Answers
Expand the given expression into partial fractions.
\(\dfrac1{z^2 - 3z + 2} = \dfrac1{(z-2)(z-1)} = \dfrac1{(2 - z) (1 - z)} = \dfrac1{1 - z} - \dfrac1{2 - z}\)
Recall the infinite geometric series,
\(\displaystyle \sum_{n=0}^\infty z^n = \dfrac1{1-z}\)
which converges in the unit disk |z| < 1.
The unit disk is a subset of the given region |z| < 2, so there are no issues with the convergence of series expansion of the first expression. For the second expression, we rearrange terms as
\(\dfrac1{2 - z} = \dfrac12 \times \dfrac1{1 - \frac z2}\)
Then if |z/2| < 1, or equivalently |z| < 2, the series expansion for this term is
\(\displaystyle \frac1{2-z} = \frac12 \sum_{n=0}^\infty \left(\frac z2\right)^n = \sum_{n=0}^\infty \frac{z^n}{2^{n+1}}\)
Putting everything together, the series expansion of the given expression over |z| < 2 is
\(\displaystyle \frac1{z^2-3z+2} = \sum_{n=0}^\infty \left(1 + \frac1{2^{n+1}}\right) z^n\)
Related Questions
3. A car with a mass of 1600 kg has a kinetic energy of 125 000 J. How fast is it moving?
Answers
The car is moving at approximately 12.5 meters per second.
The kinetic energy (KE) of an object can be calculated using the formula:
KE = 1/2 * m * \(v^2\)
where
KE = kinetic energy,
m =Mass of the object, and
v = velocity.
In this case, we are given the mass (m) of the car as 1600 kg and the kinetic energy (KE) as 125,000 J. To find the velocity .
Substituting the values , we have:
125,000 J = 1/2 * 1600 kg *\(v^2\)
Now, we can solve for v by rearranging the equation:
\(v^2\) = (2 * 125,000 J) / 1600 kg
\(v^2\) = 156.25 \(m^2/s^2\)
Taking the square root, we find:
v = √156.25\(m^2/s^2\)
v ≈ 12.5 m/s
Therefore, the car is moving at approximately 12.5 meters per second.
Know more about kinetic energy here:
https://brainly.com/question/8101588
#SPJ8
) Find mass and speed of 2 MeV electron
Answers
According to the equation E=(-1)mc2, where \(E=3.2 x 1013 J\) and \(=1.0000037\), a 2 MeV electron has a mass of \(9.11 x 1031 kg\) and a speed of \(2.195 x 108 m/s.\)
How are masses expressed in MeV?Additionally, as energy and mass are connected by Einstein's famous equation E = mc2, the masses of elementary particles are sometimes stated in electron volts as well. An electron, for instance, has a mass of 0.51 MeV/c2, where c is the speed of light.
What does 2 MeV proton mean?Moving perpendicular to a 2.5 T magnetic field is a 2 MeV proton. The proton is under a force of (1.6 10 27 kg of proton mass)
To know more about speed visit:
https://brainly.com/question/28224010
#SPJ1
Which type of mass movement is likely to result in considerable property damage, but rarely causes loss of life? a. debris avalanche b. rock fall c. mudflow d. creep
Answers
Answer:
The correct answer is D. Creep.
Explanation:
Ground creep is a slow downward movement of a hill or mountain slope without the formation of demolition forms. The decisive factor for this is the continuous flow of movement of the soil.
The main driver of collapse is the movement of the surface layer particles during expansion in a direction perpendicular to the slope, followed by vertical collapse on contraction. The visible effect of the collapsing is the inclination of fences and poles, as well as trees that grow out of the ground towards the slope and have trunks curved vertically, in more extreme cases it may be cracks on the walls of buildings.
Which of the following phrases best describes the term scientific model?
A. The application of scientific knowledge to make predictions about
an object, system, or process
B. An experiment in which variables are controlled
C. A physical copy of a scientific object, system, or process
D. A simplified representation used to explain or make predictions
about something
SUBMIT
Answers
By what multiplicative factor does the spring potential energy change if the mass attached to the spring is doubled?.
Answers
The spring potential energy is proportional to the square of the amount of stretch or compression of the spring.
What is compression?Compression is the process of reducing the size of a file or data by encoding it using fewer bits. The process of compression is used to reduce the amount of data that needs to be stored or transmitted. By compressing a file or data, it can be stored more efficiently, transferred faster, and take up less space. Compression algorithms can be lossless, meaning that no information is lost during the compression and decompression process, or lossy, meaning that some information is lost during the compression process.
Therefore, if the mass attached to the spring is doubled, the spring potential energy will be multiplied by a factor of four.
To learn more about compression
https://brainly.com/question/7602497
#SPJ1
a problem solving method that involves trying all possible solutions until one works is using_____.
Answers
Answer:
trial and error.
Explanation:
a problem solving method that involves trying all possible solutions until one works is using trail and error.
4. Calculate the total resistance of the circuit if R1=4 Ω, R2=30 Ω, R3=10Ω, R4=5Ω Determine the current strength if the circuit is connected to a voltage source with a voltage of 56 V
Answers
The total resistance of the circuit is 49 Ω. The current strength in the circuit, when connected to a voltage source of 56 V, is approximately 1.14 A.
To calculate the total resistance of the circuit, we need to determine the equivalent resistance of the resistors connected in a series.
Given:
R1 = 4 Ω
R2 = 30 Ω
R3 = 10 Ω
R4 = 5 Ω
Calculate the equivalent resistance (RT) of R1 and R2, as they are connected in series:
RT1-2 = R1 + R2
RT1-2 = 4 Ω + 30 Ω
RT1-2 = 34 Ω
Calculate the equivalent resistance (RTotal) of RT1-2 and R3, as they are connected in parallel:
1/RTotal = 1/RT1-2 + 1/R3
1/RTotal = 1/34 Ω + 1/10 Ω
1/RTotal = (10 + 34) / (34 * 10) Ω
1/RTotal = 44 / 340 Ω
1/RTotal ≈ 0.1294 Ω
RTotal ≈ 1 / 0.1294 Ω
RTotal ≈ 7.74 Ω
Calculate the equivalent resistance (RTotalCircuit) of RTotal and R4, as they are connected in series:
RTotalCircuit = RTotal + R4
RTotalCircuit = 7.74 Ω + 5 Ω
RTotalCircuit ≈ 12.74 Ω
Therefore, the total resistance of the circuit is approximately 12.74 Ω.
To determine the current strength (I) when connected to a voltage source of 56 V, we can use Ohm's Law:
I = V / RTotalCircuit
I = 56 V / 12.74 Ω
I ≈ 4.39 A
Therefore, the current strength in the circuit, when connected to a voltage source of 56 V, is approximately 4.39 A (or 1.14 A, considering significant figures).
For more such questions on current, click on:
https://brainly.com/question/24858512
#SPJ8
Define invariant transformations
Answers
Answer:
For a given system, there can be particular transformations for which the explicit equations of motion are the same for both the old and new variables. Transformations for which the equations of motion are invariant, are called invariant transformations. It will be shown that if the Lagrangian does not explicitly contain a particular coordinate of displacement qi, then the corresponding conjugate momentum, pi, is conserved. This relation is called Noether’s theorem which states “For each symmetry of the Lagrangian, there is a conserved quantity".
A car is traveling 100 km/hr. How many hours will it take to cover a distance of 850 km?
Your answer:
.118 hours
8.5 hours
7.5 hours
23 hours
Answers
Answer:
8.5 hours
Explanation:
you have two long wires separated by a distance x and oriented perpendicualr. in terms of x where would the charge have to be placed to remain stationary
Answers
When two long wires are separated by a distance x and oriented perpendicular to each other, a charge placed at certain points will remain stationary due to the balance of electric forces acting on it.
What location would the charge need to be in order to stay stationary?Here are some potential locations for the charge to remain stationary in terms of x:At the midpoint between the two wires: The charge will be equidistant from both wires, so the electric force on it from one wire will be equal and opposite to that of the other wire, resulting in a net force of zero.At a point along the line that bisects the angle between the two wires: This point is known as the "equipotential point" and is located at a distance of x/√2 from each wire. The electric forces from each wire will be equal in magnitude but opposite in direction, resulting in a net force of zero.At a point along the line that connects the two wires: This point is known as the "neutral point" and is located at a distance of x/2 from each wire. The electric forces from each wire will be equal in magnitude but opposite in direction, resulting in a net force of zero.It is important to note that the charge must be placed at these specific points in order to remain stationary, as any deviation from these points will result in the charge moving due to an unbalanced net force.
To learn more about charge refer:
brainly.com/question/18102056
#SPJ4
The components of a 15 meters per second velocity at an angle of 60 above the horizontal are
Answers
The components of a 15 meters per second velocity at an angle of 60 above the horizontal are 13.05 m / s and 0.435 m / s
Resolving the velocity into its horizontal and vertical components, it makes a right angled triangle.
Hypotenuse = V = 15 m / s
θ = 60°
Opposite side = components = \(V_{y}\)
Adjacent side = Horizontal component = \(V_{x}\)
In a right angled triangle,
sin θ = Opposite side / Hypotenuse
cos θ = Adjacent side / Hypotenuse
sin 60° = \(V_{y}\) / V
\(V_{y}\) = 15 * 0.87
\(V_{y}\) = 13.05 m / s
cos 60° = \(V_{x}\) / V
\(V_{x}\) = 0.5 * 0.87
\(V_{x}\) = 0.435 m / s
Therefore,
The horizontal component, \(V_{x}\) = 0.435 m / sThe vertical component, \(V_{y}\) = 13.05 m / s.To know more about components of velocity
https://brainly.com/question/12498991
#SPJ1
Question 6 of 10
Which statements below are true?
Check all that apply.
A. Displacement measurements must include magnitude, unit, and
direction.
B. If motion starts and stops at the same location, then the
displacement is zero.
C. Distance can be fully described with a magnitude and a unit.
D. Distance is always less than or equal to the magnitude of the
displacement.
Answers
Answer:
A, AND B,
Explanation: just trust me bro
A 20.0 newton force is used to push a 2.00 kilogram cart a distance of 5.00 meters how much work is done on the cart
Answers
Answer:
100
w=f*s
20*5=100....
100 Joules of work is done on the cart.
What is Work done?Work done by a force is defined as the product of the displacement and the component of the applied force on the object in the direction of displacement. When we push a block with some force, the body moves with some acceleration, so it is called work done.
Work done is expressed as W=Fd and its unit is joules which can be defined as the amount of work done by a force in Newton is applied to an object, as a result of which it is displaced in meter.
For above given information,
Force= 20 N
Distance= 5 m
So, work done= 20*5= 100 Joules
Thus, 100 Joules of work is done on the cart.
Learn more about Work done, here:
https://brainly.com/question/13662169
#SPJ2
Find the acceleration produced by a force of 165 N on a mass of 4.50 kg.
a.
0.027 m/s2
b.
44.1 m/s2
c.
36.67 m/s2
d.
742.5 m/s2
Answers
Answer:
c) 36.67 m/s2
Explanation:
Using the equation Force = mass x acceleration
165 N = 4.50 Kg x acceleration
165 N/4.50 Kg = acceleration
acceleration = 36.67 m/s2; when rounded to the nearest tenth
The acceleration produced by a net force on an object is and why?
A.)inversely proportional to the mass of the object.
B.)directly proportional to the magnitude of the net force
C)in the same direction as the net force
D)all of the above
Answers
Answer:
A i think
Explanation:
When a mass is suspended from a spring the latter extends over a distance of 10cm. What will be the period of oscillations of the same system if it is placed horizontal on a frictionless surface
Answers
Answer:
0.64 s
Explanation:
It's period of oscillation (T) can be determined by,
T = 2\(\pi\)\(\sqrt{\frac{l}{g} }\)
Where l is the length (extension on the spring), and g the acceleration due to gravity.
But,
l = 10 cm = 0.1 m
g = 9.8 m/\(s^{2}\)
Thus,
T = 2 x \(\frac{22}{7}\) \(\sqrt{\frac{0.1}{9.8} }\)
= 0.6350
T = 0.64 s
The period of oscillation would be 0.64 s.
A car traveling at 30 mph skids to a stop in 60 meters. If a car travels at 60 mph with the same skid conditions, then what is distance the car skids to come to a stop?
Answers
A car traveling at 60 mph and the same skid conditions will skid to a stop in 240 meters.
What is the distance a car traveling at 60 mph and the same skid conditions will skid to a stop?
The distance a car skids to come to a stop is directly proportional to the square of its speed. This means that if the speed is doubled, the distance it will take to stop will be quadrupled.
Let's use this formula to find the distance the car will skid to come to a stop at 60 mph:
(d1 / d2) = (v1^2 / v2^2)
where:
d1 = distance the car skids at 30 mph = 60 meters
v1 = speed of the car at 30 mph = 30 mph
v2 = speed of the car at 60 mph = 60 mph
d2 = distance the car skids at 60 mph (what we want to find)
Plugging in the values, we get:
(d1 / d2) = (v1^2 / v2^2)
60 / d2 = (30^2 / 60^2)
60 / d2 = 1 / 4
d2 = 4 x 60
d2 = 240 meters
Therefore, the car traveling at 60 mph will skid to a stop in 240 meters.
To learn more about skid, visit: https://brainly.com/question/30467857
#SPJ1
how much work must be done by the brakes to bring the bike rider to the stop? how far does the bicycle travel if it takes 3.5 seconds to come to rest? what is the magnitude of The breaking Force?
Answers
a) The workdone to bring the rider and bicycle to a stop = -4900J
b) △x = 21 m
c) Magnitude of the braki
Explanation:The total mass of the rider and the bicycle, m = 60 kg + 7.8 kg
m = 67.8 kg
Speed, v = 12 m/s
The initial kinetic energy of the rider and the bicycle is:
KE = 0.5 mv²
KE = 0.5 x 67.8 x 12²
KE = 4881.6 J
KE = 4900 J (to 2 significant figures)
Since both of them are brought to a stop, the final kinetic energy = 0 J
The workdone to bring the rider and bicycle to a stop = Final Kinetic Energy - Initial Kinetic Energy
The workdone to bring the rider and bicycle to a stop = 0 - 4900
The workdone to bring the rider and bicycle to a stop = -4900J
b) The acceleration is calculated as:
\(\begin{gathered} a=\frac{v-u}{t} \\ \\ a=\frac{0-12}{3.5} \\ \\ a=-3.43\text{ m/s}^2 \end{gathered}\)Calculate the distance using the equation of motion
\(\begin{gathered} v^2=u^2+2aS \\ \\ 0^2=12^2+2(-3.43)S \\ \\ 2(3.43)S=144 \\ \\ 6.86S=144 \\ \\ S=\frac{144}{6.86} \\ \\ S=21\text{ m} \\ \end{gathered}\)The bicycle travels a distance of 21 m
△x = 21 m
c) The magnitude of the braking force:
\(\begin{gathered} F=\frac{|W|}{d} \\ \\ F=\frac{4900}{21} \\ \\ F=230\text{ N \lparen to 2 significant figures\rparen} \end{gathered}\)lực ma sát có gây ra momen không?
Answers
Question in English:
Does friction cause torque?
Explanation in English:
Friction torque is the torque caused by the frictional force that occurs when two objects in contact move. Like all torques, it is a rotational force which may be measured in newton meters or pounds-feet.
The line of action of friction does not go through the center of mass, thus it creates torque about the center of mass.
Giải thích bằng tiếng Việt:
Mômen ma sát là mômen do lực ma sát gây ra khi hai vật tiếp xúc chuyển động. Giống như tất cả các mômen lực, nó là một lực quay có thể được đo bằng mét newton hoặc pound-feet.
Đường tác dụng của lực ma sát không đi qua khối tâm nên nó tạo ra mômen quay về khối tâm.
report of "fan made of plastic bottle" with string
Answers
Fan made of plastic bottle is an innovative way to reuse plastic bottles and can be easily made at home. This can be done by following simple steps, and a few materials are required to make it. The fan can be created by using a plastic bottle, scissors, string, a ruler, and a marker.
First, the bottle needs to be cut into half, and the upper part needs to be cut into three equal sections, then fold each section to make a blade. With the help of a ruler and marker, make a mark on each section, then make a hole in the center of each blade. Insert a string through the holes and tie the ends of the strings. The fan is ready to use by holding the string and swinging it back and forth.
The use of plastic bottle fans can significantly reduce the number of plastic waste and provide a practical solution to avoid environmental pollution. Besides, it is easy to make, and the materials are readily available, which can be used for various occasions, such as picnics, camping, or any outdoor activities.
In conclusion, the creation of a fan made of plastic bottle with string is an excellent way to reuse plastic bottles and can be made with simple steps. This project encourages everyone to contribute to environmental protection by utilizing what is available at home and reducing the number of plastic wastes.
For more such questions on Fan, click on:
https://brainly.com/question/29220424
#SPJ8
A photon has 8.0 x 10-15 J of energy. Planck's constant
is 6.63 x 10-34 Jos.
What is the frequency of the photon?
O 1.21 x 1019 Hz
O 8.3 x 10-20 HZ
O 1.21 10-19 Hz
O 8.3 x 1020 HZ
Answers
Answer:
^I dont know how he got 12 but the answer is A i believe
Explanation:Smart like dat
The frequency of a photon is related to its energy and Planck's constant by the equation:
frequency = energy / Planck's constant.
frequency =\((8.0 x 10-15 J) / (6.63 x 10-34 J) = 1.21 x 10^19 Hz\)
Therefore, the correct answer is \(1.21 x 10^19 Hz\)
What is Planck's constant?Planck's constant is a fundamental constant in physics that is related to the behavior of particles at the atomic and subatomic level. It is denoted by the letter "h" and is approximately equal to 6.63 x 10^-34 Joule-seconds. Planck's constant is named after Max Planck, a German physicist who proposed its existence in 1900 to explain the behavior of radiation emitted by black bodies.
Planck's constant plays a central role in quantum mechanics, which is the branch of physics that describes the behavior of particles at the atomic and subatomic level. It appears in a number of important equations, including the equation for the energy of a photon (E = hf) and the equation for the uncertainty principle (ΔxΔp ≥ h/4π).
Learn more about planck's constant here:
https://brainly.com/question/27389304
#SPJ2
What is the potential energy of a train car that has a mass of 1600 kg sitting 120 meters above the track
Answers
Answer:
\(\boxed {\boxed {\sf 1,881, 600 \ Joules}}\)
Explanation:
Potential energy is the product of mass, gravitational acceleration, and height.
\(E_p= mgh\)
The mass is 1600 kilograms and the height is 120 meters. Assuming this is on Earth, then the gravitational acceleration is 9.8 meters per square second.
\(m= 1600 \ kg\\g= 9.8 \ m/s^2 \\h= 120 \ m\)
Substitute the values into the formula.
\(E_p= ( 1600 \ kg )( 9.8 \ m/s^2)( 120 \ m)\)
Multiply the first two numbers.
\(E_p= 15680 \ kg*m/s^2 (120 \ m )\)
Multiply again.
\(E_p= 1881600 \ kg*m^2/s^2\)
1 kg square meter per square second is equal to 1 Joule. Our answer is equal to 1881600 Joules\(E_p= 1881600 \ J\)
The train's potential energy is 1,881,600 Joules.
If you live in Melbourne, Australia, the local magnetic field has a strength of about 4x10-5 T. The magnetic field vector is directed northward, making an angle of 30 deg above the horizontal. An electron in Melbourne is moving parallel to the ground, in the west direction, at a speed of 9x105 m/s. What are the magnitude and direction of the magnetic force on the electron
Answers
Answer:
\(5.76\times 10^{-18}\ \text{N}\) perpendicular to the velocity and magnetic field
Explanation:
B = Magnetic field = \(4\times 10^{-5}\ \text{T}\)
\(\theta\) = Angle the magnetic field makes with the horizontal = \(30^{\circ}\)
v = Velocity of electron = \(9\times 10^5\ \text{m/s}\)
q = Charge of electron = \(1.6\times 10^{-19}\ \text{C}\)
Magnetic force is given by
\(F=qvB\sin\theta\\\Rightarrow F=1.6\times 10^{-19}\times 9\times 10^5\times 4\times 10^{-5}\sin30^{\circ}\\\Rightarrow F=2.88\times 10^{-18}\ \text{N}\)
The magnitude of the magnetic force is \(2.88\times 10^{-18}\ \text{N}\) and the direction is perpendicular to the velocity and magnetic field.
wo small spherical balloons with equal masses m1 = m2 = 2 x 10-3 kg have charges qı = -8 x 10-9 C and q2 = -7 x 10-9 C. The two balloons are located at ři : 17 x 10-2, -2 x 10-2,0) m and 12 = (-3 x 10-2,9 x 10 p) m -2 (a) Which one of the following diagrams shows the positions of charged balloons? (b) What is the relative position vector pointing from balloon 1 to balloon 2? > m (c) Calculate a unit vector pointing in the direction of the electric force acting on balloon 2? > (d) Determine the electric force on balloon 2 by balloon 1. > N -1.533*10^-5 1.686*10^-5 0 -5 -1.533. 10 1.686 10-5 0 (e) If the distance between the balloons were increased by a factor of 5, how would the magnitude of electric force change?
Answers
The relative position vector pointing from balloon 1 to balloon 2 is -10*10^-2, 11*10^-2, 0. The magnitude of electric force change If r is increased by factor of 5 force would decrease 25 times.
m1 = m2 = 2*10^-3 kg
q1 = -8*10^-9C
q2 = -7*10^9C
r1 = 7*10^-2j + (-2*10^-2)j m
r2 = (-3*10^-2)j + (9*10^-2)j m
(a) Options not shown
(b) Relative position will be
< -10*10^-2, 11*10^-2, 0 >
(c) Unit vector will be same as part b vector direction as the force will be repulsion.
<r21> = < -0.672, 0.739, 0 >
(d) From part b
|r21| = 14.87m
F = < -1.53*10^-9,1.68*10^-9, 0>
(e) We know that
F = (kq1q2)/r^2
If r is increased by factor of 5 force would decrease 25 times.
Magnitude is a measure of the size or intensity of a physical or abstract quantity. It is commonly used in science, mathematics, and engineering to describe the strength or amount of something. Magnitude can be expressed numerically or visually, depending on the context.
In physics, magnitude is often used to describe the strength of a force or the intensity of a physical phenomenon, such as the magnitude of an earthquake or the magnitude of a magnetic field. In mathematics, magnitude can refer to the size of a number or vector, or the distance between two points in space. In general usage, magnitude can also be used to describe the importance or significance of something, such as the magnitude of a political decision or the magnitude of a humanitarian crisis.
To learn more about Magnitude visit here:
brainly.com/question/28173919
#SPJ4
can anyone heelp me pls pls
Answers
Answer: Liquid - Lotion
Suspension - Semisolid
Capsule - Solid
Explanation:
Give Brainliest if correct :)
Question 5 (15 points)
You stand on a bridge above a river and drop a rock into the water below from a
height of 35 m. (Assume no air resistance.)
Answers
a.
The acceleration of the rock as it falls is 9.8 m/s^2, which is the acceleration due to gravity.
b.
The time it takes to hit the water is 2.236 s
c.
The time it takes for the rock to hit the water if it is thrown horizontally is 0
How do we calculate?The time it takes to hit the water can be calculated using the equation:
t = √(2*h/g)
where h is the height (25 m), g is the acceleration due to gravity (9.8 m/s^2), and t is the time.
t = √(2*25/9.8) = √(5) = 2.236 s
c. The time it takes for the rock to hit the water if it is thrown horizontally can be calculated using the equation:
t = x/v
where x is the horizontal distance, v is the initial horizontal velocity (20 m/s), and t is the time. To find the horizontal distance, we can use the equation:
x = vt + 0.5a*t^2
25 = 20t + 0.59.8t^2
0.59.8t^2 + 20t - 25 = 0
Learn more about acceleration at:
https://brainly.com/question/460763
A uniform solid cylindrical flywheel has a mass of 50 kg and a radius of 40 cm. The flywheel begins to rotate faster with an acceleration of 1.5 rad/s2. The kinetic energy of the flywheel after 1 minute of rotation is:
A. 16.2 KJ
B. 180 KJ
C. 40.5 KJ
D. 32.4 KJ
Answers
The kinetic energy of the flywheel after 1 minute of rotation, given that it has a mass of 50 and radius of 40 cm is 32.4 KJ (Option D)
How do I determine the kinetic energy?We'll begin by obtaining the velocity of the flywheel. This is shown below:
Radius (r) = 40 cm = 40 / 100 = 0.4 mAcceleration (a) = 1.5 rad/s² = 1.5 × 0.4 = 0.6 m/s²Time (t) = 1 minute = 1 × 60 = 60 sVelocity (v) = ?v = at
v = 0.6 × 60
v = 36 m/s
Finally, we shall determine the kinetic energy of the flywheel. Details below:
Mass (m) = 50 KgVelocity (v) = 36 m/sKinetic energy (KE) =?KE = ½mv²
KE = ½ × 50 × 36²
KE = 25 × 1296
KE = 32400 J
Divide by 1000 to express in KJ
KE = 32400 / 1000
KE = 32.4 KJ
Thus, the kinetic energy is 32.4 KJ (Option D)
Learn more about kinetic energy:
https://brainly.com/question/7981774
#SPJ1
Demario's biology class has a quiz every other Friday. This is the third time Demario has been so worried about other personal matters that he hasn’t done quite as well on the quizzes as he might have otherwise. What has Demario upset is the fact that the professor leaves the room while the students take the quiz, and over half the class is taking the opportunity to cheat. Demario knows personally several of the other students in the class, and some of the ones Demario hangout with are among those who are cheating. Demario knows that a failure to speak to the professor about the cheating will result in his own grade being lower, since the school grades on the curve system. But if Demario does say something to the professor he will be doing his friends and the others a great harm, since cheating is taken very seriously at the school and can lead to expulsion. If Demario doesn’t “turn in” the classmates, the only other alternative is he will get a worse grade than he deserves. He will also be labled as a snitch among is peers and a cheater at the school, either of which Demario has never done. Further, if the professor somehow discovers that Demario is hiding the cheating of others, Demario will be considered an accessory to the cheating, and may be reprimanded for not turning others in, since the school operates on an honor system.
Critical thinking About Ethics Right vs Wrong
What should Demario do?
Should Demario cheat?
Should Demario turn in the cheating classmates?
Should Demario say nothing and not cheat himself?
Be specific in your answer about exactly what Demario should do. (Remember to use one of the three moral theories to solve this dilemma.)
Answers
1. It is unethical for Demario to cheat
2. Demario should not engage in cheating himself
3. Demario should not turn in cheating classmates without careful consideration
4. Reporting classmates may harm relationships, create animosity, and potentially lead to severe disciplinary actions.
What is ethics?A virtue ethics perspective may also be useful in this circumstance. Demario should make an effort to respect moral principles like honesty, fairness, and integrity while taking the potential repercussions into account and exhibiting empathy for his fellow students.
By employing this strategy, Demario behaves responsibly, deals with the problem subtly, encourages fairness in the educational setting, and upholds his or her own moral standards.
Learn more about ethics:https://brainly.com/question/26273329
#SPJ1
The magnitude of the electric field due to a point charge object at a distance 4.0 m is 9 N/C. From the same
charged object the electric field of magnitude, 16 N/C will be at a distance of
Answers
The electric field of magnitude 16 N/C will be at a distance of 6.0 meters from the charged object.
The magnitude of the electric field due to a point charge object follows the inverse square law, which states that the magnitude of the electric field is inversely proportional to the square of the distance from the charged object. Mathematically, this is expressed as:
\(E = k*q/r^2\)
where E is the electric field, k is Coulomb's constant (\(k = 9 x 10^9 N*m^2/C^2\)), q is the charge of the object, and r is the distance from the object.
We can use this formula to find the distance at which the electric field has a magnitude of 16 N/C. Let's call this distance x:
16 = \(k*q/x^2\)
We can rearrange this equation to solve for x:
x = \(\sqrt(k*q/16)\)
To find q, we need another piece of information. We know that the electric field has a magnitude of 9 N/C at a distance of 4.0 m. Using the same formula as before, we can solve for q:
9 = \(k*q/4^2\)
q = \(9*4^2/k\)
Now we can substitute this value for q into the equation for x:
x =\(\sqrt(k*(9*4^2/k)/16)\)
x =\(\sqrt(9*4^2/16)\)
x = \(\sqrt(36)\)
x = 6.0 meters
Therefore, the electric field of magnitude 16 N/C will be at a distance of 6.0 meters from the charged object.
Know more about electric field here:
https://brainly.com/question/14372859
#SPJ11
sound is capable of travelling in which medium or media ?
\( \\ \)
ty! ~
Answers
Answer:
sound travels in series of interconnected and interactive particles they travel through the followings mediumsGas, Liquid and SolidSound needs a material medium for their propagation like solid, liquid or gas to travel because the molecules of solid, liquid and gases carry sound waves from one point to another. Sound cannot progress through the vacuum because the vacuum has no molecules which can vibrate and carry the sound waves.
hope helpz~