a. u is harmonic for let u(x, y) = xy because ∂²u/∂x² + ∂²u/∂y² = 0.
b. A harmonic conjugate of u is v = (x² - y²)/2.
To determine that u is harmonic, we need to verify whether u satisfies Laplace's equation or not. Laplace's equation is given by:
∂²u/∂x² + ∂²u/∂y² = 0
On differentiating u(x, y) = xy partially, we get,
∂u/∂x = y∂u/∂y = x
On differentiating partially again, we get,
∂²u/∂x² = 0∂²u/∂y² = 0
Therefore, ∂²u/∂x² + ∂²u/∂y² = 0
Thus, u is harmonic.
To find a harmonic conjugate of u, we need to find v(x, y) such that u + iv is analytic. In other words, v must satisfy the Cauchy-Riemann equations. The Cauchy-Riemann equations are given by:
∂u/∂x = ∂v/∂y∂u/∂y = -∂v/∂x
On substituting u = xy in the above equations, we get,
∂v/∂y = x∂v/∂x = -y
On integrating the above equations, we get
v = (x² - y²)/2 + C
Thus, a harmonic conjugate of u is v = (x² - y²)/2.
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Determine the mechanical advantage of a car jack that uses an input force of 30 N and provides an output force of 600 N. pls answer quick
Answer:
Mechanical Advantage of car jack is 20
How long is a wire in a 0.86 T field that carries a current of 1.4A and experiences a force of
13 N?
A 14.2-m
The length of a wire in a 0.86 T field that carries a current of 1.4A and experiences a force of 13 N is 14.2-m.
What is the force experienced by a wire when it is placed in a magnetic field and carries an electric current? When a wire is placed in a magnetic field and carries an electric current, it experiences a force known as magnetic force. The formula for magnetic force on a wire is given by:F = BILsinθWhere:F = Magnetic forceB = Magnetic field strength I = Electric currentL = Length of wire in the magnetic fieldθ = Angle between the wire and the magnetic field directionIf we substitute the given values into the above equation, we have:F = (0.86 T)(1.4 A)(L)sin90° = 1.204L NSince F = 13 N, then:13 N = 1.204L NL = 13/1.204L = 10.7981-m≈14.2-mTherefore, the length of the wire in a 0.86 T field that carries a current of 1.4A and experiences a force of 13 N is 14.2-m.
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A man with a mass of 60 kg rides a bike with a mass of 13 kg. What is the force needed to accelerate the bike at 0.90 m/s2?
A. 65.7
B.657
C.75.6
D.756
all rules to find work in changing force in physics
Answer:
FORCE - rate of change of momentum, ie its changing velocity [change in velocity is of more concern] NEWTON
WORK - product of force and displacement, ie [velocity may be constant or variable but change in position with certain force is of more concern] JOULES
I hope you understood from this..
Calculate the Work done if the force is 2000 Newtons
and the distance is 5 km.
Answer:
10 million joules or 10,000 KJ
Explanation:
Work= Force x Displacement
convert 5km into meters -5km=5000m
W= 2000N x 5000m
w=10,000,000 Joules
or 10,000KJ
Use composition of functions to determine whether f ( x ) and g ( x ) are inverses of each other.
\(f ( x ) =\frac{4}{5}\) x + 1
\(g ( x ) = \frac{5 x - 5}{4}\)
The two compositions are: f( g(x) ) = x and g( f(x) ) = x
What is an inverse function?The inverse function is defined as a function obtained by reversing the given function.
We have given functions :
f(x) = 4/5x + 1
g(x) = (5x - 5)/4
Let's check if the functions are inverses.
f( g(x) ) = 4/5g(x) + 1 = 4/5{(5x - 5)/4} + 1 = (x - 1) + 1 = x
g( f(x) ) = (f(x) - 1)5/4 = (4/5x + 1 - 1)5/4 = x
So, f(x) and g(x) are inverses.
Hence, the two compositions are: f( g(x) ) = x and g( f(x) ) = x
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a solid sphere, a solid cylinder, and a hollow cylinder are placed at the top of an inclined plane. if all are made of the same material and are released at the same time, which one will reach the bottom first?
The solid ball will be the first to touch the bottom, followed by the solid cylinder and the hollow cylinder. The mass, radius, and distribution of the mass with respect to the rotational axis all affect an object's rotational inertia.
Why do spheres roll more quickly than cylinders?Solid sphere moves more quickly than solid cylinder because it has a lower moment of inertia and more kinetic energy during translation. Comparable solid objects move more slowly than hollow ones.
Does gravity affect the rotational inertia?If an object is supported below its center of gravity, it will balance (which can sometimes help one to find it). The distribution of an object's mass also affects its moment of inertia: More rotational inertia is added by material far from the axis of rotation than by material nearby the axis.
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Just say i had to catch a dollar bill between my 2 finger (flattened dollar bill)
Can I figure out how long it takes for the dollar bill to fall between my fingers?
A dollar bill is 6.14inches
Mass of dollar bill: 1gram
Answer:
Below
Explanation:
The trailing edge has to fall 6.14 inches ( mass is irrelevant)
d = 1/2 a t^2
6.14/12 ft = 1/2 (32.2 ft/s^2 )(t^2) shows t = .178 s
Obtain a pillow made of foam rubber. Press
down hard with your two hands on the surface
of the pillow. Then withdraw your hands
Describe what happened to its shape while you
pushed hard on the pillow and when you
withdrew your pushing. Repeat this activity on
a piece of rectangular block of wood and a
plasticine. Note the different effects.
Answer: Only foam rubber is compressible material
Explanation:
The pillow is made up of foam rubber which can be compressed easily due to the soft compressible rubber with hands on application of pressure on the surface. The shape of pillow regain its original shape when the pressure is withdrawn from the pillow. If the same activity is performed on the piece of rectangular block of wood and plasticine. Then the rectangular block of wood cannot be compressed with hand as it is a solid body. Plasticine is a putty like material. It is a clay like material and it can be compressed with hand but when the pressure is withdrawn the plasticine does not regain its shape back.
Calculate thc work that must be done on charges brought from infinity to charge & spherical shell of radius R" 0.1OO m to & total charge Q-125 mc 502 J B) 602 J C) 702 ] D) 802 J E) 902 J
The work that must be done on charges brought from infinity to a spherical shell of radius R = 0.100 m and total charge Q = 125 mc is 602J. Hence, option B is the correct answer to this question.
To calculate the work that must be done on charges brought from infinity to a spherical shell of radius R, we can use the formula for the electric potential energy, which is given by U = kq1q2/r
Where k is the Coulomb constant, q1 and q2 are the charges, and r is the distance between the charges.
In this case, the work done on a single charge of q = Q/n, where Q is the total charge on the shell and n is the number of charges, brought from infinity to a distance of r = R from the center of the spherical shell is given by:
W = qU = q(kq/R) = kq^2/R
Since the total charge on the spherical shell is Q = 125 mc and the radius of the shell is R = 0.100 m, the work done on each charge is:
W = kq^2/R = (8.99x10^9 N.m^2/C^2)(125x10^-6 C)^2/(0.100 m) = 602 J
Therefore, the work that must be done on charges brought from infinity to a spherical shell of radius R = 0.100 m and total charge Q = 125 mc is 602 J.
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While a car travels around a circular track at a constant speed, its?
While a car travels around a circular track at a constant speed, its speed is changing with direction.
What is acceleration of an object?
The acceleration of an object is the rate of change of velocity of the object with time.
The acceleration of an object moving in a circular track is known as centripetal acceleration.
a = v²/r
where;
v is the speed of the objectr is the radius of the trackThe speed of an object is a scalar quantity without direction, but when it occurs in a circular track, the speed occurs in different direction, so acceleration for constant speed in a circular track cannot be zero.
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Identify the independent, dependent, and constant variables for different experiments.
Experiment 1: A soap manufacturer runs an experiment to compare the foaming action of different dish detergents. Equal amounts of each brand of detergent are placed in identical containers half-filled with water. The water and dish detergent are at a temperature of 20°Celsius. Each container is agitated for 30 seconds, and then the height of the foam is measured.
ANSWER:
IV, Type of dish detergent. DV, height of foam. CV, type of container, amount of water in container, temperature of water, time the container is agitated.
Explanation:
Independent variable(IV)- what you change during the experiment.
dependent variable(DV)- what you're measuring during an experiment. The dependent variable is DEPENDENT because it's results DEPEND on the independent variable at play.
Constant variables(CV)- things that do not change in order to isolate the tested variables as much as possible.
g a car is being driven at a rate of 40 ft/sec when the brakes are applied. the car decelerates at a constant rate of 19 ft/sec2. how long before the car stops? round your answer to one decimal place.
The car stops after travelling a distance 42.1 ft.
What is velocity?The rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is a vector quantity with both magnitude and direction is displacement.
Given parameters:
Initial velocity of the car; u = 40 ft/sec.
Final velocity of the car; v = 0 ft/sec.
Deceleration of the car; a = 19 ft/sec².
We have to find, distance travelled by the car before stops; d = ?
For decelerated motion, we know that;
v² = u² - 2as
Putting all values, we get;
0² = 40² - 2×19×s
⇒ s = (40×40)/(2×19)
= 42.1 ft.
Hence, distance travelled by the car before stops is 42.1 ft.
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2. A car is sitting at the top of a hill that is 14 m high. The car has a mass of 53 kg. The car has
energy. Calculate it.
Which has the greater acceleration, a person going from 0 m/s to 10 m/s in 10 seconds or an ant going from 0 m/s to 0.25 m/s in 2.0 seconds?
Person-1
Initial velocity=u=0m/sFinal velocity=v=10m/sTime=10s=t\(\\ \sf\longmapsto Acceleration=\dfrac{v-u}{t}\)
\(\\ \sf\longmapsto Acceleration=\dfrac{10-0}{10}\)
\(\\ \sf\longmapsto Acceleration=\dfrac{10}{10}\)
\(\\ \sf\longmapsto Acceleration=1m/s^2\)
Person-2
initial velocity=0m/s=uFinal velocity=v=0.25m/sTime=t=2s\(\\ \sf\longmapsto Acceleration=\dfrac{0.25-0}{2}\)
\(\\ \sf\longmapsto Acceleration=\dfrac{0.25}{2}\)
\(\\ \sf\longmapsto Acceleration=0.125m/s^2\)
Person-1 is accelerating faster.
What is the characteristic of the columns in the periodic table?
Answer: The periodic table also has a special name for its vertical columns. Each column is called a group. The elements in each group have the same number of electrons in the outer orbital.
Explanation: :)
a force of 10 n holds an ideal spring with a 20-n/m spring constant in compression. the potential energy stored in the spring is:
The potential energy stored in the spring of force constant 20 N/m is 2.5 J.
What is potential energy?This is the energy of a body a virtue of its position.
To calculate the potential energy stored in the spring, we use the formula below.
Fromula:
P.E = F²/2K............. Equation 1Where:
P.E = Potential energy of the springK = Spring constantF = Force on the springFrom the question,
Given:
F = 10 NK = 20 N/mSubstitute these values into equation 1
P.E = 10²/(2×20)P.E = 2.5 JHence, the potential energy stored in the spring is 2.5 J.
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1pt If an object is moving at a constant velocity, it means that....
A. no net force is acting on it
B. a constant force is acting on it in the direction of its motion
c. a constant force is acting on it in the opposite direction of its motion
D. several forces are acting on it, but one force is greater than the others
Answer:
thecool me
Explanation:
which assumption about level of measurement is made for the chi square test?
The chi-square test assumes that the variables being analyzed are measured at a nominal or ordinal level of measurement.
In statistics, the level of measurement refers to the nature and properties of the data being collected. There are four levels of measurement: nominal, ordinal, interval, and ratio. Nominal and ordinal levels are considered categorical, while interval and ratio levels are considered numerical. The chi-square test is specifically designed for analyzing categorical data, where the observations can be classified into distinct categories or groups. It is used to determine whether there is a significant association or relationship between two categorical variables.
The test calculates the difference between the observed frequencies and the expected frequencies under the assumption of independence between the variables. It compares the observed and expected frequencies using a chi-square statistic and determines the p-value to assess the statistical significance of the association. Therefore, the chi-square test assumes that the variables being analyzed are measured at a nominal or ordinal level because it deals with categorical data and evaluates the relationship between different categories or groups.
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A iPhone charger system producing 14.5 Volts with a current flow of 43.5 Amps. What is the circuit resistance?
Answer:
The resistance of the circuit is 0.\(\bar 3\) Ω
Explanation:
The given parameters are;
The voltage the charger produces = 14.5 Volts
The current flow of the charger = 43.5 Amps
Therefore, the resistance of the circuit, R = Voltage V/(Current, I)
R = V/I = 14.5/43.5 = 1/3 = 0.\(\bar 3\) Ohms
The resistance of the circuit = 0.\(\bar 3\) Ohms
Which can be written with the symbol for the unit of resistance Ω as follows;
The resistance of the circuit = 0.\(\bar 3\) Ω.
I will be giving the brainliest to whoever.What is the PERCENT efficiency if a computer is supplied with 500 J of energy and is able to convert 400 J to useful energy?
A. 0.8 %
B. 8 %
C. 80 %
D. 800 %
Which statements describe properties of stars? Check all that apply.
The properties of stars are: mass, age, distance, metallicity (chemical composition), variability and motion through space.
What is star?An astronomical object known as a star is made up of a bright plasma spheroid that is held together by gravity. The Sun is the star that is closest to Earth.
Other stars are also visible at night with the unaided eye, but because to their great distances from Earth, they appear as stationary points of light. Many of the brightest stars have names, and the most notable stars have been grouped into constellations and asterisms.
Star catalogues have been put out by astronomers that list the known stars and offer standardized stellar labels.
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Answer: Stars produce energy through nuclear fusion.
Stars are massive objects composed of gas.
Stars are composed primarily of hydrogen and helium.
P.S can I get the brainiest?
A bullet of mass m = 0.0010 kg embeds itself in a wooden block with mass M = 0.999 kg, which then compresses a spring (k = 150 N/m ) by a distance x = 0.046 m before coming to rest. The coefficient of kinetic friction between the block and table is μ = 0.50.
a)What is the initial velocity (assumed horizontal) of the bullet?
b)What fraction of the bullet's initial kinetic energy is dissipated (in damage to the wooden block, rising temperature, etc.) in the collision between the bullet and the block?
a) The initial velocity (assumed horizontal) of the bullet can be calculated using the equation for kinetic friction:
μ = (kinetic friction) = (force of friction) / (normal force).
Since the normal force in this case is equal to the mass of the wooden block multiplied by the acceleration due to gravity (9.81 m/s2), we can write:
μ = Ff / (M*g) = 0.50
Ff = (M*g)*μ = (0.999 kg)(9.81 m/s2)(0.50) = 4.90 N
The equation for kinetic energy is Ek = 1/2mv2.
Substituting Ek = Ff * x (where x is the compression distance of the spring), we can write:
1/2mv2 = (4.90 N)(0.046 m)
Rearranging, we get:
v2 = (4.90 N)(0.046 m)/(1/2m) = (4.90 N)(0.046 m)/(0.0010 kg/2) = 94.00 m2/s2
Taking the square root of both sides gives the initial velocity of the bullet:
v = 9.70 m/s
b) The fraction of the bullet's initial kinetic energy that is dissipated in the collision can be found by comparing the initial and final kinetic energies.
The initial kinetic energy is equal to 1/2(0.0010 kg)(9.70 m/s)2 = 0.046 J.
The final kinetic energy is equal to 0, since the bullet comes to rest after the collision.
Therefore, the fraction of the bullet's initial kinetic energy that is dissipated in the collision is equal to (final energy)/(initial energy) = 0/0.046 = 0.
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if p = 269 w and q = 155 var (capacitive), find the complex power. the complex power is ( – j ) va.
The complex power is (–j) VA,Complex power is a concept used in electrical engineering to describe the total power of a circuit, including both the real power (measured in watts) and the reactive power (measured in volt-amperes reactive or VARs).
It is a complex number that has both a real part and an imaginary part.
The real part of complex power is equal to the average power dissipated in a circuit, while the imaginary part represents the reactive power, which is the power associated with the energy stored and released by inductive and capacitive elements in the circuit.
The complex power is given by :- S = P + jQ
where S is the complex power, P is the real power, and Q is the reactive power.
Given, P = 269 W and Q = 155 VAR (capacitive).
Substituting the values, we get:
S = 269 + j(-155)
S = 269 - j155
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A light bulb consumes 1800 watt-hours per day. How long does it take to consume 8100 watt-hours? days
hours X 5
It 4.5 hours for the light bulb to consume 8100 watt-hours of power.
The energy consumed by the light blub = 8100 watt-hours.
Let the time taken be t hours.
We know that;
Energy = power × time
Energy (E) = 8100 watt-hours
Power (P) = 1800 watt
Time (t) =?
8100 = 1800 × t
= 8100 / 1800
= 4.5 hours
The time taken by the light bulb is 4.5 hours.
Therefore, it could take 4.5 hours for the light bulb to consume 8100 watt-hours.
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How long of a radius must a simple pendulum be if it is to make exactly 1.00 swing per second? b) What is its frequency? c) its angular velocity? (That is, one complete oscillation takes exactly 2.00 s.
The angular velocity of the pendulum is π rad/s. The period (T) of a pendulum, or the amount of time it takes to complete one full swing, is calculated using the following formula:T = 2π√(L/g) where L is the length of the pendulum and g is the acceleration due to gravity, which is approximately 9.81 m/s2 at the Earth's surface.
Let's start by solving for the length of the pendulum if it is to make exactly 1.00 swing per second.T = 1 s (since it makes one complete swing per second)2π√(L/g) = 1 s2π√(L/9.81 m/s2) = 1 s2π√(L) = 9.81 m/s22π√(L) = 9.81 m/sL = (9.81 m/s2)/(4π2) = 0.248 m.
Therefore, the length of the pendulum should be 0.248 m in order to make exactly 1.00 swing per second.b) The frequency of a pendulum is the number of oscillations it makes per unit of time. For example, if a pendulum makes 10 oscillations per minute, its frequency is 10/60 = 0.167 Hz.The frequency of this pendulum can be calculated as follows:f = 1/T = 1/1 s = 1 Hz.
Therefore, the frequency of the pendulum is 1.00 Hz.c) The angular velocity (ω) of a pendulum is given by the formula:ω = Δθ/Δtwhere Δθ is the angle through which the pendulum swings and Δt is the time it takes to complete one oscillation.
We know that one complete oscillation takes exactly 2.00 s. The angle through which the pendulum swings is 2π radians (or 360°). Therefore,ω = Δθ/Δt = 2π/2 s = π rad/s. Therefore, the angular velocity of the pendulum is π rad/s.
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What are the groups in Mendeleev's table?
Answer: metals, non metals and semi metals
Explanation:
why can't a spacecraft go beyond earth's gravity
A spacecraft can go beyond Earth's gravity by achieving escape velocity, but it requires a significant amount of energy and fuel to do so.
And the spacecraft may still be affected by the gravitational forces of other celestial bodies.
HOW WE PROVE THAT STATEMENT?
Gravity is a fundamental force of nature that governs the motion of objects in the universe. The strength of the gravitational force depends on the mass and distance between two objects.
To escape Earth's gravity, a spacecraft must achieve a velocity of about 11.2 kilometers per second (or about 40,320 kilometers per hour), which is known as escape velocity.
To achieve this velocity, a spacecraft needs to accelerate to a high speed using a powerful rocket engine and carry enough fuel to maintain that speed until it is beyond the reach of Earth's gravity.
The rocket must also be able to withstand the extreme heat and pressure generated during the launch and ascent.
Even after a spacecraft has escaped Earth's gravity, it can still be influenced by the gravitational forces of other celestial bodies.
For example, the Moon's gravity can affect the trajectory of a spacecraft, and course corrections may be necessary to ensure the spacecraft reaches its intended destination.
In addition, the Sun's gravity can cause the spacecraft's orbit to change over time.
Overall, leaving Earth's gravity is a complex and challenging task that requires careful planning, engineering, and execution.
However, it is an essential step in exploring and studying the universe beyond our planet.
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Is the process of science described in this lesson similar to your initial ideas about how science is carried out? Explain why or why not.
The process of science followed my initial ideas e because it involved experiments.
What is the process of science?The process of science or the scientific method refers to the process which scientists follow in their discovery and explanation of natural phenomena.
The scientific method is given below:
making an observation,develop a hypothesis,making a prediction,conducting an experiment analyzing the resultspropound a lawThe process of science follows my initial ideas about the process of science because I always thought science involved experiments.
In conclusion, the process of science involves making hypothesis and conducting research.
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An electrical appliance of 1.5 kw is used for 4hour each day. The electrical energy consumed in 60 days is :
a)6kwh
b)360kwh
c)2250kwh
please help me!!
I want the correct answers
Answer:
c
Explanation:
c