Find the volume for a rectangular prism whose base is 9 cm by 4 cm and is 9 cm tall.

Answers

Answer 1

Answer:

Explanation:  The Volume of rectangular prism is product of three dimensions,

Volume = Length*Width*Height  ............(1)

Given that,

Height = 9 cm

Length = 9 cm

Width = 4 cm

 Putting values in equation (1)

volume= 9*4*9 cm  

Therefore, Volume is 324 cm.


Related Questions

What is the distance I traveled to where I stopped by the turkeys? (RW) 2.5 miles

Answers

Answer:

 Find the following for path A in the diagram: (a) The.

Explanation:

I don't know

A string, 0.15 m long, vibrating in the n = 5 harmonic, excites an open pipe, 0.82 m long, into second overtone resonance. The speed of sound in air is 345 m/s. The distance between a node and an adjacent antinode, in the string, in mm, is closest to?
answer: 150 mm

Answers

The distance between a node and an adjacent antinode in the string is closest to 30 mm.

Determining the distance

The fundamental frequency of the open pipe is given by:

f1 = v/2L

where v is the speed of sound in air and L is the length of the pipe. Substituting the given values, we get:

f1 = 345/(2 x 0.82)

= 210.97 Hz

The second overtone frequency of the pipe is 3 times the fundamental frequency:

f3 = 3f1 = 3 x 210.97

= 632.91 Hz

The frequency of the vibrating string is given by:

fs = n(v/2L)

where n is the harmonic number. Substituting the given values, we get:

fs = 5(345/2 x 0.15)

= 5750 Hz

The wavelength of the sound wave in the pipe that is in second overtone resonance is four times the length of the pipe:

λ = 4L = 4 x 0.82

= 3.28 m

The distance between a node and an adjacent antinode in the string is half of the wavelength of the vibrating string:

d = λ/2 = v/(2fs)

= 345/(2 x 5750)

= 0.03 m

= 30 mm

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To ancient peoples, why were planets special?

Answers

Answer:

Planets were like gods.

Explanation:

To the people of many ancient civilizations, the planets were thought to be deities. Our names for the planets are the Roman names for these deities. For example, Mars was the god of war and Venus the goddess of love.

How much heat has to be added to 1 gallon of water to raise the temperature from
68F to 40C?

Answers

Answer:

The heat needed to raise the temperature of 1 gallon of water from 68°F to 40°C is approximately 28,265 Joules.

Explanation:

Object 1 with mass 1=3.25 kg
is held in place on an inclined plane that makes an angle
of 40.0∘
with the horizontal. The coefficient of kinetic friction between the plane and the object is 0.535.
Object 2 with mass 2=4.75 kg
is connected to object 1 with a massless string over a massless, frictionless pulley. The objects are then released.
Calculate the magnitude
of the initial acceleration.
Calculate the magnitude
of the tension in the string once the objects are released.

Answers

The magnitude of the initial acceleration of the object is 4.2 m/s².

The tension in the string once the object starts moving is 13.65 N.

What is the  magnitude of the initial acceleration?

The magnitude of the initial acceleration of the object is calculated by applying Newton's second law of motion as follows;

F(net) = ma

m₂g - μm₁g cosθ = a(m₁ + m₂)

where;

m₁ and m₂ are the masses of the blocksg is acceleration due to gravityμ is coefficient of frictionθ is the angle of inclinationa is the acceleration

(4.75 x 9.8) - (0.535 x 3.25 x 9.8 x cos40) = a(3.25 + 4.75)

33.5 = 8a

a = 33.5/8

a = 4.2 m/s²

The tension in the string once the object starts moving is calculated as;

T = m₁a

T = 3.25 x 4.2

T = 13.65 N

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two cars both with a mass off 500kg are traveling down a road. The first car has a velocity of 65 m/s east and the second car has a velocity of 85 m/s west.​

Answers

32500 kg m/s east, 42500 kg m/s west. Second car has larger momentum
Explanation:
The momentum of an object is given by
D= mv
where
m is the mass
vis the velocity
For the first car, m = 500 kg and v = 65 m/s east, so the momentum is
PI
= (500) (65) = 32500kgm/s east
For the second car, m = 500 kg and v = 85 m/s west, so the momentum is
p2 = (500) (85) = 42500k gm/s
west
By comparing the two momentum, we see that the second car has larger
momentum.

Which of these best defines weather? (3 points) a Atmospheric conditions over 30-year period Ob Day-to-day condition of the atmosphere Ос Long-term condition of the atmosphere O d Average atmospheric condition.​

Answers

Answer:

b Day-to-day condition of the atmosphere

Explanation:

Weather is short term, Climate is long term

Answer:

Average atmospheric condition.

Explanation:

3. How are fossil fuels used to generate electrical energy?
A Heat from burning fuel spins magnets inside an electric motor.
B Heat from burning fuel creates steam that spins a turbine.
C Heat from burning fuel creates steam that turns a transformer.
D Heat from burning fuel causes an electric motor to produce a current.

Answers

Answer:

B

Explanation:

Turning a turbine is what generates the potential difference that drives electric current.

A certain sea cow can paddle 2.0 m/s in still water. If she attempts to cross a river, from the south bank to the north with a current of 3.0 m/s flowing toward the east by paddling entirely perpendicularly to the flow of the river, in what direction will she be traveling relative to an observer on shore

Answers

Answer:

v = 3.6m / s ,   θ = 56º

Explanation:

This is a relative speed exercise, let's use the Pythagorean theorem

        v = √ (v₁² + v₂²)

where v₁ is the speed of the sea still water and v₂ the speed of the current

         

let's calculate

       v = √ (2² + 3²)

        v = 3.6m / s

to find the direction we use trigonometry

      tan θ = v₂ / v₁

       θ = tan⁻¹ (v₂ / v₁)

let's calculate

       θ = tan⁻¹ (3/2)

        θ = 56º

How can you measure the strength of a force?
for 14 points

Answers

The strength of a force can be measured by using a force sensor or a spring scale. These instruments measure force in units of newtons (N) or pounds (lbs). The amount of deflection or extension of the spring is directly proportional to the force applied. The force can also be measured indirectly by measuring its effect on an object, such as the acceleration of an object under the influence of the force, using Newton's second law of motion.

A small airplane flies at 60 m/s relative to the air. The wind is blowing at 20 m/s to the south. The pilot heads this plane east. a) What is the speed, v, that the plane will travel relative to the ground

Answers

Answer:

\(V_g=63.3m/s\)

Explanation:

From the question we are told that:

Speed of Plane \(v_s=60m/s\)

Wind speed \(V_w=20m/s\)

Generally the equation for Speed of plane relative to the ground V_g is mathematically given by

 \(V_g=\sqrt{V_s^2+V_w^2}\)

 \(V_g=\sqrt{60^2+20^2}\)

 \(V_g=\sqrt{4000}\)

 \(V_g=63.3m/s\)

A bicycle slows down uniformly from vi=8.40 [m/s] to rest over a distance of 115 [m]. Each wheel and tire has an overall diameter of 0.68 [m]. Determine the magnitude of the angular acceleration of the wheel. Give your answer in units of radians per second squared.

Answers

A bicycle slows down uniformly from vi=8.40 [m/s] to rest over a distance of 115 [m]. Each wheel and tire has an overall diameter of 0.68 [m]. The magnitude of the angular acceleration of the wheel is approximately 0.0757 rad/s².

To determine the magnitude of the angular acceleration of the wheel, we need to first calculate the change in angular velocity and the time taken to come to rest. Then we can use these values to find the angular acceleration.

Calculate the initial angular velocity:

The initial linear velocity of the bicycle wheel is given by the formula v = ω * r, where v is the linear velocity, ω is the angular velocity, and r is the radius of the wheel.

The radius of the wheel is half the diameter, so r = 0.68 m / 2 = 0.34 m.

Given the initial linear velocity vi = 8.40 m/s, we can calculate the initial angular velocity ωi:

vi = ωi * r

ωi = vi / r

Calculate the final angular velocity:

The final angular velocity of the wheel is 0 rad/s since it comes to rest.

ωf = 0 rad/s

Calculate the change in angular velocity:

The change in angular velocity (Δω) is given by the formula Δω = ωf - ωi.

Δω = 0 - ωi

Calculate the time taken to come to rest:

To calculate the time taken to come to rest, we can use the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

Given the initial velocity vi = 8.40 m/s, final velocity vf = 0 m/s, and distance d = 115 m, we can calculate the acceleration a:

vf = vi + at

0 = 8.40 + a * t

We also know that the distance traveled d is related to the initial and final velocities and the time by the formula d = (vi + vf) / 2 * t:

d = (vi + vf) / 2 * t

115 = (8.40 + 0) / 2 * t

From the two equations above, we can solve for the acceleration a and the time t.

Calculate the angular acceleration:

The angular acceleration (α) is given by the formula α = Δω / t.

α = Δω / t

Substitute the values for Δω and t and calculate the angular acceleration.

Therefore, the magnitude of the angular acceleration of the wheel is approximately 0.0757 rad/s².

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What happens to the Sun's energy as it passes through the atmosphere to Earth's surface?

Answers

Some of the Sun's energy is absorbed, scattered, or reflected as it travels through the atmosphere to the surface of the Earth by a variety of atmospheric constituents, including gases, aerosols, clouds, and the Earth's surface.

What uses does the atmosphere make of solar energy?

50% of the heat energy from the Sun can reach Earth's surface thanks to the atmosphere. The Sun's energy is reflected back into space at a rate of 30%. The atmosphere greenhouse gases, such as carbon dioxide, water vapour, and methane, absorb 20% of the remaining solar energy.

When solar energy travels through the stratosphere, what happens to it?

Ozone (O3) in the upper atmosphere absorbs a substantial amount of the Sun's ultraviolet (high-energy, shortwave) light (the stratosphere). The Earth system does not become hotter as a result of solar radiation that Earth's surface or atmosphere reflect back into space. Heat is produced as a result of absorbed radiation.

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The magnitudes of the electric potential and of the electrostatic force depend on which factors? O
A. Mass and distance O
B. Distance and amount of charge O
C. Density and amount of charge O
D. Mass and amount of charge​

Answers

Answer:

Density and amount of charge O

When a skater pulls her arms in, it
reduces her moment of inertia from
2.12 kg m² to 0.699 kg-m². If she was
initially spinning 3.25 rad/s, what is
her final angular velocity?

Answers

The skater's final angular velocity is approximately 9.86 rad/s.

The skater's final angular velocity can be calculated using the principle of conservation of angular momentum. The equation for angular momentum is given by:

L = Iω

where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

Initially, the skater has an angular momentum of:

L_initial = I_initial * ω_initial

Substituting the given values:

L_initial = 2.12 kg m² * 3.25 rad/s

The skater's final angular momentum remains the same, as angular momentum is conserved:

L_final = L_initial

The final moment of inertia is given as 0.699 kg m². Therefore, the final angular velocity can be calculated as:

L_final = I_final * ω_final

0.699 kg m² * ω_final = 2.12 kg m² * 3.25 rad/s

Solving for ω_final:

ω_final = (2.12 kg m² * 3.25 rad/s) / 0.699 kg m²

Hence, the skater's final angular velocity is approximately 9.86 rad/s.

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A 1.53-kg piece of iron is hung by a vertical ideal spring. When perturbed slightly, the system is moves up and down in simple harmonic oscillations with a frequency of 1.95 Hz and an amplitude of 7.50 cm. If we choose the total potential energy (elastic and gravitational) to be zero at the equilibrium position of the hanging iron, what is the total mechanical energy of the system

Answers

Answer:

E = 0.645J

Explanation:

In order to calculate the total mechanical energy of the system, you take into account that if the zero of energy is at the equilibrium position, then the total mechanical energy is only the elastic potential energy of the spring.

You use the following formula:

\(E=U_e=\frac{1}{2}kA^2\)         (1)

k: spring constant = ?

A: amplitude of the oscillation = 7.50cm = 0.075m

The spring constant is given by:

\(f=\frac{1}{2\pi}\sqrt{\frac{k}{m}}\)

\(k=4\pi^2f^2m\)         (2)

f: frequency of the oscillation = 1.95Hz

m: mass of the piece of iron = 1.53kg

You replace the expression (1) into the equation (2) and replace the values of all parameters:

\(E=\frac{1}{2}(4\pi^2f^2m)A^2=2\pi^2f^2mA^2\\\\E=2\pi^2(1.95Hz)^2(1.53kg)(0.075m)^2=0.645J\)

The totoal mechanical energy of the system is 0.645J

Activity Problem 8.3 This problem asks you to compare the finite current element approximation to the infinite straight wire approximation for the isolated segment of wire carrying current of 2A to the right. The wire is 8cm long. Note, the finite current approximation will be a fairly poor approximation to the actual field which would be found by integration; the infinite wire field is a better approximation in this case. (a)Compute the magnetic field at point C a distance 2cm for the center of the wire using the infinite straight wire approximation. (b)Compute the magnetic field at point C using the finite current element approximation. (c)Compute the magnetic field at point E a distance 2cm from the end using the finite current element approximation.

Answers

Answer: (a) B = 2 x 10⁻⁵T

               (b) B = 1.94 x 10⁻⁵T

               (c) B = 1.8 x 10⁻⁴T

Explanation: A magnetic field due to a current passing through a straight wire is calculated using the Biot-Savart Law:

\(dB=\frac{\mu_{0}}{4.\pi} \frac{IdLXR}{r^{3}}\)

where

dL is current length element

\(\mu_{0}\) is permeability of free space (\(4.\pi.10^{-7}\)T.m/A)

(a) For a infinite straight wire:

\(B=\frac{\mu_{0}I}{2.\pi.R}\)

\(B=\frac{4.\pi.10^{-7}.2}{2.\pi.2.10^{-2}}\)

B = 2x10⁻⁵T

For an infinite, long and straight wire, magnetic field is 2x10⁻⁵T.

(b) For a finite wire:

\(B=\frac{\mu_{0}I}{2.\pi.R}\frac{L}{\sqrt{L^{2}+R^{2}} }\)

\(B=\frac{4.\pi.10^{-7}.2}{2.\pi.2.10^{-2}} \frac{8.10^{-2}}{\sqrt{(8.10^{-2})^{2}+(2.10^{-2})^{2}} }\)

B = 1.94x10⁻⁵T

The magnetic field for a finite wire in the same conditionsas infinite wire is 1.94x10⁻⁵T.

(c) For a finite wire at a point distant from the end of the wire:

\(B=\frac{\mu_{0}I}{4.\pi.L\sqrt{2} }\)

\(B=\frac{4.\pi.10^{-7}.2}{4.\pi.8.10^{-2}\sqrt{2} }\)

B = 0.18x10⁻⁵T

At a point at the end, magnetic field is 1.8x10⁻⁴T.

(Need help pls)!!!!!


(Need help pls)!!!!!

Answers

Answer:

I assume they want answer A, but it's a silly question.

Explanation:

Well, if we assume that the girls are applying equal force, as they are the same size and strength (apparently also the same resolve etc.).

Equal force in opposite directions means the composite force is null. An object that no force is applied to continues moving in the same direction, so if the doll was moving somewhere, it would keep doing so, except all of this makes no sense the doll is not in gravityless vacuum what are we even talking about.

The answer A is the least ridiculous.

What are conducting patterns?

Answers

Answer:

A conducting pattern is a pattern in which your dominant hand follows in order to establish beats and tempo to the choir. Conductors that are directing large orchestras and choirs will often times use a baton so that the entire group can clearly see the motions.

Explanation:

A piece of unsaturated air is forced to rise. The lapse rate in the surrounding air is much less than the rate in change of temperature in the rising air. The rising air is said to be ________.

Answers

Answer:

stable

Explanation:

on the off chance that the natural slip by rate is not exactly the saturated adiabatic pass rate then any rising air package will be colder than the earth, and will sink down. The climate is described as totally stable in light of the fact that regardless of if the package is saturated or not, it can't get light after certain tallness.

How can scientist best confirm and validate the result of an experiment so they can publish their findings?

A. By removing the control from the experiment

B. By adding more variables to the experiment

C. By decreasing the number of trials

D. By creating a replicable experiment

How can scientist best confirm and validate the result of an experiment so they can publish their findings?A.

Answers

\(Question\)

How can scientist best confirm and validate the result of an experiment so they can publish their findings?

Answer:

Hi, there!

D. By creating a replicable experiment Is The correct Answer!

Hope this Helps!!

-xXxAnimexXx- ♚♛♕♔ッ✨♚

Answer:. By creating a replicable experiment

Explanation:

Use the drop-down menus to complete the sentences.

The first step in a bill becoming a law is for the bill to be
.

Next, the bill goes to
to be marked up, dropped, or sent to the floor.

After that, the bill is debated on the floor and can pass on a majority vote of
.

In the next stage, the bill must go to the
to repeat the process.

After the bill is resolved in the
, it goes to the president.

Answers

The first step towards a bill becoming a law is for the bill to be introduced in Congress.

Next, the bill goes to a committee to be marked up, dropped, or sent to the floor.

After that, the bill is debated on the floor and can pass with a majority vote of the house that sponsored it.

In the next stage, the bill must go to the other chamber, to repeat the process.

After the bill is resolved in the conference committee, it goes to the president.

What is the Congress?

The Congress is sometimes referred to as Senate and it can be defined as a deliberative assembly or council of elected citizens found in the upper chamber or house of a bicameral legislature.

This ultimately implies that, Congress is a federal legislative arm of government of the United States of America, which is saddled with the responsibility of enacting and passing federal laws and bills for the citizens, with the steps enumerated above.

Generally speaking, the first step of making bill to become a law is introducing it to the Congress while the last step is the resolution of a bill if it is voted in favor by at least 44 senators, and then it finally goes to the president for assent through his or her signature.

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Complete Question:

Use the drop down menus to complete the sentences.

The first step in a bill becoming a law is for the bill to be _____.

Next the bill goes to _____ to be marked up, dropped or sent to the floor.

After that, the bill is debated on the floor and can pass on a majority vote of ____.

In the next stage, the bill must go to the ____ to repeat the process.

After the bill is resolved in the ____, it goes to the president.

What is the wavelength of a wave?

Answers

The wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.

Calculate the de moglie Wavelength of election having kinetic energy of 400 ev​

Answers

Answer:

613.5 pm

Explanation:

We know that de Broglie wavelength of an electron :

λ = 1.227 / √E nm

λ = 1.227 / √400 nm

λ = 1.227 / 20 nm

λ = 0.6135 nm

λ = 0.6135 x 10⁻⁹ m

λ = 613.5 x 10⁻¹² m

λ = 613.5 pm

Wavelength

Wavelength of election having kinetic energy of 400 ev.

Solution:

WE = 1.227 / √election nmWE = 1.227 / √e400nmWE = 1.227 / √20nmWE = 0.6136nmWE = 0.6136 x 10-⁹mWE = 613.5 x 10-¹²mWE = 613.5

A 175,000 kg space probe is landing on an alien planet with a gravitational acceleration of 8.25. If its fuel is ejected from the rocket motor at 35,000 m/s what must the mass rate of change of the space ship (delta m)/(delta t) be to achieve at upward acceleration of 2.00 m/s^2? Remember to use the generalized form of Newton's Second Law.

answer with correct units​

Answers

The mass rate of change of the space probe is approximately 28.49 kg/s .

What is the mass rate of the space probe?

To solve this problem, we can use the generalized form of Newton's Second Law, which states that the force acting on an object is equal to its mass times its acceleration:

F = ma

In this case, the force acting on the space probe is the thrust force generated by the rocket motor, which is equal to the rate of change of momentum of the ejected fuel:

F = (Δ m /Δt) * v

where;

Δ m /Δt t is the mass rate of change of the space ship, and v is the velocity of the ejected fuel, which is given as 35,000 m/s.

Since the space probe is landing on the planet, the net force acting on it should be equal to the force of gravity pulling it down minus the upward thrust force generated by the rocket motor. So we can write:

F_net = m * g - (Δ m /Δt) * v

Plugging in the values and solving for delta m / delta t, we get:

2.00 m/s² = (175,000 kg * 8.25 m/s²) - (Δ m / Δt) * 35,000 m/s

Δ m / Δt = (175,000 kg * 8.25 m/s² - 2.00 m/s² * 35,000 m/s) / 35,000 m/s

Δm / Δt ≈ 28.49 kg/s

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A cave rescue team lifts an injured spelunker directly upward and out of a sinkhole by means of a motor-driven cable. The lift is performed in three stages, each requiring a vertical distance of 5.90 m: (a) the initially stationary spelunker is accelerated to a speed of 2.30 m/s; (b) he is then lifted at the constant speed of 2.30 m/s; (c) finally he is decelerated to zero speed. How much work is done on the 69.0 kg rescue by the force lifting him during each stage

Answers

Answer:

   W₃ = 3310.49 J ,  W3 = 3310.49 J

Explanation:

We can solve this exercise in parts, the first with acceleration, the second with constant speed and the third with deceleration. Therefore it is work we calculate it in these three sections

We start with the part with acceleration, the distance traveled is y = 5.90 m and the final speed is v = 2.30 m / s. Let's calculate the acceleration with kinematics

       v2 = v₀² + 2 a₁ y

as they rest part of the rest the ricial speed is zero

        v² = 2 a₁ y

        a₁ = v² / 2y

        a₁ = 2.3² / (2 5.90)

        a₁ = 0.448 m / s²

with this acceleration we can calculate the applied force, using Newton's second law

         F -W = m a₁

         F = m a₁ + m g

         F = m (a₁ + g)

         F = 69 (0.448 + 9.8)

         F = 707.1 N

Work is defined by

         W₁ = F.y = F and cos tea

As the force lifts the man, this and the displacement are parallel, therefore the angle is zero

          W₁ = 707.1 5.9

           W₁ = 4171.89 J  W3 = 3310.49 J

Let's calculate for the second part

the speed is constant, therefore they relate it to zero

           F - W = 0

           F = W

           F = m g

           F = 60 9.8

           F = 588 A

the job is

           W² = 588 5.9

            W2 = 3469.2 J

finally the third part

in this case the initial speed is 2.3 m / s and the final speed is zero

           v² = v₀² + 2 a₂ y

            0 = vo2₀² + 2 a₂ y

            a₂ = -v₀² / 2 y

            a₂ = - 2.3²/2 5.9

            a2 = - 0.448 m / s²

we calculate the force

            F - W = m a₂

            F = m (g + a₂)

            F = 60 (9.8 - 0.448)

            F = 561.1 N

we calculate the work

            W3 = F and

            W3 = 561.1 5.9

          W3 = 3310.49 J

total work

          W_total = W1 + W2 + W3

          W_total = 4171.89 +3469.2 + 3310.49

           w_total = 10951.58 J

A concave lens causes light to diverge. Is this true or false?

Answers

Answer:

True

Explanations:

Another name for a concave lens is diverging lens.

Light rays that pass through a concave/diverging lens diverge from their axes.

Images formed by a concave lens are virtual, upright, and diminished. They are also formed between the focal point and the lens

Therefore, it is true to say that a concave lens causes light to diverge

How are gases and liquids different from each other? A. Gases can change volume, and liquids cannot. O B. Liquids can change volume, and gases cannot. C. Gases can change shape, and liquids cannot. D. Liquids can change shape, and gases cannot.​

Answers

Answer:

A.gasses can change volume, and liquids cannot

Explanation:

if you pour a glass of water you don't have to worry about it expanding such that it overflows. however if you air up a ballon you may notice that it becomes lager the warmer it gets and smaller the cooler it gets

Pls help!!
Which situation describes a system with increasing gravitational potential energy?
a boy jumping down from a tree limb
a girl stretching a horizontal spring
a bicyclist riding up a steep hill
a train speeding up on a flat track

Answers

C) a bicyclist riding up a steep hill

The metaphor for a system with rising gravitational potential energy is "a bicyclist riding up a steep hill." Let's get into greater detail:

A cyclist faces resistance from gravity as they ride up a steep slope. The cyclist's elevation, or height above the ground, rises as they cycle and climb uphill. Gravity is pulling the cyclist down the hill by exerting downward force. The cyclist must apply force to the pedals in order to move forward and overcome the pull of gravity. In order to do this, the bicyclist must transform chemical energy from their body into mechanical energy. The distance of the cyclist from the centre of the Earth grows as they ride up the hill. The height and mass of an object affect its gravitational potential energy. In this scenario, as the bicyclist's height rises, their gravitational potential energy also rises.

     Due to the higher elevation, the energy input from the biker is stored as increased potential energy. When the bicycle descends the hill or does work, this potential energy can be transformed back into kinetic energy or other types of energy.

using the laplace transform of u(t) for cos3wt, determine the solution for y(t) assuming zero initial conditions

Answers

The Laplace transform of u(t) for cos3wt, then \(y(t) = \frac{1}{6} [e^{(3it)} + e^{(-3it)}]u(t)\)

What is the function of the Laplace transform?

Laplace transform is used to solve differential equations. It is commonly used in many different professions. According to our knowledge, the Laplace transform converts a given LDE (linear differential equation) into an algebraic equation that can be solved using the basic algebraic identities.

Let Y(s) represent y's Laplace transform (t).

Since y(t) = u(t) × cos3wt, we can write:

\(Y(s) = U(s) \times [\frac {s}{(s^{2} + 9)}]\)

Using the magnitude and phase formula discussed in class, we can express y(t) as:

\(y(t) = \frac{1}{6} [e^{(3it)} + e^{(-3it)}]u(t)\)

This transform is useful for analyzing linear, time-invariant systems, and is used in many engineering fields to solve differential equations, such as in electrical, mechanical and control engineering.

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