The derivative of the function is dy/dx = 4([tex]x^{4sinx}[/tex])[(sin x) / x + (cos x) (ln x)]
y = [tex]x^{4sin x}[/tex]
Taking the log of both sides:
ln y = sin x ln [tex]x^{4}[/tex] = (sin x) * (4 ln x) = 4 (sin x)(ln x)
Now differentiate both sides. On the left you'll need to use the chain rule, and on the right you'll use the product rule:
1/y dy/dx = 4[(sin x) (1/x) + (cos x)(ln x)] = 4 [(sin x) / x + (cos x)(ln x)]
Multiply both sides by y
dy/dx = y * 4 [(sin x) / x + (cos x)(ln x)]
Since y = [tex]x^{4sinx}[/tex], we can rewrite this as:
dy/dx = [tex]x^{4sinx}[/tex] * 4 [(sin x) / x + (cos x)(ln x)]
dy/dx = 4[tex]x^{4sinx}[/tex] [(sin x) / x + (cos x)(ln x)]
Chain rule is the formula used to find the derivative of a composite function. Product rule is used to find derivative of products of two or more functions.
Therefore, the derivative of the function y = [tex]x^{4sin x}[/tex] is dy/dx = 4([tex]x^{4sinx}[/tex])[(sin x) / x + (cos x) (ln x)]
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Rodney wants to motivate his sales force to increase sales in the upcoming quarter. which channel should he choose to be the most persuasive?
In order to be most persuasive and to motivate his sales force to increase sales in the upcoming quarter, Rodney should choose a face-to-face group meeting.
Why is Face-face communication more effective?Face-to-face communication is more effective because seeing each other allows a person to understand each other’s body language and pick up on nonverbal cues.
This is important because a lot of communication can be made through non-verbal means just by observing body language.
During a face-to-face meeting, you have the ability to manipulate and attract the group’s attention and establish a sense of trust that allows for easy persuasion to the group.
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A clock in a spaceship is observed to run at a speed of only 3 4 that of a similar clock at rest on earth. how fast (in terms of c) is the spaceship moving?
The speed of spaceship which run at a speed of only 3 4 that of a similar clock at rest on earth is 2.4 x 10^8 m/s
As from the given data, the clock in a spaceship is observed to run at a speed of 3/5 of a similar clock that rest on the earth is
T/T° = 3/5
When time moves at a high rate of pace, it slows down. The quantity of time dilation increases as an object moves more quickly. The constant speed of light, independent of the source of the light and the viewpoint of the observer, is partially explained by time dilation.
The expression for the time dilation is given by
T = γT°
γ = T/T°
γ = 1/√1 - v^2/c^2 is time dilation
Substituting the values in the above equation as,
γ = T/T°
5/3 = 1/√1 - v^2/c^2
v^2/c^2 = 16/25
v = 0.8 c
v = 0.8 x 3 x 10^8 m/s
v = 2.4 x 10^8 m/s
Hence, speed of spaceship moving is
2.4 x 10^8 m/s
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River water held behind a dam is a form of ________. group of answer choices
a. potential energy
b. chemical energy
c. thermodynamics
d. kinetic energy
Potential energy is present in the river water behind a dam.
How is potential energy defined?Potential energy is a form of stored energy that is dependent on the relationship between different system components. When a spring is compressed or stretched, its potential energy increases. If a steel ball is raised above the ground as opposed to falling to the ground, it has more potential energy.The object's mass, its mass in relation to some reference points, and the gravitational field it is in all affect the potential energy of the object.Joule is the SI unit of potential energy as a result (J)As weight and height increase, gravitational potential energy rises.
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what would happen to the bulb if we had one cell and one light bulb in a series circuit
All bulbs in the circuit go out happen to the bulb if we had one cell and one light bulb in a series circuit.
A series circuit consists of a channel via each component where the entire current flows. In a parallel circuit, the branches divide the current so that only a portion of it passes through each branch.
A circuit is referred to as a series circuit when all of the devices are linked in series. Each component of a series circuit is connected in such a way that only one channel for charge to travel via the external circuit is possible.
"A circuit with the components arranged in a straight line, so that all the current goes through each component in turn," is the definition of a simple series circuit.
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Deven is describing aerobic exercise to his friend. What is the MOST
accurate statement he can make in his description?
O Aerobic exercise is generally short and intense.
O Aerobic exercise requires very little oxygen.
Aerobic exercise burns fewer calories than anaerobic exercise.
O Aerobic exercise can last continuously for many minutes.
According to the research, the correct option is Aerobic exercise can last continuously for many minutes. It is the statement that correctly he can use to make in his description about aerobic exercise.
What is aerobic exercise?They are those physical activities that aim to burn fat using a high amount of oxygen.
In this sense, these exercises allow to improve the resistance of the person, they are not very intense but are developed in long periods, unlike anaerobic exercises that are more intense and brief.
Therefore, we can conclude that according to the research, the correct option is Aerobic exercise can last continuously for many minutes. It is the statement that correctly he can use to make in his description about aerobic exercise.
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Answer: Aerobic exercise can last continuously for many minutes.
Explanation:
Got it correct
In how many ways can the elements of [n] be permuted if 1 must precede 2 and 3 is to precede 4?
No. of ways in the elements of n be permuted is n!/4
Number of elements = n
Number of face in which the element of n be permuted if 1 must proceed 2 and 3 is to precede 4.
n = 4
The possible permutation will
(1,2,3,4), (1,3,2,4),(1,3,4,2),(3,4,1,2),(3,1,2,4),(3,1,4,2)
There are 6 possible outcomes
For n= 5
With 1,2,3,4 we add 5 in the arrangement with above terms
The possible number of permutation
5×6 = 30
When n = 6
30×6 = 180.
So for an element
If 1 precede 2 and 3 is yo precede 4 is
[tex]\frac{n*(n-1)*(n-2) ........ 6*5*6*4!}{4!}[/tex]= n! ×6/4!
= n!/4
No. of ways in the elements of n be permuted is n!/4
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An astronomer observes two ordinary stars. the first one turns out to be twice as hot as the second. this means that the first one radiates:________
Two common stars are observed by an astronomer. It turns out that the first one is twice as hot as the second. This indicates that the first emits around 16 times as much energy as the second.
Describe about astronomers?Astronomers are specialists in the field of astronomy, which is the study of celestial bodies and phenomena. They use various methods to explore and understand space beyond Earth, including using telescopes, satellites, and mathematical models.
They also compile data on different astronomical objects into comprehensive databases that can be used by researchers all over the world. This helps us to better understand our universe and how it works. Additionally, astronomers work towards developing new technologies that will help us probe further into space. As we continue to learn more about our galaxy and its many inhabitants, astronomers have a significant role to play in informing society about these discoveries.
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In a certain digital waveform, the period is twice the pulse width. the duty cycle is?
A certain digital waveform has a period that is twice as wide as the pulse. the duty cycle is 50%.
Briefing:The ratio of pulse width to pulse duration is known as the duty cycle.
In actuality, duty cycle equals pulse duration divided by total out-of-band time.
i.e.) = pulse duration/total time period
So pulse width=on time + off time
i.e.)total time period
Duty Cycle=(1/2)*100
=50%.
What is digital waveform and its types?All Binary Information in Digital Systems Appear. A Digital Waveform Carries Binary Information as waveforms that represent sequences of bits – Common strategy: HIGH is 1 and LOW is 0.
What does a digital waveform look like?Digital signals typically have one of two values, such as 0V or 5V. These signals' timing graphs resemble square waves. The main distinction between analog and digital waves is that.
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The heat death of the universe is a theoretical time in the future when the universe is supposed to?
The heat death of the universe is a theoretical time in the future when the universe is supposed to use up the entire supply of entropy.
What is the heat death of the universe entropy?According to the theory of the heat death of the universe, which is also known as the Big Chill or Big Freeze, the cosmos will eventually reach a condition where there is no thermodynamic free energy and won't be able to support processes that increase entropy. As entropy rises, matter and energy continue to dissipate until our universe is infinitely chaotic, at which point events come to a halt since entropy can no longer rise. This is referred to as the universe's heat death. Some claim that nothing happens since things can't get any worse.Learn more about the heat death with the help of the given link:
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Suppose you drive through an entrance ramp at a modest speed and your acceleration is 3.0 m/s2. what will be the acceleration if you double your speed?
The acceleration if we double the speed is 27 m/s².
How to find the acceleration if we double the speed?
A centripetal acceleration, or acceleration toward the center of the circle, results from moving in a constant circular motion.
a = v²/r is the formula for calculating an object's circular motion acceleration.
Since the radius never changes, let's set it at 5 m. Using a = 3 m/s² and r = 3m to solve for the velocity, we get the following results:
Were, 3 = v²/3
simplifying the equation, we get
⇒ 9 = v²
⇒ 3 = v
When the circular path has a radius of 3 m and an acceleration of
3 m/s², the velocity is 3 m/s.
Now let's triple the velocity: 3 m/s → 9 m/s.
Let's solve for the acceleration using v = 9 m/s and r = 3 m.
a = (9)²/3
⇒ a = 81/3
⇒ a = 27
If you triple your speed, the acceleration is 27 m/s².
This makes sense because an is precisely proportional to v², which means that if your speed is tripled, your acceleration will increase by a factor of 3², or nine times.
a = 3 [tex]*[/tex] 9 = 27 m/s²
As a side note, doubling your speed would improve the acceleration by a factor of 2² - a 4 times increase.
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How does the height of a ramp affect the time it takes for an object to move down the ramp? please explain each one below:
1.How does the amount of salt affect how long it takes water to boil?
2.How does the volume of water affect how long it will take to boil?
3.How does the length of a paper airplane affect how far it will fly?
4.How do jumping jacks affect your heart rate?
The greater the height of a ramp, the shorter the time it takes for an object to move down the ramp.
The greater the amount of salt, the In addition the larger the longer it takes water to boil.
An increase in volume of water increases the time it takes to boil and vice versa.
Increase in the length of the paper airplane, the farther it will fly.
Jumping Jack increases the heart rate.
How does the height of a ramp affect the time it takes for an object to move down the ramp?A ramp is an inclined plane which is a form of simple machine that is used to lift heavy objects off the floor or to lower heavy objects down.
The greater the height of a ramp, the shorter the time it takes for an object to move down the ramp due to increased acceleration.
How does the amount of salt affect how long it takes water to boil?The addition of solutes to pure solvent raises the boiling point of the solute.
Therefore, the greater the amount of salt, the In addition the larger the longer it takes water to boil.
How does the volume of water affect how long it will take to boil?The mass of water increases with increase in volume of water.
Therefore, an increase in volume of water increases the time it takes to boil and vice versa.
How does the length of a paper airplane affect how far it will fly?For a paper airplane the larger its wings, the greater the lift generated.
The greater the lift, the farther the paper airplane will fly.
Therefore, an increase in the length of the paper airplane, the farther it will fly.
How do jumping jacks affect your heart rate?Exercise increases the heart rate.
Jumping jack is a for of exercise. Therefore, Jumping Jack increases the heart rate.
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Most active galactic nuclei are powered by:_____.
a. supermassive black holes.
b. a large number of supernovae.
c. mergers of compact objects.
c. black hole mergers.
d. extra-terrestrial civilizations.
Most active galactic nuclei are powered by: a. supermassive black holes.
A supermassive black hole is a type of huge black hole with a mass that can be millions to billions of times the mass of the Sun.
It is also known as SMBH or SBH. And inside of the back hole is a place where the material is compressed down to an enormously tiny point, and all the ideas of time and space completely break down.
What is a black hole?A black hole is a very dense space in which gravity becomes so strong that not even light is able to get out, this is because matter is compressed into a very small space. A black hole is usually formed from the remains of a star that dies in a supernova.
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When you push a crate across a level floor at constant velocity, friction between the crate and the floor is?
Answer:
The friction between the crate and the floor is the same amount as your pushing force when you push a crate across a level floor at constant velocity.
Explanation:
Remember that the force produced by two surfaces coming into contact and sliding against one another is frictional force. This is expressed by the direct relationship between frictional force and normal force.
f=μN
Where
f = frictional force
µ = coefficient of friction
N = Normal force
By dry friction, two solid surfaces in touch are opposed to one another's relative lateral motion. Dry friction is further separated into kinetic friction between moving surfaces and static friction (sometimes known as "stiction") between non-moving surfaces. Additionally, dry friction is typically caused by the interaction of surface characteristics, particularly rough surfaces.
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An ohmmeter should be connected to the circuit or component being tested ________.
Mars is roughly 60 million km from earth. How long does it take for a radio signal originating from earth to reach mars? radio signals travel at the speed of light
Answer:
200 seconds
Explanation:
60 000 000 000 m / 3 x 10^8 m/s
6 x 10 ^10 / 3 x 10^8 s
2 x 10^2 s = 200 seconds
What voltage must be applied to an 8.00 nf capacitor to store 0.160 mc of charge?
The voltage that must be applied is 20 KV
Given that,
Capacitance C = 8 nF = 8 * [tex]10^{-9}[/tex] F
Charge Q = 0.16 mC = 0.16 * [tex]10^{-3}[/tex] C
We know that C = Q / V
V = 0.16 * [tex]10^{-3}[/tex] / 8 * [tex]10^{-9}[/tex] = 20 * [tex]10^{3}[/tex] V = 20 KV
Voltage is nothing but an electromotive force.
Therefore, the voltage that must be applied is 20 KV
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A steadily flowing stream of water is funneled into a graduated cylinder for exactly 30 s, during which time 50 ml is collected. what is the volumetric flow rate of the stream? the mass flow rate?
The stream has a mass flow rate of 1.666 g/sec and a volumetric flow rate of 1.666 ml/sec.
What is the mass known as?The dimensionless quantity mass is used to represent the amount of matter contained in a particle or object (symbolized m). The kilogram is the chosen unit of mass according to the International System (SI) (kg).
How is the mass determined?The following equation can be used to determine mass = volume * density. It is possible to gauge the gravitational force acting on a mass by determining its weight. The Newton (N) is the SI unit of weight (N).
Briefing:t= 30 sec
V= 50ml
Volumetric flow rate = V/t
= 50ml/30sec
= 1.666 ml/sec
We know density of water= 1g/cm³
= 1 g/ml
So, mass flow rate = V/t
= 1g/ml * 50ml/30sec
= 1.666 g/sec.
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How long will it take a car to go from a complete stop to 44 km/hr if they are accelerating
at 5m/s²?
Answer:
Time taken = 2.444sec
Explanation:
Greetings !
Given values :-
Final velocity (Vf) =44km/hr =12.22m/s Initial velocity (Vi) = 0m/sAcceleration (a)= 5m/s²Required values:-
Time taken (t) =?Solution/ work-out:-
Firstly change the km/hr value to m/s
Then, recall the Velocity-Time Equation:
[tex]vf = vi \: + at[/tex]
substitute known variables into the equation
[tex](12.22) = (0) + (5)t[/tex]
Solve for time
[tex]t = 2.444sec[/tex]
Hope it helps!!
How far does a person travle in coming to a complete stop in 33 ms at a constant acceleration of 60g?
A person travelled a distance of 0.32m in coming to a complete stop.
Acceleration - Acceleration is the rate of change of velocity with respect to time.
It is a vector quantity.It has both the magnitude and direction. It is measured in m/s²The distance travelled is calculated as
Time t = 33ms = 33/1000 = 0.033s
Acceleration a = 60g
g = 9.8 m/s²
a = 60g = 60 × 9.8 = 588 m/s²
The person must be moving at a certain initial velocity.
Since the person is going to stop, V = 0
using equation of motion we get
V = U - at
0 = U - 588 × 0.033
0 = U - 19.404
U = 19.404 m/s
The distance travelled is
using equation of motion
V² = U² - 2aS
0 = (19.404)² - 2 × 588S
1176S = 376.51
S = 376.51 / 1176
S = 0.32 m
the distance is 0.32m
The person travelled a distance of 0.32m in coming to a complete stop.
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The rate at which a star or other object emits electromagnetic energy into space is called its:________
The rate at which a star or other object emits electromagnetic energy into space is called its luminosity.
What are luminosity and magnitude?A star's luminosity is a measurably inherent characteristic that is independent of distance. On the other hand, the concept of magnitude takes into account distance. According to the inverse-square law, the apparent magnitude is a measurement of how much the flux of light decreases with increasing distance.
The total amount of energy emitted by a star or other celestial object each second is expressed as luminosity abbreviated L. So, this is how much power a star produces. A star's bolometric luminosity is its total power output at all wavelengths.
The quantity of light emitted by a star's surface determines its brightness. How bright a star appears to a detector on Earth is known as apparent brightness. Distance affects how luminosity and apparent brightness differ from one another.
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A ball is rolled horizontally off the top of a table. After 3 seconds the ball lands on the ground with a final velocity of −3.5 m/s. Which kinematic equation would be most useful for finding the ball’s initial velocity? (Assume a= −9.8 m/s2)
The following kinematic equation will be most useful for finding the ball’s initial velocity:
v = u + at
There are three kinematic equations, out of which any one equation can be used according to the given situation. These are:
v = u+atv² -u² = 2ass = ut + 1/2at²In the above situation, a ball is rolled from the top of a table and the ball lands on the ground after 3 seconds with a final velocity of 3.5 m/s.
We have been provided by the final velocity, acceleration, and time taken by the ball, so the equation that would be most useful for finding the initial velocity will be, v =u +at.
Thus, the following kinematic equation will be most useful for finding the ball’s initial velocity:
v = u + at
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What is the force required to move a block of mass 150 pound by a distance of 5ft in 8 seconds?
Force required to move a block is 1.615 N
Given:
mass of block = m = 150 pounds = 68 kg
distance = d = 5 ft = 1.52 metres
time = t = 8 sec
To Find:
force required to move the block
Solution: Force is defined as product of mass and acceleration and it's unit is N or Newton.
Velocity = displacement/ time = 1.52 / 8 = 0.19 m/s
Acceleration = velocity/time = 0.19/8 =
0.023 m/s^2
Force = mass x acceleration = 68x0.023 = 1.615 N
Hence, force required to move the block is 1.615 N
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If you use the approximate nonrelativistic equation for the magnitude of momentum of the proton, what answer do you get?
The answer is 4.96 * 10⁻¹⁹ kg m / s
Proton is an elementary particle that is identical to the nucleus of the hydrogen atom, along with the neutron is a constituent of all other atomic nuclei, that carries a positive charge numerically equal to the charge of an electron, and has a mass of 1.673 × 10−27 kilogram
nonrelativistic equation for the magnitude of the momentum of the proton is p = m * v
Then: p = m * v
Then Let's calculate its value
After that p = 1.67 * 10⁻²⁷ * 0.99 * 3 * 10⁸
Now, p = 4.96 * 10⁻¹⁹ kg m / s
hence the answer is 4.96 * 10⁻¹⁹ kg m / s
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Suppose the link speed between the source and destination is 100 megabits (mb) per second. approximately how long will it take to send a 12 megabyte (mb) file?
Approximately About 1 second will take to send a 12-megabyte (mb) file.
What is link speed?It refers to the fastest rate at which data can travel from a wireless client to a wireless router over a wireless link. At the application layer, user actions like file transfers and web content browsing take place. Compared to the rate at the physical layer, the rate at the application layer will be substantially lower.
What Internet Speed Is Best for Using Several Devices? According to the FCC, the best ISPs for households with two or more connected devices and moderate to heavy internet usage should have download speeds of at least 12 megabits per second (Mbps). It is advised to use 25 Mbps while using four or more devices.
Anywhere from 25 to 100 Mbps is considered to be an excellent internet speed.
Up to 2 devices can stream, browse the web, and check email at speeds of 25 Mbps. A few more individuals can stream in HD or even 4K, stream music, play games, surf social media, and work from home at speeds of 50 to 100 Mbps.
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In a large perfectly quiet room, at what maximum distance could you hear a bee with a power output of 1 nw ? recall that the threshold of hearing is 10−12w/m2
Using threshold intensity, the maximum distance the sound could hear a bee is 8.92 m.
We need to know about intensity to solve this problem. Intensity can be determined as the ratio of power to the area. The magnitude of intensity can be calculated by
I = P / (4πr²)
where I is intensity, P is power and r is distance.
From the question above, we know that
P = 1 nW = 10¯⁹ W
I = 10¯¹² W/m²
By substituting the given parameters, we get
I = P / (4πr²)
10¯¹² = 10¯⁹ / (4πr²)
r² = 79.55
r = √79.55
r = 8.92 m
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The conventional system of signs that indicate relative durations of long and short sounds is called.
Musical notation is the term used to describe the common system of signs used to denote the relative duration of long and short sounds.
What is a musical notation?Music notation, often known as musical notation, is any technique used to graphically express audibly perceived music performed with instruments or sung by a human voice using written, printed, or other symbol-based representations. This includes notation for periods of silence like rests.
Throughout history, many civilizations have used different types of notation, and the knowledge of early musical notation is generally sparse. Different musical genres and cultural groups employ various methods of music notation, even during the same time period, such as the 2010s. For instance, while sheet music with staves and note-heads is the most popular method for professional classical musicians, the Nashville Number System is the main method used by professional country music session musicians.
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Theorem: there is no smallest positive rational number.theorem: there is no smallest positive rational number. a proof by contradiction of the theorem starts by assuming which fact?
Assume there is a smallest rational integer that has the following form: a/b
Then observe that we can define a/(b+1), which is strictly less than a/b because its divisor is bigger and is rational because it is the product of two numbers. Due to the contradiction created by our original claims that a/b is the smallest rational number that is possible, we might conclude that there is no such thing as the smallest rational number.
There can therefore be no smallest rational number because we may always define a smaller rational number than the one we now possess.
What is Rational number ?Any number that can be expressed as a ratio is considered reasonable. It is therefore possible to represent it as a fraction when the numerator and denominator are both full numbers.
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Parallels of _________________ measure the distance north and south of the _______________.
Parallels of Latitude measure the distance north and south of the Equator.
The distance north or south of the equator is measured by latitude. Latitude lines, often known as parallels, are imaginary lines that divide the Earth. They go east to west, although you may measure north or south. The most well-known parallel is the equator. At 0 degrees latitude, the equator is midway between the North Pole and the South Pole.
The world is divided into two halves by an equator: the Northern Hemisphere and the Southern Hemisphere. The Earth's equator is the widest point on the planet. The circumference of the Earth, measured at the Equator, is 40,075 kilometres (24,901 miles).
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A baseball has a mass of 0.144 kg. a professional pitcher throws a baseball 90 mi/h, which is 40.2 m/s. what is the magnitude of the momentum of the pitched baseball?
The magnitude of the momentum is 5.78 kgm/s
Given:
mass of baseball = 0.144 kg
initial speed = V1 = 90 m/h = 0.025 m/s
final speed = V2 = 40.2 m/s
To Find:
momentum = p
Solution: momentum, product of the mass of a particle and its velocity. Momentum is a vector quantity; i.e., it has both magnitude and direction.
∆ P = m(V2 - V1)
∆ P = 0.144(40.2 - 0.025)
∆ P = 5.78 kgm/s
Hence, magnitude of the momentum is
Hence, magnitude of the momentum is 5.78 kgm/s
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How do ribbons differ from the toolbars used in previous versions of office applications? point out the advantages of using the ribbons.
The ribbon replaces the menus and toolbars in previous versions. The Ribbon makes available most of the functions that were previously hidden in the File menus.
The ribbon is a command panel that organizes program functions into a series of tabs at the top of the screen. Ribbon tabs consist of groups of closely related commands to help users quickly find the commands they want. Each ribbon is a bar across the page.
The advantages of using the ribbons are:
The ribbon makes it easy to see and find commands for formatting a document.Ribbons are a modern way to help users find, understand, and use commands efficiently and directly with a minimum of clicks, no trial-and-error, and no reference to help.To know more about ribbon,
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