Answers
1. The equation of trajectory is: y = 5x²/4 +2x; it is equation of parabola.
2. The position vector = 2ti + (5t² +4t) j
3. The position of point M at t = 3 s is: ( 6,57).
4. The magnitude of velocity of point M at any time t is 2√(25t²+20t+5).
5. The magnitude of acceleration is 10m/s².
What is velocity?The term velocity has been defined as the rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is known as a vector quantity with both magnitude and direction. SI unit of velocity is meter/second.
Coordinates at any instant t are:
x = 2t; y = 5t² +4t
1. equation of trajectory is:
y = 5x²/4 +2x; it is equation of parabola.
2. position vector = 2ti + (5t² +4t) j
3. the position of point M at t = 3 s is: x = 2×3 = 6; y = 5×3² +4×3 = 57; i.e., ( 6,57)
4. the velocity vector of point M at any time t is = 2i + ( 10t +4) j
magnitude of velocity = √( 2² + (10t +4)² = 2√(25t²+20t+5).
5. the acceleration vector is = 10j m/s²
Therefore, its magnitude is =10m/s².
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Related Questions
15-28 a type of cuckoo clock keeps time by having a mass bouncing on a spring, usually something cute like a cherub in a chair. what spring constant is needed to produce a period of 0.500 s for a 0.0150-kg mass?
Answers
Spring constant is needed to produce a period of 0.500 s for a 0.0150-kg mass: The required spring constant is 2.368.
What is the time period of a spring-mass system?
The time period of a spring-mass system is the amount of time it takes for the system to complete one full cycle of oscillation. This time period is determined by the system's spring constant and mass, and is calculated using the formula: T = 2π√(m/k), where m is the mass of the system and k is the spring constant. In a spring-mass system, the time period is typically short and can range from a few microseconds to several seconds. The time period of a spring-mass system is an important factor when designing a system, as it can affect the performance of the system. If a system is required to complete multiple cycles of oscillation within a given amount of time, then the time period must be short enough to accommodate this.
T = 2π√(m/K)
In the given problem,
Time period , T = 0.5 s
Mass, m = 0.0150-kg
T = 2π√(m/K)
K = 4π²m/T²
= 4× π² × 0.015 / 0.5²
= 0.592/0.25
= 2.368
Therefore the required spring constant is 2.368
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When a ball at a billiard table hits another ball it is an example of elastic collision?
Answers
The collision of two billiard balls is an example of elastic collision.
An elastic collision is a collision where Kinetic energy is preserved. In this type of collision, there will be no change in overall kinetic energy and momentum.
An inelastic collision is where the Kinetic energy is not preserved. Here some of the kinetic energy is transferred to some other form of energy like thermal energy or sound energy.
In both type of collisions, momentum is preserved. There are fewer examples of perfectly elastic collision in real life. Collisions in atomic levels are examples of perfectly elastic collisions. But some collisions where the energy loss is negligible are considered elastic collisions. One such example is the collision of the billiard balls.
So when a billiard ball hits another it is an elastic collision.
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How do I improve my scope 3 emissions?
Answers
To encourage action, establish clear expectations with your vendors and engage them strategically.Companies have to go beyond data collecting and establish clear expectations on suppliers about emissions reduction in order to significantly cut upstream Scope 3 emissions.
Why are the scope 3 challenging?The enormous number of partners inside the value chain is one factor contributing to the difficulty of accounting on Scope 3 emissions.For major companies, the number of upstream supply chain partners who contribute to Category 3 emissions can range from hundreds to tens of thousands, and they may be located all over the world.
How may Level 3 GHG emissions be reduced?Reducing the amount of goods purchased can take many different forms, including switching to incoming materials with such a lower CO2 content, reducing input quantity, using recycled materials as inputs, reducing production waste, favoring more sustainable suppliers, and working with important suppliers to reduce their own carbon footprints.
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What is frequency give its formula and units?
Answers
Answer: f = c/lambda
Explanation:
f = frequency
c= speed of light constant
lambda = wavelength
Unit -> hertz (Hz)
Use the graph to calculate the distance, in m, between station B and station C.
Answers
The distance from station B to station C as seen in the velocity time graph is calculated as; 6000 m
How to interpret Velocity Time Graph?Velocity-time graph is simply defined as a plot that shows the relationship between Velocity and Time.
Now, the velocity time graph attached shows the motion of the movement of the train from station B to station C.
Now, when it comes to velocity time graph, we have to know that the area of a velocity time graph, gives us the overall distance covered by the motion it represents.
Since the velocity time graph is a trapezium shape, then we will use the are of a trapezium formula to get the distance from station B to station C.
Area of trapezium = ¹/₂(sum of parallel sides) * height
Plugging in the relevant values from the graph gives;
Distance = ¹/₂(300 + 100) * 30
Distance = ¹/₂ * 400 * 30
Distance = 6000 m
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What are 3 examples that carbon can be found in?
Answers
Carbon is also a constituent of diamonds and graphite.Diamonds, graphite, etc.Like diamond, graphite is a kind of carbon.Textiles.Carbon is found in cellulose, which is found in a variety of fabrics, including Life Itself.The basis of all life on the planet is carbon.
Where can I get examples of carbon?The majority of the carbon on Earth is preserved in sediments and rocks with the remainder found in the sea, atmosphere, or living things.These serve as the carbon cycle's reservoirs or sinks.
What kinds of objects are carbon-containing?Examples of carbon allotropes include coal, graphite, & diamonds.They differ physically while just having one type of element in common—carbon.For instance, while graphite is opaque, diamond is clear.
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What does sonar do with seafloor spreading?
Answers
Sonar is largely used by NOAA scientists to create nautical charts, find underwater navigational hazards, find and map things on the bottom like shipwrecks, and map the actual seafloor. Sonar comes in active and passive varieties.
Why do we use sonar to investigate the ocean floor?
Due to the fact that sound waves travel further in water than radar and light waves, sonar is utilised in oceanography. The passenger freighter Robert E. Lee as captured by side-scan sonar in 2001 by the HUGIN 3000 AUV.
Reversed geomagnetic field
In the early 20th century, scientists were able to first recognise the process of seafloor spreading thanks to the magnetism of mid-ocean ridges.
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892-kg sports car is moving 14.6 m/s when it rear ends with stopped car having an identical mass at a stop light. Two cars entangle and move together after the collision. What is their speed immediately after the collision
Answers
The speed of the cars immediately after the collision will be the same as their speed before the collision, which is 14.6 m/s. In a perfectly inelastic collision, the objects involved in the collision will move together with the same speed after the collision as they had before the collision. This is because the total kinetic energy of the system is conserved in a perfectly inelastic collision.
What is the power rating of an engine capable of lifting a 100 kg object 5 m vertically in 4 seconds? do not include units in your answer.
Answers
The power rating of an engine who can lift a 100kg object 5m vertically in 4 seconds is 125watt.
How to calculate the power rating of the engine?
In electrical engineering and mechanical engineering, the power rating of equipment is the highest power input allowed to flow through particular equipment. According to the particular discipline, the term power may refer to electrical or mechanical power.
From the question given :
Force (f) = 100
Time (t) = 4 seconds
Distance (d) = 5m
Work done = f * d
= 100 * 5
= 500
So, The power will be
= Work / time
= 500 / 4
= 125watt
Therefore, the power rating of the engine is 125watt.
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Why are digital signals more reliable than analog signals? (give an example as well please)
Answers
Digital signals more reliable than analog signals because of the many following reasons:
Digital signals are transmitted at a specific frequencies and amplitudes so the possibility of the signal being distorted is less than the analog signals.In Digital Signals or processing the digital information can be easily encrypted and compressed for digital use.Digital signals are time separated than analog one. What are analog Signals?Analog Signal is a Continuous type signal which has one time varying quantities such as Voltage, Pressure, etc. As in the analog audio signal the instantaneous voltage continuously varies with the sound wave's pressure.
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The primary blast cell for bone is the
O hemangioblast
O fibroblast
O chondroblast
O osteoblast
O hemocytoblast
Which of the following is NOT a type of connective tissue?
O Adipose
O Bone
O Blood
O Alveolar
O Cartilage
Connective tissue extracellular matrix is composed of
O capillaries and cells
O ground substance and cells
O collagen fibers, elastic fibers and reticular fibers
O cells and fibers
O fibers and ground substance
Which of the following statements concerning connective tissue is TRUE?
O Cartilage tissue tends to heal less rapidly than bone tissue.
O Reticular connective tissue serves as the universal packing material between other tissues.
O Connective tissues that possess a large quantity of collagen fibers often provide the framework for organs such as the spleen and lymph nodes.
O The basic difference between dense irregular and dense regular connective tissues is in the amount of elastic fibers and adipose cells present.
O A major characteristic of fibrocartilage is its unique amount of flexibility and elasticity
A ciliated version of pseudostratified columnar epithelium containing mucus-secreting goblet cells
O lines most of the respiratory tract
O aids in digestion
O is more durable than all other epithelia
O is found in some of the larger glands
O protects underlying tissues in areas subjected to abrasion in the moist linings of the esophagus, mouth and vagina
Answers
a)The primary blast cell for bone is the osteoblast b) Alveolar is NOT a type of connective tissue. c) Connective tissue extracellular matrix is composed of fibers, and a ground substance d)Cartilage tissue tends to heal less rapidly than bone tissue. e))lines most of the respiratory tract of pseudostratified columnar epithelium containing mucus-secreting goblet cells.
In addition, blast cells known as myeloblasts can form. Young blood cells made by stem cells are what these are. The synthesis of red, white, and platelet-forming blood cells can also be hampered by an excess of blast cells. Bone marrow blasts are not expected in healthy individuals. When a person develops leukemia, aberrant, immature white blood cells—known as blasts—proliferate rapidly, filling up the bone marrow and blocking the creation of other cells vital to survival, such as red blood cells and platelets. Anemia, infections, and unusual bleeding result from this. Blast cells shouldn't make up more than 5% of the bone marrow cells in healthy individuals, and they often aren't present in the blood.
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What is the velocity of a wave that has a wavelength of 3.0 m and a frequency of 12 Hz?
Answers
It travels at a speed of 36 meters per second
The velocity of a wave is a measure of how fast the wave travels through a medium. It is given by the equation v = λf, where v is the velocity, λ is the wavelength, and f is the frequency. In this case, the given wavelength is 3.0 meters and the given frequency is 12 Hertz.
Plugging these values into the equation, we can calculate the velocity of the wave:
v = (3.0 m) * (12 Hz) = 36 m/s.
This means that the wave travels at a speed of 36 meters per second.
It is important to note that the velocity of a wave depends on the properties of the medium through which it is traveling, as well as the wavelength and frequency of the wave itself.
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Is the image congruent to the preimage?
Answers
Translations, reflections, and rotations are examples of congruence transformations because the image of a figure after one of them is congruent with its preimage.
How can you tell if two images are coherent?Congruent image refers to shapes or images that are the same size and shape. Two shapes are said to be congruent if their corresponding sides and angles are of the same length.
What attributes a congruent image has?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. Images produced by dilations with scale factors k 1 are not consistent with their preimages. Dilations are neither rigid transformations or isometries.
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A room was lighted with three 100-watt bulbs for 5 hours per day. If the cost of
electricity was 9¢ per kWh, how much would be saved per day by switching to
60-watt bulbs?
Answers
To find the amount of electricity used by the 100-watt bulbs, we need to first calculate the total wattage of the bulbs by multiplying the wattage of each bulb by the number of bulbs: 100 watts/bulb * 3 bulbs = 300 watts
Next, we need to convert the time the bulbs were used from hours to seconds. Since there are 3600 seconds in an hour, the bulbs were used for 5 hours * 3600 seconds/hour = 18000 seconds.
Now we can calculate the total amount of electricity used by the 100-watt bulbs by multiplying the wattage of the bulbs by the time they were used: 300 watts * 18000 seconds = 5.4 x 10^7 joules
To convert this to kilowatt-hours, we need to divide by the number of joules in a kilowatt-hour, which is 3.6 x 10^6. This gives us a total of 1.5 kWh.
At a cost of 9¢ per kWh, the cost of using the 100-watt bulbs for 5 hours per day is 1.5 kWh * $0.09/kWh = $0.135 per day.
To find the amount of money that would be saved by switching to 60-watt bulbs, we need to repeat the above calculation using the wattage of the 60-watt bulbs instead of the 100-watt bulbs. The total wattage of the 60-watt bulbs is 60 watts/bulb * 3 bulbs = 180 watts. This means that the total amount of electricity used by the 60-watt bulbs would be 180 watts * 18000 seconds = 3.24 x 10^7 joules, or 0.9 kWh.
At a cost of 9¢ per kWh, the cost of using the 60-watt bulbs for 5 hours per day is 0.9 kWh * $0.09/kWh = $0.081 per day.
Therefore, the amount of money that would be saved by switching to 60-watt bulbs is $0.135 per day - $0.081 per day = $0.054 per day.
How do you find the maximum speed of emitted photoelectrons?
Answers
We must first calculate the kinetic energy of an emitted electron from the energy of an incoming photon and the work function of the metal surface in order to estimate the maximum speed of an emitted photoelectron (the minimum energy required for an electron to escape the metal surface).
Using the equation below, these are connected. E (total energy supplied by a photon) equals +Ek From the Planck's equation,
E=hf, where E is energy,
h is Planck's constant (6.6310(-34)Js), and
f is frequency, one may determine the energy of a single photon.
Since the wavelength is what we have here instead of the incident frequency, we can apply the equation
f=c/lambda to calculate the frequency.
F is the frequency,
c is the speed of light (3.0010(8)m/s), and
lambda is the wavelength.
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What is bulk modulus of water?
Answers
Answer:
Water has a bulk modulus of around 300,000 psi (2.1 GPa) and so a compressibility of 3.3 106 (psi)1.
Explanation:
Which ion in the ground state has the same electron configuration as an atom of neon in the ground state.
Answers
Na+ ion in the ground state has the same electron configuration as an atom of neon in the ground state.
The electronic configuration has been defined as the electron address in a atom. The electronic configuration has been based on the quantum rule for the filling of the electrons.
Neon is the tenth element with a total of 10 electrons. In writing the electron configuration for neon the first two electrons will go in the 2p orbital. Since 1s can only hold two electrons for Ne go in the 2s orbital. The remaining six electrons will go in the 2p orbital. Therefore, the Ne electron configuration 1s22s22p6.
Ne (atomic number=10) have 2,8 electron configurations. Here the atomic number of Na is 11. The configuration of Na is 2,8,1. Atomic number of Na+ is 10 and it has an electron configuration of 2,8 which is similar to Ne. Na+ ion is a positively charged particles, because they are missing one electron.
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Two packing crates of masses 10.0kg and 5.00kg are connected by a light string that passes over a frictionless pulley as shown in Figure. The 5.00kg crate lies on a smooth incline of angle 40.0 degree . Find the acceleration of the crates and the tension in the string.
Answers
The acceleration of the string is 4.3 m/s2.
What is Acceleration?We regard the positive direction for the vertical motion of mass m1 to be downward and the positive direction for the motion of mass m2 on the incline to be to the right and parallel to the incline.
There are only two ways to accelerate: changing your speed or changing your direction, or changing both. This is because velocity is both a speed and a direction.
Changing the speed at which an object is travelling is what acceleration is all about. A substance is not accelerating if its velocity is not changing. The information on the right depicts an object that is speeding as it moves northward.
Therefore, The acceleration of the string is 4.3 m/s2.
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.
Is alpha an particle?
Answers
suppose you have a microphone that is only sensitive to sounds between 400 and 1300 hz. you record the sound and look at the fft. there are large peaks at 600, 900, and 1200 hz. you know that the sound contains all (both even and odd) harmonics. what is the fundamental frequency of the sound?
Answers
the fundamental frequency is 300 Hz is the answer.
Constructive Frequency
Peak frequency differences are different by
= 1200 - 900 = 900 - 600 = 300 Hz
hence, the fundamental frequency is 300 Hz.
Since the frequency of constructive interference is an integer multiple of the fundamental frequency, the fundamental frequency can be calculated from the difference between two successive peak frequencies.
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A new building was being built. (Into active)
Answers
a 10-kg piece of aluminum sits at the bottom of a pool, right next to a 10-kg piece of lead, which is much denser than aluminum. which one has the greater buoyant force on it?
Answers
A 10-kg piece of aluminum sits at the bottom of a pool, right next to a 10-kg piece of lead. Aluminum has greater buoyant force acting on it.
Density is defined as mass per unit volume:
ρ = m /V
Where:
m = mass
V = volume
The lead is much denser than aluminum. Their densities are:
ρ_Al = 2.7 g/cm³
ρ_Pb = 11.29 g/cm³ (Pb is the symbol for lead)
From the equation, if the masses are the same, the density is inversely proportional to the volume.
In the given problem, since lead is denser than aluminum, hence, the volume of aluminum is greater than the volume of lead.
The buoyant force is equal to the weight of displaced water.
For each piece of metal, it holds
F = ρ_water x g x V_metal
Hence, the buoyant force is directly proportional to the volume of each piece of metal.
Since V_Al > V_Pb, then F_Al > F_Pb or Aluminum will experience greater buoyant force.
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How does the induction motor works?
Answers
Answer:
It uses electromagnets to create a rotating magnetic field.
Explanation:
I remember learning this in AP Physic class. The interaction between the two fields causes the rotor to turn and it creates a magnetic field!
Answer:
It generates a rotating magnetic field using electromagnets.
a 60 kg skier with an initial velocity of 12 m/s coasts up a hill. at the top of the hill, the skier is traveling at 9.75 m/s. assuming there is no friction in the skis, how high was the hill?
Answers
Answer:
The height of the hill coasted by a skier of initial velocity 12 m/s is 2.5 m. And The correct option is C 2.5 m.
The high of the hill is 2.5 m
What is conservation of energy?
It states that energy can neither be created nor be destroyed.
Mass of skier,m = 60kg
initial velocity, u = 12 m/s
Final velocity, v = 9.75 m/s
As there is no friction, energy is conserved
∴ Initial kinetic energy + Initial potential energy = Final kinetic energy + Final potential energy
1/2 mu² + 0 = 1/2m v² + mgh
1/2 u² = 1/2 v² + gh
h = u² - v² /2g
= 12² - 9.75² / 2×9.8
= 48.9375/2×9.8
= 2.496 m
≈ 2.5 m
Therefore high of the hill is 2.5 m
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an object slides across a horizontal surface such that it slows down due to the force of friction that is exerted on the object. the object and the direction of its displacement are shown in the figure. which of the following free-body diagrams could represent the forces that are exerted on the object?
Answers
F normal up, Fg down, small arrow left F friction
There are three forces acting on the sliding object across a horizontal surface. These are normal force, gravity force and friction force.
The direction of normal force is always upward. This force is acting on the object against the gravity. Gravity force is towards the center. Gravity force causes downward sliding of the object.
There is a third force also in action. Friction force exists between surface of two objects when one object is moved on the surface of another object, or is tried to move. Friction force acts against the motion of an object.
The correct option is B.
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if, in the figure below, i1 = 2 a and i2 = 6 a, which of the following is true?
Answers
In the given figure, if I = 2A and I2 = 6A, the relation between F1 and F2 is, F1 = F2.
The two forces are an action reaction forces. They act on different wires, and have equal magnitudes but opposite directions. So, they are equal.
We find the discussion of action and reaction forces in newton's third law.
According to the Newton's third law states that If there is an action force, there must be a reaction force. If there is an object A which exerts a force on object B, then object B must also exerts an equal and opposite force on object A. In other words, we can say that forces result from interactions.
Action and reaction forces acts on different objects. they exist in pair. They are always equal in magnitude and opposite in direction.
The given question is incomplete, the complete question is
n figure given below, I1-2A and I2=6a, which of the following is true? Note that F2 represents the magnet of the force on wire 2
(a) F1=3F
(b) F1=F2
(c) F1=F2/3
Option (b) is the correct answer.
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galilea was the first scientist to do which of the following
Answers
Answer: Use a refracting telescope to make important astronomical discoveries.
Explanation:
a bystander hears a siren vary in frequency from 564 hz to 376 hz as a fire truck approaches, passes by, and moves away on a straight street. what is the speed of the truck>
Answers
The vehicle travels at a speed of Vs = 68.6 m/s.
Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, velocity is a vector, whereas speed is a scalar value.
Calculation:
Varying frequency of the siren = 564 Hz to 376 Hz
speed of sound = 343 m/s
speed of truck calculation
using equation of Doppler'sWhen the truck is approaching
Fs = F₀(v - vs)/v......(i)
Doppler's equation when truck is moving away
Fs = F₁(v + vs)/v ......(ii)
equating both the equation
Fs = F₀(v - vs)/v = Fs = F₁(v + vs)/v
on simplifying the above equation we get
Vs = v(F₀ - F₁)/F₀ + F₁)
F₀ = 564Hz
F₁ = 376 Hz
now,
Vs = 343 ₓ (564 - 376)/(564 + 376)
Vs = 68.6 m/s
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Rita is riding a 7.0 kilogram bike at a velocity of 15 meters/second. rita’s mass is 42 kilograms. what is her momentum?
a. 1.0 × 102 kilogram meters/second
b. 5.2 × 102 kilogram meters/second
c. 6.3 × 102 kilogram meters/second
d. 7.4 × 102 kilogram meters/second
e. 8.5 × 102 kilogram meters/second
Answers
Rita's momentum when riding a 7kg bike at a velocity of 15m/s where her mass is 42kg is 7.4 * 10² kilogram meters / second. Therefore, the answer is D.
How to calculate Rita's momentum?In Newtonian mechanics, momentum is the product of the mass and velocity of an object. It's a vector quantity, possessing a magnitude and a direction.
Based from the question, given :
mass of bike = 7kg
mass of Rita = 42kg
velocity = 15m/s
Momentum (P) = mass * velocity
= (mass of bike + mass of rita) * 15
= (7 + 42) * 15
= 49 * 15
= 7.4 * 10² kilogram meters / second
Therefore, the answer is D.
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If Juan tried to learn a long list of words, he would be most likely to forget words that
A
appeared early in the list
B
appeared near the end of the list
C
appeared in the middle of the list
D
were very unlike the rest of the words
E
were randomly dispersed throughout the list
Answers
He is most probable to forget words that are at the (c) middle of the list if she has a Long List of Words.
What is a List of Word?
As its name suggests, a list of words is an arrangement of words which can be done in a sequential manner or non-sequential manner. It can also be called as array. It is usually written in top to bottom fashion.
Assuming that there is a twenty list of words, then mostly the eye is usually focused on the early part and the last part of the list while ignoring the words that are present in middle.
Thus, we can say that Juan is most probable forget the words appearing in the middle of the list if she has a Long List of Words.
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