The plane's heading is 4.61 degrees south of east, which is the direction the pilot needs to steer the plane in order to reach her objective and the trip takes 1.83 hours.
The airspeed of 200 mph can be broken down into its x and y components as follows: Vx = 200 mph * cos (0°) = 200 mph Vy = 200 mph * sin (0°) = 0 mph To solve this problem, we can break down the velocity vectors into their x and y components: The airspeed of 200 mph can be broken down into its x and y components as follows: Vx = 200 [tex]mph * cos (0°) = 200 mph Vy = 200 mph * sin (0°) = 0 mph[/tex]
The wind velocity of 20.0 mph at an angle of 60.0° north of east can be broken down into its x and y components as follows:[tex]Vwx = 20.0 mph * cos(60.0°) = 10.0 mph Vwy = 20.0 mph * sin(60.0°)[/tex] = 17.3 mph The resultant velocity vector is the vector sum of the airspeed and the wind velocity: Vrx = Vx + Vwx = 200 mph + 10.0 mph = 210 mpm Vry = Vy + Vwy = 0 mph + 17.3 mph = 17.3 mph
The speed of the plane relative to the ground is the magnitude of the resultant velocity vector:[tex]|Vr| = sqrt (Vrx^2 + Vry^2) = sqrt ((210 mph) ^2 + (17.3 mph) ^2) ≈ 211[/tex]mph The direction of the plane's velocity relative to the ground is given by the angle that the resultant velocity vector makes with due east:[tex]θ = atan(Vry / Vrx) = atan(17.3 mph / 210 mph) ≈[/tex] 4.7° north of east
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Complete question is :
A Plane Has An Airspeed Of 200 Mph. The Pilot Wishes To Reach Adestination 600 Mi Due East, But A Wind Is Blowing At 50 Mph In Thedirection 30o North Of Eastpart Ain What Direction Must The Pilot Head The Plane In Order To Reachher Destination? (2sig Figs)Part Bhow Long Will The Trip Take?(2 Sig Figs)Thanks!
a plane has an airspeed of 200 mph. the pilot wishes to reach adestination 600 mi due east, but a wind is blowing at 50 mph in thedirection 30o north of east
part A
in what direction must the pilot head the plane in order to reachher destination?
part B
how long will the trip take?
g when a rocket is 7 kilometers high, it is moving vertically upward at a speed of 300 kilometers per hour. at that instant, how fast is the angle of elevation of the rocket increasing, as seen by an observer on the ground 5 kilometers from the launching pad? ( hint: the angle of elevation is the angle between the horizontal ground and the line of sight with respect to the rocket. ) when the rocket is 7 kilometers high, the angle of elevation from the observer is changing at a rate of radians per hour.
Similarly, differentiating sin θ with respect to time, we get:d(sin θ)/dt = cos θ dθ/dtOn simplification, we get:dθ/dt = -300 cos θ / (7 sin² θ)When the rocket is 7 kilometers high, the angle of elevation from the observer is changing at a rate of 0.059 radians per hour. Answer: 0.059.The angle of elevation of the rocket from the observer on the ground 5 kilometers from the launching pad when the rocket is 7 kilometers high is changing at a rate of 2π radians per hour. This can be calculated using the law of sines, where the angle of elevation (α) is the opposite angle of the triangle made between the observer, the rocket, and the ground. In this case, the two sides are 7 km for the rocket's height, and 5 km for the distance from the observer to the launchpad. Therefore, the angle of elevation (α) = arcsin(5/7) = 2π radians per hour.
Given, the height of the rocket is 7 kilometers, the speed of the rocket is 300 kilometers per hour, and the observer is 5 kilometers from the launching pad. We need to find the rate of change of the angle of elevation of the rocket at that instant.The angle of elevation is the angle between the horizontal ground and the line of sight with respect to the rocket. Let's consider the triangle formed by the observer, the rocket and the launching pad, as shown in the figure below:We have, AB = 7 km and BC = 5 km. The angle of elevation, θ = ABD.To find the rate of change of the angle of elevation of the rocket, we need to differentiate the angle of elevation with respect to time.Let's first find the value of sin θ using the right-angled triangle ABD:Sin θ = AB/AD => AD = AB/sin θAD = 7/sin θDifferentiating with respect to time, we get:d(AD)/dt = d(7/sin θ)/dtUsing the quotient rule of differentiation, we get:d(AD)/dt = -7 cos θ dθ/dt / sin² θSimilarly, differentiating sin θ with respect to time, we get:d(sin θ)/dt = cos θ dθ/dtOn simplification, we get:dθ/dt = -300 cos θ / (7 sin² θ)When the rocket is 7 kilometers high, the angle of elevation from the observer is changing at a rate of 0.059 radians per hour. Answer: 0.059.
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The countercurrent mechanism functions primarily in the A. renal corpuscle. B. proximal convoluted tubule. C. distal convoluted tubule D. nephron loop.
The nephron loop is where the countercurrent mechanism predominantly operates. The Henle loop is the name of the nephron component.
Reabsorbing water and sodium chloride from the filtrate is its principal purpose. By creating urine that is extremely concentrated, this helps the body preserve water. Kidney cross slice showing the nephron (kidney tubule) in detail and its associated blood supply.
Renal tubular fluid is defined as fluid present within the lumen of a nephron loop. Glomerular filtrate is the term used to describe the fluid found inside Bowman's capsule. Urine would be regarded as the fluid contained in the collecting duct.
The fact that loop diuretics work on the Loop of Henle gives them their name. They function by blocking NKCC2 transporters in the thick ascending limb, preventing the reabsorption of sodium, potassium, and chloride.
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A body in a room at 300 k is heated to 3,000k. The amount of energy radiated each second by the body increases by a factor of:
a) 10
b) 100
c) 1,000
d) 10,000
e) 100,000
The amount of energy radiated each second by the body increases by a factor of 10000 (option D)
How do i determine the factor of increase of the energy per second?To determine the factor in which the amount of energy radiated per second increases, we shall determine the energy per second at 3000 K. Details below:
Initial temperature (T₁) = 300 KInitial energy per second (P₁) = PFinal temperature (T₂) = 3000 KFinal energy per second (P₂) = ?P₁ / T₁⁴ = P₂ / T₂⁴
P / 300⁴ = P₂ / 3000⁴
Cross multiply
300⁴ × P₂ = P × 3000⁴
Divide both sides by 300⁴
P₂ = (P × 3000⁴) / 300⁴
P₂ = P × 10000
From the above calculation, we can see that the energy per second at 3000 K, is 10000 times the energy per second at 300 K.
Therefore, we can conclude that the energy radiated increase by a factor of 10000 (option D)
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Which method will NOT reduce reactivity of observation?a) observe through a one-way observation window b) tell the person you are observing his/her behaviorc) wait until the person you are observing is accustomed to your presenced) use participant observers
One of the methods which will not reduce reactivity of observation is telling the person you are observing his/her behaviour. Correct option is B.
A practical, utilitarian approach, behavioral observation focuses on the plainly discernible ways in which the client engages with his or her surroundings. Behavioural observation can be used as a standalone technique or casually as a component of an interview, a test, or both.
Waiting until the subjects of the observation are used to the observer is one method to reduce reactivity. Another option is to have the observer document the actions without the subjects being aware of the observation.
The act of observation modifies in some manner the situation in which a participant is being observed. Within an experimental setting, reactivity is viewed as a threat to internal validity because the change in behaviour is not due to the experimental manipulation. Best choice is B.
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Two planets A and B, where B has twice the mass of A, orbit the Sun in circular orbits. The radius of the circular orbit of planet B is two times the radius of the circular orbit of planet A. What Is the ratio of the orbital period of planet B to that of planet A? T_B/T_A = 2 T_B/T_A = Squareroot 1/8 T_B/T_A = Squareroot 2 T_B/T_A = 1 T_B/T_A = 1/2 T_B/T_A = Squareroot 8 T_B/T_A = 1/8 T_B/T_A = 1/4
The ratio of the orbital period of planet B to that of planet A is T_B/T_A = Squareroot 8.
What are planets?A planet is an astronomical object that orbits a star and does not produce its own light. The vast majority of the thousands of objects we call planets orbit a star in our Solar System. This specific system includes the sun and the eight planets that orbit around it.
Two planets A and B, where B has twice the mass of A, orbit the Sun in circular orbits. The radius of the circular orbit of planet B is two times the radius of the circular orbit of planet A. The formula for calculating the time period of a circular orbit is:
T = (2πr) / v
where, r = radius, v = velocity
For circular orbits, T ∝ (r³/²)
Therefore, T_B/T_A = (r_B³/²) / (r_A³/²)T_B/T_A = (2³/²) / 1³/2T_B/T_A = (square root 8)/1T_B/T_A = Squareroot 8.
Therefore, the ratio of the orbital period of planet B to that of planet A is T_B/T_A = Squareroot 8.
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a block slides up an incline. as it's moving up the incline, what is happening to the kinetic energy k and the gravitational potential energy ug? a. k is increasing; ug is decreasing. b. k is decreasing; ug is increasing. c. k and ug are both decreasing. d. k and ug are both increasing.
The kinetic energy k and the gravitational potential energy ug of a block sliding up an incline are both decreasing during the motion up the incline. Option C is correct .
Energy is the capability to do work. There are two forms of energy: potential energy and kinetic energy.
Potential energy is stored energy as a result of an object's location or condition, whereas kinetic energy is the energy of motion.
The total energy of an object can be calculated as the sum of its potential and kinetic energies.
Since the block is moving up the incline, it is subjected to gravity. As a result, it must have both kinetic and potential energy.
Kinetic energy is associated with the motion of an object, while potential energy is associated with its position.
At the base of the slope, the block has a specific quantity of kinetic energy due to its motion.
It also has a specific amount of gravitational potential energy at the base of the slope since it is a certain distance above the Earth's surface.
As the block climbs the incline, it slows down due to the effect of gravity. This implies that its kinetic energy is decreasing.
At the same time, it is gaining height, which implies that its gravitational potential energy is decreasing as well. As a result, k and ug are both decreasing.
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Which type of energy is stored in an elastic material stretched by a force
Potential energy is stored in the elastic material when we stretch it by some distance.
The energy stored when a force is used to deform an elastic object is called elastic potential energy. The energy is conserved until the force is released and the object returns to its original shape, doing work in the process. Objects can be compressed, stretched, or twisted when deformed.
Elastic material produces elasticity when stretched or compressed. The more the material is crushed or stretched, the greater this force.
Springs have many applications, including bed springs.
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Does high air pressure mean high humidity?
Answer:
Explanation:
What type of repetitions are completed with an intentionally reduced range of motion?
When you shine a laser with unknown wavelength through a diffraction grating with 1000 slits/mm, you observe the m=1bright fringe on the screen with an angle of 26 degrees away from the center of the grating. What is the wavelength of your laser?
The wavelength of the laser is 0.4464 mm.
The equation for the diffraction grating is given as:
dsinθ = mλ
where d is the distance between the slits (in meters), θ is the angle between the central maximum and the mth bright fringe (in radians), m is the order of the bright fringe, and λ is the wavelength of the light (in meters).
The equation to calculate the wavelength of a laser is λ = d × sin θ/m, where d is the distance between two adjacent slits on the diffraction grating (in this case, 1000 slits/mm, which is equivalent to 1 mm), θ is the angle of the fringe relative to the central axis (in this case, 26 degrees), and m is the order of the fringe (in this case, m=1). Therefore, plugging in the values:
λ = 1 mm × sin 26°/1 = 0.4464 mm
The wavelength of the laser is 0.4464 mm.
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2526-kg elevator moves with a downward acceleration of 2.00 m/s2. what is the tension in the cable that supports the elevator? assume the elevator is supported by a single cable. forces exerted by the guide rails and air resistance is negligible
The tension in the cable that supports the elevator (2526-kg moves with a downward acceleration of 2.00 m/s²2) is 25,171 N.
To determine the tension in the cable, use the equation:
T = ma + Fg
Mass of the elevator, m = 2526 kg
Downward acceleration of the elevator, a = 2.00 m/s²
Force due to gravity, Fg = mg
= 2526 kg × 9.8 m/s²
= 24794.8 N (upwards)
The tension in the cable that supports the elevator is T.
Using Newton's second law of motion,
F = ma
Net force acting on the elevator,
F = T - Fg
= T - 24794.8 N
Therefore, T - 24794.8 N = ma
T = ma + Fg
= (2526 kg × 2.00 m/s²) + 24794.8 N
= 25,171 N
Therefore, the tension in the cable that supports the elevator is 25,171 N.
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a student pulls a 1500 kg suitcase along a flat sidewalk. if the cord on the suitcase breaks when the force is greater than 50n, what is the maximum acceleration that the student can achieve with the suitcase?
The maximum acceleration that the student can achieve with the 1500 kg suitcase is 50N/1500kg = 0.033 m/s2.
Acceleration is the change in velocity per unit time. Acceleration is a vector quantity that has both magnitude and direction. Acceleration is divided into deceleration acceleration and acceleration acceleration. Acceleration decreases meaning the direction of acceleration is opposite to the direction of velocity.
To calculate the maximum acceleration, we can use the following equation:
Force = Mass x Acceleration. Therefore, 50N = 1500kg x Acceleration
Solving for Acceleration, we get 50N/1500kg = 0.033 m/s2.
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A 14cm diameter champagne bottle rests on its side on top of a frictionless table. Suddenly, the cork pops and the bottle slides backward for a distance of 22.0 cm in 0.44s. If the mass of the bottle is 500 times the mass of the cork, find the distance from the original position the cork will land on the table.
The distance the cork will land on the table is [tex]d = 30 m[/tex]. If the mass of the bottle is 500 times the mass of the cork.
First, we need the initial velocity of the bottle is:
Using [tex]d = vt[/tex]
[tex](0.22) = (v)*(0.44)\\v = 0.5\ m/s[/tex]
Then, using the conservation of momentum, we can find the velocity of the cork
[tex]mv (bottle) = mv (cork)\\(500)*(0.1) = m(v)\\v = 250\ m/s[/tex]
Now, where the cork lands. It starts at a vertical height of 7 cm (the radius of the bottle and will hit the table somewhere, that is what we need to find. Where it bounces first)
Since the cork has no initial y velocity, we can find the time it would take for it to drop 7 cm.
[tex]d = v_{o}t + 0.5at^{2}\\0.07 = (0) + (0.5)*(9.8)*(t_2)\\t = 0.120 sec[/tex]
Then, using d = vt, we can find the horizontal distance it flies in that amount of time is:
[tex]d = (250)*(0.12)\\d = 30 m[/tex]
Therefore, the distance the cork will land on the table is [tex]d = 30 m[/tex].
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2. The hummingbird makes a humming sound with its wings, which beat with a frequency of 90.0 Hz. Suppose a mass is attached to a spring with a spring constant of 2.50 x 10² N/m. How large is the mass if its oscilla- tion frequency is 3.00 x 10 times that of a hummingbird's wings?
A mass on a spring will oscillate with such a period if it is coupled to a spring of spring constant k. (T). T = 2(m/k) describes this. The frequency of the oscillation would be = k/M.
What is the formula for calculating mass?By summing the masses of the each individual atom inside the compound's formula, the formula mass is determined. The ions can be regarded as atoms for the purposes of determining the formula mass since a valid formula was neutral (when no net electron gained or lost).
How can you determine the mass's frequency?Imagine a spring with an unstretched length l, a spring constant of k, and a mass M dangling from it. The resonant frequency would be k/M if the spring's mass were ignored. According to the rule that was cited, the impact of the spring masses would be to change M in the equation for to M + m/3.
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Leonardo da Vinci (1452-1519) is credited with being the first to perform quantitative experiments on friction, though his results weren't known until centuries later, due in part to the secret code (mirror writing) he used in his notebooks. Leonardo would place a block of wood on an inclined plane and measure the angle at which the block begins to slide. He reports that the coefficient of static friction was 0. 22 his experiments.
At what angle did Leonardo’s blocks begin to slide?
The angle of repose or the angle of friction is the angle at which the block starts to slide down the inclined plane. By balancing the forces operating on the block along the inclination, it may be calculated.
The gravitational force (mg) acting downhill and the normal force (N) acting perpendicular to the inclination are the forces acting on the block. The gravitational force component perpendicular to the inclination, which is calculated as mg cos, where is the angle of the incline, and the normal force are identical in magnitude.
The block can have a maximum static friction force (Ff) applied to it without it sliding down the incline if:
Ff = μs N
where s is the static friction coefficient.
The amount of the frictional force is equal to the component of the gravitational force parallel to the inclination, which is mg sin, at the instant the block just starts to slide.
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astronauts need to endure an acceleration 7 times of erath's gravitational acceleration. if one would want to train for this by using a rotational device witha. raidus of 12 m what period must be obtained
The period that must be obtained is approximately 1.76 seconds.
To determine the period that must be obtained for the training, we can use the formula for centripetal acceleration:
a = v²/r
where v is the tangential velocity and r is the radius.
The formula for the velocity of a rotating object is:
v = 2πr/T
where v is tangential velocity, π is the constant pi, and T is the rotation period.
Substituting v into the centripetal acceleration equation yields:
a = (2πr/T)²/r
The equation simplifies to
a = 4π²r/T²
The centripetal acceleration required by an astronaut is seven times greater than the gravitational acceleration on Earth. Setting these equal and solving for T gives:
T = √(4π²r/7a)
T = √(4π²(12 m)/(7*9.81 m/s²))
T ≈ 1.76 seconds
Therefore, an astronaut training for an acceleration of seven times that of the Earth's gravitational acceleration using a rotational device with a radius of 12 m must rotate for a period of 1.76 seconds.
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The speed of propagation of a sound wave in air at 27 degrees (Celsius) is about 350 m/s. Calculate, for comparison, v(rms) for nitrogen molecules at this temperature. The molar mass of nitrogen is 28.0 g/mol.
At 27 degrees Celsius, the rms speed of nitrogen molecules is roughly 515 m/s, which is faster than the sound speed in air.
How come we figure out rms velocity?The square root of the average of the square of the velocity is the root mean square velocity. It has velocity units as a result. As the particles in a typical gas sample are flowing in all directions, the average velocity for that sample is zero, which is why we use the rms velocity instead of the average.
The following formula determines a gas molecule's root mean square (rms) speed: v(rms) = √(3kT/m)
where T is the temperature in Kelvin, m is the molar mass of the gas in kg/mol, and k is Boltzmann's constant (1.38 10-23 J/K).
We must change the molar mass from g/mol to kg/mol in order to determine the rms speed of nitrogen molecules at 27 °C (300 °F):
m = 28.0 g/mol / 1000 g/kg = 0.028 kg/mol
Now we can plug in the values and solve for v(rms):
v(rms) = √(3kT/m)
v(rms) = √(3 × 1.38 × 10^-23 J/K × 300 K / 0.028 kg/mol)
v(rms) = 515 m/s (rounded to three significant figures)
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the largest optical telescopes in the world are reflecting telescopes, because it is difficult to make a refractor (lens) telescope larger than about 1 m in diameter. it is difficult because . (select all that apply.)
It is difficult to make a refractor (lens) telescope larger than about 1 m in diameter because the larger the lens, the more light it has to bend and the more glass must be used; the glass must be supported in a very precise way to ensure a good image; and manufacturing and assembly errors become more common with increasing size.
There is a limit to the maximum size of a glass lens, and as the size of the lens increases, so does its weight. If the weight is too great, the lens will deform under its own weight, causing distortion in the image.Conversely, the mirrors used in reflecting telescopes are supported from behind, allowing them to be much larger and still maintain their shape.
The Hubble Space Telescope is an example of a reflecting telescope, and it has a mirror diameter of 2.4 meters.In addition to the size limitation, there are other issues with lenses, such as chromatic aberration, which occurs when the different colors of light refract at slightly different angles, causing distortion in the image. Mirrors do not suffer from this issue. The correct answer is that it is difficult to make a refractor (lens) telescope larger than about 1 m in diameter because the glass lens has a limit to its maximum size and weight, which can cause deformation in the image.
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To go from a lower level in an atom to a higher level, an electron must give off a photon of energy lose its electric charge absorb a photon of energy wait until the atom has changed into another atom with more protons get a permission slip from Niels Bohr
An electron must absorb a photon of energy in order to go up an atom's levels. The electron gains energy as a result and jumps to a higher energy level.
An electron in an atom must absorb a photon of energy equal to the energy difference between the two levels in order to go from one level of energy to another. Excitation is the term for this action. The electron is elevated to a higher energy level after absorbing the photon. The electron will swiftly revert to its initial energy level, producing a photon with an energy equal to the difference between the two levels, as this is an unstable condition. A photon is released as a result of this procedure, which is also known as de-excitation or relaxation. Instruments that can detect this photon can be used to examine the energy levels of atoms.
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At temperatures of a few hundred kelvins the specific heat capacity of copper approximately follows the empirical formula c=α+βT+δT−2c=α+βT+δT−2, where α=349J/kg⋅K,β=0.107J/kg⋅K2α=349J/kg⋅K,β=0.107J/kg⋅K2, and δ=4.58×105J⋅kg⋅Kδ=4.58×105J⋅kg⋅K. How much heat is needed to raise the temperature of a 2.00-kg piece of copper from 20∘C to 250∘C20∘C to 250∘C?
The amount of heat required to raise a 2.0 kg piece of copper from [tex]20^\circ C[/tex] to [tex]250^\circ C[/tex] using the formula [tex]c = \alpha + \beta T + \delta T^{-2}[/tex] is [tex]1.96 \times 10^{8} J[/tex].
The formula for computing the amount of heat that is required to raise the temperature of an object is expressed as:
Q = mc∆T
Where:
Q: the amount of heat needed in joules
m: the mass of the substance in kilograms
c: the specific heat capacity of the substance in joules per kilogram per kelvin
∆T: the change in temperature in kelvin
We can use the equation to calculate the amount of heat needed to raise the temperature of a 2.00-kg piece of copper from 20∘C to 250∘C. However, it's important to note that we need to first convert the given temperatures from Celsius to Kelvin.
[tex]20^\circ C + 273 = 293 K[/tex] (Initial temperature)
[tex]250^\circ C + 273 = 523 \ K[/tex] (Final temperature)
We can now substitute the values into the formula, Q = mc∆T to get the amount of heat required.
[tex]Q = mc\Delta T[/tex]
[tex]Q = (2.00 \ kg) (\alpha + \beta T + \delta T^{-2}) (\Delta T)[/tex]
[tex]Q = 2.00 kg (\alpha\Delta T + \beta \Delta T^2 + \delta \Delta T^3)[/tex]
[tex]Q = 2.00 kg [(\alpha(523 \ K - 293 \ K) + \beta (523 K^2 - 293\ K^2) + \delta(523 \ K^3 - 293 \ K^3)][/tex]
[tex]Q=2.00 kg [(349 J/kgK \times 230\ K) + (0.107 J/kgK^2 \times 230 K^2) + (4.58 \times 10^5 JkgK \times 230 K^3)][/tex]
[tex]Q = 2.00\ kg [80270\ J + 24.61\ J + 9.8 \times 10^{7} \ J][/tex]
[tex]Q = 1.96 \times 10^{8} J[/tex]
Therefore, the amount of heat that is required to raise a 2.00-kg piece of copper from [tex]20^\circ C[/tex] to 250° C is [tex]1.96 \times 10^{8} J[/tex].
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Complete the following sentence.
A diameter is also a...
Answer:
A diameter is also a double of radius
When Joselyn went to the store she bought 2.7kg of salt water taffy. What would Joselyn do to find out how many grams she bought?A. Divide by 1000B. Multiply by 1000C. Divide by 100D. Multiply by 100
At the shop, Joselyn purchased 2700 grammes of salt water taffy.
To convert kilograms (kg) to grams (g), Joselyn would need to multiply the weight in kilograms by 1000. This is because there are 1000 grams in 1 kilogram. Therefore, to find out how many grams of salt water taffy Joselyn bought, she would need to multiply 2.7kg by 1000.
The correct answer is (B) Multiply by 1000.
Multiplying 2.7kg by 1000 gives:
2.7kg x 1000 = 2700g
So Joselyn bought 2700 grams of salt water taffy at the store.
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which type of electromagnetic radiation has more energy than visible light and can pass through the human body?
X-rays have more energy than visible light and can pass through the human body.
X-rays are a type of electromagnetic radiation that has a shorter wavelength and higher frequency than visible light. Due to their high energy, X-rays can penetrate solid objects, including the human body. This property makes X-rays useful in medical imaging, such as X-ray radiography, computed tomography (CT) scans, and mammography.
When X-rays pass through the human body, they can be absorbed by the tissues or pass through, depending on the density of the material. Bones, for example, absorb more X-rays than soft tissues like muscle or fat, which is why they appear white in X-ray images.
While X-rays can be helpful in diagnosing medical conditions, they can also be harmful if exposure is not limited or controlled. Prolonged exposure to X-rays can damage DNA and potentially lead to cancer or other health problems.
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A woman on a bicycle traveling at 10 m/s on a horizontal road stops pedaling as she starts up a hill inclined at 4. 0º to the horizontal. If friction forces are ignored, how far along the hill does she travel before stopping?
The hill does she travel before stopping is 97.5 m far along.
Apply law of conservation of energy.
Initial energy = Final energy
[tex]1/2 mv^2 = mgh[/tex]
Here, m is the mass, u is the velocity, 9 is the gravitational acceleration, and his the height upto which woman will incline on the hill.
Rearrange the above equation for h.
[tex]h=v^2/ 2g[/tex]
[tex]h = (10m/s)^2 / 2(9.8m/s2)\\h = 5.102m[/tex]
This is the vertical height from the ground. Now, calculate the slant height of this point.
l = h / sin3°
l = 5.102m / sin3°
= 97.5m
The law of conservation of energy means that the total amount of energy in a closed system remains constant over time, regardless of the transformations or transfers that occur within the system. This law is based on the principle of the first law of thermodynamics, which states that the total energy of a system and its surroundings is always conserved.
It has been experimentally verified in a wide range of physical phenomena, including chemical reactions, nuclear reactions, and mechanical processes. The law of conservation of energy has profound implications for our understanding of the physical world. It implies that energy is a fundamental quantity that is conserved in all physical processes, and it forms the basis of many important theories in physics and engineering.
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measurements on an experimental thermal reactor show that, forevery 100 neutrons emitted in fission, 10 escape while slowing downand 15 escape after having slowed down to thermal energies. neutrons are absorbed within the reactor while slowing down. of those neutrons absorbed at thermal energies, 60% are absorbed infission material What is the multiplication factor of the reactor at the time these observations are made? Suppose the thermal leakage is reduced by one third. How would this change the value of k?
The multiplication factor, k of the reactor at the time of the observations is 0.87. If the thermal leakage is reduced by one-third, the value of k would increase to 1.87.
To calculate the multiplication factor, we can use the following equation:
k = (1-nf - nt)/nt,
where nf is the fraction of neutrons emitted in fission that escape while slowing down, nt is the fraction of neutrons that escape after having slowed down to thermal energies, and nt is the fraction of neutrons absorbed in the reactor while slowing down.
Given that nf = 0.1, nt = 0.15, and nt = 0.6, we can calculate the multiplication factor, k, as follows:
k = (1 - 0.1 - 0.15)/0.6
k = 0.87
Therefore, the multiplication factor of the reactor at the time these observations are made is 0.87. If the thermal leakage is reduced by one-third, the value of k would increase to 1.87.
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a chemist determines by measurements that 0.035 moles of nitrogen gas participate in a chemical reaction. calculate the mass of nitrogen gas that participates. be sure your answer has the correct number of significant digits.
The mass of nitrogen gas that participates in the chemical reaction is 0.980 grams.
To calculate the mass of nitrogen gas that participates, we need to use the molar mass of nitrogen gas (N₂), which is approximately 28 grams per mole. We can use the following equation to relate moles and mass:
mass = moles x molar mass
So, the mass of nitrogen gas that participates is:
mass = 0.035 moles x 28 g/mol = 0.98 g
We need to round our answer to the correct number of significant digits, which is determined by the least precise measurement in the problem. Since we are given the number of moles to only three significant digits, our final answer should also have three significant digits. Therefore, the mass of nitrogen gas that participates is:
mass = 0.980 g (rounded to three significant digits)
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Terri Vogel, an amateur motorcycle racer, averages 129.77 seconds per 2.5 mile lap (in a 7 lap race) with a standard deviation of 2.26 seconds. The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps. (Source: log book of Terri Vogel) Let X be the number of seconds for a randomly selected lap. Round all answers to 4 decimal places where possible. a. What is the distribution of X?X−N(___________, _________). b. Find the proportion of her laps that are completed between 131.69 and 134.04 seconds________
.c. The fastest 4% of laps are under__________seconds.
d. The middle 70% of her laps are from seconds________ to_________ seconds.
a) The distribution of X: X-N(129.77,2.26),
b) the proportion of her laps that are completed between 131.69 and 134.04 seconds 0.1670,
c) the fastest 4% of laps are under 126.1965 seconds,
d) the middle 70% of her laps are from seconds 127.5323 to 131.0277 seconds.
a. The distribution of X is the normal distribution with a mean of 129.77 seconds and a standard deviation of 2.26 seconds. Therefore, the distribution of X is X - N(129.77, 2.26).
b. The area between 131.69 and 134.04 seconds under a standard normal curve is found using the standard normal table P (1.05) = 0.8531P (1.71) = 0.9564
Therefore, the proportion of laps completed between 131.69 and 134.04 seconds is
P(131.69 ≤ X ≤ 134.04) = P[(131.69 - 129.77)/2.26 ≤ Z ≤ (134.04 - 129.77)/2.26]
= P(0.8496 ≤ Z ≤ 1.8814) = P(Z ≤ 1.8814) - P(Z ≤ 0.8496)
= 0.9693 - 0.8023
= 0.1670
Therefore, the proportion of laps that are completed between 131.69 and 134.04 seconds is 0.1670.
c. The value corresponding to the lowest 4% is found: P (z) = 0.04. The value of z corresponding to the lowest 4% is obtained as follows:
z = P−1(0.04) = -1.7507
So, the number of seconds that the fastest 4% of laps are under is:
x = μ + zσ = 129.77 - (1.7507)(2.26)
= 126.1965
Therefore, the fastest 4% of laps are under 126.1965 seconds.
d. We know that z corresponding to the lowest 15% is -1.036 and that z corresponding to the highest 15% is 1.036.
Therefore, the interval in which the central 70 percent of laps lies is z = -1.036, 1.036
z = P(X) - P(X) = P(z ≤ X) - P(z ≤ X) = P(z ≤ -1.036) - P(z ≤ 1.036)
= 0.1492 - 0.8513
= -0.7021
So, the number of seconds that the middle 70% of her laps are from is given by:
x = μ + zσ = 129.77 + (-0.7021)(2.26) = 127.5323 and
x = μ + zσ = 129.77 + (0.7021)(2.26) = 131.0277
Therefore, the middle 70% of her laps are from seconds 127.5323 to 131.0277 seconds.
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A set of beliefs can be said to be pseudoscientific if it lacks one or more of the three features of science and _____.
A set of beliefs can be said to be pseudoscientific if it lacks one or more of the three features of science and empirical evidence.
Pseudoscience is a set of claims, beliefs, or practices that are presented as scientific but lack empirical evidence, are inconsistent with scientific facts, or are based on incorrect assumptions. Pseudoscience can be seen in a variety of fields, including medicine, psychology, and the paranormal.
Science is defined by three characteristics: empiricism, theory construction, and parsimony or simplicity. Empiricism is the use of evidence to establish scientific facts, while theory construction is the development of a conceptual framework that explains and predicts these facts.
Parsimony is the principle that the simplest explanation is the best one, meaning that theories should not include unnecessary assumptions or complexity. However, pseudoscientific practices often lack one or more of these characteristics. They may fail to use empirical evidence or instead rely on anecdotal evidence or personal experience. Their theories may not be testable or may be inconsistent with established scientific facts. They may also be unnecessarily complex or based on assumptions that have no basis in reality.
Hence, a set of beliefs can be said to be pseudoscientific if it lacks one or more of the three features of science and empirical evidence.
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interpreting data if the input force is the same for each type of pulley in the graph, which pulley has the greatest output force? explain your answer.
If the input force is the same for each type of pulley in the graph, then the pulley with the greatest output force is the one with the highest slope or gradient. This is because the slope or gradient of the line represents the mechanical advantage of the pulley system.
What is a pulley system?A pulley system is a type of simple machine that is used to make lifting heavy objects easier. It consists of a wheel with a groove in which a rope or chain can run. When force is applied to one end of the rope, the other end moves in the opposite direction, causing the object to move as well.
There are three types of pulleys: fixed, movable, and compound.
Fixed pulleys have a fixed axle and do not move, while movable pulleys have a movable axle and move with the load. Compound pulleys are a combination of fixed and movable pulleys and can provide a greater mechanical advantage.The mechanical advantage of a pulley system is calculated by dividing the output force by the input force. A pulley system with a higher mechanical advantage will require less input force to lift a given load than a pulley system with a lower mechanical advantage. This is why pulleys are used in many different types of machines, including cranes, elevators, and escalators.
In conclusion, if the input force is the same for each type of pulley in the graph, then the pulley with the greatest output force is the one with the highest slope or gradient.
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Assume the motions and currents mentioned are along the x axis and fields are in the y direction.
(a) Does an electric field exert a force on a stationary charged object?
YesNo
(b) Does a magnetic field do so?
YesNo
(c) Does an electric field exert a force on a moving charged object?
YesNo
(d) Does a magnetic field do so?
YesNo
(e) Does an electric field exert a force on a straight current-carrying wire?
YesNo
(f) Does a magnetic field do so?
YesNo
(g) Does an electric field exert a force on a beam of moving electrons?
YesNo
(h) Does a magnetic field do so?
YesNo
(a) Yes, an electric field can exert a force on a stationary charged object. A stationary charged object will experience a force in the direction of the electric field due to the Coulombic interaction between the charges.
(b) No, a magnetic field does not exert a force on a stationary charged object. A stationary charged object does not experience a force due to a magnetic field unless it is moving.
(c) Yes, an electric field can exert a force on a moving charged object. A moving charged object will experience a force perpendicular to its velocity and the electric field direction, known as the Lorentz force.
(d) Yes, a magnetic field can exert a force on a moving charged object. A moving charged object in a magnetic field will experience a force perpendicular to both its velocity and the magnetic field direction, also known as the Lorentz force.
(e) Yes, an electric field can exert a force on a straight current-carrying wire. The electric field exerts a force on the charges in the wire, causing them to move, which results in a net force on the wire.
(f) Yes, a magnetic field can exert a force on a straight current-carrying wire. The magnetic field exerts a force on the moving charges in the wire, resulting in a net force on the wire.
(g) Yes, an electric field can exert a force on a beam of moving electrons. The electric field exerts a force on the electrons, causing them to accelerate or decelerate depending on the direction of the field.
(h) Yes, a magnetic field can exert a force on a beam of moving electrons. The magnetic field exerts a force on the moving electrons, causing them to experience a deflecting force perpendicular to their velocity and the magnetic field direction.
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A gymnast balancing on a beam will put her arms out. Why does this help?
By keeping their centre of gravity over the beam, a gymnast may balance himself. The gymnast increases their moment of inertia, or resistance to rotational motion, by spreading their arms out to the sides, making it harder to unintentionally tilt or spin. As a result, their body is more stable, aiding in balance maintenance. Moreover, the centre of mass can be slightly adjusted with the arm movements to make up for any minor deviations from the equilibrium position. The gymnast can also orient oneself in relation to the beam using the visual clues provided by the arms. Overall, while balancing on a beam, a gymnast can gain various advantages from extending their arms to the side, including increased stability and many more.