if the rank of a is r, then occurs as an eigenvalue of a with multiplicity r.
If λ occurs as an eigenvalue of A with multiplicity r, then there are r linearly independent eigenvectors associated with λ, and the geometric multiplicity of λ is equal to r.
Let A be an n × n matrix. An eigenvalue of A is a scalar λ such that there is a nonzero vector x satisfying the equation Ax = λx. This equation can be rewritten as the linear system (A − λI)x = 0, where I is the identity matrix. Nontrivial solutions to this equation exist if and only if the matrix A − λI is singular, which means that its determinant is zero. Thus, the eigenvalues of A are the roots of the polynomial equation det(A − λI) = 0, which is called the characteristic equation of A. The algebraic multiplicity of an eigenvalue is the number of times it appears as a root of the characteristic equation. The geometric multiplicity of an eigenvalue is the dimension of the eigenspace associated with that eigenvalue. The eigenspace of an eigenvalue λ is the set of all eigenvectors of A associated with λ, along with the zero vector.
The rank of A is the dimension of its column space, which is the span of its column vectors. The rank of A is equal to the dimension of the row space of A, which is the span of its row vectors. The rank of A is also equal to the number of nonzero singular values of A. If the rank of A is r, then the dimension of the nullspace of A is n − r. If A has r linearly independent eigenvectors associated with a particular eigenvalue λ, then the geometric multiplicity of λ is r. If the algebraic multiplicity of λ is greater than its geometric multiplicity, then there are not enough eigenvectors to form a basis of the eigenspace associated with λ, which means that A is not diagonalizable. If the algebraic multiplicity of λ is equal to its geometric multiplicity, then A is diagonalizable. If λ occurs as an eigenvalue of A with multiplicity r, then there are r linearly independent eigenvectors associated with λ, and the geometric multiplicity of λ is equal to r.
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A rubber ball that sits motionless near the edge of a tall bookshelf has no kinetic energy. However, it does have mechanical
energy. Explain why this is possible,
It is possible because the rubber ball has mechanical energy which is equal to potential energy.
What is mechanical energy?
Mechanical energy of an object is the total energy possessed by the object, including the potential energy and the kinetic energy.
M.A = K.E + P.E
What is kinetic energy?Kinetic energy is the energy possessed by an object due to its motion.
What is potential energy?Potential energy is the energy possessed by an object due to its position.
When kinetic energy (K.E) = 0
M.A = P.E
Thus, it is possible because the rubber ball has mechanical energy which is equal to potential energy.
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1. Explain how this picture is an example of kinetic energy.
2. What factors affect the energy of the ball?
3. What change could be made to give the ball more energy?
Answer:
1. when in motion(moving) it is Kinetic energy
2. it is kinetic when moving and potential when at rest
3. by constantly kicking or moving the ball
Explanation:
What is the wavelength (in meters) of a .44 magnum bullet (20.0 grams) travelling at at 450.0 m 5-1? Remember that 1 Joule = 1 kg m? s? 1) 9.94 x 10-24 m 2) 1.49 x 10-29 m 3) 7.36 x 10-95 m O4) 1.36 x 104 m 5), 7.36 x 10-38 m
The wavelength of a .44 magnum bullet (20.0 grams) travelling at 450.0 m/s can be calculated using the formula wavelength related to mass and velocity which gives a result of \(7.36 \times 10^{-29} m\). Therefore, the correct answer is option(3).
According to de Broglie's wavelength equation,
λ = h/mv = h/p
Where,λ = wavelength, h = Planck's constant, m = mass of the object, v = velocity of the object, p = momentum of the object.
Given that, Mass of the bullet, m = 20.0 g = 0.020 kg
Velocity of the bullet, v = 450.0 m/s
Momentum of the bullet, p = mv = 0.020 kg × 450.0 m/s = 9.00 kg m/s
Now, using the equation for wavelength we can find:
\(\lambda = h/p \\= \dfrac{6.626 \times 10^{-34} J s}{ 9.00 kg m/s} \\= 7.362 \times 10^{-35} m\)
Therefore, the wavelength (in meters) of a .44 magnum bullet (20.0 grams) traveling at 450.0 m/s is \(7.36 \times 10^{-35} m\)
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A thin 6. 5-kg wheel of radius 34 cm is weighted to one side by a 1. 30-kg weight, small in size, placed 23 cm from the center of the wheel. (a) Calculate the position of the center of mass of the weighted wheel. (b) Calculate the moment of inertia about an axis through its CM, perpendicular to its face
A thin 6. 5-kg wheel of radius 34 cm is weighted to one side by a 1. 30-kg weight, small in size, placed 23 cm from the center of the wheel. The position of the center of mass of the weighted wheel is 0.026 m. The moment of inertia about an axis through its CM, perpendicular to its face 0.925 kg*m^2
(a) To find the position of the center of mass of the weighted wheel, we need to calculate the distance of the center of mass from the center of the wheel. We can use the formula:
x_cm = \((m_1 * x_1 + m_2 * x_2) / (m_1 + m_2)\)
where \(x_1\) and \(m_1\) are the position and mass of the wheel, \(x_2\) and \(m_2\) are the position and mass of the weight.
Substituting the values, we get:
x_cm = (\(6.5 kg * 0 + 1.3 kg * 0.23\) m) / (6.5 kg + 1.3 kg)
= 0.026 m
Therefore, the center of mass of the weighted wheel is 0.026 m away from the center of the wheel.
(b) To calculate the moment of inertia about an axis through its CM, perpendicular to its face, we can use the parallel axis theorem:
I = \(I_cm + m*d^2\)
where I_cm is the moment of inertia about an axis through the center of mass, m is the total mass of the system, and d is the distance between the center of mass and the axis of rotation.
The moment of inertia of a thin disk about an axis through its center is:
I_cm = \((1/2)mr^2\)
Substituting the values, we get:
d = 0.034 m - 0.026 m = 0.008
I = \((1/2)6.5 kg(0.34 m)^2 + 1.3 kg*(0.008 m)^2\)
= \(0.925 kg*m^2\)
Therefore, the moment of inertia of the weighted wheel about an axis through its CM, perpendicular to its face, is \(0.925 kg*m^2.\)
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What does the phrase "1 meter per second per second" means? A. The velocity of an object can increase by 1 meter per second, for every minute of time measured. B. The velocity of an object can increase by 1 meter per second, for every second of time measured. C. The velocity of an object can increase by 1 meter per second.
Explanation:
"1 meter per second per second" means acceleration of an object. It is equal to the rate of change of velocity. Its SI unit is \(m/s^2\).
It is simply given by :
\(a=\dfrac{dv}{dt}\)
dv is change in velocity
dt is small interval of time
"1 meter per second per second" means that the velocity of an object can increase by 1 meter per second.
thermal energy is transferred between objects only when they have different ______.
Thermal energy is transferred between objects only when they have different temperatures.
The movement of atoms and molecules within a substance is a form of energy known as thermal energy.
When two objects are in contact, or even in proximity, the atoms and molecules in the hotter object collide with those in the colder object.
Because of these effects, a portion of the kinetic energy from the more sizzling object is moved to the colder object, raising the temperature of the previous and bringing down the temperature of the last option.
A material's thermal conductivity — an estimation of how well it moves heat — decides how rapidly heat is moved between various sorts of materials.
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Instructions: Answer the following questions in the space provided. Be sure to write your responses in complete sentences.
A father pushes his daughter and son on a sled down a hill.
Part A: Other than the force exerted by the father pushing the sled, identify two additional forces that act on the sled as it travels from the top of the hill to the bottom. (2 pts)
Part B: Explain how each force you identified in Part A will affect the motion of the sled. (2 pts)
a) Two other forces that act on thee sled are the weight of the daughter and the drag force
b) The drag force slows down the sled while the weight presses it down.
What is motion?We know that motion is the result of the action of unbalanced forces. From the Newton's third law, we know that if the forces that are acting on an object are balanced that the object is not going to move from its state of rest.
In this case, we are told that a father pushes his daughter and son on a sled down a hill. The fact that the led is moving is due to the fact that there are forces that are acting on the sled.
The forces that are acting on the sled apart from the force that was applied in pushing the sled is the drag force and the weight of the son.
The drag force would determine how fast that the sled would move because it acts in opposition to the forward force and tries to slow down the sled as it is moving. The weight of the son does press the sled downwards.
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A student makes up 2 l of a 3.0 m aqueous solution of hbr. to this solution she adds 1 l of a 4 m naoh solution. what is the ph of the resulting solution?
since the concentration of Br- ions is equal to the concentration of Na+ ions, the solution will be neutral overall, The resulting solution will have a neutral pH
To find the pH of the resulting solution, we need to consider the reaction between HBr and NaOH. HBr is a strong acid and NaOH is a strong base, so they will react to form water and a salt.
First, let's find the amount of moles of HBr and NaOH used in the solution.
In 2 liters of 3.0 M HBr solution, the number of moles of HBr is:
2 L x 3.0 mol/L = 6.0 mol HBr
In 1 liter of 4.0 M NaOH solution, the number of moles of NaOH is:
1 L x 4.0 mol/L = 4.0 mol NaOH
Since HBr and NaOH react in a 1:1 ratio, the limiting reagent is NaOH because it is present in a lesser amount (4.0 mol).
The reaction between HBr and NaOH can be represented as:
HBr + NaOH → H2O + NaBr
In this reaction, NaOH completely reacts with HBr to form water (H2O) and sodium bromide (NaBr).
Now, let's calculate the concentration of the resulting solution:
The total volume of the resulting solution is 2 L + 1 L = 3 L.
The number of moles of NaBr formed is also 4.0 mol, which means the concentration of NaBr in the resulting solution is:
4.0 mol / 3 L = 1.33 M NaBr
Since NaBr is a salt, it will dissociate into Na+ and Br- ions in water. Since NaBr is a strong electrolyte, it will completely dissociate.
So, in the resulting solution, the concentration of Na+ ions is also 1.33 M, and the concentration of Br- ions is also 1.33 M.
To find the pH, we need to consider the hydrolysis of the Br- ions. Since Br- is the conjugate base of a strong acid (HBr), it is a weak base.
The hydrolysis of Br- in water can be represented as:
Br- + H2O → HBr + OH-
This reaction generates hydroxide ions (OH-) in the solution, which makes it basic.
However, since the concentration of Br- ions is equal to the concentration of Na+ ions, the solution will be neutral overall.
Conclusion in one line: The resulting solution will have a neutral pH.
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3.00 m^3 of water is at 20.0°C.
If you raise its temperature to
60.0°C, by how much will its
volume expand?
Water
ß = 207•10-6C-1
(Unit = m^3)
Answer:
9m^3
Explanation:
Given data
volume v1= 3m^3
volume v2= ???
Temperature T1= 20.0°C.
Temperature T2= 60.0°C.
Applying the relation for temperature and volume
V1/T1= V2/T2
substitute
3/20= V2/60
3*60= V2*20
180= 20*V2
180/20= V2
V2= 9m^3
Hence the final volume is 9m^3
what is the Ramsar convention?
a 1200-kg ferryboat is moving south at 20 m/s. What is the magnitude of its momentum?
Answer: 24000 kg*m/s South
Explanation:
Momentum = mass*velocity
Momentum = 1200kg*20 m/s
Momentum = 24000 kg*m/s South
The momentum of the 1200 kg ferryboat moving with a velocity of 20 m/s is 24000 kg m/s to the south.
What is momentum?Momentum is the ability with which a force can make a body moves faster. Momentum in physics is the product of velocity and mass of the body.
Hence, p = mv and the unit is kg m/s.
Momentum is a vector quantity having both magnitude and direction. Momentum have both linear and angular components where the angular momentum is the product of radius of the circular path and linear momentum.
Given that, mass of the ferryboat = 1200 Kg
velocity = 20 m/s
momentum = 1200 kg × 20 m/s
= 24000 kg m/s
Therefore, the momentum of the ferryboat is 24000 kg m/s.
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The device that is made up of many single slits that diffract light and form a diffraction pattern , is called
Gọi là máy quang phổ kế
That's a diffraction grating.
You have viewed multiple unknown astronomical objects in this lab activity. In all tests, what was your test variable (independent variable)?
The amount of an element in each object
The type of elements in each spectrum
The astronomical object viewed by the spectrometer
Answer:
Could you give information about the lab
Explanation:
Answer:
The spectrum of each astronomical object
Explanation:
I took the test and got it right
you experience night-time when group of answer choices the side of the earth you occupy is facing away from the sun. the earth revolves 90 degrees in its orbit. the earth's axis precesses. the moon blocks the sun's light.
Nighttime occurs when the side of the Earth occupied by humans is facing away from the Sun. This is due to the Earth’s rotation, which causes one full rotation every 24 hours.
What is rotation of earth?The rotation of Earth is the rotation of the planet around its own axis, which is the imaginary line drawn from its North Pole to the South Pole. This rotation moves the Sun, stars and other celestial bodies across the sky. The rotation of Earth also causes the day and night cycle. The Earth's rotation is an important factor in the stability of the planet, as it helps keep the oceans, atmosphere and landmasses in balance.
Nighttime occurs when the side of the Earth occupied by humans is facing away from the Sun. This is due to the Earth’s rotation, which causes one full rotation every 24 hours. This is in contrast to the Earth’s orbit around the Sun, which causes the year cycle. The Earth’s axis of rotation also precesses, or slowly changes orientation in space over time, making the length of day and night slightly different over long periods of time. Additionally, the Moon is able to block out the Sun’s light, creating a lunar eclipse. This gives people on Earth a unique view of the Sun being blocked out by the Moon. This is one of the most spectacular sights in the night sky.
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HELP ME ASAP PLZ!
What is the relationship between an electromagnetic wave and the vibrations of the electric and magnetic fields it moves through.
The weight of a cuboid box is 288 N. Find its mass.
Answer:
29.39 kg
Explanation:
From the question,
W = mg...................... Equation 1
Where W = weight of the cuboid box, m = mass of the cuboid box, g = acceleration due to gravity.
make m the subject of the equation
m = W/g.................. Equation 2
Given: W = 288 N
Constant: g = 9.8 m/s²
Substitute these values into equation 2
m = 288/9.8
m = 29.39 kg
An astronaut on a distant planet wants to determine its acceleration due to gravity. The astronaut throws the rock straight up with a velocity of + 15 m/s and measures a time of 20.0 seconds before the rock returns to his hand. What is the acceleration (magnitude and direction) due to gravity on this planet?
The acceleration of the rock thrown with the velocity of 15 m/s and taking 20 seconds to come back is 2.97 \(m/s^2\), and the direction of acceleration is downward.
What is Velocity?When an item is moving, its velocity indicates how quickly its location is changing as seen from a specific point of view and as measured by a specific unit of time. When time is constant, speed and distance are directly proportional, when the distance is constant,
Given:
The velocity of the rock, v = 15 m/s,
The time taken to go and return t = 20 seconds,
Now, calculate the distance traveled by the rock,
d = v/t
d = 15/10 (Time taken to go upward is half of the total time)
d = 1.5 meters
So, calculate the acceleration by the second equation of motion,
\(s = vt + 1/2at^2\)
Substitute the values,
\(1.5 = 15*10 + 1/2 * a * 10^2\)
\(a = -2.97 \ m/s^2\)
Therefore, the acceleration of the rock thrown with the velocity of 15 m/s and taking 20 seconds to come back is 2.97 \(m/s^2\) And the direction of acceleration is downward.
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N A siren emits a sound of frequency 1. 44 × 103 Hz when it is stationary with respect to an observer. The siren is moving away from a person and toward a cliff at a speed of 15 m/s. Both the cliff and the observer are at rest. Assume the speed of sound in air is 343 m/s. What is the frequency of the sound that the person will hear a. Coming directly from the siren and b. Reflected from the cliff?
To calculate the frequency of the sound heard by the person, we need to consider the Doppler effect, which describes the change in frequency due to the relative motion between the source of the sound and the observer.
The formula for the observed frequency due to the Doppler effect is given by:
f_observed = f_source * (v_sound + v_observer) / (v_sound + v_source)
where:
f_observed is the observed frequency,
f_source is the source frequency,
v_sound is the speed of sound in air, and
v_observer and v_source are the velocities of the observer and the source, respectively.
Given:
Source frequency (f_source) = 1.44 × 10^3 Hz
Speed of sound in air (v_sound) = 343 m/s
Velocity of the siren (v_source) = 15 m/s
Velocity of the observer (v_observer) = 0 m/s (since the observer is at rest)
(a) Frequency of the sound directly from the siren:
For this scenario, the observer and the siren are moving away from each other. Substituting the given values into the Doppler effect formula:
f_observed = 1.44 × 10^3 * (343 + 0) / (343 + 15)
(b) Frequency of the sound reflected from the cliff:
In this case, the sound waves are reflected by the cliff, resulting in a change in direction. The relative motion between the observer and the reflected sound is the sum of their individual velocities. Thus, we consider the observer's velocity as -15 m/s (since it's moving towards the observer).
f_observed = 1.44 × 10^3 * (343 + 0) / (343 - 15)
By performing the calculations, we can determine the frequencies of the sound heard by the person directly from the siren and reflected from the cliff.
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the temperature of the water is less than the temperature of its surroundings. Explain in terms of the particles of the water, why this is so
A portion size is always equivalent to the serving size listed on the label. A. True B. False
Answer:
Hi, there your answer is False
Explanation:
Describe the 2 main steps in protein synthesis, along with the key molecules involved in the process.
The two main steps in protein synthesis , along with the key molecules involved in the process include the following below:
Transcription -DNA is converted to mRNATranslation - mRNA is converted to protein.What is Protein?This is referred to as a biomolecule which contains amino acids and it is necessary for the growth and repair of worn out tissues in the body. They are broken down in the body by enzymes known as protease and are easily denatured by heat and chemicals.
In the process of transcription, the gene is converted into a template molecule called messenger RNA (mRNA) and involves the transfer of genetic materials.
Translation on the other hand involves protein synthesis in the ribosome in which the mRNA is converted into protein thereby making it the correct choice.
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A certain car is capable of accelerating at a rate of 0.59 m/s2. how long does it take for this car to go from a speed of 50 mi/h to a speed of 57 mi/h?
A certain car with an accelerating rate of 0.59 m/s2 will take 5.30 s to go from a speed of 50 mi/h to a speed of 57 mi/h
The formula for Uniformly varied rectilinear motion (UVRM) and procedure we will use to solve this exercise is:
t = (vf - vi) /a
Where:
vf = final velocityvi = initial velocityt = timea = accelerationInformation about the problem:
vi= 50 mi/h vf= 57 mi/ha= 0.59 m/s2t = ?By converting the velocity from mi/h to m/s, we get:
50 mi/h * (1609.34 m / 1 mi) * (1h / 3600 s) = 22.35 m/s
57 mi/h * (1609.34 m / 1 mi) * (1h / 3600 s) = 25.48 m/s
Applying the time formula, we have:
t = (vf - vi) /a
t = ( 25.48 m/s - 22.35 m/s) / 0.59 m/s2
t = 3.13 m/s /0.59 m/s2
t = 5.30 s
What is acceleration?It is a physical quantity that indicates the variation of velocity as a function of time, it is expressed in units of distance per time squared e.g.: m/sec2 ; km/h2
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arterial pressure in the pulmonary circulation is much lower than in the systemic circuit because of its proximaty to the heart (True/False)
False. The pulmonary circulation has lower arterial pressure compared to the systemic circuit due to lower resistance in the pulmonary blood vessels.
The proximity to the heart is not the determining factor for the pressure difference.
The pulmonary circulation is responsible for oxygenation and gas exchange in the lungs, which requires a lower pressure to facilitate efficient exchange of gases between the alveoli and the blood.
The pulmonary arteries receive oxygen-depleted blood from the right ventricle of the heart and distribute it to the lungs, where it gets oxygenated. The pulmonary veins then carry oxygenated blood back to the left atrium of the heart.
This lower pressure allows for optimal gas exchange without putting excessive strain on the delicate lung tissues.
In contrast, the systemic circulation supplies oxygenated blood to the body's organs and tissues, requiring higher pressure to overcome the resistance encountered in the systemic blood vessels.
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If a skateboarder is moving at 4 meters per second then changes its velocity to 10
meters per second over the course of 10 seconds what is the skateboards acceleration?
Answer:
i was doing this is it actually 0.6
Explanation:
;D
The acceleration of the skateboard from its initial velocity to the final velocity over the given time is 0.6m/s².
What is Motion?Motion is simply the change in position of an object over time.
From the First Equation of Motion;
v = u + at
Where v is final velocity, u is initial velocity, a is acceleration and t is time elapsed.
Given the data in the question;
Initial velocity u = 4m/sFinal velocity v = 10m/sTime elapsed t = 10sAcceleration of the skateboard a = ?To determine the acceleration of the skateboard, we substitute our given values into the expression above.
v = u + at
10m/s = 4m/s + ( a × 10s)
( a × 10s) = 10m/s - 4m/s
a × 10s = 6m/s
a = 6m/s ÷ 10s
a = 0.6m/s²
Therefore, the acceleration of the skateboard from its initial velocity to the final velocity over the given time is 0.6m/s².
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A humpback whale dove beneath the ocean's surface, and 310 seconds later it sang to
another whale that was 1,800 meters away. The song's sound wave traveled at a constant
velocity of 1,500 meters per second toward the other whale. How much time did it take the
sound wave to travel from one whale to the other?
The sound wave took 1.2 seconds to travel from one whale to the other.
Velocity is a physical quantity that describes the rate of change of an object's position with respect to time and includes both the speed and direction of motion. It is a vector quantity, meaning it has both magnitude and direction and is typically measured in meters per second (m/s) or other appropriate units.
The time it took for the sound wave to travel from one whale to the other can be calculated using the formula:
time = distance/velocity
In this case, the distance between the whales is 1,800 meters and the velocity of sound in water is 1,500 meters per second. Therefore:
time = 1,800 meters / 1,500 meters per second
time = 1.2 seconds
Hence, The distance between the two whales was covered by the sound wave in 1.2 seconds.
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what is formula for distance
Answer:
this is formula
Explanation:
A snow skier slowing to a stop after skiing down a mountain demonstrates the effects of what type of friction?
Answer:
I believe the answer is sliding friction
what are non-metals?
explain briefly
Answer:
In chemistry, a nonmetal is a chemical element that is mechanically weak in its most stable form, brittle if solid, and usually gains or shares electrons in chemical reactions. There is no universal agreement on which elements are nonmetals; the numbers generally range from fourteen to twenty-three, depending on the criterion or criteria of interest.
Answer:
Non-metals are those which lack all the metallic attributes. They are good insulators of heat and electricity. They are mostly gases and sometimes liquid. Some they are even solid at room temperatures like Carbon, sulphur and phosphorus.
Explanation:
Hydrogen, hydrogen, chlorine, fluorine, carbon, nitrogen, arsenic, phosphorus, selenium are examples of non-metal.
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n2 Find a linear homogeneous recurrence relation with constant coefficients that the sequence An = (n-3) (2") + NEN 2n satisfies. Do not forget to specify initial values.
The linear homogeneous recurrence relation with constant coefficients that the sequence is: An = -(-1)n + (3)n or An = (1)n + (3)n
The sequence An = (n-3)(2n) + n(2n) satisfies the linear homogeneous recurrence relation with constant coefficients. In order to prove this, we need to first find the general formula of the sequence.
The formula can be found by replacing n with n+1 as follows:
An+1 = (n+1-3)(2n+2) + (n+1)(2n+2)
An+1 = n(2n+4) + (n+1)(2n+2)
An+1 = 2n² + 4n + 2n² + 4n + n + 2n + 2
An+1 = 4n² + 7n + 2
The characteristic equation of the linear homogeneous recurrence relation is given by:
r² - 2r - 3 = 0
Solving this quadratic equation, we get:r = -1 or r = 3
Hence, the general formula of the sequence is given by:An = A(-1)n + B(3)n
Now, we need to find the values of A and B using the initial values of the sequence. The first two terms of the sequence are given by:
A0 = -6 and A1 = 2
Substituting these values in the general formula, we get:
-6 = A + B2 = -A + 3B
From the above two equations, we can solve for A and B to get:
A = -1 and B = 1
Hence, the linear homogeneous recurrence relation with constant coefficients that the sequence An = (n-3)(2n) + n(2n) satisfies is given by:
An = -(-1)n + (3)n or An = (1)n + (3)n
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