A student on a piano stool rotates freely with an angular speed of 3. 05 rev/s. The student holds a 1. 05kg mass in each outstretched arm 0. 789m from the axis of rotation. The combined momment of inertia of the student and the stool, ignoring the two masses, is 5. 33kg*m^2, a value that remains constant. As the student pulls his arms inward, his angular speed increases to 3. 54 rev/s. A) How far are the masses from the axis of rotation at this time considering the masses to be points
b) calculate the initial and final kinetic energies of the system

Answers

Answer 1

a) The distance of the masses from the axis of rotation is 0.620 m.

b) The initial kinetic energy of the system is 1.680 x 10² J and the final kinetic energy of the system is 2.020 x 10² J.

a) According to the law of conservation of angular momentum, the initial angular momentum of the system is equal to the final angular momentum. Therefore, (I1ω1) = (I2ω2), where I1 is the initial moment of inertia, ω1 is the initial angular velocity, I2 is the final moment of inertia, and ω2 is the final angular velocity.

Since the moment of inertia of the two masses is (2mr²), where m is the mass of each mass and r is the distance of each mass from the axis of rotation, the final moment of inertia is (5.33 + 2m(0.620)²) kg*m². Solving for r, we get r = 0.620 m.

b) The initial kinetic energy of the system is (1/2)I1ω1² + (1/2)mv1², where m is the mass of each mass and v1 is the initial tangential velocity. The final kinetic energy of the system is (1/2)I2ω2² + (1/2)mv2², where v2 is the final tangential velocity.

Since the work done by the student in pulling the masses inward is equal to the change in kinetic energy of the system, we have W = (1/2)mv2² - (1/2)mv1². Solving for the initial and final kinetic energies, we get KE1 = 1.680 x 10² J and KE2 = 2.020 x 10² J.

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Related Questions

In looking at the below mode values, each with n>1 use the spread in the measured max and min sustainable frequencies for each resonance and report the average frequency with the uncertainity for each of these higher order modes. Likewise calculate the fundamental frequency for each of these two modes.

n=2 max: 33.6 min: 33.3
n=3 max:48.9 mine: 47.7

Answers

For the given mode values with n > 1, we will calculate the average frequency and uncertainty for each resonance based on the spread in the measured maximum and minimum sustainable frequencies are 33.3 Hz and 47.7 Hz.

For n = 2, the maximum sustainable frequency is 33.6 Hz, and the minimum sustainable frequency is 33.3 Hz. To calculate the average frequency, we take the average of these two values: (33.6 Hz + 33.3 Hz) / 2 = 33.45 Hz. The uncertainty is obtained by taking half of the difference between the maximum and minimum frequencies: (33.6 Hz - 33.3 Hz) / 2 = 0.15 Hz. Therefore, the average frequency for n = 2 mode is 33.45 Hz with an uncertainty of ±0.15 Hz. The fundamental frequency for this mode would be the minimum sustainable frequency, which is 33.3 Hz.

For n = 3, the maximum sustainable frequency is 48.9 Hz, and the minimum sustainable frequency is 47.7 Hz. Following the same procedure, the average frequency is (48.9 Hz + 47.7 Hz) / 2 = 48.3 Hz, and the uncertainty is (48.9 Hz - 47.7 Hz) / 2 = 0.6 Hz. Therefore, the average frequency for n = 3 mode is 48.3 Hz with an uncertainty of ±0.6 Hz. The fundamental frequency for this mode is 47.7 Hz.

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a force that is at rest or moves in at a constant speed and in a constant direction is called a what force

Answers

The question is fishing for "balanced force".

But the description in the question is terrible.

what is gravity???☺️

Answers

Answer:

Gravity

Explanation:

its an invisible force that pulls objects

toward each other.

hope it helps

A force that pulls objects downwards

Starting 5.0 m from a department store mirror, Suzanne walks toward the mirror at 1.1 m/s for 2.0 s .
How far is Suzanne from her image in the mirror after 2.0 s ?
I got 2.8 m as my answer but it's telling me im wrong ):

Answers

Suzanne distance is 5.6 meters away from her image in the mirror after 2.0 seconds.

First, let's find the distance Suzanne has walked towards the mirror. We can do this by using the formula:

Distance = Speed × Time

Plug in the values:
Distance = 1.1 m/s × 2.0 s
Distance = 2.2 m

Now, let's find Suzanne's distance from the mirror after walking 2.2 meters towards it:

Initial distance from the mirror: 5.0 m
Distance walked towards the mirror: 2.2 m

Calculate the remaining distance to the mirror:

Remaining distance to mirror = Initial distance - Distance walked
Remaining distance to mirror = 5.0 m - 2.2 m
Remaining distance to mirror = 2.8 m

Finally, calculate the distance between Suzanne and her image in the mirror:

Since the image in the mirror is an equal distance behind the mirror as Suzanne is in front of the mirror, the total distance between Suzanne and her image is twice the remaining distance to the mirror:

Distance between Suzanne and her image = 2 × Remaining distance to mirror
Distance between Suzanne and her image = 2 × 2.8 m
Distance between Suzanne and her image = 5.6 m

So, Suzanne is 5.6 meters away from her image in the mirror after 2.0 seconds.

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a ball rolls from rest down an incline with a uniform acceleration of 4m/s². what is it speed after 8 seconds​

Answers

2 maybe I’m not sure but the app told me to answer some questions and I don’t know anything to be honest I hope someone will come and help you have a nice day

If the current in a wire which is placed perpendicular to a magnetic field increases the force on the wire

Answers

Answer:

The force on the wire increases

Explanation:

Since the force on the wire F = BILsinФ where B = magnetic field strength, I = current in wire, L= length of wire and Ф = angle between the magnetic field and the wire.

Given that the magnetic field and the wire are perpendicular, Ф = 90°

So, F = BILsin90° = BIL

Since B and L are constant, F ∝ I

So, if the current in the wire increases, the force on the wire also increases.

Use the equation below to answer questions (14-21). C12H22O11(s) → 12C(s) + 11H2O(g) 14)The left side of the chemical equations is the _______________________. 15)List the coefficients of the reactants ____________________ What type of chemical reaction is this equation? ________________________________ 16)The number 11 is called a ________________ 17)How many atoms in oxygen of the reactants ______________ 18)The right side is called the ________________ 20)List the four states of matter: ________________________________________________ 21)What are the number of atoms on the product side?

Answers

Answer:

14) Reactant

15) 1 .Precipitation reaction equation

16) The coefficient

17)  6.6242 × 10²⁴ atoms of oxygen

18) The product

20) The four states of matter are;

a) Solids

b) Liquids

3) Gas

4) Plasma

21) The total number of atoms in the product is 2.7099 × 10²⁵ atoms.

Explanation:

14) The left side of the chemical equation is the reactant

15) The coefficient is the number in font of the formula, here, the coefficient of the reactant C₁₂H₂₂O₁₁ is 1 .This is a precipitation reaction equation

16) The number 11 in front of the formula, H₂O, is called a coefficient

17) On mole of a substance is defined as containing one Avogadro's number, \(N_A\) of molecules

\(N_A\) ≈ 6.022 × 10²³ mol⁻¹

In the reactant, C₁₂H₂₂O₁₁, there are 11 elements of oxygen in one mole of the reactants, which gives 11 × 6.022 × 10²³ = 6.6242 × 10²⁴ atoms of oxygen in one mole of the reactants

18) The right side of the chemical equation is called the product

20) The four states of matter are;

a) Solids

b) Liquids

3) Gas

4) Plasma

21) The number of elements on the product side are;

12 Carbon  + 22 Hydrogen + 11 Oxygen = 45 Elements total

However, given that there are 12 moles of carbon, we have;

12 × 6.02 × 10²³ = 7.2264 × 10²⁴ atoms of carbon

For hydrogen, we have;

22 × 6.02 × 10²³ = 1.32484 × 10²⁵ atoms of hydrogen

For oxygen, we have;

11 × 6.02 × 10²³ = 6.6242 × 10²⁴ atoms of oxygen

The total number of atoms in the product is 7.2264 × 10²⁴ + 1.32484 × 10²⁵ + 6.6242 × 10²⁴ = 2.7099 × 10²⁵ atoms.

If the westernmost Gandalf Island has rocks dated at 32 million years old, calculate the average rate of motion of these islands. SHOW WORK

Answers

If the westernmost Gandalf Island has rocks dated at 32 million years old the average rate of motion of these islands is Distance from the rift and age of seafloor sample, option  A.

A piece of land enclosed by water is called an island. Although they are completely encircled by water, continents are not regarded as islands because of their size. Australia, the smallest continent, is larger than Greenland, the biggest island, by more than three times. In the oceans, lakes, and rivers of the world, there are many islands. Their size, environment, and types of living things all differ widely.

Some islands, like the Aleutian Islands in the American state of Alaska, are always chilly and covered with ice. Some are located in warm, tropical seas, like Tahiti. Thousands of kilometres separate many islands, like Easter Island in the South Pacific, from the closest continent. Other islands, like the Greek Cyclades in the Aegean Sea, are clustered together in what are known as archipelagoes.

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Complete question:

If the westernmost Gandalf Island has rocks dated at 32 million years old, calculate the average rate of motion of these islands.

-Distance from the rift and age of seafloor sample

-Type of rock and distance from the rift

-Age of the continent and depth of the water

-Age of the seafloor sample and age of the continent

does fire have ways to protect itself from changes in the environment

Answers

Answer:

I think no because the critical properties distinguishing life is adaptation to changing environment and self replication of the information encoding the life process. Fire does not change its process to adapt to its environment, e.g. moving toward more fuel or storing and conserving fuel when it is in short supply.

Hope this help you!:)

Suki has been exercising more and eating healthy for two weeks. However, she has not really lost any weight and cannot see a difference in her body. She does feel a little better. At the same time, she is a bit frustrated with the lack or results. What is the BEST response to Suki’s concerns?

options:
A.
Being healthy is its own reward so she should not worry about appearance.
B.
She should be seeing immediate results so she needs to try something else.
C.
It takes a while to see significant results so she should keep it up and be patient.
D.
Improving diet and exercise habits does not generally change physical appearance.

PLEASE NO LINKS

Answers

Answer:

C

Explanation:

Most often you will not see immediate results with dieting and exercising.

Exercise helps to increase the rate of metabolic activities in the body. So it will helps to reduce the issues from heavy calories. Thus increasing exercise helps to balance food  intake but to get a significant change in weight, we have to waite and continue the exercises.

What is metabolism?

Anabolism and catabolism together called as metabolism. Anabolism is the synthesis of  biological compounds whereas catabolism is breaking or decomposition reaction. These biochemical reaction regulates the functions in our body.

If we uptake high calorie  food and its not burned by digestion then it will leads to weight gain and other health issues. Fat will deposits in body if the calorious foods are not digested properly.

Exercises helps to increase the rate metabolic activities in our body. It strengthens our muscles and bones and burn extra calories of food by utilise it to work  out.

Therefore, increasing exercise will help balance the larger than usual calorie intake but It takes a while to see significant results so she should keep it up and be patient. Hence, option C is correct.

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there are 8 planets in the solar system

Answers

Answer:

-mercury

-Venus

-earth

-Mars

-Jupiter

-Saturn

-Uranus

-Neptune

Explanation:

these are the 8 planets in the solar system <3

What is similarity?

Answers

Answer:

same things

Explanation:

which of the following is not a general difference between a planet and a star? a. planets are smaller than stars. b. planets orbit stars, and stars orbit the center of the galaxy. c. planets are made of rock and stars are made of gas. d. planets dimmer than stars. e. stars generate their own light and planets don't.

Answers

The correct option is (d) i.e. planets dimmer than stars, is not a general difference between a planet and a star.

It is not accurate to say that "planets are dimmer than stars." While it is true that many planets do emit much less light than stars, it is not a universal rule. Some planets can actually reflect more light from their parent star and appear brighter than their host star in the night sky. Additionally, the brightness of a planet and a star can depend on many factors such as their distance from us, size, atmospheric conditions, and more. To compare the brightness of a planet and a star, it is better to look at their relative brightness at a specific distance and in a specific band of the light spectrum.

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Many battery-powered devices come with cords that allow them to be

plugged into electrical outlets. What change has to take place inside

the power cord in order for the device to function properly?

Answers

Answer:

The change that has to take place inside the power cord in order for the device to function properly include;

The changing of the alternating current (AC) from the electrical outlet to the direct current having a specific voltage and current value with which the device can be powered

Explanation:

A battery powered device makes use of direct current (DC) electric power from a battery, while the power normally given out at an electrical outlet comes as an alternating current (AC) electric power source.

The power cord for battery-powered device, also known as an AC/DC adapter, that allows them to be plugged into electrical outlets converts the AC electric current it obtains from the electrical outlets to DC electrical current of the appropriate voltage and amperage that the device can make use of for electric power to function and for charging the battery which is the power source for the device

Therefore, the change that has to take place in the power cord is the conversion of the electric outlet alternating current (AC) voltage and amperage values, into direct current (DC) of the required voltage and current for the device

In the dark, is the current through an LDR higher or lower than in the light?

Answers

Answer:

An LDR's resistance is high in the dark and at low light levels, allowing only a little amount of current to pass through it. An LDR's resistance is low in bright light, allowing more current to flow through it.

a rocket blasts off. in 10.0 seconds it's at 10,000 ft, traveling at 3600 mph. assuming the direction is up, calculate the acceleration. (hint: the rocket is not under constant acceleration)

a) 5280 ft/s^2

b) 528 ft/s^2

c) 100 ft/s^2

d) 200. ft/s^2

Answers

If a rocket blasts off. in 10.0 seconds it's at 10,000 ft, traveling at 3600 mph. assuming the direction is up, the acceleration of the rocket is 528 ft/s². T

The correct answer is option (b)

How do we calculate?

a = Δv / Δt

a =  acceleration

Δv =  change in velocity

Δt =  change in time.

1 mile = 5280 feet

1 hour = 3600 seconds

3600 mph = 3600 * 5280 ft / 3600 s = 5280 ft/s

Therefore , a = Δv / Δt substituting these, we have:

a = Δv / Δt = (5280 ft/s - 0 ft/s) / 10.0 s

a= 528 ft/s²

In conclusion, the acceleration of the rocket is 528 ft/s²

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the apparent weight of a body wholly immersed in water is 32N and its weight in 96N and calculate volume of the body

Answers

Answer:

0.0065 m³

Explanation:

Apparent weight = weight − buoyancy

32 N = 96 N − (1000 kg/m³) (9.8 m/s²) V

V = 0.0065 m³

A model rocket is launched straight upward with an initial speed of 25.6 m/s. It accelerates with a constant upward acceleration of 2.34 m/s2 until its engines stop at an altitude of 231 m. How long after lift-off does the rocket reach its maximum height?

Answers

First, let's calculate the rocket velocity when it stops accelerating, using Torricelli's equation:

\(\begin{gathered} V^2=V^2_0+2\cdot a\cdot d \\ V^2=25.6^2+2\cdot2.34\cdot231 \\ V^2=655.36+1081.08 \\ V^2=1736.44 \\ V=41.67\text{ m/s}^2 \end{gathered}\)

After the engine stops, the total acceleration will be the gravity acceleration, with a downwards direction and magnitude of 9.81 m/s².

The maximum height occurs when the velocity is zero, so we can use the formula below:

\(\begin{gathered} V=V_0+a\cdot t \\ 0=41.67-9.81\cdot t \\ 9.81t=41.67 \\ t=\frac{41.67}{9.81} \\ t=4.25\text{ s} \end{gathered}\)

Now we need to calculate the time spent accelerating (engine turned on):

\(\begin{gathered} V=V_0+a\cdot t \\ 41.67=25.6+2.34\cdot t \\ 2.34t=41.67-25.6 \\ 2.34t=16.07 \\ t=\frac{16.07}{2.34} \\ t=6.87\text{ s} \end{gathered}\)

Therefore the total time, since lift-off until maximum height, is:

\(\begin{gathered} t=6.87+4.25 \\ t=11.12\text{ s} \end{gathered}\)

The rocket reaches the maximum height 11.12 seconds after lift-off.

what is the wavelength of the line on star c-197’s spectrum?

Answers

The wavelength of the line on star C-197's spectrum is 517.88. A spectrum is a range of electromagnetic radiation, such as light, that is divided into separate bands based on wavelength.

Using the formulae :-

Wavelength (λ) = Speed of light (c) ÷ frequency (f).

Therefore, 517.88 = 3 x 10^8 / f,

and f = 3 x 10^8 / 517.88

= 5.81 x 10^14

The wavelength of a spectral line can be used to identify the chemical elements present in a star and to determine its temperature, density, and other physical characteristics. The wavelength of a spectral line is the distance between two consecutive peaks (or troughs) of a wave. In the case of a star's spectrum, the wavelength of a spectral line is the distance between two consecutive peaks (or troughs) in the light emitted by the star. The specific wavelength of a spectral line is unique to a particular chemical element and is characteristic of that element. To determine the wavelength of a line on a star's spectrum, the spectrum must be observed and analyzed using a spectrometer. The spectrometer splits the light from the star into its component colors and records the intensity of light at each wavelength. The resulting spectrum is a graph of the intensity of light at each wavelength. The spectral lines are the spikes in intensity that correspond to light emitted at specific wavelengths by specific chemical elements. The wavelength of a particular line on a star's spectrum can be measured by finding the position of the peak in intensity corresponding to that line and recording its wavelength.

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12. A train is traveling away from you at a constant speed.
What would a distance-time graph look like for this train?

12. A train is traveling away from you at a constant speed.What would a distance-time graph look like

Answers

Answer:

b

Explanation:because think about it its going straight so you have to coiunt the miles the train is going and boom your answer is b

Answer:

It would be choice b

Explanation:

speed is constant so they value won't change, on the other hand time is always going.

nonmetals and metals do different things when it comes to their valence electrons. one seeks to gain and the other lose. which is which?

Answers

Answer:

Nonmetals gain

while metals lose

Please help
25 Points

What Mathematical leads to the formulas for the magnitudes of displacement, velocity, and acceleration?

Answers

Answer:

displacement=specific distance

*Velocity=∆displacement/time

*acceleration=∆velocity/time

If the Spirit of Australia, a boat,reaches speeds of 318.67 mph for 0.75 hours (45 minutes), what is the distance it traveled?

Answers

Answer: 239.0025 miles.

Explanation:

First we have the relationship:

Distance  = speed*time.

Because how it is worded, i guess that the boat can mantain a constant speed of 318.67 mph for 0.75 hours.

Then, we have the speed and the time, with those values we can find the distance.

speed = 318.67 mph

Time = 0.75 hours.

Distance = 318.67 mph*0.75h = 239.0025 miles.

Holden is trying to determine the velocity of his race car. He went 20 meters east, turned around, and went 40 meters west. He turned the car one more time and went 35 meters east. His car was 15 meters from the starting line. This took 5 seconds.

What is the car’s velocity?

Answers

Answer:

3 m/s east

Explanation:

I took a test a got it right

Answer:

3 m/s east

Explanation:

Is the formula for acceleration, A = change in velocity / change in time?

Answers

Answer:

cant see to find the answer sorry :( i tried :( good luck !! youll do great <333

Explanation:

A projectile is launched at 30° above ground level. what other angle at the same speed will result in the same range?

Answers

Answer:

\(60^{\circ}\) (assuming that air resistance is negligible.)

Explanation:

Let \(g\) denote the gravitational field strength. If air resistance on the projectile is negligible:

Vertical acceleration of the projectile will be constantly \((-g)\). In other words, \(a_{y} = (-g)\).Horizontal velocity of the projectile will be constant.

Let \(\theta\) denote the angle at which the projectile is launched. Let \(v\) denote the initial velocity of the projectile:

Initial vertical velocity of the projectile will be \(u_{y} = v\, \sin(\theta)\).Initial horizontal velocity of the projectile will be \(u_{x} = v\, \cos(\theta)\).

Also because air resistance is negligible, vertical velocity of the projectile will be \(v_{y} = (-u_{y}) = (-v\, \sin(\theta))\) right before the projectile lands. In other words, while the projectile was in the air, the change in vertical velocity would be \((-v\, \sin(\theta)) - (v\, \sin(\theta)) = (-2\, v\, \sin(\theta))\).

Divide the change in velocity by acceleration to find the duration of the flight:

\(\begin{aligned}t &= \frac{v_{y} - u_{y}}{a_{y}} \\ &= \frac{(-v\, \sin(\theta)) - (v\, \sin(\theta))}{(-g)} \\ &= \frac{(-2\, v\, \sin(\theta))}{(-g)} \\ &= \frac{2\, v\, \sin(\theta)}{g}\end{aligned}\).

Range measures the horizontal distance that this projectile has travelled. At a constant horizontal velocity of \(u_{x} = v\, \cos(\theta)\), this projectile would travel a distance of:

\(\begin{aligned}(\text{range}) &= u_{x}\, t \\ &= (v\, \cos(\theta))\left(\frac{2\, v\, \sin(\theta)}{g}\right) \\ &= \frac{2\, v^{2}\, \sin(\theta)\, \cos(\theta)}{g}\end{aligned}\).

Apply the double angle identity \(2\, \sin(\theta) \, \cos(\theta) = \sin(2\, \theta)\) to further simplify this expression:

\(\begin{aligned}(\text{range}) &= \cdots \\ &= \frac{2\, v^{2}\, \sin(\theta)\, \cos(\theta)}{g} \\ &= \frac{v^{2}\, (2\, \sin(\theta)\, \cos(\theta))}{g} \\ &= \frac{v^{2}\, \sin(2\, \theta)}{g}\end{aligned}\).

Note that in this question, \(v^{2}\) and \(g\) are both constant. Hence, for another angle of elevation \(\hat{\theta}\), the range of the projectile will be the same as long as \(\sin(2\, \hat{\theta}) = \sin(2\, \theta)\).

\(\sin(2\, \hat{\theta}) = \sin(2\, (30^{\circ}))\).

Since \(0^{\circ} \le \hat{\theta} \le 90^{\circ}\), \(0^{\circ} \le 2\, \hat{\theta} \le 180^{\circ}\):

\(\sin(2\, \hat{\theta}) = \sin(180^{\circ} - 2\, \hat{\theta}) = \sin(2\, (90^{\circ} - \hat{\theta}))\).

Therefore, \(\hat{\theta} = 90^{\circ} - \theta = 90^{\circ} - 30^{\circ} = 60^{\circ}\) will ensure that \(\sin(2\, \hat{\theta}) = \sin(2\, \theta)\). Launching the projectile at \(60^{\circ}\) will reach the same range.

\(\begin{aligned}(\text{new range}) &= \frac{v^{2}\, \sin(2\, (60^{\circ}))}{g} \\ &= \frac{v^{2}\, \sin(2\, (30^{\circ}))}{g} = (\text{original range})\end{aligned}\).

Determine the new differential reading along the inclined leg of the mercury manometer of fig. P2. 62, if the pressure in pipe a is decreased 10 kpa and the pressure in pipe b remains unchanged. The fluid in a has a specific gravity of 0. 9 and the fluid in b is water

Answers

The pressure difference between two points in a manometer is given by the difference in the heights of the fluid columns in the two legs of the manometer.

If the pressure in pipe A is decreased by 10 kPa, the height of the fluid column in that leg of the manometer will decrease. The amount of decrease will depend on the specific gravity of the fluid in that leg, as well as the height of the fluid column before the pressure change. Assuming the specific gravity of the fluid in pipe A is 0.9, the decrease in pressure will cause the fluid column to decrease by (10 kPa)/(0.9 * 9.81 m/s^2), or approximately 1.15 meters. The change in the height of the fluid column in the other leg of the manometer will depend on the height of that column and the specific gravity of the fluid in that leg. To determine the new differential reading along the inclined leg of the manometer, we need to calculate the difference in the heights of the two fluid columns after the pressure change. This will be equal to the difference in the heights before the pressure change, minus the 1.15 meter decrease in the height of the fluid column in pipe A.

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Taco Bell sells 6 Tacos for $9.00. Del Taco sells 4 tacos for $8.00. is a better deal, because it costs less per taco.

Answers

Answer:

I'd say taco bell is a better deal, because you get more tacos.

Explanation:

but that's just what I think

Taco bell is a better deal if you divide the taco bell 9.00/6 you get 1.5 then if you divide 8.00/4 you get 2 so the Taco Bell would be cheaper per taco

which is not true of globular clusters? they contain 100s of thousands of stars up to millions they have a lot of young blue stars continuously being born out of nebulas they were useful in discovering the size of the milky way and where the sun is located within it they can be found in the halos of galaxies

Answers

The statement that is not true of globular clusters is "they have a lot of young blue stars continuously being born out of nebulas." Globular clusters are actually very old and contain mostly old, low-mass stars that have exhausted their fuel and are no longer actively fusing hydrogen in their cores.

Globular clusters are actually some of the oldest objects in the universe, with ages typically ranging from 10 to 13 billion years. They are densely packed groups of stars, containing hundreds of thousands to millions of stars that are gravitationally bound to each other.

The stars in globular clusters are typically low-mass stars, which are less massive than our sun. These stars have relatively long lifetimes, as they burn their fuel slowly and steadily. Over time, the stars in a globular cluster will consume their fuel and eventually exhaust it, at which point they will evolve into white dwarfs.

Because the stars in globular clusters are so old, there are no longer any new stars being formed in these clusters. Therefore, they do not contain young blue stars that are continuously being born out of nebulas.

Globular clusters are typically found in the halos of galaxies, where they orbit the galaxy in a spherical distribution. They are useful in studying the structure and dynamics of galaxies, as they provide clues about the formation and evolution of these systems.

For example, the study of globular clusters in the Milky Way was instrumental in determining the size and shape of our galaxy and the location of the Sun within it.

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A cart at the top of a 24 m hill has a mass of 32 kg. What is the cart's gravitational potential energy?​

Answers

Answer:

\(\boxed {\boxed {\sf 7526.4 \ J}}\)

Explanation:

Gravitational potential energy is energy due to position above the ground. It is found using the following formula.

\(GPE= mgh\)

where m is the mass, g is the acceleration due to gravity, and h is the height.

The cart is 32 kilograms and it is on a 24 meter hill. Assuming this is on earth, the acceleration due to gravity is 9.8 meters per square second.

\(m= 32 \ kg \\g= 9.8 \ m/s^2 \\h= 24 \ m\)

Substitute the values into the formula.

\(GPE= (32 \ kg)(9.8 \ m/s^2)(24 \ m)\)

Multiply the first two numbers.

\(GPE=313.6 \ kg*m/s^2 (24 \ m)\)

Multiply again.

\(GPE= 7526.4 \ kg*m^2/s^2\)

1 kg*m²/s² is equal to 1 Joule. Our answer is also 7526.4 Joules.

\(GPE= 7526.4 \ J\)

The cart's gravitational potential energy is 7526.4 Joules.

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