Degeneracy pressure stops the crush of gravity in all the following except:_____.A) a brown dwarf.
B) a white dwarf.
C) a neutron star.
D) a very massive main-sequence star.
E) the central core of the Sun after hydrogen fusion ceases but before helium fusion begins.

Answers

Answer 1

Degeneracy pressure stops the crush of gravity in all the following except a brown dwarf. The correct option is a.

What is Degeneracy pressure?

Electron degeneracy pressure is a subset of the broader phenomenon of quantum degeneracy pressure.

The Pauli exclusion principle prevents two identical half-integer spin particles from occupying the same quantum state at the same time.

Electron degeneracy pressure, in particular, is what protects white dwarfs from gravitational collapse, as well as the Chandrasekhar limit (the maximum mass a white dwarf can attain) arises naturally as a result of electron degeneracy physics.

Thus, the correct option is a.

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Related Questions

A man is inside an airplane and walking toward the back of the plane at 7 m/s. The plane is flying West at 245 m/s. What is the speed and direction of the plane relative to the man?



7 m/s East

238 m/s, East

252 m/s West

238 m/s, West

Answers

Answer:

7 m/s East

Explanation:

The speed of the man relative to the plane is given as 7 m/s. Given that he's walking in the corridor of the plane, this is his speed relative to the plane. Since he's moving to the back of the plane, and the aircraft is headed to west, the man's direction relative to the plane is East.

where is the energy coming from that caused the uneven heating of the earth?

Answers

Uneven heating of a earth's surface is what generates wind. The sub - teams of water & land to pay a planet load quickly it takes the sun's heat. The low wind cycle is just 1 instance of this varied warmth.

Why does heating occur unevenly?

The air in your home, the air in our heating system, and insufficient insulation are the three main causes of uneven heating, respectively. The following causes are more specific: airflow restrictions between the vents and the furnace. ducting that is defective or leaky. an insufficient heating system.

What does uneven land heating entail?

Near the equator, the land warms up more quickly in the summer, and the majority of time, the temperature of a land is greater than that of oceans. Heat rises and warms the air above the land. Due to this, winds from the oceans blow in a landward direction. Monsoon winds are what they are.

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. Reliability engineers are interested in systems having components con- nected in parallel. The phrase "in parallel" is defining as the situation that the system is functioning (reliable) if at least one of the compo- nents is functioning. In this problem, we consider a four-engine aircraft.
Let K be the number of functioning components in a parallel system, in this case, the number of functioning engine on the aircraft.
(a) What is the support of K?
(b) What is the set of the event that the aircraft is functioning?
(c) Assuming that the four engines are functioning independently, each with probability p, show that the probability of the aircraft is functioning, system reliability, equals

Answers

(a) The support of K can be given by {0, 1, 2, 3, 4}.

(b) The set of events in which the aircraft is functioning can be given as follows: {K ≥ 1}, which means the aircraft is functioning if and only if at least one of its engines is functioning properly.

(c) Let's assume that the probability of each engine functioning properly is given by p. So, the probability of any particular engine malfunctioning or not functioning properly is (1 - p).

Since the aircraft is functioning if and only if at least one of its engines is functioning properly, the probability of system reliability can be calculated using the following formula:

P(K ≥ 1) = 1 - P(K = 0)

Since each engine functions independently of each other, the probability of each engine malfunctioning can be multiplied together. Thus, we have:

P(K = 0) = (1 - p)^4

Then,

P(K ≥ 1) = 1 - P(K = 0)

= 1 - (1 - p)^4

Therefore, the probability of the aircraft functioning, which represents system reliability, is given by 1 - (1 - p)^4.

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Calculate the kinetic energy in joules of a ball of mass 40g moving at a velocity of 4 metres per second​

Answers

Given : A ball of mass 40 g moving at a velocity of 4 m/s.
To find : Calculate the kinetic energy in joules ?
Solution :
The kinetic energy formula is given by,

where, v is the velocity v=4 m/s
m is the mass m=40 g
Convert g into kg,



Substitute the values,



Therefore, the kinetic energy is 0.32 Joules.

Energy sources can be placed in two categories: renewable and nonrenewable. How do you think these two energy sources differ from each other?

Answers

Answer:

Renewable energy sources can come again, but nonrenewable is gone forever. For example, coal and gasoline are both nonrenewable.

Explanation:

12) Driving home from school one day, you spot a ball rolling out into the street (FIGURE 5-27). You brake for 1.20 s, slowing your 950-kg car from 16.0 m>s to 9.50 m>s. What was the average forceexerted on your car during braking and How far did you travel while braking?

12) Driving home from school one day, you spot a ball rolling out into the street (FIGURE 5-27). You

Answers

We are given the following information

Mass of car = 950 kg

Initial speed of car = 16.0 m/s

Final speed of car = 9.50 m/s

Time = 1.20 s

The average force exerted on the car during braking can be found using Newton's 2nd law of motion

\(F=m\cdot a\)

Where m is the mass of the car and a is the acceleration of the car.

The acceleration of the car is given by

\(\begin{gathered} a=\frac{v_f-v_i}{t} \\ a=\frac{9.50-16.0}{1.20} \\ a=-5.4167\; \; \frac{m}{s^2} \end{gathered}\)

The negative sign indicates deacceleration since the car is stopping.

So, the force is

\(\begin{gathered} F=m\cdot a \\ F=950\cdot5.4167 \\ F=5145.865\; \; N \end{gathered}\)

Therefore, an average force of 5145.865 N was exerted on your car during braking.

The distance traveled by the car while braking can be found as

\(s=v_i\cdot t+\frac{1}{2}\cdot a\cdot t^2\)

Let us substitute the given values

\(\begin{gathered} s=16.0\cdot1.20+\frac{1}{2}\cdot(-5.4167)\cdot(1.20)^2 \\ s=19.20-3.90 \\ s=15.3\; m \end{gathered}\)

Therefore, the car traveled a distance of 15.3 m while braking.

Hello, I am trying to solve this physics question, thanks.

Hello, I am trying to solve this physics question, thanks.

Answers

When they were falling, their acceleration is equal to the gravity acceleration.

When they started stopping, the time required to stop is 1.5 seconds, that is, 3 times less than the time accelerating.

Since the change in velocity when falling and when stopping is the same (same magnitude but opposite signal), the acceleration when stopping will be 3 times more than the acceleration when falling (because the change in velocity is the same and the time is 3 times less).

So we have:

\(\begin{gathered} a=-3g\\ \\ a=-3\cdot(-9.8)\\ \\ a=29.4\text{ m/s^^b2} \end{gathered}\)

Therefore the acceleration is 29.4 m/s².

when a weight w is hanging from a light vertical string, the speed of pulses on the string is v. if a second weight w is added without stretching the string, the speed of pulses on this string will now become. true or false?

Answers

It is false to say that speed of pulse remains v after adding the second weight w on the vertical string.

We know very well that speed of transverse wave v in a string is given by:

v=√T / √μ

where,

T represents the tension in the string

μ represents the linear mass density defined for the string

Now, in the given situation,

when weight is  hanging on light vertical string is W, speed of the wave v is :

v=√W / √μ ----(eq1)

On addition of  an additional weight of W, speed of the wave becomes v ' as :

v′ = √2W /√μ -----(eq2)

After comparing eq1 and eq2, we observe that

after addition of same amount of weight in the given light string, speed will increase by √2 times the previous speed.

Hence, the given statement is false.

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A sample of silty sand has a volume of 70 cm². At the natural moisture content it weighs 150.7 grams. The sample was then saturated with water and reweighed to a weight of 169.7 grams. The sample was drained by gravity until it reached a constant weight of 146.2 grams. The sample was then oven-dried at 105° C until it reached a constant weight of 139.7 grams. Assume the unit weight of water is 1 gram/cm'. Compute the following: a. water content under natural conditions b. volumetric water content under natural conditions c. saturation ratio under natural conditions d. porosity e. specific yield f. specific retention water content at saturation

Answers

Water content under natural conditions is 21.49%, Volumetric water content under natural conditions is 21.49 cm³/cm³, Saturation ratio under natural conditions is 1.231, Porosity is 99.57% and Specific yield is 9.29% and specific retention water content at saturation is 85.57%.

Volume of soil (V) = 70 cm³

Weight of natural soil (Wn) = 150.7 g

Weight of saturated soil (Ws) = 169.7 g

Weight of drained soil (Wd) = 146.2 g

Weight of oven-dried soil (Wod) = 139.7 g

Unit weight of water (γw) = 1 g/cm³

a. Water content under natural conditions:

Water content = (Ws - Wod) / Wod × 100%

Water content = (169.7 g - 139.7 g) / 139.7 g × 100%

Water content = 21.49%

b. Volumetric water content under natural conditions:

Volumetric water content = (Water content / γw) × 100%

Volumetric water content = (21.49% / 1 g/cm³) × 100%

Volumetric water content = 21.49 cm³/cm³

c. Saturation ratio under natural conditions:

Saturation ratio = (Ws - Wd) / (Wd - Wod)

Saturation ratio = (169.7 g - 146.2 g) / (146.2 g - 139.7 g)

Saturation ratio = 1.231

d. Porosity:

Porosity = (V - (Wod / γw)) / V × 100%

Porosity = (70 cm³ - (139.7 g / 1 g/cm³)) / 70 cm³ × 100%

Porosity = 99.57%

e. Specific yield:

Specific yield = (Wd - Wod) / (V × γw) × 100%

Specific yield = (146.2 g - 139.7 g) / (70 cm³ × 1 g/cm³) × 100%

Specific yield = 9.29%

f. Specific retention water content at saturation:

Specific retention = (Wd - Wod) / (Ws - Wod) × 100%

Specific retention = (146.2 g - 139.7 g) / (169.7 g - 139.7 g) × 100%

Specific retention = 85.57%

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Help please like actually someone help me PLEASE

Help please like actually someone help me PLEASE

Answers

The final speed of the motorcycle is: 67 m/sec

What is speed?

Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route. In other words, although velocity is a vector, speed is a scalar quantity.

Given that,

initial speed of the motorcycle, u=25 m/sec

Acceleration of the motorcycle, a = 7 m/sec²

According to the equation of motion,

v = u + at

v = 25 m/sec + (7m/sec²) × (6 sec)

v = 67 m/sec

Thus, final speed of the motorcycle is: 67 m/sec

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A motorist is speeding along at 33m/s when he sees a squirrel on the road 200 meters in
front of him. He tries to stop, but it takes 12 seconds for his car to stop
(a) What is the acceleration of the car? (assume acceleration was constant)
(b) Does the squirrel survive?
(c) How fast was the car moving at 100 meters?​

Answers

a) the acceleration of the car = -2.75 m/s

b) d = 198 meters. Therefore, the squirrel would survive.

c) the car moving at 100 meters with a speed of 23.22m/s

What is acceleration ?

acceleration: the rate at which the speed and direction of a moving object vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates. Even if the speed is constant, motion on a circle accelerates because the direction is always shifting. Both effects contribute to the acceleration for all other motions.

Use the kinematic equation to solve for the acceleration:

v = u +at

v = final velocity

u = initial velocity

a = acceleration

t = time

In this instance, the final velocity is 0 because he comes to a stop. We can solve for the acceleration by plugging in the given values:

0 = 33 + (12)a

0 = 33 + 12a

-33 = 12a

-33 / 12 = a  --> a = -2.75 m/s²

b) Find the amount of distance necessary to stop. Use the formula:

v^2 = u^2 + 2ad

d = distance

Plug in the values:

0² = 33² + 2(-2.75 · d)

0 = 1089 - 5.5d

-1089 = -5.5d

d = 198 meters. Therefore, the squirrel would survive.

c)

Find the velocity at 100 meters by using the same formula as before:

v^2 = u^2 + 2ad

However, in this instance, we are solving for the final velocity. Plug in the given points to solve:

vf² = 33² + 2(-2.75 · 100)

vf² = 1089 + (-550)

vf² = 539

vf = √539

vf ≈ 23.22 m/s.

the car moving at 100 meters with a speed of 23.22m/s

a) the acceleration of the car = -2.75 m/s

b) d = 198 meters. Therefore, the squirrel would survive.

c) the car moving at 100 meters with a speed of 23.22m/s

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I need help asap :>

I need help asap :>

Answers

Answer:

\(\huge\boxed{\sf v = 0.75\ m / s}\)

Explanation:

Given Data:

Wavelength = λ = 0.25 m

Frequency = f = 3 Hz

Required:

Speed = v = ?

Formula:

v = fλ

Solution:

v = (3)(0.25)

v = 0.75 m / sec

\(\rule[225]{225}{2}\)

Hope this helped!

~AH1807

According to Newton, doubling the distance between two interacting objects a. divides by 2 the gravitational force between them b. multiplies by 2 the gravitational force between them c. divides by 4 the gravitational force between them d. multiplies by 4 the gravitational forcehetween them

Answers

Answer:

c. divides by 4 the gravitational force between them

Explanation:

Newton's law of gravity says:

 F1 = G(m1*m2)/r^2

where G is the gravitational constant, m1 and m2 are the masses of objects 1 and 2, and r is the distance between the two masses.

Doubling the distance would result in:

The new distance would be = 2r

F2 = G(m1m2)/(2r)^2

F2 = G(m1m2)/4r^2

F2 = (1/4)(G(m1m2)/r^2)

F2 = (1/4)F1

The new force, F2, at twice the distance is 1/4 that of the original force, F1.

Frank is nearsighted and his glasses require a prescription of -1. 5 D. One day he can’t find his
glasses, but he does find an older pair with a prescription of -1. 0 D. What is the most distant
object that Frank can focus on while wearing this older pair of glasses?

Answers

The most distant object that Frank can focus on while wearing an older pair of glasses with a prescription of -1.0 D is 20 cm away from his eyes.

Frank's prescription for his regular glasses is -1.5 D, which means that the lenses correct for the refractive error in his eyes so that he can see distant objects clearly. If he wears an older pair of glasses with a prescription of -1.0 D, this means that the lenses are not as strong as his regular glasses and do not correct his refractive error as well.

To determine the most distant object that Frank can focus on while wearing the older pair of glasses, we can use the formula:

1/f = 1/di - 1/do

where f is the focal length of the lens, di is the distance between the lens and the object, and do is the distance between the lens and the image formed by the lens.

Since we know that the prescription of the older glasses is -1.0 D, we can use the formula:

f = 1/p

where p is the power of the lens in diopters.

Thus, f = 1/-1.0 D = -1.0 m⁻¹

Assuming that Frank's near point (closest distance he can see clearly without glasses) is 25 cm, we can set di = 0.25 m and solve for do:

1/-1.0 m⁻¹ = 1/0.25 m - 1/do

Simplifying the equation, we get:

do = 0.2 m or 20 cm

Therefore, the most distant object that Frank can focus on while wearing the older pair of glasses with a prescription of -1.0 D is 20 cm away from his eyes.

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A point charge of 5. 0 Ă— 10â€""7 C moves to the right at 2. 6 Ă— 105 m/s in a magnetic field that is directed into the screen and has a field strength of 1. 8 Ă— 10â€""2 T. What is the magnitude of the magnetic force acting on the charge? 0 N 2. 3 Ă— 10â€""3 N 23 N 2. 3 Ă— 1011 N.

Answers

The magnitude of the magnetic force acting on the charge which moves to the right is 0 N.

Given to us,

the charge \(q\) =  \(5\times 10^{-7}\) C,

the velocity \(v\) = \(2.6\times 10^5\)  m/sec,

the magnetic field \(B\) = \(10^{-2}\) T,

angle between the direction of v and B \(\theta\) = 0,

Magnetic force is as important as the electrostatic or Coulomb force. The magnitude of the magnetic force F on a charge q moving at a velocity of v in a magnetic field of strength B is given by

\(\begin{aligned}F&=qvB\ sin\Theta\\&= 5\times10^{-7}\times2.6\times10^5\times10^{-2} \times sin(0)\\&= 0\ N\\\end{aligned}\)

Hence, the magnitude of the magnetic force acting on the charge which moves to the right is 0 N

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Express the answer to 6.51 x 107
divided by7.61 x 10
in scientific notation

Answers

Answer:

Below

Explanation:

\(6.51\times 10^7 \div 7.61 \times 10\\\\\frac{6.51\times \:10^7}{7.61\times \:10}\\\\\mathrm{Multiply\:the\:numbers:}\:7.61\times \:10=76.1\\=\frac{10^7\times \:6.51}{76.1}\\\\6.51\times \:10^7=65100000\\\\=\frac{65100000}{76.1}\\\\\mathrm{Divide\:the\:numbers:}\:\frac{65100000}{76.1}=855453.35085\dots \\=855453.35085\\\\= 855.4533085 \times 10^3\)

An electric light bulb is 80% efficient. if it uses 300j of electrical energy how much light energy will it produce ? what happens to the rest of the energy ?

Answers

The energy output of an electric light bulb is 240 j.

Electricity is a form of what kind of energy?

The energy that whirling electrons in an electric conductor carry is known as electrical energy. It is a popular and practical source of energy. Lightning is an instance. Electricity is created by converting various other types of energy as well.

How is efficiency measured mathematically?

Efficiency is calculated by dividing output by input, and you may convert this value to a percentage by multiplying it by 100. Whether it is used to measure energy output or machine efficiency, it is utilized in a variety of ways to measure both work and energy.

According to question

efficiency = (useful energy out ÷ total energy in) × 100 (for a percentage efficiency)

        80   = (useful energy out ÷ 300)×100

           80   = useful energy out ÷3

              useful energy out = 240 j

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Negative charges can move from one insulator to another.
True
False

Answers

Answer:

True

Explanation:

Because in atom the negative charge become lose or gain.


During a race, a runner runs at a speed of 6 m/s. Four seconds later, she is running at a speed of 14 m/s. What is the runner's
acceleration?
A. 0.6 m/s2
B. 1.0 m/s2
C. 1.7 m/s
D. 2.0 m/s2
NEED ASAP.
WILL GIVE BRAINLIEST!

Answers

Answer:

D. 2 m/s²

Step-by-step explanation:

Initial speed of the runner (u) = 6 m/s

Final speed of the runner (v) = 14 m/s

Time taken (t) = 4 s

By using equation of motion, we get:

\( \bf \longrightarrow v = u + at \\ \\ \rm \longrightarrow 14 = 6 + 4a \\ \\ \rm \longrightarrow 14 - 6 = 6 - 6 + 4a \\ \\ \rm \longrightarrow 8 = 4a \\ \\ \rm \longrightarrow 4a = 8 \\ \\ \rm \longrightarrow \dfrac{4a}{4} = \dfrac{8}{4} \\ \\ \rm \longrightarrow a = 2 \: m {s}^{ - 2} \)

\( \therefore \) Acceleration of the runner (a) = 2 m/s²

For a series circuit, as lights are added, the voltage across each bulb increases/ decreases/ remains the same ?

For a series circuit, as lights are added, the current across each bulb increases/ decreases/ or remains the same ?


Answers

For a series circuit, as lights are added, the current across each bulb decreases.  

the world in the solar system that is most active volcanically is: a. earth b. neptune c. io d. mars e. ganymede

Answers

Io is the planet in the solar system with the highest level of volcanic activity. Option c is Correct.

Io was given her name in honor of a Zeus-favored. Zeus attempted to conceal her from his envious wife, Hera, in the Greek tale by transforming her into a thing. One of the four Galilean satellites, Io was found by Simon Marius and Galileo Galilei in 1610.

The most volcanically active globe in the solar system is the moon Io. On the surface of Io, there are even lakes of molten silicate lava. As of today, we are aware that volcanoes can be located on Mercury, Venus, Earth, the Moon, Mars, and the moon Io of Jupiter. Only two of these bodies—Earth and Io—have active volcanoes at the moment.  Option c is Correct.

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Will most likely cause the formation of a Mountain

A. Divergent boundary

B. Convergent boundary

C. Transform boundary

Answers

Answer:

Convergent boundaries. When two plates collide and one is pushed over the other, forming a mountain.

How many valence electrons does the hydrogen and oxygen have in the following picture?

How many valence electrons does the hydrogen and oxygen have in the following picture?

Answers

Answer:

can u make the picture less blurry pls

Explanation:

as shown, a 2 kg mass lies on a horizontal rough surface, while a 1 kg mass hangs vertically. the string is massless and pulley frictionless and massless. what minimum coefficient of friction will keep the blocks at rest?

as shown, a 2 kg mass lies on a horizontal rough surface, while a 1 kg mass hangs vertically. the string

Answers

In a frictionless and massless pulley system, the minimum coefficient of friction to keep the blocks at rest is 1.

How to determine minimum coefficient of friction ?

Let's assume that the 2 kg mass is on the left side and the 1 kg mass is on the right side. The forces acting on the 2 kg mass are its weight mg (directed downwards) and the friction force f (directed to the right). The forces acting on the 1 kg mass are its weight mg (directed downwards) and the tension in the string T (directed upwards).

Since the system is at rest, the net force on each mass must be zero. Therefore:

For the 2 kg mass: f = mgμ, where μ is the coefficient of friction.

For the 1 kg mass: T = mg.

Since the pulley is frictionless, the tension in the string must be the same on both sides. Therefore:

T = f.

Substituting T and f in terms of mg and μ:

mg = mgμ

μ = 1

Therefore, the minimum coefficient of friction needed to keep the blocks at rest is 1.

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Please help if possible!! Much love <3

Please help if possible!! Much love &lt;3

Answers

Newton's 2nd law of motion says:

Net force = (mass) · (acceleration) .

Newton didn't make up this law for his health.

Let's use it to answer this question about the car moving down the road.

Net force on the car = (car's mass) · (car's acceleration).

But the net force on the car is zero.  So we can write:

0 = (car's mass) · (car's acceleration).

Look at the right side of this equation.

Newton's law tells us that the product of the car's mass and the car's acceleration is zero.

That tells us that at least one of three things must be true.

Either 1). the car's mass is zero, or 2). the car's acceleration is zero, or 3). Newton was crazy.

We're pretty sure that 1). and 3). are false. The car's acceleration is zero.

What does this mean ? It means that the car's speed and direction are not changing.

That's exactly what Choice-B says.

What kind of acceleration occurs when an object speeds up?

Answers

Ans. positive acceleration

When an object is speeding up, the acceleration is in the same direction as the velocity. Thus, this object has a positive acceleration.

hen approaching a curve, it is best to: A. Search for possible collision traps and escape paths B. Stay close to the centerline if there is oncoming traffic C. Squeeze the clutch lever to slow down D. Shift to a higher gear

Answers

Squeezing the clutch lever to slow down is best to be done when approaching a curve and is denoted as option C.

What is Clutch?

This is a mechanical device which used in the engagement and disengagement of transmission system in a vehicle.

Slowing down will give the driver more time to maneuver the curves so as to prevent accident. This is why it is imperative to squeeze the clutch in such road condition.

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MATCH THE FOLLOWING

COLUMN A
1. A material used for making electro magnets
2. A device which is essential in an electric bell
3. A material which does not allow electric current to pass
4.
A magnetic device used for finding geographic directions
5. A device which makes use of heating effect of electricity.
6. A device which makes use of magnetic effect of electricity.
COLUMN B
telephones
soft iron
water geyser
electromagnet
Plastic wire
Magnetic needle​

Answers

Answer:

afrcrftftgyfygygygygygygyvyvuguvy5vyvycycy

shdhdggxshjwhwywsd dccefc


An object speeding up, an object slowing down, and an object changing direction are all examples of acceleration.
-True
-False

Answers

Answer: True

When an object is speeding up, the acceleration is in the same direction as the velocity. Thus, this object has a positive acceleration. In Example B, the object is moving in the negative direction (i.e., has a negative velocity) and is slowing down.

Write step by step solutions and justify your answers. Question 1: Evaluate a) (10 points) L {e+ (2t - 1)2 + sin(–3t) + cos 5t}. - b) (10 points) L-1 1 (s + 1)(s2 + 5 – 12) +- }

Answers

Evaluate

a) L{e+(2t - 1)² + sin(-3t) + cos(5t)}

To evaluate this Laplace transform, we'll use the basic Laplace transform properties and formulas.

Step 1: Apply the Laplace transform to each term separately.

L{e} = 1/s [Using the Laplace transform of the exponential function]

L{(2t - 1)²} = (2/s)² [Using the Laplace transform of (at + b)^n, where a, b are constants]

L{sin(-3t)} = -3/(s² + 9) [Using the Laplace transform of sin(at)]

L{cos(5t)} = s/(s² + 25) [Using the Laplace transform of cos(at)]

Step 2: Apply the linearity property of the Laplace transform to combine the individual transforms.

L{e+(2t - 1)² + sin(-3t) + cos(5t)} = L{e} + L{(2t - 1)²} + L{sin(-3t)} + L{cos(5t)}

= 1/s + (2/s)² - 3/(s² + 9) + s/(s² + 25)

= 1/s + 4/s² - 3/(s² + 9) + s/(s² + 25)

Therefore, the Laplace transform of the given expression is 1/s + 4/s² - 3/(s² + 9) + s/(s² + 25).

b) L^(-1) {1 / [(s + 1)(s² + 5 - 12)]}

To evaluate the inverse Laplace transform, we'll use partial fraction decomposition and the inverse Laplace transform formulas.

Step 1: Factorize the denominator.

(s + 1)(s² + 5 - 12) = (s + 1)(s² + 5 - 12)

= (s + 1)(s² + 4s - 7)

= (s + 1)(s + 7)(s - 1)

1 / [(s + 1)(s + 7)(s - 1)] = A / (s + 1) + B / (s + 7) + C / (s - 1)

For s^2 term: 0 = A + B + C

For s term: 0 = 6A - 6B + 8C

For constant term: 1 = -7A

From the third equation, A = -1/7. Substituting this into the second equation, we get -6/7 - 6B + 8C = 0, which simplifies to -6B + 8C = 6/7.

From the first equation, we get C = -A - B, which simplifies to C = 1/7 - B.

Substituting C into the equation -6B + 8C = 6/7, we have -6B

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