented as the result of adding M and N, tip-to-tail. If so, this is the correct choice. B) S = M - N
Here, vector S is the difference between vectors M and N. To check if this is correct, add the negative of vector N (i.e., N in the opposite direction) to vector M, tip-to-tail. If the resulting vector is S, this is the correct choice. C) S = N - M
In this option, vector S is the difference between vectors N and M. To check this, add the negative of vector M (i.e., M in the opposite direction) to vector N, tip-to-tail. If the resulting vector is S, this is the correct choice. To determine the correct answer, compare the given figure with each of these options and identify which one accurately represents the relationship between vectors M, N, and S.

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No, there is no excitation observed in the circuit after the battery is turned off.

This is because the battery is the source of energy and when it is turned off, the circuit no longer has a source of energy. The circuit is then unable to store or release any energy, so no excitation is observed.

When the battery is on, the electrons in the circuit can move freely and the current can flow, resulting in an excited state. But when the battery is off, the electrons are stuck in their current positions, so no movement or excitation is observed.

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 Gamma radiation has the most penetrating answer whereas alpha has the least .

Alpha radiation:
- Purely composed of charged particles (helium nuclei)
- Travels at 1/10 the speed of light
- Lowest penetrating power
- Capable of shallow, sunburn-like, skin damage

Beta radiation:
- Composed of charged particles (electrons or positrons)
- Travels at 9/10 the speed of light
- Intermediate penetrating power
- Causes more internal biological damage than Alpha radiation

Gamma radiation:
- Composed of high-energy photons (light)
- Travels at the speed of light
- Highest penetrating power
- Can cause the most internal biological damage due to its high energy and penetration

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The initial pressure of the gas is 100 kPa.

This problem can be solved using the combined gas law, which states:

P1V1/T1 = P2V2/T2

Where P1, V1, and T1 are the initial pressure, volume, and temperature of the gas, and P2, V2, and T2 are the final pressure, volume, and temperature.

Let's assign some variables to the given information:

P1 = initial pressure (unknown)

V1 = initial volume (1 fold)

T1 = initial absolute temperature (100%)

P2 = final pressure (P1 + 140 kPa)

V2 = final volume (0.5 fold)

T2 = final absolute temperature (120% of T1)

Using the given information, we can write:

P1V1/T1 = P2V2/T2

Substituting the values we know:

P1 * 1 / 100% = (P1 + 140 kPa) * 0.5 / 120%

Simplifying:

P1 = ((P1 + 140 kPa) * 0.5 * 100%) / 120%

P1 = (P1 + 140 kPa) / 2.4

Multiplying both sides by 2.4:

2.4 * P1 = P1 + 140 kPa

Subtracting P1 from both sides:

1.4 * P1 = 140 kPa

Dividing both sides by 1.4:

P1 = 100 kPa

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A satellite is a spacecraft that orbits Earth or another celestial body. Satellites are used for a variety of purposes, including communication, navigation, weather forecasting, and scientific research.

A space station is a large structure that is designed to be inhabited by humans for extended periods of time. Space stations are typically used for scientific research, space exploration, and testing of new technology. A space station that orbits Earth and receives and transmits signals from Earth-based stations over a wide area is called a communication satellite. Communication satellites are used to provide television, telephone, and internet services to remote areas of the world.

They are placed in orbit at a high altitude, where they can cover a large geographic area with their signals. Communication satellites are typically large and complex systems that require careful engineering and testing to ensure that they function properly. They are designed to withstand the harsh conditions of space, including extreme temperatures, radiation, and micrometeoroids.

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Equipment that is operated by a fluid under pressure, such as water or oil, is known as a hydraulic system. These systems use pressurized fluid to transmit power and perform various tasks, like lifting heavy loads or operating machinery. Common examples of hydraulic equipment include excavators, car jacks, and hydraulic brakes.

The type of equipment that is typically operated by a fluid that is under pressure, such as water or oil, includes hydraulic equipment and pneumatic equipment.

These types of equipment use the pressure of the fluid to power various mechanisms and perform tasks, such as lifting heavy objects or moving machinery.

Examples of hydraulic equipment include hydraulic presses, cranes, and excavators, while examples of pneumatic equipment include air compressors, drills, and pumps.

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The correct list that names the three types of galaxies is Elliptical, Spiral, and Irregular.

The classification of galaxies is primarily based on their shape and structure. Elliptical galaxies are characterized by their elliptical or oval shape, with a smooth and featureless appearance. Spiral galaxies have a distinct spiral arm structure, often with a central bulge. Irregular galaxies do not have a well-defined shape and exhibit a chaotic or irregular appearance. It's worth noting that there are also other specialized types of galaxies, such as lenticular galaxies (a hybrid between elliptical and spiral galaxies) and peculiar galaxies (exhibiting unusual features or interactions with other galaxies). The study of galaxies, known as galactic astronomy, continues to provide fascinating insights into the structure and evolution of the universe.

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The search that does not apply to the plain view doctrine is the use of a thermal imaging device to find drugs in a garage, as it constitutes a search without a warrant and is not a result of a lawful observation.

The plain view doctrine allows police officers to seize evidence that is in plain view without a warrant, as long as they are lawfully present in the location and the incriminating nature of the evidence is immediately apparent. Of the examples given, a) finding a gun in a lawfully stopped vehicle, b) the use of a low-flying helicopter to find marijuana plants in a field, and c) the use of binoculars in a field search, all apply to the plain view doctrine, as they involve the discovery of evidence that is in plain view and immediately apparent to the police. However, d) the use of a thermal imaging device to find drugs in a garage does not apply to the plain view doctrine, as it constitutes a search without a warrant and is not a result of a lawful observation.

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The correct answer is C. When you ride your scooter twice as fast, you have twice the momentum. Momentum is directly proportional to velocity, so when you double your velocity, your momentum also doubles.

Momentum is a physical quantity that describes the motion of an object. It is defined as the product of an object's mass and velocity. Momentum is a vector quantity, meaning it has both magnitude and direction. According to the law of conservation of momentum, the total momentum of a closed system remains constant, unless acted upon by an external force.

This principle is widely used in many areas of physics, including mechanics, fluid dynamics, and electromagnetism. Momentum is a fundamental concept in physics and has many practical applications, including in transportation, sports, and engineering.

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The ultrasonic spatula device is NOT used for congested skin conditions.

The ultrasonic spatula is a skincare device that uses ultrasonic vibrations to exfoliate and cleanse the skin. It is a non-invasive and gentle way to remove dead skin cells, debris, and oil from the skin's surface. This device can be used for a variety of skin conditions, including dull, aging, and dehydrated skin. It can help improve skin texture, reduce the appearance of fine lines and wrinkles, and enhance the skin's overall appearance. However, the ultrasonic spatula is not recommended for congested skin conditions, as it can exacerbate inflammation and irritation. Congested skin is characterized by clogged pores, blackheads, and acne, and requires more targeted treatments such as chemical exfoliants or acne treatments.

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1) For a spherical surface of radius r1 = 0.525 m, both point charges are outside the sphere. According to Gauss's Law, the total electric flux through a closed surface is equal to the net charge enclosed by the surface divided by the permittivity of free space (ε0). Since no charges are enclosed by the surface, the total electric flux is 0.

2) For a spherical surface of radius r2 = 1.65 m, only q1 is enclosed within the sphere. Using Gauss's Law, the total electric flux through the surface is:
Φ = Q_enclosed / ε0 = q1 / ε0 = (3.30 nC) / (8.85 x 10^(-12) C^2/N.m^2) ≈ 3.73 x 10^8 N.m^2/C

3) For a spherical surface of radius r3 = 2.65 m, both q1 and q2 are enclosed within the sphere. The net charge enclosed is the sum of the two point charges: Q_enclosed = q1 + q2 = 3.30 nC - 7.00 nC = -3.70 nC. Applying Gauss's Law, the total electric flux through the surface is:
Φ = Q_enclosed / ε0 = (-3.70 nC) / (8.85 x 10^(-12) C^2/N.m^2) ≈ -4.18 x 10^8 N.m^2/C

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While the center of mass coincides with the geometric center, the center of gravity is the point where the entire weight of an object appears to act. The center of gravity is affected by the distribution of mass and external forces acting on the object.

It is the point where the force of gravity appears to act on an object. Therefore, it is not always at the geometric center of an object. A simple example would be a T-shaped object, where the center of gravity would be closer to the heavier end of the T-shape. The other statements are true about Gravity: if an object is free to rotate about a pivot, the center of gravity will come to rest below the pivot, and the torque due to gravity can be calculated by considering the object's weight as acting through the center of gravity, and for objects small compared to the earth, the center of gravity and the center of mass are essentially the same. The statement that is not true about Gravity is B) the center of gravity coincides with the geometric center. The center of gravity is the point where the weight of an object appears to be concentrated, and it depends on the distribution of mass within the object. The geometric center, on the other hand, is the point at which all of the object's dimensions are balanced. While the two centers can coincide in some cases, such as for a uniform object, they do not always align.

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you used 4,320 mg of table salt on your food.

To solve the problem, we need to use the density of table salt and the volume used to calculate the mass of salt used in grams. The density of table salt is given as 2.16 g/ml, and the volume used is 2.00 ml. We can use the formula Density = Mass / Volume to find the mass of salt used. Rearranging the formula to solve for mass, we get Mass = Density × Volume.Substituting the given values into the formula, we get Mass = 2.16 g/ml × 2.00 ml = 4.32 g. However, the question asks for the mass in milligrams, so we need to convert the answer from grams to milligrams. We know that 1 g is equal to 1,000 mg, so we can multiply the answer by 1,000 to convert it to milligrams.Multiplying 4.32 g by 1,000 mg/g, we get 4,320 mg. Therefore, you used 4,320 mg of table salt on your food.

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The temperature of a star is directly related to its peak wavelength. A star with a temperature of 4500 K has the longest peak wavelength.

According to Wien's displacement law, the peak wavelength of radiation emitted by an object is inversely proportional to its temperature. The formula is given by [tex]λ_peak = b / T[/tex], where λ_peak is the peak wavelength, T is the temperature in Kelvin, and b is Wien's displacement constant (approximately 2.898 × 10^6 nm·K). As the temperature decreases, the peak wavelength increases. Therefore, a star with a temperature of 4500 K would have the longest peak wavelength among the given options. The star with a temperature of 7500 K would have a shorter peak wavelength, while the star with a temperature of 6000 K would have an intermediate peak wavelength. Hence, the star with a temperature of 4500 K has the longest peak wavelength.

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At the mouth of a submarine canyon, you would expect to find a fan-shaped accumulation of sediment called a submarine fan. Submarine canyons are deep,

steep-sided valleys that cut into the seafloor and can extend for many kilometers. They are often formed by underwater erosion from currents, landslides, and other geological processes. At the mouth of the submarine canyon, where it opens up onto the continental shelf, sediment carried by the currents can accumulate and form a fan-shaped deposit. This sediment can come from a variety of sources, including the erosion of the canyon walls, rivers that empty into the ocean, and ocean currents that transport sediment from other areas.

Submarine fans can be quite large and can play an important role in the transport of sediment and nutrients in the deep ocean. They can also be important sites of oil and gas deposits, as well as deep-sea habitats for a variety of marine organisms.

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31H→32He+ - This is a beta decay reaction ;  23290Th→22888Ra+?.- This is an alpha decay reaction ; The nuclear reaction shown below, 22490Th → 22088Rn + 42He, is also an alpha decay reaction ; alpha decay of uranium-236 (atomic number 92, mass number 236) results in the emission of alpha particle and formation of a new nucleus.

Decay reaction 31H→32He+ - This is a beta decay reaction, which means that a neutron in the nucleus of the hydrogen atom (with atomic number 1) is converted into a proton, an electron, and a neutrino. The proton stays in the nucleus, while the electron and neutrino are ejected. The resulting nucleus has atomic number 2 (helium) and mass number 32, which means it has two protons and 30 neutrons.

23290Th→22888Ra+?. This is an alpha decay reaction, which means that the nucleus of thorium (atomic number 90) emits an alpha particle, which is a helium nucleus with two protons and two neutrons. The resulting nucleus has atomic number 88 (radium) and mass number 228, which means it has 88 protons and 140 neutrons.

The nuclear reaction shown below, 22490Th → 22088Rn + 42He, is also an alpha decay reaction. The nucleus of thorium (atomic number 90) emits an alpha particle, which is a helium nucleus with two protons and two neutrons. The resulting nucleus has atomic number 88 (radon) and mass number 220, which means it has 88 protons and 132 neutrons.

The alpha decay of uranium-236 (atomic number 92, mass number 236) results in the emission of an alpha particle (helium nucleus) and the formation of a new nucleus. The new nucleus has atomic number 90 (thorium) and mass number 232, which means it has 90 protons and 142 neutrons.

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The coefficient of linear expansion of aluminum is 2.4 x 10^-5 /°C. Using these values, the change in length of the rod is found to be 0.00144 cm, or 1.44 x 10^-3 cm.

The change in length of a material due to a change in temperature can be calculated using the following formula:

ΔL = αLΔT

where ΔL is the change in length, α is the coefficient of linear expansion, L is the original length, and ΔT is the change in temperature.

The coefficient of linear expansion for aluminum is α = 2.3 x 10^-5 /°C.

Using the given values, we can calculate the initial volume of the rod:

V = L*A, where A is the cross-sectional area of the rod.

The cross-sectional area of a rod can be calculated using the formula:

A = πr^2

where r is the radius of the rod.

Assuming the rod is cylindrical, we can use the mass and density of aluminum to calculate the radius:

ρ = m/V = m/(AL)

ρ_al = 2.7 g/cm^3

m = 350 g

L = 20.0 cm

V = m/ρ = (350 g)/(2.7 g/cm^3) = 129.63 cm^3

A = V/L = πr^2

r = √(A/π) = √(129.63 cm^3/(20.0 cm * π)) = 0.205 cm

The initial length of the rod is L = 20.0 cm.

Now we can calculate the change in length:

ΔL = αLΔT

We are given that 10,000 J of energy is added to the rod by heat, but we need to know the corresponding change in temperature. To do this, we can use the specific heat capacity of aluminum, which is 0.9 J/(g·°C).

Q = mcΔT

ΔT = Q/(mc) = (10000 J)/(350 g * 0.9 J/(g·°C)) = 31.746 °C

Now we can calculate the change in length:

ΔL = αLΔT = (2.3 x 10^-5 /°C) * (20.0 cm) * (31.746 °C) = 1.47 x 10^-2 cm

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When curling the hair for a thermal design, a hard-rubber or nonflammable comb should be positioned near the base of the hair section.

This is because the heat from the curling iron or other thermal tool can cause the comb to melt or become damaged if it is too close to the heated area. Placing the comb near the base of the hair section also helps to create a smooth and even curl.

Additionally, using a nonflammable comb helps to prevent any potential fire hazards that could occur if a plastic comb were to come into contact with the heat source. Overall, positioning the comb properly and using the right type of comb are important factors in achieving a safe and effective thermal design.

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A tiny fraction, estimated to be about 5% of the total matter and energy in the universe, is accounted for by the visible matter in the form of galaxies, stars, planets, and other celestial bodies.

The visible universe, which includes our Milky Way galaxy, as well as all the other galaxies and celestial objects we can observe, only accounts for a small fraction of what is actually there. The current estimate is that visible matter makes up only about 5% of the total matter and energy in the universe. The remaining 95% is composed of dark matter and dark energy, which cannot be directly detected by our instruments and are still not well understood. Dark matter is thought to provide the gravitational glue that holds galaxies together, while dark energy is believed to be responsible for the accelerated expansion of the universe.

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The stars are 0.11 arcseconds apart. This is determined by using the formula for angular resolution: θ = 1.22 λ/D, where θ is the angular resolution in radians, λ is the wavelength of light, and D is the diameter of the telescope's mirror.

Plugging in the given values, we get: θ = 1.22 x (570 x 10^-9 m) / 0.61 m = 1.14 x 10^-6 radians. To convert this to arcseconds, we multiply by 206,265, giving us an angular resolution of 0.236 arcseconds. Since the two stars are "barely resolved," we can assume that they are just beyond this limit, so we can estimate their separation as approximately 0.11 arcseconds.

The diffraction causes light waves to spread out as they pass through an opening or aperture. In the case of a telescope, the aperture is the mirror, and the spreading of the light waves limits the telescope's ability to distinguish between two closely spaced objects. The formula for angular resolution takes into account the wavelength of light and the size of the aperture, and tells us how close together two objects must be in order to be resolved by the telescope. In this case, the stars are 18 light-years away, but their angular separation as seen from Earth is what determines whether they can be resolved or not.

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Cygnus X-1 and LMC X-3 are both believed to be black holes with unseen companions. The masses of these companions cannot be directly measured, but are inferred from observations of the black hole's motion and behavior. In the case of Cygnus X-1, the companion is thought to be a blue supergiant star with a mass around 30 times that of the Sun. For LMC X-3, the companion is thought to be a massive, compact star such as a neutron star or black hole.

However, the exact mass of the companion in either system is uncertain and subject to ongoing study and debate among astronomers.

Cygnus X-1 and LMC X-3 are indeed black holes, which are celestial objects with extremely strong gravitational forces. The masses of their unseen companions can be determined using the following steps:

Step 1: Identify the type of systems
Cygnus X-1 and LMC X-3 are both X-ray binary systems, meaning they consist of a black hole and a companion star orbiting each other.

Step 2: Determine the masses of the black holes
The masses of the black holes can be calculated using observations of the systems' X-ray emissions and the orbital motion of the companion stars.

For Cygnus X-1, the mass of the black hole is estimated to be around 14.8 solar masses (where one solar mass is the mass of our Sun).

For LMC X-3, the mass of the black hole is estimated to be around 10 solar masses.

Step 3: Unseen companions' masses
The "unseen companions" in these systems refer to the black holes themselves. Therefore, the masses of the unseen companions are:

- Cygnus X-1: Approximately 14.8 solar masses
- LMC X-3: Approximately 10 solar masses

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