The recessional velocity of a galaxy at a distance of 180 mpc will be 70 km/sec
Hubble's law, which says simply that a galaxy's velocity (or as is sometimes plotted, its redshift) is directly proportional to its distance, also tells us something important about the state of the universe. If the universe is static and unchanging, there should be no correlation between distance and velocity.
Recessional velocity is the rate at which an extragalactic astronomical object recedes (becomes more distant) from an observer as a result of the expansion of the universe. It can be measured by observing the wavelength shifts of spectral lines emitted by the object, known as the object's cosmological redshift.
Recessional velocity = Hubble's constant * distance
= 70 km/sec/Mpc * 180 Mpc
= 70 km/sec
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A stereo speaker is placed between two observers who are 40 m apart, along the line connecting them. if one observer records an intensity level of 59 db, and the other records an intensity level of 83 db, how far is the speaker from each observer?
The distance from observer A of intensity of sound 59 db is 28.64 m and the distance from observer B of intensity of sound 83 db is 11.36m
Explanation:
Let's solve this problem in parts
let's start by finding the intensity of the sound in each observer
observer A β = 59 db
β = [tex]10 log\frac{I_a}{I_o}[/tex]
where I₀ = [tex]1 \times 10^{-12}[/tex] W / m²
[tex]I_a = I_b \times 10 ^{ \frac{\beta}{10} }[/tex]
[tex]I_a = 1\times 10 ^{-12} \times 10 ^{ \frac{59}{10} }[/tex]
[tex]I_a[/tex] = [tex]2.51 \times 10 ^{-6}[/tex] W / m²
Similarly for Observer b [tex]I_b = 3.16 \times 10 ^ {-4}[/tex]
now we use that the emitted power that is constant is the intensity over the area of the sphere where the sound is distributed
P = I A
therefore for the two observers
the area of a sphere is
[tex]A= 4\pi \times r^2[/tex]
we substitute the above formula, we get
Let us call the distance from the observer A be to stereo speaker = x, so the distance from the observer B to the stereo speaker = 40- x; we substitute
[tex]I_a (35 -x) ^2 = I_b x^2[/tex]
after solving the above equation we get x = 28.64 m
This is the distance of observer A
similarly The distance from observer B is 35 - x
= 40 - 28.64
= 11.36m
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A particle moving at speed 0. 32 c has momentum p0. the speed of the particle is increased to 0. 72 c. what is its momentum now?
A particle moving at speed 0.32 c has momentum P₀. the speed of the particle is increased to 0.72 c then its momentum would be 2.25P₀.
What is momentum?It can be defined as the product of the mass and the speed of the particle, it represents the combined effect of mass and the speed of any particle, and the momentum of any particle is expressed in Kg m/s unit.
Mathematically the formula of the momentum is
P = mv
where P is the momentum of the particle
m is the mass of the particle
v is the velocity by which the particle is moving
As given in the question a particle moving at speed 0.32 c has momentum P₀. the speed of the particle is increased to 0.72 c
by using the formula of the momentum and substituting the values of the velocity
P =mv
As mentioned in the question when the particle is moving with 0.32c velocity it has a momentum of P₀
P₀ = m*(0.32c)
If the speed of the particle is increased to 0.72 c the momentum would be
P=m*(0.72c)
by dividing the second equation from the first one
P₀/P = 0.32c/0.72c
P₀/P = 0.44
P =2.25P₀
Thus, the increased momentum of the particle would be 2.25P₀
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Select the correct answer. jay bought a toy car. to make the car move, he must turn a key attached to a spring. turning the key winds the spring tight. the toy car moves when the key is released and the spring unwinds. what’s the main transformation of energy in this example? a silver color kids pedal car with a key to run it a. chemical energy to electric energy b. chemical energy to motion energy c. electric energy to motion energy d. electric energy to potential energy e. potential energy to motion energy
The main transformation of energy is chemical energy to motion energy.
How does the chemical energy is converted to motion energy?
Jay's body converted chemical energy into mechanical energy to wind up the key. Mechanical energy in the key's winding was transformed into potential energy in the spring. The spring then strives to release itself, and as the toy car rolls forward, the potential energy is transformed into kinetic energy or motion energy.
What is chemical energy?
Chemical energy is the energy that is released when chemical substances engage in a chemical reaction and change into other substances.
What is potential energy?Potential energy is the power that an object can store as a result of its position in relation to other objects, internal tensions, electric charge, or other circumstances.
What is kinetic energy?The energy that an object has as a result of motion is known as kinetic energy. It is described as the effort required to move a mass-determined body from rest to the indicated velocity.
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Hope this is correct.
A scientist is studying the outer reef section of a coral reef. what features are they likely to see?
The features the scientist is likely to see are:
A jelly-like substance referred to as mesogleaCoral PolypsBased on the fact that a coral reef is an underwater ecosystem that contains different animals and species, they contain a colony of coral polyps.
What is a Coral Reef?This refers to the underwater ecosystem that contains different animals and species.
Hence, we can see that based on the fact that a scientist is studying the outer reef section of a coral reef, he would see the distinct characteristics of the coral and these are the:
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How would you position a flat loop of wire in a changing magnetic field so that there is no induced emf in the loop?
Position the loop so that the field lines run perpendicular to the area vector or parallel to the surface so that there is no induced EMF in the loop
Magnetic Field is the region around a magnetic material or a moving electric charge within which the force of magnetism acts.
Flux is the presence of a force field in a specified physical medium, or the flow of energy through a surface. In electronics, the term applies to any electrostatic field and any magnetic field . Flux is depicted as "lines" in a plane that contains or intersects electric charge poles or magnetic poles.
As we all know that a moving charged particle will experience force by a magnetic field, the magnetic field produced by the field coil remains constant, that is, no force is experienced by electrons of the wire. So, we have to produce a relative motion between magnetic field and electrons.
Whenever the flux passing through the coil changes by any way (like either changing angle, magnetic field or area of coil), we are actually producing a relative motion between electrons and magnetic field. As a result, the electrons experience a magnetic force and shift to produce
flux = [tex]\int\limits {BAcos(theta)} \,[/tex]
theta = angle between magnetic field and area
Since we know , EMF get induced only when flux changes , if their is no flux change , no EMF can be induced
Hence , in order to not induce any kind of EMF ,we need to maintain a constant flux , but in question it is a changing magnetic field which means changing flux ,in this situation we need to align a flat loop parallel to magnetic field so , their is zero flux through the loop .
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A 1. 30 kg block slides with a speed of 0. 855 m/s on a frictionless horizontal surface until it encounters a spring with a force constant of 552 n/m. The block comes to rest after compressing the spring 4. 15 cm. Part a. Find the spring potential energy, u , the kinetic energy of the block, k , and the total mechanical energy of the system, e , for compressions of 0 cm. Part b. Find the spring potential energy, u , the kinetic energy of the block, k , and the total mechanical energy of the system, e , for compressions of 1. 00 cm. Part c. Find the spring potential energy, u , the kinetic energy of the block, k , and the total mechanical energy of the system, e , for compressions of.
a) For 0 compressions:
potential energy = U = 0 J
kinetic energy = k = 0.383 J
total mechanical energy = E = 0.383 J
b) For compression of 1 cm:
potential energy = U = 0.0228 J
kinetic energy = k = 0.155 J
total mechanical energy = E = 0.383 J
c) For compression of 2 cm :
potential energy = U = 0.1104 J
kinetic energy = k = 0.272 J
total mechanical energy = E = 0.383 J
d) For compression of 3cm:
potential energy = U = 0.248 J
kinetic energy = k = 0.177 J
total mechanical energy = E = 0.383 J
Method for solving:The equations for kinetic energy is:
k= 1/2*m*[tex]v^{2}[/tex]
The equation for elastic potential energy is:
U= 1/2*ks*[tex]x^{2}[/tex]
Where,
m= mass of the block
v= velocity
ks= spring constant
x= displacement of the spring
(a)when compression= 0 cm
U= 1/2*ks*[tex]v{2}[/tex]
U= 1/2*552*[tex](0)^{2}[/tex]
= 0 J
Kinetic energy:
k= 1/2*m*[tex]x^{2}[/tex]
k= 1/2*(1.05)*[tex](0.855)^{2}[/tex]
k= 0.383 J
Mechanical energy:
E= k + U
E= 0.383+0
E= 0.383 J
There will be no work done by friction or any other dissipative force, hence this energy will be conserved, or it will remain constant (like air resistance). This indicates that only spring potential energy will be created from the kinetic energy (there is no thermal energy due to friction, for example).
(b) spring potential = ?
U= 1/2* 457 N/m*[tex](0.01)^{2}[/tex]
U= 0.0228 J
Since the mechanical energy must remain constant, we may calculate the kinetic energy using the mechanical energy equation:
E= k + U
0.383= k + 0.0228
k= 0.383 - 0.228
k= 0.155
(c)spring constant when x= 0.02
U= 1/2*552*[tex](0.02)^{2}[/tex]
U= 0.1104 J
Using the equation of mechanical energy:
E= k +U
0.383= k+ 0.1104
k= 0.383 - 0.1104
k= 0.272 J
(d) U= 1/2*552*[tex](0.03)^{2}[/tex]
U= 0.2484 J
E= 0.383 J
k = E - U
k= 0.383- 0.206
k= 0.177
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What feature of the solar system separates the terrestrial planets from the jovian planets?
Jovian Planets have low density and no Earth like things, like the terrestrial planets.
All of the planets in our solar system,except Pluto—are categorized as either terrestrial (like Earth) or jovian (like Jupiter) planets
Terrestrial planets:
The planets Mercury, Venus, Earth, and Mars are all terrestrial. These planets are both physically and mass-wise quite small. A terrestrial planet has a dense interior of metals and a stable rocky surface. These planets are warmer than planets farther from the sun because they are closer to the sun in the solar system.Jovian planets:
Saturn, Uranus, Neptune, and Jupiter are examples of jovian planets. These planets are bigger and heavier. The surfaces of Jovian planets are not solid. Due to their size and composition, which is primarily gases, they are sometimes referred to as gas giants. Only in the deepest regions of the Jovian planets' cores can one find trace amounts of rocky elements. Jovian planets are cooler because they are farther from the sun than terrestrial planets in the solar system.Learn more about the Solar system with the help of the given link:
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A 1.4 kg bicycle tire with a radius of 33 cm rotates with an angular speed of 155 rpm. Find the angular momentum(L) of the tire, assuming it can be modeled as a hoop.
The angular momentum of the tire is 0.394KGm^2/s.
To find the answer, we have to know more about the angular momentum.
How to find the angular momentum?We have the expression for angular momentum as,[tex]L=mvr[/tex]
where, m is mass of th body, v is the linear velocity and r is the radius of the circular orbit.
It is given that,[tex]m=1.4kg\\r=33*10^{-2}m\\w=155rpm=2.58rps[/tex]
Thus, the linear velocity will be,[tex]v=rw=33*10^{-2}*2.58=0.85m/s[/tex]
Then, the angular momentum, L will be,[tex]L=mvr=1.4*0.85*33*10^{-2}=0.394Kgm^2/s[/tex]
Thus, we can conclude that, the angular momentum of the tire is 0.394KGm^2/s.
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What is the length of the color attribute?
What is the longest material key can we have in our data warehouse?
The length of the colour attribute is 6 characters.
What is a colour attribute?Each colour has a distinct look based on three essential characteristics: hue, chroma (saturation), and value (lightness). It's critical to use all three of these properties when describing colour to appropriately identify it and distinguish it from others.
What is the use of colour attributes?The HTML <font> color Attribute specifies the text color within the font element. Values of Attributes: colour name: It uses the colour name to set the text colour.
It should be noticed that colours are represented by the hex triplet.
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Which pairs of subsets of the real number system have no common elements?
Answer:
Odd and even
Explanation:
Odd and even numbers have no common elements
Who rediscovered aristarchus’s model of a heliocentric solar system? copernicus galileo kepler ptolemy
Copernicus rediscovered aristarchus’s model of a heliocentric solar system.
Aristarchus asserted that one may determine the distances between the Sun and Moon by measuring the angle between them when the Moon is half-illuminated (admittedly, the illumination itself suggested the angle). Aristarchus recognised that the Moon does not emit light of its own, but rather shines as a result of the Sun's light.
It's because Polish-born astronomer Copernicus was responsible. He initially introduced the heliocentric hypothesis in his book De revolutionibus orbium coelestium, "On the Revolutions of Celestial Bodies," which was released in.
Therefore, Copernicus rediscovered aristarchus’s model of a heliocentric solar system.
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Answer:
Copernicus
Explanation:
A heater marked 2000W/3000W is switched on for 4 hours. For the first hour it is on the highest setting and for the last 3 hours it is on the lowest setting
1.1 How much energy does it transfer to the room in kWh (9kWh)
Answer:
9 kW-hr
Explanation:
3000 W = 3 kW for 1 hr = 3 kW - hr
2000 W = 2 kW for 3 hr = 6 kW -hr
total power = 3 + 6 = 9 kW-hr
Alaskan natives often eat whale blubber while other groups of people typically do not. this is an example of __________. a. food variety b. stress c. palpability d. learned preferences please select the best answer from the choices provided a b c d
Alaskan Natives often eat whale blubber while other groups of people typically do not. (d)This is an example of learned preferences.
What are Learning Preferences?
Learning styles can be defined as the way in which an individual generally responds to specific learning situations and prefers to process different forms of information. Often, learning styles are regarded as the preferred methods for undertaking learning, for example, reader/writer, audio/visual etc., but this is a narrow definition. Learning preferences as a term is generally considered to take in a broader set of factors than just methods as they also take into account aspects that might impact on learning, such as: the environment and where and when students prefer to do their learning. For example, a student may prefer to work alone at home, and do her assignments late in the evening when the family has gone to bed. Another student may thrive in group situations and only wish to study during the day on-campus. In a nutshell, learning styles and preferences help to describe how people learn best in their context, and are useful in raising awareness about this.To learn more about Learning Preferences: https://brainly.com/question/2289046
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The electron in a ground-state h atom absorbs a photon of wavelength 97. 25 nm. to what energy level does the electron move?
The electron in a ground-state H atom absorbs a photon of wavelength 97. 25 nm. Energy level till where the electron move is 4
Rydberg's equation is formula which signifies relation of wavelength of incident photon and the energy level.
Rydberg's equation is used to find out the relation between the wavelength and the Energy Levels:
1/λ = RZ² (1/n₁² - 1/n₂²)
where, λ is wavelength = 97.25 nm
R is the Rydberg constant = 1.0967 × 10⁷ m
n₁ is the initial energy level i.e. the Ground state, n₁ = 1
n₂ is the higher energy level
On substitution of the above value:
1/97.25 × 10⁻⁹ = 1.0967 × 10⁷ ( 1 - 1/n₂²)
On solving,
⇒ n₂ = 4
Hence, the higher energy level is 4
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A red wagon with a mass of 7kg is moving with a velocity of 4 m/s straight toward a blue wagon at rest.
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Apply the Conservation of Linear Momentum:
[tex]\longrightarrow \sf{m_1 u_1 +1 + m_2 u_2 = m_1v_1 + m_2v_2}[/tex]
[tex]\longrightarrow \sf{(7 \cdot 4) + (1 \cdot 0) = (7 \cdot 3) + 1v_2}[/tex]
Solving further:
[tex]\longrightarrow \sf{28+0 = 21+ v_2}[/tex]
[tex]\longrightarrow \sf{28 = 21+ v_2}[/tex]
[tex]\longrightarrow \sf{v_2= 28- 21}[/tex]
▪ [tex]\longrightarrow \sf{v_2= 7 \dfrac{m}{s} }[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex] \boxed{\bm{v_2= 7 \dfrac{m}{s}}}[/tex]
The reason the position of a particle cannot be specified with infinite precision is the?
The reason the position of a particle cannot be specified with infinite precision is the uncertainty principle .
The position of a particle moving in a straight line is a vector which represents a point P on the line in relation to the origin O. The position of a particle is often thought of as a function of time, and we write x(t) for the position of the particle at time t.
The Heisenberg uncertainty principle is a law in quantum mechanics that limits how accurately you can measure two related variables. Specifically, it says that the more accurately you measure the momentum (or velocity) of a particle, the less accurately you can know its position, and vice versa.
The uncertainty principle (for position and momentum) states that one cannot assign exact simultaneous values to the position and momentum of a physical system. Rather, these quantities can only be determined with some characteristic “uncertainties” that cannot become arbitrarily small simultaneously
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A mass weighing 16 pounds is attached to a spring whose spring constant is 25 lb/ft. what is the period of simple harmonic motion?
The time period of the spring - mass system undergoing simple harmonic motion is 5.024 seconds.
We have a mass weighing 16 pounds which is attached to a spring whose spring constant is 25 lb/ft . This complete spring - mass system is undergoing simple harmonic motion.
We have to calculate the time period of this simple harmonic motion.
What is the formula to calculate the Time period of a spring - mass system performing Simple harmonic motion?The formula to calculate the time period of a spring - mass system undergoing simple harmonic motion is -
[tex]T=2\pi \sqrt{\frac{m}{k} }[/tex]
Where -
T is the time period of spring - mass simple harmonic motion.
m is the mass of body
k is the spring constant
In the question given -
mass (m) = 16 pounds
Spring constant (k) = 25 lb/ft
Substituting the values in the formula above -
T = [tex]2\pi \sqrt{\frac{16}{25} }[/tex] = [tex]\frac{2\pi \times4}{5}[/tex] = 5.024 seconds
Hence, the time period of the spring - mass system undergoing simple harmonic motion is 5.024 seconds.
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What is the distance traveled by an object that moves with an average velocity of 8.0 m/s for a total of 4.0 seconds? please show your work in order to earn credit for this question.
The distance traveled by the object is 32 m.
What is Kinematic equation?The motion of an object with constant acceleration is described by a set of equations known as the kinematic equations. Integrals, derivatives, and rates of change must all be understood in order to solve kinematics problems.Calculation for determining distance traveledIf an object is traveling with a consistent velocity, this is referred to as uniform motion.
The equation below gives the average speed of an item moving uniformly:
v = d/t
where
v= average speed
d = traveled distance
t= The amount of time used
The object in this problem is as follows:
v = 8.0 m/s is the average speed
The time was t = 4.0 s.
We determine the distance traveled by solving for d:
d = vt = (8.0)(4.0) = 32 m
Hence, the distance traveled by the object is 32 m.
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A 2-f and a 1-f capacitor are connected in series and a voltage is applied across the combination. the 2-f capacitor has:_______.
Half the potential difference of the the1-µF
A circuit must have a capacitance of 2 F across a 1 kV potential difference for an electrical technician. He has access to a sizable number of 1F capacitors, each of which can sustain a potential difference of no more than 400 V. Please suggest a configuration that uses the fewest capacitors possible.
The 2-mu F capacitor has the following characteristics: none of the aforementioned; half the charge of the 1-mu F capacitor; twice the charge of the 1-mu F capacitor; and half the potential difference of the 1-mu F capacitor.
Q = C V, C = Capacitance of the capacitor gives the charge stored by a capacitor with an applied voltage V. V is the applied voltage.
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Half the potential difference of the 1μf capacitor.
Charge: Q = CV where C is the capacitance in Farads, V is the voltage across the capacitor in Volts and Q is the charge measured in coulombs (C).
Energy stored: W = ½ QV = ½ CV×V
where W is the energy measured in Joules.
As the capacitance of a capacitor is equal to the ratio of the stored charge to the potential difference across its plates, giving: C = Q/V, thus V = Q/C as Q is constant across all series connected capacitors, therefore the individual voltage drops across each capacitor is determined by its its capacitance value.
When the capacitors are connected in the form of series combination, the capacitance in total is less than the individual capacitances of the series capacitors. If one, two or number of capacitors are connected in the series form, the overall effect is the single or equivalent capacitor which has the total sum of the spacings between the plates of the individual capacitors. The increase in the plate spacing results in the decreased capacitance, with all the other factors remaining unchanged.
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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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21. A person standing 49.5m from the foot of a cliff claps his hands and hears an echo 0.3
seconds later. Calculate the velocity of the sound in air
Answer:
330 m/s
Explanation:
The sound wave has to travel TO the cliff AND back = 2 * 49.5 = 99 m
magnitude of velocity = distance / time = 99m / .3 s = 330 m/s
What is the change in temperature for the aluminum wire? c what is the change in temperature for the steel wire? c what is the change in temperature for the lead pellets? c
Answer:
-79.6
-80
-81.2
Explanation:
Fart
What is the change in temperature for the aluminum wire?
-79.6
What is the change in temperature for the steel wire?
-80
What is the change in temperature for the lead pellets?
-81.2
if a 2 liter bottle of coke cost $2.34 how much does 1mL of coke cost?
1mL of coke cost =$0.00117.
The cost of 2-liter bottle of coke is $2.34
The unit of 1 liter is 1000ml.
Then the 2 liter coke bottle volume is 2000ml
The formula is ( divide the total price by the quantity).
$2.34/2000=0.00117.
The capacity of a liquid is measured in metric units of volume called liters and milliliters. There are four units of measurement for liquid volume: milliliters, centiliters, liters, and kiloliters. The values of these units vary even though they all refer to the same quantity.
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An organ pipe with a fundamental frequency f is open at both ends. if one end is closed off, the fundamental frequency will:______
The fundamental frequency will drop by half.
The lowest frequency of a periodic waveform is known as the fundamental frequency. In other words, it is the lowest frequency that can be produced by a certain instrument. The first harmonic of the instrument is another name for the fundamental frequency.
An open-ended organ pipe's basic wavelength is twice as long as the pipe itself. The fundamental wavelength is four times the pipe's length if one end is closed. The fundamental frequency decreases by half because the wavelength doubles when one end of the pipe is sealed off but the speed of sound remains unchanged.
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Suppose a comet orbits the sun on a highly eccentric orbit with an average (semimajor axis) distance of 1 au. how long does it take to complete each orbit, and how do we know?
If a comet were to orbit the sun with a highly eccentric orbit and an average (semimajor axis) distance of 1 au, we might use Kepler's third law of planetary motion to determine that each orbit would take one year to complete.
To find the answer, we need to know about the Kepler's third law of planetary motion.
What is Kepler's third law of planetary motion?The period of a planet's orbit (T) squared is equal to the size of the semi-major axis of the orbit (a) cubed when it is stated in astronomical units because T² ∝ a³ according to Kepler's Third Law. In reality, Kepler's Third Law compares a planet's orbital period and radius to those of other planets.Thus,[tex]a=1AU\\T=(1)^{3/2}=1 year[/tex]
Thus, we can conclude that, If a comet were to orbit the sun with a highly eccentric orbit and an average (semimajor axis) distance of 1 au, we might use Kepler's third law of planetary motion to determine that each orbit would take one year to complete.
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What is the maximum weight of a luminaire (lighting fixture) permitted to be hung directly from an outlet box in a ceiling?
The maximum weight of a luminaire (lighting fixture) permitted to be hung directly from an outlet box in a ceiling 50 pound.
A luminaire that weighs more than 23 kg (50 lb) shall be supported independently of the outlet box, unless the outlet box is listed for not less than the weight to be supported.
Luminaire, or light fixture, complete lighting unit, consisting of one or more lamps (bulbs or tubes that emit light), along with the socket and other parts that hold the lamp in place and protect it, wiring that connects the lamp to a power source, and a reflector that helps direct and distribute the light.
Fluorescent fixtures usually have lenses or louvers to shield the lamp (thus reducing glare) and redirect the light emitted. Luminaires include both portable and ceiling- or wall-mounted fixtures.
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Biomes on Earth have exhibited changes throughout history that have been caused by a variety of factors. Over the past 50 years, the amount of tropical rainforest acreage found throughout the world has decreased from 14.8 billion acres to 8.6 billion acres due to deforestation. What factor is likely most responsible for the changes observed in the world’s rainforests?
a.
volcanic activity
b.
human activity
c.
temperature changes
d.
solar eclipses
Please select the best answer from the choices provided
A
B
C
D
When a 20. 0-ohm resistor is connected across the terminals of a 12. 0-v battery, the terminal voltage of the battery falls 0. 30 v. what is the internal resistance of this battery
Answer:
.513 Ω
Explanation:
The current through the 20 Ω load can be found to be
(12-.3) v / 20 Ω = .585 A
This current also flows through the internal resistance and produces the .3 v drop across this resistor
V/I = R
.3 v / .585 A = .513 Ω internal resistance
A loop of area 0.100 m² is oriented at a 15.5 degree angle to a 0.500 T magnetic field. It rotates until it is at a 45.0 degree angle with the field. What is the resulting CHANGE in the magnetic flux? [?]Wb
I NEED THIS FAST PLEASE!!!
The resulting change in the magnetic flux is =0.013Wb
what is magnetic flux?
Magnetic flux is defined as the total magnetic field which passes through a given area.It is the number of magnetic field lines that is flowing in a closed area.
Given:
At degree =15.5°,magnetic flux=magnetic field=0.500T
At degree=45.0°, magnetic field=0.500T
Magnetic flux=magnetic field ×Area×cos(angle)
magnetic flux (1) = 0.500×0.1×cos(15.5)
= 0.048
magnetic flux (2) = 0.500×0.1×cos(45)
=0.035
Resulting change in flux = 0.048-0.035
= 0.013Wb
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Find the average value have of the function h on the given interval. h(u) = (ln(u))/u, [1, 5]
The average value have of the function h on the given interval is [tex]\frac{1}{2} \ln^2 (2)[/tex].
How to find the Average Value of function ?The given function is [tex]h (u) = \frac{\ln (u)}{u}[/tex] on the interval (1, 5).
The average value of function (a, b) is found by using the formula:
[tex]\frac{1}{(b -a)} \displaystyle \int^{b}_{a} f(x) dx[/tex]
Here the function is [tex]h (u) = \frac{\ln (u)}{u}[/tex] and a = 1, b = 5
Now,
[tex]\dfrac{1}{(5 - 1)} \displaystyle \int^{5}_{1} \frac{\ln (u)}{u}\ du[/tex]
[tex]= \dfrac{1}{4} \displaystyle \int^{5}_{1} \frac{\ln (u)}{u}\ du[/tex]
Substitute [tex]\ln (u) = t, dt = \frac{1}{u}\ du[/tex]
[tex]\dfrac{1}{4} \displaystyle \int^{4}_{1} \frac{\ln (u)}{u} du = \frac{1}{4} \int^{4}_{1} t (dt)[/tex]
[tex]= \frac{1}{4} \left [\frac{t^2}{2} \right ]^{4}_{1}[/tex]
[tex]= \frac{1}{8} \left [\{\ln (u)\}^2 \right ]^{4}_{1}[/tex]
[tex]= \frac{1}{8} [\{\ln (4) \}^2 - \{\ln (1) \}^2 ][/tex]
[tex]= \frac{1}{8} [\{\ln (4)\}^2 - 0][/tex]
[tex]= \frac{1}{8} \ln^2 (4)[/tex]
[tex]= \frac{2}{4} [2 \ln (2)]^2[/tex]
[tex]= \frac{1}{2} \ln^2 (2)[/tex]
Thus from the above conclusion we can say that The average value have of the function h on the given interval is [tex]\frac{1}{2} \ln^2 (2)[/tex].
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