Observing star clusters will give astronomers needed data for stellar evolution because all the stars in the have the same Age
A star changes over time through a process called stellar evolution. A star can have a life that is substantially longer than the age of the universe, ranging from a few million years for the most massive to billions of years for the least massive.
Stellar evolution is a term used to describe how stars change through time. Most stars don't seem to change much on a human time scale, but if we looked for billions of years, we would witness how stars are born, how they grow older, and then how they die. Stellar evolution is significant because it produces the majority of the components.
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The quartz crystal in a digital watch has a frequency of 32. 8 khz. what is its period of oscillation?
Time Period of Oscillation-1/32800 Hz
Time Period of Oscillation - 3.04 × 10¹.
Two related parameters are oscillation frequency and period. Actually, they are the opposites of one another. As a result, the following formula can be used to determine the quartz crystal's oscillation period:
Time Period of Oscillation = 1/Oscillation Frequency
where.
Frequency of Oscillation-32.8 KHz
Frequency of Oscillation - 32800 H₂
Therefore
Time Period of Oscillation-1/32800 Hz
Time Period of Oscillation - 3.04 × 10¹.
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The time period of oscillation is 3.04×10
what is time period?
A time period (denoted by 'T'' ) is the time taken for one complete cycle of vibration to pass a given point.[1] As the frequency of a wave increases, the time period of the wave decreases. The unit for time period is 'seconds'.
The related parameters are oscillation frequency and period.They are the opposite of the another.As a result the formula to be used is
frequency=1/time
given:
Frequency of oscillation=32.8khz=32800hz
therefore,
time period of oscillation=1/32800hz
time period of oscillation=3.04×10
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Given that ethylene has a λmax of 175nm, butadiene has a λmax of 220nm, and 2-methyl-1,3-butadiene has a λmax or 215nm, what is the λmax of 2,3,4-trimethylhexatriene?
The λmax of 2,3,4-trimethylhexatriene is 280 nm.
Ethylene has a λmax of 175nm.
Butadiene has a λmax of 220nm.
2-methyl-1,3-butadiene has a λmax or 215nm.
1,3,5-hexatriene has a λmax of 258nm.
Woodward's rules, sometimes known as Woodward-Fieser rules (after Louis Fieser) and named after Robert Burns Woodward, are a number of sets of empirically developed principles that aim to forecast the wavelength of the absorption maximum (max) in an ultraviolet-visible spectrum of a certain molecule.
By using the Woodward Fieser rule,
R- (Alkyl Group) .... +5 nm = 5 × 2 = 10
RO- (Alkoxy Group) .. +6 = 6 × 2 = 12
Adding 22nm to the λmax of 1,3,5-hexatriene as it has 2 alkyl groups and 2 alkoxy groups to form 2,3,4-trimethylhexatriene.
The λmax of 2,3,4-trimethylhexatriene is 280 nm.
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On a planet in the solar system where the sky normally scatters light of lower frequencies, its sunsets would be?
The sky will appear in blue color at the sunset, if the sky of the planet scatters light of lower frequencies.
To find the answer, we have to know more about the scattering of light.
What is scattering of light?When light travels from one medium, like air or a glass of water, to another, scattering occurs. Part of the light is absorbed by the medium's particles, followed by subsequent radiation in a particular direction. The size of the scattered light's particles and its wavelength affect how intense it is.If the sky scatters a low frequency light, during sunset, this low frequency light will be totally absorbed by the atmospheric particles, and we can only be able to see the high frequency light.Thus, we can say that the sky will appear in blue color at the sunset, if the sky of the planet scatters light of lower frequencies.
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Compute the velocity of an electron that has been accelerated through a difference of potential of 100 volts. express your answer in meters per second
The velocity of an electron that has been accelerated through a difference of potential of 100 volts will be 5.93 * [tex]10^{6}[/tex] m/s
Electrons move because they get pushed by some external force. There are several energy sources that can force electrons to move. Voltage is the amount of push or pressure that is being applied to the electrons.
By conservation of energy, the kinetic energy has to equal the change in potential energy, so KE=q*V. The energy of the electron in electron-volts is numerically the same as the voltage between the plates.
given
charge of electron = 1.6 × [tex]10^{-19}[/tex] C
mass of electron = 9.1 × [tex]10^{-31}[/tex] kg
Force in an electric field = q*E
potential energy is stored in the form of work done
potential energy = work done = Force * displacement
= q * (E * d)
= q * (V) = 1.6 × [tex]10^{-19}[/tex] * 100
stored potential energy = kinetic energy in electric field
kinetic energy = 1/2 * m * [tex]v^{2}[/tex]
= 1/2 * 9.1 × [tex]10^{-31}[/tex] * [tex]v^{2}[/tex]
equation both the equations
1/2 * 9.1 × [tex]10^{-31}[/tex] * [tex]v^{2}[/tex] = 1.6 × [tex]10^{-17}[/tex]
[tex]v^{2}[/tex] = 0.352 * [tex]10^{14}[/tex] m/s
[tex]v^{2}[/tex] = 35.2 * [tex]10^{12}[/tex]
= 5.93 * [tex]10^{6}[/tex] m/s
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When full, the innermost electron shell of argon contains ________ electrons, and the outermost shell contains ________ electrons.
The innermost electron shell of argon contains 2 electrons, and the outermost shell contains 8 electrons.
To find the answer, we have to know more about the electronic configuration.
What is the electronic configuration of Argon?As we know that, the element Argon in the periodic table has an atomic number of 18.Since its atomic number is 18, it should have 18 number of electrons in the elemental state.The first shell or K shell of Argon can carry 2 electrons, and rest of the 16 electrons will filled in the L and M shells.For, L has a maximum number of 8 electrons, and thus, the rest 8 will move to M.Thus, we can conclude that, the innermost electron shell of argon contains 2 electrons, and the outermost shell contains 8 electrons.
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What is the wavelength of maximum intensity and the total energy emitted by a celestial object at absolute zero?
Wavelength is Infinity
What is Wavelength?
A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles. This length is often defined in wireless systems in metres(m), centimetres(cm), or millimetres(mm).
A blackbody never approaches zero, hence the wavelength of the highest intensity that a heavenly object may produce is infinite. As a celestial object's temperature rises, its overall energy output increases quickly.
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What is the reactance of a 9. 0×10−2 μf capacitor connected to a 23 kv (rms), 550 hz line?
The Capacitive reactance of the capacitor is 3.22kΩ.
To find the answer, we have to study about the Capacitive reactance.
How to find the Capacitive reactance?It is given that,[tex]C=9*10^{-8}F\\f=550Hz\\[/tex]
Thus, the expression for capacitive reactance will be,[tex]X_c=\frac{1}{2\pi fC}[/tex]
By substituting values, we get,[tex]X_c=\frac{1}{2\pi *550*9*10^{-8}} \\\\X_c=3.22*10^3Ohm.[/tex]
Thus, we can conclude that, the Capacitive reactance of the capacitor is 3.22kΩ.
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If the fifth order minimum in the diffraction pattern of a thin slit is at 40° from the central maximum, what is the highest order minimum in the pattern?
The highest order minimum in the diffraction pattern [tex]7^{0}[/tex].
Diffraction patternThe same way that an imaging mode electron beam is focused on the material to create an image, a parallel electron beam is used to create diffraction patterns. The beam transmitted is focused on the screen's diffraction pattern by the intermediate lens and its chosen area aperture, which determines the beam's width.
Crystallography studies of materials can benefit from the diffraction mode. Using this mode, one can establish the space group and orientation of crystals. the anoparticle's diffraction pattern, which is depicted on the left. The little spots and rings in polycrystalline samples indicate that it is crystalline.
A disc's closely spaced tracks work as a diffraction grating to create the well-known rainbow pattern that is seen while staring at a disc, which is one of the most spectacular instances of diffraction.
If the fifth order minimum in the diffraction pattern of a thin slit is at 40° from the central maximum, what is the highest order minimum in the pattern?
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5.
A train is moving on a straight track with a speed of 70.0km/h [E]. It slows down at a rate
of 2.00m/s2 [W] in a distance of 35.0m. Determine
a.The final speed of the train. b.How much time the train took to slow down to this speed.
Answer:
t = 1.659s
Explanation:
We can use the kinematics equations to solve this questions:
v = u + at
[tex]v^{2} = u^{2} +2as[/tex]
where v = Final Velocity, u = initial velocity, a = acceleration, t = time, s = displacement
a) Given information from the question,
u = [tex]\frac{70km}{h} =\frac{(70*1000)m}{(1*3600)s} = 19.444m/s[/tex] (Convert km/h to m/s first)
a = [tex]2m/s^{2}[/tex]
s = 35m
Now we can substitute these values into the 2nd kinematics equation to find v, final velocity.
[tex]v^{2} =(19.444)^{2} +2(2)(35)\\v=\sqrt{(19.444)^{2} +2(2)(35)} \\v= 22.761m/s (5.sf)\\[/tex]
b) Now we have the final velocity, we can substitute the values into the first kinematics equation to find t , the time taken.
v = u + at
22.761 = 19.444 + 2t
2t = 22.761 - 19.444
t =[tex]\frac{22.761-19.444}{2}[/tex]
t = 1.659s
Imagine that you’re observing a collision. which action would allow you to determine whether the collision is inelastic?
Observe whether the colliding objects change their shape.
When observing a collision, we observe whether the colliding objects change their shape to see whether the collision is inelastic.
What is an inelastic collision?An inelastic collision is one in which the kinetic energy is lost. In an inelastic collision, the system's momentum is conserved, but its kinetic energy is not.
Which way does an elastic collision occur?Solution: (i) An inelastic collision occurs when the total initial kinetic energy of the bodies prior to the collision does not equal the total final kinetic energy of the bodies following the collision. Momentum is retained in (ii). In an inelastic collision, kinetic energy is not conserved.What are two instances of collisions that are completely inelastic?When two objects move as one mass after colliding, this is known as a perfectly inelastic collision. Examples: hitting a target board with an arrow. a meteor getting buried in the cracks of the Earth. The two items have united.To learn more about inelastic collision visit:
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A car starts from rest and constantly accelerates at a rate of 10 [m/s2 ] during a 402 [m] race. how fast is the car going at the finish line?
A car starts from rest and constantly accelerates at a rate of 10 [m/s2 ] during a 402 [m] race. At the finish line, the speed of the car is [tex]\mathbf{89}.\mathbf{6660}\ \mathbit{m}/\mathbit{s}[/tex].
The initial velocity of the car [tex]u = 0[/tex]
Constant acceleration [tex]a = 10~ m/s^2[/tex]
Distance of the Race [tex]d = 402~ m[/tex]
The car is accelerating with a constant acceleration [tex]a[/tex] , so the car's velocity will change with time as it approaches the finish point which is at a distance [tex]d[/tex] from the initial point.
Newton's equation is the backbone of Classical Mechanics. Let's say the velocity of the car at the finish line is [tex]v[/tex]. We know that displacement is the product of average velocity and time.
Or [tex]s=\frac{u+v}{2}\times t[/tex]
Using Newton’s first equation [tex]v\ =\ u\ +\ at[/tex]
Newton's equation of motion turns out to be,
[tex]v^2 = u^2+2ad[/tex]
[tex]v^2 = 2\times 10 \times 402[/tex]
so, [tex]v = \sqrt{8040} = 89.6667 ~m/s[/tex]
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An object is dropped from the top of a building and is observed to take 7. 2s to hit the ground. How tall is the building?.
the height of the building is H=36 m.
What is The Law of Gravity?According to Newton's law of gravity, every particle of matter in the universe is attracted to every other particle with a force that varies directly as the product of their masses and inversely as their distance from one another.
Properties of Gravity -
It is a universal attractive force. It is directly proportional to the product of the masses of the two bodies. It obey inverse square law. It is the weakest force known in nature.Examples of Gravity -
The force that holds the gases in the sun.The force that causes a ball you throw in the air to come down again.The force that causes a car to coast downhill even when you aren't stepping on the gas.v₀=0 m/s
H₀=0 m
g=10 m/s²
t=7,2 s
H - ?
[tex]H= H_{0} + v_{0}t+\frac{gt^{2} }{2} \\[/tex]
H = 0 +0 × 7.2 + 10(7.2)²/2
H = 36m
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Identify the saturation pressure corresponding to 32 degrees fahrenheit for r - 123
Hg vacuum at 20 inches is the saturation pressure that corresponds to 32 degrees Fahrenheit of R-123.
To find the answer, we need to know more about the saturation pressure.
What is saturation pressure?The saturation pressure is the pressure at which a vapor is in equilibrium with its liquid (such as steam with water).It is the highest pressure that water vapor can get at a particular temperature.R-123 refrigerant is probably hard to find these days. It was discovered that chlorine-containing refrigerants have the potential to actively harm the Ozone layer if they are released into the atmosphere.The saturation pressure that corresponds to 32 degrees Fahrenheit of R-123 is 20 inches Hg vacuum.Thus, we can conclude that, Hg vacuum at 20 inches is the saturation pressure that corresponds to 32 degrees Fahrenheit of R-123.
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A sound wave has a speed of 340 m/s and a frequency of 1000 hz. The period of the sound is closest to?
The frequency and the period are inversely proportional.
[tex]f=\dfrac{1}{T}[/tex] where T is the period
Solving the QuestionWe're given:
v = 340 m/sf = 1000 HzBecause the frequency and the period are reciprocals of each other, we can find the period of the sound by finding the reciprocal of the frequency:
[tex]T=\dfrac{1}{1000}[/tex]
Answer[tex]T=\dfrac{1}{1000}[/tex]
What's the largest number of beats per second that will be heard from which pair of tuning forks?
The largest number of beats per second that will be heard from 763 and 774 Hz pair of tuning fork .
The beat frequency is equal to the complete value of the alteration in the frequency of the two waves. The count of beats per second is equivalent to the difference in frequencies of two waves is called beat frequency.
A tuning fork is a two-pronged metal fork that can be used as an acoustic resonator. Traditionally, this tool has been used to tune musical instruments. Tuning forks work by releasing a perfect wave pattern to match a musician's instrument.
The largest number of beats per second that will be heard from 763 and 774 Hz pair of tuning fork .
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If a closed loop lies partially inside and partially outside a region of changing magnetic field, which is true about calculating the induced electric field along the path?
If a closed loop lies partially inside and partially outside a region of changing magnetic field, to calculate the induced electric field along the path we use only the area within the flux change to calculate the electric field.
Induced Electric Fields:The electrostatic field is conservative and does no net work over a closed path, whereas the induced electric field is nonconservative and does net work in transferring a charge over a closed channel. As a result, whereas the induced field cannot be connected with electric potential, the electrostatic field can.
Faraday's law can be written in terms of the induced electric field as. ∮→E⋅d→l=−dΦmdt. The electrostatic field created by a fixed charge distribution and the electric field caused by a changing magnetic field is very different from one another.
An electric field is created by a fluctuating magnetic flux. The induced emf from Faraday's law is related to the fluctuating magnetic flux and the induced electric field.
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While walking between gates at an airport, you notice a child running along a moving walkway. Estimating that the child runs at a constant speed of 2. 4 m/s relative to the surface of the walkway, you decide to try to determine the speed of the walkway itself. You watch the child run on the entire 18-m walkway in one direction, immediately turn around, and run back to his starting point. The entire trip takes a total elapsed time of 32 s. Given this information, what is the speed of the moving walkway relative to the airport terminal?.
Speed of walkway = 1.84 m/s
let x=speed of walkway
then (2.8+x)= speed of child moving in direction of walkway
then (2.8-x)= speed of child moving against direction of walkway
Travel time=distance/speed
travel time of child moving in direction of walkway=23/(2.8+x)
travel time of child moving in direction of walkway=23/(2.8-x)
total elapsed time given=29s
23/(2.8+x)+23/(2.8-x)=29
LCD=(2.8+x)(2.8-x)
23(2.8-x)+23(2.8+x)=29(2.8+x)(2.8-x)
23*2.8-23x+23*2.8+23x=29(2.8^2-x^2)
23(2.8+2.8)/29=2.8^2-x^2
x^2=(2.8)^2-(23*5.6)/29)=3.4
x=sqrt(3.4)=1.84m/s
Speed of walkway = 1.84 m/s
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The potential energy at x = 8 m is -2000 V and at x = 2 m is 400 V. What is the magnitude and direction of the electric field?
The potential energy at x = 8 m is -2000 V and at x = 2 m is 400 V. The magnitude and direction of the electric field will be 400 V/m directed parallel to the +x-axis
Electric field, an electric property associated with each point in space when charge is present in any form. The magnitude and direction of the electric field are expressed by the value of E, called electric field strength or electric field intensity or simply the electric field.
The electric potential energy of any given charge or system of changes is termed as the total work done by an external agent in bringing the charge or the system of charges from infinity to the present configuration without undergoing any acceleration.
The relation between electric field and electric potential can be generally expressed as – “Electric field is the negative space derivative of electric potential.”
Electric field = - d V / dx
-(-2000-400) = [tex]\int\ {E} \, dx[/tex]
2400 = E (8-2)
2400 V = E (6)
E = 400 V/m
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1- name the three things that must be present for a fire to exist. 2- water extinguishes fires in three ways. Name them. 3- there are two general types of hazards. Name them. 4- define each of the following characteristics of materials and tell each is important in industrial safety a. Flash point b. Flame point c. Ignition point d. Vapor pressure e. Specific gravity f. Evaporation rate g. Melting point h. Viscosity i. Boiling point.
1. Oxygen, heat, and fuel
These three things that must be present for a fire to exist.
2. (a) In order to put out the fire, it achieves this by removing the heat from it.
(b) Water can also be used to separate the fire from the oxygen source.
(c) It smothers it, preventing it from igniting more airborne oxygen.
Water extinguishes fires in these three ways.
3. (a)physical hazard
(b)chemical hazard
4.(a) If a liquid's flash point is lower than 60°C, it is regarded as flammable.
Regarding the security of spill cleaning activities, flash point is a crucial consideration.
When spilled, gasoline and other light fuels pose a considerable risk since they can ignite in the majority of ambient conditions.
(b) If your material's label contains a flame symbol, it means the substance is combustible, and you should review your SDS to learn more about the dangers and risks associated with using the substance.
(c) the lowest temperature at which combustible material ignites in air and continues to burn when heated (as in a bath of molten metal)
(d) The pressure that a vapor exerts on its condensed phases (solid or liquid) in a closed system at a specific temperature is known as vapor pressure.
(e) The difference between an object's density and that of a standard substance is its specific gravity.
Depending on its value, the specific gravity might indicate whether an object will float or sink in our reference substance.
(f) The ratio of the time needed to evaporate a test solvent to the time needed to evaporate the reference solvent under the same circumstances is the evaporation rate.
The findings can be stated as a relative rate, the percentage that evaporated within a given time frame, or the length of time needed to evaporate a given volume.
(g) The temperature at which a specific solid material melts, or transitions from a solid state to a liquid, is known as the melting point.
(h) The resistance of a fluid (liquid or gas) to a change in shape or motion of adjacent sections relative to one another is known as viscosity. Viscosity is a sign of flow resistance.
(i) The boiling point of a liquid is the temperature at which the pressure of the liquid's vapor equals the pressure of its surroundings.
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In what part of the electromagnetic spectrum does the sun radiate maximum energy? How does this compare to earth?
The visible region of the electromagnetic spectrum is where the Sun radiates maximum energy. Since Earth is substantially cooler, the majority of the radiation it emits is longwave radiation.
The complete spread of electromagnetic radiation by wavelength or frequency. Despite the fact that all electromagnetic waves have a wide range of frequencies, wavelengths, and photon energies, they all move at the speed of light in a vacuum known as the electromagnetic spectrum.
The sun emits electromagnetic waves over a wide spectrum, from radio waves with a wavelength of 10 meters to X-rays with a wavelength of 2 nanometers. Visible light, with a wavelength of around 500 nanometers, is the most powerful of them to reach the earth's surface. The visible spectrum is where the Sun's energy is most intensely emitted. The maximum amount of radiation that the Earth emits occurs at 10 mm, in the infrared heat spectrum. Since the Earth's surface temperature is far lower than that of the sun and its radiation has longer wavelengths than solar radiation, the majority of this energy is then reradiated into space. The atmosphere is easily able to absorb the longer wavelengths that the Earth radiates.
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Fetch is ________. Group of answer choices the distance between the trough of a wave and the still water level the circular pattern made by water particles when a wave passes a method of shoreline erosion control the distance over which the wind blows over open water
Fetch is the distance over which the wind blows over open water generating mechanical waves; option D
What are waves?Waves are disturbance which occur in a substance or medium which project energy as they travel along a particular plane or direction.
There are two types of waves:
mechanical waveselectromagnetic wavesMechanical waves are waves which involve the disturbances that occur in particulate matter and which require a material medium for their transmission.
Fetch is an area of ocean or lake surface over which the wind blows in a constant direction, thus generating waves.
In conclusion, mechanical waves require material media for transmission.
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The annual variation in the amount of solar radiation received varies with latitude because the ______.
The annual variation in the amount of solar radiation received varies with latitude because the direction of Earth's tilt changes with respect to the Sun during the year.
How does solar radiation vary with latitude ?
Despite the fact that high latitude regions receive more solar radiation than low latitude regions do, heat is nevertheless transported throughout the planet by the ocean and the atmosphere.
How does the amount of solar radiation received vary on Earth?
As a result of reduced radiation protection, areas closer to the equator typically experience higher levels of solar radiation exposure. However, because to the angle of the sun and the tilt of the Earth's axis, areas farther north or south receive more solar energy.What is the relationship between the annual solar radiation cycle and the annual temperature cycle?
The coldest day of the year occurs after the winter solstice, and the warmest day of the year occurs (on average, so many days) after the summer solstice, because the annual temperature cycle lags the annual radiation cycle.
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Q.9 And Q.10 correct answer with explaination
The option c will be correct in Q10.
What is angular velocity?Time rate at which an object rotates about axis or at which angular displacement between two bodies changes.
We have given is
r=4i , angular acceleration = 4j
v= radius×angular acceleration
v= 4i ×k
v=16j
When we cross i× k = j
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The ________ explains how our solar system probably formed from a giant cloud of gases and dispersed solid particles.
The nebular hypothesis explains how our solar system probably formed from a giant cloud of gases and dispersed solid particles.
What is Nebular hypothesis?The most widely accepted theory in cosmogony to explain how the solar system formed and evolved is the nebular hypothesis. It implies that gas and dust orbiting the sun are what created the solar system.
Following are the steps in nebular theory:
As part of the cloud of gas and dust condenses into a core and becomes a protostar, the nebula changes into a solar nebula. The material condensing might have been brought on by a nearby supernova shockwave. An accretion disk is formed as the protostar's surrounding material disintegrates.How did the solar system form, according to the nebular hypothesis?The nebular hypothesis states that enormous clouds of hydrogen and helium imploded. The cloud's center heated up significantly after collapsing. The system then started to rotate as it became hotter and more compressed. The formation of the solar system started at this point.
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Stellar occultations are the most accurate way to measure the _________ of a solar system object
Answer:
del mundo
Explanation:
Suppose there were no solar wind. How would the appearance of a comet in our inner solar system be different?.
If there were no solar wind, then the appearance of a comet in our inner solar system would be different because it would have only one tail instead of two.
What is a comet?A comet is a celestial body that travels across the Universe and releases gases when warms by passing near the stars such as the Sun.
Comet tail is the result of gas and dust due to this process of warming, which is directly related to solar winds.
In conclusion, if there were no solar wind, then the appearance of a comet in our inner solar system would be different because it would have only one tail instead of two.
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What is the energy (in ev) of an x-ray photon that has a wavelength of 2. 4 nm ?
_______________
λ=2,4 nm = 2,4·10⁻⁹ m
c=3·10⁸ m/s
h=6,63·10⁻³⁴ J·s = 4,14·10⁻¹⁵ eV·s
_______________
E - ?
_______________
[tex]\displaystyle \boldsymbol{E}=h\nu =h \frac{c}{\lambda} =4,14\cdot 10^{-15} \; eV\cdot s\cdot \; \frac{3\cdot 10^8\; m/s}{2,4\cdot 10^{-9}\; m} =517,5\; eV\approx \boldsymbol{518\; eV}[/tex]
Vector u has a magnitude of 5 units and a direction angle of 75°, and vector v has a magnitude of 6 units and a direction angle of 210°. what is the component form of the vector u v?
-3.90, 1.83 are the component form of the vector u v.
What is magnitude of vector?
The magnitude of a vector formula is used to calculate the length for a given vector (say v) and is denoted as |v|. So basically, this quantity is the length between the initial point and endpoint of the vector.The component form of a vector is the ordered pair that describes the changes in the x- and y-values. In the graph above x1=0, y1=0 and x2=2, y2=5. The ordered pair that describes the changes is (x²- x, y²- y), in our example (2-0, 5-0) or (2,5).We have vector u = 5 ( cos 75 i + sin 75 j )
= 1.294 i + 4.830 j
Vector v = 6 ( cos 210 i + sin 210 j )
= -5.19 i - 3 j
Now we add both component
u + v = 1.294 i + 4.830 j + (-5.19 i - 3 j)
= -3.90 i + 1.83 j
= < -3.90, 1.83>
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The correct option is (D). < -3.90, 1.83>
Vector is a quantity with both magnitude and direction. It is often represented by an arrow whose length is proportional to the magnitude of the quantity and whose direction is the same as that of the quantity.
What are vectors?
Quantities with both a magnitude and a direction are called vectors. A vector can be used to represent a vehicle's motion in the real world. 65 mph is the direction of travel for the car. In this illustration, the vector's magnitude is represented by the car's 65 mph speed and its direction by the northwest. In the study of physics, the use of vectors to depict how forces operate on objects is crucial.Given, vector u = 5 ( cos 75 i + sin 75 j ) = 1.294 i + 4.830 j
Vector v = 6 ( cos 210 i + sin 210 j ) = -5.19 i - 3 j
u + v = 1.294 i + 4.830 j + (-5.19 i - 3 j) = -3.90 i + 1.83 j
= < -3.90, 1.83>
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We see a full moon by reflected sunlight. How much earlier did the light that enters our eye leave the sun? the earth-moon and earth-sun distances are 3. 8 x 105 km and 1. 5 x 108 km
The time taken by the light reflected from sun to reach on earth will be 8.4 minutes.
To find the answer, we need to know about the distance travelled by light.
How to find the time taken by the light reflected from sun to reach on earth?So, in order to solve this problem, we must first know how far the moon is from Earth and how far the Sun is from the moon. These distances are given as 3.8×10^5 km (Earth-Moon) and 1.5×10^8 km (Sun- Earth). Since the Moon and Sun are on opposite sides of Earth during a full moon, the light's distance traveled equals,[tex]d=(1.5*10^8km)+2(3.8*10^5km)=1.51*10^8km=1.51*10^{11}m[/tex]
As we know that light travels at a speed of 300,000 km per second. then, the time taken by the light reflected from sun to reach on earth will be,[tex]t=\frac{1.51*10^{11}}{3*10^8}=503.33 s\\t=\frac{503.33}{60}=8.4min[/tex]
Thus, the time it takes for the light from the Sun to reach Earth and be recognized as 8.4 minutes.
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A spherical balloon is inflated so that its volume is increasing at the rate of 3.3 ft3/min. how rapidly is the radius of the balloon increasing when the radius is 0.65 feet?
The radius is increasing at a rate of 0.31cm/sec.
We know the volume of the balloon is increasing at a rate of 3.3 [tex]ft^{3} min[/tex]
This is expressed as:
[tex]\frac{dV}{dT}[/tex] = 3.3
The volume of a sphere is given by:
V = [tex]\frac{4}{3}[/tex]π[tex]r^{3}[/tex]
The question asks to find the rate of which the radius is increasing when the radius is 0.65 feet.
We need to find:
[tex]\frac{dr}{dt}[/tex]
Since we don't have t in our equation, we will be differentiating implicitly. We can use the chain rule for this:
[tex]\frac{dV}{dT}[/tex] = [tex]\frac{dV}{dR}[/tex].[tex]\frac{dr}{dt}[/tex]
We already know
[tex]\frac{dV}{dT}[/tex] = 3.3
∴
3.3 = [tex]\frac{dV}{dR}[/tex].[tex]\frac{dr}{dt}[/tex]
To find [tex]\frac{dV}{dR}[/tex] we differentiate V = [tex]\frac{4}{3}[/tex]π[tex]r^{3}[/tex]
∴
3.3 = 4[tex]\frac{3.3}{5.30}[/tex][tex]r^{2}[/tex].[tex]\frac{dr}{dt}[/tex]
Dividing ,
[tex]\frac{3.3}{5.30}[/tex] = [tex]\frac{dr}{dt}[/tex] = 0.622 ft/min = 0.31 cm/sec
The radius is increasing at a rate of 0.31cm/sec.
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