The total mechanical energy of the particle of mass m at the surface of the planet of mass M when the distance is R (planet's radius) is [tex] E = \frac{GmM}{R} + \frac{1}{2}mv_{e}^{2} [/tex].
When the particle is at rest at a distance "r" from the planet's center, it only has gravitational potential energy. As the particle falls to the planet's surface, some initial gravitational potential energy converts to kinetic energy.
The total mechanical energy of the particle at the planet's surface is equal to the sum of the gravitational potential energy and kinetic energy, so:
[tex] E = P + K [/tex]
[tex] E = maR + \frac{1}{2}mv_{e}^{2} [/tex] (1)
Where:
m: is the mass of the object
a: is the acceleration due to gravity on the surface of the planet
R: is the radius of the planet
[tex]v_{e}[/tex]: is the escape velocity
The acceleration due to gravity is given by:
[tex] a = \frac{GM}{R^{2}} [/tex] (2)
By entering equation (2) into (1), we have:
[tex] E =mR\frac{GM}{R^{2}} + \frac{1}{2}mv_{e}^{2} [/tex]
[tex] E = \frac{GmM}{R} + \frac{1}{2}mv_{e}^{2} [/tex]
Therefore, the total mechanical energy of the particle is [tex] E = \frac{GmM}{R} + \frac{1}{2}mv_{e}^{2} [/tex]
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why is there a difference between potential and kinetic energy?
Potential energy is stored energy because it has the potential to do something which laters turns into kinetic energy which is the moving energy.
jack goes an average of 40 m/min. How far does he jog in 1.2 hours?
Answer:
2880 (m)
Explanation:
1. the formula of distance is: L=v*t, where L - the required distance; v - average velocity; t - elapsed time.
2. if t=1.2 hours, it means 72 minutes, then
3. L=40*72=2880 m.
Type your answers to these 4 questions in the submission area.
1. What do you think a plate boundary is?
2. What is an earthquake?
3. What happens during an earthquake?
4. What do you think about the plates that make up Earth’s outer layer?
It is not possible to convert work entirely into heat. It is impossible to transfer heat from a cooler to a hotter body. The second law of thermodynamics is a consequence of the first law of thermodynamics. It is possible for heat to flow spontaneously from a hot body to a cold one or from a cold one to a hot one, depending on whether or not the process is reversible or irreversible. All of these statements are false.
Complete Question:
Which one of the following is a
true statement?
Group of answer choices.
A) The second law of thermodynamics is a consequence of the first law of thermodynamics.
B) It is possible for heat to flow spontaneously from a hot body to a cold one or from a cold one
to a hot one, depending on whether or not the process is reversible or irreversible.
C) It is not possible to convert work entirely into heat.
D) It is impossible to transfer heat from a cooler to a hotter body.
E) All of these statements are false.
Answer:
E) All of these statements are false.
Explanation:
All of the following statements are false;
I. The second law of thermodynamics is a consequence of the first law of thermodynamics. The second law of thermodynamics is about a physical quantity known as entropy while the first law of thermodynamics states that energy cannot be created or destroyed but can only be transformed from one form to another.
II. It is possible for heat to flow spontaneously from a hot body to a cold one or from a cold one
to a hot one, depending on whether or not the process is reversible or irreversible. According to the second law of thermodynamics this is false due to the entropy.
III. It is not possible to convert work entirely into heat. It is possible to completely convert work into heat because it involves transferring energy.
IV. It is impossible to transfer heat from a cooler to a hotter body.
Why could it be argued that the respiratory system is most critical to sustaining life?
Explanation:
Energy is the most important ingredient for life. Organisms use energy in diverse ways. Scientifically, energy is defined as the ability to do work. Without this ability, organisms would not exist.
So, the most important process is one that can furnish the body with energy.
The respiratory system happens to be the one that furnishes the body with energy. During respiration, the energy needs of the body is met by series of processes. Oxygen is taken in and use to liberate calories from chemical substances packed with energy. So, without respiration, the bodily energy demands will not be met.Help please !
In sexual reproduction, why is fertilization necessary to produce an organism ?
1. Fertilization allows an organism to receive a complete set of chromosomes -one set each parent .
2. Fertilization is needed to make the cell bigger . A bigger cell leads to the development of an organism .
3. Fertilization allows an organism to reproduce asexually , making identical clones of itself.
4. Fertilization is needed so that the egg cell can obtain nutrients from the sperm cell. Without these nutrients , an organism cannot develop .
Answer:
1. Fertilization allows an organism to receive a complete set of chromosomes -one set each parent.
Explanation:
Please could you help me. A race car travels along a straight length of track at 65 m/s. The race car and driver have a
combined mass of 580 kg. Calculate the total energy in the kinetic energy store of the car and
driver. Make sure you give the correct symbol for the unit. *
Answer:
1.23×10⁶ J
Explanation:
From the question given above, the following data were obtained:
Velocity (v) = 65 m/s
Mass (m) = 580 Kg
Kinetic energy (KE) =?
The kinetic energy can be obtained by using the following formula :
KE = ½mv²
Where:
KE => is the kinetic energy.
m => is the mass
v => is the velocity
With the above formula, we can obtain the kinetic energy as follow:
Velocity (v) = 65 m/s
Mass (m) = 580 Kg
Kinetic energy (KE) =?
KE = ½mv²
KE = ½ × 580 × 65²
KE= 290 × 4225
KE = 1.23×10⁶ J
Thus, the kinetic energy is 1.23×10⁶ J
A diode laser emits a wavelength of 987 nm. All of its output energy is absorbed in a detector that measures a total energy of 0.52 J over a period of 32 s. How many photons per second are being emitted by the laser?
Answer:
8.04 × 10¹⁶ photons per second
Explanation:
First, we calculate the energy per photon from E = hc/λ where h = Planck's constant = 6.63 × 10⁻³⁴ Js c = speed of light = 3 × 10⁸ m/s and λ = wavelength of laser = 987 nm = 987 × 10⁻⁹ m = 9.87 × 10⁻⁷ m
So, E = hc/λ = 6.63 × 10⁻³⁴ Js × 3 × 10⁸ m/s/9.87 × 10⁻⁷ m = 19.89/9.87 × 10⁻¹⁹ J = 2.02 × 10⁻¹⁹ J per photon.
Since we have a total of 0.52 J over a period of 32 s, the output power is 0.52 J/32 s = 0.0163 J/s.
Thus the total number of photons per second is thus in output power/energy per photon = 0.0163 J/s ÷ 2.02 × 10⁻¹⁹ J per photon
= 8.04 × 10¹⁶ photons per second
How is a physical change different to a chemical change. Give an example of a physical change.
Answer:
Physical change is different to chemical change by that physical changes can be reversed, meaning it can be turned back to its original form, but chemical changes CANNOT! Chemical change is something that creates a NEW substances that cannot be reversed. It creates new forms.
Explanation:
Example of chemical change: Change in texture- fried egg. It cannot be turned back to its original form after it is fried.
I truly hope this is helpful!!
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What is the unit vector along ⃗ = hat − hat + hat ?
Answer:
1 hat
Explanation:
A small lead ball, attached to a 1.10-m rope, is being whirled in a circle that lies in the vertical plane. The ball is whirled at a constant rate of three revolutions per second and is released on the upward part of the circular motion when it is 1.3 m above the ground. The ball travels straight upward. In the absence of air resistance, to what maximum height above the ground does the ball rise
Answer:
1.84 m
Explanation:
For the small lead ball to be balanced at the tip of the vertical circle just before it is released, the reaction force , N equal the weight of the lead ball W + the centripetal force, F. This normal reaction ,N also equals the tension T in the string.
So, T = mg + mrω² = ma where m = mass of small lead ball, g = acceleration due to gravity = 9.8 m/s², r = length of rope = 1.10 m and ω = angular speed of lead ball = 3 rev/s = 3 × 2π rad/s = 6π rad/s = 18.85 rad/s and a = acceleration of normal force. So,
a = g + rω²
= 9.8 m/s² + 1.10 m × (18.85 rad/s)²
= 9.8 m/s² + 390.85 m/s²
= 400.65 m/s²
Now, using v² = u² + 2a(h₂ - h₁) where u = initial velocity of ball = rω = 1.10 m × 18.85 rad/s = 20.74 m/s, v = final velocity of ball at maximum height = 0 m/s (since the ball is stationary at maximum height), a = acceleration of small lead ball = -400.65 m/s² (negative since it is in the downward direction of the tension), h₁ = initial position of lead ball above the ground = 1.3 m and h₂ = final position of lead ball above the ground = unknown.
v² = u² + 2a(h₂ - h₁)
So, v² - u² = 2a(h₂ - h₁)
h₂ - h₁ = (v² - u²)/2a
h₂ = h₁ + (v² - u²)/2a
substituting the values of the variables into the equation, we have
h₂ = 1.3 m + ((0 m/s)² - (20.74 m/s)²)/2(-400.65 m/s²)
h₂ = 1.3 m + [-430.15 (m/s)²]/-801.3 m/s²
h₂ = 1.3 m + 0.54 m
h₂ = 1.84 m
An object with velocity 141 ft/s has a kinetic energy of 1558.71 ft∙lbf, on a planet whose gravity is 31.5 ft/s2. What is its mass in pounds
Answer:
The mass of the object is 5.045 lbm.
Explanation:
Given;
kinetic energy of the object, K.E = 1558.71 ft.lbf
velocity of the object, V = 141 ft/s
The kinetic energy of the object is calculated as;
[tex]K.E = \frac{1}{2} mV^2\\\\mV^2 = 2K.E\\\\m = \frac{2K.E}{V^2} \\\\1 \ lbf = 32.174 \ lbm.ft/s^2\\\\m = \frac{2 \ \times \ 1558.71 \ ft.lbf \ \times \ 32.174 \ lbm.ft/s^2 }{(141 \ ft/s)2 \ \ \times \ \ \ \ 1 \ lbf\ }[/tex]
[tex]m = \frac{(2 \ \times \ 1558.71 \ \times \ 32.174) \ lbm.ft^2/s^2 }{(141 )^2\ ft^2/s^2 }\\\\m = \frac{(2 \ \times \ 1558.71 \ \times \ 32.174) \ lbm }{(141 )^2 }\\\\m = 5.045 \ lbm[/tex]
Therefore, the mass of the object is 5.045 lbm.
Gravity does 207 N of work when a 45 N object falls to the
ground. From what height does the object fall?
Answer: 4.6
Explanation:
Answer:
4.6
Explanation:
A space expedition discovers a planetary system consisting of a massive star and several spherical planets. The planets all have the same uniform mass density. The orbit of each planet is circular. In the observed planetary system, Planet A orbits the central star at the distance of 2R and takes T hours to complete one revolution around the star. Planet B orbits the central star at the distance of R. Which of the following expressions is correct for the number of hours it takes Planet B to complete one revolution around the star?
a. 1/√8T
b. 1/2T
c. 1/√4T
d. 2T
e. √8T
Answer:
[tex]T_B=(\frac{T}{\sqrt{8}})[/tex]
Explanation:
Distance of Planet A from Central star 2R
Time of Resolution T_A=T
Distance of Planet B from orbit star R
Generally the equation for Kepler's law of periods is given by
[tex]\frac{T_A^2}{T_B^2}=\frac{R_A^3}{R_B^3}[/tex]
[tex]T_B^2=T_A^2 \frac{R_A^3}{R_B^3}[/tex]
[tex]T_B^2=T_A^2 (\frac{R_A}{R_B})^3[/tex]
[tex]T_B^2=T^2 (\frac{R}{2R})^3[/tex]
[tex]T_B^2=T^2 (\frac{1}{R})^3[/tex]
[tex]T_B^2=(\frac{T^2}{8})[/tex]
Therefore the following expressions is correct for the number of hours it takes Planet B to complete one revolution around the star
[tex]T_B=(\frac{T}{\sqrt{8}})[/tex]
The number of hours that it takes for planet B to complete one revolution around the star is : ( A ) ( [tex]\frac{T}{\sqrt{8} }[/tex] )
Given data :
Distance of Planet A from massive star = 2R
Time taken by Planet A to orbit the massive star = Tₐ
Distance of Planet B from massive star = R
Time taken by Planet B to orbit the massive star = T[tex]_{b}[/tex]
To determine the proper expression exhibiting the correct number of hours it will take for Planet B to complete a revolution
we will apply Kepler's law of periods
[tex]\frac{T^{2} _{a} }{T_{b} ^{2} } = \frac{R_{a} ^{3} }{R_{b} ^{3} }[/tex]
∴ [tex]T_{b} ^{2} = T_{a} ^{2} ( \frac{R_{a} }{R_{b} } )^{3}[/tex]
[tex]T_{b} ^{2} = T^2 ( 1/R)^3[/tex]
Hence T[tex]_{b}[/tex] = ( [tex]\frac{T}{\sqrt{8} }[/tex] )
There we can conclude that The number of hours that it takes for planet B to complete one revolution around the star is : ( A ) ( [tex]\frac{T}{\sqrt{8} }[/tex] )
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What do scientists know about the future of the universe?
what dark matter is made of
why the expansion of the universe is accelerating
that stars will eventually burn out causing the universe to become cold and dark
that galaxies spin much slower than they should based on visible matter
Answer:
B. Why the expansion of the universe is accelerating
Explanation:
possibly pretty sure if not right then the answer is A. What dark matter is made of hope this helps please mark brainiest only answer plz
Why the expansion of the universe is accelerating is what scientists know
about the future of the universe.
Scientists have observed that radiation emitted by the galaxies have shifted
towards the red end of the electromagnetic spectrum. This means that there
has been an increase in the wavelength for this to occur.
This tells us that the universe is expanding which was why the wavelength
of the emission spectra experienced a shift or stretch.
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What is the most common frame of reference used by humans
Answer:
All measurements of motion will be compared to a frame of reference. Therefore, the most commonly used frame of reference is Earth itself, even though it moves.
Explanation:
Block A of mass M is at rest and attached to the top of a spring. The block compresses the spring a distance d from its uncompressed length at equilibrium. Block B of mass 2M is released from rest at a height h above block A . The two blocks collide and stick together. Express all answers in terms of d , h , M , and physical constants, as appropriate.
Required:
a. Derive an expression for the spring constant k of the spring.
b. Derive an expression for the speed of block B just before it collides with block A.
c. Derive an expression for the speed of the blocks immediately after the collision.
d. Derive an expression for the maximum compression of the spring after the collision.
e. If the collision between the blocks was elastic, would the maximum compression of the spring be greater than, less than, or equal to that found in part (d)? Justify your answer.
Answer:
a) k = Mg / d , b) v = √2gh , c) v_{f} = [tex]\frac{2}{3} \ \sqrt{2gh}[/tex], d) x² + 6d x - [tex]\frac{8}{3}[/tex] dh = 0
e)the spring must compress a greater distance.
Explanation:
a) when the block of mass M is placed on the spring, we have an equilibrium condition,
∑ F = 0
[tex]F_{e}[/tex]- W = 0
k d = Mg
k = Mg / d
b) let's use the concepts of energy to find the velocity of the block just before the collision
starting point. Position when released
Em₀ = U = m g h
lowest point. Right at the point of shock
[tex]Em_{f}[/tex] = K = ½ m v²2
as there is no friction, energy is conserved
Em₀ = Em_{f}
mg h = ½ m v²
v = √2gh
c) The velocity of the two blocks after the collision, we define a system formed by the two blocks, in such a way that the forces during the collision are internal and the moment is conserved
initial instant. Just before the crash
p₀ = 2M v + M 0
final instant. Just after the shock, before the spring compression begins
p_{f} = (2M + M) v_{f}
the moment is preserved
p₀ = p_{f}
2M v = 3M v_{f}
v_{f} = ⅔ v
v_{f} = [tex]\frac{2}{3} \ \sqrt{2gh}[/tex]
d) now we work with the joined system after the collision, let's use the concepts of energy
starting point. After shock, before beginning spring compression
Em₀ = K = ½ (3M) [tex]v_{f}^2[/tex]
Em₀ = 3/2 M (\frac{2}{3} \ \sqrt{2gh})²
Em₀ = 4/3 M gh
final point. With the spring fully compressed
Em_f = K_e + U = ½ k x² + (3M) g x
in this case we have taken the zero of gravitational potential energy at the point where the blocks collide, as there is no friction, the energy is conserved
Em₀ = Em_f
4/3 M g h = ½ k x² + 3M g x
½ k x² + 3Mg x - 4/3 Mgh = 0
we substitute the expression for k
[tex]\frac{1}{2}[/tex] ([tex]\frac{Mg}{d}[/tex]) x² + 3Mg x - [tex]\frac{4}{3}[/tex] Mgh = 0
[tex]\frac{x^{2} }{2d}[/tex] + 3 x - [tex]\frac{4}{3}[/tex]h = 0
to find the value of the spring compression, the second degree equation must be solved
x² + 6d x - [tex]\frac{8}{3}[/tex] dh = 0
x = [-6d ±[tex]\sqrt{(36 d^{2} - 4 \frac{8}{3} dh) }[/tex] ] / 2
x = [-6d ± 6d [tex]\sqrt{ 1 - \frac{32}{3 \ 36} \ \frac{h}{d} }[/tex] ]/2
x = 3d ( -1± [tex]\sqrt{ 1 - 0.296 \frac{h}{d} }[/tex] )
e) If the collision elastic force would not lose any part of the kinetic energy during the collision, therefore the speed of the block of mass M would be much higher and therefore the spring must compress a greater distance.
Certain neutron stars (extremely dense stars) are believed to be rotating at about 1 rev/s. If such a star has a radius of 15 km, what must be its minimum mass so that material on its surface remains in place during the rapid rotation
Answer:
1.9981 * 10^24 Kg
Explanation:
Given that
R = 15 * 10^3
ω = 1 rev/s = 2π rad/s
From;
g =GM/R^2 - Rω^2
If g = 0
M = R ^3ω^2/G
M = (15 * 10^3)^3 * (2π)^2/6.67 * 10^-11
M = 1.9981 * 10^24 Kg
Convert 75.170 seconds into hours.
Answer:0.02088056
Explanation:
If you Blow up a balloon, will the composition of Air inside the balloon changes? Why? Why not?
Answer:
it change by the pressure of the air and how its pulling the elastic even more
Explanation:
therefore it changes shape and has more differences than before sometimes the colour of it will go lighter if a lot of air and darker if not a lot
Which items in this image are electrically conductive?
Check all that apply
the power lines themselves
the wooden pole that supports the lines
the rubber soles on the worker's boots
the metal tools the worker uses
the wooden ladder leaning against the lines
all except the rubber boots.
The answers should be The power lines themselves and The metal tools the worker uses (the 1st and 4th choices).
(For anyone curious, the image I attached to this answer is the image given for this problem.)
What substances cannot be separated by steam distillation?
Let's say you got tired and you are now pushing with a force of 36 N. Find the acceleration of the box.
This question is incomplete, the complete question is;
A 13 kg box rests on the flat surface. The coefficient of static friction and coefficient of kinetic friction is μ_s = 0.450 and μ_k = 0.380 respectively.
Let's say you got tired and you are now pushing with a force of 36 N. Find the acceleration of the box.
Answer: the acceleration of the box is 0.9548 m/s² {backward}
Explanation:
Given that;
mass m = 13 kg
pushing the box with a force of 36 N
the acceleration of the box = ?
ones the box starts moving, kinetic frictional force starts acting.
so
f_k = μ_k × m × g
we substitute
f_k = 0.380 × 13 × 9.8
f_k = 48.412 N
force needed to keep it in motion is 48.412 N
so
Acceleration = Net Force / mass
Acceleration = (48.412 N - 36 N) / 13
Acceleration = 12.412 / 13
Acceleration = 0.9548 m/s² {backward}
Therefore, the acceleration of the box is 0.9548 m/s² {backward}
A working fluid enters a steady flow system with a velocity of 30m/s and leaves at
140m/s. The mass flow rate is 9 kg/s. The properties of the fluid entry are 13.8 bar,
0.122 m3
/kg, and internal energy 42.2 kJ/kg, and exit properties are 1.035 bar, 0.805
m3
/kg and internal energy 208 kJ/kg. Determine the work transfer in kW from the
system
Answer:
Pretty sure it’s A
Explanation:
Would ike brainliest
Humans have three types of cone cells in their eyes, which are responsible for color vision. Each type absorbs a certain part of the visible spectrum. Suppose a particular cone cell absorbs light with a wavelength of . Calculate the frequency of this light.
Answer:
This question is incomplete
Explanation:
This question is incomplete because of the absence/omission of the wavelength but the completed question is attached below.
The formula for frequency is f = c/λ
where f is the frequency (unknown)
c is the speed of light (3.0 × 10⁸ m/s)
λ is the wavelength (599 nm)
f = (3 × 10⁸) ÷ 599
f = 500834.73 Hz or 5 × 10⁵ Hz
A 700N mountain climber scales a 100m cliff. How much work is done by the mountain climber?
Answer:
70000N/m
Explanation:
Work is Force multiplied by Displacement.
Multiply 700 by 100 and you get 70000N/m
*Note: N is newtons and m is meters.
Answer: 7000N/m
Explanation: 700 x 100 = 7000
2. A 2500 kg car is slowed down uniformly from an initial velocity of 20.0 m/s to
the north by a 6250 N braking force acting opposite the car's motion. Use the
impulse-momentum theorem to answer the following questions:
a. What is the car's velocity after 2.50 s?
b. How far does the car move during 2.50 s?
c. How long does it take the car to come to a complete stop?
Answer:
13.75m/s; 42.2m; 8s
Explanation:
(a) the car's velocity after 2.50 s is 13.75 m/s
(b) The distance traveled by the car is 42.18 m
(c) the time taken for the car to come to complete stop is 8 s.
The given parameters;
mass of the car, m = 2500 kg
initial velocity of the car, u = 20 m/s
breaking applied on the car, f = 6250 N
The acceleration of the car is calculated as follows;
[tex]F = ma \\\\a = \frac{F}{m} = \frac{6250}{2500} = 2.5 \ m/s^2[/tex]
(a) Using impulse-momentum theorem, the car's velocity after 2.5 s is calculated as follows;
[tex]F = \frac{m(u-v)}{t} \\\\m(u-v) = Ft\\\\u-v = \frac{Ft}{m} \\\\v = u - \frac{Ft}{m} \\\\v = 20 - \frac{6250 \times 2.5}{2500} \\\\v = 13.75 \ m/s[/tex]
(b) The distance traveled by the car during the 2.5 s;
[tex]v^2 = u^2 - 2as\\\\2as = u^2 - v^2\\\\s = \frac{u^2 - v^2}{2a} \\\\s = \frac{20^2 - 13.75^2}{2\times 2.5} \\\\s = 42.18 \ m[/tex]
(c) The time taken for the car to come to a complete stop;
when the car stop's the final velocity, v = 0
v = u - at
0 = 20 - 2.5t
2.5t = 20
[tex]t = \frac{20}{2.5} \\\\t = 8 \ s[/tex]
Thus, the time taken for the car to come to complete stop is 8 s.
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A point charge (q1) has a magnitude of 3.0 x10-6 C. A second charge (q2) has a magnitude of -1.5 x10-6 C and is located 0.12 m from the first charge. Determine the electrostatic force each charge exerts on the other.
Answer:2.81 N
Explanation:
Given
[tex]q_1=3\times 10^{-6}\ C\\q_2=-1.5\times 10^{-6}\ C[/tex]
distance between them r=0.12 m
Electrostatic force is [tex]F=\frac{kq_1q_2}{r^2}[/tex]
Putting values
[tex]F=\dfrac{9\times 10^9\times (3\times 10^{-6})\times (-1.5\times 10^{-6})}{0.12^2}\\F=2.81\ N[/tex]
PLEASE ITS AN Emergency IF ITS RIGHT I WILL GIVE BRAINLIEST
Answer:
all of those are pisitions
Explanation:
A person should be able to find all the answers to their science questions in the text
book.
True
False
It is a false statement that a person should be able to find all the answers to their science questions in the text because there are billions of scientific questions and it is almost impossible for any kind of textbook to contain all the answers.
What is science?Science is the methodical, empirically-based pursuit and application of knowledge and understanding of the natural and social worlds.
A method of learning about the world is science. Science allows people to participate in the creation of new knowledge as well as use that knowledge to further their goals.
The idea that someone should be able to find all the answers to their scientific inquiries in the text is untrue since there are countless unanswered scientific questions, making it nearly impossible for any textbook to provide them all.
Thus, the statement is false.
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