Ex(r, t) = Re[Ey(r, t)] = ET * cos(kr - ωt + Φ). This expression gives the total amplitude and phase shift in terms of E (r.1) and Ex(r.1) of the plane wave.
To find the total electric field Ex(r, t) by adding two plane waves E₁(r, t) and E₂(r, t) with the given expressions, we will use complex notation and superposition.
First, let's write E₁ and E₂ in complex notation:
E₁(r, t) = E₁z * exp[i(kr - ωt + δ₁)]
E₂(r, t) = E₂z * exp[i(kr - ωt + δ₂)]
Now, we add them together:
Ex(r, t) = E₁(r, t) + E₂(r, t)
Ex(r, t) = E₁z * exp[i(kr - ωt + δ₁)] + E₂z * exp[i(kr - ωt + δ₂)]
Next, let's factor out the common term exp[i(kr - ωt)]:
Ex(r, t) = exp[i(kr - ωt)] * (E₁z * exp[iδ₁] + E₂z * exp[iδ₂])
Now, we can define a total amplitude ET and phase shift Φ:
ET * exp[iΦ] = E₁z * exp[iδ₁] + E₂z * exp[iδ₂]
By finding ET and Φ, we can write the total electric field as:
Ey(r, t) = ET * cos(kr - ωt + Φ)
Finally, to obtain the real part of the total electric field, take the real part of Ex(r, t):
Ex(r, t) = Re[Ey(r, t)] = ET * cos(kr - ωt + Φ)
This gives us the total electric field Ex(r, t) in terms of the amplitudes E₁z, E₂z and phase shifts δ₁, δ₂ of the two plane waves E₁(r, t) and E₂(r, t).
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( Infer this information for both the lens and mirror based on the data collected. Report these ranges in terms of f and/or 2f. For example, “When do is less than 2f.” )
What range of do values will result in a real image?
What range of do values will result in a virtual image?
What range of do values will result in a smaller image?
This exercise is about Reflection and Mirrors. It explores the relationship between convex mirrors, virtual images, and complex images as well as to object distance d₀.
Any d₀ value greater than 10 for a convex lens will produce a true or real image, while any d₀ value greater than 15 for a complex mirror will produce a real image.
What range of d₀ values will result in a virtual image?Any d₀ number less than 10 for a convex lens will result in a virtual image. Also, any d₀ value less than 15 for a complex mirror will result in a virtual picture.
What range of do values will result in a smaller image?The range of d₀ values that would result in a reduced picture in both lenses and mirrors is:
d₀ > 2 f, where is the Focal length.
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initially evacuated. A valve is opened and Air at 200kPa and 57∘C is allowed to enter the tank until the pressure is 100kPa etank is approximately ( in ∘C) 175 c. 187.5 d. 30.3 e. None tain a house at 30∘C while the outside temperature is 0∘C. The house loses heat to the outside air at a rate of 10 kW. the power (in kW ) required to drive the heat pump is: 2.5 c. 4 d. 2 e. None
To determine the power required to drive the heat pump, we can use the concept of the Coefficient of Performance (COP). The COP of a heat pump is defined as the ratio of the heat delivered to the heat absorbed from the outside environment.
In this case, the heat delivered is the heat lost by the house to the outside air, which is 10 kW.
The COP of a heat pump can be expressed as COP = Q_delivered / W_input, where Q_delivered is the heat delivered and W_input is the power input to the heat pump.
Since the COP is not provided, we cannot directly calculate the power required to drive the heat pump. However, typical values of COP for heat pumps range from 2 to 4. Let's assume a COP of 3 for this case.
Using the COP formula, we have COP = Q_delivered / W_input. Rearranging the equation, we can solve for W_input: W_input = Q_delivered / COP.
Substituting the values, W_input = 10 kW / 3 = 3.33 kW.
Therefore, the power required to drive the heat pump is approximately 3.33 kW.
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a basketball player shoots toward a basket 6.1 m away and 3.0 m above the floor. if the ball is released 1.8 m above the floor at an angle of above the horizontal, what must the initial speed be if it were to go through the basket?
The initial speed at which the ball should be released so that it goes through the basket is 7.5 m/s.
Distance between the basket and the player, x = 6.1 mHeight of the basket from the floor, y = 3 mHeight at which the ball is released, h = 1.8 mThe horizontal distance between the point where the ball is released and where it hits the ground, x is given by the expression:
x = ut cos θ
where u is the initial velocity of the ball, θ is the angle at which the ball is released, and t is the time for which the ball remains in the air. The time for which the ball remains in the air, t can be calculated as:
t = (h - u sin θ) / g
where g is the acceleration due to gravity, which is 9.8 m/s²
Substituting the given values in the above equations, we get x = u cos θt = (h - u sin θ) / gt = (1.8 - u sin θ) / gt
When the ball reaches the basket, it should have a horizontal displacement equal to the distance between the basket and the player, x, and a vertical displacement equal to the height of the basket from the ground, y. The horizontal and vertical displacements can be calculated using the following expressions:x = ut cos θy = h + ut sin θ - 0.5gt²where t is the time at which the ball hits the basket.
Substituting the given values in the above equations, we get:
x = u cos θt = (h - u sin θ) / gt = (1.8 - u sin θ) / gx = ut cos θy = h + ut sin θ - 0.5gt²
where t is the time at which the ball hits the basket.
Now, substituting t in the expressions for x and y:x = u cos θ * (1.8 - u sin θ) / g = 6.1 m y = 1.8 + u sin θ * (1.8 - u sin θ) / g - 0.5 * 9.8 * [(1.8 - u sin θ) / g]² = 3 m
Simplifying the above equations: 1.8u cos θ - u³ sin² θ / g = 6.1
cos θ + 1.8u sin θ - 0.5(1.8 - u sin θ)² = 3
On solving the above two equations simultaneously, we get the value of initial velocity, u as: u = 7.5 m/s (approx)
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TRUE/FALSE. a recently discovered extrasolar planet appears to be rockier and denser than earth. it is 16 times as massive as earth, but its diameter is only twice that of earth.
The acceleration of free fall on the planet is given by 39.2 m/s².
What is the acceleration of free fall?The acceleration of free fall is the acceleration at which a body falling freely experiences the gravitational pull of a single planet. It is also known as a gravitational acceleration.
Value of the acceleration of free fall on earth is 9.8 m/s².
The formula of acceleration of free fall on any planet is given by:
g₁ = GM/R²
As the extrasolar planet appears to be rockier and denser than earth. it is 16 times as massive as earth, but its diameter is only twice that of earth, the acceleration of free fall on any planet is given by:
g₁ = GM/R² = 16GMe/(2Re)² = 4 GMe/Re = 4g = 4× 9.8 m/s² = 39.2 m/s² .
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12/3/21 A wave in the ocean has a wavelength of 24 m and a frequency of 8 Hz,What is the wave's speed?
Answer:
192 m/sExplanation:
The speed of the wave given only it's frequency and wavelength can be found by using the formula
\(c = f \times \lambda\)
where
c is the velocity of the wave in m/s
\( \lambda\) is the wavelength in m
f is the frequency in Hz
From the question we have
c = 8 × 24 = 192
We have the final answer as
192 m/sHope this helps you
2. A race car travels a complete lap on a circular track of radius 500 m in 50 s. What is the
average velocity of the race car? (1 pt)
a. Zero
b. 100 m/s
C. 200 m/s
d. None of the above
3. In problem two. What would be the average speed? (2 pts)
1
Answer:
100m/s
Explanation:
velocity = displacement/time
The average velocity of the race car around the circular track in the given time is 62.8m/s.
Hence, option D) None of the above is the correct.
What is Average Velocity?Average velocity is simply the displacement of a particle or object over time. It is the rate of change of position of an object with respect to time.
It is expressed as;
Velocity = displacement / time
It can also be expressed as;
Velocity = circumference / time = 2πr / t
Given the data in the question;
Radius of the track r = 500mTime elapsed t = 50sAverage velocity V = ?To determine the average velocity, we substitute our values into the expression above.
V = 2πr / t
V = ( 2 × 3.14 × 500m ) / 50s
V = 3140m / 50s
V = 62.8m/s
The average velocity of the race car around the circular track in the given time is 62.8m/s.
Hence, option D) None of the above is the correct.
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who made the first detailed observations of the largest planet in our solar system?
Galileo Galilei made the first detailed observations of the largest planet in our solar system.
Who made the first observations of the largest planet?Galileo Galilei made the first detailed observations of Jupiter in solar system. Galileo is renowned for his discoveries. He was the first to report telescopic observations of mountains on the moon, moons of Jupiter, phases of Venus, and rings of Saturn. He also invented an early microscope and a predecessor to the thermometer.
Galileo's discoveries about the Moon, Jupiter's moons, Venus, and sunspots supported the idea that the Sun was the center of the Universe. Work of Galileo also laid the foundation for today's modern space probes and telescopes.
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A major disturbance that caused the ecosystem to stabilize at a new equilibrium?
Answer: If you remove all of the hawks, it stabilizes an a new equilibrium.
Explanation: For the ecosystem to stabilize at a new equilibrium, the tertiary consumer (hawks) need to be totally removed from the ecosystem. Since there's no tertiary consumer to checkmate the density of other components of the food chain, it will make form a balanced ecosystem.
A student makes a voltage divider from a 45-V battery, a 475-k
resistor, and a 235-k resistor. The output is measured across the
smaller resistor. What is the voltage?
Answer:
14.9 v
Explanation:
V = IR
The voltages across the resistors will be proprtional to the values of the resistors
45 * 235 / (235 + 475) =
Based on what you learned about light, select all of the correct statements from the following list. -High frequency photons carry more energy than long wavelength photons.
-All electromagnetic waves travel at the speed of light.
-Light can act both as a wave and a particle.
-A photon is a particle of light. X-rays and gamma rays are long wavelength photons.
-Different types of electromagnetic radiation are fundamentally different types of waves.
-The only type of electromagnetic radiation that is actually considered light is visible light.
The correct statements include:
High frequency photons carry more energy than long wavelength photons.All electromagnetic waves travel at the speed of light.Light can act both as a wave and a particle.A photon is a particle of light.option A, B, C, D
What are the incorrect statements about electromagnetic waves?
The Incorrect statements include:
Different types of electromagnetic radiation are fundamentally different types of waves. (All types of electromagnetic radiation are fundamentally the same type of wave but have different frequencies and wavelengths.)
The only type of electromagnetic radiation that is actually considered light is visible light. (All types of electromagnetic radiation are considered light, including radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.)
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Answer: A B C D
Explanation: k12 I had this quiz
Think more about the situation in the question above. If you picked a "good" thing, how might
boundaries have helped you choose the "right" think instead? If you picked the "right" thing, how
did your boundaries help you?
PLEASE HELP RIGHT NOW !
your on here to lol we must be hella failing g
The volume of a cylinder is v=πR^2H where R =radius and h= height. If the radius is 3 times the height and the volume increases at 10cm/s. How fast does the radius increase when the radius 6 cm
The rate at which the radius increases when the radius is 6 cm is approximately 0.056 cm/s.
At a radius of 6 cm, how fast does the radius increase?To determine how fast the radius increases, we can use the given information about the volume of a cylinder and its rate of change. The volume of a cylinder is given by the formula v = πR²H, where R represents the radius and H represents the height.
Given that the radius is three times the height, we can express the height as H = R/3. Substituting this value into the volume equation, we have v = πR²(R/3). Simplifying further, the volume equation becomes v = (π/3)R³.
Now, we are given that the volume increases at a rate of 10 cm/s. By taking the derivative of the volume equation with respect to time, we can determine how the radius changes over time. The derivative, dv/dt, is equal to (π/3)(3R²)(dR/dt), where dR/dt represents the rate of change of the radius.
Simplifying the equation, we have dv/dt = πR²(dR/dt). Substituting the given values, we have 10 cm/s = π(6²)(dR/dt).
Solving for dR/dt, we find that the rate at which the radius increases when the radius is 6 cm is approximately 0.056 cm/s.
Calculus and related concepts to explore the relationships between variables and their rates of change. Understanding these mathematical principles is essential for analyzing dynamic systems and their behaviors.
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Define reference point
plz help me
Answer:
a basis or standard for evaluation, assessment, or comparison; a criterion.
Explanation:
Definition of reference point. : something that is used to judge or understand something else The professor used the study as a reference point for evaluating and discussing other theories.
Answer:
something that is used to judge or understand something else
Explanation:
The professor used the study as a reference point for evaluating and discussing other theories.
What property of the wave is labeled H?
amplitude
crest
wavelength
trough
7
Mark is performing an investigation to determine what type of fertilizer helps a plant grow best. He plants ten plants of the same type
in a garden and gives them all the same amount of water and fertilizer each day. However, he gives each plant a different type of
fertilizer
Which variable in the experiment should Mark control (or keep constant)?
A location of the plants
OB amount of fertilizer given daily
Camount of water given daily
OD all of these
Reset
Submit
What does a animal and a plant cell have in common.
Answer:
Nucleus, cell membrane, cytoplasm and mitochondria
Explanation: They both have these 4 components, which is what they have in common.
A power station that is being started up for the first time generates 6120 MWh of energy over a 10 hour period. (i) If the rated power at full capacity is 660 MW, calculate how long it takes the power station to reach its full power output. (You may assume a constant increase in power from zero to full power) (ii) State what type of power station can be started up fastest and explain why the start-up times for other types of power station are slower. Explain briefly, how this is relevant to optimising the usage of windfarms. c) What is the Bremsstrahlung effect and how can it be avoided in shielding design? d) Sketch the electromagnetic field output from an antenna, describing in detail the two main regions in the output field.
(i)Therefore, it takes approximately 9.27 hours to reach its full power output.(ii)It is necessary to have quick-start power sources, this helps maintain a stable and reliable electricity supply even when wind speeds fluctuate.(c)The Bremsstrahlung effect needs to be considered to ensure proper radiation protection.(d) The near-field region is characterized by strong electric and magnetic fields while the far-field region represents the radiation zone.
(i) To calculate the time it takes for the power station to reach its full power output, we can use the formula:
Energy = Power × Time
Given that the power station generates 6120 MWh of energy over a 10-hour period and the rated power at full capacity is 660 MW, we can rearrange the formula to solve for time:
Time = Energy ÷ Power
Converting the energy to watt-hours (Wh):
Energy = 6120 MWh × 1,000,000 Wh/MWh = 6,120,000,000 Wh
Converting the power to watt-hours (Wh):
Power = 660 MW × 1,000,000 Wh/MW = 660,000,000 Wh
Now we can calculate the time:
Time = 6,120,000,000 Wh ÷ 660,000,000 Wh ≈ 9.27 hours
Therefore, it takes approximately 9.27 hours (or 9 hours and 16 minutes) for the power station to reach its full power output.
(ii) The type of power station that can be started up fastest is a gas-fired power station. Gas-fired power stations can reach full power output relatively quickly because they use natural gas combustion to produce energy.
In contrast, other types of power stations, such as coal-fired or nuclear power stations, have longer start-up times. Coal-fired power stations require time to heat up the boiler and generate steam, while nuclear power stations need to go through a complex series of procedures to ensure safe and controlled nuclear reactions.
This is relevant to optimizing the usage of windfarms because wind power is intermittent and dependent on the availability of wind. This helps maintain a stable and reliable electricity supply even when wind speeds fluctuate.
(c) The Bremsstrahlung effect is a phenomenon that occurs when charged particles, such as electrons, are decelerated or deflected by the electric fields of atomic nuclei or other charged particles. As a result, they emit electromagnetic radiation in the form of X-rays or gamma rays.
In shielding design, the Bremsstrahlung effect needs to be considered to ensure proper radiation protection. These materials effectively absorb and attenuate the emitted X-rays and gamma rays, reducing the exposure of individuals to harmful radiation.
(d) The electromagnetic field output from an antenna can be represented by two main regions:
Near-field region: This region is closest to the antenna and is also known as the reactive near-field. It extends from the antenna's surface up to a distance typically equal to one wavelength. In the near-field region, the electromagnetic field is characterized by strong electric and magnetic field components.
Far-field region: Also known as the radiating or the Fraunhofer region, this region extends beyond the near-field region.The electric and magnetic fields are perpendicular to each other and to the direction of propagation. The far-field region is further divided into the "Fresnel region," which is closer to the antenna and has some characteristics of the near field, and the "Fraunhofer region," which is farther away and exhibits the properties of the far-field.
The transition between the near-field and the far-field regions is gradual and depends on the antenna's size and operating frequency. The size of the antenna and the distance from it determine the boundary between these regions.
In summary, the near-field region is characterized by strong electric and magnetic fields, while the far-field region represents the radiation zone where the energy is radiated away as electromagnetic waves.
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which of the following terms ( or paris of terms) is used to describe how energy flows in a chemical reaction ?
The terms Exothermic and Endothermic describe how energy flows in a chemical reaction. The correct option is D.
What is energy flow in a chemical reaction?The bonds between molecules are formed and disrupted during chemical reactions.
When new bonds are created, energy is released. In contrast, energy is absorbed to dissolve bonds. Bond energy is the required force to dissolve the bonds.
When bonds in the reactants are broken in endothermic reactions, more energy is absorbed than is released when new bonds are created in the products.
The temperature of the reaction mixture drops during endothermic reactions.
Thus, the correct option is D.
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You are designing an apparatus to shoot a water balloon through a 3rd story window (25m above the ground)
Answer:
The balloon needs a vertical velocity of approximately 22.14 m/s to reach the window
Explanation:
The given parameters are;
The destination of the designed water balloon we shoot = The 3rd story window
The height of the 3rd story window which the water balloon should reach = 25 m
Therefore, we have, the equation of motion of the water balloon given as follows;
v² = u² - 2 × g × s
Where;
\(u_y\) = The initial vertical velocity of the balloon
\(v_y\) = The final vertical velocity of the balloon = 0 m/s
g = The acceleration due to gravity = 9.8 m/s
s = The height the balloon is intended reach at the final velocity becomes 0 m/s = The height of the 3rd story window
∴ s = 25 m
Substituting the values, we have;
0² = \(u_y\)² - 2 × 9.8 × 25
\(u_y\)² = 2 × 9.8 × 25 = 490
\(u_y\) = √490 = 7·√10
The initial vertical velocity of the balloon = \(u_y\) = 7·√10 m/s
Therefore, the balloon needs a vertical velocity of 7·√10 m/s which is approximately 22.14 m/s to reach the window.
thermal noise is unavoidable and can literally be found everywhere in the universe because it is due to _______ motion of ________ in electrical circuits?
Thermal noise is the unavoidable noise that occurs due to the thermal motion of particles in electrical circuits.
This type of noise is present everywhere in the universe as it is due to the thermal motion of particles.
This thermal motion is the random movement of particles that is a result of their temperature. At higher temperatures, the particles in a substance have a higher thermal motion, which results in more thermal noise.
The electrical circuit has resistance, and when a current flows through it, the resistance causes collisions between electrons and other atoms. This interaction between the moving electrons and atoms in the conductor produces thermal noise.
Thermal noise is proportional to the temperature of the conductor and is independent of the current or voltage of the signal passing through it. The power of thermal noise is given by the formula P = kTB, where k is Boltzmann's constant, T is the temperature in Kelvin, and B is the bandwidth of the signal.
Hence, it can be deduced that thermal noise is an inevitable occurrence present universally, as it arises from the thermal agitation of particles within electrical circuits. This phenomenon pervades various environments and cannot be eliminated.
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The frequency of a sound wave is 457 Hz. What is the period?
a
0.0032 s
b 0.078 s
C 0.0010 s
d 0.0022 s
The period of the sound wave having frequency of 457Hz is 0.0022 s.
What is frequency?
The frequency refers to the number of waves that pass a fixed point in unit time.
What is the relation between frequency and time period?
Time period is equal to the reciprocal of frequency.
i.e. T = 1 / f
So, The period of the sound wave having frequency of 457Hz will be
T = 1/457
∴ T = 0.002188 s
Now , rounding to the nearest value we get , 0.0022 s
Thus , The period of the sound wave having frequency of 457Hz is 0.0022 s.
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How can you make a chemical change to paper
-- burn it (it combines with Oxygen and makes new substances)
-- chew it (it combines with your saliva and makes new substances)
-- swallow it (your stomach juices dissolve it and make new substances)
I think that's as far as I should go with it.
A man drives a car at 54km/hr. He brakes and it stop in 3s. Calculate the deceleration
The deceleration of the car is approximately -5 m/s^2.
To calculate the deceleration of the car, we need to first convert the speed from kilometers per hour (km/h) to meters per second (m/s) since the standard unit of acceleration is meters per second squared (m/s^2).
Given:
Speed = 54 km/h
Time taken to stop = 3 s
To convert the speed from km/h to m/s, we can use the conversion factor: 1 km/h = 1000 m/3600 s.
Speed in m/s = (54 km/h) * (1000 m/3600 s)
= 15 m/s
Now, we can calculate the deceleration using the equation of motion:
Deceleration = (Final velocity - Initial velocity) / Time
Since the car comes to a stop, the final velocity is 0 m/s and the initial velocity is 15 m/s.
Deceleration = (0 m/s - 15 m/s) / 3 s
= -15 m/s / 3 s
= -5 m/s^2
The negative sign indicates that the deceleration is in the opposite direction of the initial velocity, which means the car is slowing down.
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What happens to the sum of the ball’s kinetic energy and potential energy as the ball rolls from point A to point E? Assume there’s no friction between the ball and the ground. An image shows a curve that starts at point A, decreases at B, then increases at C and D, and ends at E. A. The sum decreases. B. The sum increases. C. The sum remains the same. D. The sum always equals zero.
It might be the sum is the same in the given scenario. The correct option is C.
What is kinetic energy?Kinetic energy is the energy that an object has as a result of its movement.
If we intend to speed up an object, we should indeed apply force to it. Using force necessitates us to put in effort.
After work is completed, energy is transmitted to the object, as well as the object moves at a new constant speed.
Potential energy is the energy hosted by an object as a result of its position in relation to other objects, internal stresses, electric charge, or even other factors.
If there is no friction, there is nothing starting to slow down the ball, so the ball does not change or the energy does not change since the ball never stops.
Thus, the correct option is C.
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Your question seems incomplete, the probable missing image is attached below:
What is one way that light waves differ from sound waves?
Well light waves are rays of energy and sound waves are vibrations that tun into sound from our ears.
Hope it helps!
Why is temperature a good criterion for searching for Earth like exoplanets?
Answer:
Liquid water is essential for life to exist. Water can occur in a liquid state only within a specific temperature range, so knowing the temperature range on a planet will help astronomers predict whether life exists on that planet.
a bicyclist travels with an average velocity of 15km/h north, for 20 minutes .what is his displacement ?
\(▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)
Displacement is equal to ~
\(5 \: \: km\)See the attachment for solution ~
Answer:
It is 24000meter per second
Cindy notices jim coming to her house and decides to run out the door 6 meters to the west into her neighbor's
yard. afterward, cindy goes another 43 meters to the west to harry's house. it takes cindy 18 seconds to make it
to harry's.
what is cindy's average velocity?
The average velocity of Cindy is 2.72 meter per second.
To calculate Cindy's average velocity, we need to divide the total distance traveled by the time it took her to travel that distance.
Cindy traveled a total distance of 6 meters + 43 meters = 6+43=49 meters.
It took her 18 seconds to travel this distance.
Her average velocity is then 49 meters / 18 seconds = 49/18=2.72 meters per second.
This is the average speed at which Cindy was moving during the time it took her to travel from her house to Harry's house. It tells us how far Cindy traveled per unit of time, but it does not give us any information about the direction she was moving in.
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Quá trình truyền sóng là
Science question! helppppp
Let's take this problem step-by-step:
What does this problem want to solve:
⇒ find two pendulums that will swing back and forth in the least amount
of time
Therefore:
⇒ must find the equation that calculates that period or swing time of a
pendulum
Equation: \(T = 2\pi \sqrt{\frac{L}{g} }\)
L: length of the pendulumg: gravitational accelerationBased on the equation:
⇒ the longer the string is ⇒ the greater the swing time
Thus:
⇒ pendulum Y and Z will have the least amount of swing time
Answer: (B)
Hope that helps!
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