2.3 grams of wood has the same energy as 1g of oil.
The majority of wood and wood waste used as fuel in the United States is used by industry. Manufacturers of paper and wood products are the biggest industrial users. They produce steam and electricity from waste from paper and lumber mills, which saves money by lowering the number of other fuels and electricity they need to buy to run their facilities.
There are numerous power plants that primarily burn wood to produce electricity in the electric power sector, and some coal-burning power plants burn wood chips along with coal to cut down on sulfur dioxide emissions. The primary purpose of wood consumption in the business sector is heating.
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Escriba la cantidad que representan los siguientes expresiones, dada en
notación cientifica.
a) 7.1 x 10
6) 2.3 x 103
C) 1.56 10
d) 4. 19. 4. 104
Answer:
Comencemos con la primera:
si tenemos algo como:
7.1*10^n
Simplemente lo que tenemos que hacer es:
si n es positivo, movemos n veces el punto para la derecha, si no tenemos dígitos, completamos con ceros.
si n es negativo, movemos n veces el punto a la izquierda.
a) 7.1*10
aca tenemos n = 1
entonces movemos una vez el punto a la derecha:
7.1*10 = 71. = 71
b) 2.3*10^3
aca n = 3, entonces movemos el punto 3 veces a la derecha:
2.3*10^3 = 23__.
Tenemos dos huecos ahí, los cuales serán completados con ceros, entonces:
2.3*10^3 = 2,300. = 2,300
c) 1.56*10
n = 1, entonces movemos el punto una vez a la derecha:
1.56*10 = 15.6
d) 4.10^4
acá tenemos n = 4
entonces movemos el punto 4 veces a la derecha, recordar que debemos completar con ceros:
4.10^4 = 40,000. = 40,000
what is the heat from the sun reaches earth through which type of heat transfer?
Answer:
Radiation
Explanation:
Radiation is the transfer of heat energy through space by electromagnetic radiation. Most of the electromagnetic radiation that comes to the earth from the sun is invisible.
A 26 kg crate initially at rest on a horizontal floor requires a 70 N horizontal force to set it in motion. Find the coefficient of static friction between the crate and the floor.
The coefficient of static friction between the crate and the floor is calculated to be 0.275.
The frictional force when an object moves on the horizontal surface is given as,
Ff = μ N
where, N is the normal force
μ is the coefficient of static or kinematic friction
If no forces other then the weight and the normal are acting upon the y-direction, then the weight and the normal force are equal in magnitude.
N = W = m g
Given that,
Mass of the crate = 26 kg
Frictional force Ff = 70 N
Weight of the crate = 26 × 9.8 = 254.8 N
The normal force is 254.8 N.
The coefficient of static friction μ = Ff /N = 70/254.8 = 0.275
Thus, the coefficient of static friction between the crate and the floor is 0.275.
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the control voltage in an air-conditioning system comes directly from
The control voltage in an air-conditioning system typically comes directly from the system's thermostat or control panel.
The thermostat senses the room's temperature and, based on the desired temperature setting, sends a control voltage signal to the various components, such as the compressor, condenser, and evaporator, to regulate their operation. This voltage is usually lower (24 volts) compared to the main power supply voltage (120/240 volts) and is used to control the contactors or relays, which in turn switch the high-voltage components on or off. The control voltage enables precise temperature control, energy efficiency, and safe operation of the air-conditioning system, ensuring a comfortable indoor environment.
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Can nuclei of the same element have different values of Z? Of N? Of A?
Check all that apply.
O 1 Nuclei of the same element must have the same values of Z, N, and A.
O 2 Nuclei of the same element can have different values of Z.3
O 3 Nuclei of the same element can have different values of A.
O 4 Nuclei of the same element can have different values of N.
Nuclei of the same element can have different values of Z, N, and A, as these values are all related to the number of protons, neutrons, and nucleons in the nucleus, respectively. Therefore, option 2, 3, and 4 are correct.
Nuclei of the same element can have different values of Z, N, and A due to the number of protons, neutrons, and nucleons they contain, respectively. This is because the number of these particles in the nucleus can vary, although they all will still be the same element. Therefore, option 2, 3, and 4 are correct and option 1 is incorrect.
Nuclei of the same element can have different values of Z, N, and A, as these values are all related to the number of protons, neutrons, and nucleons in the nucleus, respectively. Therefore, option 2, 3, and 4 are correct.
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Please
help
me
with this problem
Answer:
speeding up
Explanation:
because its speeding up, theres going to be more newtons in the back
i really hope this is right, tell me if so
Calculate the volume of material removed from the following information. 25) Calculate the volume of material removed from the following information. In laying out a 100ft. X 100ft. square a contractor has to remove 0.2" of material from the formed square. How much material needs to be excavated from this foundation based on dimensions given?
The volume of material that needs to be excavated from the foundation is approximately 166.67 ft³.
Volume calculationTo calculate the volume of material that needs to be excavated from the foundation based on the given dimensions, we need to find the volume of the rectangular prism formed by the dimensions of the foundation and subtract the volume of the adjusted square.
Given:
Length of the foundation = 100 ftWidth of the foundation = 100 ftDepth of material to be removed = 0.2 inches = 0.2/12 ftCalculating the volume of the rectangular prism:
Volume = Length * Width * Depth
= 100 ft * 100 ft * (0.2/12) ft
= 166.67 ft³
Therefore, the volume of material that needs to be excavated from the foundation is approximately 166.67 ft³.
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A block of mass m = 3.7 kg slides from left to right across a frictionless surface withra speed v; - 7.4 m/s. It collides in a perfectly elastic collision with a second block of
mass M that is at rest. After the collision, the 3.7-kg block reverses direction, and its new speed is vf 2.2 m/s. What is M?
8.9 kg
6.8 kg
5.2 kg
7.5 kg
Answer:
5.2 kgExplanation:
#CARRY ON LEARNING #MARK BRAINLITSA satellite orbiting Earth at an orbital radius r has a velocity v. What would the velocity be if the satellite is moved to an orbital radius of 6r
Orbital velocity of satellite
\(v = \sqrt{ \frac{gm}{r} } \)
Radius of new orbit r' =6r
Thus new orbital velocity of satellite:
\(v = \sqrt{ \frac{gm}{6r} } = \frac{v}{ \sqrt{6} } \)
About Orbital speedFor satellites in circular orbits, the relationship between orbital velocity and altitude is strict. The task of a satellite launch rocket is to release the satellite at a suitable place in space, with the appropriate speed and direction of movement to put it in the desired orbit.
How a satellite stays in orbit can be thought of in two equivalent ways, both of which explain the relationship between the satellite's altitude and velocity.
The motion of the satellite can be seen as creating a centrifugal force that opposes the gravitational pull. For example, imagine attaching an object to a string and swinging it in a circle. The object is pulling outward against the string, and that outward force (centrifugal force) becomes greater the faster the object swings. At the right speed, the centrifugal force of the satellite due to motion around the earth just balances the gravitational pull, and the satellite remains in orbit.
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El tiempo de reacción de un conductor de automóvil es 0,75s. Si el automóvil puede experimentar una desaceleracion de 4m/s^2. Calcular la distancia recorrida hasta detenerse una vez recibida la señal, cuando su velocidad era 10m/s
Answer:
x_total = 20m
Explanation:
This is an exercise in kinematics, we will look for the distance it travels during the reaction time, where there is no braking, and then the distance during the deceleration.
Distance traveled during response time
v = x₁ / t
x₁ = v t
let's calculate
x₁ = 10 0.75
x₁ = 7.5 m
Now we calculate the distance during braking, the final speed is zero (v = 0)
v² = v₀² - 2 a x₂
x₂ = v₀² / 2 a
let's calculate
x₂ = 10² / (2 4)
x₂ = 12.5m
the total stopping distance is
x_total = x₁ + x₂
X_total = 7.5 + 12.5
x_total = 20m
a tiger moving with constant accleration covers the distance between two points 70 meter apart in 7 seconds . its speed as it pass the second point 15 meter per second . 1) what is the speed at the first point. 2) what us its accleration
Answer:
a = 1.428 [m/s²]
v₀ = 5 [m/s]
Explanation:
To solve this problem we must use the following equation of kinematics.
\(x=x_{o}+v_{o}*t+\frac{1}{2}*a*t^{2}\)
where:
x = final point [m]
x₀ = initial point [m]
v₀ = initial velocity [m/s]
a = acceleration [m/s²]
t = time [s]
But we need to use this additional equation.
\(v_{f}=v_{o}+a*t\)
where:
vf = final velocity = 15 [m/s]
Now we can use this equation, replacing it, in the first one. We must bear in mind that the difference among x - x₀ is equal to 70 [m]
\(x-x_{o}=v_{o}*t+\frac{1}{2}*a*t^{2} \\x-x_{o}=(v_{f}-a*t)*t+\frac{1}{2} *a*t^{2}\\70=(15-a*t)*t+\frac{1}{2}*a*t^{2}\\70=15*t-a*t^{2} +\frac{1}{2}*a*t^{2} \\70=15*t-\frac{1}{2}*a*t^{2}\\70=15*(7)-\frac{1}{2} *a*(7)^{2}\\105-70=0.5*a*49\\35=24.5*a\\a=1.428[m/s^{2} ]\)
Now replacing this value in the second equation, we can find the initial velocity.
\(15=v_{o}+1.428*7\\v_{o}=5[m/s]\)
An applied force of 75.0 N accelerates a 10.0 kg block at 3.5 m/s2 along a horizontal surface. a. How large is the frictional force? b. What is the coefficient of friction?
Answer:
a. 40.0 N
b. 0.41
Explanation:
By the second law of Newton, the net force is equal to the mass times the acceleration. In this case, the net force is the applied force less the frictional force, so
\(\begin{gathered} F_{\text{net}}=ma \\ F-F_f=ma \end{gathered}\)Where F is the applied force, Ff is the friction force, m is the mass and a is the acceleration.
Solving for Ff, we get
\(Ff=F-ma\)Now, we can replace the values
\(\begin{gathered} Ff=75.0N-(10.0\operatorname{kg})(3.5m/s^2) \\ F_f=75.0N-35.0N \\ F_f=40N \end{gathered}\)So, the frictional force is 40N
On the other hand, the force of friction is equal to the normal force times the coefficient of friction. Where the normal is equal to its weight, so
\(\begin{gathered} F_f=\mu F_n \\ F_f=\mu mg \end{gathered}\)Where μ is the coefficient of friction and g is the gravity and it is equal to 9.8 m/s². Solving for μ
\(\mu=\frac{F_f}{mg}\)Now, we can replace the values to get
\(\mu=\frac{40.0N}{10.0\operatorname{kg}(9.8m/s^2)}=0.41\)Therefore, the coefficient of friction is 0.41
Then, the answers are
a. 40.0 N
b. 0.41
Paco was driving his scooter west with an initial velocity of 4 m/s. He accelerates at 0.5 m/s2 for 30 seconds. What is his final velocity?
Answer:
19m/s
Explanation:
U= 4m/s
a = 0.5m/s²
t= 30s
V= U+at
= 4+15
=19m/s
Carbon dioxide in the blood is removed from the body through the A. kidneys B. lungs C. mouth D. skin
Answer:
C) MouthExplanation:
When we inhale air, it contains oxygen. The lungs take in oxygen and the heart and the other body parts use it.Carbon dioxide is removed from the blood mouth when we exhale.Because of hydrogen bonding which if the following characteristics are seen in water
Because of hydrogen bonding, water exhibits several unique characteristics.
Hydrogen bonding occurs between the hydrogen atom of one water molecule and the oxygen atom of another water molecule. This results in water molecules being held together by strong intermolecular forces, which leads to several unique properties of water. These include a high boiling point, high surface tension, and the ability to dissolve many substances. Additionally, hydrogen bonding also allows for water to have a higher density in its liquid state compared to its solid state, which is why ice floats on water. Overall, the presence of hydrogen bonding in water contributes to its importance as a universal solvent and a vital component of many biological processes.
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which statement illustrates how progress in engineering has affected the natural enironment
The statement that illustrates how progress in engineering has affected the natural environment is extracting mineral resources with modern mining equipment removes fertile topsoil.
What is the Natural Environment?The natural environment may be defined as anything that can be present in the surroundings of living entities whether it is a biotic or abiotic factor.
The utilization of contemporary mining tools terminates fertile topsoil and admiringly impacts the fertility of the soil. It is tough to rebuild topsoil and modern mining tools constantly damage soil fertility.
Advancement in engineering has influenced the natural environment and mining is one of the most accepted measures of this.
The complete question is as follows:
Extracting mineral resources with modern mining equipment removes fertile topsoil.Mining companies use modern equipment to extract mineral resources more efficiently.Modern mining equipment has improved the health and safety of workers.Modern mining practices provide materials that can be used for technological advances.Therefore, it is well described above.
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A car was driving at a speed of 10 m/s. In 3 seconds, it accelerated to a speed of 50 m/s. Calculate the car's acceleration.
30 m/s2
16.7 m/s2
13.3 m/s2
Answer:
\(\boxed {\boxed {\sf 13.3 \ m/s^2}}\)
Explanation:
Acceleration is the rate of change of velocity with respect to time. It is the change in velocity over the change in time, and it is calculated using the following formula.
\(a= \frac{ v_f-v_i}{t}\)
The car starts at a speed of 10 meters per second, then it accelerates to a speed of 50 meters per second. It achieves this acceleration in 3 seconds.
\(v_f\)= 50 m/s\(v_i\)= 10 m/s t= 3 sSubstitute the values into the formula.
\(a= \frac{50 \ m/s - 10 \ m/s}{3 \ s}\)
Solve the numerator.
50 m/s -10 m/s= 40 m/s\(a= \frac{40 \ m/s}{3 \ s}\)
Divide.
\(a= 13.3333333 \ m/s/s\)
\(a \approx 13.3 \ m/s^2\)
The car's acceleration is approximately 13.3 meters per second squared.
What should you do if you have a front tyre blowout? Your car will pull strongly in the direction of the side of the blowout if the front tyre goes flat. Don't hit the brakes hard or you could spin. Hold the steering wheel tightly and compensate for the pulling to one side.
In the event of a front tire blowout, hold the steering wheel tightly, compensate for the pulling, and avoid braking hard. Gradually release the accelerator, maintain control, and safely maneuver to the side of the road.
If you experience a front tire blowout while driving, it is crucial to remain calm and take appropriate actions to maintain control of your vehicle. Here's what you should do:
1. Stay calm and maintain control: It is essential to avoid panic and keep a firm grip on the steering wheel. Do not make sudden movements or overreact, as it may lead to losing control of the vehicle.
2. Do not brake forcefully: Abruptly hitting the brakes can cause the car to skid or spin out of control, especially with a front tire blowout. Instead, gradually release the accelerator pedal to slow down gradually.
3. Counteract the pulling: As the front tire goes flat, your vehicle will tend to pull strongly in the direction of the affected side.
To counteract this, apply gentle and steady pressure on the opposite side of the steering wheel. This will help you maintain a straight path and prevent veering into other lanes or obstacles.
4. Signal and move to a safe location: Once you have regained control, use your turn signals to indicate your intention to change lanes.
Slowly and safely maneuver your vehicle to the side of the road or a designated safe area away from traffic.
5. Assess the situation and seek assistance: After coming to a stop, evaluate the condition of the tire and call for roadside assistance or change the tire yourself if you have the necessary skills and equipment.
Remember, prevention is key, so regularly inspect and maintain your tires to minimize the risk of blowouts.
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Find the horizontal component and the vertical component
Answer:
v=3.66,h-3.66
Explanation:
vertical = 10sin60 - 10sin 30
horizontal =10cos60 + 10cos 30
v = 10×0.8660-10×0.5
h = 10×0.5 + 10 × 0.8660
v=8.660-5.0 = 3.66
h= 5.0-8.660 = -3.66
Determine the value of the information in scientific notation. The moon is approximately 3. 63 × 108 meters from Earth. What is 3. 63 × 108 in standard notation?.
Answer:
d
Explanation:
Answer:
363,000,000
Explanation:
Got it right on the assignment EDGE 2022.
what is the oxidation number of the noble gases such as xenon and argon?
How many joules of energy will a stock tank heater rated at 1500 watts use in a 24 hour period?
A stock tank heater rated at 1500 watts will use 1,29,600 kJ of energy in a 24 hour period.
Given :
Power = 1500 WTime = 24 hours = 24 x 3600 sec = 86,400 secWe know that
Energy = Power x time
E = P * t
E = 1500 x 24 x 3600
E = 129600000 J ( or 129600 kJ)
Hence, a stock tank heater rated at 1500 watts will use 1,29,600 kJ of energy in a 24 hour period.
The formula that links energy and power is:
Energy = Power x Time.
The unit of energy is the joule, the unit of power is the watt, and the unit of time is the second.
If we know the power in watts of an appliance and how many seconds it is used we can calculate the number of joules of electrical energy which have been converted to sortie other form.
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The question is in the photo.
Answer:
Mitochondria (animal) and Chloroplast (plant)
You are standing on the surface of a spherical asteroid 10 km in diameter, of density 3000 kg/m3.
Part A
Calculate the escape velocity from the asteroid in km/s.
Express your answer in kilometers per second using two significant figures.
Calculate the escape velocity from the asteroid in mph.
Express your answer in miles per hour using three significant figures
The correct answer for the (A) Escape velocity is \(570\) (B) Escape velocity is \(0.57\) in Km/h and (c). Escape velocity is \(1.27\) in mph.
Given:
Diameter of asteroid D = \(10\) km
Radius R = \(5\) Km
Density \(\rho\) = \(3000\) kg/m³
Unit conversion;
\(1\) m/s = \(0.001\) Km/s
\(1\) m/s = \(2.23694\) mph
(A)To calculate Escape velocity:
Use the formula;
\(v_e = \sqrt{\dfrac{2GM}{R} }\)
Gravitational Constant \(G\) = \(6.67430\)
To calculate Mass(\(M\)) of the asteroid, Calculate Volume(\(V\)) of the sphere and multiply it with density(\(\rho\)).
\(V= \dfrac{4}{3} \pi R^3 \\\\\rho = \dfrac{M}{V}\)
\(M = \rho*V\)
= \(523598775000\) Kg
Escape velocity:
\(v_e = \sqrt{\dfrac{2*6.67430 * 10^{-11} * 523598775000}{5000} }\)
\(= 570\) m/s
(B)Escape velocity in Km/s:
\(v_e = \dfrac{570}{1000}\)
\(= 0.57\) Km/s
(B)Escape velocity in mph:
\(v_e = 0.57 * 2.23694\)
\(= 1.27\) mph
Escape velocity is \(570\) m/s. In Km/h is \(0.57\) and In mph is \(1.27\) .
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Cross-training employees is only necessary in the genetic science industry.
O True
O False
Answer: False
Explanation:
Answer:
False
Explanation:
soap bubbles can display impressive colors, which are the result of the enhanced reflection of light of particular wavelengths from the bubbles' walls. for a soap solution with an index of refraction of 1.29, find the minimum wall thickness that will enhance the reflection of light of wavelength 729 nm in air.
Soap bubbles reflect certain wavelengths of light, find minimum wall thickness for enhanced reflection of 729 nm light.
When light passes through a material with a higher refractive index than air, such as soap solution, it can be reflected back with greater intensity.
The thickness of the soap bubble's wall determines which wavelengths of light are reflected more efficiently.
To find the minimum wall thickness for enhanced reflection of 729 nm light, we can use the equation for constructive interference:
2nt = mλ, where n is the refractive index of the soap solution, t is the wall thickness, m is the order of the interference, and λ is the wavelength of the light in air.
Solving for t, we get t = (mλ)/(2n), or t = (729 nm)/(2*1.29) = 224 nm for m=1.
Therefore, the minimum wall thickness for enhancing the reflection of 729 nm light in air is 224 nm.
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a girl delivering newspapers travels three blocks west, four blocks north, and then six blocks east. a. what is her resultant displacement? b. what is the total distance she travels?
After a girl delivering newspapers travels three blocks west, four blocks north, and then six blocks east, her total displacement is 5 blocks. While the total distance covered is 13 blocks.
What is displacement?A displacement is a vector in geometry and mechanics whose length is the smallest distance between the beginning and final positions of a moving point P.
If an item moves relative to a reference frame, such as a lecturer moving to the right of a whiteboard or a passenger moving toward the back of an airliner, the object's location changes. This shift in location is referred to as displacement.
Displacement (change in position) = Last position – initial position
To Calculate displacement, let displacement be (d)
d = -3i + 4j + 6i (-i because she turned west, +i because she turned east)
d = 3i + 4j
d = √(3² + 4²)
d = √(9 + 16)
d = √25
d = 5 blocks.
Total distance (Td_ = Sum of all the blocks traveled.
Td = 3 + 4 + 6
Td = 13 blocks.
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calculate the distance travelled by a car moving with 40 m/s velocity in 2 hours
Answer:
14,400m
Explanation:
The formula for calculating speed is S=D/T.
S=speed( in meters per second- m/s)
D=distance(in meters)
T=time( in seconds)
For our case:
S=40m/s
D=?
Time=2 hours=60min x 60 sec=3600seconds
Now make D the subject.
D=S x T
D=4m/s x 3600s=14,400m
Therefore our answer is
14 400 m or 14.4 km
The cooper family hijacks a UAV (Unmanned Aerial Vehicle). What do you know about UAVs and how they are used today?
Interstellar movie☝️
Interstellar is a movie about the human race being faced with a
civilization ending blight. A small group of brave individuals explore
possible new habitable worlds for humans. The following questions
will help guide you through the movie and hopefully get you
thinking about the future.
1. The Cooper family hijacks a UAV (Unmanned Aerial Vehicle).
What do you know about UAVs and how they are used today?
2. While at the parent-teacher conference, Murphy’s teacher
mentions that the Apollo program -- the same program that
landed humans on the Moon -- was just propaganda to
convince the Soviet Union to bankrupt themselves trying to do
the same. The reason for this was to encourage children to
take care of their own planet, rather than wasting precious
resources day dreaming of leaving it. Which side of the fence
would you sit on? Would you look for ways to save Earth and
our ability to stay there, or would you look to the sky, and find
a new planet to live on? Why?
3. A) What natural disaster(s) is Earth suffering from in the beginning of Interstellar?
B) If one of these happened now what actions would you take to protect yourself?
4. Cooper, Doyle, Romilly, and Dr. Brand (female) rendezvous with the Endurance in orbit around Earth. Once
onboard, they begin to spin the Endurance. Why? (Think about the physics happening here!) Draw a diagram.
5. Why or why isn’t space exploration important for the people in the movie interstellar? Why or why isn’t
space exploration important in today’s society? Defend your answers.
6. Explain time dilation as best as you can.
7. A) Estimate how long Dr. Mann went without human contact while on the ice planet:
The Lazarus mission was __________ years ago. It takes _______ years to get to Saturn from Earth. Cooper
and Dr. Brand were on Miller’s planet for approximately __________ years. This means the total time Dr.
Mann went without human contact is: ___________ years.
B) Consider the longest time away from human contact you've experienced. What did you do to keep yourself
occupied?
Useful Vocabulary
Blight: A specific symptom affecting plants in
response to infection by a pathogenic organism. The
potato famine of Ireland was caused by blight.
Event horizon: Is a point in which not even light can
escape the gravitational influence of the black hole.
Maroon: The intentional action of leaving someone
in a remote area such as an inhabitable island.
Rendezvous: When two objects meet and typically
dock together while in space.
Time dilation: A difference of elapsed time between
two events as measured by observers either moving
relative to each other or differently situated from
gravitational masses.
UAV: Unmanned Aerial Vehicles are remote
controlled or autonomous flying vehicles.
Unmanned aerial vehicles (UAVs) are typically used for a variety of purposes such as:
Monitoring and surveillance.Remote sensingPhotographyDisaster responseWhat is an unmanned aerial vehicle?An unmanned aerial vehicle (UAV) is also referred to as a drone and it can be defined as an aircraft that is designed and developed to be piloted or controlled by a remote control (ground-based controller) and on-board computer systems.
This ultimately implies that, an unmanned aerial vehicle (UAV) is a class of aircrafts that can fly without any human pilot, cabin crew, or passengers on board.
In conclusion, unmanned aerial vehicles (UAVs) carries no human pilot and are typically used for a variety of purposes such as:
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Two people, Micah and Lyra, with different near points are equally close to an object. Both inspect the object through the same magnifier by holding the lens close to the eye. Micah's near point is located farther away from his eye than Lyra's near point is located relative to her eye. Micah will experience a larger magnification for which of the following reasons?
When the object is located at his near point, the angular size of the object is smaller for Micah than for Lyra.
Micah sees a larger image than Lyra sees.
Micah can see the image clearly from a larger distance than Lyra can.
Lyra can see the image clearly from a larger distance than Micah can.
The angular size of the image relative to the angular size of the object at the near point is greater for Micah than for Lyra.
Micah will experience a larger magnification is because the angular size of the object is smaller for Micah than for Lyra.
Why angular size of the object is smaller for Micah than for Lyra?
The magnification produced by a magnifier is given by the formula:
M = (25cm/f) + 1, where f is the focal length of the magnifier.
The magnification is larger when the focal length is smaller. However, in this case, both Micah and Lyra are using the same magnifier, so the focal length is the same for both of them.
The near point is the closest distance at which an object can be brought into focus by the eye. The near point varies from person to person, and it depends on the elasticity of the lens and the shape of the eye. In this case, Micah's near point is located farther away from his eye than Lyra's near point is located relative to her eye. This means that Micah's eye has less ability to focus on close objects than Lyra's eye.
When an object is located at the near point, the image formed on the retina is at its maximum size.
The angular size of the object is given by the formula:
θ = tan⁻¹ (s/d), where s is the size of the object and d is the distance between the object and the eye.
Since Micah's near point is farther away than Lyra's near point, the distance d is larger for Micah. This means that the angular size of the object is smaller for Micah than for Lyra.
When Micah uses the magnifier to inspect the object, the magnification will be larger because the angular size of the object is smaller.
This is because the magnification is proportional to the ratio of the angular size of the image to the angular size of the object.
Since the angular size of the object is smaller for Micah, the angular size of the image produced by the magnifier will be larger, resulting in a larger magnification for Micah.
Therefore, the correct reason why Micah will experience a larger magnification is because the angular size of the object is smaller for Micah than for Lyra when the object is located at his near point.
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When the object is located at his near point, the angular size of the object is smaller for Micah than for Lyra, for which reason Micah will experience a larger magnification.
The statement that is correct for the given question is "When the object is located at his near point, the angular size of the object is smaller for Micah than for Lyra."
Micah and Lyra are two people with different near points but are equally close to an object.
Both inspect the object through the same magnifier by holding the lens close to the eye. In this context, magnification is the ratio of the size of the image seen through the magnifier to the size of the object when viewed directly.
The distance between the object and the lens must be greater than the focal length of the lens to create a virtual image. Micah's near point is located farther away from his eye than Lyra's near point is located relative to her eye.
So, Micah will experience a larger magnification for the reason that when the object is located at his near point, the angular size of the object is smaller for Micah than for Lyra.
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