Answer:
A) v = 148,242.72 m/s
B) v = 6,328,025.58 m/s
Explanation:
To solve this, we will equate electric potential to kinetic energy.
Formula for Electric potential is qV where q is charge and V is potential difference.
While formula for kinetic energy is ½mv² where m is mass and v is velocity
Thus;
qV = ½mv²
Let us make the velocity the formula;
v = √(2qV/m)
A) PROTON
Charge of proton has a constant value of 1.6 × 10^(-19) C
Mass of proton has a constant value of 1.66 × 10^(-27) kg
We are given that potential difference = 114 V.
So, v = √(2qV/m)
Thus; v = √(2*1.6 × 10^(-19)*114/(1.66 × 10^(-27)))
v = 148,242.72 m/s
B) ELECTRON
Charge of electron has a constant value of 1.6 × 10^(-19) C
Mass of electron has a constant value of 9.11 × 10^(-31) kg
v = √(2qV/m)
Thus;
v = √(2*1.6*10^(-19)*114)/(9.11 × 10^(-31)))
v = 6,328,025.58 m/s
PLZ HELP WILL GIVE BRAINLIEST
A 77kg diver jumps from a 8.18m high diving platform. What is the speed in m/s of the diver right before she hits the water?
Answer:
12.7m/s
Explanation:
Given parameters:
Mass of the diver = 77kg
Height = 8.18m
Unknown:
Final velocity = ?
Solution:
To solve this problem, we use one of the motion equations.
v² = u² + 2gh
v is the final velocity
u is the initial velocity
g is the acceleration due to gravity
h is the height
v² = 0² + (2 x 9.8 x 8.18)
v² = 160.3
v = 12.7m/s
The speed of a cart is increased uniformly from 0.32 meters per second to 1.43 meters per second in 1.82 seconds. The cart’s acceleration is
Answer:
0.610m/s^2
Explanation:
Acceleration is defined as the ΔV/ΔT. In this case, the change in velocity is 1.43-0.32=1.11 m/s. The change in time is 1.82 seconds. Plugging in what we know, it will result in an acceleration of 0.610 m/s^2.
Difference between Weightlessness in space and weightlessness during free fall.
Weightlessness in space and weightlessness during free fall may appear similar in terms of the sensation experienced, but they occur under different circumstances and have distinct underlying causes. Here are the key differences between the two:
1.Environment:
Space: Weightlessness in space refers to the state experienced by astronauts in orbit around the Earth or in deep space. They are in a microgravity environment, far away from any significant gravitational forces.
Free fall: Weightlessness during free fall occurs when an object is falling under the influence of gravity, experiencing zero-gravity conditions momentarily. This typically happens when an object is in a state of free fall, such as during skydiving or in an airplane during a parabolic flight.
2.Gravitational Forces:
Space: In space, weightlessness is the result of being in constant free fall around the Earth. Although gravity is still present, the gravitational forces are counterbalanced by the centrifugal force created by the orbiting motion. This results in a continuous state of free fall, giving the sensation of weightlessness.
Free fall: Weightlessness during free fall occurs due to the absence of support forces countering the force of gravity. When an object is in free fall, there are no contact forces pushing against it, leading to a sense of weightlessness.
3.Duration:
Space: Weightlessness in space can last for an extended period, as long as the object or person remains in orbit or deep space. Astronauts aboard the International Space Station (ISS), for example, experience weightlessness for months at a time.
Free fall: Weightlessness during free fall is relatively brief and temporary. It occurs during the duration of the free fall, which can last for a few seconds to a couple of minutes, depending on the specific circumstances.
4.Context:
Space: Weightlessness in space is a constant state for astronauts. They adapt to this environment and conduct various experiments, work on scientific research, and live aboard the spacecraft for extended periods.
Free fall: Weightlessness during free fall is typically experienced as part of a recreational activity or a specific scientific experiment. It is a brief moment of weightlessness within the context of a larger activity, such as skydiving, parabolic flights, or drop towers.
While both weightlessness in space and weightlessness during free fall share the absence of apparent gravity and the sensation of floating, they occur in different environments, are caused by different factors, and have varying durations and contexts.
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A mass of 4 kg is traveling over a quarter circular ramp with a radius of 10 meters. At the bottom of the incline the mass is moving at 21.3 m/s and at the top of the incline the mass is moving at 2.8 m/s. What is the work done by all non-conservative force in Joules?
Answer:
499.7 J
Explanation:
Since total mechanical energy is conserved,
U₁ + K₁ + W₁ = U₂ + K₂ + W₂ where U₁ = potential energy at bottom of incline = mgh₁, K₁ = kinetic energy at bottom of incline = 1/2mv₁² and W₁ = work done by friction at bottom of incline, and U₂ = potential energy at top of incline = mgh₂, K₁ = kinetic energy at top of incline = 1/2mv₂² and W₂ = work done by friction at top of incline. m = mass = 4 kg, h₁ = 0 m, v₁ = 21.3 m/s, W₁ = 0 J, h₂ = radius of circular ramp = 10 m, v₂ = 2.8 m/s, W₂ = unknown.
So, U₁ + K₁ + W₁ = U₂ + K₂ + W₂
mgh₁ + 1/2mv₁² + W₁ = mgh₂ + 1/2mv₂² + W₂
Substituting the values of the variables into the equation, we have
mgh₁ + 1/2mv₁² + W₁ = mgh₂ + 1/2mv₂² + W₂
4 kg × 9.8 m/s²(0) + 1/2 × 4 kg × (21.3 m/s)² + 0 = 4 kg × 9.8 m/s² × 10 m + 1/2 × 4 kg × (2.8 m/s)² + W₂
0 + 2 kg × 453.69 m²/s² = 392 kgm²/s² + 2 kg × 7.84 m²/s² + W₂
907.38 kgm²/s² = 392 kgm²/s² + 15.68 kgm²/s² + W₂
907.38 kgm²/s² = 407.68 kgm²/s² + W₂
W₂ = 907.38 kgm²/s² - 407.68 kgm²/s²
W₂ = 499.7 kgm²/s²
W₂ = 499.7 J
Since friction is a non-conservative force, the work done by all the non-conservative forces is thus W₂ = 499.7 J
Which is not one of the basic nutrients of your body?
1.Vitamins
2.Minerals
3.Molecules
4.Protein
Directions: Analyze and illustrate the given problems. Show your mathematical equations.
1. How much work is done when you lift an object that weighs 180 N to a height of 12 meters?
2. A cylindrical container having a mass of 50 kg is being pushed up an inclined plane. How much work
is done on the container when it is 6 meters above the floor?
3. How much work do you do to a 16-N rock that you carry horizontally across a 4m room?
Answer:
1. 2160 J
2. 2940 J
3. 64 J
Explanation:
1. Determination of the work done.
Weight (W) = 180 N
Height (h) = 12 m
Workdone =?
Wd = W × h
Wd = 180 × 12
Wd = 2160 J
Thus, the Workdone is 2160 J
2. Determination of the work done.
Mass (m) = 50 Kg
Height (h) = 6 m
Acceleration due to gravity (g) = 9.8 m/s²
Workdone =?
Wd = mgh
Wd = 50 × 9.8 × 6
Wd = 2940 J
Thus, the Workdone is 2940 J
3. Determination of the work done.
Force (F) = 16 N
Distance (d) = 4 m
Workdone =?
Wd = F × d
Wd = 16 × 4
Wd = 64 J
Thus, the Workdone is 64 J
Why was the discovery and explanation of the photoelectric effect so important in thehistory of physics? [The photoelectric effect provided a key piece of evidence that lightwas transmitted in discrete packets of energy, or quanta.]
The photoelectric effect is so important since it showed that energy was transfered in discrete packets of energy [Proving that light has a particle-like behavior] and that energy can be transfered by ligth. It allowed the development of modern computation and electronics as well as allowing the creating and use of the photoelectric effect to draw power from solar radiation and more.
The evidence is that under experimentation [thing that cannot be replicated by simply using words] the voltimeter [Not any ordinary voltimeter, a very sensitive one] connected to the metal surface was able to detect a sligth increment of voltage when the metal surface was hit by light. Meaning that when light impacted the atoms that composed the structure of the metal surface some electrons were detatched from the atoms and generated a flow of current, inducing a electric charge.
A cement mixer of radius 2.5 m turns with a period of 50 sec/rev. What is the centripetal force of a
small piece of dried cement of mass 50 g stuck to the inside wall of the mixer?
The centripetal force acting on the small piece of dried cement is 0.01 N when mass 50 g stuck to the inside wall of mixer.
Centripetal force :Any force that alters velocity in the direction toward the center of a circular motion is referred to as a centripetal force. The centripetal force is produced by the portion of the force that is perpendicular to the velocity.
Evaluating :The period of the cement mixer can be calculated as:
T = 50 sec/rev
= 2πr/v,
where r is the radius of the mixer and
v is the velocity of the piece of dried cement.
Solving for v, we get v = 2πr/T.
Substituting the given values, we get
v = 2π(2.5 m)/(50 sec/rev)
= 0.314 m/s.
The centripetal force acting on the piece of dried cement can be calculated using the formula :
F = m v² / r,
where m is the mass of the cement,
v is the velocity, and
r is the radius of the mixer.
Substituting the given values, we get
F = (0.05 kg)(0.314 m/s)²/(2.5 m)
= 0.01 N.
Therefore, the centripetal force acting on the small piece of dried cement is 0.01 N.
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What is sound waves
Sound waves are a type of mechanical wave that propagate through a medium, typically air but also other materials such as water or solids.
Characteristics of sound wavesFrequency: the frequency of a sound wave refers to the number of cycles or vibrations it completes per second and is measured in Hertz (Hz).
Amplitude: the amplitude of a sound wave refers to the maximum displacement or intensity of the wave from its equilibrium position. It represents the loudness or volume of the sound, with larger amplitudes corresponding to louder sounds and smaller amplitudes corresponding to softer sounds.
Wavelength: the wavelength of a sound wave is the distance between two consecutive points in the wave that are in phase, such as from one peak to the next or one trough to the next. It is inversely related to the frequency of the wave.
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omparing Technological Design and Scientific Investigation
Explain how the stages of technological design are similar to the process of scientific investigation. Use specific stages from each process to support your answer
Answer:
杰恩斯克克斯克奇沃伊斯克克斯克什德布德克什恩克恩德恩克恩茨克杰兹姆克斯恩斯姆斯姆德恩德姆德武伊乔奥斯克斯杰德布德赫德夫赫富伊什杰吉迪赫德赫夫赫德
Answer:
Scientists learn more about the natural world through investigation by identifying a problem, researching related information, designing and conducting an investigation, analyzing the results, evaluating the conclusion, and communicating the findings. Engineers follow similar steps when creating new products or solutions through technological design. The four stages of technological design include identifying a need, designing and implementing a solution, and evaluating the solution.
(a) Find the frequency ratio between the two frequencies f1 = 320 Hz and
½2 = 576 Hz.
S) If we go down from / by an interval of a fourth, find the frequency ratio filfi.
(c) Find the frequency of f3.
The frequency ratio between two frequencies f1 and f2 is given by:
frequency ratio = f2 / f1
Substituting the given values, we get:
frequency ratio = 576 Hz / 320 Hz = 1.8
Therefore, the frequency ratio between the two frequencies f1 = 320 Hz and f2 = 576 Hz is 1.8.
What is the frequency of f3?(b) If we go down from f1 by an interval of a fourth, we get a frequency that is 5 semitones lower. The frequency ratio for a single semitone is given by:
2^(1/12) ≈ 1.05946
Going down by 5 semitones, we get a frequency ratio of:
1 / (2^(5/12)) ≈ 0.84090
Therefore, the frequency ratio between f1 and the frequency that is a fourth below it is approximately 0.84090.
(c) To find the frequency of f3, we need to know the interval between f1 and f3. Let's assume that f3 is a fifth above f2. The frequency ratio for a fifth is given by:
2^(7/12) ≈ 1.49831
Therefore, the frequency of f3 is:
f3 = f1 * (2^(7/12)) * (2^(7/12)) = 320 Hz * 1.49831 * 1.49831 ≈ 716 Hz
Therefore, the frequency of f3 is approximately 716 Hz.
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Which factor limits interference between waves? A constant phase relationship between waves Similar wave amplitudes Unequal wavelengths Radiation through the same region
Answer:
Unequal Wavelengths
Explanation:
Got it right on the exam
Unequal wavelengths limit interference between waves because the waves will have different frequencies and will not be able to form a stable interference pattern. When waves of different wavelengths interact, they will interfere constructively and destructively at different points, creating an unpredictable pattern.
Answer:
Unequal wavelengths
Explanation:
Got it correct on the quiz.
Two stars have the same luminosity. The first star is one light year away from your telescope. The second star is two light years away from your telescope. The first star’s brightness is:A. two times as great as the second star’sB. four times as great as the second star’s.C. sixteen times as great as the second star’s.D. equal to the second star’s.
f = L / (4pi'd2), where:
f: apparent brightness
L: luminosity
d: distance of star
(p and i' stay constant between the two stars, so let's make them both equal to 1)
Let's say the closer star has a distance of 1 and the further has a distance of 2, and they both have a luminosity of L.
Apparent brightness of further star:
f = L/(4*2^2) = L/16
Apparent brightness of closer star:
f = L/(4*1^2) = L/4
As you can see here, the apparent brightnesses of the two stars differ by a factor of 4.
Answer: B. four times as great as the second star’s.
65. If Jill was traveling at 300 miles in 4 hours due South what was his velocity in miles per second,
a) 75 miles per hour due south
c) 5 miles per second due south
b) .02 miles per second due south d) 1 mile per hour due south
The velocity of Jill is 0.02 miles per second due south, the correct option is b.
What is Velocity?The total displacement covered by any object per unit of time is known as velocity.
the mathematical expression for velocity is given by
\(Velocity = \dfrac{Displacement }{Time }\)
1 hour = 3600 seconds
4 hours = 4*3600 seconds
= 14400 seconds
Total displacement covered by the Jill = 300 miles
Total time taken by Jill = 14400 seconds
\(Velocity =\dfrac{300 miles }{14400seconds}\)
The velocity of Jill is 0.02 miles per second due south
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if the police are chasing a runaway car why is knowing the velocity of the car important
If you only know its speed, that's not enough information to catch it. You could even chase it at DOUBLE that speed, and you'd never catch it if you were chasing in the wrong direction.
You also have to know the DIRECTION the runaway car is going, so that you can chase in the same direction.
Now that you know its speed AND direction, you know its velocity. You need that information to have any chance of catching it.
What is the difference between chronic and acute stress?
Acute stress is long-term, while chronic stress is short in duration.
Acute stress is short-term, while chronic stress endures over time.
Chronic stress varies by geographic location, while acute stress is universal.
Chronic stress is not harmful, while acute stress has negative consequences.
Answer:
The correct difference between chronic and acute stress is:
Acute stress is short-term, while chronic stress endures over time.
Explanation:
Acute stress refers to the immediate and temporary response of the body to a specific stressful event or situation. It is often characterized by a rapid increase in heart rate, heightened alertness, and the release of stress hormones like adrenaline. Acute stress is a normal and natural response to perceived threats or challenges, and once the stressor is removed or resolved, the body returns to its normal state.
On the other hand, chronic stress is long-term and persists over an extended period. It is typically caused by ongoing or recurring stressors, such as work pressures, financial difficulties, relationship problems, or chronic health conditions. Chronic stress can have a cumulative and prolonged impact on physical and mental well-being. It may lead to a range of health issues, including cardiovascular problems, weakened immune system, digestive disorders, anxiety, depression, and burnout.
Chronic stress is considered detrimental to overall health, while acute stress, when experienced in moderation, can actually be beneficial as it can enhance performance and help individuals deal with immediate challenges. It is important to manage chronic stress effectively through stress-reducing techniques, self-care practices, and seeking support when needed to prevent its negative consequences on health and well-being.
A cell contains 20% solute. If it is placed in a solution with 35% solute, what will happen to the cell?
A construction worker is working on top of a building that is 305m tall. He finishes a pop can and throws it off the top of the building with a velocity of 4.9m/s. Ignoring air resistance, how far did the pop can land from the base of the building?[39m]
Answer:
Explanation:
We do not know because we do not know what the throw angle was.
If we ASSUME a horizontal throw,
time to drop from vertical rest.
t = √(2h/g) = √(2(305)/9.8) = 7.89 s
horizontal distance covered
d = vt = 4.9(7.89) = 38.658... which rounds to 39 m
hopefully his co-workers are under cover as the velocity at ground impact would be 77 m/s or 278 km/hr ... speeds which could cause severe injury or death from the impact of an empty aluminum can. Fortunately real air resistance will reduce the terminal velocity greatly. Still a stunt that would get most workers fired immediately.
How are magnetic fields like vectors?
Answer:Magnetic fields from two sources add up as vectors at each point, so the strength of the field is not necessarily the sum of the strengths1. Magnetic fields are vectors, which means they have direction as well as size. Therefore, the sum of two magnetic fields is not simply the sum of their magnitudes2.
Explanation:
how many newtons does a 190 lb person weigh? express your answer in newtons. activate to select the appropriate template from the following choices. operate up and down arrow for selection and press enter to choose the input value typeactivate to select the appropriates symbol from the following choices. operate up and down arrow for selection and press enter to choose the input value type w
The weight of a 190 lb person is 844.5 N.
What is the definition of 1 Newton?Newton is the SI (International System) unit of force, named after Sir Isaac Newton, a famous physicist, and mathematician. It is defined as the force required to accelerate a mass of one kilogram at a rate of one meter per second squared (1 N = 1 kg m/s²).
To convert pounds (lb) to Newtons (N), we need to use the conversion factor:
1 lb = 4.45 N
Therefore, a 190 lb person weighs:
190 lb × 4.45 N/lb = 844.5 N
So the weight of a 190 lb person is 844.5 N.
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A 2000 kg car moves at a speed of 30 m/s. To reach this speed, it was necessary to burn 0.1 l of gas. Burning gas provides 30 MJ/l of source energy. Determine the energy efficiency (in %) of this car.
The energy efficiency of the car is approximately 16.7%.
The energy efficiency of a car is the ratio of the useful work output (in this case, the kinetic energy of the car) to the total energy input (in this case, the energy released by burning the gasoline). The equation for energy efficiency is:
Efficiency = Useful work output / Total energy inputThe useful work output can be calculated as the kinetic energy of the car using the equation:
KE = 0.5mv²where m is the mass of the car and v is its velocity.
Substituting the given values:
KE = 0.5 x 2000 kg x (30 m/s)² = 900,000 JThe total energy input is the energy released by burning 0.1 L of gasoline, which is:
Total energy input = 0.1 L x 30 MJ/L = 3 MJ = 3,000,000 JSubstituting these values into the equation for efficiency:
Efficiency = (900,000 J / 3,000,000 J) x 100% = 0.3 x 100% = 16.7%Therefore, the energy efficiency of the car is approximately 16.7%.
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What is needed for a combustion reaction to take place?
What is formed in any combustion reaction?
Mercury reacts with oxygen to form mercuric oxide. Is this a combustion reaction?
What are the products of any combustion reaction involving a hydrocarbon?
Answer:
Question: What is needed for a combustion reaction to take place?
Answer: In order for a combustion to take place there are 3 main ingredients that must be present: Oxygen, Heat and Fuel.
Question: What is formed in any combustion reaction?
Answer: Combustion reactions always have two products: carbon dioxide and water. Combustion always produces water vapor.
Question: Mercury reacts with oxygen to form mercuric oxide. Is this a combustion reaction?
Answer: Yes, it is a combustion reaction.
Question: What are the products of any combustion reaction involving a hydrocarbon?
Answer: carbon dioxide and water are the products of any combustion reaction involving a hydrocarbon.
A tsunami, an ocean wave generated by an earthquake, propagates along the open ocean at 700 km/hr and has a wavelength of 750 km. What is the frequency of the waves in such a tsunami?.
Taking into account the definition of wavelength, frecuency and propagation speed, the frequency of the waves in the tsunami is 2.59×10⁻⁴ Hz.
What is wavelength, frecuency and propagation speedFirst of all, wavelength is the minimum distance between two successive points on the wave that are in the same state of vibration. It is expressed in units of length (m).
On the other side, frequency is the number of vibrations that occur in a unit of time. Its unit is s⁻¹ or hertz (Hz).
Finally, the propagation speed is the speed with which the wave propagates in the medium, that is, it is the magnitude that measures the speed at which the wave disturbance propagates along its displacement.
The propagation speed relate the wavelength (λ) and the frequency (f) inversely proportional using the following equation:
v = f×λ
Frequency of the waves in the tsunamiIn this case, you know:
v=700 km/h= 0.194 km/sf= ?λ= 750 kmReplacing:
0.194 m/s=f× 750 km
Solving:
f= 0.194 m/s ÷ 750 km
λ= 2.59×10⁻⁴ Hz
In summary, the frequency of the waves in the tsunami is 2.59×10⁻⁴ Hz.
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When the applied force is 150 N and the friction is 94 N, what is the motion? A. Accelerated motion b. Decelerated motion c. No motion D. Uniform motion
Answer:
the answer to this question is Accelerated motion
A 0.160kg glider is moving to the right on a frictionless, horizontal air track with a speed of 0.820m/s . It has a head-on collision with a 0.300kg glider that is moving to the left with a speed of 2.27m/s . Suppose the collision is elastic.
Part A
Find the magnitude of the final velocity of the 0.160kg glider. m/s
Part B
Find the direction of the final velocity of the 0.160kg glider.
i. to the right
ii. to the left
Part C
Find the magnitude of the final velocity of the 0.300kg glider. m/s
Part D
Find the direction of the final velocity of the 0.300kg glider.
Answer:
A) v_{f1} = -3.2 m / s, B) LEFT , C) v_{f2} = -0.12 m / s, D) LEFT
Explanation:
This is a collision exercise that can be solved using momentum conservation, for this we define a system formed by gliders, so that the forces during the collision are internal and the moment is conserved.
Let's use the subscript 1 for the lightest glider m1 = 0.160 kg and vo1 = 0.820 m / s
subscript 2 for the heaviest glider me² = 0.820 kg and vo2 = -2.27 m / s
Initial instant. Before the crash
p₀ = m₁ v₀₁ + m₂ v₀₂
Final moment. After the crash
p_f = m₁ v_{f1} + m₂ v_{f2}
p₀ = p_f
m₁ v₀₁ + m₂ v₀₂ = m₁ v_{f1} + m₂ v_{f2}
as the shock is elastic, energy is conserved
K₀ = K_f
½ m₁ v₀₁² + ½ m₂ v₀₂² = ½ m₁ \(v_{f1}^2\) + ½ m₂ \(v_{f2}^2\)
m₁ (v₀₁² - v_{f1}²) = m₂ (v_{f2}² -v₀₂²)
let's make the relationship
(a + b) (a-b) = a² -b²
m₁ (v₀₁ + v_{f1}) (v₀₁-v+{f1}) = m₂ (v_{f2} + v₀₂) (v_{f2} -v₀₂)
let's write our two equations
m₁ (v₀₁ -v_{f1}) = m₂ (v_(f2) - v₀₂) (1)
m₁ (v₀₁ + v_{f1}) (v₀₁-v_{f1}) = m₂ (v_{f2} + v₀₂) (v_{f2} -v₀₂)
we solve
v₀₁ + v_{f2} = v_{f2} + v₀₂
we substitute in equation 1 and obtain
M = m₁ + m₂
\(v_{f1} = \frac{m_1-m_2}{M} v_o_1 + 2 \frac{m_2}{M} v_f_2\)
\(v_f_2 = \frac{2m_1}{M} v_o_1 + \frac{m_2-m_1}{M} v_o_2\)vf2 = 2m1 / mm vo1 + m2-m1 / mm vo2
we calculate the values
m₁ + m₂ = 0.160 +0.3000 = 0.46 kg
v_{f1} = \(\frac{ 0.160 -0.300} {0.460} \ 0.820 + \frac{2 \ 0300}{0.460} \ (-2.27)\)
v_{f1} = -0,250 - 2,961
v_{f1} = - 3,211 m / s
v_{f2} = \(\frac{2 \ 0.160}{0.460} \ 0.820 + \frac{0.300 - 0.160}{0.460 } \ (-2.27)\)
v_{f2} = 0.570 - 0.6909
v_{f2} = -0.12 m / s
now we can answer the different questions
A) v_{f1} = -3.2 m / s
B) the negative sign indicates that it moves to the left
C) v_{f2} = -0.12 m / s
D) the negative sign indicates that it moves to the LEFT
Solve for x. ln(2x-2) - ln(x-1)= ln x
Remember the following property of logarithms:
\(\ln (a)-\ln (b)=\ln (\frac{a}{b})\)Use this property to simplify the left member of the equation and solve for x:
\(\begin{gathered} \ln (2x-2)-\ln (x-1)=\ln (x) \\ \Rightarrow\ln (\frac{2x-2}{x-1})=\ln (x) \\ \Rightarrow\frac{2x-2}{x-1}=x \\ \Rightarrow2x-2=x(x-1) \\ \Rightarrow2(x-1)=x(x-1) \end{gathered}\)Since the factor (x-1) appears at both sides of the equation, we can simplify it as long as x is different from 1 (since the factor should not be equal to 0). Then:
\(x=2\)Plug in x=2 into the original equation to check the solution:
\(\begin{gathered} \ln (2(2)-2)-\ln (2-1)=\ln (2) \\ \Rightarrow\ln (4-2)-\ln (1)=\ln (2) \\ \Rightarrow\ln (2)-\ln (1)=\ln (2) \end{gathered}\)Since ln(1)=0, then:
\(\ln (2)=\ln (2)\)Therefore, the solution is x=2.
You have a friend who reports that he falls asleep easily around 11 PM but then awakens for about an hour most nights around two or 3 AM he seems near exhausted what would be the traditional exclamation for his problem how much the information contribute by anthropologists change this view? Give the anthropological view what recommendations would you make your friend?
It is highly recommended that this friend who is suffering from insomnia visits the doctor and eat foods rich in serotonin.
What is insomnia?Insomnia is a medical condition in which an individual is unable to sleep or has short periods of interrupted sleep.
A friend who falls asleep easily and then has difficulty going to sleep is probably suffering from insomnia.
It is recommended that this friend who is suffering from insomnia visits the doctor and eat foods rich in serotonin.
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distinguish between static and dynamic friction
Which of the following is NOT an application of concave mirrors and parabolic reflectors?Select one:a.satellite dishesb.increasing field of viewc.telescopesd.solar cookers
We will have that the less likely to be applicative of these is option D.
A wire loop in the shape of a circle spins in a uniform magnetic field. How does the torque on the loop change if the radius of the wire is doubled at the same time that the current flowing through the wire is quadrupled?
a. It increases by a factor of 2
b. It increases by a factor of 4
c. It increases by a factor of 8
d. t increases by a factor of 16
e. None of the above
The torque on the loop increases by a factor of 16.
option D.
What is the torque on wire loop?The torque on a wire loop in a magnetic field is given by the equation:
τ = NIABsinθ
Where;
τ is the torqueN is the number of turns in the wire loopI is the current flowing through the wireA is the area of the loopB is the magnetic field strengthθ is the angle between the magnetic field and the normal to the loopIf the radius of the wire is doubled, then the area of the loop becomes four times larger.
Also, if the current flowing through the wire is quadrupled, then the torque becomes four times larger.
The torque on the loop increases by a factor of 4 x 4 = 16.
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