Using the concepts of Extensive and Intensive Properties, we got The specific volume of a substance is the volume per gram of substance. It is an example of physical extensive property.
Physical characteristics of matter are classified into two types: intense properties and extended properties.
An extensive property is a property that is affected by the amount of materials in a sample. Mass and volume are the two examples of extensive characteristics. An intense property is a property of matter that is determined only by the kind of matter in a sample and not by its quantity.
All the specific properties are extensive properties. It can be understood with the example of a specific volume, which is defined as the volume per gram of substance. Therefore, it includes mass.
Thus, it is an extensive property.
Hence, The specific volume of a substance is the volume per gram of substance. It is an example of physical extensive property.
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a sector of a circle of radius 3in has an area of 25in^2 . find the central angle of the sector. do not round any intermediate computations. round your answer to the nearest tenth.
The Central angle of Sector is 305.73° . The Central angle of sector is defined as the angle formed by two radii.
The Sector Area of a circle is the amount of space enclosed within the sector boundary. A sector always starts from the center of the circle. A circle sector is defined as the portion of the circle bounded between two radii and their adjacent arcs.
Mathematically, A = (θ/360°) × π r²
where, A---> area of sector of circle
θ----> Central angle of sector
r ----> radius of circle
pi (π) = 3.14
we have, Radius of circle (r) = 3 inch
Area of sector of circle (A) = 24 inch²
we have to find out the value of central angle of Sector .
putting the values in above formula we get,
24 = (θ/360°) × 3.14 ×(3)²
=> θ/360° = 24/28.26 = 0.849
=> θ = 360×0.849 = 305.73°
Hence, Central angle of sector is 305.73° ..
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A tone i dropped from 45 meter high building how will it be moving when it reache the ground and what will it velocity be
The stone reach in 3 second and with velocity 15m/s.
To find time
s = 1/2 a [tex]t^{2}[/tex]
s = distance, given = 45 meter
a = acceleration, given = 10 m/[tex]s^{2}[/tex]
Put these values in formula to get time, s = 1/2 a [tex]t^{2}[/tex]
t = 3 s
Now, to find velocity.
v = s/t
v = 45/3
v = 15 m/s
Therefore, the stone reach in 3 second and with velocity 15m/s.
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although g is closer to the equator than d, it is cooler. what is the most likely factor that would contribute to this difference?
The correct answer is the most likly factor that contribute to this difference is angle of solar radiation and temprature.
Seasonal temperatures of sites at various latitudes are influenced by the angle of incoming solar radiation. The incoming solar energy is more direct (almost perpendicular or closer to a 90° angle) when the sun's rays hit the surface of the Earth close to the equator. Warmer temperatures result from the solar radiation being concentrated over a smaller surface area. Higher latitudes have narrower solar radiation angles, which spread energy across a broader region of the surface and result in cooler temperatures. Surface temperatures are typically warmer at lower latitudes and cooler at higher latitudes because the angle of radiation varies with latitude (even though higher latitudes have more hours of daylight during the summer months).
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a hypothetical weak acid, ha, dissociates in water according to the reaction below. if the ph of a 0.400 m aqueous solution of ha is 3.87, what is the value of ka for ha
The dissociation constant Ka for weak acid HA is 0.25× 10⁻⁷.
Equilibrium constant of a chemical reaction is known as dissociation associated with acid-base reactions. Species HA is an acid that dissociates into the conjugate base of the acid, A , and the hydrogen ion, H⁺ .
First, write the balanced formula for the partial ionization of the acid,
HA(aq) + H₂O(l) ⇌ A⁻ (aq)+H₃O⁺(aq)
Note that there is a 1:1 molar ratio everywhere For every mole of acid that ionizes in aqueous solution, you get 1 mole of its conjugate base and 1 mole of the hydronium ion H₃O⁺.
The equilibrium concentration of hydronium ions can now be calculated from the pH value of the solution.
pH = - log ( [ H₃O⁺]) = [ H₃O⁺ ]= 10⁻ᵖᴴ
For the given question we have a pH of 3.87 which means [H₃O⁺] = 10⁻³·⁸⁷
and concentration of H₂O is 0.400M.
By definition the acid dissociation constant Ka equals to
Ka = [ A⁻ ] [H₃O⁺ ] / [HA]
The acid dissociation constant equation is written using equilibrium concentrations. Therefore, if the reaction produced a hydronium ion concentration equal to 10⁻⁴ M, it also produced a conjugate base concentration equal to 10⁻⁴M. The initial concentration of the acid is much higher than the concentrations of the conjugate base and hydronium ion, so they can be approximated as constants.
Ka = 10⁻⁴ × 10⁻⁴/ 0.400 = 0.25× 10⁻⁷
Hence, the dissociation constant of acid Ka is 0.25× 10⁻⁷.
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g a solution is made by dissolving 15.5 g of calcium chloride, cacl2, in enough water to make exactly 100 ml of solution. what is the concentration (molarity) of the following in mol/l?
A solution is made by dissolving 15.5 g of calcium chloride, cacl2, in enough water to make exactly 100 ml of solution. The a solution is made by dissolving 15.5 g of calcium chloride, cacl2, in enough water to make exactly 100 ml of solution will be 1.4 mol /L
given
volume of solution = 100 mL = 0.1 L
number of moles = mass / molar mass
= 15.5 / 111 = 0.14 mol
molarity = number of moles of solute / volume of the solution
= 0.14 / 0.1 = 1.4 mol /L
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a pendulum is swinging back and forth around its equilibrium position. at which point does the bob has the maximum speed?
The correct answer is Position D where bob has the maximum speed.
Where is the peak kinetic energy during a pendulum swing?
At its lowest point, when the weight is travelling the quickest, an active pendulum possesses the highest kinetic energy. The total of kinetic and potential energy, or mechanical energy, is always present in an ideal pendulum system.
The restoring force is therefore directed in the same direction as the bob is travelling, to the right. The bob will gain speed as a result of this push, reaching its top speed at point D, which is the equilibrium position.
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What are the examples of forms of globalization?.
Examples of forms of globalization: Economic globalization, political globalization, and cultural globalization.
In easy terms, globalization is the manner with the aid of which human beings and items flow effortlessly throughout borders. mainly, it is an economic idea – the mixing of markets, alternatives, and investments with few boundaries to gradually drift services and products among international locations.
An instance of environmental globalization would be the collection of global Tropical wooden agreement treaties (1983, 1994, 2006), setting up global Tropical wooden business enterprises,s and promoting sustainable control of tropical forests. excellent examples of cultural globalization are, for example, the trading of commodities including coffee or avocados. espresso is stated to be originally from Ethiopia and eaten up inside the Arabid vicinity. nonetheless, due to industrial trades after the 11th century, it's far from nowadays referred to as a globally fed-on commodity.
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An object is thrown off a cliff with a horizontal speed of 10 m/sec. After 3 seconds the object hits the ground. Find the height of the cliff.
The height of the cliff is 30 m.
How to find the height of the cliff?Between distance/height, speed and time can be understood as follows.
The formula for distance/height is speed times time or written
s = (v) (t)
The formula for time is distance divided by speed or written
t = s ÷ v.
v is the symbol for speed (velocity),
s is the distance,
and t is the time.
The formula for speed is distance divided by time or written v = s ÷ t.
To determine the height of the cliff, use the equation:
S = (v) (t)
We have,
Speed of object thrown from the cliff = 10 m/s ⇒ (v)
The time it takes the object to hit the ground = 3 s ⇒ t
So, the height of the cliff is:
S = (10) (3)
= 30 m
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The 2 substances in the containers below were heated to 50 degrees Celsius; then left to cool to room Temp of 20 degrees Celsius. Which will reach room temperature first?
Answer' RA
Explanation: I need points mb gang
A piece of what nasa space shuttle was recently discovered by a film crew in the atlantic ocean?.
A piece of the Challenger Space Shuttle was recently discovered by a film crew in the atlantic ocean.
Challenger became the first space commute to be destroyed in a project twist of fate. The accrued debris of the vessel is currently buried in decommissioned missile silos at launch complex 31, Cape Canaveral Air pressure Station.
On January 28, 1986, the gap travel Challenger broke aside 73 seconds into its flight, killing all seven group individuals aboard. The spacecraft disintegrated 46,000 ft (14 km) above the Atlantic Ocean, off the coast of Cape Canaveral, Florida, at 11:39 a.m. EST (sixteen:39 UTC).
A massive segment of the destroyed space go back and forth Challenger has been found buried in sand at the bottom of the Atlantic.
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At which point does the train on time his roller coaster have the most kinetic energy? Explain
The point of time at which the train in roller coaster will have the most kinetic energy is at the lowest point of the roller coaster.
KE = 1 / 2 m v²
KE = Kinetic energy
m = Mass
v = Velocity
KE ∝ v²
In a roller coaster no external force is applied. It works on the principle of law of conservation of energy. Initially it is raised to a height where it gains potential energy. From there due to downwards motion, potential energy is converted into kinetic energy. So in the lowest point of its motion, potential energy is fully converted into kinetic energy and hence it will be maximum at this point.
Therefore, the point of time at which the train in roller coaster will have the most kinetic energy is at the lowest point of the roller coaster.
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a jet moving at 500 km/h due east is in a region where the wind is moving at 120.0 km/h in a direction 30.00 degrees north of east. what is the speed of the aircraft relative to the ground
The speed of the aircraft relative to the ground is 606.9 km/h.
Solution:
x-y coordinate system:
x is positive east. Similarly, y is positive north.
Now let's decompose each vector into x-y
500 km/h due east = (500, 0)
120 km/h at 30 north of east
= (120cos(30), 120 x sin(30)
= (120 x [tex]\frac{\sqrt{3} }{2} , 120*\frac{1}{2}[/tex])
= (60 x [tex]\sqrt{3}[/tex], (60)
Adding the vectors.
= (500,0)+(60 x [tex]\sqrt{(3)}[/tex],(60)
= (500 + 60 x [tex]\sqrt{(3)}[/tex],60
= (500 + 60 x 1.73,60)
= (500 + 103.8,60)
= (603.8,60)
Returning back to polar form
Magnitude = [tex]\sqrt{603.923^{2}+60^{2} } = 606.9[/tex]
The speed of the aircraft relative to the ground is equal to the speed of the aircraft relative to the air plus the velocity of the air relative to the ground. In other words, it neither moves closer nor farther away from you. They move at 80 km/h relative to the observer next to the track. They do not move relative to the textbook.
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A projectile i launched horizontally on a table that it 40 cm high. The projectile land 10 m away. What i the horizontal
velocity of the projectile a it leave the launcher?
The horizontal velocity of the projectile it leaves the launcher is 0.283 m/s.
The horizontal speed of a projectile is regular, and there's a vertical acceleration because of gravity; its cost is 9.8 m/s/s, down, The vertical speed of a projectile changes via nine.8 m/s every second, The horizontal motion of a projectile is impartial to its vertical movement.
Projectile motion is a form of motion experienced with the aid of an object or particle that is projected in a gravitational field, such as from Earth's floor, and movements alongside a curved route below the action of gravity best.
Projectile motion is the movement of an object thrown (projected) into the air. After the initial force that launches the item, it most effectively reports the pressure of gravity. The object is known as a projectile, and its route is called its trajectory.
Calculation:-
Horizontal distance = 40 cm
= 0.4 m
height of table = 10 m
Let vertical velocity is 0.
S = ut +1/2 at²
10 = 0 + 0.5 × 10 t²
t² = 10/5
t = 1.414 sec.
At the same time, it will take to cover a horizontal distance of 0.4 m.
Velocity = distance/time
= 0.4/1,414
= 0.283 m/s
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A radio wave has a wavelength of 1000m and a frequency of 3x10^5 Hz. Calculate the wave speed.
Answer:
300000000 m/s
Explanation:
wave Speed = Wavelength x Wave Frequency
wave speed = 1000m * 300000
wave speed = 300000000 m/s
a uniform horizontal beam 8 m long is attached by a frictionless pivot to a wall. a cable making an angle of 37o, attached to the beam 5 m from the pivot point, supports the beam, which has a mass of 600 kg. the breaking point of the cable is 8000 n. a man of mass 95 kg walks out along the beam. how far can he walk before the cable breaks?
The man can move 0.59 meters from the pivot by walking. The external force is countered by the tension of the string.
Tension, a type of force (pulling force), arises down the length of a rope or string when an external force acts at one of the ends.
Assume for the moment that the person is 'd' away.
Tnet = 0
The answer to the query is
mgd + (Mg * L/2) = T* d'sin
Given,
Θ = 37°
d' =5m
L= 8m
M = 600kg
m = 95kg
T = 8000N
If we solve for d, we obtain
8000 = ((600 * 9.8 *4) + (95 * 9.8 * d)) / 5 sin37°
d= ((8000*5*sin37°) - (8000*9.8*4)) / 95*9.8
d = 0.59m
He can therefore walk 0.59 meters from the pivot.
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a neutron star is a compact star that forms from the gravitational collapse of a very massive star. during the collapse, what is the behavior of the moment of inertia of the neutron star and that of the angular velocity of the star?
The behavior of the moment of inertia of the neutron star and that of the angular velocity of the star is The angular velocity increases.
angular speed is the time charge at which an object rotates or revolves approximately an axis. Angular speed is represented via the Greek letter omega (ω, on occasion Ω). it's far measured in perspective in keeping with unit time; as a result, the SI unit of angular pace is radians per 2nd.
In physics, angular speed or rotational pace (ω or Ω), also called angular frequency vector, is a pseudovector illustration of the way fast the angular position or orientation of an object changes with time (i.e. how quickly an item rotates or revolves relative to a point or axis). The value of the pseudovector represents the angular velocity, the charge at which the object rotates or revolves, and its course every day to the immediate aircraft of rotation or angular displacement. The orientation of angular pace is conventionally unique by the right-hand rule.
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mars has a mass of 6.40 x 1023 kg and a radius of 3.40 x 103 km. based on this data, what is the acceleration due to gravity at the surface of mars?
Mars has a mass of 6.40 x 1023 kg and a radius of 3.40 x 103 km. based on this data, The acceleration due to gravity at the surface of mars will be 3.69 [tex]m/s^{2}[/tex]
g = G M / [tex]R^{2}[/tex]
g = acceleration due to gravity on mars
G = gravitation constant
R = Radius
M = mass
g = 6.67 * [tex]10^{-11}[/tex] * 6.40 * [tex]10^{23}[/tex] / [tex](3.40 * 10^{6}) ^{2}[/tex]
= 3.69 [tex]m/s^{2}[/tex]
The acceleration due to gravity at the surface of mars will be 3.69 [tex]m/s^{2}[/tex]
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Calculate the temperature increase ΔT in a 1.40 kg sample of water that results from the conversion of 19% of the gravitational potential energy directly to heat energy in the world's tallest waterfall, the 807-m ‑tall Salto Angel in Canaima National Park, Venezuela.
According to the given statement As a result, the water's temperature increased by 0.36°C.
What does increase in temperature mean?Higher temperatures raise the likelihood that heat waves may occur more frequently and last longer. Extreme heat can be deadly, resulting in conditions like heat exhaustion and heat stroke as well as actual mortality. Additionally, increased temperatures have the potential to trigger a variety of additional alterations globally.
Briefing:The formula below is used to determine the temperature rise (T).
ΔT = 0.19gh/c............. Equation 1
Where:
T stands for temperature rise.
g = Gravitational acceleration
Height is h,
While water's specific heat capacity is c.
From the question,
Given:
h = 807 m
g = 9.8 m/s²
c = 4184 J/kgK
Substitute these values into equation 1
ΔT = (0.19×807×9.8)/4184
ΔT = 0.36°C
As a result, the water's temperature increased by 0.36°C.
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A 65. 0-kilogram astronaut weighs 638 newtons at the surface of earth. What is the mass of the astronaut at the surface of the moon, where the acceleration due to gravity is 1. 62 meters per second squared?.
Astronauts still weigh 65 kg. Mass is constant or does not change anywhere.
A person's mass is constant whether he is on Earth or on the Moon because mass is an essential property of matter. There is no difference in the mass of astronauts on Earth and on the moon. Mass is a constant value, but a person's weight varies depending on their position on the earth.
Weight is the downward force exerted on a person or body by gravity. Whether measured on Earth or on the ISS, the mass does not change. Weight may change due to gravitational forces such as B. On the moon, the weight is reduced to one-sixth of what it is on Earth. Astronauts and their spacecraft still have mass and are subject to Earth's gravity.
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I'm having trouble with moments can someone help
The distance from 3 kg mass is 19.143 m.
Torque is defined as the made of the importance of the force and the perpendicular distance of the line of action of a force from the axis of rotation. The image for torque is usually. , the lowercase Greek letter tau. whilst being called second of pressure, its miles are normally denoted through M.
Calculation:-
net anticlockwise = net clockwise
30×3 +70x = 110×13
90 + 70x = 1430
70X = 1430 - 90
X = 1340/70
= 19.143 m
In physics and mechanics, torque is the rotational equivalent of linear pressure. it's also known as the moment, moment of pressure, rotational force, or turning effect, relying on the field of taking a look at. It represents the capability of pressure to provide trade within the rotational motion of the frame.
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A 7 kg bird has 10 joules of kinetic energy. How
fast is it flying?
Answer:
The velocity of the bird is 2 m /sec.
Explanation:
The formula for kinetic energy is given.
Where m is mass, and v is the velocity.
As given
A 4.0 kg bird has 8.0 joules of kinetic energy.
m = 4.0 kg
K.E = 8.0 joules
Putting in the formula
Thus
v = 2 m/sec
Therefore the velocity of the bird is 2 m /sec.
an atwood's machine (see the figure below) consists of two masses: one of mass 4.43 kg and the other of mass 10.9 kg. when released from rest, what is the acceleration of the system? (enter the magnitude in m/s2.)
acceleration of system we got 4.15m[tex]s^{2}[/tex]
We are well aware that two bodies with different masses are hung from the pulley in Atwood's novel.
The following provides the atwood's acceleration:
a=((m2-m1)/(m2+m1))
g, where g is the acceleration caused by gravity and m2 and m1 are the masses of the heavier and lighter bodies, respectively.
In response to the question, m2=10.9, m1=4.43, and g=9.8
in above formula, we got
a=[(10.9-4.43)/(10.9+4.43)]×9.8
=>a=[(6.47)/(15.33)]×9.8
=>a=4.15m.
Consequently, an atwood machine is created with two masses: one weighing 4.43 kg and the other 10.9 kg. The system accelerates at a rate of 4.15 m/s when it is freed from rest..
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elbow flexion: angular velocity of 2 radians/s. movement took 0.5 s. what was the change in position in degrees?
The change in position in degrees will be 57.30°
angular velocity = change in angular rotation / change in time
given
angular velocity = 2 rad/s
time = 0.5 seconds
change in position = angular velocity * change in time
= 2 * 0.5 = 1 rad
1 radian = 180 / π = 57.30 °
The change in position in degrees will be 57.30°
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If we detect that the intensity of the light from a star is mostly constant but drops slightly to a new constant value for a while and then returns to its normal level and repeats this behavior at regular intervals, we can reasonably suspect that?.
Locating stars hidden by nebulae that would typically obscure other stars.
Unlike other waves in the electromagnetic spectrum, radio waves have huge frequencies. Since they are significantly larger than an atom and have a large wavelength, atomic nuclei cannot obstruct or deflect them. In contrast, gamma rays and other short-wavelength electromagnetic radiation can easily be blocked and deflected by atomic nuclei since they are smaller than atoms. When such radiation passes through a nebula cloud, it is greatly attenuated. Thus, this obstacle is circumvented by radio waves.Radio waves are an electromagnetic radiation type that are most commonly used in communication devices like radios, mobile phones, and televisions. These gadgets take in radio waves and transform them into sound waves by causing mechanical movements in the speaker.To know more about stars
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if the speed of a wave doubles while the wavelength remains the same, what happens to the frequency?
The speed of the wave is doubled while the wavelength remains same, the frequency of the wave will also become double.
The wavelength of the wave is given by the formula,
y = c/v
Where,
y is the wavelength,
c is the speed of the wave,
v is the frequency of the wave.
Now, let us say, if we doubles speed of the wave, then the frequency becomes v',
So we can write,
y = 2c/v'
Putting, c/y = v,
v' = 2v.
So, if the speed of the wave is doubled, then the frequency of the wave will also be doubled.
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Can a car moving toward right have direction of acceleration toward the left?? How??
Since the acceleration is to the left it will have a negative acceleration in the coordinate system.
If the acceleration points in the same direction as the velocity the object is accelerating. Also, if the acceleration is in the opposite direction of the velocity the object will slow down. The direction of acceleration depends on whether the object is accelerating or decelerating and the direction the object is moving. When an object is accelerated, its acceleration is usually in the same direction as its motion.
When an object slows down its acceleration is in the opposite direction of its motion. Axel has the right not to step on the brake and accelerator at the same time. This, combined with the fact that the driver presses the right and center paddles at the same time eliminates that concern.
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on a circular path of radius 11 cm in air around a solenoid with increasing magnetic field, the emf is 33 volts. a wire with resistance 5 ohms is placed along the path. what is the current in the wire? a
The current in the wire is found to be 4.72 A.
Electric current is nothing but the rate of flow of electrons in a conductor. The SI unit of current is ampere.
Given that,
Radius of circular path = 11 cm = 0.11 m
EMF of the solenoid, E = 33 volts
Resistance of the wire, R = 7 ohms
We need to find the current in the wire. It is calculated using ohm's law. Its mathematical relation is given by
E = IR
I = E/R = 33/7 = 4.72 A
Thus, the current in the wire is 4.72 A.
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a rocket is launched straight up from the earth's surface at a speed of 18000 m/s. what is its speed when it is very far away (infinity) from the earth?
The speed when it is very far away from the earth is 1.41 ×[tex]10^{4}[/tex]m/s.
As we know that total energy is the sum of kinetic energy and potential energy.
In the same way, when the rocket starts its motion from the Earth's surface, its mechanical energy is the sum of kinetic energy and potential energy.
So initially the total energy is:
E(i) = K(i) + U(i)
= 1/2 mu² + (-GM/r)
Let's assume that m is the mass of the rocket.
u = initial velocity =1.8 × [tex]10^{4}[/tex]m/s
G = 6.67 ×[tex]10^{-11}[/tex]m³[tex]kg^{-1}[/tex] [tex]s^{-2}[/tex]
M = mass of earth = 5.97 × [tex]10^{24}[/tex]kg
r = distance of the rocket from the Earth's center = 6.37 ×[tex]10^{6}[/tex]
Now the final total energy is:
E(f) = K(f) + P(f)
Potential energy is zero as at infinity distance from Earth is taken as zero.
E = 1/2 mv²
v = final speed
As initial energy is equal to final energy
1/2 mu² + GM/r = 1/2 mv²
v = [tex]\sqrt{u^{2} - GM/r }[/tex]
=[tex]\sqrt{(1.8 * 10^{4} - 6.67 * 10^{-11 } * 5.97* 10^{24} / 6.37 * 10^{6} }[/tex]
= 1.41 ×[tex]10^{4}[/tex]m/s
Therefore the speed is 1.41 ×[tex]10^{4}[/tex]m/s
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If a vehicle is moving at a constant speed of 60 miles per hour, how many miles will it travel in 1 hour and 20 minutes?.
The vehicle will travel a total of 80 miles in 1 hour and 20 minutes.
The vehicle is moving at a constant speed of 60 miles per hour.
It means that in one hour, the vehicle travels 60 miles.
So, we can write,
Miles travelled in hour = 60
Miles travelled in one minute = 60/60
Miles travelled in one minute = 1 mile
Total time given is 1 hours and 20 minutes.
1 hours = 60 minutes,
Hence, total time = 60+20
Total time = 80 minutes.
So, the distance travelled in 80 minutes = 80 x 80 miles,
Miles travelled in 80 minutes = 80 miles/
So, the vehicle travelled 80 miles in 1 hour and 20 minutes.
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The irr of normal project x is greater than the irr of normal project y, and both irrs are greater than zero. Also, the npv of x is greater than the npv of y at the cost of capital. If the two projects are mutually exclusive, project x should definitely be selected, and the investment made, provided we have confidence in the data. Put another way, it is impossible to draw npv profiles that would suggest not accepting project x.
This statement is True. Project X should be definitely select, and the investment made, provided we have confidence in the data.
Based on the IRR decision rule, an...
Mutually exclusive projects in capital budgeting are a group of investments that limit the investor's choices to only one. The selection is limited to one project due to limited funding. The net present value (NPV) and the internal rate of return (IRR) are two capital budgeting methods that can be used in the appraisal process. The internal rate of return calculates the discount rate that makes the NPV equal to zero, while the net present value appraises projects based on their current worth.
Two events (or propositions) are mutually exclusive or disjoint in logic and probability theory if they cannot both occur at the same time. The results of a single coin flip, which can result in either heads or tails but not both, serve as an obvious illustration.
In the coin-tossing example, both outcomes are theoretically collectively exhaustive. This indicates that at least one of the outcomes must occur, and as a result, these two possibilities collectively exhaust all other possibilities.
However, not all events that are mutually exclusive are all-inclusive. For instance, the outcomes 1 and 4 of a single roll of a six-sided die are mutually exclusive (neither may occur at the same time), yet these are not all possible possibilities (other options;
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