The ratio of the maximum efficiencies with which engines can turn heat into work and work into heat is always less than one, and hence option a is correct.
The efficiency of an engine refers to the ratio of the useful work output to the total energy input, and this efficiency can be expressed in terms of heat. Heat can be converted into work through the process of thermodynamics, and the efficiency with which this conversion takes place is determined by the specific engine design.
The efficiency with which an engine can turn heat into work is referred to as thermal efficiency, denoted by EWH, while the efficiency with which an engine can turn work into heat is referred to as reversed efficiency, denoted by EHW.
According to the second law of thermodynamics, the maximum efficiency with which an engine can convert heat into work is always less than the maximum efficiency with which the same engine can convert work into heat.
The maximum efficiency with which an engine can convert heat into work is determined by the Carnot cycle, while the maximum efficiency with which an engine can convert work into heat is determined by the Clausius inequality. These theoretical limits are never achieved in practical engines, but they serve as a benchmark for comparing the performance of different engines.
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if a gymnast leaves the ground with a vertical velocity of 9.81 m/s when doing a back flip, where in her trajectory will her center of mass be 1.0 seconds later?
The correct option is B. Her trajectory will her center of mass be 1.0 seconds later at the apex.
\(V = V_0 - g*t\)
where,
\(V_0 = initial velocity\)
acceleration due to gravity = 9.8 m/s^2
t = 1.0 seconds
substituting the above values in the equation;
\(V_0 = 9.8 m/s + 9.8m/s^2*1.0 sec\\V_0 = 19.6 m/s\)
**Hence after 1.0 sec the gymnast would almost reach 19.6 m as distance.
According to the trajectory of mass thrown uniformly,
\(H_(max)= v^2/ 2*g = 19.6^2/2*9.8 = 19.6 m\) ----> indicates the mass reaches the peak after a time of 1.0 seconds
Speed is the directional velocity of an item in motion as an indication of its price of exchange in the role as located from a selected frame of reference and as measured through a specific widespread of time (e.g. 60 km/h northbound). speed is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of our bodies.
Velocity is a physical vector amount; both value and route are had to outline it. The scalar absolute value (magnitude) of velocity is referred to as pace, being a coherent derived unit whose quantity is measured in the SI (metric system) as meters according to 2nd (m/s or m⋅s−1). as an example, "five meters per 2d" is a scalar, while "five meters in keeping with 2d east" is a vector. If there may be a change in velocity, course, or both, then the object is said to be present process an acceleration.
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Complete Question:
If a gymnast leaves the ground with a vertical velocity of 9.81 m/s when doing a back flip, where in her trajectory will her center of mass be 1.0 sec later? Show the equation applied!
a) Approaching the apex
b) at the apex
c) descending from the apex
d) on the ground
e) not enough information
On average the moon is 3.84 x 10 m from the earth: Given that the velocity of light is c = 3.00 *
m/s how much time is required for tight to get to the earth from the moon? State your result in
seconds.
Time required by the light to get to the earth from the moon is 0.00101 seconds.
Average distance between moon and the sun is 3.84 x 10^5 m.
As we know that, light is an electromagnet wave, it does not requires a medium to travel, so it will travel with the speed of 3.8 x 10^8 m/s.
Hereby, it is known to us that,
Speed = Distance/Time.
Time required by the light to travel from moon to the earth can be find by using,
Time = Distance/Speed
Time = 3.84x10^5/3.8x10^8
Time = 1.01 x 10^-3
Time = 0.00101 seconds.
As the speed of light taken was already in unit of Meter per second. So, the answer will be in seconds.
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12. a) What is the gravitational attraction of the sun
on the earth? (b) of the earth on the sun?
Answer:
About 3.54x1022 N.
Explanation: The gravitational force between the Sun and the Earth is about 3.54x1022 N. This force keeps the Earth orbiting around the Sun. The gravitational force from the other planets does slightly affect the Earth's orbit, but the gravitational pull from the other planets and the Moon is still very small. Sorry if I get this wrong. I am in 5th grade! ♥
Why is voltage the same in a parallel circuit?
Answer:
the voltage is the same in all parallel components because by definition you have connected them together with wires that are assumed to have negligible resistance. the voltage at each end of the wire is the same ( ideally ) . so all the components have to have the same voltage.
What was the rate of reaction in trial 3? select the closest answer. A. 9. 55×10−6 m⋅s−1 b. 4. 86×10−6 m⋅s−1 c. 7. 33×10−6 m⋅s−1 d. 6. 58×10−6 m⋅s−1
Unfortunately, the information about trial 3 and the rate of reaction is missing in the given question. Without specific data or context,
The given question asks for the rate of reaction in trial 3 but does not provide the necessary information to calculate it. In order to determine the rate of reaction, specific data such as the change in concentration or the time taken for the reaction needs to be provided. Without this information, it is not possible to accurately determine the rate of reaction. The rate of reaction is a measure of how quickly reactants are converted into products and is influenced by factors such as temperature, concentration, and the presence of catalysts. Therefore, without the relevant data for trial 3, it is not possible to calculate or provide an answer regarding the rate of reaction in that specific trial.
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Horizontal and vertical motions of a projectile are independent of each other. What is meant by this?.
The vertical and horizontal parts of a projectile are perpendicular and independent of one another over a short distance.
Depending on the force imposed on it, horizontal motion is defined as a projectile motion in a horizontal plane. The vertical and horizontal parts of a projectile are perpendicular and independent of one another over a short distance.
Throughout the course of a projectile's flight, the horizontal component of its speed remains constant. This is because the projectile experiences no horizontal force after being launched. As a result, the projectile moves horizontally at a fixed speed.
The following equation is used to determine how far a bullet travels;
d = vt, where
t = Time
d = Distance
v = velocity
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A solid disk and a hoop are mounted on low friction bearings on the same axis and can be brought together so they couple and rotate as one unit. The disk with rotational inertia 2.8 kg*m*m about it central axis, is set spinning CCW at 420 rev/min. the hoop with rotational inertia 6.3 kg*m*m about its central axis, is set spinning clockwise at 610 rev/min. They then couple together. What is their angular speed after they couple?
We will have the following:
First, we transform the revolutions per second to radians, that is:
\(\begin{cases}-420rev/\min =-840\pi/\min =-14\pi/s \\ \\ 610\text{rev}/\min =1220\pi/\min =\frac{61\pi}{3}/s\end{cases}\)Now, we will have that the final angular velocit will be given by:
\(-14\pi/s+\frac{6\pi}{3}/s=-12\pi/s\)So, the angular speed after coupling is -12pi/s. [That is the total angular speed will be counterclock wise]
To find a virtual image in a planar mirror or due to reflection at a flat surface, one needs to use at least ___ rays. The image is located where the light rays ____.
We need to use two rays, such as one that is parallel to the principal axis and one that passes through the focal point, to locate the virtual image in a planar mirror or due to reflection at a flat surface.
To find a virtual image in a planar mirror or due to reflection at a flat surface, one needs to use at least two rays. The image is located where the light rays intersect.
Virtual imageVirtual images are images that are not real; instead, they are created by our eyes when light rays appear to come from a point behind a surface. Virtual images are formed when light rays appear to diverge from a point behind a mirror or lens, rather than converging to that point. If we hold a piece of paper against a mirror and move it around, we'll notice that we can see the image in various locations behind the mirror. As a result, virtual images have no physical existence and cannot be projected onto a screen.
For finding the virtual image in a planar mirror or due to reflection at a flat surface, one needs to use at least two rays. One of the most important concepts in geometric optics is that when light strikes a surface, it is reflected, refracted, or absorbed. Because of the law of reflection, it is simple to determine the location of the virtual image of an object reflected by a flat surface. We need to use two rays, such as one that is parallel to the principal axis and one that passes through the focal point, to locate the virtual image in a planar mirror or due to reflection at a flat surface.
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A wave has a wavelength of 2.5 m and a frequency of 150 Hz. What is its speed? (Note: c= f)
380 m/s
200 m/s
60 m/s
500 m/s
If a wave has a wavelength of 2.5 m and a frequency of 150 Hz, then the speed of the wave would be
What is Wavelength?It can be understood in terms of the distance between any two similar successive points across any wave for example wavelength can be calculated by measuring the distance between any two successive crests.
As given in the problem If a wave has a wavelength of 2.5 m and a frequency of 150 Hz, then we have to find the speed of the wave,
The speed of the wave = frequency of the wave × wavelength
= 150 × 2.5
=375 meters / seconds
Thus, the speed of the wave would be 375 meters / seconds.
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8. (10) If the annual real rate of interest is 6%, and the expected inflation rate is 2%, what would be the nominal rate of interest according to Fisher hypothesis
The Fisher hypothesis, proposed by economist Irving Fisher, relates the nominal interest rate (i) to the real interest rate (r) and the expected inflation rate (π). According to the Fisher hypothesis, the nominal interest rate is equal to the sum of the real interest rate and the expected inflation rate.
To calculate the nominal interest rate, we can use the following formula:
i = r + π
Given that the annual real rate of interest (r) is 6% and the expected inflation rate (π) is 2%, we can substitute these values into the formula to find the nominal interest rate (i):
i = 6% + 2% = 8%
Therefore, the nominal interest rate, according to the Fisher hypothesis, would be 8%.
The Fisher hypothesis suggests that if the real interest rate remains constant, changes in the expected inflation rate will lead to corresponding changes in the nominal interest rate. When expected inflation is higher, lenders will demand higher nominal interest rates to compensate for the erosion of purchasing power over time. Conversely, if expected inflation is lower, nominal interest rates may decrease as lenders require less compensation for inflation.
It is important to note that the Fisher hypothesis assumes rational expectations, meaning that individuals accurately predict future inflation rates. In practice, however, inflation expectations can be influenced by various factors, and actual inflation may deviate from expectations. Nonetheless, the Fisher hypothesis provides a useful framework for understanding the relationship between real and nominal interest rates in an inflationary environment.
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6. A persen was travelling inside a car in winter season. Suddenly a high potential(voltage) wire broke and fell on his car. He immediately stopped car and called on emergency number 100 for help. He got an advice to stay within the car unless technicians of Electricity Authority arrive for help. a. Why do wires often break in winter season? [1] b. Why do you think the technician advised the person to sit inside the car unless help arrives? [2] c. What happens if he opens the door and slowly moves out of car?
Wires often break in the winter season due to several factors such as cold weather, ice, and snow accumulation. The technician likely advised the person to stay inside the car because the car acts as a protective cage that can prevent electric shock. it is essential to stay inside the car until trained professionals arrive to safely remove the high voltage wire and ensure that the area is safe.
a. Wires often break in the winter season due to several factors such as cold weather, ice, and snow accumulation. These conditions can cause the wires to become brittle, and if they are subject to mechanical stress, they can break easily.
b. The technician likely advised the person to stay inside the car because the car acts as a protective cage that can prevent electric shock. When a high voltage wire falls on a car, the car's metal body acts as a Faraday cage, which protects the person inside from electric shock.
c. If the person were to open the car door and step outside, they would become part of the electrical circuit and could be subject to electric shock. Electric shocks can cause severe injury or death, depending on the severity of the shock and the duration of exposure. Therefore, it is essential to stay inside the car until trained professionals arrive to safely remove the high voltage wire and ensure that the area is safe.
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easy one giving brainly if correct
Answer:
c) Liquid
Explanation:
Liquid takes the shape of its container and has a specific volume. On the other hand, solid and gas don't.
the two exploded pieces of the shell land at the same time. at the moment of landing, what is the distance xcm from the mortar to the center of mass of the exploded pieces?
The distance xcm from the mortar to the center of mass of the exploded pieces is xcm = 1.00d.
Therefore, the distance xcm from the mortar to the center of mass of the exploded pieces is found as follows:
When an object is thrown upward, it will move upward until the velocity reaches zero at its highest point. The acceleration of an object in free fall is -9.81 m/s². This acceleration is constant since it is only affected by gravity. Therefore, the distance traveled by an object in free fall is given by the formula
d = v₀₊ + 1/2gt²
Where v₀ is the initial velocity (in this case, ₀ since the objects are at rest at the moment of explosion), t is the time of flight, g is the acceleration due to gravity.
Since both pieces land at the same time, they have the same time of flight. We can set the distance traveled by the two pieces equal to each other and solve for xcm. That is
d₁ = d₂
v₀₊ + 1/2gt² = v₀₊ + 1/2gt²
Canceling v₀₊ and solving for t, we have
t = √(2d/g)
Substituting this value of t into the first equation above, we have
d₁ = 1/2gt²
d₂ = 1/2gt²
Substituting the given value of g = 9.81 m/s² and assuming that d₁ + d₂ = xcm, we have
xcm = 1/2gt²
= 1/2(9.81)(2d/g)
= 1.00d
Therefore, the distance xcm from the mortar to the center of mass of the exploded pieces is xcm = 1.00d.
Full task:
The two exploded pieces of the shell land at the same time. At the moment of landing, what is the distance xcm from the mortar to the center of mass of the exploded pieces?
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[12 QUESTION An ambulance moving at a constant speed along a straight horizontal road, em sound with a constant frequency. When the ambulance approaches a detec mounted next to the road a frequency of f is recorded. After passing the detector frequency of 0,55 f is recorded Calculate the speed of the ambulance. Take the speed of sound in air as 340 m-s-¹.
The speed of the ambulance is approximately 187.27 m/s. To calculate the speed of the ambulance, we can use the formula for the Doppler effect.
The Doppler effect relates the frequency of the sound emitted by the ambulance to the frequency detected by the detector:
f_detected = f_emitted * (v_sound + v_detector) / (v_sound + v_ambulance)
where v_sound is the speed of sound in air, v_detector is the speed of the detector (which we assume to be zero), and v_ambulance is the speed of the ambulance. We know that f_detected = 0.55f_emitted when the ambulance has passed the detector, and that f_emitted is constant. We can also substitute v_sound = 340 m/s.
Thus, we have:
0.55f_emitted = f_emitted * (340 + 0) / (340 + v_ambulance)
Solving for v_ambulance, we get:
v_ambulance = 187.27 m/s
Therefore, the speed of the ambulance is approximately 187.27 m/s.
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a playground merry-go-round has a mass of 120 kg and a radius of 1.80 m and it is rotating with an angular velocity of 0.600 rev/s. what is its angular velocity (in rev/s) after a 21.0 kg child gets onto it by grabbing its outer edge? the child is initially at rest.
The value of the final angular velocity = 0.44 rev/s
How to calculate the angular velocity?Let Initial angular momentum = \(L_{i}\)
Let Final angular momentum = \(L_{f}\)
Here, mass of merry go round = \(m_{m}\) = 120 kg
radius= r = 1.8 m
initial angular velocity = \(w_{i} = 1.2 \pi\)rad/s
mass of the child = \(m_{c}\) = 21kg
By law of conservation of angular momentum,
\(L_{i}=L_{f}\\\\I_{m}w_{i}=I_{m+c} w_{f}\\\\w _{f} =\frac{I_{m}w_{i}}{I_{m+c}}\)
Here, substitute \(I = \frac{mr^{2} }{2}\)
\(w _{f} =\frac{I_{m}w_{i}}{I_{m+c}}\\\\w _{f} =\frac{\frac{m_{m}{r _{m}}^{2}}{2} w_{i}}{\frac{m_{m}{r _{m}}^{2}}{2}+{m_{c}r_{c}}^{2} }\\\\w _{f}= \frac{\frac{120(1.8)^{2} }{2} *1.2\pi}{\frac{120(1.8)^{2} }{2} +21(1.8)^{2}}\\\\w _{f} = 2.8 rad/s\)
The value of the final angular velocity = 2.8 rad/s
=2.8/2 π
= 0.44rev/s
What is angular velocity?The rotation rate, which refers to how quickly an object rotates or revolves in relation to another point, is measured vectorially using angular velocity. The speed at which an object rotates or revolves around an axis is known as its angular velocity. Because a point on a rotating object constantly changes direction, it is challenging to determine the direction of the angular velocity. The rotating object only has a fixed direction at its axis.To learn more about angular velocity, refer:
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Which of the following amounts of particles represents an isotope of Cesium-137?
Any amount of particles with 55 protons and a different number of neutrons than 82 would represent an isotope of Cesium-137.
An isotope of Cesium-137 would have the same number of protons (55) as regular Cesium-137, but a different number of neutrons. Therefore, the amount of particles that represents an isotope of Cesium-137 would be the one with the same number of protons and a different number of neutrons. The atomic mass of regular Cesium-137 is 137, which means it has 82 neutrons (137 - 55). Therefore, any amount of particles with 55 protons and a different number of neutrons than 82 would represent an isotope of Cesium-137. In summary, Isotopes are elements with the same number of protons but different numbers of neutrons.
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An isotope of Cesium-137 contains 55 protons and 82 neutrons, resulting in a total of 137 particles in its nucleus. This specific isotope is represented by the symbol Cs-137.
An isotope of Cesium-137 is any sample that contains the same number of particles as a pure sample of Cesium-137, which has 55 protons and 82 neutrons. Therefore, any sample with 137 particles that includes 55 protons and 82 neutrons would be an isotope of Cesium-137.It is a radioactive isotope of caesium that is formed as one of the more common fission products by the nuclear fission of uranium-235 and other fissionable isotopes in nuclear reactors and nuclear weapons.
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What is the phase of water when its temperature is 150 °C?
HELP ASAP!!!! Ashley and Rachel are driving bumper cars. Ashley's bumper car is moving and she collides with Rachel bumper car, which is not moving. Describe what happens to the momentum of both cars During this collision.
Answer:
Rachels car moves and ashleys stops
Explanation:
When Ashley's moving car collides with Rachel's bumper car which is at rest then some of the momentum of Ashley's car is transferred to Rachel's car causing it to move.
What is the conservation of momentum?Conservation of momentum states that the momentum of a system is constant if there is the absence of external forces on the system. The momentum of an object can be conserved and is a vector quantity.
Momentum can be defined as the multiplication of the mass of a particle and its velocity. The law of conservation of momentum is confirmed by experiment and can be deduced mathematically on the presumption that space is uniform.
Conservation of linear momentum is derived from Newton’s second law of motion states that the total momentum remains the same in an isolated system.
The total momentum of Ashley's car and Rachel's car remains conserved. After the collision, the momentum transferred from Ashley's car and Rachel's car which makes it move.
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what size tw copper conductor should be used for the branch circuit? (show all of your calculations in your word-processing document.)
To determine the size of the copper conductor needed for a branch circuit, we need to consider the load and the allowable ampacity. The National Electrical Code (NEC) provides guidelines for selecting conductor sizes based on the expected load and the length of the circuit.
Here are the steps to calculate the conductor size:
1. Determine the load: Find out the total load that will be connected to the circuit. This includes all the devices and appliances that will be powered by the circuit.
2. Calculate the ampacity: Ampacity is the maximum current that a conductor can carry without exceeding its temperature rating. It is determined by the type of conductor and its size. Refer to the NEC tables to find the ampacity rating for the specific conductor size.
3. Consider the length of the circuit: Longer circuits experience more resistance, which affects the ampacity. Refer to the NEC tables to find the adjusted ampacity based on the length of the circuit.
4. Apply the derating factors: Depending on the type of installation and the number of conductors in the circuit, derating factors may be applied to the ampacity. Refer to the NEC for the specific derating factors.
5. Select the conductor size: Compare the adjusted ampacity with the load. Choose the conductor size that has an ampacity rating equal to or greater than the calculated load.
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Part apart complete: What must be the high temperature if the Carnot efficiency is to be 30%? Express your answer using two significant figures. A. 303 K B. 513 K C. 330 K D. 570 K
the Carnot efficiency and how it relates to temperature. The Carnot efficiency is the maximum possible efficiency of a heat engine operating between two temperatures, and it is calculated by dividing the difference in temperature between
the hot and cold reservoirs by the temperature of the hot reservoir. This is expressed as:aEfficiency = (Th - Tc) / Th
Where Th is the temperature of the hot reservoir and Tc is the temperature of the cold reservoir.To achieve a Carnot efficiency of 30%, we need to solve for Th in the equation above. Rearranging the equation, we get:
where T_low is the low temperature, T_high is the high temperature, and the efficiency is expressed as a decimal (i.e., 30% = 0.3). We need to solve for T_high: 0.3 = 1 - (T_low / T_high)We don't have a specific value for T_low in the question, so let's assume T_low = 273 K, 0°C.Now, we can solve for T_high: 0.3 = 1 - (273 / T_high)0.3 * T_high = 273T_high = 273 / 0.3T_high ≈ 910 K this value is not among the provided options. Without knowing the exact value of T_low, we can't determine which option is correct. To we would need more information about the system or the value of T_low.
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why x ray is called an electromagnetic wave
I need to know the solution and the formula.
Statement:
A non-deformed spring is 15 cm long. When a 2.0 N force is applied to it, its length becomes 19 cm.
To find out:
The spring constant of the spring.
Solution:
Force (F) = 2 NExtension of the spring (x) = (19 - 15) cm= 4 cm= 0.04 m [since we have to find the answer in N/m]Let the spring constant of the spring be k.We know, the formula of spring force, i.e.,F = kxPutting the values in the above formula, we get2 N = k × 0.04 mor, k = 2 N ÷ 0.04 mor, k = 50 N/mAnswer:
The spring constant of this spring is 50 N/m.
Hope you could understand.
If you have any query, feel free to ask.
What is the function of a heart rate monitor?
O to monitor blood pressure
O to track abnormal heart rhythm
O to estimate VO2max
O to track how fast a heart beats
Answer:
O- to track how fast a heart beats
Explanation:
if the density of wood is 0.5g/cm3 what is the mass of 1cm3
Answer:
O. 5 g
Explanation:
It literally says for every cm3 its 0.5 g
A light wave was calculated to have a length of 4x10^-7 m. what would the energy in the wave be?
λ = 5 x 10^-7 m, i.e the wavelength
to find:the energy in the wave.
solution:= c / λ
c =( 3 x 10^ 8 m/s)
f = 3x10^8ms-¹ /5 x10^-7m
= 6x10^14 Hz.
Ax a x = 26 m/s2 m / s 2 , ay a y = 10 m/s2 m / s 2 . find the vector's direction.
Given,
\(Ax =26 m/s^{2} \\Ay = 10 m/s^{2}\)
As we know that slope of any line passing from (x,y) point has the slope as \(\frac{y}{x}\) i.e. Tan \(\alpha\)
Vector's Direction can be calculated by \(\alpha\) = Tan⁻¹ \(\frac{Y}{X}\) ,
where \(\alpha\) is the angle with the horizontal X-axis.
therefore,
\(\alpha\) = Tan⁻¹ \(\frac{10}{26}\)
\(\alpha\) = 23.375°
The vector's direction is the angle that the vector makes with the horizontal axis, i.e. with the X-axis. The direction of the vector is given by turning the angle of the vector around its tail to the east counterclockwise.
Therefore, the vector's direction for the given vector is 23.375° from the X-axis i.e. the vector Ax = 26 m/s2, Ay= 10 m/s2 points towards the North-East direction.
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Which is an example of radiation? select two options. troy’s hand is burned when he touches hot wax. earth is heated by energy from the sun. a hot dog is held over a fire and gets warm. soup is heated in a microwave. water is boiled in a pot on a stove burner.
Answer:
microwave, and the sun
Explanation:
the microwave uses radiation waves to heat the food, the sun has gamma rays which are also radiant
Correct choices are
Earth is heated by energy from the Sun.A hot dog is held over a fire and gets warm.Soup is heated in a microwaveWhat is radiation?Every material on the earth releases radiation of different frequency and wavelengths.
Let us consider each of the choices one by one.
Troy’s hand is burned when he touches hot wax.In this case the energy is transferred through conduction not radiation, therefore this is not a correct choice.Earth is heated by energy from the Sun.
Energy is transferred from the sun to the earth only through radiation, therefore this choice is correct.A hot dog is held over a fire and gets warm.
Air is too poor a conductor to transfer heat through conduction, and if the hot dog is held directly above the fire, heat transfer through convection is possible, but also energy is transferred through radiation. Therefore this choice also counts as correct.Soup is heated in a microwave. YES
Microwave radiation is used to warm the soup. This choice is correct.Water is boiled in a pot on a stove burner.
In this case energy is transferred from the burner to the water though conduction, and from the base of the water and upwards through convection. No energy transfer through radiation is possible here, therefore this choice is not correct.Hence the correct choices are
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find the sample standard deviation of these values. round to the nearest 100th 1 12 1 3 2 1 a) 4.32 b) 5.34 c) 3.33 d) 0
The sample standard deviation is approximately 4.69.
Let's perform the calculations:
1. Calculate the mean:
Mean (x) = (1 + 12 + 3 + 2 + 1) / 5 = 19 / 5 = 3.8
2. Calculate the difference between each value and the mean:
1 - 3.8 = -2.8
12 - 3.8 = 8.2
3 - 3.8 = -0.8
2 - 3.8 = -1.8
1 - 3.8 = -2.8
3. Square each difference:
\((-2.8)^2\) = 7.84
\((8.2)^2\) = 67.24
\((-0.8)^2\) = 0.64
\((-1.8)^2\) = 3.24
\((-2.8)^2\) = 7.84
4. Calculate the sum of the squared differences:
Sum of squared differences = 7.84 + 67.24 + 0.64 + 3.24 + 7.84 = 87.8
5. Calculate the sample variance:
Sample variance (\(s^2\)) = Sum of squared differences / (n - 1) = 87.8 / (5 - 1) = 87.8 / 4 = 21.95
6. Take the square root of the sample variance to obtain the sample standard deviation:
Sample standard deviation (s) = √(\(s^2\)) = √(21.95) ≈ 4.689
Rounding to the nearest 100th, the sample standard deviation is approximately 4.69.
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today, this part of kansas is rolling hills and farm fields. describe the environment ni which the sediment ni this rock sample (photograph )x was deposited there about 290 million years ago.
The environment was quite different. Based on the sediment in the rock sample (photograph X), it is likely that this area was once covered by a shallow sea or ocean. The presence of fine-grained sediment, such as silt and clay, suggests that the water was relatively calm and quiet.
About 290 million years ago, during the Paleozoic era, Kansas was covered by a shallow sea known as the Permian Sea. The sedimentary rocks found in Kansas, including limestone, sandstone, and shale, were deposited in this sea over millions of years.
The environment in which sediment is deposited can provide clues about the conditions of the area at the time. Based on the type of rock you mentioned, it is likely that the sediment was deposited in a marine environment, such as a shallow sea or a shoreline. The limestone could have been formed from the accumulation of shells and other organic material from marine organisms, while the sandstone and shale could have been deposited by erosion and transport of sediment from nearby land.
In terms of the landscape, it is possible that the area that is now Kansas was a low-lying coastal plain, with rivers and streams carrying sediment into the sea. The rolling hills and farm fields seen today are a result of more recent geologic processes, such as erosion and deposition by wind and water.
Overall, the sediment in the rock sample you mentioned was likely deposited in a marine environment in what is now Kansas, during the time period of the Permian Sea.
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A ball is thrown horizontally from the roof of a building 50. m tall and lands
45 m from the base. What was the ball's initial speed?
Answer:7.92 m/s
Explanation:
A ball is thrown horizontally from the roof of a building 50. m tall and lands 45 m from the base then the ball's initial speed is 14.10 m/s
What is speed?The rate of change of position of an object in any direction is called speed. Speed is scalar quantity.
speed = distance/time
s=d/t
Where,
s is the speed in m/sec
d is the distance travaled in m
t is the time taken in sec
Given that in the question ball travel a height from building of 50 m to a distance 45 m from the base so total distance travelled is given as 45 m.
Body is travelling downward under the influence of gravity.
Using equation of motion under gravity,
y = ut + ½gt² , where u = 0 m/s in y direction and
y = ½gt²
t² = 2y / g
t² = 2*50/9.8
t = 3.19 sec
ball's initial speed in x direction is given as
u = 45/3.19
u= 14.10 m/sec.
The balls initial speed is given as 14.10 m/sec.
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