The complete factorization is 2 (2x-1)².
What is factorization?Factorization is a way of dividing mathematical algebraic statements into their components. The components will produce the original phrase if we multiply them once more.
Factorization is a way of dividing mathematical algebraic statements into their components. If we multiply the components again, we get the original equation.
Factorising is the opposite of extending brackets. Fully factorizing an expression implies putting it in brackets and removing the greatest common factors. Finding the largest common factor between each item in the phrase is the simplest method of factorization.
Given,
= 8x² - 8x +2
= 8x² - (4+4)x +2
= 8x² - 4x + 4x +2
= 4x (2x -1) -2 (2x-1)
= (4x-2) (2x-1)
= 2 (2x-1) (2x-1)
= 2 (2x-1)²
Thus, complete factorization is 2 (2x-1)².
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On a train moving , 75 m/s you roll a ball towards the front of the train with a speed of 5m/s. Your friend standing some unknown distance away from you catches it. To a person outside the train, the ball traveled 220m until it was caught. How far away is your friend standing from you?
The distance of your friend from you is 15.7 m.
What is the time of motion of ball?
The time take for the ball to travel to you friend is calculated by applying the principle of relative velocity as shown below.
( Vt - Vb ) t = d
where;
Vt is the velocity of the trainVb is the velocity of the ballt is the time of motion of the balld is the distance travelled by the ball( Vt - Vb ) t = d
(75 - 5) t = 220
70t = 220
t = 220 / 70
t = 3.14 s
The distance of your friend from you is calculated as;
d1 = 5 m/s x 3.14 s
d1 = 15.7 m
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you observe a galaxy with a hydrogen beta absorption line 496.0 nm. the laboratory wavelength of this line is 486.1 nm. what is the galaxy's distance from us in mega-light years (mly)?
The galaxy with a hydrogen beta absorption of 496 nm then the galaxy's distance from us in mega-light years (mly) will be equal to 277.54 Mly.
What is Wavelength?
The distance between two identical locations (adjacent crests) in successive cycles is known as the wavelength, and it is used to describe waveform signals that are transmitted over wires or into space. Typically, in wireless systems, this length is specified in meters (m), centimeters (cm), or millimeters (mm).
As per the given information in the question,
The line's hydrogen laboratory wavelength, λ = 486.1 nm
The galaxy's spectrum's wavelength, λ' = 496.0 nm
Then, the change in wavelength,
Δλ = λ' - λ
Δλ = 9.9 nm
The speed of light, c = 2.998 × 10⁵ km/s
Use the equation of Doppler's effect,
v = c × Δλ/λ
v = 6,105.75 km/s
So, the radial velocity will be 6105.78 km/s.
v = H₀d
Here, v is the velocity of the galaxy, d is the distance between galaxies and H₀ is Hubble's constant.
d = v/H₀
d = 6105.75/22
d = 277.54 Mly
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Match each term with its definition.MorphemePhonemeGrammarSyntax1)smallest units of sound that carry meaning on their own2)smallest units of sound that make a difference in meaning3)combined set of rules that govern use of a particular language4)rules for forming speech sounds into phrases and sentences
All the terms are related to languages.
Morpheme - smallest units of sound that carry meaning on their own
Phoneme -smallest units of sound that make a difference in meaning
Grammar - a combined set of rules that govern the use of a particular language
Syntax - rules for forming speech sounds into phrases and sentences
The smallest linguistic unit capable of meaning modification is the phoneme.
Morphemes are divided into two distinct types, bases (or roots) and affixes.
Most people think of grammar as a set of rules that help us form sentences.It covers a variety of language-related topics, such as Parts of speech (verbs, adjectives, nouns, adverbs, prepositions, conjunctions, modifiers, etc.) Clauses (e.g. independent, dependent, compound) (e.g. independent, dependent, compound)
The sequence of grammatical elements like subjects, verbs, direct and indirect objects, etc. is determined by syntax in English.
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what is the power output, in watts, of the combined resistance when the motor is operating at full speed?
A watt is equivalent to an amp multiplied by a volt. All done! Therefore, watt = amp X volt. This equation is also sometimes written as W=A X V.
What does watt mean?The power unit is the watt. It refers to the quantity of energy required for a given object to operate as well as the rate during which energy is used up. A joule of energy (or one watt) is equal to one joule of electricity flowing for one second.
What distinguishes one watt from another?Watts, which are determined by multiplying Amps by Volts, are used to measure energy. As the wattage rises, the appliance produces more power and output. This is the amount of water that the hosepipe example would emit.
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The solar system is 25,000 light years from the center of our Milky Way galaxy. One light year is the distance light travels in one year at a speed of 3.0 x 108 m/s. Astronomers have determinedthat the solar system is orbiting the center of the galaxy at a speed of 230 km/s.
a. Assuming the orbit is circular, what is the period of the solarsystem’s orbit? Give your answer in years.
b. Our solar system was formed roughly 5 billion years ago. How many orbits has it completed?
c. The gravitational force on the solar system is the net force due to all the matter inside our orbit. Most of that matter is concentrated near the center of the galaxy. Assume that the matter has a spherical distribution, like a giant star. What is the approximate mass of the galactic center?
d. Assume that the sun is a typical star with a typical mass. If galactic matter is made up of stars, approximately how many stars are in the center of the galaxy?
a. The period of the solar system's orbit, assuming the orbit is circular, is [tex]2.05X10^{8} years[/tex].
b. There have been 24.4 completed revolutions.
c. The star has a mass of [tex]1.87X10^{41}[/tex] kg.
d. There are [tex]9.45X10^{10}[/tex] stars in the galaxy's center.
a. Distance equals 25,000 light years.
[tex]3X10^{8}[/tex]m/s equals the speed of light (c)
230 m/s is the astronomers' speed.
Using the time period formula,
[tex]t=\frac{d}{v}[/tex]
[tex]t= \frac{2\pi r}{v}[/tex]
r = distance
t = time, and v = speed.
Fill out the formula with the value
[tex]t = \frac{2\pi * 25000 * 9.46 * 10^{15} }{230 * 10^{3} }[/tex]
[tex]t= 6.460*10^{15} sec[/tex]
Number of years
[tex]t= \frac{6.460*10^{15} }{3.15*10^{7} } \\t= 2.05*10^{8} years[/tex]
Consequently, the solar system's orbit lasts [tex]2.05*10^{8}[/tex].
b. The solar system's average age is Tn=5 billion years, or [tex]5* 10^{9}[/tex] years.
The number of completed revolutions can be computed as
[tex]N=\frac{T^{n} }{T} \\N= \frac{5*10^{9}years }{2.05*10^{8}years } \\N=24.4[/tex]
24.4 revolutions have been completed.
c. The solar system's radius, r=25000 light years
velocity = 230 km/s
We can determine the big star's mass as
[tex]M= \frac{v^2r}{G} \\[/tex]
By substituting values, we obtain
[tex]M= \frac{(230*10^{3})^2* (25000*3*10^{8}*365*24*60*60m) }{(6.67*10^{-11} N/kg^2.m^2)}[/tex]
[tex]M= 1.87*10^{41} kg[/tex]
The star has a mass of [tex]1.87*10^{41} kg[/tex].
d. The sun's mass, [tex]M_{s}[/tex], is [tex]1.99*10^{30} kg[/tex]
The star's number can be computed using
[tex]N=\frac{mass of glactic center}{mass of sun} \\N= \frac{1.88*10^{41} }{1.99*10^{30} } \\N= 9.45*10^{10}[/tex]
There are [tex]9.45*10^{10}[/tex] beginnings, or around 94.5 billion, each year.
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what is the greatest average speed ????v of blood flow at 37∘c37∘c in an artery of radius 2.25 mm2.25 mm if the flow is to remain laminar? take the density of blood to be 1025 kg/m3,1025 kg/m3, and the viscosity to be 2.084×10−3 pa·s.
Average speed of blood flow is given by:
V = n*Re/(rho*d)
n = viscosity of blood = 2.084*10^-3 Pa.s
Re = max reynolds number for which flow remains laminar = 2000
rho = density of blood = 1025 kg/m^3
d = diameter of artery = 2*radius = 2*2.50 mm = 5.0*10^-3 m
So,
V = 2.084*10^-3*2000/(1025*5.0*10^-3)
V = 0.813 m/sec
Any external force that acts against movement is called __________. A. Gravityb. Efficiencyc. Resistanced. Momentum.
Answer:
the answer is resistance
a ball is shot from the ground straight up into the air with initial velocity of 48 ft/sec. assuming that the air resistance can be ignored, how high does it go?
The ball goes up to 35.83 ft high. The result is obtained by using the formula of motion with constant acceleration.
What is motion with a constant acceleration?A motion along a straight line with a constant acceleration is a motion which the initial and final velocity change. There are 3 important formulas in this case for vertical motion.
v₁ = v₀ + gt
v₁² = v₀² + 2gh
h = v₀t + 1/2 gt²
Where
v₀ = initial velocity (m/s)v₁ = final velocity (m/sg = acceleration due to gravity (9.8 m/s²)t = time (s)h = height (m)Note: If the object goes up, the value of g is (-).
A ball moves from the ground straight up with a velocity of 48 ft/sec. Find the height of the ball!
First, we change the unit of initial velocity.
v₀ = 48 ft/sec
v₀ = 48 × 0.3048 m/s
v₀ = 14.63 m/s
The ball will go up to a certain height. At the maximum height, the velocity of the ball is 0. Thus, we can use the following formula to find h.
v₁² = v₀² - 2gh
0 = (14.63)² - 2(9.8)h
214.04 = 19.6h
h = 10.92 m
h = 10.92/0.3048 ft
h = 35.83 ft
Hence, the ball will go straight up to a height of 35.83 ft.
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the velocity of a wave with a wavelength of 4.700 m and frequency of 54.00 hz is (5 points) 25.38 m/s 33.85 m/s 114.9 m/s 253.8 m/s
The velocity of this wave is 253.8 m/s.
Wavelength is the distance of the starting point of a wave till its ending point. The length of the wave is known as wavelength. The waves will interact via constructive interference, which is possible only when the wavelength and phase of the waves are the same.
Frequency is the number of waves that pass a fixed point.
Given,
Wavelength = 4.7 m
Frequency = 54 Hz
Velocity of any wave is given by a formula,
Velocity = wavelength * frequency
Velocity = 4.7 * 54
Velocity = 253.8 m/s
Therefore, the velocity of this wave is 253.8 m/s
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in taking your pulse, you count 67 heartbeats in 1 minmin. part a what is the period of your heart oscillations?
The period of your heart oscillations = 60 / 67 cycles/min.
How do you find the period of oscillation?T = 2(m/k) describes this. We may calculate the period and, thus, the frequency by measuring the length of one full oscillation. Be aware that the period of a pendulum is independent of its mass, but the period of a mass on a spring is independent of the spring's length.Number of oscillations that were completed in the given unit of time. f = 1/T = ω/2π 4. Period of time (T) T = 2 /Section overview. A repetitive oscillation is known as periodic motion. The period T is the length of one oscillation. The frequency f is the number of oscillations per unit of time.Given data :
Time taken for 67 heart beats = 1 min = 1* 60 seconds =60 s The time taken for 1 heart beat = 60 / 67
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(b) Explain the behaviour of the light at points Y and Z.
ray of
light
not to scale
Help
At a point, Y refraction is observed and the light ray is moving away from the normal means going from the denser to the rarer medium, at point Z, the light ray is moving towards the normal, which means travelling in the denser medium.
What is Refraction?The redirection of a wave as it travels through one medium and into another is called refraction. The wave's altered speed or a shift in the medium might both result in a redirection. Refraction of light is governed by Snell's rule, which states that for a given set of media, the ratio of the sines of the angle of incidence and angle of refraction is equal to the phase velocities (v1/v2) or, alternatively, the refractive indices (n2/n1) of the two media.
What is a Denser medium?A medium is said to be optically denser if the speed of light is lower in it. In terms of optical density, glass is a denser medium than air.
Hence, at a point, Y refraction is observed and the light ray is moving away from the normal means going from the denser to the rarer medium, at point Z, the light ray is moving towards the normal, which means travelling in the denser medium.
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he purpose of low beam headlights is to provide better visibility to a driver driving in fog, rain and smoke. a) true b) false
Answer: True
Explanation:
how much work does an elevator motor do to lift a 1500 kg elevator a height of 100 m ? express your answer with the appropriate units.
1.47 MJ work does an elevator motor do to lift a 1500 kg elevator a height of 100 m.
What is work in a physics?In physics, the term "work" refers to the energy transfer that takes place when an item is displaced over a distance by such an external force, at least a portion of which is supplied in the displacement direction. Stimulates into an object to cause some displacement is what is referred to as work. The ability to perform tasks is referred to as energy. The work is consistently the same.
Briefing:Work is simply the result of force multiplied by distance, so:
Work = Force * Distance
In this instance, force is simply equal to the elevator's weight, so:
Work = mass * gravity * distance
Work = 1500 kg * 9.8 m/s^2 * 100 m
Work = 1,470,000 J = 1.47 MJ
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A 1500-kg car moving at 25 m/s hits an initially uncompressed horizontal spring with spring constant of 2. 0 ? 106 n/m. What is the maximum compression of the spring? (neglect the mass of the spring. ).
A 1500-kg car moving around 25 m/s collides with a horizontal spring that is initially uncompressed but has a spring stiffness of 2.0?106 n/m as well as a max compress of x = 0.68 meters.
What is another word for compression?Compress, constrict, contract, inflate, and shrink are a few words that frequently replace the word compress. While all of these phrases refer to "decreasing in bulk or area," compress indicates squeezing over resistance into a constricted area with a certain shape.
Briefing:Considering that,
The automobile weighs 1500 kg.
Vehicle speed, v = 25 m/s
spring's spring constant, k=2×10⁶ N/m
Let x be the greatest distance the spring may compress before breaking,
1/2mv²=1/2kx²
1/2mv²=1/2kx²
x=[tex]\sqrt{mv^{2} /k}[/tex]
x=[tex]\sqrt{1500*25x^{2} /2*10^{6} }[/tex]
x = 0.68 meters
The spring is thereby compressed by 0.68 meters.
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the mechanical advantage for a machine is defined as the output force divided by the input force. since the output force is typically greater than the input force, this value is normally greater than one. for an ideal machine, what would be another way of representing the mechanical advantage? the mechanical advantage for a machine is defined as the output force divided by the input force. since the output force is typically greater than the input force, this value is normally greater than one. for an ideal machine, what would be another way of representing the mechanical advantage? (output distance)/(input distance)
The mechanical advantage can also be represented as the ratio of output work divided by input work. This ratio is usually greater than one, indicating that the machine is doing more work than the input force is providing.
What is mechanical advantage?
The force amplified by using a device, mechanical device, or machine system is known as mechanical advantage. To achieve the desired output force amplification, the device trades off input troops against movement. The law of the lever serves as a model for this. Mechanisms are machine parts made to control forces and motion in this way. An ideal transmission system does not increase or decrease power. Consequently, the ideal machine is devoid of a power source, frictionless, and built from rigid materials that do not flex or wear.
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suppose you were to find all of the angles 8 at which two very narrow slits separated by a/2 would produce minimum. how would this set of angles be different from the set of angles given by your equation in part iii above?
This set of angles would be the angles at which destructive interference occurs, which is 180° apart from the angles at which constructive interference occurs.
What is Intensity?
The power transmitted per unit area is known as the intensity as well as flux of radiant energy.
Uses of Intensity
Intensity is most frequently used to describe the average power transfer above one period of the wave. Other situations where energy is transmitted can also be described in terms of intensity.
Hence, The set of angles given by the equation in Part III is the set of angles at which the maximum intensity of light is produced.
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This set of angles would be the angles at which destructive interference occurs, which is 180° apart from the angles at which constructive interference occurs.
What is Intensity?
The power transmitted per unit area is known as the intensity as well as flux of radiant energy.
Uses of Intensity
Intensity is most frequently used to describe the average power transfer above one period of the wave. Other situations where energy is transmitted can also be described in terms of intensity.
Hence, The set of angles given by the equation in Part III is the set of angles at which the maximum intensity of light is produced.
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A 0,200-kg piece of lead at 100.0°C is dropped into a calorimeter. The calorimeter is a copper can of mass
5.00 x 102 kg and already contains 0.100 kg of water at 20.0°C. Calculate the final temperature if the specific heats of water, lead, and copper are 4.20 x 103 J/kg.K, 1.30 x 102 J/kg.K, and 4.00 x 103 J/kg:K respectively.
Answer:
24.5°C
Explanation:
A painter (of mass 79 kg) needs to reach out from a scaffolding to paint the side of a building, so he lays a plank across two bars of the scaffolding, and puts a heavy bucket of mass 23 kg directly over one of the bars (see figure). You can assume the plank is massless, and is long enough to reach to the other building. Show answer no attempt if the bars are separated by a distance 2. 9 m, how far, d, from the bar on the the right can the painter walk before the plank starts to fall?
0.84 m is the distance the painter walk before the plank starts to fall.
What is Torque?Torque is a measure of the force that rotates an object about an axis. A force accelerates an object with linear kinematics. Similarly, torque causes angular acceleration. Therefore, torque can be defined as the rotational equivalent of a linear force. The straight line around which an object rotates is called the axis of rotation. In physics, torque is simply the tendency of a force to twist or twist. Various terms such as moment and moment of force are used interchangeably to describe torque. The distance from the point of force application to the axis of rotation is sometimes called the moment arm or lever arm.
Mass of the painter (m₁) = 79 kg
Weight of painter (w₁) = 79 × 9.8
= 774.2 N
Mass of bucket (m₂) = 74 kg
Weight of bucket (w₂) = 23 × 9.8
= 225.4 N
Distance between them (L) = 2.9 m
Let d be the distance at which the painter can walk before the plank starts to fall.
At distance d, the torque due to painter and bucket is equal to each other:
T₁ = T₂
w₁d = w₂L
d = (w₂L)/w₁
d = (225.4 × 2.9)/774.2
d = 0.84 m
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An ideal gas is initially in a state that corresponds to point 1 on the graph above, where it has pressure P1 volume V1, and temperature T1. The gas undergoes an isothermal process represented by the curve shown, which takes it to a final state 3 at temperature T3. If T2 and T4 are the temperatures the gas would have at points 2 and 4, respectively, which of the following relationships is true? a. t1
b. t1
c. t1
d. t1=t2
e. t1=t4
The following relationship is true T1 < T2.
An ideal gas is defined as a gas in which all collisions between atoms or molecules are perfectly elastic and no intermolecular attractive forces occur. It can be thought of as a collection of perfectly rigid spheres that collide but do not interact.
The volume of gas particles is negligible. Gas particles are the same size and have no intermolecular forces as other gas particles. Gas particles move randomly according to Newton's laws of motion. Gas particles undergo perfectly elastic collisions without losing energy. This is the relationship between four variables and describes the state of the gas.
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In addition to science courses like physics and chemistry, what other types of courses are becoming increasingly relevant to space science careers?.
Structural engineering is the other course that are increasingly becoming relevant to space science careers
What are Space science careers ?Investigating how gravity affects the human body, building the telescopes of the future. providing accessible explanations of solar system discoveries. These are just a few examples of the projects that people involved in space exploration employment work on.
Learning how to repair space stations, aircraft, or even make space shuttles or items you'll need in space requires knowledge in civil engineering, which is the notion of designing large transportation projects.
Structural engineering is the other course that are increasingly becoming relevant to space science careers
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A truck is traveling at 25 m/s on a slippery road. The driver slams on the brakes and the truck starts to skid. If the coefficient of kinetic friction between the tires and the road is 0. 20, how far will the truck skid before stopping?.
If the coefficient of kinetic friction among the tires and the street is 0. 20, 312.5m far will the truck skid before stopping.
What is kinetic friction?
Kinetic friction is defined as a force that acts between moving surfaces. A body moving on the surface experiences a force in the opposite direction of its movement. The magnitude of the force will depend on the coefficient of kinetic friction between the two materials.
m = the mass of the truck
N = normal reaction
g = 9.8 m/s²
μ = 0.2, the coefficient of kinetic friction
The resistive force on the truck is
F = μN = μmg = 0.2*(9.8)m = 1.96m N
The acceleration (actually deceleration) is
a = F/m = -1.96 m/s²
Let d = distance for the truck to come to rest from an initial velocity of u = 35 m/s.
Then
u² + 2ad = 0
(35 m/s)² + 2(-1.96 m/s²)(d m) = 0
d = 35²/3.92 = 312.5 m
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Find its moment of inertia about an axis perpendicular to its plane and passing through the midpoint of the line connecting its two ends.
A) Moment of inertia about an axis passing through the point where the two segments meet : [tex]$I_A=\frac{1}{12} M L^2$[/tex]
B) Moment of inertia passing through the point where the midpoint of the line connects to its two ends: [tex]$I x=\frac{1}{3} M L^2$[/tex]
What is Moment of inertia?
The term "moment of inertia" refers to a physical quantity that quantifies a body's resistance to having its speed of rotation along an axis changed by the application of a torque (turning force). The axis might be internal or exterior, fixed or not.
A) The moment of inertia about an axis passing through the point where the two segments meet is [tex]$I_A=\frac{1}{12} M L^2$[/tex]given that the rod is bent at the center and distance from all the points to the axis remains the same, the moment of inertia about the center will remain the same.
B) Determine the moment of inertia about an axis passing through the point midpoint of the line which connects the two ends
First step: determine the distance between the ends ( d )
After applying Pythagoras theorem[tex]$\mathrm{d}=\frac{\sqrt{2}}{2} L$[/tex]
Next step : determine distance between the two axis [tex]$(\mathrm{x})$[/tex]
After applying Pythagoras theorem
[tex]\mathrm{x}=\frac{\sqrt{2}}{4} L$$[/tex]
Final step : Calculate the value of [tex]$\mathrm{I}_{\mathrm{x}}$[/tex]
applying Parallel Axis Theorem
[tex]$$I_x=I_8+M x^2$$[/tex]
[tex]$$\begin{aligned}& =\frac{1}{12} M L^2+\frac{1}{4} M L^2 \\& \therefore \quad I x=\frac{1}{3} M L^2 \\&\end{aligned}$$[/tex]
Hence we can conclude that Moment of inertia about an axis passing through the point where the two segments meet: [tex]$I_A=\frac{1}{12} M L^2$[/tex], Moment of inertia passing through the point where the midpoint of the line connects its two ends: [tex]$I x=\frac{1}{3} M L^2$[/tex]
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an explosion in a rigid pipe shoots out three pieces. a 6 g piece comes out the right end. a 4 g piece comes out the left end with twice the speed of the 6 g piece. from which end does the third piece emerge?
In an explosion a 6 g piece comes out of the right end and a 4 g piece comes out of the left end at twice the speed of the 6 g piece and the third piece comes out of the right end.
Initially all three balls are at rest so u = 0
Given m1 = 6g and m2=4g where m is the mass of balls
Let v1 be the velocity of the first ball = v(i) (denoted as (i) since the right end points to the positive X axis)
Let velocity v2 of second ball = 2(v)(-i) (denoted as (-i) since left end points negative X axis)
Mass of the third ball m3 = m and its velocity v3 = v'
By applying conservation of momentum
m1(u1) + m2(u2) + m3(u3) = m1(v1) + m2(v2) + m3(v3)
Since all balls are initially at rest u1 = u2 = u3 = u = 0
0 = (6×10⁻³)(v)(i) + (4×10⁻³)(2v)(-i) + m(v')
m(v') = (2×10⁻³)(v)(i)
v’ = (2×10⁻³)(v)(i)/(m)
So positive (i) indicates right end
So the third ball comes from the right end.
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in which direction does a first quarter moon rise? a) north b) south c) east d) west e) the moon becomes a first quarter moon only after it has risen and changed phase.
The first quarter moon rises in the East. Option (c) is the right answer.
The first quarter moon occurs halfway between the new moon and the full moon. One-quarter of the moon is visible from Earth, meaning that you see half the daylit side of the moon.
Just like the Sun and the nighttime stars, the Moon's apparent rising in the east and set in the west each day is not from the Moon's orbit around the Earth, it's from the Earth spinning. The lunar orbit is slower and harder to see but you can still spot it.
The moon rises in the east and sets in the west, every day. It has to. The rising and setting of all celestial objects are due to Earth's continuous daily spin beneath the sky.
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Two strings are made of the same material and have waves of equal speed. String 1 is thick; string 2 is thin.
Is the tension in string 1 greater than, less than, or equal to the tension in string 2?
greater than the tension in string 2
equal to the tension in string 2
less than the tension in string 2
PART B
Choose the best explanation from among the following:
Equal wave speeds implies equal tensions.
String 1 must have a greater tension to compensate for its greater mass per length.
String 2 will have a greater tension because it is thinner than string 1.
The tension in string 1 is lesser than to the tension in string 2.
What is meant by tension in a string?
It is possible to refer to tension as the action-reaction pair of forces acting at each end of the aforementioned elements. Tension is defined as the pulling force transmitted axially by a string, rope, chain, or other similar object, or by each end of a rod, truss member, or other comparable three-dimensional object.
The tension in the string has a square root relationship with wave speed, while the linear density of the wire has a square root relationship with wave speed. v=sqrt(T/u)
A larger thickness suggests a higher linear density (mass per length. Thus, the speed would be slower. The wave in string 1 moves slower than the wave in string 2, and vice versa.
According to a thick string, there is a lot of mass per length and the wave speed is slow.
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"Which of the following characteristics of Earth's relationship to the Sun explains the existence of Earth's seasons? Choose all that apply: ANSWER: Earth's axis always points in the same direction relative to the stars_ Earth spins on its axis completing one rotation each day: Earth orbits around the Sun, completing one orbit each year: Earth's axis is tilted relative to its orbital plane. Earth has a satellite called the Moon, which rotates around Earth. Correct art B What is the June solstice? ANSWER: The time of the year when Earth's geographic North and South Poles are leaning in similar ways toward the Sun the time of the year when Earth's geographic North Pole is leaning most directly toward the Sun the time of the year when Earth's geographic North Pole is leaning most directly away from the Sun Correct art C How does the inclination of Earth's axis change over the course of a year? ANSWER:"
The following characteristics of Earth's relationship to the Sun explain the existence of Earth's seasons is:
Earth orbits around the Sun, completing one orbit each yearEarth spins on its axis completing one rotation each dayEarth's axis is tilted relative to its orbital plane.Earth's axis always points in the same direction relative to the stars.The tilt of the earth's axis creates the seasons. Throughout the year, different parts of the world receive the most direct sunlight. So when the North Pole tilts toward the Sun, it's summer in the Northern Hemisphere. And when the Antarctic tilts toward the Sun the northern hemisphere will be in winter.
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a student has built a 15 cm long pinhole camera for a science fair project. she wants to photograph her 180 cm tall friend and have the image in the film be 5 cm high. how far should the front of the camera be from her friend?
Considering that there is a certain distance between both the student's friend as well as the camera's front, 540 cm or 5.4m
What is distance?
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting as well as ending point. The term "displacement" refers to a change in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial position to the ending position. For instance, if an object shifts from position A to position B, its position changes. Displacement is the term used to describe this shift in an object's position.
Let d be determined by the separation between the student's friend and the camera's front.
5.0cm/15cm = 180cm/d
d = (15cm)(180cm)/5.0cm
= 540cm or 5.4m
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what eyepiece focal length will give the microscope an overall angular magnification of 250? assume a length ll
The eye piece focal length is fe = -0.19 m where, fe= focal length of eye ,
What is the focal length?What Is Focal Length? Focal length is the distance (measured in millimeters) between the point of convergence of your lens and the sensor or film recording the image. The focal length of your film or digital camera lens dictates how much of the scene your camera will be able to capture.
Briefing : According to the question we assume ,
let The focal length is F(o) =5.5 mm = -.00055m and distance between objective and eyepiece = 19 cm
This negative sign shows the the microscope is diverging light
The angular magnification is m=250
The distance between the objective and the eyepieces lenses is z=19cm=0.19m
Generally the magnification is mathematically represented as
m={z-fe/fe}{0.25/f(o)}
Where fe is the eyepiece focal length of the microscope
Now making fe the subject of the formula,
fe=z/{(1-1{M-fo)/0.25}
then : fe=0.19/([tex]1-(\frac{250+ - 0.0055}{.25} )[/tex])}
= fe = -0.19 m
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Complete Question : The distance between the objective and eyepiece lenses in a microscope is 19 cm . The objective lens has a focal length of 5.5 mm .What eyepiece focal length will give the microscope an overall angular magnification of 250?
A solenoidal coil with 30 turns of wire is wound tightly around another coil with 310 turns. The inner solenoid is 20.0 cm long and has a diameter of 2.50 cm. At a certain time, the current in the inner solenoid is 0.150 A and is increasing at a rate of 1700 A/s.
Part A For this time, calculate the average magnetic flux through each turn of the inner solenoid.
Part B For this time, calculate the mutual inductance of the two solenoids.
Part C For this time, calculate the emf induced in the outer solenoid by the changing current in the inner solenoid.
Mutual inductance is the property by which one coil affects the current and voltage of the other coil.
Magnetic flux us the total magnetic field around both the coils.
EMF are invisible energy around the coils, which are mainly referred to as radiation.
How to find mutual inductance, magnetic flux and EMF around two coils?
We know
N = 30 turns
N¹= 310 turns
Inner solenoid length L¹= 20 CM= 0.2m long
Diameter d¹= 2.5 CM= 0.025m
Current i¹= 0.150 A
Rate of increase in current = di¹/dt= 1700A/s
Part A : magnetic flux = ∅¹= B¹A¹
B¹= ûⁿ × n¹ × i¹ = 2.92× 10↑-4T
Thus, ∅= 2.92×10↑-4× π/4×0.025²
= 1.432×10↑-7 Wb
Part B
Magnetic flux in one coil× number of turns in second coil = mutual inductance× current in the first coil
∅¹ × N² = Mi¹
= 1.432×10^-7 ×30
M × 0.150=1.432×10^-7×30
M=2.86×10^-5H
Part C
E = M di¹/dt
= 2.86×10^-5×1700 V
= 0.048 V
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In view of both the given query The inner solenoid's mean flux density per rotation is 1.43 * 10⁻⁷ Wb, or the two solenoids' mutual coupling is 2.86 x 10⁻⁴ H. The induced emf in the exterior loop is 4.86 * 10⁻¹ V.
How do solenoids function?A solenoid operates by creating an electromagnetic field surrounding an armature, which is a moving core. The electromagnetic field causes the armature to move, and when it does, it opens and closing valves or switches, converting mechanical energy into electrical movements and force.
Briefing:Given:
N1 = 310 revolutions in the inner solenoid.
N2 = 30 is the number of revolutions in the outer solenoid.
The inner solenoid's length is 20 cm, or 0.2 meters.
Inner solenoid radius = r = diameter/2 = 2.50/2 = 1.25 cm = 0.0125 m
The inner solenoid's current I is equal to 0.150 A.
1700 A/s is the current growth rate, di/dt.
A). Average magnetic flux across the inner solenoid's turns is equal to BA.
Include the values:
Average magnetic flux via the inner solenoid's turns:
= [4π x 10⁻⁷][310/0.2][0.150]π(0.0125)²
= 1.43 * 10⁻⁷ Wb
B). The two solenoids' mutual inductance is given by M = N2 x (average flux) / current.
= (30 x 1.43 * 10⁻⁷) / 0.150
= 2.86 x 10⁻⁴ H
C). The change in current there in inner solenoid causes an induced emf in the outer magnet that is equal to M*di/dt.
= 2.86 x 10⁻⁴ * 1700
= 4.86 * 10⁻¹ V
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when ashley sat on a rotating stool holding a set of weights close to her body, her rate of rotation changed when she moved the weights away from her body. did her rate or rotation slow down or speed up? why did this occur? did this violate the conservation of energy?
Reduced moment of inertia because of the frictional effects of the Moon-driven tides.
What is conservation of energy?A fundamental law of chemistry and physics stating that despite internal changes, an isolated system's total power remains static. The first conservation of energy is based on this principle, which is far more commonly phrased as the fact that electricity cannot be generated or destroyed. According to the rule of conservation of energy, energy can only be transformed from one type of energy to another and cannot be created or destroyed. This indicates that unless energy is added from the outside, a system constantly has the same quantity of energy.
What is the principle of conserving energy?According to the conservation of energy principle, energy is neither created nor destroyed. It has the capacity to change types. The validity of the conservation of energy principle, like that of mass, depends on experimental observations; as a result, it is an empirical law.
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